  We relate the combinatorial definitions of the type $A_n$ and type $C_n$
Stanley symmetric functions, via a combinatorially defined "double Stanley
symmetric function," which gives the type $A$ case at $(\mathbf{x},\mathbf{0})$
and gives the type $C$ case at $(\mathbf{x},\mathbf{x})$. We induce a type $A$
bicrystal structure on the underlying combinatorial objects of this function
which has previously been done in the type $A$ and type $C$ cases. Next we
prove a few statements about the algebraic relationship of these three Stanley
symmetric functions. We conclude with some conjectures about what happens when
we generalize our constructions to type $C$.


  A crown with $k$ spikes is an edge-disjoint union of a cycle $C$ and a
matching $M$ of size $k$ such that each edge of $M$ has exactly one vertex in
common with $C$. We prove that if $G$ is an $(n,d,\lambda)$-graph with
$\lambda/d\le 0.001$ and $d$ is large enough, then $G$ contains a crown on $n$
vertices with $\lfloor n/2\rfloor$ spikes. As a consequence, such $G$ contains
a Hamilton cycle in its square $G^2$.


  The Muon Ionization Cooling Experiment (MICE) collaboration has developed the
MICE Analysis User Software (MAUS) to simulate and analyze experimental data.
It serves as the primary codebase for the experiment, providing for offline
batch simulation and reconstruction as well as online data quality checks. The
software provides both traditional particle-physics functionalities such as
track reconstruction and particle identification, and accelerator physics
functions, such as calculating transfer matrices and emittances. The code
design is object orientated, but has a top-level structure based on the
Map-Reduce model. This allows for parallelization to support live data
reconstruction during data-taking operations. MAUS allows users to develop in
either Python or C++ and provides APIs for both. Various software engineering
practices from industry are also used to ensure correct and maintainable code,
including style, unit and integration tests, continuous integration and load
testing, code reviews, and distributed version control. The software framework
and the simulation and reconstruction capabilities are described.


  We present results on disordered amorphous films which are expected to
undergo a field-tuned Superconductor-Insulator Transition.The addition of a
parallel ground plane in proximity to the film changes the character of the
transition.Although the screening effects expected from "dirty-boson" theories
are not evident,there is evidence that the ground plane couples a certain type
of dissipation into the system,causing a dissipation-induced phase
transition.The dissipation due to the phase transition couples similarly into
quantum phase transition systems such as superconductor-insulator transitions
and Josephson junction arrays.


  In this note, in the context of the AdS/CFT correspondence, the holographic
derivation of the Wilsonian effective action is proposed. Then, the exact RG
equation in the boundary theory is derived from the Wheeler-DeWitt equation of
the bulk, following the suggestion of
arXiv:hep-th/9912012,arXiv:hep-th/9912018, and arXiv:1010.1264. The
relationship between the exact RG and Stochastic Quantization is briefly
discussed.


  CONTEXT. The maximum size of the Galactic stellar disk is not yet known. Some
studies have suggested an abrupt drop-off of the stellar density of the disk at
Galactocentric distances $R\gtrsim 15$ kpc, which means that in practice no
disk stars or only very few of them should be found beyond this limit. However,
stars in the Milky Way plane are detected at larger distances. In addition to
the halo component, star counts have placed the end of the disk beyond 20 kpc,
although this has not been spectroscopically confirmed so far.
  AIMS. Here, we aim to spectroscopically confirm the presence of the disk
stars up to much larger distances.
  METHODS. With data from the LAMOST and SDSS-APOGEE spectroscopic surveys, we
statistically derived the maximum distance at which the metallicity
distribution of stars in the Galactic plane is distinct from that of the halo
populations.
  RESULTS. Our analysis reveals the presence of disk stars at R>26 kpc (99.7%
C.L.) and even at R>31 kpc (95.4% C.L.).


  Feature selection is one of the most fundamental problems in machine
learning. An extensive body of work on information-theoretic feature selection
exists which is based on maximizing mutual information between subsets of
features and class labels. Practical methods are forced to rely on
approximations due to the difficulty of estimating mutual information. We
demonstrate that approximations made by existing methods are based on
unrealistic assumptions. We formulate a more flexible and general class of
assumptions based on variational distributions and use them to tractably
generate lower bounds for mutual information. These bounds define a novel
information-theoretic framework for feature selection, which we prove to be
optimal under tree graphical models with proper choice of variational
distributions. Our experiments demonstrate that the proposed method strongly
outperforms existing information-theoretic feature selection approaches.


  In dense molecular clouds, interstellar grains are covered by mantles of iced
molecules. The formation of the grain mantles has two important consequences:
it removes species from the gas phase and promotes the synthesis of new
molecules on the grain surfaces. The composition of the mantle is a strong
function of the environment which the cloud belongs to. Therefore, clouds in
high-zeta galaxies, where conditions -like temperature, metallicity and cosmic
rays flux- are different from those in the Milky Way, will have different grain
mantles. In the last years, several authors have suggested that silicate grains
might grow by accretion of silicon bearing species on smaller seeds. This would
occur simultaneously to the formation of the iced mantles and be greatly
affected by its composition as a function of time. In this work, we present a
numerical study of the grain mantle formation in high-zeta galaxies and we
quantitatively address the possibility of silicate growth. We find that the
mantle thickness decreases with increasing redshift, from about 120 to 20
layers for z varying from 0 to 8. Furthermore, the mantle composition is also a
strong function of the cloud redshift, with the relative importance of CO, CO2,
ammonia, methane and methanol highly varying with z. Finally, being Si-bearing
species always a very minor component of the mantle, the formation of silicates
in molecular clouds is practically impossible.


  Conventional autonomous Unmanned Air Vehicle (abbr. UAV) autopilot systems
use Global Navigation Satellite System (abbr. GNSS) signal for navigation.
However, autopilot systems fail to navigate due to lost or jammed GNSS signal.
To solve this problem, information from other sensors such as optical sensors
are used. Monocular Simultaneous Localization and Mapping algorithms have been
developed over the last few years and achieved state-of-the-art accuracy. Also,
map matching localization approaches are used for UAV localization relatively
to imagery from static maps such as Google Maps. Unfortunately, the accuracy
and robustness of these algorithms are very dependent on up-to-date maps. The
purpose of this research is to improve the accuracy and robustness of map
relative Particle Filter based localization using a downward-facing optical
camera mounted on an autonomous aircraft. This research shows how image
similarity to likelihood conversion function impacts the results of Particle
Filter localization algorithm. Two parametric image similarity to likelihood
conversion functions (logistic and rectifying) are proposed. A dataset of
simulated aerial imagery is used for experiments. The experiment results are
shown, that the Particle Filter localization algorithm using the logistic
function was able to surpass the accuracy of state-of-the-art ORB-SLAM2
algorithm by 2.6 times. The algorithm is shown to be able to navigate using
up-to-date maps more accurately and with an average decrease of precision by
30% using out-of-date maps.


  We propose a particularly structured Boltzmann machine, which we refer to as
a dynamic Boltzmann machine (DyBM), as a stochastic model of a
multi-dimensional time-series. The DyBM can have infinitely many layers of
units but allows exact and efficient inference and learning when its parameters
have a proposed structure. This proposed structure is motivated by postulates
and observations, from biological neural networks, that the synaptic weight is
strengthened or weakened, depending on the timing of spikes (i.e., spike-timing
dependent plasticity or STDP). We show that the learning rule of updating the
parameters of the DyBM in the direction of maximizing the likelihood of given
time-series can be interpreted as STDP with long term potentiation and long
term depression. The learning rule has a guarantee of convergence and can be
performed in a distributed matter (i.e., local in space) with limited memory
(i.e., local in time).


  A sub-population of energetic rotation-powered pulsars show high fluxes of
pulsed non-thermal hard X-ray emission. While this MeV pulsar population
includes some radio-loud pulsars like the Crab, a significant number have no
detected radio or GeV emission, a mystery since gamma- ray emission is a common
characteristic of pulsars with high spin-down power. Their steeply rising hard
X-ray spectral energy distributions (SEDs) suggest peaks at 0.1 - 1 MeV but
they have not been detected above 200 keV. Several upcoming and planned
telescopes may shed light on the MeV pulsars. The Neutron star Interior
Composition ExploreR (NICER) will observe pulsars in the 0.2 - 12 keV band and
may discover additional MeV pulsars. Planned telescopes, such as All-Sky
Medium-Energy Gamma-Ray Observatory (AMEGO) and e-ASTROGAM, will detect
emission above 0.2 MeV and polarization in the 0.2 - 10 MeV band. We present a
model for the spectrum and polarization of MeV pulsars where the X-ray emission
comes from electron- positron pairs radiating in the outer magnetosphere and
current sheet. This model predicts that the peak of the SED increases with
surface magnetic field strength if the pairs are produced in polar cap
cascades. For small inclination angles, a range of viewing angles can miss both
the radio pulse and the GeV pulse from particles accelerating near the current
sheet. Characterizing the emission and geometry of MeV pulsars can thus provide
clues to the source of pairs and acceleration in the magnetosphere.


  We propose a theory of two-magnon {\it resonant\/} Raman scattering from
antiferromagnetic insulators, which contains information both on the magnetism
and the carrier properties in the lighly doped phases. We argue that the
conventional theory does not work in the resonant regime, in which the energy
of the incident photon is close to the gap between the conduction and valence
bands. We identify the diagram which gives the dominant contribution to Raman
intensity in this regime and show that it can explain the unusual features in
the two-magnon profile and in the two-magnon peak intensity dependence on the
incoming photon frequency.


  We introduce a new numerical method for the time-dependent Maxwell equations
on unstructured meshes in two space dimensions. This relies on the introduction
of a new mesh, which is the barycentric-dual cellular complex of the starting
simplicial mesh, and on approximating two unknown fields with integral
quantities on geometric entities of the two dual complexes. A careful choice of
basis-functions yields cheaply invertible block-diagonal system matrices for
the discrete time-stepping scheme. The main novelty of the present contribution
lies in incorporating arbitrary polynomial degree in the approximating
functional spaces, defined through a new reference cell. The presented method,
albeit a kind of Discontinuous Galerkin approach, requires neither the
introduction of user-tuned penalty parameters for the tangential jump of the
fields, nor numerical dissipation to achieve stability. In fact an exact
electromagnetic energy conservation law for the semi-discrete scheme is proved
and it is shown on several numerical tests that the resulting algorithm
provides spurious-free solutions with the expected order of convergence.


  The non-classical nature of quantum states, often illustrated using
entanglement measures or quantum discord, constitutes a resource for quantum
information protocols. However, the non-classicality of a quantum system cannot
be encapsulated as a property of the state alone, as the set of available
measurements used to extract information on the system is typically restricted.
In this work we study how the non-classicality of quantum measurements,
quantified via their incompatibility, is influenced by quantum noise and,
further, how a non-Markovian environment may help us in maintaining the
measurement resources.


  In this note we prove the analogue of the Atiyah-Segal completion theorem for
equivariant twisted K-theory in the setting of an arbitrary compact Lie group G
and an arbitrary twisting of the usually considered type. The theorem
generalizes a result by C. Dwyer, who has proven the theorem for finite G and
twistings of a more restricted type. While versions of the general result have
been known to experts, to our knowledge no proof appears in the current
literature. Our goal is to fill in this gap. The proof we give proceeds in two
stages. We first prove the theorem in the case of a twisting arising from a
graded central extension of G, following the Adams-Haeberly-Jackowski-May proof
of the classical Atiyah-Segal completion theorem. After establishing that the
theorem holds for this special class of twistings, we then deduce the general
theorem by a Mayer-Vietoris argument.


  We present an alternative organizational scheme for developing effective
theories of 2- and 3-body systems that is systematic, accurate, and efficient
with controlled errors. To illustrate our approach we consider the bound state
and scattering properties of the 2- and 3-nucleon systems. Our approach
combines the computational benefits of using separable potentials with the
improved convergence properties of potentials evolved with a renormalization
group procedure. Long ago Harms showed that any potential can be expanded in a
series of separable terms, but this fact is only useful if the expansion can be
truncated at low order. The separable expansion provides an attractive
organizational scheme that incorporates the two body bound state in the leading
term while allowing for systematic corrections thereafter. We show that when
applied to a renormalization group-evolved potential, the separable expansion
converges rapidly, with accurate results for both 2- and 3-body scattering
processes using only two separable terms.


  While a randomized control trial is considered the gold standard for
estimating causal treatment effects, there are many research settings in which
randomization is infeasible or unethical. In such cases, researchers rely on
analytical methods for observational data to explore causal relationships.
Difference-in-differences (DID) is one such method that, most commonly,
estimates a difference in some mean outcome in a group before and after the
implementation of an intervention or policy and compares this with a control
group followed over the same time (i.e., a group that did not implement the
intervention or policy). Although DID modeling approaches have been gaining
popularity in public health research, the majority of these approaches and
their extensions are developed and shared within the economics literature.
While extensions of DID modeling approaches may be straightforward to apply to
observational data in any field, the complexities and assumptions involved in
newer approaches are often misunderstood. In this paper, we focus on recent
extensions of the DID method and their relationships to linear models in the
setting of staggered treatment adoption over multiple years. We detail the
identification and estimation of the average treatment effect among the treated
using potential outcomes notation, highlighting the assumptions necessary to
produce valid estimates. These concepts are described within the context of
Medicaid expansion and retention in care among people living with HIV (PWH) in
the United States. While each DID approach is potentially valid, understanding
their different assumptions and choosing an appropriate method can have
important implications for policy-makers, funders, and public health as a
whole.


  The optical afterglow spectrum of GRB050401 (at z=2.8992+/-0.0004) shows the
presence of a DLA, with log(nHI)=22.6+/-0.3. This is the highest column density
ever observed in a DLA, and is about five times larger than the strongest DLA
detected so far in any QSO spectrum. From the optical spectrum, we also find a
very large Zn column density, allowing us to infer an abundance of
[Zn/H]=-1.0+/-0.4. These large columns are supported by the X-ray spectrum from
Swift-XRT which shows a column density (in excess of Galactic) of
log(nH)=22.21^{+0.06}_{-0.08} assuming solar abundances (at z=2.9). The
comparison of this X-ray column density, which is dominated by absorption due
to alpha-chain elements, and the HI column density derived from the Ly-alpha
absorption line, allows us to derive a metallicity for the absorbing matter of
[alpha/H]=-0.4+/-0.3. The optical spectrum is reddened and can be well
reproduced with a power-law with SMC extinction, where A_V=0.62+/-0.06. But the
total optical extinction can also be constrained in a way which is independent
of the shape of the extinction curve: from the optical-to-X-ray spectral energy
distribution we find, 0.5<~A_V<~4.5. However, even this upper limit,
independent of the shape of the extinction curve, is still well below the dust
column that is inferred from the X-ray column density, i.e.
A_V=9.1^{+1.4}_{-1.5}. This discrepancy might be explained by a small dust
content with high metallicity (low dust-to-metals ratio). `Grey' extinction
cannot explain the discrepancy since we are comparing the metallicity to a
measurement of the total extinction (without reference to the reddening).
Little dust with high metallicity may be produced by sublimation of dust grains
or may naturally exist in systems younger than a few hundred Myr.


  We consider the uplift of co-dimension two defect solutions of seven
dimensional gauged supergravity to eleven dimensions, previously found by two
of the authors. The uplifted solutions are expressed as Lin-Lunin-Maldacena
solutions and an infinite family of regular solutions describing holographic
defects is found using the electrostatic formulation of LLM solutions.


  Graph Neural Networks (GNNs) have greatly advanced the semi-supervised node
classification task on graphs. The majority of existing GNNs are trained in an
end-to-end manner that can be viewed as tackling a bi-level optimization
problem. This process is often inefficient in computation and memory usage. In
this work, we propose a new optimization framework for semi-supervised learning
on graphs. The proposed framework can be conveniently solved by the alternating
optimization algorithms, resulting in significantly improved efficiency.
Extensive experiments demonstrate that the proposed method can achieve
comparable or better performance with state-of-the-art baselines while it has
significantly better computation and memory efficiency.


  In a recent survey paper we introduced one-sided multipliers between two
different operator spaces. Here we give some basic theory for these maps.


  Various topics in and around Goldstone Boson Production and Decay in CHPT are
discussed, in particular I describe some of the progress in $p^6$ Chiral
Perturbation Theory Calculations, the progress in calculating hadronic
contributions to the muon anomalous magnetic moment, here comparing the two
latest results of the light-by-light in some detail. I also present some
progress in various $\eta$ and $K$ decays and their relevance for CHPT.


  Computer aided diagnosis (CAD) systems are designed to assist clinicians in
various tasks, including highlighting abnormal regions in a medical image. A
common approach consists in training a voxel-level binary classifier on a set
of feature vectors extracted from normal and pathological areas in patients'
scans. However, many pathologies (such as epilepsy) are characterized by
lesions that may be located anywhere in the brain, have various shapes, sizes
and texture. An adequate representation of such a heterogeneity requires a
significant amount of annotated data which is a major issue in the medical
domain. Therefore, we built on a previously proposed approach that considers
epilepsy lesion detection task as a voxel-level outlier detection problem. It
consists in building a oc-SVM classifier for each voxel in the brain volume
using a small number of clinically-guided features El Azami et al., 2016. Our
goal in this study is to make a step forward by replacing the handcrafted
features with automatically learnt representations using neural networks. We
propose a novel version of siamese networks trained on patches extracted from
healthy patients' scans only. This network, composed of stacked autoencoders as
subnetworks, is regularized by the reconstruction error of the patches. It is
designed to learn representations that bring patches centered at the same voxel
localization 'closer' with respect to the chosen metric (i.e. cosine). Finally,
the middle layer representations of the subnetworks are fed to oc-SVM
classifiers at voxel-level. The method is validated on 3 patients' MRI scans
with confirmed epilepsy lesions and shows a promising performance.


  The achievement of Bose-Einstein condensation of photons (phBEC) in a
dye-filled microcavity has led to a renewed interest in the density
distribution of the ideal Bose gas in a two-dimensional harmonic oscillator. We
present measurements of the radial profile of photons inside the microcavity
below and above the critical point for phBEC with a good signal-to-noise ratio.
We obtain a good agreement with theoretical profiles obtained using exact
summation of eigenstates.


  Weak convergence of the empirical copula process indexed by a class of
functions is established. Two scenarios are considered in which either some
smoothness of these functions or smoothness of the underlying copula function
is required.
  A novel integration by parts formula for multivariate, right continuous
functions of bounded variation, which is perhaps of independent interest, is
proved. It is a key ingredient in proving weak convergence of a general
empirical process indexed by functions of bounded variation.


  We study how the interplay between the memory immune response and pathogen
mutation affects epidemic dynamics in two related models. The first explicitly
models pathogen mutation and individual memory immune responses, with contacted
individuals becoming infected only if they are exposed to strains that are
significantly different from other strains in their memory repertoire. The
second model is a reduction of the first to a system of difference equations.
In this case, individuals spend a fixed amount of time in a generalized immune
class. In both models, we observe four fundamentally different types of
behavior, depending on parameters: (1) pathogen extinction due to lack of
contact between individuals, (2) endemic infection (3) periodic epidemic
outbreaks, and (4) one or more outbreaks followed by extinction of the epidemic
due to extremely low minima in the oscillations. We analyze both models to
determine the location of each transition. Our main result is that pathogens in
highly connected populations must mutate rapidly in order to remain viable.


  In 1978, W. Thurston revolutionized low diemsional topology with his work on
hyperbolic 3-manifolds. In this paper, we discuss what is currently known about
knots in the 3-sphere with hyperbolic complements. Then focus is on geometric
invariants coming out of the hyperbolic structures. This is one of a collection
of articles to appear in the Handbook of Knot Theory.


  This paper reviews the recent literature on solving the Boolean
satisfiability problem (SAT), an archetypal NP-complete problem, with the help
of machine learning techniques. Despite the great success of modern SAT solvers
to solve large industrial instances, the design of handcrafted heuristics is
time-consuming and empirical. Under the circumstances, the flexible and
expressive machine learning methods provide a proper alternative to solve this
long-standing problem. We examine the evolving ML-SAT solvers from naive
classifiers with handcrafted features to the emerging end-to-end SAT solvers
such as NeuroSAT, as well as recent progress on combinations of existing CDCL
and local search solvers with machine learning methods. Overall, solving SAT
with machine learning is a promising yet challenging research topic. We
conclude the limitations of current works and suggest possible future
directions.


  We investigate the effects of acceleration during non-linear electron-beam
relaxation in magnetized plasma in the case of electron transport in solar
flares. The evolution of electron distribution functions is computed using a
three-dimensional particle-in-cell electromagnetic code. Analytical estimations
under simplified assumptions are made to provide comparisons. We show that,
during the non-linear evolution of the beam-plasma system, the accelerated
electron population appears. We found that, although the electron beam loses
its energy efficiently to the thermal plasma, a noticeable part of the electron
population is accelerated. For model cases with initially monoenergetic beams
in uniform plasma, we found that the amount of energy in the accelerated
electrons above the injected beam-electron energy varies depending the plasma
conditions and could be around 10-30% of the initial beam energy. This type of
acceleration could be important for the interpretation of non-thermal electron
populations in solar flares. Its neglect could lead to the over-estimation of
accelerated electron numbers. The results emphasize that collective plasma
effects should not be treated simply as an additional energy-loss mechanism,
when hard X-ray emission in solar flares is interpreted, notably in the case of
RHESSI data.


  Half-life number sequences collected from nuclear data charts are found to
obey the Newcomb-Benford law. Based on this fact, it has been suggested
recently, that this law should be used to test the quality of nuclear decay
models. In this paper we briefly recall how, when and why the Newcomb-Benford
law can be observed in a set of numbers with a given probability distribution.
We investigate the special case of nuclear half-lives, and show that the law
provides no additional clue in understanding decay half-lives. Thus, it can
play no significant role in testing nuclear decay theories.


  The frog model is a branching random walk on a graph in which particles
branch only at unvisited sites. Consider an initial particle density of $\mu$
on the full $d$-ary tree of height $n$. If $\mu= \Omega( d^2)$, all of the
vertices are visited in time $\Theta(n\log n)$ with high probability.
Conversely, if $\mu = O(d)$ the cover time is $\exp(\Theta(\sqrt n))$ with high
probability.


  Traveling waves are analyzed in a model of the Hantavirus infection of deer
mice. The existence of two kinds of wave phenomena is predicted. An
environmental parameter governs a transition between two regimes of
propagation. In one of them the front of infection lags behind at a constant
rate. In the other, fronts of susceptible and infected mice travel at the same
speed, separated by a constant delay. The dependence of the delay on system
parameters is analyzed numerically and through a piecewise linearization.


  Binary function similarity detection plays an important role in a wide range
of security applications. Existing works usually assume that the query function
and target function share equal semantics and compare their full semantics to
obtain the similarity. However, we find that the function mapping is more
complex, especially when function inlining happens.
  In this paper, we will systematically investigate cross-inlining binary
function similarity detection. We first construct a cross-inlining dataset by
compiling 51 projects using 9 compilers, with 4 optimizations, to 6
architectures, with 2 inlining flags, which results in two datasets both with
216 combinations. Then we construct the cross-inlining function mappings by
linking the common source functions in these two datasets. Through analysis of
this dataset, we find that three cross-inlining patterns widely exist while
existing work suffers when detecting cross-inlining binary function similarity.
Next, we propose a pattern-based model named CI-Detector for cross-inlining
matching. CI-Detector uses the attributed CFG to represent the semantics of
binary functions and GNN to embed binary functions into vectors. CI-Detector
respectively trains a model for these three cross-inlining patterns. Finally,
the testing pairs are input to these three models and all the produced
similarities are aggregated to produce the final similarity. We conduct several
experiments to evaluate CI-Detector. Results show that CI-Detector can detect
cross-inlining pairs with a precision of 81% and a recall of 97%, which exceeds
all state-of-the-art works.


  We perform a high-statistics precision calculation of nucleon matrix elements
using an open sink method allowing us to explore a wide range of sink-source
time separations. In this way the influence of excited states of nucleon matrix
elements can be studied. As particular examples we present results for the
nucleon axial charge $g_A$ and for the first moment of the isovector
unpolarized parton distribution $<x>_{u-d}$. In addition, we report on
preliminary results using the generalized eigenvalue method for nucleon matrix
elements. All calculations are performed using $N_f=2+1+1$ maximally twisted
mass Wilson fermions.


  Robots are widely deployed in space environments because of their versatility
and robustness. However, adverse gravity conditions and challenging terrain
geometry expose the limitations of traditional robot designs, which are often
forced to sacrifice one of mobility or manipulation capabilities to attain the
other. Prospective climbing operations in these environments reveals a need for
small, compact robots capable of versatile mobility and manipulation. We
propose a novel robotic concept called ReachBot that fills this need by
combining two existing technologies: extendable booms and mobile manipulation.
ReachBot leverages the reach and tensile strength of extendable booms to
achieve an outsized reachable workspace and wrench capability. Through their
lightweight, compactable structure, these booms also reduce mass and complexity
compared to traditional rigid-link articulated-arm designs. Using these
advantages, ReachBot excels in mobile manipulation missions in low gravity or
that require climbing, particularly when anchor points are sparse. After
introducing the ReachBot concept, we discuss modeling approaches and strategies
for increasing stability and robustness. We then develop a 2D analytical model
for ReachBot's dynamics inspired by grasp models for dexterous manipulators.
Next, we introduce a waypoint-tracking controller for a planar ReachBot in
microgravity. Our simulation results demonstrate the controller's robustness to
disturbances and modeling error. Finally, we briefly discuss next steps that
build on these initially promising results to realize the full potential of
ReachBot.


  We show that if $\mathfrak{g}$ is a Frobenius seaweed, then the spectrum of
the adjoint of a principal element consists of an unbroken set of integers
whose multiplicities have a symmetric distribution. Our methods are
combinatorial.


  We investigate the influence of a temperature-dependent shear viscosity over
entropy density ratio eta/s on the transverse momentum spectra and elliptic
flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the
elliptic flow in sqrt(s_NN) = 200 GeV Au+Au collisions at RHIC is dominated by
the viscosity in the hadronic phase and in the phase transition region, but
largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the
highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity
and insensitive to the hadronic viscosity.


  Data augmentation is widely used as a part of the training process applied to
deep learning models, especially in the computer vision domain. Currently,
common data augmentation techniques are designed manually. Therefore they
require expert knowledge and time. Moreover, augmentations are
dataset-specific, and the optimal augmentations set on a specific dataset has
limited transferability to others. We present a simple and explainable method
called $\textbf{Safe Augmentation}$ that can learn task-specific data
augmentation techniques that do not change the data distribution and improve
the generalization of the model. We propose to use safe augmentation in two
ways: for model fine-tuning and along with other augmentation techniques. Our
method is model-agnostic, easy to implement, and achieves better accuracy on
CIFAR-10, CIFAR-100, SVHN, Tiny ImageNet, and Cityscapes datasets comparing to
baseline augmentation techniques. The code is available at
$\href{https://github.com/Irynei/SafeAugmentation}{https://github.com/Irynei/SafeAugmentation}$.


  We exploit the near-horizon conformal symmetry of rapidly spinning black
holes to determine universal properties of their magnetospheres. Analytic
expressions are derived for the limiting form of the magnetosphere in the
near-horizon region. The symmetry is shown to imply that the black hole
Meissner effect holds for free Maxwell fields but is generically violated for
force-free fields. We further show that in the extremal limit, near-horizon
plasma particles are infinitely boosted relative to accretion flow. Active
galactic nuclei powered by rapidly spinning black holes are therefore natural
sites for high-energy particle collisions.


  Cardiovascular diseases, including Heart Failure (HF), remain a leading
global cause of mortality, often evading early detection. In this context,
accessible and effective risk assessment is indispensable. Traditional
approaches rely on resource-intensive diagnostic tests, typically administered
after the onset of symptoms. The widespread availability of electrocardiogram
(ECG) technology and the power of Machine Learning are emerging as viable
alternatives within smart healthcare. In this paper, we propose several
multi-modal approaches that combine 30-second ECG recordings and approximate
long-term Heart Rate Variability (HRV) data to estimate the risk of HF
hospitalization. We introduce two survival models: an XGBoost model with
Accelerated Failure Time (AFT) incorporating comprehensive ECG features and a
ResNet model that learns from the raw ECG. We extend these with our novel
long-term HRVs extracted from the combination of ultra-short-term beat-to-beat
measurements taken over the day. To capture their temporal dynamics, we propose
a survival model comprising ResNet and Transformer architectures (TFM-ResNet).
Our experiments demonstrate high model performance for HF risk assessment with
a concordance index of 0.8537 compared to 14 survival models and competitive
discrimination power on various external ECG datasets. After transferability
tests with Apple Watch data, our approach implemented in the myHeartScore App
offers cost-effective and highly accessible HF risk assessment, contributing to
its prevention and management.


  We discuss interfaces in spin glasses. We present new theoretical results and
a numerical method to characterize overlap interfaces and the stability of the
spin-glass phase in extended disordered systems. We use this definition to
characterize the low temperature phase of hierarchical spin-glass models. We
use the Replica Symmetry Breaking theory to evaluate the cost for an overlap
interface, which in these models is particularly simple. A comparison of our
results from numerical simulations with the theoretical predictions shows good
agreement.


  Language model based methods are powerful techniques for text classification.
However, the models have several shortcomings. (1) It is difficult to integrate
human knowledge such as keywords. (2) It needs a lot of resources to train the
models. (3) It relied on large text data to pretrain. In this paper, we propose
Semi-Supervised vMF Neural Topic Modeling (S2vNTM) to overcome these
difficulties. S2vNTM takes a few seed keywords as input for topics. S2vNTM
leverages the pattern of keywords to identify potential topics, as well as
optimize the quality of topics' keywords sets. Across a variety of datasets,
S2vNTM outperforms existing semi-supervised topic modeling methods in
classification accuracy with limited keywords provided. S2vNTM is at least
twice as fast as baselines.


  Standard proofs of Lusin's theorem, using simple functions, are sometimes
quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do
not believe our approach, by way of inverse images, is new. However, this
particular proof is strikingly clear and succinct.


  As the take-up of Long Term Evolution (LTE)/4G cellular accelerates, there is
increasing interest in technologies that will define the next generation (5G)
telecommunication standard. This paper identifies several emerging technologies
which will change and define the future generations of telecommunication
standards. Some of these technologies are already making their way into
standards such as 3GPP LTE, while others are still in development.
Additionally, we will look at some of the research problems that these new
technologies pose.


  The strong symmetric genus of a finite group G is the smallest genus of a
closed orientable topological surface on which G acts faithfully as a group of
orientation preserving automorphisms. In this paper we complete the calculation
of the strong symmetric genus for each finite Coxeter group excluding the group
E8.


  We investigate whether arbitrarily small perturbations in global AdS space
are generically unstable and collapse into black holes on the time scale set by
gravitational interactions. We argue that current evidence, combined with our
analysis, strongly suggests that a set of nonzero measure in the space of
initial conditions does not collapse on this time scale. We perform an analysis
in position space to study this puzzle, and our formalism allows us to directly
study the vanishing-amplitude limit. We show that gravitational
self-interaction leads to tidal deformations which are equally likely to focus
or defocus energy, and we sketch the phase diagram accordingly. We also clarify
the connection between gravitational evolution in global AdS and holographic
thermalization.


  We investigate atomic Fermi-Bose mixtures in inhomogeneous and random optical
lattices in the limit of strong atom-atom interactions. We derive the effective
Hamiltonian describing the dynamics of the system and discuss its low
temperature physics. We demonstrate possibility of controlling the interactions
at local level in inhomogeneous but regular lattices. Such a control leads to
the achievement of Fermi glass, quantum Fermi spin glass, and quantum
percolation regimes involving bare and/or composite fermions in random
lattices.


  In this paper, we propose a deep-learning-based approach to a class of
multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM)
has been proven successful as a model reduction technique of flow problems in
heterogeneous and high-contrast porous media. The key ingredients of GMsFEM
include mutlsicale basis functions and coarse-scale parameters, which are
obtained from solving local problems in each coarse neighborhood. Given a fixed
medium, these quantities are precomputed by solving local problems in an
offline stage, and result in a reduced-order model. However, these quantities
have to be re-computed in case of varying media. The objective of our work is
to make use of deep learning techniques to mimic the nonlinear relation between
the permeability field and the GMsFEM discretizations, and use neural networks
to perform fast computation of GMsFEM ingredients repeatedly for a class of
media. We provide numerical experiments to investigate the predictive power of
neural networks and the usefulness of the resultant multiscale model in solving
channelized porous media flow problems.


  Many problems in high-dimensional statistics and optimization involve
minimization over nonconvex constraints-for instance, a rank constraint for a
matrix estimation problem-but little is known about the theoretical properties
of such optimization problems for a general nonconvex constraint set. In this
paper we study the interplay between the geometric properties of the constraint
set and the convergence behavior of gradient descent for minimization over this
set. We develop the notion of local concavity coefficients of the constraint
set, measuring the extent to which convexity is violated, which govern the
behavior of projected gradient descent over this set. We demonstrate the
versatility of these concavity coefficients by computing them for a range of
problems in low-rank estimation, sparse estimation, and other examples. Through
our understanding of the role of these geometric properties in optimization, we
then provide a convergence analysis when projections are calculated only
approximately, leading to a more efficient method for projected gradient
descent in low-rank estimation problems.


  In terms of log canonical threshold, we characterize plurisubharmonic
functions with logarithmic asymptotical behaviour.


  The capability of a reinforcement learning (RL) agent heavily depends on the
diversity of the learning scenarios generated by the environment. Generation of
diverse realistic scenarios is challenging for real-time strategy (RTS)
environments. The RTS environments are characterized by intelligent
entities/non-RL agents cooperating and competing with the RL agents with large
state and action spaces over a long period of time, resulting in an infinite
space of feasible, but not necessarily realistic, scenarios involving complex
interaction among different RL and non-RL agents. Yet, most of the existing
simulators rely on randomly generating the environments based on predefined
settings/layouts and offer limited flexibility and control over the environment
dynamics for researchers to generate diverse, realistic scenarios as per their
demand. To address this issue, for the first time, we formally introduce the
benefits of adopting an existing formal scenario specification language,
SCENIC, to assist researchers to model and generate diverse scenarios in an RTS
environment in a flexible, systematic, and programmatic manner. To showcase the
benefits, we interfaced SCENIC to an existing RTS environment Google Research
Football(GRF) simulator and introduced a benchmark consisting of 32 realistic
scenarios, encoded in SCENIC, to train RL agents and testing their
generalization capabilities. We also show how researchers/RL practitioners can
incorporate their domain knowledge to expedite the training process by
intuitively modeling stochastic programmatic policies with SCENIC.


  Predicting the morphodynamics of sedimentary landscapes due to fluvial and
aeolian flows requires answering the following questions: Is the flow strong
enough to initiate sediment transport, is the flow strong enough to sustain
sediment transport once initiated, and how much sediment is transported by the
flow in the saturated state (i.e., what is the transport capacity)? In the
geomorphological and related literature, the widespread consensus has been that
the initiation, cessation, and capacity of fluvial transport, and the
initiation of aeolian transport, are controlled by fluid entrainment of bed
sediment caused by flow forces overcoming local resisting forces, whereas
aeolian transport cessation and capacity are controlled by impact entrainment
caused by the impacts of transported particles with the bed. Here the physics
of sediment transport initiation, cessation, and capacity is reviewed with
emphasis on recent consensus-challenging developments in sediment transport
experiments, two-phase flow modeling, and the incorporation of granular
physics' concepts. Highlighted are the similarities between dense granular
flows and sediment transport, such as a superslow granular motion known as
creeping (which occurs for arbitrarily weak driving flows) and system-spanning
force networks that resist bed sediment entrainment; the roles of the magnitude
and duration of turbulent fluctuation events in fluid entrainment; the
traditionally overlooked role of particle-bed impacts in triggering entrainment
events in fluvial transport; and the common physical underpinning of transport
thresholds across aeolian and fluvial environments. This sheds a new light on
the well-known Shields diagram, where measurements of fluid entrainment
thresholds could actually correspond to entrainment-independent cessation
thresholds.


  It is pointed out that the higher-order symmetries of the Camassa-Holm (CH)
equation are nonlocal and nonlocality poses problems to obtain higher-order
conserved densities for this integrable equation (J. Phys. A: Math. Gen. 2005,
{\bf 38} 869-880). This difficulty is circumvented by defining a nolinear
hierarchy for the CH equation and an explicit expression is constructed for the
nth-order conserved density.


  For a given zero mean curvature surface $X$ (in the Lorentz Minkowski space)
having folded singularity, we construct a family of maxface and minface, having
increasing cuspidal crosscaps, converging to $X$. We include a general
discussion of this.


  Quantum simulation on NISQ devices is severely limited by short coherence
times. A variational pulse-shaping algorithm known as ctrl-VQE was recently
proposed to address this issue by eliminating the need for parameterized
quantum circuits, which lead to long state preparation times. Here, we find the
shortest possible pulses for ctrl-VQE to prepare target molecular wavefunctions
for a given device Hamiltonian describing coupled transmon qubits. We find that
the time-optimal pulses that do this have a bang-bang form consistent with
Pontryagin's maximum principle. We further investigate how the minimal state
preparation time is impacted by truncating the transmons to two versus more
levels. We find that leakage outside the computational subspace (something that
is usually considered problematic) speeds up the state preparation, further
reducing device coherence-time demands. This speedup is due to an enlarged
solution space of target wavefunctions and to the appearance of additional
channels connecting initial and target states.


  The Walecka many-body field theory is investigated in the context of quantum
nonextensive statistical mechanics, characterized by a dimensionless parameter
$q$. We consider nuclear matter described statistically by a power-law
distribution which generalizes the standard Fermi-Dirac distribution ($q = 1$).
We show that the scalar and vector meson fields become more intense due to the
nonextensive effects ($q \neq 1$). From a numerical treatment, we also show
that as the nonextensive parameter $q$ increases, the nucleon effective mass
diminishes and the equation of state becomes stiffer. Finally, the usual
Maxwell construction seems not to be necessary for isotherms with temperatures
in the range 14 Mev$<k_BT<$20 MeV.


  Query complexity is a common tool for comparing quantum and classical
computation, and it has produced many examples of how quantum algorithms differ
from classical ones. Here we investigate in detail the role that oracles play
for the advantage of quantum algorithms. We do so by using a simulation
framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms
that solve some problems with the same success probability and number of
queries as the quantum algorithms. The framework can be simulated using only
classical resources at a constant overhead as compared to the quantum resources
used in quantum computation. Our results clarify the assumptions made and the
conditions needed when using quantum oracles. Using the same assumptions on
oracles within the simulation framework we show that for some specific
algorithms, like the Deutsch-Jozsa and Simon's algorithms, there simply is no
advantage in terms of query complexity. This does not detract from the fact
that quantum query complexity provides examples of how a quantum computer can
be expected to behave, which in turn has proved useful for finding new quantum
algorithms outside of the oracle paradigm, where the most prominent example is
Shor's algorithm for integer factorization.


  This paper presents the idea ofmono-nizingbinocular videos and a frame-work
to effectively realize it. Mono-nize means we purposely convert abinocular
video into a regular monocular video with the stereo informationimplicitly
encoded in a visual but nearly-imperceptible form. Hence, wecan impartially
distribute and show the mononized video as an ordinarymonocular video. Unlike
ordinary monocular videos, we can restore from itthe original binocular video
and show it on a stereoscopic display. To start,we formulate an
encoding-and-decoding framework with the pyramidal de-formable fusion module to
exploit long-range correspondences between theleft and right views, a
quantization layer to suppress the restoring artifacts,and the compression
noise simulation module to resist the compressionnoise introduced by modern
video codecs. Our framework is self-supervised,as we articulate our objective
function with loss terms defined on the input:a monocular term for creating the
mononized video, an invertibility termfor restoring the original video, and a
temporal term for frame-to-framecoherence. Further, we conducted extensive
experiments to evaluate ourgenerated mononized videos and restored binocular
videos for diverse typesof images and 3D movies. Quantitative results on both
standard metrics anduser perception studies show the effectiveness of our
method.


  $K\pi$ scattering and $K_{\mu 4}$ decays are studied at leading order of
improved chiral perturbation theory. It is shown that high precision $K_{\mu
4}$ experiments at, e.g., DA$\Phi$NE should allow for a direct measurement of
the quark mass ratio $m_s$/${\hat m}$.


  This paper proposes a first-order total variation diminishing (TVD) treatment
for coarsening and refining of local timestep size in response to dynamic local
variations in wave speeds for nonlinear conservation laws. The algorithm is
accompanied with a proof of formal correctness showing that given a
sufficiently small minimum timestep the algorithm will produce TVD solution for
nonlinear scalar conservation laws. A key feature of the algorithm is its
formulation as a discrete event simulation, which allows for easy and efficient
parallelization using existing software. Numerical results demonstrate the
stability and adaptivity of the method for the shallow water equations. We also
introduce a performance model to load balance and explain the observed
performance gains. Performance results are presented for a single node on
Stampede2's Skylake partition using an optimistic parallel discrete event
simulator. Results show the proposed algorithm recovering 59%-77% of the
theoretically achievable speed-up with the discrepancies being attributed to
the cost of computing the CFL condition and load imbalance.


  Dev (2002) discussed some exact solutions of anisotropic stars for special
forms of TOV for constant energy density. Considering Bijalwan (2011) ansatz
for charged perfect fluids we present here some exact solutions to the
generalized TOV equation for anisotropic fluids by representing equation in
terms for radial pressure. Consequently, radial pressure is found to be an
invertible arbitrary function of w(=c1+c2r^2), where c1 and c2 is nonzero are
arbitrary constants, and r is the radius of star, i.e. p=p(w) . We present a
general solution for anisotropic fluid in terms for w. We list and discuss some
old and new solutions which fall in this category. Consequently, we present
solutions for generalized TOV considering different forms of anisotropy factor
in terms of w. Also, we investigated solutions of generalized TOV with negative
density gradient (NDG).


  In this paper, a high noise immune time-domain inversion cascade network
(TICaN) is proposed to reconstruct scatterers from the measured electromagnetic
fields. The TICaN is comprised of a denoising block aiming at improving the
signal-to-noise ratio, and an inversion block to reconstruct the
electromagnetic properties from the raw time-domain measurements. The
scatterers investigated in this study include complicated geometry shapes and
high contrast, which cover the stratum layer, lossy medium and hyperfine
structure, etc. After being well trained, the performance of the TICaN is
evaluated from the perspective of accuracy, noise-immunity, computational
acceleration, and generalizability. It can be proven that the proposed
framework can realize high-precision inversion under high-intensity noise
environments. Compared with traditional reconstruction methods, TICaN avoids
the tedious iterative calculation by utilizing the parallel computing ability
of GPU and thus significantly reduce the computing time. Besides, the proposed
TICaN has certain generalization ability in reconstructing the unknown
scatterers such as the famous Austria rings. Herein, it is confident that the
proposed TICaN will serve as a new path for real-time quantitative microwave
imaging for various practical scenarios.


  Access control models have been developed to control authorized access to
sensitive resources. This control of access is important as there is now a need
for collaborative resource sharing between multiple organizations over open
environments like the internet. Although there are multiple access control
models that are being widely used, these models are providing access control
within a closed environment i.e. within the organization using it. These models
have restricted capabilities in providing access control in open environments.
Attribute-Based Access Control (ABAC) has emerged as a powerful access control
model to bring fine-grained authorization to organizations that possess
sensitive data and resources and want to collaborate over open environments. In
an ABAC system, access to resources that an organization possess can be
controlled by applying policies on attributes of the users. These policies are
conditions that need to be satisfied by the requester in order to gain access
to the resource. In this paper, we provide an introduction to ABAC and by
carrying forward the architecture of ABAC, we propose a Decentralized Policy
Information Point (PIP) model. Our model proposes the decentralization of PIP,
which is an entity of the ABAC model that allows the storage and query of user
attributes and enforces fine-grained access control for controlling the access
of sensitive resources over multiple domains. Our model makes use of the
concept of a cryptographic primitive called Attribute-Based Signature (ABS) to
keep the identities of the users involved, private. Our model can be used for
collaborative resource sharing over the internet. The evaluation of our model
is also discussed to reflect the application of the proposed decentralized PIP
model.


  Flow past a line vortex in a simple perfect fluid or superfluid gives rise to
a transverse Magnus force that is given by the well known Joukowski lift
formula. The problem of generalising this to multiconstituent superfluid models
has been controversial since it was originally posed by the work of Iordanski
in the context of the Landau 2-constituent model for He-4 at finite
temperature. The present work deals not just with this particular case but with
the generic category of perfect multiconstituent models including the kind
proposed for a mixture of He-4 and He-3 by Andreev and Bashkin. It is shown
here (using a relativistic approach) that each constituent will provide a
contribution proportional to the product of the corresponding momentum
circulation integral with the associated asymptotic current density.


  The convergence to equilibrium of renormalized solutions to
reaction-cross-diffusion systems in a bounded domain under no-flux boundary
conditions is studied. The reactions model complex balanced chemical reaction
networks coming from mass-action kinetics and thus do not obey any growth
condition, while the diffusion matrix is of cross-diffusion type and hence
nondiagonal and neither symmetric nor positive semi-definite, but the system
admits a formal gradient-flow or entropy structure. The diffusion term
generalizes the population model of Shigesada, Kawasaki and Teramoto to an
arbitrary number of species. By showing that any renormalized solution
satisfies the conservation of masses and a weak entropy-entropy production
inequality, it can be proved under the assumption of no boundary equilibria
that {\it all} renormalized solutions converge exponentially to the complex
balanced equilibrium with a rate which is explicit up to a finite dimensional
inequality.


  Motivated by recent work on the utility of Mellin space for representing
conformal correlators in $AdS$/CFT, we study its suitability for representing
dual conformal integrals of the type which appear in perturbative scattering
amplitudes in super-Yang-Mills theory. We discuss Feynman-like rules for
writing Mellin amplitudes for a large class of integrals in any dimension, and
find explicit representations for several familiar toy integrals. However we
show that the power of Mellin space is that it provides simple representations
even for fully massive integrals, which except for the single case of the
4-mass box have not yet been computed by any available technology. Mellin space
is also useful for exhibiting differential relations between various multi-loop
integrals, and we show that certain higher-loop integrals may be written as
integral operators acting on the fully massive scalar $n$-gon in $n$
dimensions, whose Mellin amplitude is exactly 1. Our chief example is a very
simple formula expressing the 6-mass double box as a single integral of the
6-mass scalar hexagon in 6 dimensions.


  Experimental information has been derived from the neutron-proton correlation
function in order to deduce the time sequence of neutrons and protons emitted
at 45 degrees in the E/A = 45 MeV 58Ni + 27Al reaction.


  Let M(1) be the vertex algebra for a single free boson. We classify
irreducible modules of certain vertex subalgebras of M(1) generated by two
generators. These subalgebras correspond to the W(2, 2p-1)--algebras with
central charge $1- 6 \frac{(p - 1) ^{2}}{p}$ where p is a positive integer, $p
\ge 2$. We also determine the associated Zhu's algebras.


  For slowly evolving, discrete-time-dependent systems of difference equations
(iterated maps), we believe the simplest means of demonstrating the validity of
the averaging method at first order is by way of a lemma that we call Besjes'
inequality. In this paper, we develop the Besjes inequality for identity maps
with perturbations that are (i) at low-order resonance (periodic with short
period) and (ii) far from low-order resonance in the discrete time. We use
these inequalities to prove corresponding first-order averaging principles,
together with a principle of adiabatic invariance on extended timescales; and
we generalize and apply these mathematical results to model problems in
accelerator beam dynamics, and to the Henon map.


  Cross sections for e+e- to hadons, pi+pi- J/Psi, and mu+mu- have been
measured in the vicinity of the Psi(2S) resonance using the BESII detector
operated at the BEPC. The Psi(2S) total width; partial widths to hadrons,
pi+pi- J/Psi, muons; and corresponding branching fractions have been determined
to be Gamma(total)= (264+-27) keV; Gamma(hadron)= (258+-26) keV, Gamma(mu)=
(2.44+-0.21) keV, and Gamma(pi+pi- J/Psi)= (85+-8.7) keV; and Br(hadron)=
(97.79+-0.15)%, Br(pi+pi- J/Psi)= (32+-1.4)%, Br(mu)= (0.93+-0.08)%,
respectively.


  High resolution X-ray observations indicate that the entropy profiles in the
central regions of some massive cooling flow clusters are well approximated by
powerlaws. McCarthy and coworkers recently accounted for this trend with an
analytic model that includes the detailed effects of radiative cooling.
Interestingly, these authors found that cooling (and subsequent inflow of the
gas) naturally establishes approximate steady-state powerlaw entropy profiles
in the cores of clusters. However, the origin of this behavior and its
dependence on initial conditions have yet to be elucidated. In the present
study, we explain this trend in the context of the self-similar cooling wave
model developed previously by Bertschinger (1989). It is shown that the
logarithmic slope of the entropy profile in the cores of relaxed cooling flow
clusters is given by a simple analytic function that depends only on the
logarithmic slopes of the local gravitational potential and the cooling
function. We discuss a number of potentially interesting uses of the above
result, including: (1) a way of measuring the shapes of gravitational
potentials of cooling flow clusters (which may, for example, be compared with
the results of the standard hydrostatic equilibrium method); (2) a simple
method for constructing realistic analytic cluster models that include the
effects of radiative cooling; and (3) a test of the reliability of cooling
routines implemented in analytic models and hydrodynamic simulations.


  Electron transport through molecular quantum dots coupled to a single
vibrational mode is studied in the Kondo regime. We apply a generalized
Schrieffer-Wolff transformation to determine the effective low-energy
spin-spin-vibron-interaction. From this model we calculate the nonlinear
conductance and find Kondo sidebands located at bias-voltages equal to
multiples of the vibron frequency. Due to selection rules, the side-peaks are
found to have strong gate-voltage dependences, which can be tested
experimentally. In the limit of weak electron-vibron coupling, we employ a
perturbative renormalization group scheme to calculate analytically the
nonlinear conductance.


  Light propagation in disordered media is a fundamental and important problem
in optics and photonics. In particular, engineering light-matter interaction in
disordered cold atomic ensembles is one of the central topics in modern quantum
and atomic optics. The collective response of dense atomic gases under light
excitation, which crucially depends on the spatial distribution of atoms and
the geometry of the ensemble, has important impacts on quantum technologies
like quantum sensors, atomic clocks and quantum information storage. Here we
analyze near-resonant light transmission in two-dimensional dense ultracold
atomic ensembles with short-range positional correlations. Based on the
coupled-dipole simulations under different atom number densities and
correlation lengths, we show that the collective effects are strongly
influenced by those positional correlations, manifested as significant shifts
and broadening or narrowing of transmission resonance lines. The results show
that mean-field theories like Lorentz-Lorenz relation are not capable of
describing such collective effects. We further investigate the statistical
distribution of eigenstates, which are significantly affected by the interplay
between dipole-dipole interactions and position correlations. This work can
provide profound implications on collective and cooperative effects in cold
atomic ensembles as well as the study of mesoscopic physics concerning light
transport in strongly scattering disordered media.


  We report a study of electronic transport in van der Waals heterostructures
composed of flakes of the antiferromagnetic Mott insulator a-RuCl_3 placed on
top of monolayer graphene Hall bars. While the zero-field transport shows a
strong resemblance to that of isolated graphene, we find a consistently
$p$-type Hall effect suggestive of multiband conduction, along with a
non-monotonic and gate-voltage-dependent excursion of the resistivity at low
temperatures that is reminiscent of transport in the presence of a magnetic
phase transition. We interpret these data as evidence for charge transfer from
graphene to a-RuCl_3 in an inhomogeneous device yielding both highly- and
lightly-doped regions of graphene, while the latter shows a particular
sensitivity to magnetism in the a-RuCl_3. Thus proximity to graphene is a means
to access magnetic properties of thin layers of magnetic insulators.


  Given two graphs $H$ and $F$, the generalized Tur\'an number
$\mathrm{ex}(n,H,F)$ is the largest number of copies of $H$ in an $n$-vertex
$F$-free graph. For every $F$ and sufficiently large $n$, we present an
extremal graph for a generalized Tur\'an problem, i.e., an $F$-free $n$ vertex
graph $G$ that for some $H$ contains exactly $\mathrm{ex}(n,H,F)$ copies of
$H$.


  In this paper, we provide three different ways to partition the polytope of
doubly substochastic matrices into subpolytopes via the prescribed row and
column sums, the sum of all elements and the sub-defect respectively. Then we
characterize the extreme points of each type of convex subpolytopes. The
relations of the extreme points of the subpolytopes in the three partitions are
also given.


  This paper considers several aspects of random matrix universality in deep
neural networks. Motivated by recent experimental work, we use universal
properties of random matrices related to local statistics to derive practical
implications for deep neural networks based on a realistic model of their
Hessians. In particular we derive universal aspects of outliers in the spectra
of deep neural networks and demonstrate the important role of random matrix
local laws in popular pre-conditioning gradient descent algorithms. We also
present insights into deep neural network loss surfaces from quite general
arguments based on tools from statistical physics and random matrix theory.


  The synthesis of technology and the medical industry has partly contributed
to the increasing interest in Medical Cyber-Physical Systems (MCPS). While
these systems provide benefits to patients and professionals, they also
introduce new attack vectors for malicious actors (e.g. financially-and/or
criminally-motivated actors). A successful breach involving a MCPS can impact
patient data and system availability. The complexity and operating requirements
of a MCPS complicates digital investigations. Coupling this information with
the potentially vast amounts of information that a MCPS produces and/or has
access to is generating discussions on, not only, how to compromise these
systems but, more importantly, how to investigate these systems. The paper
proposes the integration of forensics principles and concepts into the design
and development of a MCPS to strengthen an organization's investigative
posture. The framework sets the foundation for future research in the
refinement of specific solutions for MCPS investigations.


  We provide an extensive study of the sub-ohmic spin-boson model with power
law density of states J(\omega)=\omega^s (with 0<s<1), focusing on the
equilibrium dynamics of the three possible spin components, from very weak
dissipation to the quantum critical regime. Two complementary methods, the
bosonic Numerical Renormalization Group (NRG) and Majorana diagrammatics, are
used to explore the physical properties in a wide range of parameters. We show
that the bosonic self-energy is the crucial ingredient for the description of
critical fluctuations, but that many-body vertex corrections need to be
incorporated as well in order to obtain quantitative agreement of the
diagrammatics with the numerical simulations. Our results suggest that the
out-of-equilibrium dynamics in dissipative models beyond the Bloch-Redfield
regime should be reconsidered in the long-time limit. Regarding also the
spin-boson Hamiltonian as a toy model of quantum criticality, some of the
insights gained here may be relevant for field theories of electrons coupled to
bosons in higher dimensions.


  This thesis sums up the research work I performed as a PhD student in
Sapienza Universit\`a di Roma, and \'Ecole Normale Sup\'erieure, Paris, under
the joint supervision of Prof. Giorgio Parisi and Dr. Francesco Zamponi. The
thesis focuses on the theoretical study of metastable glasses prepared through
non-equilibrium protocols. The first two chapters contain a review of the
phenomenology of equilibrium supercooled liquids and non-equilibrium glasses,
along with an exposition of the theoretical tools used up to now to approach
the glass problem; the third chapter contains a review of the theoretical tools
which are employed in the following of the thesis; the following two chapters
contain our main result, namely a mean-field and first-principles theory of
metastable glassy states which, as we show, is both able to reproduce known
observations and to formulate new predictions and insights into the very nature
of the glass phase, with tangible consequences in terms of behavior at high
densities (or equivalently, low temperatures) and elasto-plastic response under
strain; the last two chapters contain a numerical check of some of the results,
and our conclusions and proposals for further research. The results I report in
the present work have been for the most part already published, but here they
are presented in a consistent and (as much as possible) self-contained manner.


  Let (T,M) be a complete local domain containing the integers. Let p1
\subseteq p2 \subseteq ... \subseteq pn be a chain of nonmaximal prime ideals T
such that T_pn is a regular local ring. We construct a chain of excellent local
domains An \subseteq A1 such that for each i, the completion of Ai is T, the
generic formal fiber of Ai is local with maximal ideal pi, and if I is a
nonzero ideal of Ai then Ai/I is complete. Consequently, if in addition T is a
UFD, then we can construct a chain of excellent local UFDs satisfying the same
conditions.


  We derive the key expressions to robustly address the eigenfunction
expansion-based analysis of electromagnetic (EM) fields produced by current
sources within planar non-birefringent anisotropic medium (NBAM) layers. In
NBAM, the highly symmetric permeability and permittivity tensors can induce
directionally-dependent, but polarization independent, propagation properties
supporting "degenerate" characteristic polarizations, i.e. four
linearly-independent eigenvectors associated with only two (rather than four)
unique, non-defective eigenvalues. We first explain problems that can arise
when the source(s) specifically reside within NBAM planar layers when using
canonical field expressions. To remedy these problems, we exhibit alternative
spectral-domain field expressions, immune to such problems, that form the
foundation for a robust eigenfunction expansion-based analysis of time-harmonic
EM radiation and scattering within such type of planar-layered media. Numerical
results demonstrate the high accuracy and stability achievable using this
algorithm.


  By using a combination of heteroepitaxial growth, structure refinement based
on synchrotron x-ray diffraction and first-principles calculations, we show
that the symmetry-protected Dirac line nodes in the topological semimetallic
perovskite SrIrO3 can be lifted simply by applying epitaxial constraints. In
particular, the Dirac gap opens without breaking the Pbnm mirror symmetry. In
virtue of a symmetry-breaking analysis, we demonstrate that the original
symmetry protection is related to the n-glide operation, which can be
selectively broken by different heteroepitaxial structures. This symmetry
protection renders the nodal line a nonsymmorphic Dirac semimetallic state. The
results highlight the vital role of crystal symmetry in spin-orbit-coupled
correlated oxides and provide a foundation for experimental realization of
topological insulators in iridate-based heterostructures.


  Visual context is important in object recognition and it is still an open
problem in computer vision. Along with the advent of deep convolutional neural
networks (CNN), using contextual information with such systems starts to
receive attention in the literature. At the same time, aerial imagery is
gaining momentum. While advances in deep learning make good progress in aerial
image analysis, this problem still poses many great challenges. Aerial images
are often taken under poor lighting conditions and contain low resolution
objects, many times occluded by trees or taller buildings. In this domain, in
particular, visual context could be of great help, but there are still very few
papers that consider context in aerial image understanding. Here we introduce
context as a complementary way of recognizing objects. We propose a dual-stream
deep neural network model that processes information along two independent
pathways, one for local and another for global visual reasoning. The two are
later combined in the final layers of processing. Our model learns to combine
local object appearance as well as information from the larger scene at the
same time and in a complementary way, such that together they form a powerful
classifier. We test our dual-stream network on the task of segmentation of
buildings and roads in aerial images and obtain state-of-the-art results on the
Massachusetts Buildings Dataset. We also introduce two new datasets, for
buildings and road segmentation, respectively, and study the relative
importance of local appearance vs. the larger scene, as well as their
performance in combination. While our local-global model could also be useful
in general recognition tasks, we clearly demonstrate the effectiveness of
visual context in conjunction with deep nets for aerial image understanding.


  Does the human lifespan have an impenetrable biological upper limit which
ultimately will stop further increase in life lengths? This question is
important for understanding aging, and for society, and has led to intense
controversies. Demographic data for humans has been interpreted as showing
existence of a limit, or even as an indication of a decreasing limit, but also
as evidence that a limit does not exist. This paper studies what can be
inferred from data about human mortality at extreme age. We show that in
western countries and Japan and after age 110 the probability of dying is about
47% per year. Hence there is no finite upper limit to the human lifespan.
Still, given the present stage of biotechnology, it is unlikely that during the
next 25 years anyone will live longer than 128 years in these countries. Data,
remarkably, shows no difference in mortality after age 110 between sexes,
between ages, or between different lifestyles or genetic backgrounds. These
results, and the analysis methods developed in this paper, can help testing
biological theories of ageing and aid confirmation of success of efforts to
find a cure for ageing.


  We exploit the information derived from geographical coordinates to
endogenously identify spatial regimes in technologies that are the result of a
variety of complex, dynamic interactions among site-specific environmental
variables and farmer decision making about technology, which are often not
observed at the farm level. Controlling for unobserved heterogeneity is a
fundamental challenge in empirical research, as failing to do so can produce
model misspecification and preclude causal inference. In this article, we adopt
a two-step procedure to deal with unobserved spatial heterogeneity, while
accounting for spatial dependence in a cross-sectional setting. The first step
of the procedure takes explicitly unobserved spatial heterogeneity into account
to endogenously identify subsets of farms that follow a similar local
production econometric model, i.e. spatial production regimes. The second step
consists in the specification of a spatial autoregressive model with
autoregressive disturbances and spatial regimes. The method is applied to two
regional samples of olive growing farms in Italy. The main finding is that the
identification of spatial regimes can help drawing a more detailed picture of
the production environment and provide more accurate information to guide
extension services and policy makers.


  Supermassive black hole masses (MBH) can dynamically be estimated with
various methods and using different kinematic tracers. Different methods have
only been cross-checked for a small number of galaxies and often show
discrepancies. To understand these discrepancies, detailed cross-comparisons of
additional galaxies are needed. We present the first part of our
cross-comparison between stellar- and gas-based MBH estimates in the nearby
fast-rotating early-type galaxy NGC 6958. The measurements presented here are
based on ground-layer adaptive optics-assisted Multi-Unit Spectroscopic
Explorer (MUSE) science verification data at around 0.6 arcsec spatial
resolution. The spatial resolution is a key ingredient for the measurement and
we provide a Gaussian parametrisation of the adaptive optics-assisted point
spread function (PSF) for various wavelengths. From the MUSE data, we extracted
the stellar kinematics and constructed dynamical models. Using an axisymmetric
Schwarzschild technique, we measured an MBH of (3.6+2.7-2.4)\times 10^8 Msun at
3\sigma significance taking kinematical and dynamical systematics
(e.g.,radially-varying mass-to-light ratio) into account. We also added a dark
halo, but our data does not allow to constrain the dark matter fraction. Adding
dark matter with an abundance matching prior results in a 25 per cent more
massive black hole. Jeans anisotropic models return MBH of (4.6+2.5-2.7) \times
10^8 Msun and (8.6+0.8-0.8) \times 10^8 Msun at 3\sigma confidence for
spherical and cylindrical alignment of the velocity ellipsoid, respectively. In
a follow-up study, we will compare the stellar-based MBH with those from cold
and warm gas tracers, which will provide additional constraints for the MBH for
NGC 6958, and insights into assumptions that lead to potential systematic
uncertainty.


  Over a finite-dimensonal algbera $A$, simple $A$-modules that have projective
dimension one have special properties. For example, Geigle-Lenzing studied them
in connection to homological epimorphisms of rings, and they have also appeared
in work concerning the finitistic dimension conjecture. If we however work in a
$d$-cluster-tilting subcategory, then not all simples are contained in this
subcategory. In this context, a replacement might be to work with idempotent
ideals instead, and utilise the theory of Auslander-Platzeck-Todorov. We
introduce the notion of a fabric idempotent as an analogue of the localising
modules studied by Chen-Krause, and to illustrate the theory we show that they
provide rich combinatorial properties. An application is to extend the
classification of singularity categories of Nakayama algebras by Chen-Ye to
higher Nakayama algebras.


  Garonzi and Lucchini~\cite{GL} explored finite groups $G$ possessing a normal
$2$-covering, where no proper quotient of $G$ exhibits such a covering. Their
investigation offered a comprehensive overview of these groups, delineating
that such groups fall into distinct categories: almost simple, affine, product
action, or diagonal.
  In this paper, we focus on the family falling under the diagonal type.
Specifically, we present a thorough classification of finite diagonal groups
possessing a normal $2$-covering, with the attribute that no proper quotient of
$G$ has such a covering.


  Touchard-Riordan-like formulas are some expressions appearing in enumeration
problems and as moments of orthogonal polynomials. We begin this article with a
new combinatorial approach to prove these kind of formulas, related with
integer partitions. This gives a new perspective on the original result of
Touchard and Riordan. But the main goal is to give a combinatorial proof of a
Touchard-Riordan--like formula for q-secant numbers discovered by the first
author. An interesting limit case of these objects can be directly interpreted
in terms of partitions, so that we obtain a connection between the formula for
q-secant numbers, and a particular case of Jacobi's triple product identity.
  Building on this particular case, we obtain a "finite version" of the triple
product identity. It is in the form of a finite sum which is given a
combinatorial meaning, so that the triple product identity can be obtained by
taking the limit. Here the proof is non-combinatorial and relies on a
functional equation satisfied by a T-fraction. Then from this result on the
triple product identity, we derive a whole new family of Touchard-Riordan--like
formulas whose combinatorics is not yet understood. Eventually, we prove a
Touchard-Riordan--like formula for a q-analog of Genocchi numbers, which is
related with Jacobi's identity for (q;q)^3 rather than the triple product
identity.


  Ensuring the privacy of research participants is vital, even more so in
healthcare environments. Deep learning approaches to neuroimaging require large
datasets, and this often necessitates sharing data between multiple sites,
which is antithetical to the privacy objectives. Federated learning is a
commonly proposed solution to this problem. It circumvents the need for data
sharing by sharing parameters during the training process. However, we
demonstrate that allowing access to parameters may leak private information
even if data is never directly shared. In particular, we show that it is
possible to infer if a sample was used to train the model given only access to
the model prediction (black-box) or access to the model itself (white-box) and
some leaked samples from the training data distribution. Such attacks are
commonly referred to as Membership Inference attacks. We show realistic
Membership Inference attacks on deep learning models trained for 3D
neuroimaging tasks in a centralized as well as decentralized setup. We
demonstrate feasible attacks on brain age prediction models (deep learning
models that predict a person's age from their brain MRI scan). We correctly
identified whether an MRI scan was used in model training with a 60% to over
80% success rate depending on model complexity and security assumptions.


  Stereodynamics of cold collisions has become a fertile ground for quantized
studies of molecular collisions and control of the collision outcome. A
benchmark process for stereodynamic control is rotational transition in He+HD
collisions. This process was recently probed experimentally by Perreault et al.
by examining quenching from $j=2$ to $j'=0$ state in the $v=1$ vibrational
manifold. Here, through explicit quantum scattering calculations on a highly
accurate ab initio interaction potential for He+H$_2$, we reveal how a
combination of two shape resonances arising from $l=1$ and $l=2$ partial waves
controls the stereodynamic outcome rather than a single $l=2$ partial wave
attributed in the experiment. Further, for collision energies below 0.5
cm$^{-1}$, it is shown that stereodynamic preference for integral cross section
follows a simple universal trend.


  The expressiveness of neural networks highly depends on the nature of the
activation function, although these are usually assumed predefined and fixed
during the training stage. Under a signal processing perspective, in this paper
we present Expressive Neural Network (ENN), a novel model in which the
non-linear activation functions are modeled using the Discrete Cosine Transform
(DCT) and adapted using backpropagation during training. This parametrization
keeps the number of trainable parameters low, is appropriate for gradient-based
schemes, and adapts to different learning tasks. This is the first non-linear
model for activation functions that relies on a signal processing perspective,
providing high flexibility and expressiveness to the network. We contribute
with insights in the explainability of the network at convergence by recovering
the concept of bump, this is, the response of each activation function in the
output space. Finally, through exhaustive experiments we show that the model
can adapt to classification and regression tasks. The performance of ENN
outperforms state of the art benchmarks, providing above a 40% gap in accuracy
in some scenarios.


  This work focuses on dimension-reduction techniques for modelling conditional
extreme values. Specifically, we investigate the idea that extreme values of a
response variable can be explained by nonlinear functions derived from linear
projections of an input random vector. In this context, the estimation of
projection directions is examined, as approached by the Extreme Partial Least
Squares (EPLS) method--an adaptation of the original Partial Least Squares
(PLS) method tailored to the extreme-value framework. Further, a novel
interpretation of EPLS directions as maximum likelihood estimators is
introduced, utilizing the von Mises-Fisher distribution applied to hyperballs.
The dimension reduction process is enhanced through the Bayesian paradigm,
enabling the incorporation of prior information into the projection direction
estimation. The maximum a posteriori estimator is derived in two specific
cases, elucidating it as a regularization or shrinkage of the EPLS estimator.
We also establish its asymptotic behavior as the sample size approaches
infinity. A simulation data study is conducted in order to assess the practical
utility of our proposed method. This clearly demonstrates its effectiveness
even in moderate data problems within high-dimensional settings. Furthermore,
we provide an illustrative example of the method's applicability using French
farm income data, highlighting its efficacy in real-world scenarios.


  Although deep learning has significantly improved Face Recognition (FR),
dramatic performance deterioration may occur when processing Low Resolution
(LR) faces. To alleviate this, approaches based on unified feature space are
proposed with the sacrifice under High Resolution (HR) circumstances. To deal
with the huge domain gap between HR and LR domains and achieve the best on both
domains, we first took a closer look at the impacts of several resolution
augmentations and then analyzed the difficulty of LR samples from the
perspective of the model gradient produced by different resolution samples.
Besides, we also find that the introduction of some resolutions could help the
learning of lower resolutions. Based on these, we divide the LR samples into
three difficulties according to the resolution and propose a more effective
Multi-Resolution Augmentation. Then, due to the rapidly increasing domain gap
as the resolution decreases, we carefully design a novel and effective metric
loss based on a LogExp distance function that provides decent gradients to
prevent oscillation near the convergence point or tolerance to small distance
errors; it could also dynamically adjust the penalty for errors in different
dimensions, allowing for more optimization of dimensions with large errors.
Combining these two insights, our model could learn more general knowledge in a
wide resolution range of images and balanced results can be achieved by our
extremely simple framework. Moreover, the augmentations and metrics are the
cornerstones of LRFR, so our method could be considered a new baseline for the
LRFR task. Experiments on the LRFR datasets: SCface, XQLFW, and large-scale
LRFR dataset: TinyFace demonstrate the effectiveness of our methods, while the
degradation on HRFR datasets is significantly reduced.


  We study the force production dynamics of undulating elastic plates as a
model for fish-like inertial swimmers. Using a beam model coupled with
Lighthill's large-amplitude elongated-body theory, we explore different
localised actuations at one extremity of the plate (heaving, pitching, and a
combination of both) in order to quantify the reactive and resistive
contributions to the thrust. The latter has the form of a quadratic drag in
large Reynolds number swimmers and has recently been pointed out as a crucial
element in the thrust force balance. We validate the output of a weakly
nonlinear solution to the fluid--structure model using thrust force
measurements from an experiment with flexible plates subjected to the three
different actuation types. The model is subsequently used in a self-propelled
configuration ---with a skin friction model that balances thrust to produce a
constant cruising speed--- to map the reactive versus resistive thrust
production in a parameter space defined by the aspect ratio and the actuation
frequency. We show that this balance is modified as the frequency of excitation
changes and the response of the elastic plate shifts between different resonant
modes, the pure heaving case being the most sensitive to the modal response
with drastic changes in the reactive/resistive contribution ratio along the
frequency axis. We analyse also the role of the phase lag between the heaving
and pitching components in the case of combined actuation, showing in
particular a non-trivial effect on the propulsive efficiency.


  We study metastable behavior in a discrete nonlinear Schr\"odinger equation
from the viewpoint of Hamiltonian systems theory. When there are $n < \infty$
sites in this equation, we consider initial conditions in which almost all the
energy is concentrated in one end of the system. We are interested in
understanding how energy flows through the system, so we add a dissipation of
size $\gamma$ at the opposite end of the chain, and we show that the energy
decreases extremely slowly. Furthermore, the motion is localized in the phase
space near a family of breather solutions for the undamped system. We give
rigorous, asymptotic estimates for the rate of evolution along the family of
breathers and the width of the neighborhood within which the trajectory is
confined.


  We analyze the evolution of massive (log$_{10}$ [$M_\star/M_\odot$] $>10$)
galaxies at $z \sim$ 4--8 selected from the JWST Cosmic Evolution Early Release
Science (CEERS) survey. We infer the physical properties of all galaxies in the
CEERS NIRCam imaging through spectral energy distribution (SED) fitting with
dense basis to select a sample of high redshift massive galaxies. Where
available we include constraints from additional CEERS observing modes,
including 18 sources with MIRI photometric coverage, and 28 sources with
spectroscopic confirmations from NIRSpec or NIRCam wide-field slitless
spectroscopy. We sample the recovered posteriors in stellar mass from SED
fitting to infer the volume densities of massive galaxies across cosmic time,
taking into consideration the potential for sample contamination by active
galactic nuclei (AGN). We find that the evolving abundance of massive galaxies
tracks expectations based on a constant baryon conversion efficiency in dark
matter halos for $z \sim$ 1--4. At higher redshifts, we observe an excess
abundance of massive galaxies relative to this simple model. These higher
abundances can be explained by modest changes to star formation physics and/or
the efficiencies with which star formation occurs in massive dark matter halos,
and are not in tension with modern cosmology.


  Calculation of elastic p8Li- and p9Li-scattering differential cross sections,
performed at two energies 0.07 and 0.7 GeV/nucleon within Glauber multiple
diffraction scattering, are presented and discussed. Three-body wave functions:
alpha-t-n (for 8Li) and 7Li-n-n (for 9Li) with realistic potentials of
intercluster interactions were used there. Sensitivity of elastic scattering to
proton-nucleus interaction and nuclear structure has been studied. In
particular, dependence of differential cross section on contribution of
higher-order collisions, scattering at core and at periphery nucleons, on
contribution of minor wave function components has been calculated. Comparison
was made with available experimental data and with optical model calculations.


  We study the masses and the leptonic decay widths of heavy quarkonium in the
dual Ginzburg-Landau (DGL) theory of QCD, in which the abelian monopole
condensation plays an essential role for color confinement. The effect of color
screening due to the light quark pair creation is introduced by the infrared
momentum cutoff in the gluon propagator. We find that the color screening
effect is important to reproduce the properties of the heavy quarkonium, in
particular the leptonic decay width. We also discuss the underlying systematics
of the heavy quark spectroscopy in the DGL theory.


  We develop a system which must be able to perform the same inferences that a
human reader of an accident report can do and more particularly to determine
the apparent causes of the accident. We describe the general framework in which
we are situated, linguistic and semantic levels of the analysis and the
inference rules used by the system.


  We consider a family of character sums as multiplicative analogues of
Kloosterman sums. Using Gauss sums, Jacobi sums and Deligne's bound for
hyper-Kloosterman sums, we establish asymptotic formulae for any real
(positive) moments of the above character sum as the character runs over all
non-trivial multiplicative characters mod $p.$ Moreover, an arcsine law is also
established as a consequence of the method of moments. The evaluations of these
moments also allow us to obtain asymptotic formulae for moments of such
character sums weighted by special $L$-values (at $1/2$ and $1$).


  There are presently two models for quantum walks on graphs. The "coined" walk
uses discrete time steps, and contains, besides the particle making the walk, a
second quantum system, the coin, that determines the direction in which the
particle will move. The continuous walk operates with continuous time. Here a
third model for a quantum walk is proposed, which is based on an analogy to
optical interferometers. It is a discrete-time model, and the unitary operator
that advances the walk one step depends only on the local structure of the
graph on which the walk is taking place. No quantum coin is introduced. This
type of walk allows us to introduce elements, such as phase shifters, that have
no counterpart in classical random walks. Walks on the line and cycle are
discussed in some detail, and a probability current for these walks is
introduced. The relation to the coined quantum walk is also discussed. The
paper concludes by showing how to define these walks for a general graph.


  We found that the real time reverse transcription-polymerase chain reaction
(RT-PCR) detection of viral RNA from sputum or nasopharyngeal swab has a
relatively low positive rate in the early stage to determine COVID-19 (named by
the World Health Organization). The manifestations of computed tomography (CT)
imaging of COVID-19 had their own characteristics, which are different from
other types of viral pneumonia, such as Influenza-A viral pneumonia. Therefore,
clinical doctors call for another early diagnostic criteria for this new type
of pneumonia as soon as possible.This study aimed to establish an early
screening model to distinguish COVID-19 pneumonia from Influenza-A viral
pneumonia and healthy cases with pulmonary CT images using deep learning
techniques. The candidate infection regions were first segmented out using a
3-dimensional deep learning model from pulmonary CT image set. These separated
images were then categorized into COVID-19, Influenza-A viral pneumonia and
irrelevant to infection groups, together with the corresponding confidence
scores using a location-attention classification model. Finally the infection
type and total confidence score of this CT case were calculated with Noisy-or
Bayesian function.The experiments result of benchmark dataset showed that the
overall accuracy was 86.7 % from the perspective of CT cases as a whole.The
deep learning models established in this study were effective for the early
screening of COVID-19 patients and demonstrated to be a promising supplementary
diagnostic method for frontline clinical doctors.


  In the framework of spacetime with torsion and without curvature, the Dirac
particle spin precession in the rotational system is studied. We write out the
equivalent tetrad of rotating frame, in the polar coordinate system, through
considering the relativistic factor, and the resultant equivalent metric is a
flat Minkowski one. The obtained rotation-spin coupling formula can be applied
to the high speed rotating case, which is consistent with the expectation.


  In this work we study the interleaving distance between merge trees from a
combinatorial point of view. We use a particular type of matching between trees
to obtain a novel formulation of the distance. With such formulation, we tackle
the problem of approximating the interleaving distance by solving linear
integer optimization problems in a recursive and dynamical fashion, obtaining
lower and upper bounds. We implement those algorithms to compare the outputs
with another approximation procedure presented by other authors. We believe
that further research in this direction could lead to faster algorithms to
compute the distance and novel theoretical developments on the topic.


  A plausible definition of "reasoning" could be "algebraically manipulating
previously acquired knowledge in order to answer a new question". This
definition covers first-order logical inference or probabilistic inference. It
also includes much simpler manipulations commonly used to build large learning
systems. For instance, we can build an optical character recognition system by
first training a character segmenter, an isolated character recognizer, and a
language model, using appropriate labeled training sets. Adequately
concatenating these modules and fine tuning the resulting system can be viewed
as an algebraic operation in a space of models. The resulting model answers a
new question, that is, converting the image of a text page into a computer
readable text.
  This observation suggests a conceptual continuity between algebraically rich
inference systems, such as logical or probabilistic inference, and simple
manipulations, such as the mere concatenation of trainable learning systems.
Therefore, instead of trying to bridge the gap between machine learning systems
and sophisticated "all-purpose" inference mechanisms, we can instead
algebraically enrich the set of manipulations applicable to training systems,
and build reasoning capabilities from the ground up.