  All stars are born in molecular clouds, and most in giant molecular clouds
(GMCs), which thus set the star formation activity of galaxies. We first review
their observed properties, including measures of mass surface density, Sigma,
and thus mass, M. We discuss cloud dynamics, concluding most GMCs are
gravitationally bound. Star formation is highly clustered within GMCs, but
overall is very inefficient. We compare properties of star-forming clumps with
those of young stellar clusters (YSCs). The high central densities of YSCs may
result via dynamical evolution of already-formed stars during and after star
cluster formation. We discuss theoretical models of GMC evolution, especially
addressing how turbulence is maintained, and emphasizing the importance of GMC
collisions. We describe how feedback limits total star formation efficiency,
epsilon, in clumps. A turbulent and clumpy medium allows higher epsilon,
permitting formation of bound clusters even when escape speeds are less than
the ionized gas sound speed.


  The Pierre Auger Observatory is the largest observatory of high-energy cosmic
rays. It is located in Argentina and has been taking data since January 2004.
Extensive air showers initiated by cosmic rays are measured by the hybrid
detector, which combines the sampling of particle density at ground by
water-Cherenkov tanks and the measurement of atmospheric fluorescence light by
telescopes. New detection techniques, like radio and microwave measurement, are
also being tested. Results regarding the energy spectrum, mass composition and
arrival directions of cosmic rays are presented here.


  Observing and understanding the movement of an intruder through opaque dense
suspensions such as quicksand remains a practical and conceptual challenge.
Here we use an ultrasonic probe to investigate the dynamics of a steel ball
sinking in a 3D dense glass bead packing saturated by water. We show that the
frictional model developed for dry granular media can be used to describe the
ball motion induced by horizontal vibration. From this rheology we infer the
static friction coefficient and effective viscosity that decrease when
increasing the vibration intensity. Our main finding is that the
vibration-induced reduction of the yield stress and increase of the sinking
depth are presumably due to induced slipping at the grain contacts but without
visible plastic rearrangements of grains, in contrast to dry granular packings.
To explain these results, we propose a mechanism of acoustic lubrication that
reduces the inter-particle friction and leads to a decrease of the yield
stress. This scenario is different from the mechanism of liquefaction usually
invoked in loosely packed quicksands where the vibration-induced compaction
increases the pore pressure and decreases the confining pressure on the solid
skeleton, thus reducing the granular resistance to external load.


  Levitated nanoparticles in vacuum are prime candidates for generating
macroscopic quantum superposition states of massive objects. Most protocols for
preparing these states necessitate coherent expansion beyond the scale of the
zero-point motion to produce sufficiently delocalized and pure phase-space
distributions. Here, we spatially expand and subsequently recontract the
thermal state of a levitated nanoparticle by modifying the stiffness of the
trap holding the particle. We achieve state-expansion factors of 25 in standard
deviation for a particle initially feedback-cooled to a center-of-mass thermal
state of \SI{155}{\milli\kelvin}. Our method relies on a hybrid scheme
combining an optical trap, for cooling and measuring the particle's motion,
with a Paul trap for expanding its state. Consequently, state expansion occurs
devoid of measurement backaction from photon recoil, making this approach
suitable for coherent wavefunction expansion in future experiments.


  A conjecture of Fuglede states that a bounded measurable set $\Omega$ in
space, of measure 1, can tile space by translations if and only if the Hilbert
space $L^2(\Omega)$ has an orthonormal basis consisting of exponentials. If
$\Omega$ has the latter property it is called spectral. We generalize a result
of Fuglede, that a triangle in the plane is not spectral, proving that every
non-symmetric convex domain is not spectral.


  Gamma-ray bursts are associated with catastrophic cosmic events. They appear
when a new black hole, created after the explosion of a massive star or the
merger of two compact stars, quickly accretes the matter around it and ejects a
transient relativistic jet in our direction. This review discusses the various
types of gamma-ray bursts, their progenitors, their beaming and their rate in
the local universe. We emphasize the broad astrophysical interest of GRB
studies, and the crucial role of high-energy satellites as exclusive suppliers
of GRB alerts and initial locations.


  This paper presents a novel formulation and solution of orbit determination
over finite time horizons as a learning problem. We present an approach to
orbit determination under very broad conditions that are satisfied for n-body
problems. These weak conditions allow us to perform orbit determination with
noisy and highly non-linear observations such as those presented by range-rate
only (Doppler only) observations. We show that domain generalization and
distribution regression techniques can learn to estimate orbits of a group of
satellites and identify individual satellites especially with prior
understanding of correlations between orbits and provide asymptotic convergence
conditions. The approach presented requires only visibility and observability
of the underlying state from observations and is particularly useful for
autonomous spacecraft operations using low-cost ground stations or sensors. We
validate the orbit determination approach using observations of two spacecraft
(GRIFEX and MCubed-2) along with synthetic datasets of multiple spacecraft
deployments and lunar orbits. We also provide a comparison with the standard
techniques (EKF) under highly noisy conditions.


  The Sagittarius Dwarf Spheroidal galaxy (Sgr) is investigated as a target for
DM annihilation searches utilising J-factor distributions calculated directly
from a high-resolution hydrodynamic simulation of the infall and tidal
disruption of Sgr around the Milky Way. In contrast to past studies, the
simulation incorporates DM, stellar and gaseous components for both the Milky
Way and the Sgr progenitor galaxy. The simulated distributions account for
significant tidal disruption affecting the DM density profile. Our estimate of
the J-factor value for Sgr, $J_{\text{Sgr}}=1.48\times 10^{10}$ M$_\odot^2$
kpc$^{-5}$ ($6.46\times10^{16}\ \text{GeV}\ \text{cm}^{-5}$), is significantly
lower than found in prior studies. This value, while formally a lower limit, is
likely close to the true J-factor value for Sgr. It implies a DM cross-section
incompatibly large in comparison with existing constraints would be required to
attribute recently observed $\gamma$-ray emission from Sgr to DM annihilation.
We also calculate a J-factor value using a NFW profile fitted to the simulated
DM density distribution to facilitate comparison with past studies. This NFW
J-factor value supports the conclusion that most past studies have
overestimated the dark matter density of Sgr on small scales. This, together
with the fact that the Sgr has recently been shown to emit $\gamma$-rays of
astrophysical origin, complicate the use of Sgr in indirect DM detection
searches.


  Uncrewed autonomous vehicles (UAVs) have made significant contributions to
reconnaissance and surveillance missions in past US military campaigns. As the
prevalence of UAVs increases, there has also been improvements in counter-UAV
technology that makes it difficult for them to successfully obtain valuable
intelligence within an area of interest. Hence, it has become important that
modern UAVs can accomplish their missions while maximizing their chances of
survival. In this work, we specifically study the problem of identifying a
short path from a designated start to a goal, while collecting all rewards and
avoiding adversaries that move randomly on the grid. We also provide a possible
application of the framework in a military setting, that of autonomous casualty
evacuation. We present a comparison of three methods to solve this problem:
namely we implement a Deep Q-Learning model, an $\varepsilon$-greedy tabular
Q-Learning model, and an online optimization framework. Our computational
experiments, designed using simple grid-world environments with random
adversaries showcase how these approaches work and compare them in terms of
performance, accuracy, and computational time.


  The rising trend of using voice as a means of interacting with smart devices
has sparked worries over the protection of users' privacy and data security.
These concerns have become more pressing, especially after the European Union's
adoption of the General Data Protection Regulation (GDPR). The information
contained in an utterance encompasses critical personal details about the
speaker, such as their age, gender, socio-cultural origins and more. If there
is a security breach and the data is compromised, attackers may utilise the
speech data to circumvent the speaker verification systems or imitate
authorised users. Therefore, it is pertinent to anonymise the speech data
before being shared across devices, such that the source speaker of the
utterance cannot be traced. Voice conversion (VC) can be used to achieve speech
anonymisation, which involves altering the speaker's characteristics while
preserving the linguistic content.


  Surface plasmon enhanced processes and hot-carrier dynamics in plasmonic
nanostructures are of great fundamental interest to reveal light-matter
interactions at the nanoscale. Using plasmonic tunnel junctions as a platform
supporting both electrically- and optically excited localized surface plasmons,
we report a much greater (over 1000x) plasmonic light emission at upconverted
photon energies under combined electro-optical excitation, compared with
electrical or optical excitation separately. Two mechanisms compatible with the
form of the observed spectra are interactions of plasmon-induced hot carriers
and electronic anti-Stokes Raman scattering. Our measurement results are in
excellent agreement with a theoretical model combining electro-optical
generation of hot carriers through non-radiative plasmon excitation and
hot-carrier relaxation. We also discuss the challenge of distinguishing
relative contributions of hot carrier emission and the anti-Stokes electronic
Raman process. This observed increase in above-threshold emission in plasmonic
systems may open avenues in on-chip nanophotonic switching and hot carrier
photocatalysis.


  Notably innovative technologies will permit compact and affordable advanced
accelerators as the linear collider and X-ray free-electron lasers (XFELs) with
accelerating gradients over twice the value achieved with current technologies.
In particular XFEL is able to produce coherent X-ray pulses with peak
brightness 10 orders of magnitude greater than preceding approaches, which has
revolutionized numerous fields through imaging of the nanoscopic world at the
time and length scale of atom-based systems, that is of femtosecond and
Angstrom. There is a strong interest for combining these two fields, to form a
proper tool with the goal of producing a very compact XFEL in order to
investigate multi-disciplinary researches in chemistry, biology, materials
science, medicine and physics.
  In the framework of the Ultra -Compact XFEL project (UC-XFEL) under study at
the UCLA, an ultra high gradient higher harmonic RF accelerating structure for
the longitudinal space phase linearization is foreseen. To this aim, a Ka-Band
linearizer (34.2 GHz) with an integrated voltage of at least 15 MV working on
6th harmonic with respect to the main Linac frequency (5.712 GHz) is required.
We here present the electromagnetic design of a cold ultra compact Ka-band SW
linearizer, 8 cm long, working on pi mode with an ultra high accelerating
gradient (beyond 100 MV/m) and minimum surface electric field for minimizing
the probability of RF breakdown. Moreover, we discuss a TW option and compare
it with the initial SW structure, by means of main RF parameters as well as
beam-dynamics considerations. The numerical electromagnetic studies have been
performed by using the well known SuperFish, HFSS and CST.


  Collaborative robotic industrial cells are workspaces where robots
collaborate with human operators. In this context, safety is paramount, and for
that a complete perception of the space where the collaborative robot is
inserted is necessary. To ensure this, collaborative cells are equipped with a
large set of sensors of multiple modalities, covering the entire work volume.
However, the fusion of information from all these sensors requires an accurate
extrinsic calibration. The calibration of such complex systems is challenging,
due to the number of sensors and modalities, and also due to the small
overlapping fields of view between the sensors, which are positioned to capture
different viewpoints of the cell. This paper proposes a sensor to pattern
methodology that can calibrate a complex system such as a collaborative cell in
a single optimization procedure. Our methodology can tackle RGB and Depth
cameras, as well as LiDARs. Results show that our methodology is able to
accurately calibrate a collaborative cell containing three RGB cameras, a depth
camera and three 3D LiDARs.


  The purpose of this note is to provide a summary of the recent work of the
authors on two variations of the pointwise convergence problem for the
solutions to the fractional Schr\"odinger equations; convergence along a
tangential line and along a set of lines, as exhibiting some new results in
each setting. For the former case, we make a simple observation on a path along
a tangential curve of exponential order. We discuss counterexamples for the
latter case that show some of the known smooth regularities are essentially
optimal.


  Terabytes of data are collected by wind turbine manufacturers from their
fleets every day. And yet, a lack of data access and sharing impedes exploiting
the full potential of the data. We present a distributed machine learning
approach that preserves the data privacy by leaving the data on the wind
turbines while still enabling fleet-wide learning on those local data. We show
that through federated fleet-wide learning, turbines with little or no
representative training data can benefit from more accurate normal behavior
models. Customizing the global federated model to individual turbines yields
the highest fault detection accuracy in cases where the monitored target
variable is distributed heterogeneously across the fleet. We demonstrate this
for bearing temperatures, a target variable whose normal behavior can vary
widely depending on the turbine. We show that no turbine experiences a loss in
model performance from participating in the federated learning process,
resulting in superior performance of the federated learning strategy in our
case studies. The distributed learning increases the normal behavior model
training times by about a factor of ten due to increased communication overhead
and slower model convergence.


  An introductory overview of vector spaces, algebras, and linear geometries
over an arbitrary commutative field is given. Quotient spaces are emphasized
and used in constructing the exterior and the symmetric algebras of a vector
space. Affine geometries are introduced and generalized by projective
completion. General projective geometries are briefly introduced. Tensor
products and multilinear functions are treated. The exterior algebra of a
vector space and that of its dual are used in treating linear geometry and
Grassmann's regressive product is treated. Scalar product spaces,
orthogonality, and the Hodge star based on a general basis are covered.


  We sketch a tentative proof of P-completeness for the $\beta$-convertibility
problem on untyped planar (a.k.a. ordered or non-commutative) $\lambda$-terms.


  In this work we study a finite horizon optimal liquidation problem with
multiplicative price impact in algorithmic trading, using market orders. We
analyze the case when an agent is trading on a market with two financial
assets, whose difference of log-prices is modelled with a mean-reverting
process. The agent's task is to liquidate an initial position of shares of one
of the two financial assets, without having the possibility of trading the
other stock. The criterion to be optimized consists in maximising the expected
final value of the agent, with a running inventory penalty. The main result of
this paper consists in finding a classical solution of the
Hamilton-Jacobi-Bellman (HJB) equation associated to this problem, which is
proved to not coincide with the value function. However, we find the value
function as a solution to the forward-backward stochastic differential equation
(FBSDE) associated to the problem. We provide numerical tests showing that the
HJB and FBSDE solutions are close to each other and analysing performance of
the described model. We also prove a verification theorem and a comparison
principle for the viscosity solution to the HJB equation.


  The characteristic feature of the ground state configuration of the Skyrme
model description of nuclei is the absence of recognizable individual nucleons.
The ground state of the skyrmion with baryon number 2 is axially symmetric, and
is well approximated by a simple rational map, which represents a direct
generalization of Skyrme's hedgehog ansatz for the nucleon. If the Lagrangian
density is canonically quantized this configuration may support excitations
that lie close and possible below the threshold for pion decay, and therefore
describe dibaryons. The quantum corrections stabilize these solutions, the mass
density of which have the correct exponential fall off at large distances.


  A space $X$ is called a $k_{R}$-space, if $X$ is Tychonoff and the necessary
and sufficient condition for a real-valued function $f$ on $X$ to be continuous
is that the restriction of $f$ on each compact subset is continuous. In this
paper, we mainly discuss the $k_{R}$-property on the free topological groups,
and generalize some well-known results of K. Yamada's in the free topological
groups.


  The climates of terrestrial planets with a small amount of water on their
surface, called land planets, are significantly different from the climates of
planets having a large amount of surface water. Land planets have a higher
runaway greenhouse threshold than aqua planets, which extends the inner edge of
the habitable zone inward. Land planets also have the advantage of avoiding
global freezing due to drier tropics, leading to a lower planetary albedo. In
this study, we systematically investigate the complete freezing limit for
various surface water distribution using a three-dimensional dynamic
atmospheric model. As in a previous study, we found that a land planet climate
has dry tropics that result in less snow and fewer clouds. The complete
freezing limit decreases from that for aqua planets (92% S0, where S0 is
Earth's present insolation) to that for land planets (77% S0) with an
increasing dry area. Values for the complete freezing limit for zonally uniform
surface water distributions are consistently lower than those for meridionally
uniform surface water distribution. This is because the surface water
distribution in the tropics in the meridionally uniform cases causes ice-albedo
feedback until a planet lapses into the complete freezing state. For a surface
water distribution using the topographies of the terrestrial planets, the
complete freezing limit has values near those for the meridionally uniform
cases. Our results indicate that the water distribution is important for the
onset of a global ice-covered state for Earth-like exoplanets.


  In the last decade, deep learning algorithms have become very popular thanks
to the achieved performance in many machine learning and computer vision tasks.
However, most of the deep learning architectures are vulnerable to so called
adversarial examples. This questions the security of deep neural networks (DNN)
for many security- and trust-sensitive domains. The majority of the proposed
existing adversarial attacks are based on the differentiability of the DNN cost
function.Defence strategies are mostly based on machine learning and signal
processing principles that either try to detect-reject or filter out the
adversarial perturbations and completely neglect the classical cryptographic
component in the defence. In this work, we propose a new defence mechanism
based on the second Kerckhoffs's cryptographic principle which states that the
defence and classification algorithm are supposed to be known, but not the key.
To be compliant with the assumption that the attacker does not have access to
the secret key, we will primarily focus on a gray-box scenario and do not
address a white-box one. More particularly, we assume that the attacker does
not have direct access to the secret block, but (a) he completely knows the
system architecture, (b) he has access to the data used for training and
testing and (c) he can observe the output of the classifier for each given
input. We show empirically that our system is efficient against most famous
state-of-the-art attacks in black-box and gray-box scenarios.


  The prospect of informed and optimal decision-making regarding the operation
and maintenance (O&M) of structures provides impetus to the development of
structural health monitoring (SHM) systems. A probabilistic risk-based
framework for decision-making has already been proposed. However, in order to
learn the statistical models necessary for decision-making, measured data from
the structure of interest are required. Unfortunately, these data are seldom
available across the range of environmental and operational conditions
necessary to ensure good generalisation of the model.
  Recently, technologies have been developed that overcome this challenge, by
extending SHM to populations of structures, such that valuable knowledge may be
transferred between instances of structures that are sufficiently similar. This
new approach is termed population-based structural heath monitoring (PBSHM).
  The current paper presents a formal representation of populations of
structures, such that risk-based decision processes may be specified within
them. The population-based representation is an extension to the hierarchical
representation of a structure used within the probabilistic risk-based decision
framework to define fault trees. The result is a series, consisting of systems
of systems ranging from the individual component level up to an inventory of
heterogeneous populations. The current paper considers an inventory of wind
farms as a motivating example and highlights the inferences and decisions that
can be made within the hierarchical representation.


  We explore spectral properties of a Two-Component Advective Flow (TCAF)
around a neutron star. We compute the effects of thermal Comptonization of soft
photons emitted from a Keplerian disc and the boundary layer of the neutron
star by the post-shock region of a sub-Keplerian flow, formed due to the
centrifugal barrier. The shock location $X_s$ is also the inner edge of the
Keplerian disc. We compute a series of realistic spectra assuming a set of
electron temperatures of the post-shock region $T_{CE}$, the temperature of the
normal boundary layer (NBOL) $T_{NS}$ of the neutron star and the shock
location $X_s$. These parameters depend on the disc and halo accretion rates
($\dot{m_d}$ and $\dot{m_h}$, respectively) which control the resultant
spectra. We find that the spectrum becomes harder when $\dot{m}_h$ is
increased. The spectrum is controlled strongly by $T_{NS}$ due to its proximity
to the Comptonizing cloud since photons emitted from the NBOL cool down the
post-shock region very effectively. We also show the evidence of spectral
hardening as the inclination angle of the disc is increased.


  To improve the problem that the parameter identification for fuzzy neural
network has many time complexities in calculating, an improved T-S fuzzy
inference method and an parameter identification method for fuzzy neural
network are proposed. It mainly includes three parts. First, improved fuzzy
inference method based on production term for T-S Fuzzy model is explained.
Then, compared with existing Sugeno fuzzy inference based on Compositional
rules and type-distance fuzzy inference method, the proposed fuzzy inference
algorithm has a less amount of complexity in calculating and the calculating
process is simple. Next, a parameter identification method for FNN based on
production inference is proposed. Finally, the proposed method is applied for
the precipitation forecast and security situation prediction. Test results
showed that the proposed method significantly improved the effectiveness of
identification, reduced the learning order, time complexity and learning error.


  We give a recipe to generate "nonlocal" constants of motion for ODE
Lagrangian systems and we apply the method to find useful constants of motion
for dissipative system, for the Lane-Emden equation, and for the Maxwell-Bloch
system with RWA.


  Comparison of appropriate theoretical derived line ratios with observational
data can yield estimates of a plasma's physical parameters, such as electron
density or temperature. The usual practice in the calculation of the line ratio
is the assumption of excitation by electrons/protons followed by radiative
decay. Furthermore, it is normal to use the so-called coronal approximation,
i.e. one only considers ionization and recombination to and from the ground
state. A more accurate treatment is to include the ionization/recombination to
and from meta-stable levels. Here, we apply this to two lines from adjacent
ionization stages; Mg IX 368A and Mg X 625A, which has been shown to be a very
useful temperature diagnostic. At densities typical of coronal hole conditions,
the difference between the electron temperature derived assuming the zero
density limit compared with the electron density dependent
ionization/recombination is small. This however is not the case for flares
where the electron density is orders of magnitude larger. The derived
temperature for the coronal hole at solar maximum is around 1.04 MK compared to
just below 0.82 MK at solar minimum.


  Carbon nanotubes have properties depending on the arrangement of carbon atoms
on the tube walls, called chirality. Also it has been tried to grow nanotubes
of only one chirality for more than a decade it is still not possible today. A
narrowing of the distribution of chiralities, however, which is a first step
towards chirality control, has been observed for the growth of nanotubes on
catalysts composed of nickel and iron. In this paper, we have calculated
carbon-metal bond energies, adhesion energies and charge distributions of
carbon nanotube caps on Ni, Fe and NiFe alloy clusters using density functional
theory. A growth model using the calculated energies was able to reproduce the
experimental data of the nanotube growth on the alloy catalysts. The electronic
charge was found to be redistributed from the catalyst particles to the edges
of the nanotube caps in dependence of the chiral angles of the caps increasing
the reactivity of the edge atoms. Our study develops an explanation for the
chirality enrichment in the carbon nanotube growth on alloy catalyst particles.


  Consider Vlasov-Poisson system with a fixed ion background and periodic
condition on the space variables, in any dimension d\geq2. First, we show that
for general homogeneous equilibrium and any periodic x-box, within any small
neighborhood in the Sobolev space W_{x,v}^{s,p} (p>1,s<1+(1/p)) of the steady
distribution function, there exist nontrivial travelling wave solutions (BGK
waves) with arbitrary traveling speed. This implies that nonlinear Landau
damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria
and in any period box. The BGK waves constructed are one dimensional, that is,
depending only on one space variable. Higher dimensional BGK waves are shown to
not exist. Second, for homogeneous equilibria satisfying Penrose's linear
stability condition, we prove that there exist no nontrivial invariant
structures in the (1+|v|^{2})^{b}-weighted H_{x,v}^{s} (b>((d-1)/4), s>(3/2))
neighborhood. Since arbitrarilly small BGK waves can also be constructed near
any homogeneous equilibria in such weighted H_{x,v}^{s} (s<(3/2)) norm, this
shows that s=(3/2) is the critical regularity for the existence of nontrivial
invariant structures near stable homogeneous equilibria. These generalize our
previous results in the one dimensional case.


  Any successful model of dark matter must explain the diversity of observed
Milky Way (MW) satellite density profiles, from very dense ultrafaints to
large, low density satellites such as Crater~II that appear to be larger their
anticipated host dark matter haloes. We consider cold dark matter (CDM), warm
dark matter (WDM, 3.3keV thermal relic power spectrum), and a self-interacting
dark matter model (SIDM) that induces gravothermal collapse in low mass
subhaloes. Predictions for these density profiles are complicated by the
limitations of simulation resolution in the stripping of subhaloes by the MW
system, therefore we make predictions for satellite properties in these three
models using $N$-body simulations combined with a semi-analytic halo stripping
algorithm. We find that most CDM and WDM subhaloes of mass $>10^{8}$$M_{\odot}$
are large enough after stripping to fit most satellites; however, the required
amount of stripping often requires a stronger tidal field than is available on
the subhalo's orbit. The lower concentrations of WDM subhaloes enable this
model to explain the required satellite masses with less stripping than is
necessary for CDM, and is thus consistent with orbits of larger pericentres.
SIDM cores offer the best fits to massive, low density satellites at the
expense of predicting many $>10^{9}$$M_{\odot}$ subhaloes to host low density
satellites with no observed analogue. We conclude that an SIDM model must have
a very high velocity-dependent cross-section in order to match all satellites,
and that WDM offers a marginally better fit than CDM to the MW satellite mass
function.


  In the Local Group spiral galaxy M33, we investigate the correlation between
the star formation rate (SFR) surface density, Sigma_SFR, and the gas density
Sigma_gas (molecular, atomic, and total). We also explore whether there are
other physical quantities, such as the hydrostatic pressure and dust optical
depth, which establish a good correlation with Sigma_SFR. We use the Ha,
far-ultraviolet (FUV), and bolometric emission maps to infer the SFR locally at
different spatial scales, and in radial bins using azimuthally averaged values.
Most of the local analysis is done using the highest spatial resolution allowed
by gas surveys, 180 pc. The Kennicutt-Schmidt (KS) law, Sigma_SFR \propto
(Sigma_gas)^n is analyzed by three statistical methods. At all spatial scales,
with Ha emission as a SFR tracer, the KS indices n are always steeper than
those derived with the FUV and bolometric emissions. We attribute this to the
lack of Ha emission in low luminosity regions where most stars form in small
clusters with an incomplete initial mass function at their high mass end. For
azimuthally averaged values the depletion timescale for the molecular gas is
constant, and the KS index is n_H2 = 1.1 +- 0.1. Locally, at a spatial
resolution of 180 pc, the correlation between Sigma_SFR and Sigma_gas is
generally poor, even though it is tighter with the molecular and total gas than
with the atomic gas alone. Considering only positions where the CO J=1-0 line
is above the 2-sigma detection threshold and taking into account uncertainties
in Sigma_H2 and Sigma_SFR, we obtain a steeper KS index than obtained with
radial averages: n_H2 = 2.22 +- 0.07 (for FUV and bolometric SFR tracers),
flatter than that relative to the total gas (n_Htot = 2.59 +- 0.05). [abridged]


  We study the energy-landscape network of Lennard-Jones clusters as a model of
a glass forming system. We find the stable basins and the first order saddles
connecting them, and identify them with the network nodes and links,
respectively. We analyze the network properties and model the system's
evolution. Using the model, we explore the system's response to varying cooling
rates, and reproduce many of the glass transition properties. We also find that
the static network structure gives rise to a critical temperature where a
percolation transition breaks down the space of configurations into
disconnected components. Finally, we discuss the possibility of studying the
system mathematically with a trap-model generalized to networks.


  We introduce a modification of Perron's method, where semi-solutions are
considered in a carefully defined asymptotic sense. With this definition, we
can show, in a rather elementary way, that in a zero-sum game or a control
problem (with or without model uncertainty), the value function over all
strategies coincides with the value function over Markov strategies discretized
in time. Therefore, there are always discretized Markov $\varepsilon$-optimal
strategies, (uniform with respect to the bounded initial condition). With a
minor modification, the method produces a value and approximate saddle points
for an asymmetric game of feedback strategies vs. counter-strategies.


  Expected duality and approximation properties are shown to fail on Bergman
spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an
operator satisfying certain mapping properties, positive duality and
approximation results are proved. Such operators are constructed on generalized
Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of
Laurent series of Bergman functions is shown. This extends a classical result
on Hardy spaces of the unit disc.


  In this article, we have introdued D-fuzzy sets. We have discussed the
notions of inclusion, union, intersection, complementation and convexity of
such D-fuzzy sets. Also we have proved separation theorem of convex D-fuzzy
sets.


  Visual tracking addresses the problem of identifying and localizing an
unknown target in a video given the target specified by a bounding box in the
first frame. In this paper, we propose a dual network to better utilize
features among layers for visual tracking. It is observed that features in
higher layers encode semantic context while its counterparts in lower layers
are sensitive to discriminative appearance. Thus we exploit the hierarchical
features in different layers of a deep model and design a dual structure to
obtain better feature representation from various streams, which is rarely
investigated in previous work. To highlight geometric contours of the target,
we integrate the hierarchical feature maps with an edge detector as the coarse
prior maps to further embed local details around the target. To leverage the
robustness of our dual network, we train it with random patches measuring the
similarities between the network activation and target appearance, which serves
as a regularization to enforce the dual network to focus on target object. The
proposed dual network is updated online in a unique manner based on the
observation that the target being tracked in consecutive frames should share
more similar feature representations than those in the surrounding background.
It is also found that for a target object, the prior maps can help further
enhance performance by passing message into the output maps of the dual
network. Therefore, an independent component analysis with reference algorithm
(ICA-R) is employed to extract target context using prior maps as guidance.
Online tracking is conducted by maximizing the posterior estimate on the final
maps with stochastic and periodic update. Quantitative and qualitative
evaluations on two large-scale benchmark data sets show that the proposed
algorithm performs favourably against the state-of-the-arts.


  Understanding video content and generating caption with context is an
important and challenging task. Unlike prior methods that typically attempt to
generate generic video captions without context, our architecture
contextualizes captioning by infusing extracted information from relevant text
data. We propose an end-to-end sequence-to-sequence model which generates video
captions based on visual input, and mines relevant knowledge such as names and
locations from contextual text. In contrast to previous approaches, we do not
preprocess the text further, and let the model directly learn to attend over
it. Guided by the visual input, the model is able to copy words from the
contextual text via a pointer-generator network, allowing to produce more
specific video captions. We show competitive performance on the News Video
Dataset and, through ablation studies, validate the efficacy of contextual
video captioning as well as individual design choices in our model
architecture.


  The correlation function of the trajectory exactly at the Feigenbaum point of
the logistic map is investigated and checked by numerical experiments. Taking
advantage of recent closed analytical results on the symbol-to-symbol
correlation function of the generating partition, we are in position to justify
the deep algorithmic structure of the correlation function apart from numerical
constants. A generalization is given for arbitrary $m\cdot 2^{\infty}$
Feigenbaum attractors.


  We perform a suite of two- and three-dimensional magnetohydrodynamic (MHD)
simulations with the Athena code of the non-driven Kelvin-Helmholtz instability
in the subsonic, weak magnetic field limit. Focusing the analysis on the
non-linear turbulent regime, we quantify energy transfer on a scale-by-scale
basis and identify the physical mechanisms responsible for energy exchange by
developing the diagnostic known as spectral energy transfer function analysis.
At late times when the fluid is in a state of MHD turbulence, magnetic tension
mediates the dominant mode of energy injection into the magnetic reservoir,
whereby turbulent fluid motions twist and stretch the magnetic field lines.
This generated magnetic energy turbulently cascades to smaller scales, while
being exchanged backwards and forwards with the kinetic energy reservoir, until
finally being dissipated. Incorporating explicit dissipation pushes the
dissipation scale to larger scales than if the dissipation were entirely
numerical. For scales larger than the dissipation scale, we show that the
physics of energy transfer in decaying MHD turbulence is robust to numerical
effects.


  The dichromatic number $\vec{\chi}(D)$ of a digraph $D$ is the minimum number
of colours needed to colour the vertices of a digraph such that each colour
class induces an acyclic subdigraph. A digraph $D$ is $k$-dicritical if
$\vec{\chi}(D) = k$ and each proper subdigraph $H$ of $D$ satisfies
$\vec{\chi}(H) < k$.
  For integers $k$ and $n$, we define $d_k(n)$ (respectively $o_k(n)$) as the
minimum number of arcs possible in a $k$-dicritical digraph (respectively
oriented graph). Kostochka and Stiebitz have shown that $d_4(n) \geq
\frac{10}{3}n -\frac{4}{3}$. They also conjectured that there is a constant $c$
such that $o_k(n) \geq cd_k(n)$ for $k\geq 3$ and $n$ large enough. This
conjecture is known to be true for $k=3$ (Aboulker et al.).
  In this work, we prove that every $4$-dicritical oriented graph on $n$
vertices has at least $(\frac{10}{3}+\frac{1}{51})n-1$ arcs, showing the
conjecture for $k=4$. We also characterise exactly the $k$-dicritical digraphs
on $n$ vertices with exactly $\frac{10}{3}n -\frac{4}{3}$ arcs.


  We suggest theoretical explanation of the high upper critical magnetic field,
perpendicular to conducting chains, Hc2, experimentally observed in the
superconductor (TMTSF)2ClO4, in terms of singlet superconducting pairing. In
particular, we compare the results of d-wave-like nodal, d-wave-like node-less,
and s-wave scenarios of superconductivity. We show that, in d-wave-like nodal
scenario, superconductivity can naturally exceed both the orbital upper
critical magnetic field and Clogston-Shandrasekhar paramagnetic limit as well
as reach experimental value, Hc2 = 6T, in contrast to d-wave-like node-less and
s-wave scenarios. In our opinion, the obtained results are strongly in favor of
d-wave-like nodal superconductivity in (TMTSF)2ClO4, whereas, in a sister
compound, (TMTSF)2PF6, we expect either the existence of triplet order
parameter or the coexistence of triplet and singlet order parameters.


  We present a conceptually simple and intuitive method to calculate and to
measure the dissimilarities among 2D shapes. Several methods to interpret and
to visualize the resulting dissimilarity matrix are presented and compared.


  Collisionless plasma shocks are efficient sources of non-thermal particle
acceleration in space and astrophysical systems. We use hybrid (kinetic ions --
fluid electrons) simulations to examine the non-linear feedback of the
self-generated energetic particles (cosmic rays, CRs) on the shock
hydrodynamics. When CR acceleration is efficient, we find evidence of both an
upstream precursor, where the inflowing plasma is compressed and heated, and a
downstream postcursor, where the energy flux in CRs and amplified magnetic
fields play a dynamical role. For the first time, we assess how non-linear
magnetic fluctuations in the postcursor preferentially travel away from the
shock at roughly the local Alfv\'en speed with respect to the downstream
plasma. The drift of both magnetic and CR energy with respect to the thermal
plasma substantially increases the shock compression ratio with respect to the
standard prediction, in particular exceeding 4 for strong shocks. Such
modifications also have implications for the spectrum of the particles
accelerated via diffusive shock acceleration, a significant result detailed in
a companion paper, Caprioli, Haggerty & Blasi 2020, arXiv:2009.00007
[astro-ph.HE].


  Instruction-Level Redundancy (ILR) is a well-known approach to tolerate
transient CPU faults. It replicates instructions in a program and inserts
periodic checks to detect and correct CPU faults using majority voting, which
essentially requires three copies of each instruction and leads to high
performance overheads. As SIMD technology can operate simultaneously on several
copies of the data, it appears to be a good candidate for decreasing these
overheads. To verify this hypothesis, we propose Elzar, a compiler framework
that transforms unmodified multithreaded applications to support triple modular
redundancy using Intel AVX extensions for vectorization. Our experience with
several benchmark suites and real-world case-studies yields mixed results:
while SIMD may be beneficial for some workloads, e.g., CPU-intensive ones with
many floating-point operations, it exhibits higher overhead than ILR in many
applications we tested. We study the sources of overheads and discuss possible
improvements to Intel AVX that would lead to better performance.


  In this paper, we study Lusztig's $a$-function for a Coxeter group with
unequal parameters. We determine that function explicitly in the ``asymptotic
case'' in type $B_n$, where the left cells have been determined in terms of a
generalized Robinson--Schensted correspondence by Bonnaf\'e and the second
author. As a consequence, we can also show that all of Lusztig's conjectural
properties (P1)--(P15) hold in this case, except possibly (P9), (P10) and
(P15). Our methods rely on the ``leading matrix coefficients'' introduced by
the first author. We also interprete the ideal structure defined by the
two-sided cells in the associated Iwahori--Hecke algebra $\bH_n$ in terms of
the Dipper--james--Murphy basis of $\bH_n$.


  Obtaining the state of the art performance of deep learning models imposes a
high cost to model generators, due to the tedious data preparation and the
substantial processing requirements. To protect the model from unauthorized
re-distribution, watermarking approaches have been introduced in the past
couple of years. We investigate the robustness and reliability of
state-of-the-art deep neural network watermarking schemes. We focus on
backdoor-based watermarking and propose two -- a black-box and a white-box --
attacks that remove the watermark. Our black-box attack steals the model and
removes the watermark with minimum requirements; it just relies on public
unlabeled data and a black-box access to the classification label. It does not
need classification confidences or access to the model's sensitive information
such as the training data set, the trigger set or the model parameters. The
white-box attack, proposes an efficient watermark removal when the parameters
of the marked model are available; our white-box attack does not require access
to the labeled data or the trigger set and improves the runtime of the
black-box attack up to seventeen times. We as well prove the security
inadequacy of the backdoor-based watermarking in keeping the watermark
undetectable by proposing an attack that detects whether a model contains a
watermark. Our attacks show that a recipient of a marked model can remove a
backdoor-based watermark with significantly less effort than training a new
model and some other techniques are needed to protect against re-distribution
by a motivated attacker.


  We demonstrate that the blocks of a profinite group whose defect groups are
cyclic have a Brauer tree algebra structure analogous to the case of finite
groups. We show further that the Brauer tree of a block with defect group
$\mathbb{Z}_{p}$ is of star type.


  We characterize the electron doping evolution of
(Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ by means of angle-resolved photoemission.
Concomitant with the metal insulator transition around $x\approx0.05$ we find
the emergence of coherent quasiparticle states forming a closed small Fermi
surface of volume $3x/2$, where $x$ is the independently measured La
concentration. The quasiparticle weight $Z$ remains large along the entire
Fermi surface, consistent with the moderate renormalization of the low-energy
dispersion. This indicates a conventional, weakly correlated Fermi liquid state
with a momentum independent residue $Z\approx0.5$ in lightly doped
Sr$_3$Ir$_2$O$_7&.


  While the search of high Tc superconductivity was driven mostly by trial and
error methodology searching for novel materials, here we provide a
quasi-first-principle quantum theory for engineering superconductivity in
artificial high-Tc superlattices (AHTS) with period d, ranging from 5.28 down
to 3 nanometers, made of superconducting quantum wells of variable thickness L.
An important feature of our quantum design is the key role of the interface
internal electric field giving Rashba spin-orbit coupling (SOC) in the
nanoscale quantum superconducting building blocks. By tuning the geometrical
conformational parameter L/d around its magic ratio 2/3 we predict the
superconducting dome of Tc versus doping characteristic of unconventional
superconductors. Quantum size effects, controlled by L/d, change the energy
width and splitting of two quantum subbands formed by the electronic space
charge confined in superconducting nano-layers. The theoretical superconducting
dome Tc versus charge density controlled by the Fano-Feshbach resonance between
two superconducting gaps has been able to predict experimental results on
cuprate AHTS by tuning the geometry of superlattices of quantum wells made of
superconducting layers (S) of thickness L of modulation doped stoichiometric
Mott insulator La2CuO4 with no chemical dopants, with interface space charge
confined within normal metal (N) overdoped cuprate layers


  Collisionless shocks and plasma turbulence are crucial ingredients for a
broad range of astrophysical systems. The shock-turbulence interaction, and in
particular the transmission of fully developed turbulence across the
quasi-perpendicular Earth's bow shock, is here addressed using a combination of
spacecraft observations and local numerical simulations. An alignment between
the Wind (upstream) and MMS (downstream) spacecraft is used to study the
transmission of turbulent structures across the shock, revealing an increase of
their magnetic helicity content in its downstream. Local kinetic simulations,
in which the dynamics of turbulent structures is followed through their
transmission across a perpendicular shock, confirm this scenario, revealing
that the observed magnetic helicity increase is associated with the compression
of turbulent structures at the shock front.


  The parallel algorithm for loading large sparse matrices from files into
distributed memories of high performance computing (HPC) systems is presented.
This algorithm was designed specially for matrices stored in files in the
space-effcient adaptive-blocking hierarchical storage format (ABHSF). The
algorithm can be used even if matrix storing and loading procedures use a
different number of processes, different matrix-processes mapping, or different
in-memory storage format. The file format based on the utilization of the HDF5
library is described as well. Finally, the presented experimental study
evaluates the proposed algorithm empirically.


  We study suspensions of rigid particles in a plane Couette flow with
deformable elastic walls. We find that, in the limit of vanishing inertia, the
elastic walls induce shear thinning of the suspension flow such that the
effective viscosity decreases as the wall deformability increases. This
shear-thinning behavior originates from the interactions between rigid
particles, soft wall and carrier fluid; an asymmetric wall deformation induces
a net lift force acting on the particles which therefore migrate towards the
bulk of the channel. Based on our observations, we provide a closure for the
suspension viscosity which can be used to model the rheology of suspensions
with arbitrary volume fraction in elastic channels.


  Dependence of photo-induced FMR (phi-FMR) on incident angle of excitation and
probing laser beams has been studied in a [Co (dCo = 0.78 nm) / Pd (dPd = 0.81
nm) ]5 multi-layer film with the aim to find experimentally the limitation of
inducement and detection of magnetization dynamics with oblique light
incidence. We have found, in the experiments changing the incident angle of a
pump beam, that phi-FMR is observed up to the grazing incident angle of 88
degrees with p-polarized excitation pulses, whereas it disappears at the
incidence angle of around 65 degrees with s-polarized excitation. As for the
experiments changing the incident angle of a probe beam, phi-FMR disappears at
the incidence angle of 65 degrees for both s- and p-polarizations, whereas it
reappears with further increasing the angle for the p-polarization and vanishes
at 75 degrees.


  We analyze the convergence rates to a planar interface in the Mullins-Sekerka
model by applying a relaxation method based on relationships among distance,
energy, and dissipation. The relaxation method was developed by two of the
authors in the context of the 1-d Cahn-Hilliard equation and the current work
represents an extension to a higher dimensional problem in which the curvature
of the interface plays an important role. The convergence rates obtained are
optimal given the assumptions on the initial data.


  We explore the possibility of three phases in the core of neutron star in a
form of triple layers. From the center, strange quark matter, kaon condensed
nuclear matter and nuclear matter form a triple layer. We discuss how the phase
of strange quark matter is smoothly connected to kaon condensed nuclear matter
phase. We also demonstrate that the compact star with triple layered structure
can be a model compatible with the 1.97-solar-mass object PSR J1614-2230
recently observed.


  The concept of category from mathematics happens to be useful to computer
programmers in many ways. Unfortunately, all "good" explanations of categories
so far have been designed by mathematicians, or at least theoreticians with a
strong background in mathematics, and this makes categories especially
inscrutable to external audiences. More specifically, the common explanatory
route to approach categories is usually: "here is a formal specification of
what a category is; then look at these known things from maths and theoretical
computer science, and admire how they can be described using the notions of
category theory." This approach is only successful if the audience can fully
understand a conceptual object using only its formal specification. In
practice, quite a few people only adopt conceptual objects by abstracting from
two or more contexts where the concepts are applicable, instead. This is the
road taken below: reconstruct the abstractions from category theory using
scratches of understanding from various fields of computer engineering.


  We consider compressive imaging problems, where images are reconstructed from
a reduced number of linear measurements. Our objective is to improve over
existing compressive imaging algorithms in terms of both reconstruction error
and runtime. To pursue our objective, we propose compressive imaging algorithms
that employ the approximate message passing (AMP) framework. AMP is an
iterative signal reconstruction algorithm that performs scalar denoising at
each iteration; in order for AMP to reconstruct the original input signal well,
a good denoiser must be used. We apply two wavelet based image denoisers within
AMP. The first denoiser is the "amplitude-scaleinvariant Bayes estimator"
(ABE), and the second is an adaptive Wiener filter; we call our AMP based
algorithms for compressive imaging AMP-ABE and AMP-Wiener. Numerical results
show that both AMP-ABE and AMP-Wiener significantly improve over the state of
the art in terms of runtime. In terms of reconstruction quality, AMP-Wiener
offers lower mean square error (MSE) than existing compressive imaging
algorithms. In contrast, AMP-ABE has higher MSE, because ABE does not denoise
as well as the adaptive Wiener filter.


  The Isabelle/HOL proof assistant has a powerful library for continuous
analysis, which provides the foundation for verification of hybrid systems.
However, Isabelle lacks automated proof support for continuous artifacts, which
means that verification is often manual. In contrast, Computer Algebra Systems
(CAS), such as Mathematica and SageMath, contain a wealth of efficient
algorithms for matrices, differential equations, and other related artifacts.
Nevertheless, these algorithms are not verified, and thus their outputs cannot,
of themselves, be trusted for use in a safety critical system. In this paper we
integrate two CAS systems into Isabelle, with the aim of certifying symbolic
solutions to ordinary differential equations. This supports a verification
technique that is both automated and trustworthy.


  We propose a new metric between probability measures on a compact metric
space that mirrors the Riemannian manifold-like structure of quadratic optimal
transport but includes entropic regularization. Its metric tensor is given by
the Hessian of the Sinkhorn divergence, a debiased variant of entropic optimal
transport. We precisely identify the tangent space it induces, which turns out
to be related to a Reproducing Kernel Hilbert Space (RKHS). As usual in
Riemannian geometry, the distance is built by looking for shortest paths. We
prove that our distance is geodesic, metrizes the weak-star topology, and is
equivalent to a RKHS norm. Still it retains the geometric flavor of optimal
transport: as a paradigmatic example, translations are geodesics for the
quadratic cost on $\mathbb{R}^d$. We also show two negative results on the
Sinkhorn divergence that may be of independent interest: that it is not jointly
convex, and that its square root is not a distance because it fails to satisfy
the triangle inequality.


  We prove that in the polynomial ring $Q=\mathsf{k}[x,y,z,w]$, with
$\mathsf{k}$ an algebraically closed field of characteristic zero, all
Gorenstein homogeneous ideals $I$ such that $(x,y,z,w)^4\subseteq I \subseteq
(x,y,z,w)^2$ can be obtained by \emph{doubling} from a grade three perfect
ideal $J\subset I$ such that $Q/J$ is a locally Gorenstein ring. Moreover, a
graded minimal free resolution of the $Q$-module $Q/I$ can be completely
described in terms of a graded minimal free resolution of the $Q$-module $Q/J$
and a homogeneous embedding of a shift of the canonical module $\omega_{Q/J}$
into $Q/J$.


  Motivated by the first observation of the double-charm tetraquark
$T_{cc}^+(3875)$ by the LHCb Collaboration, we investigate the nature of
$T_{cc}^+$ as an isoscalar $DD^*$ hadronic molecule in a meson-exchange
potential model incorporated by the coupled-channel effects and three-body
unitarity. The $D^0D^0\pi^+$ invariant mass spectrum can be well-described and
the $T_{cc}^+$ pole structure can be precisely extracted. Under the hypothesis
that the interactions between the heavy flavor hadrons can be saturated by the
light meson-exchange potentials, the near-threshold dynamics of $T_{cc}^+$ can
shed light on the binding of its heavy-quark spin symmetry (HQSS) partner
$D^*D^*$ ($I=0$) and on the nature of other heavy hadronic molecule candidates
such as $X(3872)$ and $Z_c(3900)$ in the charmed-anticharmed systems. The
latter states can be related to $T_{cc}^+$ in the meson-exchange potential
model with limited assumptions based on the SU(3) flavor symmetry relations.
The combined analysis, on the one hand, indicates the HQSS breaking effects
among those HQSS partners, and on the other hand, highlights the role played by
the short and long-distance dynamics for the near threshold $D^{(*)}D^{(*)}$
and $D^{(*)}\bar{D}^{(*)}+c.c.$ systems.


  We present a method for performing atomistic spin dynamic simulations. A
comprehensive summary of all pertinent details for performing the simulations
such as equations of motions, models for including temperature, methods of
extracting data and numerical schemes for performing the simulations is given.
The method can be applied in a first principles mode, where all interatomic
exchange is calculated self-consistently, or it can be applied with frozen
parameters estimated from experiments or calculated for a fixed
spin-configuration. Areas of potential applications to different magnetic
questions are also discussed. The method is finally applied to one situation
where the macrospin model breaks down; magnetic switching in ultra strong
fields.


  The magnetic and electronic properties of metal phthalocyanines (MPc) and
fluorinated metal phthalocyanines (F$_{16}$MPc) are studied by means of spin
density functional theory (SDFT). Several metals (M) such as Ca, all first
d-row transition metals and Ag are investigated. By considering different open
shell transition metals it is possible to tune the electronic properties of
MPc, in particular the electronic molecular gap and total magnetic moment.
Besides assigning the structural and electronic properties of MPc and
F$_{16}$MPc, the vibrational modes analysis of the ScPc\textendash ZnPc series
have been studied and correlated to experimental measurements when available.


  Four-dimensional conformal fishnet theory is an integrable scalar theory
which arises as a double scaling limit of $\gamma$-deformed maximally
supersymmetric Yang-Mills. We give a perturbative reformulation of
$\gamma$-deformed super-Yang-Mills theory in twistor space, and implement the
double scaling limit to obtain a twistor description of conformal fishnet
theory. The conformal fishnet theory retains an abelian gauge symmetry on
twistor space which is absent in space-time, allowing us to obtain
cohomological formulae for scattering amplitudes that manifest conformal
invariance. We study various classes of scattering amplitudes in twistor space
with this formalism.


  We define a divisorial motivic zeta function for stable curves with marked
points which agrees with Kapranov's motivic zeta function when the curve is
smooth and unmarked. We show that this zeta function is rational, and give a
formula in terms of the dual graph of the curve.


  A first order differential equation with a periodic operator coefficient
acting in a pair of Hilbert spaces is considered. This setting models both
elliptic equations with periodic coefficients in a cylinder and parabolic
equations with time periodic coefficients. Our main results are a construction
of a pointwise projector and a spectral splitting of the system into a finite
dimensional system of ordinary differential equations with constant
coefficients and an infinite dimensional part whose solutions have better
properties in a certain sense. This complements the well-known asymptotic
results for periodic hypoelliptic problems in cylinders (Kuchment) and for
elliptic problems in quasicylinders (Nazarov).
  As an application we give a center manifold reduction for a class of
non-linear ordinary differential equations in Hilbert spaces with periodic
coefficients. This result generalizes the known case with constant coefficients
(Mielke).


  We review various derivations of the partition function of the
two-dimensional Ising Model of ferromagnetism and proofs of the stability of
matter, paying attention to passages where there would appear to be a lacuna
between steps or where the structure of the argument is not so straightforward.
Authors cannot include all the intermediate steps, but sometimes most readers
and especially students will be mystified by such a transition. Moreover,
careful consideration of such lacunae points to interesting physics and not
only mathematical technology. Also, when reading the original papers, the
structure of the physics argument may be buried by the technical moves.
Improvements in the derivations, in subsequent papers by others, may well be
clearer and more motivated. But, there is remarkably little written and
published about how to read some of the original papers, and the subsequent
ones, yet students and their teachers would often benefit from such guidance. I
should note that much of the discussion below will benefit from having those
papers in front of you.


  It is shown that the neutron matter interacting through Argonne V18
pair-potential plus modern variants of Urbana or Illinois three-body forces is
unstable. For the energy of $N$ neutrons $E(N)$, which interact through these
forces, we prove mathematically that $E(N) = -cN^3 + \mathcal{O}(N^{8/3})$,
where $c>0$ is a constant. This means that: (i) the energy per particle and
neutron density diverge rapidly for large neutron numbers; (ii) bound states of
$N$ neutrons exist for $N$ large enough. The neutron matter collapse is
possible due to the form of the repulsive core in three-body forces, which
vanishes when three nucleons occupy the same site in space. The old variant of
the forces Urbana VI, where the phenomenological repulsive core does not vanish
at the origin, resolves this problem. We prove that to prevent the collapse one
should add a repulsive term to the Urbana IX potential, which should be larger
than 50 MeV when 3 nucleons occupy the same spatial position.


  Dirichlet p-branes in the background of pp waves are constructed using the
massive Green-Schwarz worldsheet action for open strings. These branes are
localized at the origin and only for $p=7, 5, 3$ preserve half the
supersymmetries. The spectrum of the brane theory is analyzed and is found to
be in agreement with the spectrum of the small fluctuations of the world-volume
super Yang-Mills theory in this background. These branes are expected to
correspond to objects that are nonperturbative in $N$ in the dual gauge theory.


  We express the heavy quark diffusion coefficient as the temporal variation of
a Wilson line along the Schwinger-Keldysh contour. This generalizes the
classical formula for diffusion as a force-force correlator to a non-abelian
theory. We use this formula to compute the diffusion coefficient in strongly
coupled $\N=4$ Yang-Mills by studying the fluctuations of a string in
$AdS_5\times S_5$. The string solution spans the full Kruskal plane and gives
access to contour correlations. The diffusion coefficient is
$D=2/\sqrt{\lambda} \pi T$ and is therefore parametrically smaller than
momentum diffusion, $\eta/(e+p)=1/4\pi T$. The quark mass must be much greater
than $T\sqrt{\lambda}$ in order to treat the quark as a heavy quasi-particle.
The result is discussed in the context of the RHIC experiments.


  Local operations with classical communication (LOCC) and separable operations
are two classes of quantum operations that play key roles in the study of
quantum entanglement. Separable operations are strictly more powerful than
LOCC, but no simple explanation of this phenomenon is known. We show that, in
the case of von Neumann measurements, the ability to interpolate measurements
is an operational principle that sets apart LOCC and separable operations.


  This note shows a property of degree-parity preservation for $K$-types under
Howe's theta correspondence. As its application, we deduce the preservation of
parity of all $K$-types occurring in an arbitrary irreducible
$(\mathfrak{g},K)$-module of any Lie group in reductive dual pairs.


  Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the
Painlev\'e equation is equal to the series of $c=1$ Virasoro conformal blocks.
We study similar series of $c=-2$ conformal blocks and relate it to Painlev\'e
theory. The arguments are based on Nakajima-Yoshioka blowup relations on
Nekrasov partition functions. We also study series of $q$-deformed $c=-2$
conformal blocks and relate it to $q$-Painlev\'e equation. As an application,
we prove formula for the tau function of $q$-Painlev\'e $A_7^{(1)'}$ equation.


  A central question in verification is characterizing when a system has
invariants of a certain form, and then synthesizing them. We say a system has a
$k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear
(non-strict) inequalities -- equivalently, an intersection of $k$ (closed) half
spaces -- as an invariant. We present a sufficient condition -- solely in terms
of eigenvalues of the $A$-matrix -- for an $n$-dimensional linear dynamical
system to have a $k$-LI. Our proof of sufficiency is constructive, and we get a
procedure that computes a $k$-LI if the condition holds. We also present a
necessary condition, together with many example linear systems where either the
sufficient condition, or the necessary is tight, and which show that the gap
between the conditions is not easy to overcome. In practice, the gap implies
that using our procedure, we synthesize $k$-LI for a larger value of $k$ than
what might be necessary. Our result enables analysis of continuous and hybrid
systems with linear dynamics in their modes solely using reasoning in the
theory of linear arithmetic (polygons), without needing reasoning over
nonlinear arithmetic (ellipsoids).


  A detailed spectroscopic study, from lambda 3700 A to 1 um, was performed for
a sample of 34 HII galaxies in order to derive fundamental parameters for their
HII regions and ionizing sources, as well as gaseous metal abundances. All the
spectra included the nebular [SIII]9069,9532 A lines, given their importance in
the derivation of the S/H abundance and relevant ionization diagnostics. A
systematic method was followed to correct the near-IR [SIII] line fluxes for
the effects of the atmospheric transmission.A comparative analysis of the
predictions of the empirical abundance indicators R23 and S23 has been
performed. The relative hardness of their ionizing sources was studied using
the eta parameter, and exploring the role played by metallicity. For 22
galaxies of the sample a direct value of te[SIII] was derived, along with their
ionic and total S/H abundances. Their ionic and total O/H abundances were
derived using direct determinations of te[OIII].For the rest of the objects,
the total S/H abundance was derived using S23. The abundance range covered by
our sample goes from 1/20 solar up to solar metallicity. The mean S/O ratio
derived is log (S/O)=-1.68+/-0.20 dex, 1 sigma below the solar S/O value. The
S/O abundance ratio shows no significant trend with O/H over the range of
abundance covered in this work, in agreement with previous findings.There is a
trend for HII galaxies with lower gaseous metallicity to present harder
ionizing spectra. We compared the distribution of the ionic ratios O+/O++ vs.
S+/S++ derived for our sample with the predictions of a grid of photoionization
models performed for different stellar effective temperatures. This analysis
indicates that a large fraction of galaxies in our sample seem to be ionized by
extremely hard spectra.


  Unmanned aerial vehicle (UAV) has recently attracted a lot of attention as a
candidate to meet the 6G ubiquitous connectivity demand and boost the
resiliency of terrestrial networks. Thanks to the high spectral efficiency and
low latency, non-orthogonal multiple access (NOMA) is a potential access
technique for future communication networks. In this paper, we propose to use
the UAV as a moving base station (BS) to serve multiple users using NOMA and
jointly solve for the 3D-UAV placement and resource allocation problem. Since
the corresponding optimization problem is non-convex, we rely on the recent
advances in artificial intelligence (AI) and propose AdaptSky, a deep
reinforcement learning (DRL)-based framework, to efficiently solve it. To the
best of our knowledge, AdaptSky is the first framework that optimizes NOMA
power allocation jointly with 3D-UAV placement using both sub-6GHz and
millimeter wave mmWave spectrum. Furthermore, for the first time in NOMA-UAV
networks, AdaptSky integrates the dueling network (DN) architecture to the DRL
technique to improve its learning capabilities. Our findings show that AdaptSky
does not only exhibit a fast-adapting learning and outperform the
state-of-the-art baseline approach in data rate and fairness, but also it
generalizes very well. The AdaptSky source code is accessible to use here:
https://github.com/Fouzibenfaid/AdaptSky


  The thin films of lead free magneto-electric compound AlFeO3 have been
deposited using pulsed laser deposition technique. X-ray diffraction, X-ray
absorption spectroscopy and reflectivity measurements established the
orthorhombic structure and material density of 4.5g/cc which is comparable with
bulk AlFeO3. The Raman mode corresponding to AlFeO3 was found to vanish when
magnetic field of 800 Oe was applied at room temperature. Additionally, it was
observed that the Raman phonon mode present at the room temperature becomes
invisible in the temperature window of 280K-236K and reappears below it. The
detailed analysis of magnetization showed a change in magnetic order in this
temperature interval. The invisibility of Raman phonon mode corresponding to
AlFeO3 have been attributed to the lattice deformation caused by the
magnetoelastic effect. The presence of strong spin-lattice coupling is also
validated by the renormalization of phonon frequencies below 200 K.


  Molecular signalling in living cells occurs at low copy numbers and is
thereby inherently limited by the noise imposed by thermal diffusion. The
precision at which biochemical receptors can count signalling molecules is
intimately related to the noise correlation time. In addition to passive
thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can
transiently bind to molecular motors and are actively transported across
biological cells. Active transport is most beneficial when trafficking occurs
over large distances, for instance up to the order of 1 metre in neurons. Here
we explain how intermittent active transport allows for faster equilibration
upon a change in concentration triggered by biochemical stimuli. Moreover, we
show how intermittent active excursions induce qualitative changes in the noise
in effectively one-dimensional systems such as dendrites. Thereby they allow
for significantly improved signalling precision in the sense of a smaller
relative deviation in the concentration read-out by the receptor. On the basis
of linear response theory we derive the exact mean field precision limit for
counting actively transported molecules. We explain how intermittent active
excursions disrupt the recurrence in the molecular motion, thereby facilitating
improved signalling accuracy. Our results provide a deeper understanding of how
recurrence affects molecular signalling precision in biological cells and novel
diagnostic devices.


  We explicitly find the minima as well as the minimum points of the geodesic
length functions for the family of filling (hence non-simple) closed curves,
$a^2b^n$ ($n\ge 3$), on a complete one-holed hyperbolic torus in its relative
Teichm\"uller space, where $a, b$ are simple closed curves on the one-holed
torus which intersect exactly once transversely. This provides concrete
examples for the problem to minimize the geodesic length of a fixed filling
closed curve on a complete hyperbolic surface of finite type in its relative
Teichm\"uller space.


  An approximate mean square error (MSE) expression for the performance
analysis of implicitly defined estimators of non-random parameters is proposed.
An implicitly defined estimator (IDE) declares the minimizer/maximizer of a
selected cost/reward function as the parameter estimate. The maximum likelihood
(ML) and the least squares estimators are among the well known examples of this
class. In this paper, an exact MSE expression for implicitly defined estimators
with a symmetric and unimodal objective function is given. It is shown that the
expression reduces to the Cramer-Rao lower bound (CRLB) and misspecified CRLB
in the large sample size regime for ML and misspecified ML estimation,
respectively. The expression is shown to yield the Ziv-Zakai bound (without the
valley filling function) for the maximum a posteriori (MAP) estimator when it
is used in a Bayesian setting, that is, when an a-priori distribution is
assigned to the unknown parameter. In addition, extension of the suggested
expression to the case of nuisance parameters is studied and some
approximations are given to ease the computations for this case. Numerical
results indicate that the suggested MSE expression not only predicts the
estimator performance in the asymptotic region; but it is also applicable for
the threshold region analysis, even for IDEs whose objective functions do not
satisfy the symmetry and unimodality assumptions. Advantages of the suggested
MSE expression are its conceptual simplicity and its relatively straightforward
numerical calculation due to the reduction of the estimation problem to a
binary hypothesis testing problem, similar to the usage of Ziv-Zakai bounds in
random parameter estimation problems.


  Perturbative QCD is applied to investigate the near threshold heavy
quarkonium photoproduction at large momentum transfer. We take into account the
contributions from the leading three-quark Fock states of the nucleon. The
dominant contribution comes from the three-quark Fock state with one unit quark
orbital angular momentum (OAM) whereas that from zero quark OAM is suppressed
at the threshold. From our analysis, we also show that there is no direct
connection between the near threshold heavy quarkonium photoproduction and the
gluonic gravitational form factors of the nucleon. Based on the comparison
between our result and recent GlueX data of $J/\psi$ photoproduction, we make
predictions for $\psi'$ and $\Upsilon$ (1S,2S) states which can be tested in
future experiments.


  We study the properties of M and F theory compactifications to three and four
dimensions with background fluxes. We provide a simple construction of
supersymmetric vacua, including some with orientifold descriptions. These
vacua, which have warp factors, typically have fewer moduli than conventional
Calabi-Yau compactifications. The mechanism for anomaly cancellation in the
orientifold models involves background RR and NS fluxes. We consider in detail
an orientifold of $K3\times T^2$ with background fluxes. After a combination of
T and S-dualities, this type IIB orientifold is mapped to a compactification of
the SO(32) heterotic string on a non-Kahler space with torsion.


  The surface tension of rough interfaces between coexisting phases in 2D and
3D Ising models are discussed in view of the known results and some original
calculations presented in this paper. The results are summarised in a formula,
which allows to interpolate the corrections to finite-size scaling between two
and three dimensions. The physical meaning of an analytic continuation to
noninteger values of the spatial dimensionality d is discussed. Lattices and
interfaces with properly defined fractal dimensions should fulfil certain
requirements to possibly have properties of an analytic continuation from
d-dimensional hypercubes. Here 2 appears as the marginal value of d below which
the (d-1)-dimensional interface splits in disconnected pieces. Some
phenomenological arguments are proposed to describe such interfaces. They show
that the character of the interfacial fluctuations at d<2 is not the same as
provided by a formal analytic continuation from d-dimensional hypercubes with d
>= 2. It, probably, is true also for the related critical exponents.


  It is pointed out that the heavy singlet neutrinos characteristic of
leptogenesis develop asymmetries in the abundances of the two helicity states
as a result of the same mechanism that generates asymmetries in the standard
lepton sector. Neutrinos and standard leptons interchange asymmetries in
collisions with each other. It is shown that an appropriate quantum number,
B-L', combining baryon, lepton and neutrino asymmetries, is not violated as
fast as the standard B-L. This suppresses the washout effects relevant for the
derivation of the final baryon asymmetry. One presents detailed calculations
for the period of neutrino thermal production in the framework of the singlet
seesaw mechanism.


  Digital holography (DH) is a powerful tool for surface profilometry of
objects with sub-wavelength precision. In this article, we demonstrate
full-cascade-linked synthetic-wavelength DH (FCL-SW-DH) for nanometer-precision
surface metrology of millimeter-size stepped objects. 300 modes of optical
frequency comb (OFC) with different wavelengths are sequentially extracted at a
step of mode spacing from a 10GHz-spacing, 3.72THz-spanning electro-optic
modulator OFC (EOM-OFC). The resulting 299 synthetic wavelengths and a single
optical wavelength are used to generate a fine-step wide-range cascade link
covering within a wavelength range of 1.54 um to 29.7 mm. We determine the
0.1000mm-stepped surface with axial uncertainty of 6.1 nm within the maximum
axial range of 14.85 mm.


  Novel view synthesis has seen major advances in recent years, with 3D
Gaussian splatting offering an excellent level of visual quality, fast training
and real-time rendering. However, the resources needed for training and
rendering inevitably limit the size of the captured scenes that can be
represented with good visual quality. We introduce a hierarchy of 3D Gaussians
that preserves visual quality for very large scenes, while offering an
efficient Level-of-Detail (LOD) solution for efficient rendering of distant
content with effective level selection and smooth transitions between levels.We
introduce a divide-and-conquer approach that allows us to train very large
scenes in independent chunks. We consolidate the chunks into a hierarchy that
can be optimized to further improve visual quality of Gaussians merged into
intermediate nodes. Very large captures typically have sparse coverage of the
scene, presenting many challenges to the original 3D Gaussian splatting
training method; we adapt and regularize training to account for these issues.
We present a complete solution, that enables real-time rendering of very large
scenes and can adapt to available resources thanks to our LOD method. We show
results for captured scenes with up to tens of thousands of images with a
simple and affordable rig, covering trajectories of up to several kilometers
and lasting up to one hour. Project Page:
https://repo-sam.inria.fr/fungraph/hierarchical-3d-gaussians/


  We calculate the pi+ K+ scattering length in fully-dynamical lattice QCD with
domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at
a lattice spacing of b=0.125 fm, lattice spatial size of L =2.5 fm and at pion
masses of m_pi=290, 350, 490 and 600 MeV. The lattice data, analyzed at
next-to-leading order in chiral perturbation theory, allows an extraction of
the full pi K scattering amplitude at threshold. Extrapolating to the physical
point gives m_pi a_3/2 = -0.0574 (+- 0.0016)(+0.0024 -0.0058) and m_pi a_1/2 =
0.1725 (+- 0.0017)(+0.0023 -0.0156) for the I=3/2 and I=1/2 scattering lengths,
respectively, where the first error is statistical and the second error is an
estimate of the systematic due to truncation of the chiral expansion.


  The interaction cross sections for $^A Na + ^{12}C$ reaction are calculated
using Glauber model. The continuum Hartree-Bogoliubov theory has been
generalized to treat the odd particle system and take the continuum into
account. The theory reproduces the experimental result quite well. The matter
distributions from the proton drip line to the neutron drip line in Na isotopes
have been systematically studied and presented. The relation between the shell
effects and the halos has been examined. The tail of the matter distribution
shows a strong dependence on the shell structure. The neutron N=28 closure
shell fails to appear due to the coming down of the $2p_{3/2}$ and $2p_{1/2}$.
The development of the halo was understood as changes in the occupation in the
next shell or the sub-shell close to the continuum limit. The central proton
density is found to be decreasing near the neutron drip line, which is due to
the proton-neutron interaction. However the diffuseness of the proton density
does not change for the whole Na isotopes.


  Thin films of amorphous (a)-TiO2 are ubiquitous as photocatalysts, protective
coatings, photoanodes and in memory application, where they are exposed to
excess electrons and holes. We investigate trapping of excess electrons and
holes in the bulk of pure amorphous titanium dioxide, a-TiO2, using hybrid
density functional theory (h-DFT) calculations. Fifty 270-atom a-TiO2
structures were produced using classical molecular dynamics and their
geometries fully optimised using h-DFT simulations. They have the density,
distribution of atomic coordination numbers and radial pair-distribution
functions in agreement with experiment. The calculated average a-TiO2 band gap
is 3.25 eV with no states splitting into the band gap. Trapping of excess
electrons and holes in a-TiO2 is predicted at precursor sites, such as
elongated Ti-O bonds. Single electron and hole polarons have average trapping
energies (ET) of -0.4 eV and -0.8 eV, respectively. We also identify several
types of electron and hole bipolaron states and discuss their stability. These
results can be used for understanding the mechanisms of photo-catalysis and
improving the performance of electronic devices employing a-TiO2 films.


  Human-robot collaboration (HRC) has emerged as a hot research area at the
intersection of control, robotics, and psychology in recent years. It is of
critical importance to obtain an expressive but meanwhile tractable model for
human beings in HRC. In this paper, we propose a model called Vector
Autoregressive POMDP (VAR-POMDP) model which is an extension of the traditional
POMDP model by considering the correlation among observations. The VAR-POMDP
model is more powerful in the expressiveness of features than the traditional
continuous observation POMDP since the traditional one is a special case of the
VAR-POMDP model. Meanwhile, the proposed VAR-POMDP model is also tractable, as
we show that it can be effectively learned from data and we can extend
point-based value iteration (PBVI) to VAR-POMDP planning. Particularly, in this
paper, we propose to use the Bayesian non-parametric learning to decide
potential human states and learn a VAR-POMDP model using data collected from
human demonstrations. Then, we consider planning with respect to PCTL which is
widely used as safety and reachability requirement in robotics. Finally, the
advantage of using the proposed model for HRC is validated by experimental
results using data collected from a driver-assistance test-bed.


  Compressed Sensing MRI (CS-MRI) aims at reconstructing de-aliased images from
sub-Nyquist sampling k-space data to accelerate MR Imaging, thus presenting two
basic issues, i.e., where to sample and how to reconstruct. To deal with both
problems simultaneously, we propose a novel end-to-end Probabilistic
Under-sampling and Explicable Reconstruction neTwork, dubbed PUERT, to jointly
optimize the sampling pattern and the reconstruction network. Instead of
learning a deterministic mask, the proposed sampling subnet explores an optimal
probabilistic sub-sampling pattern, which describes independent Bernoulli
random variables at each possible sampling point, thus retaining robustness and
stochastics for a more reliable CS reconstruction. A dynamic gradient
estimation strategy is further introduced to gradually approximate the
binarization function in backward propagation, which efficiently preserves the
gradient information and further improves the reconstruction quality. Moreover,
in our reconstruction subnet, we adopt a model-based network design scheme with
high efficiency and interpretability, which is shown to assist in further
exploitation for the sampling subnet. Extensive experiments on two widely used
MRI datasets demonstrate that our proposed PUERT not only achieves
state-of-the-art results in terms of both quantitative metrics and visual
quality but also yields a sub-sampling pattern and a reconstruction model that
are both customized to training data.


  Strongly-interacting systems consisting of particles that interact through a
large scattering length satisfy universal relations that relate many of their
central properties to the contact, which measures the number of pairs with
small separations. We use the operator product expansion of quantum field
theory to derive the universal relation for the inelastic 2-body loss rate. A
simple universal relation between the loss rate and the contact is obtained by
truncating the expansion after the lowest dimension operator. We verify the
universal relation explicitly by direct calculations in the low-density limit
at nonzero temperature. This universal relation can be tested experimentally
using ultracold quantum gases of atoms in hyperfine states that have an
inelastic spin-relaxation channel.


  A theoretical study on the stimulated Brillouin scattering (SBS) in a
sub-wavelength anisotropic waveguide is conducted. The optical, photoelastic
and mechanical anisotropies of the waveguide materials are all taken into
account. First, the integral formulae for calculating the acousto-optical
coupling coefficients (AOCCs) due to the photoelastic and moving interface
effects in SBS are extended to an optically anisotropic waveguide. Then, with
the extended formulae, the SBSs in an elliptical nanowire with strong
transverse anisotropies are simulated. In the simulations, the elastic fields
are computed with the inclusion of mechanical anisotropy. Observable effects of
the strong transverse anisotropies are found in numerical results. Most
notably, the SBS gains of some elastic modes are found to be very sensitive to
the small misalignment between the waveguide axes and the principal material
axes. Detailed physical interpretations of this interesting phenomenon are
provided. This interesting phenomenon implies an attractive way for more
sensitive tuning of the SBS gain without significantly changing the phononic
frequency.


  Estimation of third-order statistics relies on the availability of a huge
amount of data records, which can pose severe challenges on the data collecting
hardware in terms of considerable storage costs, overwhelming energy
consumption, and unaffordably high sampling rate especially when dealing with
high-dimensional data such as wideband signals. To overcome these challenges,
this paper focuses on the reconstruction of the third-order cumulants under the
compressive sensing framework. Specifically, this paper derives a transformed
linear system that directly connects the cross-cumulants of compressive
measurements to the desired third-order statistics. We provide sufficient
conditions for lossless third-order statistics reconstruction via solving
simple least-squares, along with the strongest achievable compression ratio. To
reduce the computational burden, we also propose an approach to recover
diagonal cumulant slices directly from compressive measurements, which is
useful when the cumulant slices are sufficient for the inference task at hand.
All the proposed techniques are tested via extensive simulations. The developed
joint sampling and reconstruction approach to third-order statistics estimation
is able to reduce the required sampling rates significantly by exploiting the
cumulant structure resulting from signal stationarity, even in the absence of
any sparsity constraints on the signal or cumulants.


  It is extremely challenging to probe the charm-quark Yukawa coupling at
hadron colliders primarily due to the large Standard Model (SM) background
(including $h\to b\bar b$) and the lack of an effective trigger for the signal
$h\to c\bar c$. We examine the feasibility of probing this coupling at the LHC
via a Higgs radiative decay $h\rightarrow c\bar{c}\gamma$. The existence of an
additional photon in the final state may help for the signal identification and
background suppression. Adopting a refined triggering strategy and utilizing
basic machine learning, we find that a coupling limit of about 8 times the SM
value may be reached with $2\sigma$ sensitivity after the High Luminosity LHC
(HL-LHC). Our result is comparable and complementary to other projections for
direct and indirect probes of $h\to c\bar c$ at the HL-LHC. Without a
significant change in detector capabilities, there would be no significant
improvement for this search from higher energy hadron colliders.


  In this paper, we will recover Hamilton's Harnack inequality for the Ricci
flow from the view point of Hyperbolic thermostat.


  We investigate holographic fermions in general asymptotically scaling
geometries with hyperscaling violation exponent $\theta$, which is a natural
generalization of fermions in Lifshitz spacetime. We prove that the retarded
Green functions in this background satisfy the ARPES (angle-resolved
photoemission spectroscopy) sum rules by introducing a dynamical source on a UV
brane for zero density fermionic systems. The big difference from the Lifshitz
case is that the mass of probe fermions decoupled from the UV theory and thus
has no longer been restricted by unitarity bound. We also study finite density
fermions at finite temperature, with dynamical exponent $z=2$. We find that the
dispersion relation is linear but the logarithm of the spectral function is not
linearly related to the logarithm of $k_\bot =k-k_F$, independent of charge $q$
and $\theta$. Furthermore, we show that with the increasing of charge, new
branches of Fermi surfaces emerge and tend to gathering together to form a
shell-like structure when the charge reaches some critical value beyond which a
wide band pattern appears in the momentum-charge plane. However, all sharp
peaks will be smoothed out when $\theta$ increases, no matter how much large
the charge is.


  Outbursting AM CVn stars exhibit outbursts similar to those observed in
different types of dwarf novae. Their light-curves combine the characteristic
features of SU UMa, ER UMa, Z Cam, and WZ Sge-type systems but also show a
variety of properties never observed in dwarf novae. The compactness of AM CVn
orbits and their unusual chemical composition make these systems valuable
testbeds for outburst models. We aim for a better understanding of the role of
helium in the accretion disc instability mechanism, testing the model for dwarf
novae outbursts in the case of AM CVn stars, and aim to explain the outburst
light-curves of these ultra-compact binaries. We calculated the properties of
the hydrogen-free AM CVn stars using our previously developed numerical code
adapted to the different chemical composition of these systems and supplemented
with formulae accounting for mass transfer rate variations, additional sources
of the disc heating, and the primary's magnetic field. We discovered how
helium-dominated discs react to the thermal-viscous instability and were able
to reproduce various features of the outburst cycles in the light-curves of AM
CVn stars. The AM CVn outbursts can be explained by the suitably adapted
dwarf-nova disc instability model but, as in the case of its application to
hydrogen-dominated cataclysmic variables, one has to resort to additional
mechanisms to account for the observed superoutbursts, dips, cycling states,
and standstills. We show that the enhanced mass-transfer rate, due presumably
to variable irradiation of the secondary, must not only be taken into account
but is a determining factor that shapes AM CVn star outbursts. The cause of the
variable secondary's irradiation has yet to be understood; the best candidate
is the precession of a tilted/warped disc.


  We introduce a one-parameter family of SU(N) gauge actions which, when used
in combination with an HMC update algorithm, prevent the gauge system from
entering an artificial bulk-"phase". We briefly discuss the mechanism behind
the bulk-prevention and present test results for different SU(N) gauge groups.


  The percolation properties of equatorial strips of the two dimensional O(3)
nonlinear $\sigma$ model are investigated numerically. Convincing evidence is
found that a sufficently narrow strip does not percolate at arbitrarily low
temperatures. Rigorous arguments are used to show that this result implies both
the presence of a massless phase at low temperature and lack of asymptotic
freedom in the massive continuum limit. A heuristic estimate of the transition
temperature is given which is consistent with the numerical data.


  Deep learning-based recommendation models are used pervasively and broadly,
for example, to recommend movies, products, or other information most relevant
to users, in order to enhance the user experience. Among various application
domains which have received significant industry and academia research
attention, such as image classification, object detection, language and speech
translation, the performance of deep learning-based recommendation models is
less well explored, even though recommendation tasks unarguably represent
significant AI inference cycles at large-scale datacenter fleets. To advance
the state of understanding and enable machine learning system development and
optimization for the commerce domain, we aim to define an industry-relevant
recommendation benchmark for the MLPerf Training andInference Suites. The paper
synthesizes the desirable modeling strategies for personalized recommendation
systems. We lay out desirable characteristics of recommendation model
architectures and data sets. We then summarize the discussions and advice from
the MLPerf Recommendation Advisory Board.


  We prove a Central Limit Theorem for the proportion of infected individuals
for an epidemic model by dealing with a discrete time system of simple random
walks on a complete graph with n vertices. Each random walk makes a role of a
virus. Individuals are all connected as vertices in a complete graph. A virus
duplicates each time it hits a susceptible individual, dying as soon as it hits
an already infected individual. The process stops as soon as there is no more
viruses. This model is closely related to some epidemiologial models like those
for virus dissemination in a computer network.


  The renormalization group (RG) flow for the two-dimensional sine-Gordon model
is determined by means of Polchinski's RG equation at next-to-leading order in
the derivative expansion. In this work we have two different goals, (i) to
consider the renormalization scheme-dependence of Polchinski's method by
matching Polchinski's equation with the Wegner-Houghton equation and with the
real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go
beyond the local potential approximation in the gradient expansion in order to
clarify the supposed role of the field-dependent wave-function renormalization.
The well-known Coleman fixed point of the sine-Gordon model is recovered after
linearization, whereas the flow exhibits strong dependence on the choice of the
renormalization scheme when non-linear terms are kept. The RG flow is compared
to those obtained in the Wegner-Houghton approach and in the dilute gas
approximation for the two-dimensional Coulomb-gas.


  Road vehicle travel at a reasonable speed involves some risk, even when using
computer-controlled driving with failure-free hardware and perfect sensing. A
fully-automated vehicle must continuously decide how to allocate this risk
without a human driver's oversight. These are ethical decisions, particularly
in instances where an automated vehicle cannot avoid crashing. In this chapter,
I introduce the concept of moral behavior for an automated vehicle, argue the
need for research in this area through responses to anticipated critiques, and
discuss relevant applications from machine ethics and moral modeling research.


  A two-parameter sequence of orthogonal polynomials $\{P_n( x; \lambda,
t)\}_{n\ge 0}$ with respect to the weight function $x^\alpha e^{- \lambda x}
\rho_\nu(x t),\ \alpha > -1,\ \lambda, t \ge 0, \ \rho_{\nu}(x)= 2 x^{\nu/2}
K_\nu(2\sqrt x),\ x >0, \nu \ge 0$, where $K_\nu(z)$ is the modified Bessel
function, is investigated. The case $\lambda=0$ corresponds to the Prudnikov
polynomials and $t=0$ is related to the Laguerre polynomials. A special
one-parameter case $\{P_n( x; 1-t, t)\}_{n\ge 0},\ t \in [0,1]$ is analyzed as
well.