  The dwarf satellite galaxies of the Milky Way Crater II and Antlia II have
uncommonly low dynamical mass densities, due to their large size and low
velocity dispersion. Previous work have failed to identify formation scenarios
within the $\Lambda$CDM framework and have invoked cored dark matter haloes,
processed by tides. I show that the tidal evolution of $\Lambda$CDM NFW haloes
is richer than previously recognised: tidal heating causes the innermost
regions of haloes that fall short of the mass-concentration relation to expand
significantly, resulting in the formation of giant, kinematically cold
satellites like Crater II and Antlia II. Furthermore, while the satellite is
reaching apocenter, extra-tidal material can cause an even more inflated
appearance. When present, as likely for the larger Antlia II, nominally unbound
material can be recognised thanks to its somewhat hotter kinematics and
line-of-sight velocity gradient. Contrary to other formation scenarios, Crater
II and Antlia II may well have experienced very little mass loss, as in fact
hinted by their observed metallicity. If indeed a satellite of NGC1052, tidal
evolution of a low-concentration halo may similarly have led to the formation
of NGC1052-DF2.


  Edge federated learning (FL) is an emerging paradigm that trains a global
parametric model from distributed datasets based on wireless communications.
This paper proposes a unit-modulus over-the-air computation (UMAirComp)
framework to facilitate efficient edge federated learning, which simultaneously
uploads local model parameters and updates global model parameters via analog
beamforming. The proposed framework avoids sophisticated baseband signal
processing, leading to low communication delays and implementation costs.
Training loss bounds of UMAirComp FL systems are derived and two low-complexity
large-scale optimization algorithms, termed penalty alternating minimization
(PAM) and accelerated gradient projection (AGP), are proposed to minimize the
nonconvex nonsmooth loss bound. Simulation results show that the proposed
UMAirComp framework with PAM algorithm achieves a smaller mean square error of
model parameters' estimation, training loss, and test error compared with other
benchmark schemes. Moreover, the proposed UMAirComp framework with AGP
algorithm achieves satisfactory performance while reduces the computational
complexity by orders of magnitude compared with existing optimization
algorithms. Finally, we demonstrate the implementation of UMAirComp in a
vehicle-to-everything autonomous driving simulation platform. It is found that
autonomous driving tasks are more sensitive to model parameter errors than
other tasks since the neural networks for autonomous driving contain sparser
model parameters.


  We study the application of the method of regions to Feynman integrals with
massless propagators contributing to off-shell Green's functions in Minkowski
spacetime (with non-exceptional momenta) around vanishing external masses,
$p_i^2\to 0$. This on-shell expansion allows us to identify all
infrared-sensitive regions at any power, in terms of infrared subgraphs in
which a subset of the propagators become collinear to external lightlike
momenta and others become soft. We show that each such region can be viewed as
a solution to the Landau equations, or equivalently, as a facet in the Newton
polytope constructed from the Symanzik graph polynomials. This identification
allows us to study the properties of the graph polynomials associated with
infrared regions, as well as to construct a graph-finding algorithm for the
on-shell expansion, which identifies all regions using exclusively
graph-theoretical conditions. We also use the results to investigate the
analytic structure of integrals associated with regions in which every
connected soft subgraph connects to just two jets. For such regions we prove
that multiple on-shell expansions commute. This applies in particular to all
regions in Sudakov form-factor diagrams as well as in any planar diagram.


  Clusters of galaxies are effective gravitational lenses able to magnify
background galaxies and making it possible to probe the fainter part of the
galaxy population. Submillimeter galaxies, which are believed to be
star-forming galaxies at typical redshifts of 2 to 3, are a major contaminant
to the extended Sunyaev-Zeldovich (SZ) signal of galaxy clusters. For a proper
quantification of the SZ signal the contribution of submillimeter galaxies
needs to be quantified. The aims of this study are to identify submillimeter
sources in the field of the Bullet Cluster (1E 0657-56), a massive cluster of
galaxies at z~0.3, measure their flux densities at 870 micron, and search for
counterparts at other wavelengths to constrain their properties. We carried out
deep observations of the submillimeter continuum emission at 870 micron using
the Large APEX BOlometer CAmera (LABOCA) on the Atacama Pathfinder EXperiment
(APEX) telescope. Several numerical techniques were used to quantify the noise
properties of the data and extract sources. In total, seventeen sources were
found. Thirteen of them lie in the central 10 arcminutes of the map, which has
a pixel sensitivity of 1.2 mJy per 22 arcsec beam. After correction for flux
boosting and gravitational lensing, the number counts are consistent with
published submm measurements. Nine of the sources have infrared counterparts in
Spitzer maps. The strongest submm detection coincides with a source previously
reported at other wavelengths, at an estimated redshift z~2.7. If the submm
flux arises from two images of a galaxy magnified by a total factor of 75, as
models have suggested, its intrinsic flux would be around 0.6 mJy, consistent
with an intrinsic luminosity below 10^12 L_sun.


  It is shown that multi-dimensional generalization of the vector product is
only possible in seven dimensional space.


  The schurian fusions of the association scheme of a Galois affine plane of
prime order are completely identified.


  We study the Weil representation $\rho$ of a curve over a $p$-adic field with
potential reduction of compact type. We show that $\rho$ can be reconstructed
from its stable reduction. For superelliptic curves of the form $y^n=f(x)$ at
primes $p$ whose residue characteristic is prime to the exponent $n$ we make
this explicit.


  We have investigated the possible existence of a $^7$H resonant state,
considered as a five-body system consisting of a $^3$H core with four valence
neutrons. To this aim, an effective n-$^3$H potential is constructed in order
to reproduce the low energy elastic neutron scattering on $^3$H phase shifts
and the $^5$H resonant ground state in terms of $^3$H-n-n system. The
variational Gaussian Expansion Method is used to solve the 5-body
Schr\"{o}dinger equation, while the resonant state parameters were estimated by
means of the stabilization method. We have not found any sign of a narrow low
energy resonance in the vicinity of $^3$H+4n threshold. However, we have
identified a very broad structure at $E_R\approx 9$ MeV above this threshold,
which corresponds to the $^7$H J$^{\pi}$=1/2$^+$ ground state. In the vicinity
of this state, we have also identified a broad structure corresponding to the
ground state of $^6$H isotope with quantum numbers $J^{\pi}=2^-$.


  Modularity in robotics holds great potential. In principle, modular robots
can be disassembled and reassembled in different robots, and possibly perform
new tasks. Nevertheless, actually exploiting modularity is yet an unsolved
problem: controllers usually rely on inter-module communication, a practical
requirement that makes modules not perfectly interchangeable and thus limits
their flexibility. Here, we focus on Voxel-based Soft Robots (VSRs),
aggregations of mechanically identical elastic blocks. We use the same neural
controller inside each voxel, but without any inter-voxel communication, hence
enabling ideal conditions for modularity: modules are all equal and
interchangeable. We optimize the parameters of the neural controller-shared
among the voxels-by evolutionary computation. Crucially, we use a local
self-attention mechanism inside the controller to overcome the absence of
inter-module communication channels, thus enabling our robots to truly be
driven by the collective intelligence of their modules. We show experimentally
that the evolved robots are effective in the task of locomotion: thanks to
self-attention, instances of the same controller embodied in the same robot can
focus on different inputs. We also find that the evolved controllers generalize
to unseen morphologies, after a short fine-tuning, suggesting that an inductive
bias related to the task arises from true modularity.


  We study the extension of Minimal Supersymmetric Standard Model by adding one
singlet and one hypercharge zero SU(2) triplet chiral superfield. The triplet
sector gives an additional contributions to the scalar masses and we find that
the lightest CP-even Higgs boson can have a mass of 119-120 GeV at the tree
level, and radiative correction raises the value to 125 GeV. In this model no
significant contributions from stop loops is needed to get the required Higgs
mass which alleviates the fine tuning problem of fixing the stop mass to a high
precision at the GUT scale. In addition this model gives a neutralino dark
matter of mass around 100 GeV which is a mixture of Higgsino and Triplino with
a dark matter density consistent with WMAP observations. The spin-independent
scattering cross-section with nucleons is 10^(-43) cm^2, which makes it
consistent with the bounds from direct detection experiments like XENON100 and
others.


  The particular choice of the gauge group for Yang-Mills theory plays an
important role when it comes to the influence of matter fields. In particular,
both the chosen gauge group and the representation of the matter fields yield
structural differences in the quenched case. Especially, the qualitative
behavior of the Wilson potential is strongly dependent on this selection.
Though the algebraic reasons for this observation is clear, it is far from
obvious how this behavior can be described besides using numerical simulations.
Herein, it is investigated how the group structure appears in the
Dyson-Schwinger equations, which as a hierarchy of equations for the
correlation functions have to be satisfied. It is found that there are
differences depending on both the gauge group and the representation of the
matter fields. This provides insight into possible truncation schemes for
practical calculations using these equations.


  Denial-of-Service (DoS) and Distributed DoS (DDoS) attacks can cause serious
problems in wireless networks due to limited network and host resources.
Attacker traceback is a promising solution to take a proper countermeasure near
the attack origins, to discourage attackers from launching attacks, and for
forensics. However, attacker traceback in Mobile Ad-hoc Networks (MANETs) is a
challenging problem due to the dynamic topology, and limited network resources.
It is especially difficult to trace back attacker(s) when they are moving to
avoid traceback. In this paper, we introduce the ATTENTION protocol framework,
which pays special attention to MAC layer abnormal activity under attack.
ATTENTION consists of three classes, namely, coarse-grained traceback,
fine-grained traceback and spatio-temporal fusion architecture. For
energy-efficient attacker searching in MANETs, we also utilize small-world
model. Our simulation analysis shows 79% of success rate in DoS attacker
traceback with coarse-grained attack signature. In addition, with fine-grained
attack signature, it shows 97% of success rate in DoS attacker traceback and
83% of success rate in DDoS attacker traceback. We also show that ATTENTION has
robustness against node collusion and mobility.


  A sensor name, typically an alphanumeric string, encodes the key context
(e.g., function and location) of a sensor needed for deploying smart building
applications. Sensor names, however, are curated in a building vendor-specific
manner using different structures and vocabularies that are often esoteric.
They thus require tremendous manual effort to annotate on a per-building basis;
even to just segment these sensor names into meaningful chunks. In this paper,
we propose a fully automated self-supervised framework, Sensei, which can learn
to segment sensor names without any human annotation. Specifically, we employ a
neural language model to capture the underlying sensor naming structure and
then induce self-supervision based on information from the language model to
build the segmentation model. Extensive experiments on five real-world
buildings comprising thousands of sensors demonstrate the superiority of Sensei
over baseline methods.


  A locally metric connection on a smooth manifold $M$ is a torsion-free
connection $D$ on $TM$ with compact restricted holonomy group
$\mathrm{Hol}_0(D)$. If the holonomy representation of such a connection is
irreducible, then $D$ preserves a conformal structure on $M$. Under some
natural geometric assumption on the life-time of incomplete geodesics, we prove
that conversely, a locally metric connection $D$ preserving a conformal
structure on a compact manifold $M$ has irreducible holonomy representation,
unless $\mathrm{Hol}_0(D)=0$ or $D$ is the Levi-Civita connection of a
Riemannian metric on $M$. This result generalizes Gallot's theorem on the
irreducibility of Riemannian cones to a much wider class of connections. As an
application, we give the geometric description of compact conformal manifolds
carrying a tame closed Weyl connection with non-generic holonomy.


  The electronic structure of the nitrogenase metal cofactors is central to
nitrogen fixation. However, the P-cluster and iron molybdenum cofactor, each
containing eight irons, have resisted detailed characterization of their
electronic properties. Through exhaustive many-electron wavefunction
simulations enabled by new theoretical methods, we report on the low-energy
electronic states of the P-cluster in three oxidation states. The energy scales
of orbital and spin excitations overlap, yielding a dense spectrum with
features we trace to the underlying atomic states and recouplings. The clusters
exist in superpositions of spin configurations with non-classical spin
correlations, complicating interpretation of magnetic spectroscopies, while the
charges are mostly localized from reorganization of the cluster and its
surroundings. Upon oxidation, the opening of the P-cluster significantly
increases the density of states, which is intriguing given its proposed role in
electron transfer. These results demonstrate that many-electron simulations
stand to provide new insights into the electronic structure of the nitrogenase
cofactors.


  In standard bootstrap percolation, a subset A of the n x n grid is initially
infected. A new site is then infected if at least two of its neighbours are
infected, and an infected site stays infected forever. The set A is said to
percolate if eventually the entire grid is infected. A percolating set is said
to be minimal if none of its subsets percolate. Answering a question of
Bollobas, we show that there exists a minimal percolating set of size 4n^2/33 +
o(n^2), but there does not exist one larger than (n + 2)^2/6.


  We calculate the tunneling current through long line junctions of a $\nu=5/2$
quantum Hall liquid and i) another $\nu=5/2$ liquid, ii) an integer quantum
Hall liquid and iii) a quantum wire. Momentum resolved tunneling provides
information about the number, propagation directions and other features of the
edge modes and thus helps distinguish several competing models of the 5/2
state. We investigate transport properties of two proposed Abelian states: $K=8
state and 331 state, and four possible non-Abelian states: Pfaffian,
edge-reconstructed Pfaffian, and two versions of the anti-Pfaffian state. We
also show that the non-equilibrated anti-Pfaffian state has a different
resistance from other proposed states in the bar geometry.


  In a technological landscape that is quickly moving toward dense multi-CPU
and multi-core computer systems, where using multithreading is an increasingly
popular application design decision, it is important to choose a proper model
for distributing tasks across multiple threads that will result in the best
efficiency for the application and the system as a whole. The work described in
this paper creates, implements and evaluates various models of distributing
tasks to CPU threads and investigates their characteristics for use in modern
high-performance network servers. The results presented here comprise a roadmap
of models for building multithreaded server applications for modern server
hardware and Unix-like operating systems.


  In the early 2000's, Littlejohn and Wellman developed a general left-definite
theory for certain self-adjoint operators by fully determining their domains
and spectral properties. The description of these domains do not feature
explicit boundary conditions. We present characterizations of these domains
given by the left-definite theory for all operators which possess a complete
system of orthogonal eigenfunctions, in terms of classical boundary conditions.


  This work discusses the source broadcasting problem, i.e. transmitting a
source to many receivers via a broadcast channel. The optimal rate-distortion
region for this problem is unknown. The separation approach divides the problem
into two complementary problems: source successive refinement and broadcast
channel transmission. We provide bounds on the loss incorporated by applying
time-sharing and separation in source broadcasting. If the broadcast channel is
degraded, it turns out that separation-based time-sharing achieves at least a
factor of the joint source-channel optimal rate, and this factor has a positive
limit even if the number of receivers increases to infinity. For the AWGN
broadcast channel a better bound is introduced, implying that all achievable
joint source-channel schemes have a rate within one bit of the separation-based
achievable rate region for two receivers, or within $\log_2 T$ bits for $T$
receivers.


  The literature has shown that combining a few non-Personal Identifiable
Information (non-PII) is enough to make a user unique in a dataset including
millions of users. This work demonstrates that a combination of a few non-PII
items can be activated to nanotarget users. We demonstrate that the combination
of the location and {5} rare ({13} random) skills in a LinkedIn profile is
enough to become unique in a user base of {$\sim$970M} users with a probability
of 75\%. The novelty is that these attributes are publicly accessible to anyone
registered on LinkedIn and can be activated through advertising campaigns. We
ran an experiment configuring ad campaigns using the location and skills of
three of the paper's authors, demonstrating how all the ads using $\geq13$
skills were delivered exclusively to the targeted user. We reported this
vulnerability to LinkedIn, which initially ignored the problem, but fixed it as
of November 2023.%This nanotargeting may expose LinkedIn users to privacy and
security risks such as malvertising or manipulation.


  Current induced magnetization switching and resistance associated with domain
walls pinned in nanoconstrictions have both been previously reported in
(Ga,Mn)As based devices, but using very dissimilar experimental schemes and
device geometries . Here we report on the simultaneous observation of both
effects in a single nanodevice, which constitutes a significant step forward
towards the eventual realization of spintronic devices which make use of domain
walls to store, transport, and manipulate information.


  The variational problem of gravity theories is directly related to black hole
thermodynamics. For asymptotically locally AdS backgrounds it is known that
holographic renormalization results in a variational principle in terms of
equivalence classes of boundary data under the local asymptotic symmetries of
the theory, which automatically leads to finite conserved charges satisfying
the first law of thermodynamics. We show that this connection holds well beyond
asymptotically AdS black holes. In particular, we formulate the variational
problem for $\mathcal{N}=2$ STU supergravity in four dimensions with boundary
conditions corresponding to those obeyed by the so called `subtracted
geometries'. We show that such boundary conditions can be imposed covariantly
in terms of a set of asymptotic second class constraints, and we derive the
appropriate boundary terms that render the variational problem well posed in
two different duality frames of the STU model. This allows us to define finite
conserved charges associated with any asymptotic Killing vector and to
demonstrate that these charges satisfy the Smarr formula and the first law of
thermodynamics. Moreover, by uplifting the theory to five dimensions and then
reducing on a 2-sphere, we provide a precise map between the thermodynamic
observables of the subtracted geometries and those of the BTZ black hole.
Surface terms play a crucial role in this identification.


  Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth
$K$-varieties, and let $V$ be a finite dimensional $K$-vector space. For two
algebraic morphisms $\varphi:X\rightarrow V$ and $\psi:Y\rightarrow V$ we
define a convolution operation, $\varphi*\psi:X\times Y\to V$, by
$\varphi*\psi(x,y)=\varphi(x)+\psi(y)$. We then study the singularity
properties of the resulting morphism, and show that as in the case of
convolution in analysis, it has improved smoothness properties.
  Explicitly, we show that for any morphism $\varphi:X\rightarrow V$ which is
dominant when restricted to each irreducible component of $X$, there exists
$N\in\mathbb{N}$ such that for any $n>N$ the $n$-th convolution power
$\varphi^{n}:=\varphi*\dots*\varphi$ is a flat morphism with reduced geometric
fibers of rational singularities (this property is abbreviated (FRS)). By a
theorem of Aizenbud and Avni, for $K=\mathbb{Q}$, this is equivalent to good
asymptotic behavior of the size of the $\mathbb{Z}/p^{k}\mathbb{Z}$-fibers of
$\varphi^{n}$ when ranging over both $p$ and $k$.
  More generally, we show that given a family of morphisms
$\{\varphi_{i}:X_{i}\rightarrow V\}$ of complexity $D\in\mathbb{N}$ (i.e. that
the number of variables and the degrees of the polynomials defining $X_{i}$ and
$\varphi_{i}$ are bounded by $D$), there exists $N(D)\in\mathbb{N}$ such that
for any $n>N(D)$, the morphism $\varphi_{1}*\dots*\varphi_{n}$ is (FRS).


  Due to the merit of establishing volumetric data, X-ray computed tomography
(XCT) is increasingly used as a non-destructive evaluation technique in the
quality control of advanced manufactured parts with complex non-line-of-sight
features. However, the cost of measurement time and data storage hampers the
adoption of the technique in production lines. Commercial fast XCT utilises
X-ray detectors with fast detection capability, which can be expensive and
results a large amount of data. This paper discussed a different approach,
where fast XCT was realised via the acquisition of a small number of projection
images instead of full projection images. An established total variation (TV)
algorithm was used to handle the reconstruction. The paper investigates the
feasibility of using the TV algorithm in handling a significantly reduced
number of projection images for reconstruction. This allows a reduction of
measurement time from fifty-two minutes to one minute for a typical industrial
XCT system. It also enables a reduction of data size proportionally. A test
strategy including both quantitative and qualitative test metrics was
considered to evaluate the effectiveness of the reconstruction algorithm. The
qualitative evaluation includes both the signal to noise ratio and the contrast
to noise ratio. The quantitative evaluation was established using reference
samples with different internal and external geometries. Simulation data were
used in the assessment considering various influence factors, such as X-ray
source property and instrument noise. The results demonstrated the possibility
of using advanced reconstruction algorithms in handling XCT measurements with a
significantly limited number of projection images for dimensional measurements.


  We study the Gaussent-Littelmann formula for Hall-Littlewood polynomials and
we develop combinatorial tools to describe the formula in a purely
combinatorial way for type A_n, B_n and C_n. This description is in terms of
Young tableaux and arises from identifying one-skeleton galleries that appear
in the Gaussent-Littelmann formula with Young tableaux. Furthermore, we show by
using these tools that the Gaussent-Littelmann formula and the well-known
Macdonald formula for Hall-Littlewood polynomials for type A_n are the same.


  The most common method for calculating accurate numerical solutions for
complicated linear differential equations - for example, finding eigenvalues
and eigenfunctions of the Schrodinger equation for many-electron atoms - is the
variational method with some convenient basis of functions. This leads to a
finite matrix representation of the operators involved; and standard numerical
operations - such as Gaussian elimination - may be employed. When the basis
functions are not orthogonal, one expects substantial loss of numerical
accuracy in those matrix manipulations; and so multiple-precision arithmetic is
often required for useful results. In this paper, for the first time, we offer
a way to estimate the rate at which numerical cancellations will grow in
severity as one increases the basis size. For the familiar case of using simple
power series, x^n, n<N as the basis instead of orthogonal polynomials, we
predict a loss of about 2N bits or 4N bits of numerical accuracy.


  Contemporary power grids are being challenged by rapid voltage fluctuations
that are caused by large-scale deployment of renewable generation, electric
vehicles, and demand response programs. In this context, monitoring the grid's
operating conditions in real time becomes increasingly critical. With the
emergent large scale and nonconvexity however, the existing power system state
estimation (PSSE) schemes become computationally expensive or yield suboptimal
performance. To bypass these hurdles, this paper advocates deep neural networks
(DNNs) for real-time power system monitoring. By unrolling an iterative
physics-based prox-linear solver, a novel model-specific DNN is developed for
real-time PSSE with affordable training and minimal tuning effort. To further
enable system awareness even ahead of the time horizon, as well as to endow the
DNN-based estimator with resilience, deep recurrent neural networks (RNNs) are
also pursued for power system state forecasting. Deep RNNs leverage the
long-term nonlinear dependencies present in the historical voltage time series
to enable forecasting, and they are easy to implement. Numerical tests showcase
improved performance of the proposed DNN-based estimation and forecasting
approaches compared with existing alternatives. In real load data experiments
on the IEEE 118-bus benchmark system, the novel model-specific DNN-based PSSE
scheme outperforms nearly by an order-of-magnitude the competing alternatives,
including the widely adopted Gauss-Newton PSSE solver.


  For each $n > 0$ there is a one complex parameter family of homeomorphisms of
the circle consisting of linear fractional transformations `conjugated by $z
\to z^n$'. We show that these families are free of relations, which determines
the structure of `the group of homeomorphisms of finite type'. We also discuss
a number of questions regarding factorization for more robust groups of
homeomorphisms of the circle in terms of these basic building blocks, and the
correspondence between smoothness properties of the homeomorphisms and decay
properties of the parameters.


  We propose a new unsupervised and non-parametric method to detect change
points in intricate quasi-periodic signals. The detection relies on optimal
transport theory combined with topological analysis and the bootstrap
procedure. The algorithm is designed to detect changes in virtually any
harmonic or a partially harmonic signal and is verified on three different
sources of physiological data streams. We successfully find abnormal or
irregular cardiac cycles in the waveforms for the six of the most frequent
types of clinical arrhythmias using a single algorithm. The validation and the
efficiency of the method are shown both on synthetic and on real time series.
Our unsupervised approach reaches the level of performance of the supervised
state-of-the-art techniques. We provide conceptual justification for the
efficiency of the method and prove the convergence of the bootstrap procedure
theoretically.


  Contributing to history has never been as easy as it is today. Anyone with
access to the Web is able to play a part on Wikipedia, an open and free
encyclopedia. Wikipedia, available in many languages, is one of the most
visited websites in the world and arguably one of the primary sources of
knowledge on the Web. However, not everyone is contributing to Wikipedia from a
diversity point of view; several groups are severely underrepresented. One of
those groups is women, who make up approximately 16% of the current contributor
community, meaning that most of the content is written by men. In addition,
although there are specific guidelines of verifiability, notability, and
neutral point of view that must be adhered by Wikipedia content, these
guidelines are supervised and enforced by men.
  In this paper, we propose that gender bias is not about participation and
representation only, but also about characterization of women. We approach the
analysis of gender bias by defining a methodology for comparing the
characterizations of men and women in biographies in three aspects: meta-data,
language, and network structure. Our results show that, indeed, there are
differences in characterization and structure. Some of these differences are
reflected from the off-line world documented by Wikipedia, but other
differences can be attributed to gender bias in Wikipedia content. We
contextualize these differences in feminist theory and discuss their
implications for Wikipedia policy.


  In this paper we propose a distributed version of a randomized
block-coordinate descent method for minimizing the sum of a partially separable
smooth convex function and a fully separable non-smooth convex function. Under
the assumption of block Lipschitz continuity of the gradient of the smooth
function, this method is shown to have a sublinear convergence rate. Linear
convergence rate of the method is obtained for the newly introduced class of
generalized error bound functions. We prove that the new class of generalized
error bound functions encompasses both global/local error bound functions and
smooth strongly convex functions. We also show that the theoretical estimates
on the convergence rate depend on the number of blocks chosen randomly and a
natural measure of separability of the objective function.


  This paper considers two-dimensional stratified water waves propagating under
the force of gravity over an impermeable flat bed and with a free surface. We
prove the existence of a global continuum of classical solutions that are
periodic and traveling. These waves, moreover, can exhibit large density
variation, speed and amplitude.


  We present a study of the upper critical field of the newly discovered heavy
fermion superconductor UTe$_2$ by magnetoresistivity measurements in pulsed
magnetic fields up to 60~T and static magnetic fields up to 35~T. We show that
superconductivity survives up to the metamagnetic transition at $H_{\rm m}
\approx 35$~T at low temperature. Above $H_{\rm m}$ superconductivity is
suppressed. At higher temperature superconductivity is enhanced under magnetic
field leading to reentrance of superconductivity or an almost temperature
independent increase of $H_{\rm c2}$. By studying the angular dependence of the
upper critical field close to the $b$ axis (hard magnetization axis) we show
that the maximum of the reentrant superconductivity temperature is depinned
from the metamagnetic field. A key ingredient for the field-reinforcement of
superconductivity on approaching $H_{\rm m}$ appears to be an immediate
interplay with magnetic fluctuations and a possible Fermi-surface
reconstruction.


  In this article, we present a Bayesian hierarchical model for predicting a
latent health state from longitudinal clinical measurements. Model development
is motivated by the need to integrate multiple sources of data to improve
clinical decisions about whether to remove or irradiate a patient's prostate
cancer. Existing modeling approaches are extended to accommodate measurement
error in cancer state determinations based on biopsied tissue, clinical
measurements possibly not missing at random, and informative partial
observation of the true state. The proposed model enables estimation of whether
an individual's underlying prostate cancer is aggressive, requiring surgery
and/or radiation, or indolent, permitting continued surveillance. These
individualized predictions can then be communicated to clinicians and patients
to inform decision-making. We demonstrate the model with data from a cohort of
low risk prostate cancer patients at Johns Hopkins University and assess
predictive accuracy among a subset for whom true cancer state is observed.
Simulation studies confirm model performance and explore the impact of
adjusting for informative missingness on true state predictions. R code and
simulated data available at
https://github.com/rycoley/prediction-prostate-surveillance.


  In the detection of anemia, leukemia and other blood diseases, the number and
type of leukocytes are essential evaluation parameters. However, the
conventional leukocyte counting method is not only quite time-consuming but
also error-prone. Consequently, many automation methods are introduced for the
diagnosis of medical images. It remains difficult to accurately extract related
features and count the number of cells under the variable conditions such as
background, staining method, staining degree, light conditions and so on.
Therefore, in order to adapt to various complex situations, we consider RGB
color space, HSI color space, and the linear combination of G, H and S
components, and propose a fast and accurate algorithm for the segmentation of
peripheral blood leukocytes in this paper. First, the nucleus of leukocyte was
separated by using the stepwise averaging method. Then based on the
interval-valued fuzzy sets, the cytoplasm of leukocyte was segmented by
minimizing the fuzzy divergence. Next, post-processing was carried out by using
the concave-convex iterative repair algorithm and the decision mechanism of
candidate mask sets. Experimental results show that the proposed method
outperforms the existing non-fuzzy sets methods. Among the methods based on
fuzzy sets, the interval-valued fuzzy sets perform slightly better than
interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets.


  Making use of the SO(3,1) Lorentz algebra, we derive in this paper two series
of Gauss-Bonnet type identities involving torsion, one being of the Pontryagin
type and the other of the Euler type. Two of the six identities involve only
torsional tensorial entities and are purely torsional topological invariants.


  We provide an analysis of the structure of renormalisation scheme invariants
for the case of $\phi^4$ theory, relevant in four dimensions. We give a
complete discussion of the invariants up to four loops and include some partial
results at five loops, showing that there are considerably more invariants than
one might naively have expected. We also show that one-vertex reducible
contributions may consistently be omitted in a well-defined class of schemes
which of course includes MSbar.


  We use basic tools of descriptive set theory to prove that a closed set
$\mathcal S$ of marked groups has $2^{\aleph_0}$ quasi-isometry classes
provided every non-empty open subset of $\mathcal S$ contains at least two
non-quasi-isometric groups. It follows that every perfect set of marked groups
having a dense subset of finitely presented groups contains $2^{\aleph_0}$
quasi-isometry classes. These results account for most known constructions of
continuous families of non-quasi-isometric finitely generated groups. They can
also be used to prove the existence of $2^{\aleph_0}$ quasi-isometry classes of
finitely generated groups having interesting algebraic, geometric, or
model-theoretic properties.


  The critical dynamics of relaxational stochastic models with nonconserved
$n$-component order parameter $\bm{\phi}$ and no coupling to other slow
variables ("model A") is investigated in film geometries for the cases of
periodic and free boundary conditions. The Hamiltonian $\mathcal{H}$ governing
the stationary equilibrium distribution is taken to be O(n) symmetric and to
involve, in the case of free boundary conditions, the boundary terms
$\int_{\mathfrak{B}_j}\mathring{c}_j \phi^2/2$ associated with the two
confining surface planes $\mathfrak{B}_j$, $j=1,2$, at $z=0$ and $z=L$, where
the enhancement variables $\mathring{c}_j$ are presumed to be subcritical or
critical. A field-theoretic RG study of the dynamic critical behavior at
$d=4-\epsilon$ bulk dimensions is presented, with special attention paid to the
cases where the classical theories involve zero modes at $T_{c,\infty}$. This
applies when either both $\mathring{c}_j$ take the critical value
$\mathring{c}_{\text{sp}}$ associated with the special surface transition, or
else periodic boundary conditions are imposed. Owing to the zero modes, the
$\epsilon$ expansion becomes ill-defined at $T_{c,\infty}$. Analogously to the
static case, the field theory can be reorganized to obtain a well-defined
small-$\epsilon$ expansion involving half-integer powers of $\epsilon$,
modulated by powers of $\ln\epsilon$. Explicit results for the scaling
functions of $T$-dependent finite-size susceptibilities at temperatures $T\ge
T_{c,\infty}$ and of layer and surface susceptibilities at the bulk critical
point are given to orders $\epsilon$ and $\epsilon^{3/2}$, respectively. For
the case of periodic boundary conditions, the consistency of the expansions to
$O(\epsilon^{3/2})$ with exact large-$n$ results is shown.


  We consider the problem of selfish agents in discrete-time queuing systems,
where competitive queues try to get their packets served. In this model, a
queue gets to send a packet each step to one of the servers, which will attempt
to serve the oldest arriving packet, and unprocessed packets are returned to
each queue. We model this as a repeated game where queues compete for the
capacity of the servers, but where the state of the game evolves as the length
of each queue varies, resulting in a highly dependent random process. Earlier
work by the authors [EC'20] shows that with no-regret learners, the system
needs twice the capacity as would be required in the coordinated setting to
ensure queue lengths remain stable despite the selfish behavior of the queues.
In this paper, we demonstrate that this way of evaluating outcomes is myopic:
if more patient queues choose strategies that selfishly maximize their long-run
success rate, stability can be ensured with just $\frac{e}{e-1}\approx 1.58$
times extra capacity, better than what is possible assuming the no-regret
property.
  As these systems induce highly dependent processes, our analysis draws
heavily on techniques from probability theory. Though these systems are random
under any fixed policies by the queues, we show that, surprisingly, these
systems have deterministic and explicit asymptotic behavior. We show that the
asymptotic growth rates of queues can be written as a ratio of a submodular and
modular function, which provides significant game-theoretic properties. Our
equilibrium analysis then relies on a novel deformation argument towards a more
analyzable solution that differs significantly from previous price of anarchy
results. While the intermediate points will not be equilibria, this analytic
structure will ensure that this deformation is monotonic along this continuous
path.


  This article presents conceptual and methodological frameworks to prioritise
interventions on the Colombian P\'aramo. The mode of analysis that our work
takes up is that of questioning value and related categories as definite
empirically perceived phenomena. We contend that the valuation of ecosystem
services -- even in its post-normal forms -- and the ecosystem services
framework not only fail to examine value-based categories, but reproduce the
problematic aspects of value-based social relations, which ultimately bear on
the ecological issues affecting the P\'aramo. Upon this premise we set out to
formalise a (computational) dialogical scenario where arguments stating
distinct, and often contradictory, actions delineate possible forms of
appropriating the P\'aramo, while motivating the examination of their defining
sociality.


  A silicon light source at communication wavelength is the bottleneck for
developing monolithically integrated silicon photonics. Doping silicon with
erbium ions was believed to be one of the most promising approaches but suffers
from the aggregation of erbium ions that are efficient non-radiative centers,
formed during the standard rapid thermal treatment. Here, we apply a deep
cooling process following the high-temperature annealing to suppress the
aggregation of erbium ions by flushing with Helium gas cooled in liquid
nitrogen. The resultant light emitting efficiency is increased to a record 14%
at room temperature, two orders of magnitude higher than the sample treated by
the standard rapid thermal annealing. The deep-cooling-processed Si samples
were further made into light-emitting diodes. Bright electroluminescence with a
spectral peak at 1.54 um from the silicon-based diodes was also observed at
room temperature. With these results, it is promising to develop efficient
silicon lasers at communication wavelength for the monolithically integrated
silicon photonics.


  Several issues regarding the Blandford-Znajek process are discussed to
demonstrate that it can be an effective mechanism for powering the gamma ray
bursts. Using a simple circuit analysis it is argued that the disk power
increases the effective power of the black hole-accretion disk system, although
a part of disk power can be dissipated into black hole entropy. Within the
framework of the force-free magnetosphere with the strong magnetic field, the
magnetically dominated MHD flow is found to support the Blandford-Znajek
process and it is demonstrated that the possible magnetic repulsion by the
rotating black hole will not affect the efficiency substantially.


  Investigation of the resonances $X(4140)$ and $X(4274)$, which were recently
confirmed by the LHCb Collaboration [1], is carried out by treating them as the
color triplet and sextet $[cs][\bar{c}\bar {s}]$ diquark-antidiquark states
with the spin-parity $J^{P}=1^{+}$, respectively. We calculate the masses and
meson-current couplings of these tetraquarks in the context of QCD two-point
sum rule method by taking into account the quark, gluon and mixed vacuum
condensates up to eight dimensions. We also study the vertices
$X(4140)J/\psi\phi$ and $X(4274)J/\psi\phi$, and evaluate corresponding strong
couplings $g_{X(4140)J/\psi\phi}$ and $ g_{X(4274)J/\psi\phi}$ by means of QCD
light-cone sum rule method, and a technique of the soft-meson approximation. In
turn, these couplings contain a required information to determine the width of
the $X(4140)\to J/\psi\phi$ and $X(4274) \to J/\psi\phi$ decay channels. We
compare our results for the masses and decay widths of the $X(4140)$ and
$X(4274)$ resonances with the LHCb data, and alternative theoretical
predictions.


  We perform simulations based on the Penna model for biological ageing, now
with the purpose of studying sympatric speciation, that is, the division of a
single species into two or more populations, reproductively isolated, but
without any physical barrier separating them. For that we introduce a new kind
of competition among the individuals, using a modified Verhulst factor. The new
competition depends on some specific phenotypic characteristic of each
individual, which is represented by a pair of bitstrings. These strings are
read in parallel and have no age structure. In this way, each individual genome
consists of two parts. The first one has an age-structure and is related to the
appearance of inherited diseases; the second part is not structured and takes
into account the competition for the available resources. We also introduce
sexual selection into the model, making use of another non-structured and
independent pair of bitstrings.
  In this thesis we present three different models; two of them use, besides
the competition, a sudden change in the ecology to obtain speciation. They were
motivated by the speciation process observed in the Darwin finches, a family of
birds that inhabits the Galapagos Islands, and also by that observed in the
cichlids, a family of fish that lives in the Nicaragua Lakes and in the Vitoria
Lake, in Africa. The third model does not use any ecological change: sympatric
speciation is obtained depending only on the strength of competition among
individuals with similar phenotypic characteristics.


  Recently, Beierle and Leander found two new sporadic quadratic APN
permutations in dimension 9. Up to EA-equivalence, we present a single
trivariate representation of those two permutations as $C_u \colon
(\mathbb{F}_{2^m})^3 \rightarrow (\mathbb{F}_{2^m})^3, (x,y,z) \mapsto
(x^3+uy^2z, y^3+uxz^2,z^3+ux^2y)$, where $m=3$ and $u \in
\mathbb{F}_{2^3}\setminus\{0,1\}$ such that the two permutations correspond to
different choices of $u$. We then analyze the differential uniformity and the
nonlinearity of $C_u$ in a more general case. In particular, for $m \geq 3$
being a multiple of 3 and $u \in \mathbb{F}_{2^m}$ not being a 7-th power, we
show that the differential uniformity of $C_u$ is bounded above by 8, and that
the linearity of $C_u$ is bounded above by $8^{1+\lfloor \frac{m}{2} \rfloor}$.
Based on numerical experiments, we conjecture that $C_u$ is not APN if $m$ is
greater than $3$. We also analyze the CCZ-equivalence classes of the quadratic
APN permutations in dimension 9 known so far and derive a lower bound on the
number of their EA-equivalence classes. We further show that the two sporadic
APN permutations share an interesting similarity with Gold APN permutations in
odd dimension divisible by 3, namely that a permutation EA-inequivalent to
those sporadic APN permutations and their inverses can be obtained by just
applying EA transformations and inversion to the original permutations.


  Noble liquid detectors have become an attractive option for exploring physics
beyond the standard model. Current experiments are using these detectors to
search for dark matter interactions, neutrinoless double beta decay, and other
phenomena. Improved energy resolution can be leveraged from an optimized
combination of two detection channels: ionization and scintillation.
Experimentally, a microscopic anti-correlation behavior between these signals
has been observed, but it has not been described from first principles. Making
measurements in a third channel would provide useful information about the
microscopic anti-correlation phenomenon. Work is currently underway at Drexel
University to develop solid argon and xenon bolometers, which would be able to
utilize a heat channel in addition to ionization and scintillation. Present
efforts are aimed at developing a method for growing small noble solid samples
via vapor deposition onto a substrate over a wide range of temperatures down to
10 K. Understanding the sample growth is the first step to develop techniques
for integrating detector components to measure ionization and scintillation
signals. This will allow for improved characterization of noble solids as
detector media. In the future, efforts will be focused on the growth of these
detectors in the Drexel dilution refrigerator, where samples can be cooled to
20 mK to include bolometric measurements for the simultaneous readout of the
three detection channels.


  We report on the long-term variability of the Be/X-ray binary LS I +61 235/RX
J0146.9+6121. New optical spectroscopic and infrared photometric observations
confirm the presence of global one-arm oscillations in the circumstellar disc
of the Be star and allow us to derive a V/R quasi-period of 1240+-30 days.
Pronounced shell events, reminiscent of the spectacular variations in Be stars,
are also seen. We have found that the J, H and K infrared photometric bands
vary in correlation with the spectroscopic V/R variations, implying that the
one-armed disc oscillations are prograde. The effect of the oscillations is not
only seen in the Halpha line but also in the He I6678 and Paschen lines. Since
these lines are formed at different radii in the equatorial disc of the Be
star, such effect confirms the global nature of the perturbation. The Keplerian
disc has been found to be denser than the average of a sample of isolated Be
stars, which may be indicative of some kind of interaction with the compact
companion. Finally, from a Rossi X-ray Timing Explorer observation we derive a
spin period of the neutron star of 1404.5+-0.5 s.


  Closed geodesic lines on an ellipsoid in d-dimensional Euclidean space are
considered. Explicit algebro-geometric condition for closedness of such a
geodesic is given. The obtained condition is discussed in light of
theta-functions theory and compared with some recent related results.


  We derive theoretical guarantees for the exact recovery of piecewise constant
two-dimensional images from a minimal number of non-uniform Fourier samples
using a convex matrix completion algorithm. We assume the discontinuities of
the image are localized to the zero level-set of a bandlimited function, which
induces certain linear dependencies in Fourier domain, such that a multifold
Toeplitz matrix built from the Fourier data is known to be low-rank. The
recovery algorithm arranges the known Fourier samples into the structured
matrix then attempts recovery of the missing Fourier data by minimizing the
nuclear norm subject to structure and data constraints. This work adapts
results by Chen and Chi on the recovery of isolated Diracs via nuclear norm
minimization of a similar multifold Hankel structure. We show that exact
recovery is possible with high probability when the bandlimited function
describing the edge set satisfies an incoherency property. Finally, we
demonstrate the algorithm on the recovery of undersampled MRI data.


  This paper takes an axiomatic and calculational view of diversity (or
"N-version programming"), where multiple implementations of the same
specification are executed in parallel to increase dependability. The central
notion is "adjudication": once we have multiple, potential different, outcomes,
how do we come to a single result? Adjudication operators are explicitly
defined and some general properties for these explored.


  We study a patrolling game played on a network $Q$, considered as a metric
space. The Attacker chooses a point of $Q$ (not necessarily a node) to attack
during a chosen time interval of fixed duration. The Patroller chooses a unit
speed path on $Q$ and intercepts the attack (and wins) if she visits the
attacked point during the attack time interval. This zero-sum game models the
problem of protecting roads or pipelines from an adversarial attack. The payoff
to the maximizing Patroller is the probability that the attack is intercepted.
Our results include the following: (i) a solution to the game for any network
$Q$, as long as the time required to carry out the attack is sufficiently
short, (ii) a solution to the game for all tree networks that satisfy a certain
condition on their extremities, and (iii) a solution to the game for any attack
duration for stars with one long arc and the remaining arcs equal in length. We
present a conjecture on the solution of the game for arbitrary trees and
establish it in certain cases.


  The Chow variety of polynomials that decompose as a product of linear forms
has been studied for more than 100 years. Finding equations in the ideal of
secant varieties of Chow varieties would enable one to measure the complexity
the permanent to prove Valiant's conjecture $\mathbf{VP\neq VNP}$. In this
article, I use the method of prolongation to obtain equations for secant
varieties of Chow varieties as $GL(V)$-modules.


  We modeled the evolution of the Milky Way to trace the distribution in space
and time of four prerequisites for complex life: the presence of a host star,
enough heavy elements to form terrestrial planets, sufficient time for
biological evolution and an environment free of life-extinguishing supernovae.
We identified the Galactic habitable zone (GHZ) as an annular region between 7
and 9 kiloparsecs from the Galactic center that widens with time and is
composed of stars that formed between 8 and 4 billion years ago. This GHZ
yields an age distribution for the complex life that may inhabit our Galaxy. We
found that 75% of the stars in the GHZ are older than the Sun.


  We consider the problem of the observability of positively expansive maps by
the time series associated to continuous real functions. For this purpose we
prove a general result on the generic observability of a locally injective map
of a compact metric space of finite topological dimension, extending earlier
work by Gutman [6]. We apply this result to partially solve the problem of
finding the minimal number of functions needed to observe a positively
expansive map. We prove that two functions are necessary and sufficient for
positively expansive maps on tori.


  Consider an infinite sequence of independent, uniformly chosen points from
$[0,1]^d$. After looking at each point in the sequence, an overseer is allowed
to either keep it or reject it, and this choice may depend on the locations of
all previously kept points. However, the overseer must keep at least one of
every two consecutive points. We call a sequence generated in this fashion a
\emph{two-thinning} sequence. Here, the purpose of the overseer is to control
the discrepancy of the empirical distribution of points, that is, after
selecting $n$ points, to reduce the maximal deviation of the number of points
inside any axis-parallel hyper-rectangle of volume $A$ from $nA$. Our main
result is an explicit low complexity two-thinning strategy which guarantees
discrepancy of $O(\log^{2d+1} n)$ for all $n$ with high probability (compare
with $\Theta(\sqrt{n\log\log n})$ without thinning). The case $d=1$ of this
result answers a question of Benjamini.
  We also extend the construction to achieve the same asymptotic bound for
($1+\beta$)-thinning, a set-up in which rejecting is only allowed with
probability $\beta$ independently for each point. In addition, we suggest an
improved and simplified strategy which we conjecture to guarantee discrepancy
of $O(\log^{d+1} n)$ (compare with $\theta(\log^d n)$, the best known
construction of a low discrepancy sequence). Finally, we provide theoretical
and empirical evidence for our conjecture, and provide simulations supporting
the viability of our construction for applications.


  In this paper, we study the evolution of iterated equilibrium distributions
for the Gamma and Weibull families of distributions as the iteration step
increases. We characterize their moments and the pointwise limit of the
distribution functions corresponding to the iterated distributions. As a
byproduct, we obtain approximations for higher order moments of the residual
lifetime.


  A comprehensive theory encompassing the kinetics of sol-to-gel transition is
yet to be formulated due to break-down of the mean-field Smoluchowski Equation.
Using high temporal-resolution Monte Carlo simulation of irreversible
aggregation systems, we show that this transition has three distinct regimes
with kinetic exponent z ranging between 1 and 2, corresponding to aggregation
of sol clusters proceeding to the ideal gel point (IGP); z ranging between 2
and 5.7 for gelation of sol clusters beyond IGP; and z ranging between 2 and
3.5 for a hitherto unidentified regime involving aggregation of gels when
monomer-dense. We further establish universal power-law scaling relationships
that connect the kinetics of these three regimes.


  Quantum key distribution (QKD) uses individual light quanta in quantum
superposition states to guarantee unconditional communication security between
distant parties. In practice, the achievable distance for QKD has been limited
to a few hundred kilometers, due to the channel loss of fibers or terrestrial
free space that exponentially reduced the photon rate. Satellite-based QKD
promises to establish a global-scale quantum network by exploiting the
negligible photon loss and decoherence in the empty out space. Here, we develop
and launch a low-Earth-orbit satellite to implement decoy-state QKD with over
kHz key rate from the satellite to ground over a distance up to 1200 km, which
is up to 20 orders of magnitudes more efficient than that expected using an
optical fiber (with 0.2 dB/km loss) of the same length. The establishment of a
reliable and efficient space-to-ground link for faithful quantum state
transmission constitutes a key milestone for global-scale quantum networks.


  With the aim of describing real-time electron dynamics, we introduce an
adiabatic approximation for the equation of motion of the one-body
reduced-density matrix (one-matrix). The eigenvalues of the one-matrix, which
represent the occupation numbers of single-particle orbitals, are obtained from
the constrained minimization of the instantaneous ground state energy
functional rather than from their dynamical equations. To clarify the
motivation for this minimization condition, we discuss a sequence of adiabatic
energy functionals, each obeying a minimum principle. The performance of the
approximation vis-a`-vis nonadiabatic effects is assessed in real-time
simulations for a two-site Hubbard model. Due to the presence of
Landau-Zener-type transitions, the system evolves into a nonstationary state
with persistent oscillations in the observables. The amplitude and phase of the
oscillations exhibit resonance behavior both with respect to the strength of
the electron-electron interaction and the rate of variation of the external
potential. Both types of resonances have the same origin -- the interference of
dynamical and scattering phases.


  We report the observation of all-optically tunable Raman fluorescence from a
single quantum dot. The Raman photons are produced in an optically-driven
Lambda-system defined by subjecting the single electron charged quantum dot to
a magnetic field in Voigt geometry. Detuning the driving laser from resonance,
we tune the frequency of the Raman photons by about 2.5 GHz. The number of
scattered photons and the linewdith of the Raman photons are investigated as a
function of detuning. The study presented here could form the basis of a new
technique for investigating spin-bath interactions in the solid state.


  In this paper we study some low energy effects of a light stabilized radion
in the Randall-Sundrum scenario. We find that the NLC 500 with its projected
precision level will be able to probe the radion contribution to the anomalous
magnetic moment and electric quadrupole moment of W boson for values of radion
vev up to 500 Gev. On the other hand the BNL experiment E821 will be able to
test the radion contribution to $a_{\mu}$ for 1 Tev radion vev and $m_{\phi}\le
m_{\mu}$. We have also shown that the higgs-radion mixing induces a 2.6%
correction in the WWh coupling. Finally by comparing the radionstrahlung with
the higgsstrahlung process we have found that the LEPI bound on the higgs mass
based on $Z\to hl\bar{l}$ decay mode suggests a lower bound of about 35 Gev on
the radion mass.


  We present a formula for the degree of the discriminant of irreducible
representations of a Lie group, in terms of the roots of the group and the
highest weight of the representation. The proof uses equivariant cohomology
techniques, namely, the theory of Thom polynomials, and a new method for their
computation. We study the combinatorics of our formulas in various special
cases.


  The present document focuses on the theoretical foundations of the nuclear
energy density functional (EDF) method. As such, it does not aim at reviewing
the status of the field, at covering all possible ramifications of the approach
or at presenting recent achievements and applications. The objective is to
provide a modern account of the nuclear EDF formalism that is at variance with
traditional presentations that rely, at one point or another, on a {\it
Hamiltonian-based} picture. The latter is not general enough to encompass what
the nuclear EDF method represents as of today. Specifically, the traditional
Hamiltonian-based picture does not allow one to grasp the difficulties
associated with the fact that currently available parametrizations of the
energy kernel $E[g',g]$ at play in the method do not derive from a genuine
Hamilton operator, would the latter be effective. The method is formulated from
the outset through the most general multi-reference, i.e. beyond mean-field,
implementation such that the single-reference, i.e. "mean-field", derives as a
particular case. As such, a key point of the presentation provided here is to
demonstrate that the multi-reference EDF method can indeed be formulated in a
{\it mathematically} meaningful fashion even if $E[g',g]$ does {\it not} derive
from a genuine Hamilton operator. In particular, the restoration of symmetries
can be entirely formulated without making {\it any} reference to a projected
state, i.e. within a genuine EDF framework. However, and as is illustrated in
the present document, a mathematically meaningful formulation does not
guarantee that the formalism is sound from a {\it physical} standpoint. The
price at which the latter can be enforced as well in the future is eventually
alluded to.


  The construction of machine learning models involves many bi-level
multi-objective optimization problems (BL-MOPs), where upper level (UL)
candidate solutions must be evaluated via training weights of a model in the
lower level (LL). Due to the Pareto optimality of sub-problems and the complex
dependency across UL solutions and LL weights, an UL solution is feasible if
and only if the LL weight is Pareto optimal. It is computationally expensive to
determine which LL Pareto weight in the LL Pareto weight set is the most
appropriate for each UL solution. This paper proposes a bi-level
multi-objective learning framework (BLMOL), coupling the above decision-making
process with the optimization process of the UL-MOP by introducing LL
preference $r$. Specifically, the UL variable and $r$ are simultaneously
searched to minimize multiple UL objectives by evolutionary multi-objective
algorithms. The LL weight with respect to $r$ is trained to minimize multiple
LL objectives via gradient-based preference multi-objective algorithms. In
addition, the preference surrogate model is constructed to replace the
expensive evaluation process of the UL-MOP. We consider a novel case study on
multi-task graph neural topology search. It aims to find a set of Pareto
topologies and their Pareto weights, representing different trade-offs across
tasks at UL and LL, respectively. The found graph neural network is employed to
solve multiple tasks simultaneously, including graph classification, node
classification, and link prediction. Experimental results demonstrate that
BLMOL can outperform some state-of-the-art algorithms and generate
well-representative UL solutions and LL weights.


  Partial differential equations (PDEs) are widely used for the description of
physical and engineering phenomena. Some key parameters involved in PDEs, which
represent certain physical properties with important scientific
interpretations, are difficult or even impossible to measure directly.
Estimating these parameters from noisy and sparse experimental data of related
physical quantities is an important task. Many methods for PDE parameter
inference involve a large number of evaluations for numerical solutions to PDE
through algorithms such as the finite element method, which can be
time-consuming, especially for nonlinear PDEs. In this paper, we propose a
novel method for the inference of unknown parameters in PDEs, called the
PDE-Informed Gaussian Process (PIGP) based parameter inference method. Through
modeling the PDE solution as a Gaussian process (GP), we derive the manifold
constraints induced by the (linear) PDE structure such that, under the
constraints, the GP satisfies the PDE. For nonlinear PDEs, we propose an
augmentation method that transforms the nonlinear PDE into an equivalent PDE
system linear in all derivatives, which our PIGP-based method can handle. The
proposed method can be applied to a broad spectrum of nonlinear PDEs. The
PIGP-based method can be applied to multi-dimensional PDE systems and PDE
systems with unobserved components. Like conventional Bayesian approaches, the
method can provide uncertainty quantification for both the unknown parameters
and the PDE solution. The PIGP-based method also completely bypasses the
numerical solver for PDEs. The proposed method is demonstrated through several
application examples from different areas.


  The Pampilhosa da Serra Space Observatory (PASO) is located in the center of
the continental Portuguese territory, in the heart of a certified Dark Sky
destination by the Starlight Foundation (Aldeias do Xisto) and has been an
instrumental asset to advance science, education and astrotourism
certifications. PASO hosts astronomy and Space Situational Awareness (SSA)
activities including a node of the Portuguese Space Surveillance \& Tracking
(SST) infrastructure network, such as a space radar currently in test phase
using GEM radiotelescope, a double Wide Field of View Telescope system, a EUSST
optical sensor telescope. These instruments allow surveillance of satellite and
space debris in LEO, MEO and GEO orbits. The WFOV telescope offers spectroscopy
capabilities enabling light curve analysis and cosmic sources monitoring.
Instruments for Space Weather are being considered for installation to monitor
solar activities and expand the range of SSA services.


  Galileo determined distances to stars based on the assumption that stars were
suns, the apparent sizes of stars as seen through his telescope, and basic
geometry. However, the apparent sizes that he measured were the result of
diffraction and not related to the actual sizes of the stars. Galileo's methods
and observations were good, but since he was unknowingly observing diffraction
artifacts and not the physical bodies of stars he greatly underestimated the
distances to the stars.


  Model predictive control (MPC) has proven its applicability in power
conversion control with its fast dynamic response to reference changes while
ensuring critical system constraints are satisfied. Even then, the
computational burden still remains a challenge for many MPC variants. In this
regard, this paper formulates an indirect MPC scheme for grid-side wind
converters. A quadratic program with linear constraints is solved in a receding
horizon fashion with a subsequent PWM modulator. To facilitate its solution
within a few hundreds of microseconds, its decision variables (modulating
signals) are restricted to a specific frequency content. This approach limits
the increase in problem size due to horizon length. In case studies, the
proposed MPC exhibits fast response in faults and operates the converter within
its safety limits.


  A convex projective surface is the quotient of a properly convex open
$\Omega$ of $\mathbb{P}(\R)$ by a discret subgroup $\Gamma$ of
$\mathrm{SL}_3(\R)$. We give some caracterisations of the fact that a convex
projective surface is of finite volume for the Busemann's measure. We deduce of
this that if $\Omega$ is not a triangle then $\Omega$ is strictly convex, with
$\Cc^1$ boundary and that a convex projective surface $S$ is of finite volume
if and only if the dual surface is of finite volume.


  A biomimetic model of cell-cell communication was developed to probe the
passive molecular transport across ion channels inserted in synthetic lipid
bilayers formed between contacting droplets arranged in a linear array.
Diffusion of a fluorescent probe across the array was measured for different
pore concentrations. The diffusion characteristic time scale is found to vary
non-linearly with the pore concentration. Our measurements are successfully
modeled by a continuous time random walk description, whose waiting time is the
first exit time from a droplet through a cluster of pores. The size of the
cluster of pores is found to increase with their concentration. Our results
provide a direct link between the mesoscopic permeation properties and the
microscopic characteristics of the pores such as their number, size and spatial
arrangement.


  We present an approach to support partiality in type-level computation
without compromising expressiveness or type safety. Existing frameworks for
type-level computation either require totality or implicitly assume it. For
example, type families in Haskell provide a powerful, modular means of defining
type-level computation. However, their current design implicitly assumes that
type families are total, introducing nonsensical types and significantly
complicating the metatheory of type families and their extensions. We propose
an alternative design, using qualified types to pair type-level computations
with predicates that capture their domains. Our approach naturally captures the
intuitive partiality of type families, simplifying their metatheory. As
evidence, we present the first complete proof of consistency for a language
with closed type families.


  We study the dynamics of a quantum spin Hall edge coupled to a magnet with
its own dynamics. Using spin transfer torque principles, we analyze the
interplay between spin currents in the edge state and dynamics of the axis of
the magnet, and draw parallels with circuit analogies. As a highlighting
feature, we show that while coupling to a magnet typically renders the edge
state insulating by opening a gap, in the presence of a small potential bias,
spin-transfer torque can restore perfect conductance by transferring angular
momentum to the magnet. In the presence of interactions within the edge state,
we employ a Luttinger liquid treatment to show that the edge, when subject to a
small voltage bias, tends to form a unique dynamic rotating spin wave state
that naturally couples into the dynamics of the magnet. We briefly discuss
realistic physical parameters and constraints for observing this interplay
between quantum spin Hall and spin-transfer torque physics.


  We present observations made with the newly commissioned Keck laser-guide
star adaptive optics system of 6 objects in M31 that are alleged in multiple
recent studies to be young globular clusters (GCs); all are supposed to have
ages less than 5 Gyr. The resulting FWHM of the PSF core in our images is ~70
mas. The four youngest of these objects are asterisms; they are with certainty
not young GCs in M31. Based on their morphology, the two oldest are GCs in M31.
While the M31 GCs with ages 5 -- 8 Gyr appear to be mostly genuine, it appears
that many of the alleged very young GCs in M31 are spurious identifications.
This problem will be even more severe in studies of the GC systems of more
distant spiral galaxies now underway, for which imaging at the spatial
resolution of our observations in M31 may not be adequate to detect sample
contamination by asterisms.


  The hybrid architecture of convolution neural networks (CNN) and Transformer
has been the most popular method for medical image segmentation. However, the
existing networks based on the hybrid architecture suffer from two problems.
First, although the CNN branch can capture image local features by using
convolution operation, the vanilla convolution is unable to achieve adaptive
extraction of image features. Second, although the Transformer branch can model
the global information of images, the conventional self-attention only focuses
on the spatial self-attention of images and ignores the channel and
cross-dimensional self-attention leading to low segmentation accuracy for
medical images with complex backgrounds. To solve these problems, we propose
vision Transformer embrace convolutional neural networks for medical image
segmentation (TEC-Net). Our network has two advantages. First, dynamic
deformable convolution (DDConv) is designed in the CNN branch, which not only
overcomes the difficulty of adaptive feature extraction using fixed-size
convolution kernels, but also solves the defect that different inputs share the
same convolution kernel parameters, effectively improving the feature
expression ability of CNN branch. Second, in the Transformer branch, a
(shifted)-window adaptive complementary attention module ((S)W-ACAM) and
compact convolutional projection are designed to enable the network to fully
learn the cross-dimensional long-range dependency of medical images with few
parameters and calculations. Experimental results show that the proposed
TEC-Net provides better medical image segmentation results than SOTA methods
including CNN and Transformer networks. In addition, our TEC-Net requires fewer
parameters and computational costs and does not rely on pre-training. The code
is publicly available at https://github.com/SR0920/TEC-Net.


  A class of one-dimensional Fokker-Plank equations having a common stationary
solution, which is a power function of the state of the process, was found. We
prove that these equations also have generalized self-similar solutions which
describe the temporary transition from one stationary state to another. The
study was motivated by problems arising in mathematical modeling of genome size
evolution.


  We show that all of the Sch\"{u}tzenberger complexes of an Adian inverse
semigroup are finite if the Sch\"{u}tzenberger complex of every positive word
is finite. This enables us to solve the word problem for certain classes of
Adian inverse semigroups (and hence for the corresponding Adian semigroups and
Adian groups).


  The precise nature of complex structural relaxation as well as an explanation
for the precipitous growth of relaxation time in cooling glass-forming liquids
are essential to the understanding of vitrification of liquids. The dramatic
increase of relaxation time is believed to be caused by the growth of one or
more correlation lengths, which has received much attention recently. Here, we
report a direct link between the growth of a specific local-geometrical-order
and an increase of dynamic-length-scale as the atomic dynamics in metallic
glass-forming liquids slow down. Although several types of local
geometrical-orders are present in these metallic liquids, the growth of
icosahedral ordering is found to be directly related to the increase of the
dynamic-length-scale. This finding suggests an intriguing scenario that the
transient icosahedral ordering could be the origin of the dynamic-length-scale
in metallic glass-forming liquids.


  We define and give explicit construction of the universal tree-graded space
with a given collection of pieces. We apply that to proving uniqueness of
asymptotic cones of relatively hyperbolic groups whose peripheral subgroups
have unique asymptotic cones. Modulo the Continuum Hypothesis, we show that if
an asymptotic cone of a geodesic metric space is homogeneous and has cut
points, then it is the universal tree-graded space with pieces - maximal
connected subsets without their own cut points. Thus it is completely
determined by its collection of pieces.


  Background: MicroRNAs, post-transcriptional repressors of gene expression,
play a pivotal role in gene regulatory networks. They are involved in core
cellular processes and their dysregulation is associated to a broad range of
human diseases. This paper focus on a minimal microRNA-mediated regulatory
circuit, in which a protein-coding gene (host gene) is targeted by a microRNA
located inside one of its introns. Results: Autoregulation via intronic
microRNAs is widespread in the human regulatory network, as confirmed by our
bioinformatic analysis, and can perform several regulatory tasks despite its
simple topology. Our analysis, based on analytical calculations and
simulations, indicates that this circuitry alters the dynamics of the host gene
expression, can induce complex responses implementing adaptation and Weber's
law, and efficiently filters fluctuations propagating from the upstream network
to the host gene. A fine-tuning of the circuit parameters can optimize each of
these functions. Interestingly, they are all related to gene expression
homeostasis, in agreement with the increasing evidence suggesting a role of
microRNA regulation in conferring robustness to biological processes. In
addition to model analysis, we present a list of bioinformatically predicted
candidate circuits in human for future experimental tests. Conclusions: The
results presented here suggest a potentially relevant functional role for
negative self-regulation via intronic microRNAs, in particular as a homeostatic
control mechanism of gene expression. Moreover, the map of circuit functions in
terms of experimentally measurable parameters, resulting from our analysis, can
be a useful guideline for possible applications in synthetic biology.


  We consider the class of dual-unitary quantum circuits in $1+1$ dimensions
and introduce a notion of ``solvable'' matrix product states (MPSs), defined by
a specific condition which allows us to tackle their time evolution
analytically. We provide a classification of the latter, showing that they
include certain MPSs of arbitrary bond dimension, and study analytically
different aspects of their dynamics. For these initial states, we show that
while any subsystem of size $\ell$ reaches infinite temperature after a time
$t\propto \ell$, irrespective of the presence of conserved quantities, the
light-cone of two-point correlation functions displays qualitatively different
features depending on the ergodicity of the quantum circuit, defined by the
behavior of infinite-temperature dynamical correlation functions. Furthermore,
we study the entanglement spreading from such solvable initial states,
providing a closed formula for the time evolution of the entanglement entropy
of a connected block. This generalizes recent results obtained in the context
of the self-dual kicked Ising model. By comparison, we also consider a family
of non-solvable initial mixed states depending on one real parameter $\beta$,
which, as $\beta$ is varied from zero to infinity, interpolate between the
infinite temperature density matrix and arbitrary initial pure product states.
We study analytically their dynamics for small values of $\beta$, and highlight
the differences from the case of solvable MPSs.


  We report the first-principles study on the H-intercalated Cr-based
superconductor KCr$_3$As$_3$H$_x$. Our results show a paramagnetic ground state
for KCr$_3$As$_3$H. The electronic structure consists of two
quasi-one-dimensional (Q1D) Fermi-surfaces and one 3D Fermi-surface which are
mainly contributed by Cr-d$_{z^2}$, d$_{x^2-y^2}$ and d$_{xy}$ orbitals. The
bare electron susceptibility shows a $\Gamma$-centered imaginary peak,
indicating possible ferromagnetic spin fluctuations. Upon moderate hole doping,
the system undergoes a Lifshitz transition, which may enhance the Q1D feature
of the system. The Bader charge analysis and electron localization functions
reveal a strong bonding nature of hydrogen in KCr$_3$As$_3$H, which results in
a nontrivial electron doping in KCr$_3$As$_3$H.


  We investigate the dynamics of high aspect ratio nanowires trapped axially in
a single gradient force optical tweezers. A power spectrum analysis of the
Brownian dynamics reveals a broad spectral resonance of the order of a kHz with
peak properties that are strongly dependent on the input trapping power.
Modelling of the dynamical equations of motion of the trapped nanowire that
incorporate non-conservative effects through asymmetric coupling between
translational and rotational degrees of freedom provides excellent agreement
with the experimental observations. An associated observation of persistent
cyclical motion around the equilibrium trapping position using winding analysis
provides further evidence for the influence of non-conservative forces.


  We discuss an alternative version of non- relativistic Newtonian mechanics in
terms of a real Hilbert space mathematical framework. It is demonstrated that
the physics of this scheme correspondent with the standard formulation.
Heisenberg-Schrodinger non-relativistic quantum mechanics is considered
adequate and complete. Since the suggested theory is dispersion free, linear
superposition principle is not violated but cannot affect results of
measurements due to spectral decomposition theorem for self-adjoint operators
(the collapse of wave function).


  We show that any interacting integrable model possesses a class of initial
states for which the leading corrections to ballistic transport are
subdiffusive rather than diffusive. These initial states are natural to realize
experimentally and include the domain wall initial condition that has been the
object of much recent scrutiny. Upon performing numerical matrix product state
simulations in the spin-$1/2$ XXZ chain, we find that such states can exhibit
subdiffusive $t^{1/3}$ scaling of fronts of spin, energy and entanglement
entropy across the entire range of anisotropies. This demonstrates that
Tracy-Widom scaling is not incompatible with model interactions, as was
previously believed.


  We present a construction of integrable quantum spin chains where local
spin-spin interactions are weighted by ``position''-dependent potential
containing abelian non-local spin dependance. This construction applies to the
previously defined three general quadratic reflection-type algebras:
respectively non-dynamical, semidynamical, fully dynamical.


  Ramsey's theorem for $n$-tuples and $k$-colors ($\mathsf{RT}^n_k$) asserts
that every k-coloring of $[\mathbb{N}]^n$ admits an infinite monochromatic
subset. We study the proof-theoretic strength of Ramsey's theorem for pairs and
two colors, namely, the set of its $\Pi^0_1$ consequences, and show that
$\mathsf{RT}^2_2$ is $\Pi^0_3$ conservative over $\mathsf{I}\Sigma^0_1$. This
strengthens the proof of Chong, Slaman and Yang that $\mathsf{RT}^2_2$ does not
imply $\mathsf{I}\Sigma^0_2$, and shows that $\mathsf{RT}^2_2$ is
finitistically reducible, in the sense of Simpson's partial realization of
Hilbert's Program. Moreover, we develop general tools to simplify the proofs of
$\Pi^0_3$-conservation theorems.


  Sequential rate-distortion (SRD) theory provides a framework for studying the
fundamental trade-off between data-rate and data-quality in real-time
communication systems. In this paper, we consider the SRD problem for
multi-dimensional time-varying Gauss-Markov processes under mean-square
distortion criteria. We first revisit the sensor-estimator separation
principle, which asserts that considered SRD problem is equivalent to a joint
sensor and estimator design problem in which data-rate of the sensor output is
minimized while the estimator's performance satisfies the distortion criteria.
We then show that the optimal joint design can be performed by semidefinite
programming. A semidefinite representation of the corresponding SRD function is
obtained. Implications of the obtained result in the context of zero-delay
source coding theory and applications to networked control theory are also
discussed.


  We consider the well motivated model of the (standard) supersymmetric F-term
hybrid inflation (FHI) which can be realized close to the grand unification
scale. The predicted scalar spectral index $n_s$ cannot be smaller than 0.98
and can exceed unity including corrections from minimal supergravity, if the
number of e-foldings corresponding to the pivot scale $k_*=0.002/{\rm Mpc}$ is
around 50. These results are marginally consistent with the fitting of the
Wilkinson microwave anisotropy probe data by the standard power-law
cosmological model with cold dark matter and a cosmological constant. However,
$n_s$ can be reduced by restricting the number of e-foldings that $k_*$
suffered during FHI. The additional e-foldings required for solving the horizon
and flatness problems can be generated by a subsequent stage of fast-roll
[slow-roll] modular inflation realized by a string modulus which does [does
not] acquire effective mass before the onset of modular inflation.


  Smartphones and other mobile devices are today pervasive across the globe. As
an interesting side effect of the surge in mobile communications, mobile
network operators can now easily collect a wealth of high-resolution data on
the habits of large user populations. The information extracted from mobile
network traffic data is very relevant in the context of population mapping: it
provides a tool for the automatic and live estimation of population densities,
overcoming the limitations of traditional data sources such as censuses and
surveys. In this paper, we propose a new approach to infer population densities
at urban scales, based on aggregated mobile network traffic metadata. Our
approach allows estimating both static and dynamic populations, achieves a
significant improvement in terms of accuracy with respect to state-of-the-art
solutions in the literature, and is validated on different city scenarios.


  Many distributed systems work on a common shared state; in such systems,
distributed agreement is necessary for consistency. With an increasing number
of servers, these systems become more susceptible to single-server failures,
increasing the relevance of fault-tolerance. Atomic broadcast enables
fault-tolerant distributed agreement, yet it is costly to solve. Most practical
algorithms entail linear work per broadcast message. AllConcur -- a leaderless
approach -- reduces the work, by connecting the servers via a sparse resilient
overlay network; yet, this resiliency entails redundancy, limiting the
reduction of work. In this paper, we propose AllConcur+, an atomic broadcast
algorithm that lifts this limitation: During intervals with no failures, it
achieves minimal work by using a redundancy-free overlay network. When failures
do occur, it automatically recovers by switching to a resilient overlay
network. In our performance evaluation of non-failure scenarios, AllConcur+
achieves comparable throughput to AllGather -- a non-fault-tolerant distributed
agreement algorithm -- and outperforms AllConcur, LCR and Libpaxos both in
terms of throughput and latency. Furthermore, our evaluation of failure
scenarios shows that AllConcur+'s expected performance is robust with regard to
occasional failures. Thus, for realistic use cases, leveraging redundancy-free
distributed agreement during intervals with no failures improves performance
significantly.


  Axially-stacked quantum dots (QDs) in nanowires (NWs) have important
applications in fabricating nanoscale quantum devices and lasers. Although
their performances are very sensitive to crystal quality and structures, there
is relatively little study on defect-free growth with Au-free mode and
structure optimisation for achiving high performances. Here, we report a
detailed study of the first self-catalyzed defect-free axially-stacked deep
NWQDs. High structural quality is maintained when 50 GaAs QDs are placed in a
single GaAsP NW. The QDs have very sharp interfaces (1.8~3.6 nm) and can be
closely stacked with very similar structural properties. They exhibit the
deepest carrier confinement (~90 meV) and largest exciton-biexciton splitting
(~11 meV) among non-nitride III-V NWQDs, and can maintain good optical
properties after being stored in ambient atmosphere for over 6 months due to
excellent stability. Our study sets a solid foundation to build
high-performance axially-stacked NWQD devices that are compatible with CMOS
technologies.


  We present a generic computational framework for the simulation of viral
capsid assembly which is quantitative and specific. Starting from PDB files
containing atomic coordinates, the algorithm builds a coarse grained
description of protein oligomers based on graph rigidity. These reduced protein
descriptions are used in an extended Gillespie algorithm to investigate the
stochastic kinetics of the assembly process. The association rates are obtained
from a diffusive Smoluchowski equation for rapid coagulation, modified to
account for water shielding and protein structure. The dissociation rates are
derived by interpreting the splitting of oligomers as a process of graph
partitioning akin to the escape from a multidimensional well. This modular
framework is quantitative yet computationally tractable, with a small number of
physically motivated parameters. The methodology is illustrated using two
different viruses which are shown to follow quantitatively different assembly
pathways. We also show how in this model the quasi-stationary kinetics of
assembly can be described as a Markovian cascading process in which only a few
intermediates and a small proportion of pathways are present. The observed
pathways and intermediates can be related a posteriori to structural and
energetic properties of the capsid oligomers.


  The Anthena Vortex Lattice (AVL) [1] program describes aerodynamic and
flight-dynamic analysis of rigid aircraft of arbitrary configuration and we use
it to analyse the stability modes of a Boeing 737-800 under various small
perturbations about trimmed equilibrium. We perturb the aircraft's free-stream
velocity, its banking angle, its mass (which can be considered in conditions
such as fuel dumping) and also analyse how it behaves at different heights
(different air densities). We then compute the time it takes the various
stability modes to return to equilibrium and show that this time obeys the
logistic growth model for the Dutch roll and Short period mode when the
velocity is perturbed and when varying the height above sea level of the
aircraft.


  The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a
Zimm-type model with crosslink statistics taken either from bond percolation or
Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of
the random connectivity on the dynamics of molecular clusters, the Zimm-type
model also accounts for hydrodynamic interactions on a preaveraged level. The
incoherent intermediate scattering function is computed in thermal equilibrium,
its critical behaviour near the sol-gel transition is analysed and related to
the scaling of cluster diffusion constants at the critical point. Second,
non-equilibrium dynamics is studied by looking at stress relaxation in a simple
shear flow. Anomalous stress relaxation and critical rheological properties are
derived. Some of the results contradict long-standing scaling arguments, which
are shown to be flawed by inconsistencies.


  Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in
which rare "scarred" eigenstates mediate weak ergodicity breaking. One open
question is to understand the most general setting in which these states arise.
In this work, we develop a generic construction that embeds a new class of
QMBS, rainbow scars, into the spectrum of an arbitrary Hamiltonian. Unlike
other examples of QMBS, rainbow scars display extensive bipartite entanglement
entropy while retaining a simple entanglement structure. Specifically, the
entanglement scaling is volume-law for a random bipartition, while scaling for
a fine-tuned bipartition is sub-extensive. When internal symmetries are
present, the construction leads to multiple, and even towers of rainbow scars
revealed through distinctive non-thermal dynamics. Remarkably, certain
symmetries can lead rainbow scars to arise in translation-invariant models. To
this end, we provide an experimental road map for realizing rainbow scar states
in a Rydberg-atom quantum simulator, leading to coherent oscillations distinct
from the strictly sub-volume-law QMBS previously realized in the same system.


  We investigate the properties of self-bound ultradilute Bose-Bose mixtures,
beyond the Lee-Huang-Yang description. Our approach is based on the
determination of the beyond mean-field corrections to the phonon modes of the
mixture in a self-consistent way and calculation of the associated equation of
state. The newly obtained ground state energies show excellent agreement with
recent quantum Monte Carlo calculations, providing a simple and accurate
description of the self-bound mixtures with contact type interaction. We
further show numerical results for the equilibrium properties of the finite
size droplet, by adjusting the Gross-Pitaevskii equation. Our analysis is
extended to the one-dimensional mixtures where an excellent agreement with
quantum Monte Carlo predictions is found for the equilibrium densities.
Finally, we discuss the effects of temperature on the stability of the liquid
phase.


  We show that the latest thermostatistical formalism based on the Havrda &
Charvat-Dar\'oczy-Tsallis entropy $S_q [ \rho ] = (q-1)^{-1}(1- tr (\rho^q))$
proposed by Tsallis, Mendes and Plastino is {\em equivalent} to the first one
proposed by Tsallis in 1988. Here, equivalent means: {\em the ``equilibrium''
state predicted by either formalism using $q$ leads to the same expectation
values for all observables as that predicted by the other formalism using
$1/q$''}. We also point out once again that the basic property of {\em
transitivity of equilibrium} (e.g., the $0^{th}$ Law of Thermodynamics) fails
in these formalisms.


  Chemical reaction networks (CRNs) formally model chemistry in a well-mixed
solution. CRNs are widely used to describe information processing occurring in
natural cellular regulatory networks, and with upcoming advances in synthetic
biology, CRNs are a promising programming language for the design of artificial
molecular control circuitry. Due to a formal equivalence between CRNs and a
model of distributed computing known as population protocols, results transfer
readily between the two models.
  We show that if a CRN respects finite density (at most O(n) additional
molecules can be produced from n initial molecules), then starting from any
dense initial configuration (all molecular species initially present have
initial count Omega(n), where n is the initial molecular count and volume),
then every producible species is produced in constant time with high
probability.
  This implies that no CRN obeying the stated constraints can function as a
timer, able to produce a molecule, but doing so only after a time that is an
unbounded function of the input size. This has consequences regarding an open
question of Angluin, Aspnes, and Eisenstat concerning the ability of population
protocols to perform fast, reliable leader election and to simulate arbitrary
algorithms from a uniform initial state.


  In this work we empirically measure the detection efficiency of Kepler
pipeline used to create the final Kepler Threshold Crossing Event (TCE; Twicken
et al. 2016) and planet candidate catalogs (Thompson et al. 2018), a necessary
ingredient for occurrence rate calculations using these lists. By injecting
simulated signals into the calibrated pixel data and processing those pixels
through the pipeline as normal, we quantify the detection probability of
signals as a function of their signal strength and orbital period. In addition
we investigate the dependence of the detection efficiency on parameters of the
target stars and their location in the Kepler field of view. We find that the
end-of-mission version of the Kepler pipeline returns to a high overall
detection efficiency, averaging a 90-95% rate of detection for strong signals
across a wide variety of parameter space. We find a weak dependence of the
detection efficiency on the number of transits contributing to the signal and
the orbital period of the signal, and a stronger dependence on the stellar
effective temperature and correlated noise properties. We also find a weak
dependence of the detection efficiency on the position within the field of
view. By restricting the Kepler stellar sample to stars with well-behaved
correlated noise properties, we can define a set of stars with high detection
efficiency for future occurrence rate calculations.


  We build upon previous work that used coherent states as a measurement of the
local phase space and extended the flux operator by adapting the Husimi
projection to produce a vector field called the Husimi map. In this article, we
extend its definition from continuous systems to lattices. This requires making
several adjustments to incorporate effects such as group velocity and multiple
bands. Several phenomena which uniquely occur in lattice systems, like
group-velocity warping and internal Bragg diffraction, are explained and
demonstrated using Husimi maps. We also show that scattering points between
bands and valleys can be identified in the divergence of the Husimi map.