  Three epochs in development of chemical dynamics are presented. We try to
understand the modern research programs in the light of classical works. Three
eras (or waves) of chemical dynamics can be revealed in the flux of research
and publications. These waves may be associated with leaders: the first is the
van't Hoof wave, the second may be called the Semenov--Hinshelwood wave and the
third is definitely the Aris wave. Of course, the whole building was impossible
without efforts of hundreds of other researchers. Some of of them are mentioned
in our brief review.


  In this paper, we investigate the monotonicity of the functions $t \mapsto
\frac{\sum_{k=0}^\infty a_k w_k(t)}{\sum_{k=0}^\infty b_k w_k(t)}$ and $x
\mapsto \frac{\int_\alpha^\beta f(t) w(t,x) \textrm{d} t}{\int_\alpha^\beta
g(t) w(t,x) \textrm{d} t}$, focusing on case where the monotonicity of
$a_k/b_k$ and $f(t)/g(t)$ change once. The results presented also provide
insights into the monotonicity of the ratios of two power series, two
$\mathcal{Z}$-transforms, two discrete Laplace transforms, two discrete Mellin
transforms, two Laplace transforms, and two Mellin transforms. Finally, we
employ these monotonicity rules to present several applications in the realm of
special functions and stochastic orders.


  The old adage says that it is better to be lucky than to be good, but when it
comes to winning NCAA tournament pools, do you need to be both? This paper
attempts to answer this question using data from the 2014 men's basketball
tournament and more than 400 predictions of game outcomes submitted to a
contest hosted by the website Kaggle. We begin by describing how we built a
prediction model for men's basketball tournament outcomes under the binomial
log-likelihood loss function. Next, under different sets of true underlying
game probabilities, we simulate tournament outcomes and imputed pool standings,
in an effort to determine how much of an entry's success can be attributed to
luck. While one of our two submissions finished first in the Kaggle contest, we
estimate that this winning entry had no more than about a 12% chance of doing
so, even under the most optimistic of game probability scenarios.


  We propose a new jet algorithm for deep-inelastic scattering (DIS) that
accounts for the forward-backward asymmetry in the Breit frame. The Centauro
algorithm is longitudinally invariant and can cluster jets with Born
kinematics, which enables novel studies of transverse-momentum-dependent
observables. Furthermore, we show that spherically-invariant algorithms in the
Breit frame give access to low-energy jets from current fragmentation. We
propose novel studies in unpolarized, polarized, and nuclear DIS at the future
Electron-Ion Collider.


  Video-aided grammar induction aims to leverage video information for finding
more accurate syntactic grammars for accompanying text. While previous work
focuses on building systems for inducing grammars on text that are well-aligned
with video content, we investigate the scenario, in which text and video are
only in loose correspondence. Such data can be found in abundance online, and
the weak correspondence is similar to the indeterminacy problem studied in
language acquisition. Furthermore, we build a new model that can better learn
video-span correlation without manually designed features adopted by previous
work. Experiments show that our model trained only on large-scale YouTube data
with no text-video alignment reports strong and robust performances across
three unseen datasets, despite domain shift and noisy label issues. Furthermore
our model yields higher F1 scores than the previous state-of-the-art systems
trained on in-domain data.


  A recently fertile strand of research in Group Theory is developing
non-abelian analogues of classical combinatorial results for arithmetic Cayley
graphs, describing properties such as growth, expansion, mixing, diameter, etc.
We consider these problems for the symmetric and alternating groups. The case
of normal Cayley graphs (those generated by unions of conjugacy classes) has
seen significant progress via character theory (whereby Larsen and Shalev
resolved several open problems), but the general case still remains poorly
understood. In this paper we generalise the background assumption from being
normal to being global (a pseudorandomness condition), replacing character
bounds by spectral estimates for convolution operators of global functions,
thus obtaining qualitative generalisations of several results on normal Cayley
graphs. Furthermore, our theory in the pseudorandom setting can be applied (via
density increment arguments) to several results for general sets that are not
too sparse, including analogues of Polynomial Freiman-Ruzsa, Bogolyubov's
lemma, Roth's theorem, the Waring problem and essentially sharp estimates for
the diameter problem of Cayley graphs whose density is at least exponential in
-n. Our main tool is a sharp new hypercontractive inequality for global
functions on the symmetric group.


  With the railway transportation Industry moving actively towards automation,
accurate location and inventory of wayside track assets like traffic signals,
crossings, switches, mileposts, etc. is of extreme importance. With the new
Positive Train Control (PTC) regulation coming into effect, many railway safety
rules will be tied directly to location of assets like mileposts and signals.
Newer speed regulations will be enforced based on location of the Train with
respect to a wayside asset. Hence it is essential for the railroads to have an
accurate database of the types and locations of these assets. This paper talks
about a real-world use-case of detecting railway signals from a camera mounted
on a moving locomotive and tracking their locations. The camera is engineered
to withstand the environment factors on a moving train and provide a consistent
steady image at around 30 frames per second. Using advanced image analysis and
deep learning techniques, signals are detected in these camera images and a
database of their locations is created. Railway signals differ a lot from road
signals in terms of shapes and rules for placement with respect to track. Due
to space constraint and traffic densities in urban areas signals are not placed
on the same side of the track and multiple lines can run in parallel. Hence
there is need to associate signal detected with the track on which the train
runs. We present a method to associate the signals to the specific track they
belong to using a video feed from the front facing camera mounted on the lead
locomotive. A pipeline of track detection, region of interest selection, signal
detection has been implemented which gives an overall accuracy of 94.7% on a
route covering 150km with 247 signals.


  The detection of gravitational radiation, emitted in the aftermath of the
excitation of neutron star quasi-normal modes, has the potential to provide
unprecedented access to the properties of matter in the star interior, and shed
new light on the dynamics of nuclear interactions at microscopic level. Of
great importance, in this context, will be the sensitivity to themodelling of
three-nucleon interactions, which are known to play a critical role in the
high-density regime. We report the results of a calculation of the frequencies
and damping times of the fundamental mode, carried out using the equation of
state of Akmal, Pandharipande and Ravenhall as a baseline, and varying the
strength of the isoscalar repulsive term the Urbana IX potential within a range
consistent with multimessenger astrophysical observations. The results of our
analysis indicate that repulsive three-nucleon interactions strongly affect the
stiffness of the equation of state, which in turn determines the pattern of the
gravitational radiation frequencies, largely independent of the mass of the
source. The observational implications are also discussed.


  Relativistic nuclear collisions data on two-particle correlations exhibit
structures as function of relative azimuthal angle and rapidity. A unified
description of these near-side and away-side structures is proposed for low to
moderate transverse momentum. It is based on the combined effect of tubular
initial conditions and hydrodynamical expansion. Contrary to expectations, the
hydrodynamics solution shows that the high energy density tubes (leftover from
the initial particle interactions) give rise to particle emission in two
directions and this is what leads to the various structures. This description
is sensitive to some of the initial tube parameters and may provide a probe of
the strong interaction. This explanation is compared with an alternative one
where some triangularity in the initial conditions is assumed. A possible
experimental test is suggested.


  In the past year domain wall fermion simulations have moved from exploratory
stages to the point where systematic effects can be studied with different
gauge couplings, volumes, and lengths in the fifth dimension. Results are
presented here for the chiral condensate, the light hadron spectrum, and the
strange quark mass. We focus especially on the pseudoscalar meson mass and show
that, in small volume, the correlators used to compute it can be contaminated
to different degrees by topological zero modes. In large volume a nonlinear
extrapolation to the chiral limit, e.g. as expected from quenched chiral
perturbation theory, is needed in order to have a consistent picture of low
energy chiral symmetry breaking effects.


  Spontaneous decay process of an excited atom placed inside or outside (near
the surface) a carbon nanotube is analyzed. Calculations have been performed
for various achiral nanotubes. The effect of the nanotube surface has been
demonstrated to dramatically increase the atomic spontaneous decay rate -- by 6
to 7 orders of magnitude compared with that of the same atom in vacuum. Such an
increase is associated with the nonradiative decay via surface excitations in
the nanotube.


  We consider the nonlinear Kalman filtering problem using Kullback-Leibler
(KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear
Kalman filters, nonlinear Kalman filters do not have closed form Gaussian
posteriors because of a lack of conjugacy due to the nonlinearity in the
likelihood. In this paper we propose novel algorithms to optimize the forward
and reverse forms of the KL divergence, as well as the alpha-divergence which
contains these two as limiting cases. Unlike previous approaches, our
algorithms do not make approximations to the divergences being optimized, but
use Monte Carlo integration techniques to derive unbiased algorithms for direct
optimization. We assess performance on radar and sensor tracking, and options
pricing problems, showing general improvement over the UKF and EKF, as well as
competitive performance with particle filtering.


  Multistage sampling is commonly used for household surveys when there exists
no sampling frame, or when the population is scattered over a wide area.
Multistage sampling usually introduces a complex dependence in the selection of
the final units, which makes asymptotic results quite difficult to prove. In
this work, we consider multistage sampling with simple random without
replacement sampling at the first stage, and with an arbitrary sampling design
for further stages. We consider coupling methods to link this sampling design
to sampling designs where the primary sampling units are selected
independently. We first generalize a method introduced by [Magyar Tud. Akad.
Mat. Kutat\'{o} Int. K\"{o}zl. 5 (1960) 361-374] to get a coupling with
multistage sampling and Bernoulli sampling at the first stage, which leads to a
central limit theorem for the Horvitz--Thompson estimator. We then introduce a
new coupling method with multistage sampling and simple random with replacement
sampling at the first stage. When the first-stage sampling fraction tends to
zero, this method is used to prove consistency of a with-replacement bootstrap
for simple random without replacement sampling at the first stage, and
consistency of bootstrap variance estimators for smooth functions of totals.


  Asking questions is a pervasive human activity, but little is understood
about what makes them difficult to answer. An analysis of a pair of large
databases, of New York Times crosswords and questions from the quiz-show
Jeopardy, establishes two orthogonal dimensions of question difficulty:
obscurity (the rarity of the answer) and opacity (the indirectness of question
cues, operationalized with word2vec). The importance of opacity, and the role
of synergistic information in resolving it, suggests that accounts of
difficulty in terms of prior expectations captures only a part of the
question-asking process. A further regression analysis shows the presence of
additional dimensions to question-asking: question complexity, the answer's
local network density, cue intersection, and the presence of signal words. Our
work shows how question-askers can help their interlocutors by using contextual
cues, or, conversely, how a particular kind of unfamiliarity with the domain in
question can make it harder for individuals to learn from others. Taken
together, these results suggest how Bayesian models of question difficulty can
be supplemented by process models and accounts of the heuristics individuals
use to navigate conceptual spaces.


  In this paper we review the theoretical issues involved in the direct
detection of supersymmetric (SUSY) dark matter. After a brief discussion of the
allowed SYSY parameter space we focus on the determination of the traditional
neutralino detection rates, in experiments which measure the energy of the
recoiling nucleus, such as the coherent and spin induced rates and the
dependence of the rate on the motion of the Earth (modulation effect). Then we
examine the novel features appearing in directional experiments, which detect
the recoiling nucleus in a given direction. Next we estimate the branching
ratios for transitions to accessible excited nuclear levels. Finally we comment
on the event rates leading to the atom ionization and subsequent detection of
the outgoing electrons.


  We outline a method for constructing effectively two-dimensional isotropic
optical media that are perfectly and omnidirectionally invisible for both TE
and TM waves provided that their wavenumber does not exceed a preassigned value
$\alpha$. This relies on the observation that a complex scattering potential
$v(x,y)$ displays perfect invisibility for wavenumbers $k\leq\alpha$ provided
that its Fourier transform with respect to $y$, which we denote by $\tilde
v(x,\mathfrak{K}_y)$, vanishes for $\mathfrak{K}_y\leq 2\alpha$. We use this
result to construct the permittivity profile for a realistic optical slab that
is perfectly invisible in the wavenumber window $[0,\alpha]$.


  Knots are familiar entities that appear at a captivating nexus of art,
technology, mathematics, and science. As topologically stable objects within
field theories, they have been speculatively proposed as explanations for
diverse persistent phenomena, from atoms and molecules to ball lightning and
cosmic textures in the universe. Recent experiments have observed knots in a
variety of classical contexts, including nematic liquid crystals, DNA, optical
beams, and water. However, no experimental observations of knots have yet been
reported in quantum matter. We demonstrate here the controlled creation and
detection of knot solitons in the order parameter of a spinor Bose-Einstein
condensate. The experimentally obtained images of the superfluid directly
reveal the circular shape of the soliton core and its accompanying linked
rings. Importantly, the observed texture corresponds to a topologically
non-trivial element of the third homotopy group and demonstrates the celebrated
Hopf fibration, which unites many seemingly unrelated physical contexts. Our
observations of the knot soliton establish an experimental foundation for
future studies of their stability and dynamics within quantum systems.


  We present results from calculations of the physical conditions necessary for
the occurrence of 36.169 ($4_{-1}-3_{0}\, E$), 44.070 ($7_{0}-6_{1}\,A^+$),
84.521 ($5_{-1}-4_{0}\,E$), and 95.169 ($8_{0}-7_{1}\,A^+$) GHz methanol
(CH$_3$OH) maser emission lines near supernova remnants (SNRs), using the
MOLPOP-CEP program. The calculations show that given a sufficient methanol
abundance, methanol maser emission arises over a wide range of densities and
temperatures, with optimal conditions at $n\sim 10^4-10^6$ cm$^{-3}$ and $T>60$
K. The 36~GHz and 44~GHz transitions display more significant maser optical
depths compared to the 84~GHz and 95~GHz transitions over the majority of
physical conditions. It is also shown that line ratios are an important and
applicable probe of the gas conditions. The line ratio changes are largely a
result of the $E$-type transitions becoming quenched faster at increasing
densities. The modeling results are discussed using recent observations of
CH$_3$OH and hydroxyl (OH) masers near the supernova remnants G1.4$-$0.1, W28,
and Sgr A East.


  Sliced inverse regression (SIR) is a pioneer tool for supervised dimension
reduction. It identifies the effective dimension reduction space, the subspace
of significant factors with intrinsic lower dimensionality. In this paper, we
propose to refine the SIR algorithm through an overlapping slicing scheme. The
new algorithm, called overlapping sliced inverse regression (OSIR), is able to
estimate the effective dimension reduction space and determine the number of
effective factors more accurately. We show that such overlapping procedure has
the potential to identify the information contained in the derivatives of the
inverse regression curve, which helps to explain the superiority of OSIR. We
also prove that OSIR algorithm is $\sqrt n $-consistent and verify its
effectiveness by simulations and real applications.


  We use a self-consistent strong-coupling expansion for the self-energy
(perturbation theory in the hopping) to describe the nonequilibrium dynamics of
strongly correlated lattice fermions. We study the three-dimensional
homogeneous Fermi-Hubbard model driven by an external electric field showing
that the damping of the ensuing Bloch oscillations depends on the direction of
the field, and that for a broad range of field strengths, a long-lived
transient prethermalized state emerges. This long-lived transient regime
implies that thermal equilibrium may be out of reach of the time scales
accessible in present cold atom experiments, but shows that an interesting new
quasi-universal transient state exists in nonequilibrium governed by a
thermalized kinetic energy but not a thermalized potential energy. In addition,
when the field strength is equal in magnitude to the interaction between atoms,
the system undergoes a rapid thermalization, characterized by a different
quasi-universal behavior of the current and spectral function for different
values of the hopping.


  Electronic Raman scattering experiments in a wide variety of materials
(ranging from mixed-valence materials to Kondo insulators to high-temperature
superconductors) show anomalous behavior in the B_{1g} channel when the system
is on the insulating side of the metal-insulator transition. Here we provide an
exact solution for B_{1g} Raman scattering in the Falicov-Kimball model, show
how these theoretical results are universal near the metal-insulator transition
and show how they produce the two main features seen in experiments near a
quantum critical point: (i) the rapid appearance of low-energy spectral weight
as T is increased from 0 and (ii) the existence of an isosbestic point (where
the Raman response is independent of T at a characteristic frequency).


  We have conducted a spectral line survey in the 3 mm and 2 mm bands toward
two positions in a spiral arm of M51 (NGC 5194) with the IRAM 30 m telescope.
In this survey, we have identified 13 molecular species, including CN, CCH,
N2H+, HNCO, and CH3OH. Furthermore, 6 isotopologues of the major species have
been detected. On the other hand, SiO, HC3N, CH3CN, and the deuterated species
such as DCN and DCO+ are not detected. The deuterium fractionation ratios are
evaluated to be less than 0.8 % and 1.2 % for DCN/HCN and DCO+/HCO+,
respectively. By comparing the results of the two positions with different star
formation activities, we have found that the observed chemical compositions do
not strongly depend on star formation activities. They seem to reflect a
chemical composition averaged over the 1-kpc scale region including many giant
molecular clouds. Among the detected molecules CN, CCH, and CH3OH are found to
be abundant. High abundances of CN, and CCH are consistent with the above
picture of a wide spread distribution of molecules, because they can be
produced by photodissociation. On the other hand, it seems likely that CH3OH is
liberated into the gas phase by shocks associated with large scale phenomena
such as cloud-cloud collisions and/or by non-thermal desorption processes such
as photoevaporation due to cosmic-ray induced UV photons. The present result
demonstrates a characteristic chemical composition of a giant molecular cloud
complex in the spiral arm, which can be used as a standard reference for
studying chemistry in AGNs and starbursts.


  The $^8$B solar neutrino flux as measured by Super-Kamiokande is consistent
with the $^{37}$Ar production rate in $^{37}$Cl at Homestake. GALLEX and SAGE,
continue to observe $^{71}$Ge production rates in $^{71}$Ga that are consistent
with the minimal signal expected from the solar luminosity. The observed $^8$B
solar neutrino flux is in good agreement with that predicted by the standard
solar model of Dar and Shaviv with nuclear reaction rates that are supported by
recent measurements of nuclear fusion cross sections at low energies. The
measurements of Super-Kamiokande, SAGE and GALLEX suggest that the expected the
pep, $^7$Be and NO solar neutrino fluxes are strongly suppressed. This can be
explained by neutrino oscillations and the Mikheyev-Smirnov-Wolfenstein effect.
Since neither a flavor change, nor a terrestrial variation, nor a spectral
distortion of the $^8$B solar neutrino flux has been observed yet, the solar
neutrino problem does not provide conclusive evidence for neutrino properties
beyond the standard electroweak model. The deviations of the experimental
results from those predicted by the standard solar models may reflect the
approximate nature of of solar models and of our knowledge of nuclear reaction
rates, radiation transport and particle diffusion in dense stellar plasmas.
Only future observations of spectral distortions, or terrestrial modulation or
flavor change of solar neutrinos in solar neutrino experiments, such as
Super-Kamiokande, SNO, Borexino and HELLAZ will be able to establish that
neutrino properties beyond the minimal standard electroweak model are
responsible for the solar neutrino problem.


  The star formation history (SFH) is a key issue in the evolution of galaxies.
In this work, we developed a model based on a Gaussian and gamma function
mixture to fit SFHs with varying numbers of components. Our primary objective
was to use this model to reveal the shape of SFHs and the corresponding
physical driving factors. Specifically, we applied this model to fit SFHs from
the TNG100-1 simulation. Our study led to the following findings: 1) Our model
fits with TNG star formation histories well, especially for high-mass and red
galaxies; 2) A clear relationship exists between the number and shape of fitted
components and the mass and color of galaxies, with notable differences
observed between central/isolated and satellite galaxies. 3) Our model allowed
us to extract different episodes of star formation within star formation
histories with ease and analyze the duration and timing of each star formation
episode. Our findings indicated a strong relationship between the timing of
each star formation episode and galaxy mass and color.


  Grassland monitoring is essential for the sustainable development of
grassland resources. Traditional Internet of Things (IoT) devices generate
critical ecological data, making data loss unacceptable, but the harsh
environment complicates data collection. Unmanned Aerial Vehicle (UAV) and
mobile edge computing (MEC) offer efficient data collection solutions,
enhancing performance on resource-limited mobile devices. In this context, this
paper is the first to investigate a UAV-enabled time-sensitive data collection
problem (TSDCMP) within grassland monitoring edge networks (GMENs). Unlike many
existing data collection scenarios, this problem has three key challenges.
First, the total amount of data collected depends significantly on the data
collection duration and arrival time of UAV at each access point (AP). Second,
the volume of data at different APs varies among regions due to differences in
monitoring objects and vegetation coverage. Third, the service requests time
and locations from APs are often not adjacent topologically. To address these
issues, We formulate the TSDCMP for UAV-enabled GMENs as a mixed-integer
programming model in a single trip. This model considers constraints such as
the limited energy of UAV, the coupled routing and time scheduling, and the
state of APs and UAV arrival time. Subsequently, we propose a novel cooperative
heuristic algorithm based on temporal-spatial correlations (CHTSC) that
integrates a modified dynamic programming (MDP) into an iterated local search
to solve the TSDCMP for UAV-enabled GMENs. This approach fully takes into
account the temporal and spatial relationships between consecutive service
requests from APs. Systematic simulation studies demonstrate that the
mixed-integer programming model effectively represents the TSDCMP within
UAV-enabled GMENs.


  The notion of a Fermi surface (FS) is one of the most ingenious concepts
developed by solid state physicists during the past century. It plays a central
role in our understanding of interacting electron systems. Extraordinary
efforts have been undertaken, both by experiment and by theory, to reveal the
FS of the high temperature superconductors (HTSC), the most prominent strongly
correlated superconductors. Here, we discuss some of the prevalent methods used
to determine the FS and show that they lead generally to erroneous results
close to half filling and at low temperatures, due to the large superconducting
gap (pseudogap) below (above) the superconducting transition temperature. Our
findings provide a perspective on the interplay between strong correlations and
superconductivity and highlight the importance of strong coupling theories for
the characterization as well as the determination of the underlying FS in ARPES
experiments.


  Following the recent trend in explicit neural memory structures, we present a
new design of an external memory, wherein memories are stored in an Euclidean
key space $\mathbb R^n$. An LSTM controller performs read and write via
specialized read and write heads. It can move a head by either providing a new
address in the key space (aka random access) or moving from its previous
position via a Lie group action (aka Lie access). In this way, the "L" and "R"
instructions of a traditional Turing Machine are generalized to arbitrary
elements of a fixed Lie group action. For this reason, we name this new model
the Lie Access Neural Turing Machine, or LANTM.
  We tested two different configurations of LANTM against an LSTM baseline in
several basic experiments. We found the right configuration of LANTM to
outperform the baseline in all of our experiments. In particular, we trained
LANTM on addition of $k$-digit numbers for $2 \le k \le 16$, but it was able to
generalize almost perfectly to $17 \le k \le 32$, all with the number of
parameters 2 orders of magnitude below the LSTM baseline.


  The global structure of the current flows in pulsar magnetospheres is
investigated, with rough calculations of the elements in the magnetospheric
circuit. It is emphasized that the potential of critical field lines is the
same as that of interstellar medium, and that the pulsars whose rotation axes
and magnetic dipole axes are parallel should be positively charged, in order to
close the pulsar's current flows. The statistical relation between the radio
luminosity and pulsar's electric charge (or the spindown power) may hint that
the millisecond pulsars could be low-mass bare strange stars.


  We review the AIM 2020 challenge on virtual image relighting and illumination
estimation. This paper presents the novel VIDIT dataset used in the challenge
and the different proposed solutions and final evaluation results over the 3
challenge tracks. The first track considered one-to-one relighting; the
objective was to relight an input photo of a scene with a different color
temperature and illuminant orientation (i.e., light source position). The goal
of the second track was to estimate illumination settings, namely the color
temperature and orientation, from a given image. Lastly, the third track dealt
with any-to-any relighting, thus a generalization of the first track. The
target color temperature and orientation, rather than being pre-determined, are
instead given by a guide image. Participants were allowed to make use of their
track 1 and 2 solutions for track 3. The tracks had 94, 52, and 56 registered
participants, respectively, leading to 20 confirmed submissions in the final
competition stage.


  Determination of refractive index of micro-disks of a calcinated
($1100^\circ$C in air) photo-resist SZ2080$^\mathrm{TM}$ was carried out using
transmission and reflection spectroscopy. Interference fringes at specific
wavenumbers/wavelengths were selected for determination of the optical
thickness, hence, the refractive index when the thickness of micro-disks was
measured by scanning electron microscopy (SEM). Refractive index of disks of
$\sim 6\pm 1~\mu$m thickness were determined at visible and IR (2.5-13~$\mu$m)
spectral ranges and where $2.2\pm 0.2$ at visible and IR wavelengths.
Peculiarities of optical characterisation of micro-optical structures are
discussed in view of possible uncertainties in the definition of geometric
parameters, shape and mass density redistribution.


  While federated learning (FL) eliminates the transmission of raw data over a
network, it is still vulnerable to privacy breaches from the communicated model
parameters. In this work, we propose \underline{H}ierarchical
\underline{F}ederated Learning with \underline{H}ierarchical
\underline{D}ifferential \underline{P}rivacy ({\tt H$^2$FDP}), a DP-enhanced FL
methodology for jointly optimizing privacy and performance in hierarchical
networks. Building upon recent proposals for Hierarchical Differential Privacy
(HDP), one of the key concepts of {\tt H$^2$FDP} is adapting DP noise injection
at different layers of an established FL hierarchy -- edge devices, edge
servers, and cloud servers -- according to the trust models within particular
subnetworks. We conduct a comprehensive analysis of the convergence behavior of
{\tt H$^2$FDP}, revealing conditions on parameter tuning under which the
training process converges sublinearly to a finite stationarity gap that
depends on the network hierarchy, trust model, and target privacy level.
  Leveraging these relationships, we develop an adaptive control algorithm for
{\tt H$^2$FDP} that tunes properties of local model training to minimize
communication energy, latency, and the stationarity gap while striving to
maintain a sub-linear convergence rate and meet desired privacy criteria.
  Subsequent numerical evaluations demonstrate that {\tt H$^2$FDP} obtains
substantial improvements in these metrics over baselines for different privacy
budgets, and validate the impact of different system configurations.


  The Wigner quasiprobability distribution of a narrowband single-photon state
was reconstructed by quantum state tomography using photon-number-resolving
measurements with transition-edge sensors (TES) at system efficiency 58(2)%.
This method makes no assumptions on the nature of the measured state, save for
the limitation on photon flux imposed by the TES. Negativity of the Wigner
function was observed in the raw data without any inference or correction for
decoherence.


  We study the atomic embeddability testing problem, which is a common
generalization of clustered planarity (c-planarity, for short) and
thickenability testing, and present a polynomial-time algorithm for this
problem, thereby giving the first polynomial-time algorithm for c-planarity.
  C-planarity was introduced in 1995 by Feng, Cohen, and Eades as a variant of
graph planarity, in which the vertex set of the input graph is endowed with a
hierarchical clustering and we seek an embedding (crossing free drawing) of the
graph in the plane that respects the clustering in a certain natural sense.
Until now, it has been an open problem whether c-planarity can be tested
efficiently, despite relentless efforts. The thickenability problem for
simplicial complexes emerged in the topology of manifolds in the 1960s. A
2-dimensional simplicial complex is thickenable if it embeds in some orientable
3-dimensional manifold. Recently, Carmesin announced that thickenability can be
tested in polynomial time.
  Our algorithm for atomic embeddability combines ideas from Carmesin's work
with algorithmic tools previously developed for weak embeddability testing. We
express our results purely in terms of graphs on surfaces, and rely on the
machinery of topological graph theory.
  Finally, we give a polynomial-time reduction from atomic embeddability to
thickenability thereby showing that both problems are polynomially equivalent,
and show that a slight generalization of atomic embeddability to the setting in
which clusters are toroidal graphs is NP-complete.


  We discuss the dynamics and thermodynamics of systems with long-range
interactions. We contrast the microcanonical description of an isolated
Hamiltonian system to the canonical description of a stochastically forced
Brownian system. We show that the mean-field approximation is exact in a proper
thermodynamic limit. The equilibrium distribution function is solution of an
integrodifferential equation obtained from a static BBGKY-like hierarchy. It
also optimizes a thermodynamical potential (entropy or free energy) under
appropriate constraints. We discuss the kinetic theory of these systems. In the
$N\to +\infty$ limit, a Hamiltonian system is described by the Vlasov equation.
To order 1/N, the collision term of a homogeneous system has the form of the
Lenard-Balescu operator. It reduces to the Landau operator when collective
effects are neglected. We also consider the motion of a test particle in a bath
of field particles and derive the general form of the Fokker-Planck equation.
The diffusion coefficient is anisotropic and depends on the velocity of the
test particle. This can lead to anomalous diffusion. For Brownian systems, in
the $N\to +\infty$ limit, the kinetic equation is a non-local Kramers equation.
In the strong friction limit $\xi\to +\infty$, or for large times $t\gg
\xi^{-1}$, it reduces to a non-local Smoluchowski equation. We give explicit
results for self-gravitating systems, two-dimensional vortices and for the HMF
model. We also introduce a generalized class of stochastic processes and derive
the corresponding generalized Fokker-Planck equations. We discuss how a notion
of generalized thermodynamics can emerge in complex systems displaying
anomalous diffusion.


  Optical-coherence tomography (OCT) is a technique that employs light in order
to measure the internal structure of semi-transparent, e.g. biological,
samples. It is based on the interference pattern of low-coherence light.
Quantum-OCT (QOCT), instead, employs the correlation properties of entangled
photon pairs, for example, generated by the process of spontaneous parametric
downconversion (SPDC). The usual QOCT scheme uses photon pairs characterised by
a joint-spectral amplitude with strict spectral anti-correlations. It has been
shown that, in contrast with its classical counterpart, QOCT provides
resolution enhancement and dispersion cancellation. In this paper, we revisit
the theory of QOCT and extend the theoretical model so as to include photon
pairs with arbitrary spectral correlations. We present experimental results
that complement the theory and explain the physical underpinnings appearing in
the interference pattern. In our experiment, we utilize a pump for the SPDC
process ranging from continuous wave to pulsed in the femtosecond regime, and
show that cross-correlation interference effects appearing for each pair of
layers may be directly suppressed for a sufficiently large pump bandwidth. Our
results provide insights and strategies that could guide practical
implementations of QOCT.


  Natural fliers like bats exploit the complex fluid-structure interaction
between their flexible membrane wings and the air with great ease. Yet,
replicating and scaling the balance between the structural and fluid-dynamical
parameters of unsteady membrane wings for engineering applications remains
challenging. In this study, we introduce a novel bio-inspired membrane wing
design and systematically investigate the fluid-structure interactions of
flapping membrane wings. The membrane wing can passively camber and its leading
and trailing edges rotate with respect to the stroke plane. We find optimal
combinations of the membrane properties and flapping kinematics that
out-perform their rigid counterparts both in terms of increased stroke-average
lift and efficiency but the improvements are not persistent over the entire
input parameter space. The lift and efficiency optima occur at different angles
of attack and effective membrane stiffnesses which we characterise with the
aeroelastic number. At optimal aeroelastic numbers, the membrane has a moderate
camber between 15% and 20% and its leading and trailing edges align favourably
with the flow. Higher camber at lower aeroelastic numbers leads to reduced
aerodynamic performance due to negative angles of attack at the leading edge
and an over-rotation of the trailing edge. Most of the performance gain of the
membrane wings with respect to rigid wings is achieved in the second half of
the stroke when the wing is decelerating. The stroke-maximum camber is reached
around mid-stroke but is sustained during most of the remainder of the stroke
which leads to an increase in lift and a reduction in power. Our results show
that combining the effect of variable stiffness and angle of attack variation
can significantly enhance the aerodynamic performance of membrane wings and has
the potential to improve the control capabilities of micro air vehicles.


  Additive manufacturing (AM) offers an unprecedented opportunity for the quick
production of complex shaped parts directly from a powder precursor. But its
application to functional materials in general and magnetic materials in
particular is still at the very beginning. Here we present the first attempt to
computationally study the microstructure evolution and magnetic properties of
magnetic materials (e.g. Fe-Ni alloys) processed by selective laser melting
(SLM). SLM process induced thermal history and thus the residual stress
distribution in Fe-Ni alloys are calculated by finite element analysis (FEA).
The evolution and distribution of the $\gamma$-Fe-Ni and FeNi$_3$ phase
fractions were predicted by using the temperature information from FEA and the
output from CALculation of PHAse Diagrams (CALPHAD). Based on the relation
between residual stress and magnetoelastic energy, magnetic properties of SLM
processed Fe-Ni alloys (magnetic coercivity, remanent magnetization, and
magnetic domain structure) are examined by micromagnetic simulations. The
calculated coercivity is found to be in line with the experimentally measured
values of SLM-processed Fe-Ni alloys. This computation study demonstrates a
feasible approach for the simulation of additively manufactured magnetic
materials by integrating FEA, CALPHAD, and micromagnetics.


  In this article, we give advice on transitioning to a more agile delivery
model for large-scale agile development projects based on experience from the
Parental Benefit Project of the Norwegian Labour and Welfare Administration.
The project modernized a central part of the organizations IT portfolio and
included up to ten development teams working in parallel. The project
successfully changed from using a delivery model which combined traditional
project management elements and agile methods to a more agile delivery model
with autonomous teams and continuous deployment. This transition was completed
in tandem with the project execution. We identify key lessons learned which
will be useful for other organizations considering similar changes and report
how the new delivery model reduced risk and opened up a range of new
possibilities for delivering the benefits of digitalization.


  With the development of 3D scanning technologies, 3D vision tasks have become
a popular research area. Owing to the large amount of data acquired by sensors,
unsupervised learning is essential for understanding and utilizing point clouds
without an expensive annotation process. In this paper, we propose a novel
framework and an effective auto-encoder architecture named "PSG-Net" for
reconstruction-based learning of point clouds. Unlike existing studies that
used fixed or random 2D points, our framework generates input-dependent
point-wise features for the latent point set. PSG-Net uses the encoded input to
produce point-wise features through the seed generation module and extracts
richer features in multiple stages with gradually increasing resolution by
applying the seed feature propagation module progressively. We prove the
effectiveness of PSG-Net experimentally; PSG-Net shows state-of-the-art
performances in point cloud reconstruction and unsupervised classification, and
achieves comparable performance to counterpart methods in supervised
completion.


  Generalizability is an important problem in deep neural networks, especially
in the context of the variability of data acquisition in clinical magnetic
resonance imaging (MRI). Recently, the Spatially Localized Atlas Network Tiles
(SLANT) approach has been shown to effectively segment whole brain non-contrast
T1w MRI with 132 volumetric labels. Enhancing generalizability of SLANT would
enable broader application of volumetric assessment in multi-site studies.
Transfer learning (TL) is commonly used to update the neural network weights
for local factors; yet, it is commonly recognized to risk degradation of
performance on the original validation/test cohorts. Here, we explore TL by
data augmentation to address these concerns in the context of adapting SLANT to
anatomical variation and scanning protocol. We consider two datasets: First, we
optimize for age with 30 T1w MRI of young children with manually corrected
volumetric labels, and accuracy of automated segmentation defined relative to
the manually provided truth. Second, we optimize for acquisition with 36 paired
datasets of pre- and post-contrast clinically acquired T1w MRI, and accuracy of
the post-contrast segmentations assessed relative to the pre-contrast automated
assessment. For both studies, we augment the original TL step of SLANT with
either only the new data or with both original and new data. Over baseline
SLANT, both approaches yielded significantly improved performance (signed rank
tests; pediatric: 0.89 vs. 0.82 DSC, p<0.001; contrast: 0.80 vs 0.76, p<0.001).
The performance on the original test set decreased with the new-data only
transfer learning approach, so data augmentation was superior to strict
transfer learning.


  Direct imaging of exoplanets requires establishing and maintaining a high
contrast dark field (DF) within the science image to a high degree of precision
(10^-10). Current approaches aimed at establishing the DF, such as electric
field conjugation (EFC), have been demonstrated in the lab and have proven
capable of high contrast DF generation. The same approaches have been
considered for the maintenance of the DF as well. However, these methods rely
on phase diversity measurements which require field modulation; this interrupts
the DF and consequently competes with the science acquisition. In this paper,
we introduce and demonstrate spatial linear dark field control (LDFC) as an
alternative technique by which the high contrast DF can be maintained without
modulation. Once the DF has been established by conventional EFC, spatial LDFC
locks the high contrast state of the DF by operating a closed-loop around the
linear response of the bright field (BF) to wavefront variations that modify
both the BF and the DF. We describe here the fundamental operating principles
of spatial LDFC and provide numerical simulations of its operation as a DF
stabilization technique that is capable of wavefront correction within the DF
without interrupting science acquisition.


  Control of gas exchange between a leafs interior and the surrounding air is
accomplished by variations in the turgor pressures in the small epidermal and
guard cells that cover the leafs surface. These pressures respond to changes in
light intensity and color, temperature, CO2 concentration, and air humidity.
The dynamical equations that describe these processes are formally identical to
those that define computation in a two layer, adaptive, cellular nonlinear
network. This identification suggests that leaf gas exchange processes can be
understood as a kind of analog computation.


  Characterization of the properties of young brown dwarfs are important to
constraining the formation of objects at the extreme low-mass end of the IMF.
While young brown dwarfs share many properties with solar-mass T Tauri stars,
differences may be used as tests of how the physics of accretion/outflow and
disk chemistry/dissipation depend on the mass of the central object. This
article summarizes the presentations and discussions during the splinter
session on 'Disks, accretion and outflows of brown dwarfs' held at the
CoolStars17 conference in Barcelona in June 2012. Recent results in the field
of brown dwarf disks and outflows include the determination of brown dwarf disk
masses and geometries based on Herschel far-IR photometry (70-160 um),
accretion properties based on X-Shooter spectra, and new outflow detections in
the very low-mass regime.


  The liquid-vapor phase separation is investigated via lattice Boltzmann
simulations in three dimensions. After expressing length and time scales in
reduced physical units, we combined data from several large simulations (on
$512^3$ nodes), with different values of viscosity, surface tension and
temperature, to obtain a single curve of rescaled length $\hat{l}$ as a
function of rescaled time $\hat{t}$. We find evidence of the existence of
kinetic and inertial regimes with growth exponents $\alpha_d=1/2$ and
$\alpha_i=2/3$ over several time decades, with a crossover from $\alpha_d$ to
$\alpha_i$ at $\hat{t} \simeq 1$. This allows us to rule out the existence of a
viscous regime with $\alpha_v=1$ in three-dimensional liquid-vapor isothermal
phase separation, differently from what happens in binary fluid mixtures. An
in-depth analysis of the kinetics of the phase separation process, as well as a
characterization of the morphology and the flow properties, are further
presented in order to provide clues into the dynamics of the phase-separation
process.


  In many applications, hypothesis testing is based on an asymptotic
distribution of statistics. The aim of this paper is to clarify and extend
multiple correction procedures when the statistics are asymptotically Gaussian.
We propose a unified framework to prove their asymptotic behavior which is
valid in the case of highly correlated tests. We focus on correlation tests
where several test statistics are proposed. All these multiple testing
procedures on correlations are shown to control FWER. An extensive simulation
study on correlation-based graph estimation highlights finite sample behavior,
independence on the sparsity of graphs and dependence on the values of
correlations. Empirical evaluation of power provides comparisons of the
proposed methods. Finally validation of our procedures is proposed on real
dataset of rats brain connectivity measured by fMRI. We confirm our theoretical
findings by applying our procedures on a full null hypotheses with data from
dead rats. Data on alive rats show the performance of the proposed procedures
to correctly identify brain connectivity graphs with controlled errors.


  A precessing source frame, constructed using the Newtonian orbital angular
momentum ${\bf L_{\rm N}}$, can be invoked to model inspiral gravitational
waves from generic spinning compact binaries. An attractive feature of such a
precessing convention is its ability to remove all spin precession induced
modulations from the orbital phase evolution. However, this convention usually
employs a post-Newtonian (PN) accurate precessional equation, appropriate for
the PN accurate orbital angular momentum ${\bf L}$, to evolve the ${\bf L_{\rm
N}}$-based precessing source frame. This influenced us to develop inspiral
waveforms for spinning compact binaries in a precessing convention that
explicitly employ ${\bf L}$ to describe the binary orbits. Our approach
introduces certain additional 3PN order terms in the evolution equations for
the orbital phase and frequency with respect to the usual ${\bf L_{\rm
N}}$-based implementation of the precessing convention. We examine the
practical implications of these additional terms by computing the match between
inspiral waveforms that employ ${\bf L}$ and ${\bf L_{\rm N}}$-based precessing
conventions. The match estimates are found to be smaller than the optimal
value, namely $0.97$, for a non-negligible fraction of unequal mass spinning
compact binaries.


  There has been a significant focus on modelling emotion ambiguity in recent
years, with advancements made in representing emotions as distributions to
capture ambiguity. However, there has been comparatively less effort devoted to
the consideration of temporal dependencies in emotion distributions which
encodes ambiguity in perceived emotions that evolve smoothly over time.
Recognizing the benefits of using constrained dynamical neural ordinary
differential equations (CD-NODE) to model time series as dynamic processes, we
propose an ambiguity-aware dual-constrained Neural ODE approach to model the
dynamics of emotion distributions on arousal and valence. In our approach, we
utilize ODEs parameterised by neural networks to estimate the distribution
parameters, and we integrate additional constraints to restrict the range of
the system outputs to ensure the validity of predicted distributions. We
evaluated our proposed system on the publicly available RECOLA dataset and
observed very promising performance across a range of evaluation metrics.


  We propose a computationally efficient statistical method to obtain
distributional properties of annual maximum 24 hour precipitation on a 1 km by
1 km regular grid over Iceland. A latent Gaussian model is built which takes
into account observations, spatial variations and outputs from a local
meteorological model. A covariate based on the meteorological model is
constructed at each observational site and each grid point in order to
assimilate available scientific knowledge about precipitation into the
statistical model. The model is applied to two data sets on extreme
precipitation, one uncorrected data set and one data set that is corrected for
phase and wind. The observations are assumed to follow the generalized extreme
value distribution. At the latent level, we implement SPDE spatial models for
both the location and scale parameters of the likelihood. An efficient MCMC
sampler which exploits the model structure is constructed, which yields fast
continuous spatial predictions for spatially varying model parameters and
quantiles.


  We obtain lower bounds for the number of nodal domains of Hecke
eigenfunctions on the sphere. Assuming the generalized Lindelof hypothesis we
prove that the number of nodal domains of any Hecke eigenfunction grows with
the eigenvalue of the Laplacian. By a very different method, we show
unconditionally that the average number of nodal domains of degree l Hecke
eigenfunctions grows significantly faster than the uniform growth obtained
under Lindelof.


  Artificial intelligence (AI) promotes the polymer design paradigm from a
traditional trial-and-error approach to a data-driven style. Achieving high
thermal conductivity (TC) for intrinsic polymers is urgent because of their
importance in the thermal management of many industrial applications such as
microelectronic devices and integrated circuits. In this work, we have proposed
a robust AI-assisted workflow for the inverse design of high TC polymers. By
using 1144 polymers with known computational TCs, we construct a surrogate deep
neural network model for TC prediction and extract a polymer-unit library with
32 sequences. Two state-of-the-art multi-objective optimization algorithms of
unified non-dominated sorting genetic algorithm III (U-NSGA-III) and q-noisy
expected hypervolume improvement (qNEHVI) are employed for sequence-ordered
polymer design with both high TC and synthetic possibility. For triblock
polymer design, the result indicates that qNHEVI is capable of exploring a
diversity of optimal polymers at the Pareto front, but the uncertainty in
Quasi-Monte Carlo sampling makes the trials costly. The performance of
U-NSGA-III is affected by the initial random structures and usually falls into
a locally optimal solution, but it takes fewer attempts with lower costs. 20
parallel U-NSGA-III runs are conducted to design the pentablock polymers with
high TC, and half of the candidates among 1921 generated polymers achieve the
targets (TC > 0.4 W/(mK) and SA < 3.0). Ultimately, we check the TC of 50
promising polymers through molecular dynamics simulations and reveal the
intrinsic connections between microstructures and TCs. Our developed
AI-assisted inverse design approach for polymers is flexible and universal, and
can be extended to the design of polymers with other target properties.


  Cloud networks are difficult to monitor because they grow rapidly and the
budgets for monitoring them are limited. We propose a framework for estimating
network metrics, such as latency and packet loss, with guarantees on estimation
errors for a fixed monitoring budget. Our proposed algorithms produce a
distribution of probes across network paths, which we then monitor; and are
based on A- and E-optimal experimental designs in statistics. Unfortunately,
these designs are too computationally costly to use at production scale. We
propose their scalable and near-optimal approximations based on the Frank-Wolfe
algorithm. We validate our approaches in simulation on real network topologies,
and also using a production probing system in a real cloud network. We show
major gains in reducing the probing budget compared to both production and
academic baselines, while maintaining low estimation errors, even with very low
probing budgets.


  We present a new potential barrier that presents the phenomenon of
superradiance when the reflection coefficient $R$ is greater than one. We
calculated the transmission and reflection coefficients for three different
regions. The results are compared with those obtained for the hyperbolic
tangent potential barrier and the step potential barrier. We also present the
solution of the Klein-Gordon equation with the Lambert-W potential barrier in
terms of the Heun Confluent functions.


  We formulate a bulk spectroscopic method for direct measurement of the
topological invariant of nondegenerate band crossings in Weyl semimetals. We
demonstrate how polarization-resolved resonant x-ray scattering captures the
winding of the Berry flux around Weyl nodes. The spectra obtained by the
proposed strategy feature an integer number of zero-crossings that is directly
related to the topological charge of the measured nodes. We benchmark the
proposed protocol on TaAs, using realistic low-energy models derived from
density-functional theory to accurately represent the states close to the Fermi
level, including sizable deviations from the idealized linear dispersion. We
conclude that the proposed measurement, which is within the reach of current
experimental setups, yields direct signatures of nontrivial band topology in
spectroscopy of three-dimensional bulk matter.


  Circulant matrices are an important tool widely used in coding theory and
cryptography. A circulant matrix is a square matrix whose rows are the cyclic
shifts of the first row. Such a matrix can be efficiently stored in memory
because it is fully specified by its first row. The ring of $n \times n$
circulant matrices can be identified with the quotient ring
$\mathbb{F}[x]/(x^n-1)$. In consequence, the strong algebraic structure of the
ring $\mathbb{F}[x]/(x^n-1)$ can be used to study properties of the collection
of all $n\times n$ circulant matrices. The ring $\mathbb{F}[x]/(x^n-1)$ is a
special case of a group algebra and elements of any finite dimensional group
algebra can be represented with square matrices which are specified by a single
column. In this paper we study this representation and prove that it is an
injective Hamming weight preserving homomorphism of $\mathbb{F}$-algebras and
classify it in the case where the underlying group is abelian.
  Our work is motivated by the desire to generalize the BIKE cryptosystem (a
contender in the NIST competition to get a new post-quantum standard for
asymmetric cryptography). Group algebras can be used to design similar
cryptosystems or, more generally, to construct low density or moderate density
parity-check matrices for linear codes.


  An unsupervised shape analysis is proposed to learn concepts reflecting shape
commonalities. Our approach is two-fold: i) a spatial topology analysis of
point cloud segment constellations within objects is used in which
constellations are decomposed and described in a hierarchical and symbolic
manner. ii) A topology analysis of the description space is used in which
segment decompositions are exposed in. Inspired by Persistent Homology, groups
of shape commonality are revealed. Experiments show that extracted persistent
commonality groups can feature semantically meaningful shape concepts; the
generalization of the proposed approach is evaluated by different real-world
datasets. We extend this by not only learning shape concepts using real-world
data, but by also using mental simulation of artificial abstract objects for
training purposes. This extended approach is unsupervised in two respects:
label-agnostic (no label information is used) and instance-agnostic (no
instances preselected by human supervision are used for training). Experiments
show that concepts generated with mental simulation, generalize and
discriminate real object observations. Consequently, a robot may train and
learn its own internal representation of concepts regarding shape appearance in
a self-driven and machine-centric manner while omitting the tedious process of
supervised dataset generation including the ambiguity in instance labeling and
selection.


  In this chapter, I present the main X-ray observational characteristics of
black-hole binaries and low magnetic field neutron-star binaries, concentrating
on what can be considered similarities or differences, with particular emphasis
on their fast-timing behaviour.


  Spinel oxides are recognized as promising Fenton-like catalysts for the
degradation of antibiotics. However, the catalytic performance is restrained by
the poor electron transfer rate (ETR). Herein, hollow NiCo2O4@C nanocages are
rationally designed and prepared to accelerate ETR in peroxymonosulfate (PMS)
activation for tetracycline (TC) degradation.


  At high energies, elastic hadronic cross sections, such as $pp, \overline p
p, \pi^{\pm} p$, are dominated by vacuum exchange, which in leading order of
the $1/N_c$ expansion has been identified as the BFKL Pomeron or its strong AdS
dual the closed string Reggeized graviton \cite{Brower:2006ea}. However the
difference of particle anti-particle cross sections are given by a so-called
Odderon, carrying C = -1 vacuum quantum numbers identified in weak coupling
with odd numbers of exchanged gluons. Here we show that in the dual description
the Odderon is the Reggeized Kalb-Ramond field ($B_{\mu\nu}$) in the
Neveu-Schwartz sector of closed string theory. To first order in strong
coupling, the high energy contribution of Odderon is evaluated for ${\cal N} =
4$ Super Yang-Mills by a generalization of the gravity dual analysis for
Pomeron in Ref. \cite{Brower:2006ea}. The consequence of confinement on the
Odderon are estimated in the confining QCD-like $AdS^5$ hardwall model of
Polchinski and Strassler \cite{Polchinski:2001tt}.


  Macroscale robotic systems have demonstrated great capabilities of high
speed, precise, and agile functions. However, the ability of soft robots to
perform complex tasks, especially in centimeter and millimeter scale, remains
limited due to the unavailability of fast, energy-efficient soft actuators that
can programmably change shape. Here, we combine desirable characteristics from
two distinct active materials: fast and efficient actuation from dielectric
elastomers and facile shape programmability from liquid crystal elastomers into
a single shape changing electrical actuator. Uniaxially aligned monoliths
achieve strain rates over 120%/s with energy conversion efficiency of 20% while
moving loads over 700 times the actuator weight. The combined actuator
technology offers unprecedented opportunities towards miniaturization with
precision, efficiency, and more degrees of freedom for applications in soft
robotics and beyond.


  For a finite-dimensional semisimple Lie algebra $\mathfrak{g}$, the
Jacobson--Morozov theorem gives a construction of subalgebras $\mathfrak{sl}_2
\subset \mathfrak{g}$ corresponding to nilpotent elements of $\mathfrak{g}$. In
this note, we propose an extension of the Jacobson--Morozov theorem to the
symmetrizable Kac--Moody setting and give a proof of this generalization in the
case of rank two hyperbolic Kac--Moody algebras. We also give a proof for an
arbitrary symmetrizable Kac--Moody algebra under some stronger restrictions.


  We show that every K_4-free graph G with n vertices can be made bipartite by
deleting at most n^2/9 edges. Moreover, the only extremal graph which requires
deletion of that many edges is a complete 3-partite graph with parts of size
n/3. This proves an old conjecture of P. Erdos.


  In this paper, we study the sum rate performance of zero-forcing (ZF) and
regularized ZF (RZF) precoding in large MISO broadcast systems under the
assumptions of imperfect channel state information at the transmitter and
per-user channel transmit correlation. Our analysis assumes that the number of
transmit antennas $M$ and the number of single-antenna users $K$ are large
while their ratio remains bounded. We derive deterministic approximations of
the empirical signal-to-interference plus noise ratio (SINR) at the receivers,
which are tight as $M,K\to\infty$. In the course of this derivation, the
per-user channel correlation model requires the development of a novel
deterministic equivalent of the empirical Stieltjes transform of large
dimensional random matrices with generalized variance profile. The
deterministic SINR approximations enable us to solve various practical
optimization problems. Under sum rate maximization, we derive (i) for RZF the
optimal regularization parameter, (ii) for ZF the optimal number of users,
(iii) for ZF and RZF the optimal power allocation scheme and (iv) the optimal
amount of feedback in large FDD/TDD multi-user systems. Numerical simulations
suggest that the deterministic approximations are accurate even for small
$M,K$.


  Usually the $\ell_2$-norm plays vital roles in quantum physics, acting as the
probability of states. In this paper, we show the important roles of
$\ell_1$-norm in Yang-Baxter quantum system, in connection with both the braid
matrix and quantum entanglements. Concretely, we choose the 2-body and 3-body
S-matrices, constrained by Yang-Baxter equation. It has been shown that for
2-body case, the extreme values of $\ell_1$-norm lead to two types of braid
matrices and 2-qubit Bell states. Here we show that for the 3-body case, due to
the constraint of YBE, the extreme values of $\ell_1$-norm lead to both 3-qubit
$|GHZ\rangle$ (local maximum) and $|W\rangle$ (local minimum) states, which
cover all 3-qubit genuine entanglements for pure states under SLOCC. This is a
more convincing proof for the roles of $\ell_1$-norm in quantum mechanics.


  There has been rapid development of systems that yield strong interactions
between freely propagating photons in one dimension via controlled coupling to
quantum emitters. This raises interesting possibilities such as quantum
information processing with photons or quantum many-body states of light, but
treating such systems generally remains a difficult task theoretically. Here,
we describe a novel technique in which the dynamics and correlations of a few
photons can be exactly calculated, based upon knowledge of the initial photonic
state and the solution of the reduced effective dynamics of the quantum
emitters alone. We show that this generalized "input-output" formalism allows
for a straightforward numerical implementation regardless of system details,
such as emitter positions, external driving, and level structure. As a specific
example, we apply our technique to show how atomic systems with infinite-range
interactions and under conditions of electromagnetically induced transparency
enable the selective transmission of correlated multi-photon states.


  We describe high-fidelity entangling gates between singlet-triplet qubits
(STQs) which are coupled via one quantum state (QS). The QS can be provided by
a quantum dot itself or by another confined system. The orbital energies of the
QS are tunable using an electric gate close to the QS, which changes the
interactions between the STQs independent of their single-qubit parameters.
Short gating sequences exist for the controlled NOT (CNOT) operations. We show
that realistic quantum dot setups permit excellent entangling operations with
gate infidelities below $10^{-3}$, which is lower than the quantum error
correction threshold of the surface code. We consider limitations from
fabrication errors, hyperfine interactions, spin-orbit interactions, and charge
noise in GaAs and Si heterostructures.


  In a world increasingly dominated by AI applications, an understudied aspect
is the carbon and social footprint of these power-hungry algorithms that
require copious computation and a trove of data for training and prediction.
While profitable in the short-term, these practices are unsustainable and
socially extractive from both a data-use and energy-use perspective. This work
proposes an ESG-inspired framework combining socio-technical measures to build
eco-socially responsible AI systems. The framework has four pillars:
compute-efficient machine learning, federated learning, data sovereignty, and a
LEEDesque certificate.
  Compute-efficient machine learning is the use of compressed network
architectures that show marginal decreases in accuracy. Federated learning
augments the first pillar's impact through the use of techniques that
distribute computational loads across idle capacity on devices. This is paired
with the third pillar of data sovereignty to ensure the privacy of user data
via techniques like use-based privacy and differential privacy. The final
pillar ties all these factors together and certifies products and services in a
standardized manner on their environmental and social impacts, allowing
consumers to align their purchase with their values.


  Intractable posterior distributions of parameters with intractable
normalizing constants depending upon the parameters are known as doubly
intractable posterior distributions. The terminology itself indicates that
obtaining Bayesian inference from such posteriors is doubly difficult compared
to traditional intractable posteriors where the normalizing constants are
tractable and admit traditional Markov Chain Monte Carlo (MCMC) solutions.
  As can be anticipated, a plethora of MCMC-based methods have originated in
the literature to deal with doubly intractable distributions. Yet, it remains
very much unclear if any of the methods can satisfactorily sample from such
posteriors, particularly in high-dimensional setups.
  In this article, we consider efficient Monte Carlo and importance sampling
approximations of the intractable normalizing constant for a few values of the
parameters, and Gaussian process interpolations for the remaining values of the
parameters, using the approximations. We then incorporate this strategy within
the exact iid sampling framework developed in Bhattacharya (2021a) and
Bhattacharya (2021b), and illustrate the methodology with simulation
experiments comprising a two-dimensional normal-gamma posterior, a
two-dimensional Ising model posterior, a two-dimensional Strauss process
posterior and a 100-dimensional autologistic model posterior. In each case we
demonstrate great accuracy of our methodology, which is also computationally
extremely efficient, often taking only a few minutes for generating 10, 000 iid
realizations on 80 processors.


  We show a curious identity on root systems which gives the evaluation of the
volume of the spherical simpleces cut by the cone generated by simple roots.


  In this paper an artificial delay based impedance controller is proposed for
robotic manipulators with uncertainty in dynamics. The control law unites the
time delayed estimation (TDE) framework with a second order switching
controller of super twisting algorithm (STA) type via a novel generalized
filtered tracking error (GFTE). While time delayed estimation framework
eliminates the need for accurate modelling of robot dynamics by estimating the
uncertain robot dynamics and interaction forces from immediate past data of
state and control effort, the second order switching control law in the outer
loop provides robustness against the time delayed estimation (TDE) error that
arises due to approximation of the manipulator dynamics. Thus, the proposed
control law tries to establish a desired impedance model between the robot end
effector variables i.e. force and motion in presence of uncertainties, both
when it is encountering smooth contact forces and during free motion.
Simulation results for a two link manipulator using the proposed controller
along with convergence analysis are shown to validate the proposition.


  In this paper we introduce and prove some properties of
$(\alpha;\beta)$-normal operators according to semi-Hilbertian space
structures. Furthermore we s,ate various inequalities between the A-operator
norm and A-numerical radius of $(\alpha,\beta)$-normal operators in semi
Hilbertian spaces.


  The advection-diffusion and wave equations are the fundamental equations
governing any physical law and therefore arise in many areas of physics and
astrophysics. For complex problems and geometries, only numerical simulations
can give insight into quantitative and accurate behavior of the seeked
solutions. The standard numerical algorithm to solve partial differential
equations is to split the space and time discretisation separately into
different uncorrelated methods. Time is usually advanced by explicit schemes,
or, for too restrictive time steps, by implicit or semi-implicit algorithms.
This separate time and space slicing is artificial and sometimes unpractical.
Indeed, treating space and time directions symmetrically and simultaneously
without splitting is highly recommended in some problems like diffusion.
  It is the purpose of this work to present a simple numerical algorithm to
solve the standard linear scalar advection-diffusion and wave equations using a
fully spectral method in a two-dimensional Cartesian $(x,t)$ bounded space-time
domain. Generalization in three-dimensions $(x,y,t)$ is shown for the pure
diffusion problem. The basic idea is to expand the unknown function in
Chebyshev polynomials for the spatial variables $(x,y)$ as well as for the time
variable $t$. We show typical examples and demonstrate the spectral accuracy of
the method. The great advantage of fully spectral methods resides in their
high-accuracy for a relatively small number of grid points (for sufficiently
smooth solutions) compared to standard time-stepping techniques.


  In this work we improve upon previous results on the expansion of the
interaction energy of two atoms. On the one hand we prove the van der
Waals-London's law, assuming that only one of the ground state eigenspaces of
the atoms is irreducible in an appropriate sense. On the other hand we prove
strict monotonicity of the interaction energy at large distances and, under
more restrictive assumptions, we provide the leading order of its first two
derivatives. The first derivative is interpreted as the force in Physics.
Moreover, the estimates of the first two derivatives provide a rigorous proof
of the monotonicity and concavity of the interaction energy at large distances.


  Hexagonal boron nitride is an ideal dielectric to form two-dimensional
heterostructures due to the fact that it can be exfoliated to be just few atoms
thick and its a very low density of defects. By placing graphene nanoribbons on
high quality hexagonal boron nitride it is possible to create ideal quasi one
dimensional (1D) systems with very high mobility. The availability of high
quality one-dimensional electronic systems is of great interest also given that
when in proximity to a superconductor they can be effectively engineered to
realize Majorana bound states. In this work we study how a boron nitride
substrate affects the electronic properties of graphene nanoribbons. We
consider both armchair and zigzag nanoribbons. Our results show that for some
stacking configurations the boron nitride can significantly affect the
electronic structure of the ribbons. In particular, for zigzag nanoribbons, due
to the lock between spin and sublattice degree of freedom at the edges, the
hexagonal boron nitride can induce a very strong spin-splitting of the spin
polarized, edge sates. We find that such spin-splitting can be as high as
40~meV.


  We highlight what seems to be a remaining subtlety in the argument for the
cancellation of the total anomaly associated with the M5-brane in M-theory.
Then we prove that this subtlety is resolved under the hypothesis that the
C-field flux is charge-quantized in the generalized cohomology theory called
J-twisted Cohomotopy.


  By considering linear-order departures from general relativity, we compute a
novel expression for the weak lensing convergence power spectrum under
alternative theories of gravity. This comprises an integral over a 'kernel' of
general relativistic quantities multiplied by a theory-dependent 'source' term.
The clear separation between theory-independent and -dependent terms allows for
an explicit understanding of each physical effect introduced by altering the
theory of gravity. We take advantage of this to explore the degeneracies
between gravitational parameters in weak lensing observations.


  The name "K3 surfaces" was coined by A. Weil in 1957 when he formulated a
research programme for these surfaces and their moduli. Since then, irreducible
holomorphic symplectic manifolds have been introduced as a higher dimensional
analogue of K3 surfaces. In this paper we present a review of this theory
starting from the definition of K3 surfaces and going as far as the global
Torelli theorem for irreducible holomorphic symplectic manifolds as recently
proved by M. Verbitsky. For many years the last open question of Weil's
programme was that of the geometric type of the moduli spaces of polarised K3
surfaces. We explain how this problem has been solved. Our method uses
algebraic geometry, modular forms and Borcherds automorphic products. We
collect and discuss the relevant facts from the theory of modular forms with
respect to the orthogonal group O(2,n). We also give a detailed description of
quasi pull-back of automorphic Borcherds products. This part contains
previously unpublished results. We apply our geometric-automorphic method to
study moduli spaces of both polarised K3 surfaces and irreducible symplectic
varieties.


  We consider neutrino flavour and spin oscillations in a magnetic field using
formalism of wave packets. Decoherence effects due to neutrino wave packets
separation are studied. The considered effects are especially important for
describing astrophysical neutrino oscillations, since they propagate on
kiloparsec scale and bigger. The obtained results are of interest for neutrino
telescopes IceCube, Baikal-GVD and KM3NeT, and also can be applied for
description of supernovae neutrino oscillations effects would be detected by
JUNO and Hyper-Kamiokande.


  Despite its clinical utility, medical image segmentation (MIS) remains a
daunting task due to images' inherent complexity and variability. Vision
transformers (ViTs) have recently emerged as a promising solution to improve
MIS; however, they require larger training datasets than convolutional neural
networks. To overcome this obstacle, data-efficient ViTs were proposed, but
they are typically trained using a single source of data, which overlooks the
valuable knowledge that could be leveraged from other available datasets.
Naivly combining datasets from different domains can result in negative
knowledge transfer (NKT), i.e., a decrease in model performance on some domains
with non-negligible inter-domain heterogeneity. In this paper, we propose
MDViT, the first multi-domain ViT that includes domain adapters to mitigate
data-hunger and combat NKT by adaptively exploiting knowledge in multiple small
data resources (domains). Further, to enhance representation learning across
domains, we integrate a mutual knowledge distillation paradigm that transfers
knowledge between a universal network (spanning all the domains) and auxiliary
domain-specific branches. Experiments on 4 skin lesion segmentation datasets
show that MDViT outperforms state-of-the-art algorithms, with superior
segmentation performance and a fixed model size, at inference time, even as
more domains are added. Our code is available at
https://github.com/siyi-wind/MDViT.


  The main goal of this paper is to give a pedagogical introduction to Quantum
Information Theory-to do this in a new way, using network diagrams called
Quantum Bayesian Nets. A lesser goal of the paper is to propose a few new
ideas, such as associating with each quantum Bayesian net a very useful density
matrix that we call the meta density matrix.


  The search for low-mass dark matter (DM) goes in parallel with the
identification of new detection channels and the development of suitable
detectors. Detection of the resulting small energy depositions is challenging:
it requires extremely high sensitivity, only achievable by cryogenic thermal
detectors, which might be put to the limit. Understanding the processes which
can limit performances of these detectors can be thus crucial for evaluating
the feasibility of the proposed new detection schemes and to design the
detectors and tune their performance. In this paper we focus on a promising
detection scheme, the excitation of single optical phonons in polar materials,
to evaluate one of the possible limiting factors of cryogenic thermal
detectors, i.e. the phonon dynamics in the target/absorber. We present a
detailed theoretical analysis, within an entirely ab initio scheme, of the
downconversion and propagation processes undergone by optical phonons, created
by the interaction of a low-mass DM particle in an Al2O3 target, until they
reach the interface with a phonon Al collector. After a preliminary
methodological survey that reveals the limitations of any Relaxation Time
Approximation based method, we developed a 3D beyond-RTA phonon Monte Carlo
that allowed us to introduce the spatial dimension of the device and address
questions about impact of target size and scattering position. We analyse also
the effect of the phonon energy and wavevector and show that isotopes can,
perhaps counterintuitively, result in a larger heat flux by providing transport
channels of higher velocities, thus favoring detection. Our results suggest
that, though challenging, the direct detection of light DM via athermal phonon
generation appears feasible, and that the phonon downconversion followed by
quasi-ballistic propagation does not appear to be a major bottleneck in terms
of reducing the signal.


  We theoretically study the spin-polarized current flowing through a Josephson
junction (JJ) in a spin injection device. When the spin-polarized current is
injected from a ferromagnet (FM) in a superconductor (SC), the charge current
is carried by the superconducting condensate (Cooper pairs), while the spin-up
and spin-down currents flow in the equal magnitude but in the opposite
direction in SC, because of no quasiparticle charge current in SC. This
indicates that not only the Josephson current but also the spin current flow
across JJ at zero bias voltage, thereby generating Joule heating by the spin
current. The result provides a new method for detecting the spin current by
measuring Joule heating at JJ.


  As the volume of data being produced is increasing at an exponential rate
that needs to be processed quickly, it is reasonable that the data needs to be
available very close to the compute devices to reduce transfer latency. Due to
this need, local filesystems are getting close attention to understand their
inner workings, performance, and more importantly their limitations. This study
analyzes few popular Linux filesystems: EXT4, XFS, BtrFS, ZFS, and F2FS by
creating, storing, and then reading back one billion files from the local
filesystem. The study also captured and analyzed read/write throughput, storage
blocks usage, disk space utilization and overheads, and other metrics useful
for system designers and integrators. Furthermore, the study explored other
side effects such as filesystem performance degradation during and after these
large numbers of files and folders are created.


  It is generally accepted that the dynamics of relativistic particles in the
lab frame can be described by taking into account the relativistic dependence
of the particles momenta on the velocity, with no reference to Lorentz
transformations. The electrodynamics problem can then be treated within a
"single inertial frame" description. To evaluate radiation fields from moving
charged particles we need their velocities and positions as a function of the
lab frame time t. The relativistic motion of a particle in the lab frame is
described by Newton's second law corrected for the relativistic dependence of
the particle momentum on the velocity. In all standard derivations the
trajectories in the source part of the usual Maxwell's equations are identified
with the trajectories $\vec{x}(t)$ calculated by using the "corrected" Newton's
second law. This way of coupling fields and particles is considered correct. We
argue that this procedure needs to be changed by demonstrating a
counterintuitive: the results of conventional theory of radiation by
relativistically moving charges are not consistent with the principle of
relativity. The trajectory of a particle in the lab frame consistent with the
usual Maxwell's equations, is found by solving the dynamics equation in
manifestly covariant form, with the proper time $\tau$ used to parameterize the
particle world-line in space-time. We find a difference between the "true"
particle trajectory $\vec{x}(t)$ calculated or measured in the conventional
way, and the covariant particle trajectory $\vec{x}_{cov}(t)$ calculated by
projecting the world-line to the lab frame and using t to parameterize the
trajectory curve. The difference is due to a choice of convention, but only
$\vec{x}_{cov}(t)$ is consistent with the usual Maxwell's equations: therefore,
a correction of the conventional synchrotron-cyclotron radiation theory is
required.


  We present for the first time to the nuclear physics community the
Hamiltonian Mean Field (HMF) model. The model can be solved analytically in the
canonical ensemble and shows a second-order phase transition in the
thermodynamic limit. Numerical microcanonical simulations show interesting
features in the out-of-equilibrium regime: in particular the model has a
negative specific heat. The potential relevance for nuclear multifragmentation
is discussed.


  The longest common substring with $k$-mismatches problem is to find, given
two strings $S_1$ and $S_2$, a longest substring $A_1$ of $S_1$ and $A_2$ of
$S_2$ such that the Hamming distance between $A_1$ and $A_2$ is $\le k$. We
introduce a practical $O(nm)$ time and $O(1)$ space solution for this problem,
where $n$ and $m$ are the lengths of $S_1$ and $S_2$, respectively. This
algorithm can also be used to compute the matching statistics with
$k$-mismatches of $S_1$ and $S_2$ in $O(nm)$ time and $O(m)$ space. Moreover,
we also present a theoretical solution for the $k = 1$ case which runs in $O(n
\log m)$ time, assuming $m\le n$, and uses $O(m)$ space, improving over the
existing $O(nm)$ time and $O(m)$ space bound of Babenko and Starikovskaya.


  Few-shot named entity recognition can identify new types of named entities
based on a few labeled examples. Previous methods employing token-level or
span-level metric learning suffer from the computational burden and a large
number of negative sample spans. In this paper, we propose the Hybrid
Multi-stage Decoding for Few-shot NER with Entity-aware Contrastive Learning
(MsFNER), which splits the general NER into two stages: entity-span detection
and entity classification. There are 3 processes for introducing MsFNER:
training, finetuning, and inference. In the training process, we train and get
the best entity-span detection model and the entity classification model
separately on the source domain using meta-learning, where we create a
contrastive learning module to enhance entity representations for entity
classification. During finetuning, we finetune the both models on the support
dataset of target domain. In the inference process, for the unlabeled data, we
first detect the entity-spans, then the entity-spans are jointly determined by
the entity classification model and the KNN. We conduct experiments on the open
FewNERD dataset and the results demonstrate the advance of MsFNER.


  Humans and animals explore their environment and acquire useful skills even
in the absence of clear goals, exhibiting intrinsic motivation. The study of
intrinsic motivation in artificial agents is concerned with the following
question: what is a good general-purpose objective for an agent? We study this
question in dynamic partially-observed environments, and argue that a compact
and general learning objective is to minimize the entropy of the agent's state
visitation estimated using a latent state-space model. This objective induces
an agent to both gather information about its environment, corresponding to
reducing uncertainty, and to gain control over its environment, corresponding
to reducing the unpredictability of future world states. We instantiate this
approach as a deep reinforcement learning agent equipped with a deep
variational Bayes filter. We find that our agent learns to discover, represent,
and exercise control of dynamic objects in a variety of partially-observed
environments sensed with visual observations without extrinsic reward.


  We define the Analytical signature, the Hodge signature and the de Rham
signature for a foliated manifold with boundary with foliation transverse to
the boundary. We show that all these signatures coincide and a Hirzebruch
formula is valid.


  Let X be an infinite, compact, metrizable space of finite covering dimension
and h a minimal homeomorphism of X. We prove that the crossed product of C(X)
by h absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension.
As a consequence, these algebras are determined up to isomorphism by their
graded ordered K-theory under the necessary condition that their projections
separate traces. This result applies, in particular, to those crossed products
arising from uniquely ergodic homeomorphisms.


  In 1992 G. B. Ermentrout and J. B. McLeod published a landmark study of
traveling wave fronts for a differential-integral equation modeling a neural
network. Since then a number of authors have extended the model by adding an
additional equation for a "recovery variable", thus allowing the possibility of
traveling pulse type solutions. In a recent paper G. Faye gave perhaps the
first rigorous proof of the existence (and stability) of a traveling pulse
solution for such a model. The excitatory weight function J used in this work
allowed the system to be reduced to a set of four coupled ODEs, and a specific
firing rate function S, with parameters, was considered. The method of
geometric singular perturbation was employed, together with blow-ups. In this
paper, while keeping the same J, we extend Faye's work by obtaining both the
fast and slow waves and by removing Faye's hypothesis that the wave passes
"under the knee". We also consider a more general set of functions S, and we
use only standard ode methods.


  Based on the spontaneous breaking of chiral symmetry, chiral perturbation
theory (ChPT) is believed to approximate confinement scale QCD. Dedicated and
increasingly accurate experiments and improving lattice calculations are
confirming this belief, and we are entering a new era in which we can test
confinement scale QCD in some well chosen reactions. This is demonstrated with
an overview of low energy experimental tests of ChPT predictions of $\pi\pi$
scattering, pion properties, $\pi$N scattering and electromagnetic pion
production. These predictions have been shown to be consistent with QCD in the
meson sector by increasingly accurate lattice calculations. At present there is
good agreement between experiment and ChPT calculations, including the $\pi\pi$
and $\pi$N s wave scattering lengths and the $\pi^{0}$ lifetime. Recent,
accurate pionic atom data are in agreement with chiral calculations once
isospin breaking effects due to the mass difference of the up and down quarks
are taken into account, as was required to extract the $\pi\pi$ scattering
lengths. In addition to tests of the theory, comparisons between $\pi\pi$ and
$\pi$N interactions based on general chiral principles are discussed. Lattice
calculations are now providing results for the fundamental, long and
inconclusively studied, $\pi$N $\sigma$ term and the contribution of the
strange quark to the mass of the proton. Increasingly accurate experiments in
electromagnetic pion production experiments from the proton which test ChPT
calculations (and their energy region of validity) are presented. These
experiments are also beginning to measure the final state $\pi$N interaction.
This paper is based on the concluding remarks made at the Chiral Dynamics
Workshop CD12 held at Jefferson Lab in Aug. 2012.


  We investigate the contact process on scale-free networks evolving by a
stationary dynamics whereby each vertex independently updates its connections
with a rate depending on its power. This rate can be slowed down or speeded up
by virtue of decreasing or increasing a parameter $\eta$, with
$\eta\downarrow-\infty$ approaching the static and $\eta\uparrow\infty$ the
mean-field case. We identify the regimes of slow, fast and ultra-fast
extinction of the contact process. Slow extinction occurs in the form of
metastability, when the contact process maintains a certain density of infected
states for a time exponential in the network size. In our main result we
identify the metastability exponents, which describe the decay of metastable
densities as the infection rate goes to zero, in dependence on $\eta$ and the
power-law exponent $\tau$. While the fast evolution cases have been treated in
a companion paper, Jacob, Linker, M\"orters (2019), the present paper looks at
the significantly more difficult cases of slow network evolution. We describe
various effects, like degradation, regeneration and depletion, which lead to a
rich picture featuring numerous first-order phase transitions for the
metastable exponents. To capture these effects in our upper bounds we develop a
new martingale based proof technique combining a local and global analysis of
the process.


  I use a time-dependent Lagrangian formalism and a variational trial function
to study the dynamics of a two-component vortex in a spin-orbit coupled
Bose-Einstein condensate (BEC). For a single-component BEC, various experiments
have validated this theoretical approach, for example a thermal quench that
yields a quantized vortex in roughly 25% of trials. To be definite, I assume
the specific spin-orbit form used in recent NIST experiments, which introduces
a spatial asymmetry because of the external Raman laser beams. I here
generalize this formalism to include a two-component order parameter that has
quantized circulation in each component but not necessarily with the same
circulation. For example a singly quantized vortex in just one component yields
a BEC analog of the half-quantum vortex familiar in $^3$He-A and in $p$-wave
chiral superconductors. This and other unusual two-component vortices have both
periodic trajectories and unbounded trajectories that leave the condensate,
depending on the initial conditions. The optimized phase of the order parameter
induces a term in the particle current that cancels the contribution from the
vector potential, leaving pure circulating current around the vortex.


  Using the concept of fractional derivatives of Riemann$-$Liouville on time
scales, we first introduce right fractional Sobolev spaces and characterize
them. Then, we prove the equivalence of some norms in the introduced spaces,
and obtain their completeness, reflexivity, separability and some imbeddings.
Finally, as an application, we propose a recent method to study the existence
of weak solutions of fractional boundary value problems on time scales by using
variational method and critical point theory, and by constructing an
appropriate variational setting, we obtain two existence results of the
problem.


  The use of machine learning (ML) based techniques has become increasingly
popular in the field of bioacoustics over the last years. Fundamental
requirements for the successful application of ML based techniques are curated,
agreed upon, high-quality datasets and benchmark tasks to be learned on a given
dataset. However, the field of bioacoustics so far lacks such public benchmarks
which cover multiple tasks and species to measure the performance of ML
techniques in a controlled and standardized way and that allows for
benchmarking newly proposed techniques to existing ones. Here, we propose BEANS
(the BEnchmark of ANimal Sounds), a collection of bioacoustics tasks and public
datasets, specifically designed to measure the performance of machine learning
algorithms in the field of bioacoustics. The benchmark proposed here consists
of two common tasks in bioacoustics: classification and detection. It includes
12 datasets covering various species, including birds, land and marine mammals,
anurans, and insects. In addition to the datasets, we also present the
performance of a set of standard ML methods as the baseline for task
performance. The benchmark and baseline code is made publicly available at
\url{https://github.com/earthspecies/beans} in the hope of establishing a new
standard dataset for ML-based bioacoustic research.


  We prove two sharp sufficient conditions for hamiltonian cycles in balanced
bipartite directed graph. Let $D$ be a strongly connected balanced bipartite
directed graph of order $2a$. Let $x,y$ be distinct vertices in $D$. $\{x,y\}$
dominates a vertex $z$ if $x\rightarrow z$ and $y\rightarrow z$; in this case,
we call the pair $\{x,y\}$ dominating.
  (i) {\it If $a\geq 4$ and $max \{d(x), d(y)\}\geq 2a-1$ for every dominating
pair of vertices $\{x,y\}$, then either $D$ is hamiltonian or $D$ is isomorphic
to one exceptional digraph of order eight.}
  (ii) {\it If $a\geq 5$ and $d(x)+d(y)\geq 4a-3$ for every dominating pair of
vertices $\{x,y\}$, then $D$ is hamiltonian.}
  The first result improves a theorem of R. Wang (arXiv:1506.07949 [math.CO]),
the second result, in particular, establishes a conjecture due to Bang-Jensen,
Gutin and Li (J. Graph Theory , 22(2), 1996) for strongly connected balanced
bipartite digraphs of order at least ten.


  Objective collapse theories propose modifications to Schr\"odinger's equation
that solve the quantum measurement problem by interpolating between microscopic
quantum dynamics and projective evolution of macroscopic objects. Objective
collapse theories extending the equilibrium description of spontaneous symmetry
breaking to spontaneous violations of unitarity in quantum dynamics were
recently shown to possess a physical white noise limit when applied to initial
two-state superpositions. Here, we show the existence of a generic physical
white noise limit for models of spontaneous unitarity violation applicable to
any initial state. We show that in this limit, the emergence of Born rule
statistics is enforced by a fluctuation-dissipation relation, and that the
ensemble averaged probability densities follow the GKSL master equation
corresponding to a linear quantum semi-group, guaranteeing the absence of
superluminal signalling.


  The concept of entropy is not uniquely relevant to the statistical mechanics
but among others it can play pivotal role in the analysis of a time series,
particularly the stock market data. In this area sudden events are especially
interesting as they describe abrupt data changes which may have long-lasting
effects. Here, we investigate the impact of such events on the entropy of
financial time series. As a case study we assume data of polish stock market in
the context of its main cumulative index. This index is discussed for the
finite time periods before and after outbreak of the 2022 Russian invasion of
Ukraine, acting as the sudden event. The analysis allows us to validate the
entropy-based methodology in assessing market changes as driven by the extreme
external factors. We show that qualitative features of market changes can be
captured quantitatively in terms of the entropy. In addition to that, the
magnitude of the impact is analysed over various time periods in terms of the
introduced entropic index. To this end, the present work also attempts to
answer whether or not the recent war can be considered as a reason or at least
catalyst to the current economic crisis.