  In recent years, there has been a substantial amount of work in reverse
mathematics concerning natural mathematical principles that are provable from
$\RT$, Ramsey's Theorem for Pairs. These principles tend to fall outside of the
"big five" systems of reverse mathematics and a complicated picture of
subsystems below $\RT$ has emerged. In this paper, we answer two open questions
concerning these subsystems, specifically that $\ADS$ is not equivalent to
$\CAC$ and that $\EM$ is not equivalent to $\RT$.


  This article addresses the question of when physical laws and their
consequences can be computed. If a physical system is capable of universal
computation, then its energy gap can't be computed. At an even more fundamental
level, the most concise, simply applicable formulation of the underlying laws
of physics is uncomputable. That is, physicists are in the same boat as
mathematicians: many quantities of interest can be computed, but not all.


  Mission critical data dissemination in massive Internet of things (IoT)
networks imposes constraints on the message transfer delay between devices. Due
to low power and communication range of IoT devices, data is foreseen to be
relayed over multiple device-to-device (D2D) links before reaching the
destination. The coexistence of a massive number of IoT devices poses a
challenge in maximizing the successful transmission capacity of the overall
network alongside reducing the multi-hop transmission delay in order to support
mission critical applications. There is a delicate interplay between the
carrier sensing threshold of the contention based medium access protocol and
the choice of packet forwarding strategy selected at each hop by the devices.
The fundamental problem in optimizing the performance of such networks is to
balance the tradeoff between conflicting performance objectives such as the
spatial frequency reuse, transmission quality, and packet progress towards the
destination. In this paper, we use a stochastic geometry approach to quantify
the performance of multi-hop massive IoT networks in terms of the spatial
frequency reuse and the transmission quality under different packet forwarding
schemes. We also develop a comprehensive performance metric that can be used to
optimize the system to achieve the best performance. The results can be used to
select the best forwarding scheme and tune the carrier sensing threshold to
optimize the performance of the network according to the delay constraints and
transmission quality requirements.


  The recently discovered iron-based superconductors A$_{y}$Fe$_{2-x}$Se$_{2}$
($A$=K, Rb, Cs, Tl) show a long-range antiferromagnetic order with an
unexpected high transition temperature $T_N \sim 550$ K and a unique $\sqrt{5}
\times \sqrt{5}$ vacancy order. Taking the extended $J_1$-$J_2$ model as a
minimal model, we investigate the finite-temperature magnetic phase transitions
in a square lattice with a $\sqrt{5} \times \sqrt{5}$ vacancy superstructure by
using large-scale Monte Carlo simulations. By the parallel tempering technique,
the block spin checkerboard and stripe antiferromagnetic states are detected to
be the groundstates for three representative sets of model parameters. The
short-time dynamic approach is applied to accurately determine the critical
temperature as well as the static and dynamic exponents. Our results indicate
that the dramatic enhancement of the critical temperature as observed in
experiments should be mainly due to a combination effect of the vacancy order
and the block lattice contraction.


  I perform a simple analysis of a random sample of Gaia satellite ERD3 sources
in an attempt to answer the question posed sincerely by a visual artist: What
color is the universe?


  We present online boosting algorithms for multilabel ranking with top-k
feedback, where the learner only receives information about the top k items
from the ranking it provides. We propose a novel surrogate loss function and
unbiased estimator, allowing weak learners to update themselves with limited
information. Using these techniques we adapt full information multilabel
ranking algorithms (Jung and Tewari, 2018) to the top-k feedback setting and
provide theoretical performance bounds which closely match the bounds of their
full information counterparts, with the cost of increased sample complexity.
These theoretical results are further substantiated by our experiments, which
show a small gap in performance between the algorithms for the top-k feedback
setting and that for the full information setting across various datasets.


  The main purpose of this work is in reducing the queuing delays in major
supermarkets or other shopping centers by means of an Electronic Smart Cart
System which will introduce an intellectual approach to billing process through
RFID technology. Smart Cart System is a cooperative performance of three
separate systems: a website developed for the shopping market, electronic smart
cart device and anti-theft RFID gates. This project focuses on developing the
electronic smart cart device itself. It involves an embedded electronic
hardware that consists of an OLED display, Arduino Mega 2560 board, a
specifically designed PCB, a Wi-Fi module, 13.56 MHz HF RFID reader, a power
supply and a shopping cart.


  Spectroscopic mapping by scanning transmission electron microscopy coupled
with electron energy loss spectroscopy (STEM-EELS) is a powerful technique for
determining the structure and chemistry of a wide range of materials and
interfaces. The extension of this technique to cryogenic temperatures opens the
door to new experiments across many fields including materials physics, energy
storage and conversion, and biology. Such experiments, however, often face
signal limitations due to sample sensitivity or the need for rapid data
acquisition under less stable cryogenic conditions. Compared to traditional
indirect detection systems such as charge coupled devices (CCDs), direct
electron detectors (DEDs) offer improved detective quantum efficiencies,
narrower point spread functions, and superior signal-to-noise ratios. Here, we
compare the performance of a Gatan K2 Summit DED to an UltraScan 1000 CCD for
use in signal-limited atomic-resolution STEM-EELS experiments. Due to its
improved point spread function, the DED's energy resolution remains comparable
to that of the CCD at a 5 times lower dispersion, providing simultaneous access
to a much broader total energy range without sacrificing spectral resolution.
More importantly, the benefits of direct detection enable a variety of
low-signal experiments, including atomic-resolution mapping of minor and high
energy edges such as the La-M$_{2,3}$ edge at 1123 eV and the Bi-M$_{4,5}$ edge
at 2580 eV. For rapid acquisitions at 400 spectra per second, elemental maps
recorded with the DED show an up to 40 percent increase in atomic lattice
fringe contrast compared to those acquired with the CCD. Taking advantage of
these performance improvements and the fast readout of the K2 DED, we use
direct detection STEM-EELS to demonstrate atomic-resolution elemental mapping
at cryogenic temperatures.


  We prove an expansion for densities in the free CLT and apply this result to
an expansion in the entropic free central limit theorem assuming a moment
condition of order 8 for the free summands.


  We present simple string models which dynamically break supersymmetry without
non-Abelian gauge dynamics. The Fayet model, the Polonyi model, and the
O'Raifeartaigh model each arise from D-branes at a specific type of
singularity. D-brane instanton effects generate the requisite exponentially
small scale of supersymmetry breaking.


  Simple drawings are drawings of graphs in which any two edges intersect at
most once (either at a common endpoint or a proper crossing), and no edge
intersects itself. We analyze several characteristics of simple drawings of
complete multipartite graphs: which pairs of edges cross, in which order they
cross, and the cyclic order around vertices and crossings, respectively. We
consider all possible combinations of how two drawings can share some
characteristics and determine which other characteristics they imply and which
they do not imply. Our main results are that for simple drawings of complete
multipartite graphs, the orders in which edges cross determine all other
considered characteristics. Further, if all partition classes have at least
three vertices, then the pairs of edges that cross determine the rotation
system and the rotation around the crossings determine the extended rotation
system. We also show that most other implications -- including the ones that
hold for complete graphs -- do not hold for complete multipartite graphs. Using
this analysis, we establish which types of isomorphisms are meaningful for
simple drawings of complete multipartite graphs.


  Let $B_1$ be the unit open disk in $\Real^2$ and $M$ be a closed Riemannian
manifold. In this note, we first prove the uniqueness for weak solutions of the
harmonic map heat flow in $H^1([0,T]\times B_1,M)$ whose energy is
non-increasing in time, given initial data $u_0\in H^1(B_1,M)$ and boundary
data $\gamma=u_0|_{\partial B_1}$. Previously, this uniqueness result was
obtained by Rivi\`{e}re (when $M$ is the round sphere and the energy of initial
data is small) and Freire (when $M$ is an arbitrary closed Riemannian
manifold), given that $u_0\in H^1(B_1,M)$ and $\gamma=u_0|_{\partial B_1}\in
H^{3/2}(\partial B_1)$. The point of our uniqueness result is that no boundary
regularity assumption is needed. Second, we prove the exponential convergence
of the harmonic map heat flow, assuming that energy is small at all times.


  We establish sharp pointwise estimates for the ground states of some singular
fractional Schr\"odinger operators on relatively compact Euclidean subsets. The
considered operators are of the type
$(-\Delta)^{\alpha/2}|_\Om-c|x|^{-\alpha}$, where $(-\Delta)^{\alpha/2}|_\Om$
is the fraction-Laplacien on an open subset $\Om$ in $\R$ with zero exterior
condition and $0<c\leq(\frac{d-\alpha}{2})^2$. The intrinsic ultracontractivity
property for such operators is discussed as well and a sharp large time
asymptotic for their heat kernels is derived.


  We consider a quantum communication task between two users Alice and Bob, in
which Alice and Bob exchange their respective quantum information by means of
local operations and classical communication assisted by shared entanglement.
Here, we assume that Alice and Bob may have quantum side information, not
transferred, and classical communication is free. In this work, we derive
general upper and lower bounds for the least amount of entanglement which is
necessary to perfectly perform this task, called the state exchange with
quantum side information. Moreover, we show that the optimal entanglement cost
can be negative when Alice and Bob make use of their quantum side information.
We finally provide conditions on the initial state for the state exchange with
quantum side information which give the exact optimal entanglement cost.


  Using data collected in the DELPHI detector at LEP-1, measurements of the
inclusive tau branching ratios for decay modes containing one, three, or five
charged particles have been performed, giving the following results:
  B_1 = B(\tau^- -> (particle)^- \geq 0pi^0 \geq 0K^0 \nu_\tau(\bar{\nu})) =
(85.316 +/- 0.093 +/- 0.049)%;
  B_3 = B(\tau^- -> 2h^-h^+ \geq 0pi^0 \geq 0K^0 \nu_\tau) = (14.569 +/- 0.093
+/- 0.048)%;
  B_5 = B(\tau^- -> 3h^-2h^+ \geq 0pi^0 \geq 0K^0 \nu_\tau) = (0.115 +/- 0.013
+/- 0.006)%, where h is either a charged pi or K meson. The first quoted
uncertainties are statistical and the second systematic.


  The Arizona-NOAO Temporal Analysis and Response to Events System (ANTARES) is
a joint project of the National Optical Astronomy Observatory and the
Department of Computer Science at the University of Arizona. The goal is to
build the software infrastructure necessary to process and filter alerts
produced by time-domain surveys, with the ultimate source of such alerts being
the Large Synoptic Survey Telescope (LSST). The ANTARES broker will add value
to alerts by annotating them with information from external sources such as
previous surveys from across the electromagnetic spectrum. In addition, the
temporal history of annotated alerts will provide further annotation for
analysis. These alerts will go through a cascade of filters to select
interesting candidates. For the prototype, `interesting' is defined as the
rarest or most unusual alert, but future systems will accommodate multiple
filtering goals. The system is designed to be flexible, allowing users to
access the stream at multiple points throughout the process, and to insert
custom filters where necessary. We describe the basic architecture of ANTARES
and the principles that will guide development and implementation.


  Given multiple datasets with different label spaces, the goal of this work is
to train a single object detector predicting over the union of all the label
spaces. The practical benefits of such an object detector are obvious and
significant application-relevant categories can be picked and merged form
arbitrary existing datasets. However, naive merging of datasets is not possible
in this case, due to inconsistent object annotations. Consider an object
category like faces that is annotated in one dataset, but is not annotated in
another dataset, although the object itself appears in the latter images. Some
categories, like face here, would thus be considered foreground in one dataset,
but background in another. To address this challenge, we design a framework
which works with such partial annotations, and we exploit a pseudo labeling
approach that we adapt for our specific case. We propose loss functions that
carefully integrate partial but correct annotations with complementary but
noisy pseudo labels. Evaluation in the proposed novel setting requires full
annotation on the test set. We collect the required annotations and define a
new challenging experimental setup for this task based one existing public
datasets. We show improved performances compared to competitive baselines and
appropriate adaptations of existing work.


  Despite the crucial importance of accelerating text generation in large
language models (LLMs) for efficiently producing content, the sequential nature
of this process often leads to high inference latency, posing challenges for
real-time applications. Various techniques have been proposed and developed to
address these challenges and improve efficiency. This paper presents a
comprehensive survey of accelerated generation techniques in autoregressive
language models, aiming to understand the state-of-the-art methods and their
applications. We categorize these techniques into several key areas:
speculative decoding, early exiting mechanisms, and non-autoregressive methods.
We discuss each category's underlying principles, advantages, limitations, and
recent advancements. Through this survey, we aim to offer insights into the
current landscape of techniques in LLMs and provide guidance for future
research directions in this critical area of natural language processing.


  An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle
dynamics based on an affine simple root system. It is a `cross' between two
well-known integrable multi-particle dynamics, an affine Toda molecule and a
Sutherland system. Polynomials describing the equilibrium positions of affine
Toda-Sutherland systems are determined for all affine simple root systems.


  While deep neural network models offer unmatched classification performance,
they are prone to learning spurious correlations in the data. Such dependencies
on confounding information can be difficult to detect using performance metrics
if the test data comes from the same distribution as the training data.
Interpretable ML methods such as post-hoc explanations or inherently
interpretable classifiers promise to identify faulty model reasoning. However,
there is mixed evidence whether many of these techniques are actually able to
do so. In this paper, we propose a rigorous evaluation strategy to assess an
explanation technique's ability to correctly identify spurious correlations.
Using this strategy, we evaluate five post-hoc explanation techniques and one
inherently interpretable method for their ability to detect three types of
artificially added confounders in a chest x-ray diagnosis task. We find that
the post-hoc technique SHAP, as well as the inherently interpretable Attri-Net
provide the best performance and can be used to reliably identify faulty model
behavior.


  We present an X-ray, radio and optical study of the cluster A2717. The
central D galaxy is associated with a Wide-Angled-Tailed (WAT) radio source. A
Rosat PSPC observation of the cluster shows that the cluster has a well
constrained temperature of 2x10^7 K. The pressure of the intracluster medium
was found to be comparable to the mininum pressure of the radio source
suggesting that the tails may in fact be in equipartition with the surrounding
hot gas.


  The best beam steering directions are estimated through beam training, which
is one of the most important and challenging tasks in millimeter-wave and
sub-terahertz communications. Novel array architectures and signal processing
techniques are required to avoid prohibitive beam training overhead associated
with large antenna arrays and narrow beams. In this work, we leverage recent
developments in true-time-delay (TTD) arrays with large delay-bandwidth
products to accelerate beam training using frequency-dependent probing beams.
We propose and study two TTD architecture candidates, including analog and
hybrid analog-digital arrays, that can facilitate beam training with only one
wideband pilot. We also propose a suitable algorithm that requires a single
pilot to achieve high-accuracy estimation of angle of arrival. The proposed
array architectures are compared in terms of beam training requirements and
performance, robustness to practical hardware impairments, and power
consumption. The findings suggest that the analog and hybrid TTD arrays achieve
a sub-degree beam alignment precision with 66% and 25% lower power consumption
than a fully digital array, respectively. Our results yield important design
trade-offs among the basic system parameters, power consumption, and accuracy
of angle of arrival estimation in fast TTD beam training.


  We construct a field-theoretic description of spin waves in hexagonal
antiferromagnets with three magnetic sublattices and coplanar $120^\circ$
magnetic order. The three Goldstone modes can be separated by point-group
symmetry into a singlet $\alpha_{0}$ and a doublet $(\beta_x,\beta_y)$. The
$\alpha_0$ singlet is described by the standard theory of a free relativistic
scalar field. The field theory of the $(\beta_x,\beta_y)$ doublet is analogous
to the theory of elasticity of a two-dimensional isotropic solid with distinct
longitudinal and transverse "speeds of sound". The well-known Heisenberg models
on the triangular and kagome lattices with nearest-neighbour exchange turn out
to be special cases with accidental degeneracy of the spin-wave velocities. The
speeds of sound can be readily calculated for any lattice model. We apply this
approach to the compounds of the Mn$_3$X family with stacked kagome layers.


  Knowing the degree of semantic contrast between words has widespread
application in natural language processing, including machine translation,
information retrieval, and dialogue systems. Manually-created lexicons focus on
opposites, such as {\rm hot} and {\rm cold}. Opposites are of many kinds such
as antipodals, complementaries, and gradable. However, existing lexicons often
do not classify opposites into the different kinds. They also do not explicitly
list word pairs that are not opposites but yet have some degree of contrast in
meaning, such as {\rm warm} and {\rm cold} or {\rm tropical} and {\rm
freezing}. We propose an automatic method to identify contrasting word pairs
that is based on the hypothesis that if a pair of words, $A$ and $B$, are
contrasting, then there is a pair of opposites, $C$ and $D$, such that $A$ and
$C$ are strongly related and $B$ and $D$ are strongly related. (For example,
there exists the pair of opposites {\rm hot} and {\rm cold} such that {\rm
tropical} is related to {\rm hot,} and {\rm freezing} is related to {\rm
cold}.) We will call this the contrast hypothesis. We begin with a large
crowdsourcing experiment to determine the amount of human agreement on the
concept of oppositeness and its different kinds. In the process, we flesh out
key features of different kinds of opposites. We then present an automatic and
empirical measure of lexical contrast that relies on the contrast hypothesis,
corpus statistics, and the structure of a {\it Roget}-like thesaurus. We show
that the proposed measure of lexical contrast obtains high precision and large
coverage, outperforming existing methods.


  Chemical heterogeneity of solid surfaces disrupts the adsorption of
surfactants from the bulk liquid. While its presence can hinder the performance
of some formulations, bespoke chemical patterning could potentially facilitate
controlled adsorption for nanolithography applications. Although some
computational studies have investigated the impact of regularly patterned
surfaces on surfactant adsorption, in reality many interesting surfaces are
expected to be stochastically disordered and this is an area unexplored via
simulations. In this paper we describe a new algorithm for the generation of
randomly disordered chemically heterogeneous surfaces and use it to explore the
adsorption behaviour of four model nonionic surfactants. Using novel analysis
methods we interrogate both the global surface coverage (adsorption isotherm)
and behaviour in localised regions. We observe trends in adsorption
characteristics as surfactant size, head/tail ratio, and surface topology are
varied and connect these to underlying physical mechanisms. We believe that our
methods and approach will prove useful to researchers seeking to tailor surface
patterns to calibrate nonionic surfactant adsorption.


  The community structure of a complex network can be determined by finding the
partitioning of its nodes that maximizes modularity. Many of the proposed
algorithms for doing this work by recursively bisecting the network. We show
that this unduely constrains their results, leading to a bias in the size of
the communities they find and limiting their effectivness. To solve this
problem, we propose adding a step to the existing algorithms that does not
increase the order of their computational complexity. We show that, if this
step is combined with a commonly used method, the identified constraint and
resulting bias are removed, and its ability to find the optimal partitioning is
improved. The effectiveness of this combined algorithm is also demonstrated by
using it on real-world example networks. For a number of these examples, it
achieves the best results of any known algorithm.


  The eigenvalue spacing of a uniformly chosen random finite unipotent matrix
in its permutation action on lines is studied. We obtain bounds for the mean
number of eigenvalues lying in a fixed arc of the unit circle and offer an
approach toward other asymptotics. For the case of all unipotent matrices, the
proof gives a probabilistic interpretation to identities of Macdonald from
symmetric function theory. For the case of upper triangular matrices over a
finite field, connections between symmetric function theory and a probabilistic
growth algorithm of Borodin emerge..


  This work is an endeavor to develop a deep learning methodology for automated
anatomical labeling of a given region of interest (ROI) in brain computed
tomography (CT) scans. We combine both local and global context to obtain a
representation of the ROI. We then use Relation Networks (RNs) to predict the
corresponding anatomy of the ROI based on its relationship score for each
class. Further, we propose a novel strategy employing nearest neighbors
approach for training RNs. We train RNs to learn the relationship of the target
ROI with the joint representation of its nearest neighbors in each class
instead of all data-points in each class. The proposed strategy leads to better
training of RNs along with increased performance as compared to training
baseline RN network.


  We present a method for calculating precise distances to asteroids using only
two nights of data from a single location --- far too little for an orbit ---
by exploiting the angular reflex motion of the asteroids due to Earth's axial
rotation. We refer to this as the rotational reflex velocity method. While the
concept is simple and well-known, it has not been previously exploited for
surveys of main-belt asteroids. We offer a mathematical development, estimates
of the errors of the approximation, and a demonstration using a sample of 197
asteroids observed for two nights with a small, 0.9-meter telescope. This
demonstration used digital tracking to enhance detection sensitivity for faint
asteroids, but our distance determination works with any detection method.
Forty-eight asteroids in our sample had known orbits prior to our observations,
and for these we demonstrate a mean fractional error of only 1.6% between the
distances we calculate and those given in ephemerides from the Minor Planet
Center. In contrast to our two-night results, distance determination by fitting
approximate orbits requires observations spanning 7--10 nights. Once an
asteroid's distance is known, its absolute magnitude and size (given a
statistically-estimated albedo) may immediately be calculated. Our method will
therefore greatly enhance the efficiency with which 4-meter and larger
telescopes can probe the size distribution of small (e.g. 100 meter) main belt
asteroids. This distribution remains poorly known, yet encodes information
about the collisional evolution of the asteroid belt --- and hence the history
of the Solar System.


  One major problem in the study of numerical semigroups is determining the
growth of the semigroup tree. In the present work, infinite chains of numerical
semigroups in the semigroup tree, firstly introduced in Bras-Amor\'os and
Nulygin (2009), are studied. Computational results show that these chains are
rare, but without them the tree would not be infinite. It is proved that for
each genus $g\geq 5$ there are more semigroups of that genus not belonging to
infinite chains than semigroups belonging. The reference Bras-Amor\'os and
Bulygin (2009) presented a characterization of the semigroups that belong to
infinite chains in terms of the coprimality of the left elements of the
semigroup as well as a result on the cardinality of the set of infinite chains
to which a numerical semigroup belongs in terms of the primality of the
greatest common divisor of these left elements. We revisit these results and
fix an imprecision on the cardinality of the set of infinite chains to which a
semigroup belongs in the case when the greatest common divisor of the left
elements is a prime number. We then look at infinite chains in subtrees with
fixed multiplicity. When the multiplicity is a prime number there is only one
infinite chain in the tree of semigroups with such multiplicity. When the
multpliplicity is $4$ or $6$ we prove a self-replication behavior in the
subtree and prove a formula for the number of semigroups in infinite chains of
a given genus and multiplicity $4$ and $6$, respectively.


  In his seminal work, Weinstein considered the question of the ground states
for discrete Schr\"odinger equations with power law nonlinearities, posed on
${\mathbb Z}^d$. More specifically, he constructed the so-called normalized
waves, by minimizing the Hamiltonian functional, for fixed power $P$ (i.e.
$l^2$ mass). This type of variational method allows one to claim, in a
straightforward manner, set stability for such waves.
  In this work, we revisit and build upon Weinstein's work in several
directions. First, for the normalized waves, we show that they are in fact
spectrally stable as solutions of the corresponding discrete NLS evolution
equation. Next, we construct the so-called homogeneous waves, by using a
different constrained optimization problem. Importantly, this construction
works for all values of the parameters, e.g. $l^2$ supercritical problems. We
establish a rigorous criterion for stability, which decides the stability on
the homogeneous waves, based on the classical
Grillakis-Shatah-Strauss/Vakhitov-Kolokolov quantity $\partial_\omega
\|\varphi_\omega\|_{l^2}^2$. In addition, we provide some symmetry results for
the solitons. Finally, we complement our results with numerical computations,
which showcase the full agreement between the conclusion from the GSS/VK
criterion vis-\'a-vis with the linearized problem. In particular, one observes
that it is possible for the stability of the wave to change as the spectral
parameter $\omega$ varies, in contrast with the corresponding continuous NLS
model.


  Most generally, dynamic functional connectivity (FC) refers to the
non-instantaneous couplings across timeseries from a set of brain areas, here
as measured by fMRI. This is in contrast to static FC, which is defined as
purely instantaneous relations. In this chapter, we provide a hands-on
description of a non-exhaustive selection of different methods used to estimate
dynamic FC (such as sliding windows, clustering approaches, Hidden Markov
Models, and multivariate autoregressive models), and we explain, using
practical examples, how data should be prepared for dynamic FC analyses and how
models of dynamic FC can be evaluated. We also discuss current developments in
the dynamic FC research field, including challenges of reliability and
reproducibility, and perspectives of using dynamic FC for prediction.


  We give tight upper bounds on the numerical range of square matrices in terms
of their Frobenius (Euclidian) norm and a combinatorial parameter similar to
the clique number of graphs. Our results imply a concise form of the
fundamental theorem of Turan in extremal graph theory.


  We investigate the optimal performance of dense sensor networks by studying
the joint source-channel coding problem. The overall goal of the sensor network
is to take measurements from an underlying random process, code and transmit
those measurement samples to a collector node in a cooperative multiple access
channel with potential feedback, and reconstruct the entire random process at
the collector node. We provide lower and upper bounds for the minimum
achievable expected distortion when the underlying random process is Gaussian.
When the Gaussian random process satisfies some general conditions, we evaluate
the lower and upper bounds explicitly, and show that they are of the same order
for a wide range of power constraints. Thus, for these random processes, under
these power constraints, we express the minimum achievable expected distortion
as a function of the power constraint. Further, we show that the achievability
scheme that achieves the lower bound on the distortion is a separation-based
scheme that is composed of multi-terminal rate-distortion coding and
amplify-and-forward channel coding. Therefore, we conclude that separation is
order-optimal for the dense Gaussian sensor network scenario under
consideration, when the underlying random process satisfies some general
conditions.


  Using vector and axial-vector correlators within finite energy sum rules with
inputs from a chiral quark model, coupled to the Polyakov loop, with nonlocal
vector interactions, we extend our previous work to confirm the equivalence
between the continuum threshold $s_0$ and the trace of the Polyakov loop $\Phi$
as order parameters for the deconfinement transition at finite temperature $T$
and quark chemical potential $\mu$. The obtained results are in agreement with
our initial conclusion, where we showed that $s_0(T,\mu)$ and $\Phi(T,\mu)$
provide the same information for the QCD deconfinement transition.


  Deep learning is emerging as an effective tool in drug discovery, with
potential applications in both predictive and generative models. Generative
Flow Networks (GFlowNets/GFNs) are a recently introduced method recognized for
the ability to generate diverse candidates, in particular in small molecule
generation tasks. In this work, we introduce double GFlowNets (DGFNs). Drawing
inspiration from reinforcement learning and Double Deep Q-Learning, we
introduce a target network used to sample trajectories, while updating the main
network with these sampled trajectories. Empirical results confirm that DGFNs
effectively enhance exploration in sparse reward domains and high-dimensional
state spaces, both challenging aspects of de-novo design in drug discovery.


  State equations (SEs) were firstly introduced in the approximate message
passing (AMP) to describe the mean square error (MSE) in compressed sensing.
Since then a set of state equations have appeared in studies of logistic
regression, robust estimator and other high-dimensional statistics problems.
Recently, a convex Gaussian min-max theorem (CGMT) approach was proposed to
study high-dimensional statistic problems accompanying with another set of
different state equations. This paper provides a uniform viewpoint on these
methods and shows the equivalence of their reduction forms, which causes that
the resulting SEs are essentially equivalent and can be converted into the same
expression through parameter transformations. Combining these results, we show
that these different state equations are derived from several equivalent
reduction forms. We believe that this equivalence will shed light on
discovering a deeper structure in high-dimensional statistics.


  Fix an integer $d\geq 2$. The parameters $c_0\in \bar{\mathbb{Q}}$ for which
the unicritical polynomial $f_{d,c}(z)=z^d+c\in \mathbb{C}[z]$ has finite
postcritical orbit, also known as Misiurewicz parameters, play a significant
role in complex dynamics. Recent work of Buff, Epstein, and Koch proved the
first known cases of a long-standing dynamical conjecture of Milnor using their
arithmetic properties, about which relatively little is otherwise known.
Continuing our work in a companion paper, we address further arithmetic
properties of Misiurewicz parameters, especially the nature of the algebraic
integers obtained by evaluating the polynomial defining one such parameter at a
different Misiurewicz parameter. In the most challenging such combinations, we
describe a connection between such algebraic integers and the multipliers of
associated periodic points. As part of our considerations, we also introduce a
new class of polynomials we call $p$-special, which may be of independent
number theoretic interest.


  Let $(M^\circ, g)$ be an asymptotically conic manifold, in the sense that
$M^\circ$ compactifies to a manifold with boundary $M$ in such a way that $g$
becomes a scattering metric on $M$. A special case of particular interest is
that of asymptotically Euclidean manifolds, where $\partial M = S^{n-1}$ and
the induced metric at infinity is equal to the standard metric. We study the
resolvent kernel $(P + k^2)^{-1}$ and Riesz transform of the operator $P =
\Delta_g + V$, where $\Delta_g$ is the positive Laplacian associated to $g$ and
$V$ is a real potential function $V$ that is smooth on $M$ and vanishes to some
finite order at the boundary.
  In the first paper in this series we made the assumption that $n \geq 3$ and
that $P$ has neither zero modes nor a zero-resonance and showed (i) that the
resolvent kernel is conormal to the lifted diagonal and polyhomogeneous at the
boundary on a blown up version of $M^2 \times [0, k_0]$, and (ii) the Riesz
transform of $P$ is bounded on $L^p(M^\circ)$ for $1 < p < n$, and that this
range is optimal unless $V \equiv 0$ and $M^\circ$ has only one end. In the
present paper, we perform a similar analysis assuming again $n \geq 3$ but
allowing zero modes and zero-resonances. We find the precise range of $p$ for
which the Riesz transform (suitably defined) of $P$ is bounded on $L^p(M)$ when
zero modes (but not resonances, which make the Riesz transform undefined) are
present. Generically the Riesz transform is bounded for $p$ precisely in the
range $(n/(n-2), n/3)$, with a bigger range possible if the zero modes have
extra decay at infinity.


  Transition state theory was introduced in the 1930s to account for chemical
reactions. Central to this theory is the idea of a potential energy surface
(PES). It was assumed that such a surface could be constructed using
eigensolutions of the Schr\"{o}dinger equation for the molecular (Coulomb)
Hamiltonian but at that time such calculations were not possible. Nowadays
quantum mechanical ab-initio electronic structure calculations are routine and
from their results PESs can be constructed which are believed to approximate
those assumed derivable from the eigensolutions. It is argued here that this
belief is unfounded. It is suggested that the potential energy surface
construction is more appropriately regarded as a legitimate and effective
modification of quantum mechanics for chemical purposes


  We introduce a hybrid method to determine neutrino mass hierarchy by
simultaneous measurements of detector responses induced by antineutrino and
neutrino fluxes from accretion and cooling phase of type II supernova. The
(anti)neutrino-nucleus cross sections for $^{12}$C, $^{16}$O, $^{56}$Fe and
$^{208}$Pb are calculated in the framework of relativistic nuclear energy
density functional and weak Hamiltonian, while the cross sections for inelastic
scattering on free protons, $p(\bar{\nu}_{e},e^{+})n$, are obtained using
heavy-baryon chiral perturbation theory. The simulations of (anti)neutrino
fluxes emitted from a protoneutron star in a core-collapse supernova include
collective and Mickheev-Smirnov-Wolfenstein effects inside star. The emission
rates of elementary decay modes of daughter nuclei are calculated for normal
and inverted neutrino mass hierarchy. It is shown that simultaneous use of
(anti)neutrino detectors with different target material and time dependence of
the signal allow to determine the neutrino mass hierarchy from the ratios of
$\nu_e / $ $\bar{\nu}_e$ induced particle emissions. The hybrid method favors
detectors with heavier target nuclei ($^{208}$Pb) for the neutrino sector,
while for antineutrinos the use of free protons and light nuclei
($\text{H}_2\text{O}$ or $\text{-CH}_2\text{-}$) represent appropriate choice.


  We discuss the role of pseudo-fermions in the analysis of some
two-dimensional models, recently introduced in connection with non self-adjoint
hamiltonians. Among other aspects, we discuss the appearance of exceptional
points in connection with the validity of the extended anti-commutation rules
which define the pseudo-fermionic structure.


  In asserting a competitive market environment as a justification for
regulatory forbearance, the Telecommunications Act of 1996 finally articulated
a clear standard for the FCC's public interest standard, one of the most
protean concepts in communications. This seeming clarity has not, however,
inhibited intense political conflict over the term. This paper examines public
and regulatory debate over the AOL Time Warner merger as an example of the way
in which the linkage between competitions and commons policy becomes relevant
to communications policy, particularly in relation to mass media, and discusses
interpretations of the public interest in the current FCC. The paper proposes
that the Telecom Act's goal of fostering economic competition among information
service providers, and the democratic ideal of nurturing public relationships
and behaviors can be linked. Competition policy that creates the opportunity
for untrammeled interactivity also provides a sine qua non to nurture the
social phenomenon of the commons. The linked concepts of competition and
commons could also provide useful ways to interpret the public interest in
policy arenas as spectrum allocation and intellectual property.


  We study the polytope model for the affine type $A$ Kirillov-Reshetikhin
crystals and prove that the action of the affine Kashiwara operators can be
described in a remarkable simple way. Moreover, we investigate the
combinatorial $R$-matrix on a tensor product of polytopes and characterize the
map explicitly on the highest weight elements. We further give a formula for
the local energy function and provide an alternative proof for the perfectness.
We determine for any dominant highest weight element $\Lambda$ of level $\ell$
the elements $b_{\Lambda}, b^{\Lambda}$ involved in the definition of perfect
crystals and give an explicit description of the ground-state path in the
tensor product of polytopes.


  In \cite{Diaz} beta type I and II doubly singular distributions were
introduced and their densities and the joint densities of nonzero eigenvalues
were derived. In such matrix variate distributions $p$, the dimension of two
singular Wishart distributions defining beta distribution is larger than $m$
and $q$, degrees of freedom of Wishart matrices. We found simple formula to
compute exact largest eigenvalue distribution for doubly singular beta ensemble
in case of identity scale matrix, $\Sigma=I$. Distribution is presented in
terms of existing expression for CDF of Roy's statistic: $\lambda_{max} \sim
max \ eig\left\{ W_q(m, I)W_q(p-m+q, I)^{-1}\right\}$, where $W_k(n, I)$ is
Wishart distribution with $k$ dimensions, $n$ degrees of freedom and identity
scale matrix.


  The high-frequency excitations in glasses and supercooled liquids belong to
the great mysteries of the physics of condensed matter. While the fast process,
located at GHz-THz, can be interpreted as encaged molecular motion, the
occurrence of the boson peak (BP), dominating at THz frequencies, still is
controversially debated. Two scenarios have evolved during recent years: the BP
is truly collective in nature or, alternatively, it results from localized
modes. To help solving this controversy, we have investigated the
high-frequency dielectric loss of plastic crystals (PCs), having long-range
translational but no orientational order. Having in mind the well-defined
phonon modes in PCs compared to canonical glasses, and the infrared silence of
acoustic phonon modes, millimeter-wave and far-infrared spectroscopy should
provide valuable hints on the true origin of the BP. Here we show that PCs
exhibit a BP-like feature with markedly different spectral shape compared to
canonical glasses, evidencing that mixing of collective phonon with local
relaxational modes causes the BP. In addition, we find clear evidence for a
fast process also in PCs.


  We use statistical equilibrium equations to investigate the IRAC color space
of shocked molecular hydrogen. The location of shocked H_2 in [3.6]-[4.5] vs
[4.5]-[5.8] color is determined by the gas temperature and density of neutral
atomic hydrogen. We find that high excitation H_2 emission falls in a unique
location in the color-color diagram and can unambiguously be distinguished from
stellar sources. In addition to searching for outflows, we show that the IRAC
data can be used to map the thermal structure of the shocked gas. We analyze
archival Spitzer data of Herbig-Haro object HH 54 and create a temperature map,
which is consistent with spectroscopically determined temperatures.


  In this paper, we study a sequential decision-making problem faced by
e-commerce carriers related to when to send out a vehicle from the central
depot to serve customer requests, and in which order to provide the service,
under the assumption that the time at which parcels arrive at the depot is
stochastic and dynamic. The objective is to maximize the expected number of
parcels that can be delivered during service hours. We propose two
reinforcement learning (RL) approaches for solving this problem. These
approaches rely on a look-ahead strategy in which future release dates are
sampled in a Monte-Carlo fashion and a batch approach is used to approximate
future routes. Both RL approaches are based on value function approximation -
one combines it with a consensus function (VFA-CF) and the other one with a
two-stage stochastic integer linear programming model (VFA-2S). VFA-CF and
VFA-2S do not need extensive training as they are based on very few
hyper-parameters and make good use of integer linear programming (ILP) and
branch-and-cut-based exact methods to improve the quality of decisions. We also
establish sufficient conditions for partial characterization of optimal policy
and integrate them into VFA-CF/VFA-2S. In an empirical study, we conduct a
competitive analysis using upper bounds with perfect information. We also show
that VFA-CF and VFA-2S greatly outperform alternative approaches that: 1) do
not rely on future information, or 2) are based on point estimation of future
information, or 3) employ heuristics rather than exact methods, or 4) use exact
evaluations of future rewards.


  Annealing of crystalline multilayers composed of two miscible elements
usually causes interfacial mixing of the constituent atoms, possibly leading to
the formation of binary alloys at the interfaces. Magnetron sputtered c-Ni/a-Zr
multilayers deposited at room temperature were vacuum annealed isochronally at
200degC and 400degC to observe thermal stability of the interfaces constituting
the crystalline/amorphous multilayers. Control over the interfacial behaviour
can aid the formation of materials with novel properties. The resultant changes
in structural and magnetic properties of the multilayers were investigated in
detail through X-ray Reflectivity, Polarized Neutron Reflectivity, SIMS and
SQUID-based magnetization measurement techniques. The compositional variations
in the amorphous mixed layers formed at the Ni-on-Zr and Zr-on-Ni interfaces
due to atomic transport, were carefully observed as a function of annealing.
Interface widths proceeded to increase with annealing at the expense of the Ni
and Zr layers. The Ni-on-Zr interface was seen to be unstable at both
temperatures; but the overall response of the interfaces to atomic diffusion
was more pronounced when the multilayers were annealed at 400degC. Under
conditions of supersaturation of atoms within restricted spaces of the
interfacial layers and the limited availability of components within the
multilayer, unexpected demixing effects were observed at both the interfaces. A
large increase in magnetic moment obtained after annealing at 400degC, was
attributed to the high densification of the Ni layers as well as to the
incorporation of Ni crystallites into the Zr-on-Ni interface layers.


  Quantum computing can be realized with numerous different hardware platforms
and computational protocols. A highly promising approach to foster scalability
is to apply a photonic platform combined with a measurement-induced quantum
information processing protocol where gate operations are realized through
optical measurements on a multipartite entangled quantum state -- a so-called
cluster state. Heretofore, a few quantum gates on non-universal or non-scalable
cluster states have been, but a full set of gates for universal scalable
quantum computing has not been realized. We propose and demonstrate the
deterministic implementation of a multi-mode set of measurement-induced quantum
gates in a large two-dimensional (2D) optical cluster state using
phase-controlled continuous variable quadrature measurements. Each gate is
simply programmed into the phases of the high-efficiency quadrature
measurements which execute the transformations by teleportation through the
cluster state. Using these programmable gates, we demonstrate a small quantum
circuit consisting of 10 single-mode gates and 2 two-mode gates on a three-mode
input state. On this platform, fault-tolerant universal quantum computing is
possible if the cluster state entanglement is improved and a supply of
Gottesman-Kitaev-Preskill qubits is available. Moreover, it operates at the
telecom wavelength and is therefore network connectable without quantum
transducers.


  Mobile robotics datasets are essential for research on robotics, for example
for research on Simultaneous Localization and Mapping (SLAM). Therefore the
ShanghaiTech Mapping Robot was constructed, that features a multitude
high-performance sensors and a 16-node cluster to collect all this data. That
robot is based on a Clearpath Husky mobile base with a maximum speed of 1 meter
per second. This is fine for indoor datasets, but to collect large-scale
outdoor datasets a faster platform is needed. This system paper introduces our
high-speed mobile platform for data collection. The mapping robot is secured on
the rear-steered flatbed car with maximum field of view. Additionally two
encoders collect odometry data from two of the car wheels and an external
sensor plate houses a downlooking RGB and event camera. With this setup a
dataset of more than 10km in the underground parking garage and the outside of
our campus was collected and is published with this paper.


  We study the QCD phase structure at high temperature and density adopting a
histogram method. Because the quark determinant is complex at finite density,
the Monte-Carlo method cannot be applied directly. We use a reweighting method
and try to solve the problems which arise in the reweighting method, i.e. the
sign problem and the overlap problem. We discuss the chemical potential
dependence of the probability distribution function in the heavy quark mass
region and examine the applicability of the approach in the light quark region.


  In this article we examine the Layer phase of the five dimensional,
anisotropic, Abelian gauge model. Our results are to be compared with the ones
of the 4D U(1) gauge model in an attempt to verify that four dimensional
physics governs the four dimensional layers. The main results are: i) From the
analysis of Wilson loops we verified the $\frac{1}{R}$ behavior, in the layered
phase, for the potential between heavy charges. The renormalized fine structure
constant in the layer phase is found to be equal to that of 4D Coulomb
phase,$\alpha_{layer}$=$\alpha_{4D}$. ii) Based on the helicity modulus
analysis we show that the layers are in the Coulomb phase while the transverse
bulk space is in the confining phase. We also calculated the renormalized
coupling $\beta_{R}$ and found results compatible with those obtained from the
Coulomb potential. Finally we calculated the potential in the 5D Coulomb phase
and found $\frac{1}{R^{2}}$ behavior for the static $q \bar{q}$ potential. From
the study of the helicity modulus we have a possible estimate for the five
dimensional renormalized fine structure constant in the region of the critical
value of the bare gauge coupling.


  Acoustic lenses are employed in a variety of applications, from biomedical
imaging and surgery, to defense systems, but their performance is limited by
their linear operational envelope and complexity. Here we show a dramatic
focusing effect and the generation of large amplitude, compact acoustic pulses
(sound bullets) in solid and fluid media, enabled by a tunable, highly
nonlinear acoustic lens. The lens consists of ordered arrays of granular
chains. The amplitude, size and location of the sound bullets can be controlled
by varying static pre-compression on the chains. We support our findings with
theory, numerical simulations, and corroborate the results experimentally with
photoelasticity measurements. Our nonlinear lens makes possible a qualitatively
new way of generating high-energy acoustic pulses, enabling, for example,
surgical control of acoustic energy.


  Mutualistic communities have an internal structure that makes them resilient
to external per- turbations. Late research has focused on their stability and
the topology of the relations between the different organisms to explain the
reasons of the system robustness. Much less attention has been invested in
analyzing the systems dynamics. The main population models in use are modifi-
cations of the logistic equation with additional terms to account for the
benefits produced by the interspecific interactions. These models have
shortcomings as the so called r - K formulation of logistic equation diverges
under some conditions. In this work, we introduce a model for population
dynamics under mutualism inspired by the logistic equation but avoiding
singularities. The model is mathematically simpler than the widely used type II
models, although it shows similar complexity in terms of fixed points and
stability of the dynamics. Furthermore, each term of our model has a more
direct ecological interpretation, which can facilitate the measurement of the
rates involved in field campaigns. We perform an analytical stability analysis
and numerical simulations to study the model behavior in more general
interaction scenarios including tests of the resilience of its dynamics under
external perturbations. Despite its simplicity, our results indicate that the
model dynamics shows an important richness that can be used to gain further
insights in the dynamics of mutualistic communities.


  We present BV(RI)_C photometric measurements of the dM4-type V374 Peg
covering ~430 days. The star has a mass of ~0.28M_Sun, so it is supposed to be
fully convective. Previous observations detected almost-rigid-body rotation and
stable, axisymmetric poloidal magnetic field. Our photometric data agree well
with this picture, one persistent active nest is found on the stellar surface.
Nevertheless, the surface is not static: night-to-night variations and frequent
flaring are observed. The flares seem to be concentrated on the brighter part
of the surface. The short-time changes of the light curve could indicate
emerging flux ropes in the same region, resembling to the active nests on the
Sun. We have observed flaring and quiet states of V374 Peg changing on monthly
timescale.


  We introduce Ev-TTA, a simple, effective test-time adaptation algorithm for
event-based object recognition. While event cameras are proposed to provide
measurements of scenes with fast motions or drastic illumination changes, many
existing event-based recognition algorithms suffer from performance
deterioration under extreme conditions due to significant domain shifts. Ev-TTA
mitigates the severe domain gaps by fine-tuning the pre-trained classifiers
during the test phase using loss functions inspired by the spatio-temporal
characteristics of events. Since the event data is a temporal stream of
measurements, our loss function enforces similar predictions for adjacent
events to quickly adapt to the changed environment online. Also, we utilize the
spatial correlations between two polarities of events to handle noise under
extreme illumination, where different polarities of events exhibit distinctive
noise distributions. Ev-TTA demonstrates a large amount of performance gain on
a wide range of event-based object recognition tasks without extensive
additional training. Our formulation can be successfully applied regardless of
input representations and further extended into regression tasks. We expect
Ev-TTA to provide the key technique to deploy event-based vision algorithms in
challenging real-world applications where significant domain shift is
inevitable.


  The air fluorescence technique is used to detect ultra-high energy cosmic
rays (UHECR), and to estimate their energy. Of fundamental importance is the
photon yield due to excitation by electrons, in air of various densities and
temperatures. After our previous report, the experiment has been continued
using a Sr90 $\beta$ source to study the pressure dependence of photon yields
for radiation in nitrogen and dry air. The photon yields in 15 wave bands
between 300 nm and 430 nm have been determined. The total photon yield between
300 nm and 406 nm (used in most experiments) in air excited by a 0.85 MeV
electron is 3.81+-0.13 (+-13 % systematics) photons per meter at 1013 hPa and
20 $^{\circ}$C. The air density and temperature dependencies of 15 wave bands
are given for application to UHECR observations.


  Rectangular treemaps are often the method of choice to visualize large
hierarchical datasets. Nowadays such datasets are available over time, hence
there is a need for (a) treemaps that can handle time-dependent data, and (b)
corresponding quality criteria that cover both a treemap's visual quality and
its stability over time. In recent years a wide variety of (stable) treemapping
algorithms has been proposed, with various advantages and limitations. We aim
to provide insights to researchers and practitioners to allow them to make an
informed choice when selecting a treemapping algorithm for specific
applications and data. To this end, we perform an extensive quantitative
evaluation of rectangular treemaps for time-dependent data. As part of this
evaluation we propose a novel classification scheme for time-dependent
datasets. Specifically, we observe that the performance of treemapping
algorithms depends on the characteristics of the datasets used. We identify
four potential representative features that characterize time-dependent
hierarchical datasets and classify all datasets used in our experiments
accordingly. We experimentally test the validity of this classification on more
than 2000 datasets, and analyze the relative performance of 14 state-of-the-art
rectangular treemapping algorithms across varying features. Finally, we
visually summarize our results with respect to both visual quality and
stability to aid users in making an informed choice among treemapping
algorithms. All datasets, metrics, and algorithms are openly available to
facilitate reuse and further comparative studies.


  We model the electrons/positrons produced by dark matter annihilations in the
colliding galaxy cluster system 1E0657-56 (the bullet cluster). These charged
particles, confined by the Magnetic field, clearly trace the path of the
bullet, which passes through the main cluster with a speed of 3000-5000 km/s.
Adding the effect of dark matter substructure (subhalos) in each cluster we
find the annihilation rate is enhancedgreatly and the density of positrons in
the trail is similar to that within the bullet cluster. This opens the door to
unambiguous detection of the annihilation signal through the SZ effect, at
significant separation from the thermal electrons.


  We report a first-principle study on electronic structure and simulation of
the spin-polarized scanning tunneling microscopy graphic of a benzene/Fe4N
interface. Fe4N is a compound ferromagnet suitable for many spintronic
applications. We found that, depending on the particular termination schemes
and interface configurations, the spin polarization on the benzene surface
shows a rich variety of properties ranging from cosine-type oscillation to
polarization inversion. Spin-polarization inversion above benzene is resulting
from the hybridizations between C pz and the out-of-plane d orbitals of Fe
atom.


  When trained on large, unfiltered crawls from the internet, language models
pick up and reproduce all kinds of undesirable biases that can be found in the
data: they often generate racist, sexist, violent or otherwise toxic language.
As large models require millions of training examples to achieve good
performance, it is difficult to completely prevent them from being exposed to
such content. In this paper, we first demonstrate a surprising finding:
pretrained language models recognize, to a considerable degree, their
undesirable biases and the toxicity of the content they produce. We refer to
this capability as self-diagnosis. Based on this finding, we then propose a
decoding algorithm that, given only a textual description of the undesired
behavior, reduces the probability of a language model producing problematic
text. We refer to this approach as self-debiasing. Self-debiasing does not rely
on manually curated word lists, nor does it require any training data or
changes to the model's parameters. While we by no means eliminate the issue of
language models generating biased text, we believe our approach to be an
important step in this direction.


  This paper introduces DogSurf - a newapproach of using quadruped robots to
help visually impaired people navigate in real world. The presented method
allows the quadruped robot to detect slippery surfaces, and to use audio and
haptic feedback to inform the user when to stop. A state-of-the-art GRU-based
neural network architecture with mean accuracy of 99.925% was proposed for the
task of multiclass surface classification for quadruped robots. A dataset was
collected on a Unitree Go1 Edu robot. The dataset and code have been posted to
the public domain.


  Although recent Siamese network-based trackers have achieved impressive
perceptual accuracy for single object tracking in LiDAR point clouds, they
usually utilized heavy correlation operations to capture category-level
characteristics only, and overlook the inherent merit of arbitrariness in
contrast to multiple object tracking. In this work, we propose a radically
novel one-stream network with the strength of the instance-level encoding,
which avoids the correlation operations occurring in previous Siamese network,
thus considerably reducing the computational effort. In particular, the
proposed method mainly consists of a Template-aware Transformer Module (TTM)
and a Multi-scale Feature Aggregation (MFA) module capable of fusing spatial
and semantic information. The TTM stitches the specified template and the
search region together and leverages an attention mechanism to establish the
information flow, breaking the previous pattern of independent
\textit{extraction-and-correlation}. As a result, this module makes it possible
to directly generate template-aware features that are suitable for the
arbitrary and continuously changing nature of the target, enabling the model to
deal with unseen categories. In addition, the MFA is proposed to make spatial
and semantic information complementary to each other, which is characterized by
reverse directional feature propagation that aggregates information from
shallow to deep layers. Extensive experiments on KITTI and nuScenes demonstrate
that our method has achieved considerable performance not only for
class-specific tracking but also for class-agnostic tracking with less
computation and higher efficiency.


  We study integral points on the quadratic twists $\mathcal{E}_D:y^2=x^3-D^2x$
of the congruent number curve. We give upper bounds on the number of integral
points in each coset of $2\mathcal{E}_D(\mathbb{Q})$ in
$\mathcal{E}_D(\mathbb{Q})$ and show that their total is $\ll
(3.8)^{\mathrm{rank} \mathcal{E}_D(\mathbb{Q})}$. We further show that the
average number of non-torsion integral points in this family is bounded above
by $2$. As an application we also deduce from our upper bounds that the system
of simultaneous Pell equations $aX^2-bY^2=d$, $bY^2-cZ^2=d$ for pairwise
coprime positive integers $a,b,c,d$, has at most $\ll (3.6)^{\omega(abcd)}$
integer solutions.


  Dynamic behavior of a quantum Heisenberg ferromagnet in the presence of a
periodically oscillating magnetic field has been analyzed by means of the
effective field theory with two spin cluster. The dynamic equation of motion
has been constructed with the help of a Glauber type stochastic process and
solved for a simple cubic lattice. After the phase diagrams given, the behavior
of the hysteresis loop area, coercive field and remanent magnetization with the
anisotropy in the exchange interaction has been investigated in detail.
Especially, by comparing of the magnitudes of the hysteresis loop area in the
high anisotropy limit (i.e. Ising model) and low anisotropy limit (i.e.
isotropic Heisenberg model), detailed description of the hysteresis loop area
with the anisotropy in the exchange interaction given. Some interesting
features have been obtained about this behavior as well as in phase diagrams
such as tricritical points.


  Let $M$ be a $10$-dimensional closed oriented smooth manifold. Set
$$\mathcal{D}_{M} := \{ x \in H^{2}(M; \Z/2) \mid x^{2} + w_{2}(M) x \in
\rho_{2} ( TH^{4}(M;\Z) ) \}.$$ Suppose that $H_{1}(M;\Z)=0$ and
$\mathcal{D}_{M} \subset \rho_{2}( H^{2}(M; \Z) )$. Then the necessary and
sufficient conditions for $M$ to admit a stable almost complex structure are
determined in terms of the characteristic classes and cohomology ring of $M$.


  In a 21 cm neutral hydrogen survey of approximately 55 sq deg out to a
redshift of cz=8340 km/s, we have identified 75 extragalactic HI sources. These
objects comprise a well-defined sample of extragalactic sources chosen by means
that are independent of optical surface brightness selection effects. In this
paper we describe the Arecibo survey procedures and HI data, follow-up VLA HI
observations made of several unusual sources, and Kitt Peak B-, R-, and I-band
photometry for nearly all of the galaxies. We have also gathered information
for some of the optically detected galaxies within the same search volume. We
examine how samples generated by different types of search techniques overlap
with selection by HI flux. Only the least massive HI object, which is among the
lowest mass HI sources previously found, does not have a clear optical
counterpart, but a nearby bright star may hide low surface brightness emission.
However the newly-detected systems do have unusual optical properties. Most of
the 40 galaxies that were not previously identified in magnitude-limited
catalogs appear to be gas-dominated systems, and several of these systems have
HI mass-to-light ratios among the largest values ever previously found. These
gas-dominated objects also tend to have very blue colors, low surface
brightnesses, and no central bulges, which correlate strongly with their
relative star-to-gas content.


  Context: With the increasing knowledge of the terrestrial planets due to
recent space probes it is possible to model their rotation with increasing
accuracy. Despite that fact, an accurate determination of Venus precession and
nutation is lacking.
  Aims : Although Venus rotation has been studied in several aspects, a full
and precise analytical model of its precession-nutation motion remains to be
constructed. We propose to determine this motion with up-to-date physical
parameters of the planet
  Methods: We adopt a theoritical framework already used for a precise
precession-nutation model of the Earth, based on a Hamiltonian formulation,
canonical equations and an accurate development of the perturbing function due
to the Sun.
  Results: After integrating the disturbing function and applying the canonical
equations, we can evaluate the precession constant $\dot{\Psi}$ and the
coefficients of nutation, both in longitude and in obliquity. We get
$\dot{\Psi}=4474".35/Jcy \pm 66.5 $, corresponding to a precession period of
$28965.10 \pm 437$ years. This result, based on recent estimations of the Venus
moment of inertia is significantly different from previous estimations. The
largest nutation coefficient in longitude with an argument $2L_{S}$ (where
$L_{S}$ is the longitude of the Sun) has a 2"19 amplitude and a 112.35 d
period. We show that the coefficients of nutation of Venus due to its
triaxiality are of the same order of amplitude as these values due to its
dynamical flattening, unlike of the Earth, for which they are negligible.


  Solutions of Fredholm integral equations of the second kind with oscillatory
kernels likely exhibit oscillation. Standard numerical methods applied to
solving equations of this type have poor numerical performance due to the
influence of the highly rapid oscillation in the solutions. Understanding of
the oscillation of the solutions is still inadequate in the literature and thus
it requires further investigation. For this purpose, we introduce a notion to
describe the degree of oscillation of an oscillatory function based on the
dependence of its norm in a certain function space on the wavenumber. Based on
this new notion, we construct structured oscillatory spaces with oscillatory
structures. The structured spaces with a specific oscillatory structure can
capture the oscillatory components of the solutions of Fredholm integral
equations with oscillatory kernels. We then further propose oscillation
preserving Galerkin methods for solving the equations by incorporating the
standard approximation subspace of spline functions with a finite number of
oscillatory functions which capture the oscillation of the exact solutions of
the integral equations. We prove that the proposed methods have the optimal
convergence order uniformly with respect to the wavenumber and they are
numerically stable. A numerical example is presented to confirm the theoretical
estimates.


  Branch instructions dependent on hard-to-predict load data are the leading
branch misprediction contributors. Current state-of-the-art history-based
branch predictors have poor prediction accuracy for these branches. Prior
research backs this observation by showing that increasing the size of a
256-KBit history-based branch predictor to its 1-MBit variant has just a 10%
reduction in branch mispredictions.
  We present the novel Load Driven Branch Predictor(LDBP) specifically
targeting hard-to-predict branches dependent on a load instruction. Though
random load data determines the outcome for these branches, the load address
for most of these data has a predictable pattern. This is an observable
template in data structures like arrays and maps. Our predictor model exploits
this behavior to trigger future loads associated with branches ahead of time
and use its data to predict the branch's outcome. The predictable loads are
tracked, and the precomputed outcomes of the branch instruction are buffered
for making predictions. Our experimental results show that compared to a
standalone 256-Kbit IMLI predictor, when LDBP is augmented with a 150-Kbit
IMLI, it reduces the average branch mispredictions by 20% and improves average
IPC by 13.1% for benchmarks from SPEC CINT2006 and GAP benchmark suite.


  It is now accepted that accretion onto classical T Tauri stars is controlled
by the stellar magnetosphere, yet to date most accretion models have assumed
that their magnetic fields are dipolar. By considering a simple steady state
accretion model with both dipolar and complex magnetic fields we find a
correlation between mass accretion rate and stellar mass of the form $\dot{M}
\propto M_{\ast}^{\alpha}$, with our results consistent within observed
scatter. For any particular stellar mass there can be several orders of
magnitude difference in the mass accretion rate, with accretion filling factors
of a few percent. We demonstrate that the field geometry has a significant
effect in controlling the location and distribution of hot spots, formed on the
stellar surface from the high velocity impact of accreting material. We find
that hot spots are often at mid to low latitudes, in contrast to what is
expected for accretion to dipolar fields, and that particularly for higher mass
stars, the accretion flow is predominantly carried by open field lines.


  A systematic off-shell reduction scheme from five to four space-time
dimensions is presented for supergravity theories with eight supercharges. It
is applicable to theories with higher-derivative couplings and it is used to
address a number of open questions regarding BPS black holes in five
dimensions. Under this reduction the 5D Weyl multiplet becomes reducible and
decomposes into the 4D Weyl multiplet and an extra Kaluza-Klein vector
multiplet. The emergence of the pseudoscalar field of the latter multiplet and
the emergence of the 4D R-symmetry group are subtle features of the reduction.
The reduction scheme enables to determine how a 5D supersymmetric Lagrangian
with higher-derivative couplings decomposes upon dimensional reduction into a
variety of independent 4D supersymmetric invariants, without the need for
imposing field equations. In this way we establish, for example, the existence
of a new N=2 supersymmetric invariant that involves the square of the Ricci
tensor. Finally we resolve the questions associated with the 5D Chern-Simons
terms for spinning BPS black holes and their relation to the corresponding 4D
black holes.


  We show that a generic quasi-periodic Schr\"odinger operator in
$L^2(\mathbb{R})$ has purely singular spectrum. That is, for any minimal
translation flow on a finite-dimensional torus, there is a residual set of
continuous sampling functions such that for each of these sampling functions,
the Schr\"odinger operator with the resulting potential has empty absolutely
continuous spectrum.


  Studies of geometrical theories suggest that fundmental problems of
quantization arise from the disparate usage of displacement operators. These
may be the source of a concealed inconsistency in the accepted formalism of
quantum physics. General relativity and related theories cannot be quantized by
the classical procedure. It is necessary to avoid the construction of
differential equations by operators applied algebraically. For such theories,
Von Neumann's theorem concerning hidden variables is avoided. A specified
alternative class of gravitational-quantum-electrodynamic theories is possible.


  The equations of unsymmetrical 2-phase induction motors are established and a
computer representation is developed from these equations. Computer
representation of single phase motors are developed by extension and
modification of the unsymmetrical 2-phase induction motors representation.
These equations of an unsymmetrical 2-phase induction motors are describe the
dynamic performance of equations of unsymmetrical 2-phase induction motors. The
system is simulated to verify its capability such as input phase voltage,
stator and rotor currents, electromagnetic torque and rotor speed. The
performance of an unsymmetrical 2-p


  A probabilistic reconstruction of genealogies in a polyploid population (from
2x to 4x) is investigated, by considering genetic data analyzed as the
probability of allele presence in a given genotype. Based on the likelihood of
all possible crossbreeding patterns, our model enables us to infer and to
quantify the whole potential genealogies in the population. We explain in
particular how to deal with the uncertain allelic multiplicity that may occur
with polyploids. Then we build an \textit{ad hoc} penalized likelihood to
compare genealogies and to decide whether a particular individual brings
sufficient information to be included in the taken genealogy. This decision
criterion enables us in a next part to suggest a greedy algorithm in order to
explore missing links and to rebuild some connections in the genealogies,
retrospectively. As a by-product, we also give a way to infer the individuals
that may have been favored by breeders over the years. In the last part we
highlight the results given by our model and our algorithm, firstly on a
simulated population and then on a real population of rose bushes. Most of the
methodology relies on the maximum likelihood principle and on graph theory.


  We give some explicit calculations for stable distributions and convergence
to them, mainly based on less explicit results in Feller (1971). The main
purpose is to provide ourselves with easy reference to explicit formulas and
examples. (There are probably no new results.)


  In this paper we use a generating function approach to record and calculate
entries of the Minkowski tensors of a polytope. We focus on ''surface
tensors'', extending the methods used in arXiv:1807.10258 for moments of the
uniform distribution which correspond to volume tensors. In this context we
also extend the definition of the adjoint polynomial to the boundary complex of
a polytope with simplicial facets. In the case of simplicial polytopes we give
an explicit formulation for these surface tensors.


  Sujets qui sont plus particulierement abordes dans ce cours:
  1. Elements de cosmologie, l'Univers homogene Les principes cosmologiques et
leurs verifications observationnelles Histoire thermique de l'Univers
Inflation, motivations et principe de base
  2. Elements de cosmologie, l'Univers inhomogene La croissance des
fluctuations Pourquoi un modele avec de la Matiere Noire Froide ? Evidences de
l'existence de matiere noire
  3. La dynamique gravitationnelle, les theories lineaires L'approximation
Newtonnienne avec un seul flot Description Eulerienne ou description
Lagrangienne Vers la dynamique non-lineaire: l'effondrement spherique
  4. Le regime quasilineaire Effet du couplage de mode: la skewness La
hierarchie des correlations en regimes quasi-lineaire Les termes sous-dominants
du developpement perturbatif
  5. Application aux proprietes statistiques des champs de distorsions
gravitationnelles La relation entre convergence locale et densite projetee
Variance et skewness de la convergence locale
  6. Vers le regime fortement non-lineaire Les solutions auto-similaires et les
modeles hierarchiques Distribution de matiere et distribution de lumiere


  The COmmon Muon and Proton Apparatus for Structure and Spectroscopy (COMPASS)
is a multi-purpose fixed-target experiment at the CERN Super Proton Synchrotron
(SPS) aimed at studying the structure and spectrum of hadrons. The two-stage
spectrometer has a good acceptance for charged as well as neutral particles
over a wide kinematic range and is thus able to measure a wide range of
reactions. Light mesons are studied with negative (mostly $\pi^-$) and positive
($p$, $\pi^+$) hadron beams with a momentum of 190 GeV/$c$. The light-meson
spectrum is investigated in various final states produced in diffractive
dissociation reactions at squared four-momentum transfers to the target between
0.1 and 1.0 (GeV/$c$)$^2$. The flagship channel is the $\pi^-\pi^+\pi^-$ final
state, for which COMPASS has recorded the currently largest data sample. These
data not only allow for measuring the properties of known resonances with high
precision, but also for searching for new states. Among these is a new
resonance-like signal, the $a_1(1420)$, with unusual properties. The findings
are confirmed by the analysis of the $\pi^-\pi^0\pi^0$ final state. Possible
bias introduced by the parametrizations used to describe the $\pi\pi$ $S$-wave
is studied using a novel analysis technique, which extracts the amplitude of
the $\pi^+\pi^-$ sub-system as a function of $3\pi$ mass from the data. Of
particular interest is the resonance content of the partial wave with
spin-exotic $J^{PC} = 1^{-+}$ quantum numbers, which are forbidden for
quark-antiquark states. This wave is studied in the two $3\pi$ channels.
Further insight is gained by studying diffractively produced $\pi^-\eta$ or
$\pi^-\eta'$ final states.


  We investigate the cleaving behavior of LiFeAs and determine its surface
electronic structure by detailed density functional calculations. We show that
due to the neutral surface of LiFeAs after cleaving, barely any influence of
the surface on the electronic states is present. Therefore the data of surface
sensitive probes such as angle resolved photoemission spectroscopy (ARPES)
represent to a high degree the bulk electronic structure. This we highlighted
by a direct comparison of the calculations to ARPES spectra.


  Evidence for the decay mode $X(3872)\rightarrow\psi(2S)\gamma$ in
$B^+\rightarrow X(3872)K^+$ decays is found with a significance of 4.4 standard
deviations. The analysis is based on a data sample of proton-proton collisions,
corresponding to an integrated luminosity of 3fb$^{-1}$ collected with the LHCb
detector, at centre-of-mass energies of 7 and 8TeV. The ratio of the branching
fraction of the $X(3872)\to\psi(2S)\gamma$ decay to that of the
$X(3872)\rightarrow J/\psi \gamma$ decay is measured to be $$
\frac{Br(X(3872)\rightarrow\psi(2S)\gamma)}{Br(X(3872)\rightarrow
J/\psi\gamma)} = 2.46\pm0.64\pm0.29, %\pm0.06,$$ where the first uncertainty is
statistical and the second is systematic. The measured value agrees with
expectations for a pure charmonium interpretation of the $X(3872)$ state and a
mixture of charmonium and molecular interpretations. However, it does not
support a pure $D\bar{D}^{*}$ molecular interpretation of the $X(3872)$state.


  Natural language generation lies at the core of generative dialogue systems
and conversational agents. We describe an ensemble neural language generator,
and present several novel methods for data representation and augmentation that
yield improved results in our model. We test the model on three datasets in the
restaurant, TV and laptop domains, and report both objective and subjective
evaluations of our best model. Using a range of automatic metrics, as well as
human evaluators, we show that our approach achieves better results than
state-of-the-art models on the same datasets.


  The molecular gas, H$_2$, that fuels star formation in galaxies is difficult
to observe directly. As such, the ratio of $L_{\rm IR}$ to $L^\prime_{\rm CO}$
is an observational estimation of the star formation rate compared with the
amount of molecular gas available to form stars, which is related to the star
formation efficiency and the inverse of the gas consumption timescale. We test
what effect an IR luminous AGN has on the ratio $L_{\rm IR}/L^\prime_{\rm CO}$
in a sample of 24 intermediate redshift galaxies from the 5 mJy Unbiased
Spitzer Extragalactic Survey (5MUSES). We obtain new CO(1-0) observations with
the Redshift Search Receiver on the Large Millimeter Telescope. We diagnose the
presence and strength of an AGN using Spitzer IRS spectroscopy. We find that
removing the AGN contribution to $L_{\rm IR}^{\rm tot}$ results in a mean
$L_{\rm IR}^{\rm SF}/L^\prime_{\rm CO}$ for our entire sample consistent with
the mean $L_{\rm IR}/L^\prime_{\rm CO}$ derived for a large sample of star
forming galaxies from $z\sim0-3$. We also include in our comparison the
relative amount of polycyclic aromatic hydrocarbon emission for our sample and
a literature sample of local and high redshift Ultra Luminous Infrared Galaxies
and find a consistent trend between $L_{6.2}/L_{\rm IR}^{\rm SF}$ and $L_{\rm
IR}^{\rm SF}/L^\prime_{\rm CO}$, such that small dust grain emission decreases
with increasing $L_{\rm IR}^{\rm SF}/L^\prime_{\rm CO}$ for both local and high
redshift dusty galaxies.


  The optimal stochastic control problem with a quadratic cost functional for
linear partial differential equations (PDEs) driven by a state-and
control-dependent white noise is formulated and studied. Both finite-and
infinite-time horizons are considered. The multi-plicative white noise dynamics
of the system give rise to a new phenomenon of singularity to the associated
Riccati equation and even to the Lyapunov equation. Well-posedness of both
Riccati equation and Lyapunov equation are obtained for the first time. The
linear feedback coefficient of the optimal control turns out to be singular and
expressed in terms of the solution of the associated Riccati equation. The null
controllability is shown to be equivalent to the existence of the solution to
Riccati equation with the singular terminal value. Finally, the controlled
Anderson model is addressed as an illustrating example.


  This is the second part in a series of papers on multi-step schemes for
solving coupled forward backward stochastic differential equations (FBSDEs). We
extend the basic idea in our former paper [W. Zhao, Y. Fu and T. Zhou, SIAM J.
Sci. Comput., 36 (2014), pp. A1731-A1751] to solve high-dimensional FBSDEs, by
using the spectral sparse grid approximations. The main issue for solving high
dimensional FBSDEs is to build an efficient spatial discretization, and deal
with the related high dimensional conditional expectations and interpolations.
In this work, we propose the sparse grid spatial discretization. We use the
sparse grid Gaussian-Hermite quadrature rule to approximate the conditional
expectations. And for the associated high dimensional interpolations, we adopt
an spectral expansion of functions in polynomial spaces with respect to the
spatial variables, and use the sparse grid approximations to recover the
expansion coefficients. The FFT algorithm is used to speed up the recovery
procedure, and the entire algorithm admits efficient and high accurate
approximations in high-dimensions, provided that the solutions are sufficiently
smooth. Several numerical examples are presented to demonstrate the efficiency
of the proposed methods.


  Let ${\cal G}$ and ${\cal H}$ be minor-closed graph classes. The pair $({\cal
H},{\cal G})$ is an Erd\H{o}s-P\'osa pair (EP-pair) if there is a function $f$
where, for every $k$ and every $G\in{\cal G},$ either $G$ has $k$ pairwise
vertex-disjoint subgraphs not belonging to ${\cal H},$ or there is a set
$S\subseteq V(G)$ where $|S|\leq f(k)$ and $G-S\in{\cal H}.$ The classic result
of Erd\H{o}s and P\'osa says that if $\mathcal{F}$ is the class of forests,
then $({\cal F},{\cal G})$ is an EP-pair for every ${\cal G}$. The class ${\cal
G}$ is an EP-counterexample for ${\cal H}$ if ${\cal G}$ is minimal with the
property that $({\cal H},{\cal G})$ is not an EP-pair. We prove that for every
${\cal H}$ the set $\mathfrak{C}_{\cal H}$ of all EP-counterexamples for ${\cal
H}$ is finite. In particular, we provide a complete characterization of
$\mathfrak{C}_{\cal H}$ for every ${\cal H}$ and give a constructive upper
bound on its size. Each class ${\cal G}\in \mathfrak{C}_{\cal H}$ can be
described as all minors of a sequence of grid-like graphs $\langle
\mathscr{W}_{k} \rangle_{k\in \mathbb{N}}.$ Moreover, each $\mathscr{W}_{k}$
admits a half-integral packing: $k$ copies of some $H\not\in{\cal H}$ where no
vertex is used more than twice. This gives a complete delineation of the
half-integrality threshold of the Erd\H{o}s-P\'osa property for minors and
yields a constructive proof of Thomas' conjecture on the half-integral
Erd\H{o}s-P\'osa property for minors (recently confirmed, non-constructively,
by Liu). Let $h$ be the maximum size of a graph in ${\cal H}.$ For every class
${\cal H},$ we construct an algorithm that, given a graph $G$ and a $k,$ either
outputs a half-integral packing of $k$ copies of some $H \not\in {\cal H}$ or
outputs a set of at most ${2^{k^{\cal O}_h(1)}}$ vertices whose deletion
creates a graph in ${\cal H}$ in time $2^{2^{k^{{\cal O}_h(1)}}}\cdot |G|^4\log
|G|.$


  We reexamine the problem of having nonconservative equations of motion arise
from the use of a variational principle. In particular, a formalism is
developed that allows the inclusion of fractional derivatives. This is done
within the Lagrangian framework by treating the action as a Volterra series. It
is then possible to derive two equations of motion, one of these is an advanced
equation and the other is retarded.


  We study the quantum limits in an optomechanical sensor based on a detuned
high-finesse cavity with a movable mirror. We show that the radiation pressure
exerted on the mirror by the light in the detuned cavity induces a modification
of the mirror dynamics and makes the mirror motion sensitive to the signal.
This leads to an amplification of the signal by the mirror dynamics, and to an
improvement of the sensor sensitivity beyond the standard quantum limit, up to
an ultimate quantum limit only related to the mechanical dissipation of the
mirror. This improvement is somewhat similar to the one predicted in detuned
signal-recycled gravitational-waves interferometers, and makes a high-finesse
cavity a model system to test these quantum effects


  The temperature dependence of the sum of the QCD up- and down-quark masses,
$(m_u + m_d)$ and the pion decay constant, $f_\pi$, are determined from two
thermal finite energy QCD sum rules for the pseudoscalar-current correlator.
This quark-mass remains mostly constant for temperatures well below the
critical temperature for deconfinement/chiral-symmetry restoration. As this
critical temperature is approached, the quark-mass increases sharply with
increasing temperature. This increase is far more pronounced if the temperature
dependence of the pion mass (determined independently from other methods) is
taken into account. The behavior of $f_\pi(T)$ is consistent with the
expectation from chiral symmetry, i.e. that it should follow the thermal
dependence of the quark condensate, independently of the quark mass.


  Ruderman-Kittel-Kasuya-Yosida interaction even if their wave functions lack
direct overlap. Theory predicts that spin-orbit scattering leads to a
Dzyaloshinskii-Moriya type enhancement of this indirect exchange interaction,
giving rise to chiral exchange terms. Here we present a combined spin-polarized
scanning tunneling microscopy, angle-resolved photoemission, and density
functional theory study of MnO$_2$ chains on Ir(100). Whereas we find
antiferromagnetic Mn--Mn coupling along the chain, the inter-chain coupling
across the non-magnetic Ir substrate turns out to be chiral with a
$120^{\circ}$ rotation between adjacent MnO$_2$ chains. Calculations reveal
that the Dzyaloshinskii-Moriya interaction results in spin spirals with a
periodicity in agreement with experiment. Our findings confirm the existence of
indirect chiral magnetic exchange, potentially giving rise to exotic phenomena,
such as chiral spin-liquid states in spin ice systems or the emergence of new
quasiparticles.


  In this paper we obtain a recursive formula for the shuffle product and apply
it to derive two restricted decomposition formulas for multiple zeta values
(MZVs). The first formula generalizes the decomposition formula of Euler and is
similar to the restricted formula of Eie and Wei for MZVs with one strings of
1's. The second formula generalizes the previous results to the product of two
MZVs with one and two strings of 1's respectively.


  Realization by linear vector fields is constructed for any Lie algebra which
admits a biorthogonal system and for its any suitable representation. The
embedding into Lie algebras of linear vector fields is analogous to the
classical Jordan-Schwinger map. A number of examples of such Lie algebras of
linear vector fields is computed. In particular, we obtain examples of the
twisted Heisenberg-Virasoro Lie algebra and the Schr\"odinger-Virasoro Lie
algebras among others. More generally, we construct an embedding of an
arbitrary locally convex topological algebra into the Cuntz algebra.


  Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel
spinors are found. For Lorentzian Weyl manifolds admitting recurrent null
vector fields are introduced special local coordinates similar to Kundt and
Walker ones. Using that, the local form of all Lorentzian Weyl spin manifolds
with weighted parallel spinors is given. The Einstein-Weyl equation for the
obtained Weyl structures is analyzed and examples of Einstein-Weyl spaces with
weighted parallel spinors are given.


  In successive refinement of information, the decoder refines its
representation of the source progressively as it receives more encoded bits.
The rate-distortion region of successive refinement describes the minimum rates
required to attain the target distortions at each decoding stage. In this
paper, we derive a parametric characterization of the rate-distortion region
for successive refinement of abstract sources. Our characterization extends
Csiszar's result to successive refinement, and generalizes a result by Tuncel
and Rose, applicable for finite alphabet sources, to abstract sources. This
characterization spawns a family of outer bounds to the rate-distortion region.
It also enables an iterative algorithm for computing the rate-distortion
region, which generalizes Blahut's algorithm to successive refinement. Finally,
it leads a new nonasymptotic converse bound. In all the scenarios where the
dispersion is known, this bound is second-order optimal.
  In our proof technique, we avoid Karush-Kuhn-Tucker conditions of optimality,
and we use basic tools of probability theory. We leverage the Donsker-Varadhan
lemma for the minimization of relative entropy on abstract probability spaces.


  We present results from a search for additional transiting planets in 24
systems already known to contain a transiting planet. We model the transits due
to the known planet in each system and subtract these models from lightcurves
obtained with the SuperWASP survey instruments. These residual lightcurves are
then searched for evidence of additional periodic transit events. Although we
do not find any evidence for additional planets in any of the planetary systems
studied, we are able to characterise our ability to find such planets by means
of Monte Carlo simulations. Artificially generated transit signals
corresponding to planets with a range of sizes and orbital periods were
injected into the SuperWASP photometry and the resulting lightcurves searched
for planets. As a result, the detection efficiency as a function of both the
radius and orbital period of any second planet, is calculated. We determine
that there is a good (> 50 per cent) chance of detecting additional,
Saturn-sized planets in P ~ 10 d orbits around planet-hosting stars that have
several seasons of SuperWASP photometry. Additionally, we confirm previous
evidence of the rotational stellar variability of WASP-10, and refine the
period of rotation. We find that the period of the rotation is 11.91 \pm 0.05
d, and the false alarm probability for this period is extremely low (~
10^{-13}).


  Dimerized valence bond solids appear naturally in spin-1/2 systems on
bipartite lattices, with the geometric frustrations playing a key role both in
their stability and the eventual `melting' due to quantum fluctuations. Here,
we ask the question of the stability of such dimerized solids in spin-1
systems, taking the anisotropic square lattice with bilinear and biquadratic
spin-spin interactions as a paradigmatic model. The lattice can be viewed as a
set of coupled spin-1 chains, which in the limit of vanishing inter-chain
coupling are known to possess a stable dimer phase. We study this model using
the density matrix renormalization group (DMRG) and infinite projected
entangled-pair states (iPEPS) techniques, supplemented by the analytical
mean-field and linear flavor wave theory calculations. While the latter
predicts the dimer phase to remain stable up to a reasonably large
interchain-to-intrachain coupling ratio $r \lesssim 0.6$, the DMRG and iPEPS
find that the dimer solid melts for much weaker interchain coupling not
exceeding $r\lesssim 0.15$. We find the transition into a magnetically ordered
state to be first order, manifested by a hysteresis and order parameter jump,
precluding the deconfined quantum critical scenario. The apparent lack of
stability of dimerized phases in 2D spin-1 systems is indicative of strong
quantum fluctuations that melt the dimer solid.


  We analyzed recent experimental data on the disassembly of $^{28}$Si into
7$\alpha$ in terms of a hybrid $\alpha$-cluster model. We calculated the
probability of breaking into several $\alpha$-like fragments for high $l$-spin
values for identical and non-identical spin zero nuclei. Resonant energies were
found for each $l$-value and compared to the data and other theoretical models.
Toroidal-like structures were revealed in coordinate and momentum space when
averaging over many events at high $l$. The transition from quantum to
classical mechanics is highlighted.


This paper has been withdrawn by the author because of copyright reasons.


  We consider the skew-product semiflow which is generated by a scalar
reaction-diffusion equation \begin{equation*}
u_{t}=u_{xx}+f(t,u,u_{x}),\,\,t>0,\,x\in S^{1}=\mathbb{R}/2\pi \mathbb{Z},
\end{equation*} where $f$ is uniformly almost periodic in $t$. The structure of
the minimal set $M$ is thoroughly investigated under the assumption that the
center space $V^c(M)$ associated with $M$ is no more than $2$-dimensional. Such
situation naturally occurs while, for instance, $M$ is hyperbolic or uniquely
ergodic. It is shown in this paper that $M$ is a $1$-cover of the hull $H(f)$
provided that $M$ is hyperbolic (equivalently, ${\rm dim}V^c(M)=0$). If ${\rm
dim}V^c(M)=1$ (resp. ${\rm dim}V^c(M)=2$ with ${\rm dim}V^u(M)$ being odd),
then either $M$ is an almost $1$-cover of $H(f)$ and topologically conjugate to
a minimal flow in $\mathbb{R}\times H(f)$; or $M$ can be (resp. residually)
embedded into an almost periodically (resp. almost automorphically) forced
circle-flow $S^1\times H(f)$.
  When $f(t,u,u_x)=f(t,u,-u_x)$ (which includes the case $f=f(t,u)$), it is
proved that any minimal set $M$ is an almost $1$-cover of $H(f)$. In
particular, any hyperbolic minimal set $M$ is a $1$-cover of $H(f)$.
Furthermore, if ${\rm dim}V^c(M)=1$, then $M$ is either a $1$-cover of $H(f)$
or is topologically conjugate to a minimal flow in $\mathbb{R}\times H(f)$. For
the general spatially-dependent nonlinearity $f=f(t,x,u,u_{x})$, we show that
any stable or linearly stable minimal invariant set $M$ is residually embedded
into $\mathbb{R}^2\times H(f)$.


  This article provides an introduction to surface code quantum computing. We
first estimate the size and speed of a surface code quantum computer. We then
introduce the concept of the stabilizer, using two qubits, and extend this
concept to stabilizers acting on a two-dimensional array of physical qubits, on
which we implement the surface code. We next describe how logical qubits are
formed in the surface code array and give numerical estimates of their
fault-tolerance. We outline how logical qubits are physically moved on the
array, how qubit braid transformations are constructed, and how a braid between
two logical qubits is equivalent to a controlled-NOT. We then describe the
single-qubit Hadamard, S and T operators, completing the set of required gates
for a universal quantum computer. We conclude by briefly discussing physical
implementations of the surface code. We include a number of appendices in which
we provide supplementary information to the main text.


  It is shown that the compact Lie group SU(3) admits an Sp(2)Sp(1)-structure
whose distinguished 2-forms $\omega_1,\omega_2,\omega_3$ span a differential
ideal. This is achieved by first reducing the structure further to a subgroup
isomorphic to SO(3).