  The use of low-cost sensors in conjunction with high-precision
instrumentation for air pollution monitoring has shown promising results in
recent years. One of the main challenges for these sensors has been the quality
of their data, which is why the main efforts have focused on calibrating the
sensors using machine learning techniques to improve the data quality. However,
there is one aspect that has been overlooked, that is, these sensors are
mounted on nodes that may have energy consumption restrictions if they are
battery-powered. In this paper, we show the usual sensor data gathering process
and we study the existing trade-offs between the sampling of such sensors, the
quality of the sensor calibration, and the power consumption involved. To this
end, we conduct experiments on prototype nodes measuring tropospheric ozone,
nitrogen dioxide, and nitrogen monoxide at high frequency. The results show
that the sensor sampling strategy directly affects the quality of the air
pollution estimation and that each type of sensor may require different
sampling strategies. In addition, duty cycles of 0.1 can be achieved when the
sensors have response times in the order of two minutes, and duty cycles
between 0.01 and 0.02 can be achieved when the sensor response times are
negligible, calibrating with hourly reference values and maintaining a quality
of calibrated data similar to when the node is connected to an uninterruptible
power supply.


  Invisible particles frequently appear in final state in studying physics at
colliders. Experimental precision is also low in measuring missing energy. In
this paper, we propose a general approach for studying process involving
invisible particles. We provided two kinematical observables which are
sensitive to production kinematics in different regions, and hence are
complementary. Usage of our approach is illustrated by three examples. It is
shown that our observables are still useful in case of that the significance
S/B is relatively low.


  We investigate 1, 2, 3, and 4 monolayers of iron grown on the (001) surface
of ZnSe using spin density functional theory, plane-wave expansion, and
ultrasoft pseudopotentials. An ideal structure of the interface is plausible
due to the very small lattice mismatch between both materials. However, we
observe dramatic deviations from this idealized configuration. The most
distinctive variations arise in the case of a single monolayer. Here a
terminating Zn layer is buoying upwards. The thicker the Fe layer the weaker
are the relaxations in the iron region. Nevertheless, in the case of the
Se-terminated surface, the structure changes significantly inside the
semiconductor near the interface. The profiles of the electronic density and
the magnetization perpendicular to the surface are quite sensitive to the
change from the ideal to the real structure.


  We study the elliptic sinh-Gordon and sine-Gordon equations on the real plane
and we introduce new families of solutions. We use a Backlund transformation
that connects the elliptic versions of sinh-Gordon and sine-Gordon equations.
As an application, we construct new harmonic maps between surfaces, when the
target is of constant curvature -1.


  In this report we demonstrate a novel concept for a planar cavity polariton
beam amplifier using non-resonant excitation. In contrast to resonant
excitation schemes, background carriers are injected which form excitons,
providing both gain and a repulsive potential for a polariton condensate. Using
an attractive potential environment induced by a locally elongated cavity
layer, the repulsive potential of the injected background carriers is
compensated and a significant amplification of polariton beams is achieved
without beam distortion.


  A new and relatively unexplored research direction in robotics systems is the
coordination of humans and robots working as a team. In this paper, we focus
upon problem domains and tasks in which multiple robots, humans and other
agents are cooperating through coordination to satisfy a set of goals or to
maximize utility. We are primarily interested in applications of human robot
coordination in entertainment and other activities of daily life. We discuss
the teamwork problem and propose an architecture to address this.


  The aim of this note is to present simple proofs of the completeness of
Manakov's integrals for a motion of a rigid body fixed at a point in $\mathbb
R^n$, as well as for geodesic flows on a class of homogeneous spaces
$SO(n)/SO(n_1)\times\dots\times SO(n_r)$.


  Boson clouds around black holes exhibit interesting physical phenomena
through the Penrose process of superradiance, leading to black hole spin-down.
Axionic clouds are of particular interest, since the axion Compton wavelength
could be comparable to the Schwarzschild radius, leading to the formation of
"gravitational atoms" with a black hole nucleus. These clouds collapse under
certain conditions, leading to a "Bosenova". We model the dynamics of such
unstable boson clouds by a simple cellular automaton and show that it exhibits
self-organized criticality. Our results suggest that the evolution through the
black hole Regge plane is due to self-organized criticality.


  Traffic forecasting is a complex multivariate time-series regression task of
paramount importance for traffic management and planning. However, existing
approaches often struggle to model complex multi-range dependencies using local
spatiotemporal features and road network hierarchical knowledge. To address
this, we propose MultiSPANS. First, considering that an individual recording
point cannot reflect critical spatiotemporal local patterns, we design
multi-filter convolution modules for generating informative ST-token embeddings
to facilitate attention computation. Then, based on ST-token and
spatial-temporal position encoding, we employ the Transformers to capture
long-range temporal and spatial dependencies. Furthermore, we introduce
structural entropy theory to optimize the spatial attention mechanism.
Specifically, The structural entropy minimization algorithm is used to generate
optimal road network hierarchies, i.e., encoding trees. Based on this, we
propose a relative structural entropy-based position encoding and a multi-head
attention masking scheme based on multi-layer encoding trees. Extensive
experiments demonstrate the superiority of the presented framework over several
state-of-the-art methods in real-world traffic datasets, and the longer
historical windows are effectively utilized. The code is available at
https://github.com/SELGroup/MultiSPANS.


  We investigate the phase diagram of a general class of $4$-dimensional exact
regular hairy planar black holes. For some particular values of the parameters
in the moduli potential, these solutions can be embedded in $\omega$-deformed
$\mathcal{N}=8$ gauged supergravity. We construct the hairy soliton that is the
ground state of the theory and show that there exist first order phase
transitions.


  Federated learning is an emerging technique for training models from
decentralized data sets. In many applications, data owners participating in the
federated learning system hold not only the data but also a set of domain
knowledge. Such knowledge includes human know-how and craftsmanship that can be
extremely helpful to the federated learning task. In this work, we propose a
federated learning framework that allows the injection of participants' domain
knowledge, where the key idea is to refine the global model with knowledge
locally. The scenario we consider is motivated by a real industry-level
application, and we demonstrate the effectiveness of our approach to this
application.


  Techniques for detecting mirrors from static images have witnessed rapid
growth in recent years. However, these methods detect mirrors from single input
images. Detecting mirrors from video requires further consideration of temporal
consistency between frames. We observe that humans can recognize mirror
candidates, from just one or two frames, based on their appearance (e.g. shape,
color). However, to ensure that the candidate is indeed a mirror (not a picture
or a window), we often need to observe more frames for a global view. This
observation motivates us to detect mirrors by fusing appearance features
extracted from a short-term attention module and context information extracted
from a long-term attention module. To evaluate the performance, we build a
challenging benchmark dataset of 19,255 frames from 281 videos. Experimental
results demonstrate that our method achieves state-of-the-art performance on
the benchmark dataset.


  The dual holographic description has enjoyed many successes in explaining
fundamental properties of the early stages of relativistic heavy ion collisions
up to the formation of a minimal-viscosity quark-gluon fluid. However, there
have been few attempts to extend its application beyond this stage. Here we
explore the prospects for such an extension beyond the time of hadronization.
Our discussion makes use of recent insights into the duality of entanglement
properties of field theory states in the edge of Anti-de Sitter space and
non-trivial topologies of horizons in the bulk, often referred to as ER = EPR
duality. We discuss this topic from the point of view of heavy-ion
phenomenology, review several relevant concepts, and map out a path toward
combining them into a comprehensive, at least semiquantitative description of
relativistic heavy ion collisions. We outline possible next steps in this
direction.


  Polar ice develops anisotropic crystal orientation fabrics under deformation,
yet ice is most often modelled as an isotropic fluid. We present
three-dimensional simulations of the crystal orientation fabric of Derwael Ice
Rise including the surrounding ice shelf using a crystal orientation tensor
evolution equation corresponding to a fixed velocity field. We use a
semi-Lagrangian numerical method that constrains the degree of crystal
orientation evolution to solve the equations in complex flow areas. We perform
four simulations based on previous studies, altering the rate of evolution of
the crystal anisotropy and its dependence on a combination of the strain rate
and deviatoric stress tensors. We provide a framework for comparison with radar
observations of the anisotropy field, outlining areas where the assumption of
one vertical eigenvector may not hold and provide resulting errors in measured
eigenvalues. We recognise the areas of high horizontal divergence at the ends
of the flow divide as important areas to make comparisons with observations.
Here, poorly constrained model parameters result in the largest difference in
fabric type. These results are important in the planning of future campaigns
for gathering data to constrain model parameters and as a link between
observations and computationally-efficient, simplified models of anisotropy.


  A significant body of recent research in the field of Learning Analytics has
focused on leveraging machine learning approaches for predicting at-risk
students in order to initiate timely interventions and thereby elevate
retention and completion rates. The overarching feature of the majority of
these research studies has been on the science of prediction only. The
component of predictive analytics concerned with interpreting the internals of
the models and explaining their predictions for individual cases to
stakeholders has largely been neglected. Additionally, works that attempt to
employ data-driven prescriptive analytics to automatically generate
evidence-based remedial advice for at-risk learners are in their infancy.
  eXplainable AI is a field that has recently emerged providing cutting-edge
tools which support transparent predictive analytics and techniques for
generating tailored advice for at-risk students. This study proposes a novel
framework that unifies both transparent machine learning as well as techniques
for enabling prescriptive analytics, while integrating the latest advances in
large language models. This work practically demonstrates the proposed
framework using predictive models for identifying at-risk learners of programme
non-completion. The study then further demonstrates how predictive modelling
can be augmented with prescriptive analytics on two case studies in order to
generate human-readable prescriptive feedback for those who are at risk using
ChatGPT.


  We verify a recent conjecture of Kenyon/Szendroi, arXiv:0705.3419, by
computing the generating function for pyramid partitions. Pyramid partitions
are closely related to Aztec Diamonds; their generating function turns out to
be the partition function for the Donaldson--Thomas theory of a non-commutative
resolution of the conifold singularity {x1x2 -x3x4 = 0}. The proof does not
require algebraic geometry; it uses a modified version of the domino shuffling
algorithm of Elkies, Kuperberg, Larsen and Propp.


  We present a partition of quantum observables in an open quantum system which
is inherited from the division of the underlying Hilbert space or configuration
space. It is shown that this partition leads to the definition of an
inhomogeneous continuity equation for generic, non-local observables. This
formalism is employed to describe the local evolution of the von Neumann
entropy of a system of independent quantum particles out of equilibrium.
Crucially, we find that all local fluctuations in the entropy are governed by
an entropy current operator, implying that the production of entanglement
entropy is not measured by this partitioned entropy. For systems linearly
perturbed from equilibrium, it is shown that this entropy current is equivalent
to a heat current, provided that the system-reservoir coupling is partitioned
symmetrically. Finally, we show that any other partition of the coupling leads
directly to a divergence of the von Neumann entropy. Thus, we conclude that
Hilbert-space partitioning is the only partition of the von Neumann entropy
which is consistent with the Laws of Thermodynamics.


  Kilonovae produced by the coalescence of compact binaries with at least one
neutron star are promising standard sirens for an independent measurement of
the Hubble constant ($H_0$). Through their detection via follow-up of
gravitational-wave (GW), short gamma-ray bursts (sGRBs) or optical surveys, a
large sample of kilonovae (even without GW data) can be used for $H_0$
contraints. Here, we show measurement of $H_0$ using light curves associated
with four sGRBs, assuming these are attributable to kilonovae, combined with
GW170817. Including a systematic uncertainty on the models that is as large as
the statistical ones, we find $H_0 = 73.8^{+6.3}_{-5.8}$\,$\mathrm{km}$
$\mathrm{s}^{-1}$ $\mathrm{Mpc}^{-1}$ and $H_0 =
71.2^{+3.2}_{-3.1}$\,$\mathrm{km}$ $\mathrm{s}^{-1}$ $\mathrm{Mpc}^{-1}$ for
two different kilonova models that are consistent with the local and
inverse-distance ladder measurements. For a given model, this measurement is
about a factor of 2-3 more precise than the standard-siren measurement for
GW170817 using only GWs.


  We study the solution describing a non-extreme dilatonic (p+1)-brane
intersecting a D-dimensional extreme dilatonic domain wall, where one of its
longitudinal directions is along the direction transverse to the domain wall,
in relation to the Randall-Sundrum type model. The dynamics of the probe
(p+1)-brane in such source background reproduces that of the probe p-brane in
the background of the (D-1)-dimensional source p-brane. However, as for a probe
test particle, the dynamics in one lower dimensions is reproduced, only when
the source (p+1)-brane is uncharged.


  We take a long term look at initial employment trends for new doctorates with
an eye towards gender, citizenship, and gender and citizenship differences by
analyzing data from 1991-2015 AMS-ASA-IMS-MAA- SIAM Annual Surveys. The data
show that the unemployment rate for women has been equal to or lower than the
rate for men during most of the last quarter century. The one exception is that
between 2001 and 2015 the unemployment rate for women who are not U.S. citizens
was higher than the rate for non-citizen men. The unemployment rates are higher
for males who are U.S. citizens than for non-citizen males in the last fifteen
years, a puzzling trend. The data show that men from all pure math programs are
considerably more likely than women to take jobs at the top-ranking and
top-producing math departments. The data show women take jobs at departments in
which the highest degree is a bachelor's degree at much higher rates and men
take jobs in business and industry at considerably higher rates. We also find
that men from the top-ranking or top-producing doctoral programs tend to be
more likely to take jobs at academic institutions or research institutes at
least on a par with their degreegranting institutions.


  Coverings of convex bodies have emerged as a central component in the design
of efficient solutions to approximation problems involving convex bodies.
Intuitively, given a convex body $K$ and $\epsilon> 0$, a covering is a
collection of convex bodies whose union covers $K$ such that a constant factor
expansion of each body lies within an $\epsilon$ expansion of $K$. Coverings
have been employed in many applications, such as approximations for diameter,
width, and $\epsilon$-kernels of point sets, approximate nearest neighbor
searching, polytope approximations, and approximations to the Closest Vector
Problem (CVP).
  It is known how to construct coverings of size $n^{O(n)} /
\epsilon^{(n-1)/2}$ for general convex bodies in $\textbf{R}^n$. In special
cases, such as when the convex body is the $\ell_p$ unit ball, this bound has
been improved to $2^{O(n)} / \epsilon^{(n-1)/2}$. This raises the question of
whether such a bound generally holds. In this paper we answer the question in
the affirmative.
  We demonstrate the power and versatility of our coverings by applying them to
the problem of approximating a convex body by a polytope, under the
Banach-Mazur metric. Given a well-centered convex body $K$ and an approximation
parameter $\epsilon> 0$, we show that there exists a polytope $P$ consisting of
$2^{O(n)} / \epsilon^{(n-1)/2}$ vertices (facets) such that $K \subset P
\subset K(1+\epsilon)$. This bound is optimal in the worst case up to factors
of $2^{O(n)}$. As an additional consequence, we obtain the fastest
$(1+\epsilon)$-approximate CVP algorithm that works in any norm, with a running
time of $2^{O(n)} / \epsilon ^{(n-1)/2}$ up to polynomial factors in the input
size, and we obtain the fastest $(1+\epsilon)$-approximation algorithm for
integer programming. We also present a framework for constructing coverings of
optimal size for any convex body (up to factors of $2^{O(n)}$).


  Deep neural networks have empowered accurate device-free human activity
recognition, which has wide applications. Deep models can extract robust
features from various sensors and generalize well even in challenging
situations such as data-insufficient cases. However, these systems could be
vulnerable to input perturbations, i.e. adversarial attacks. We empirically
demonstrate that both black-box Gaussian attacks and modern adversarial
white-box attacks can render their accuracies to plummet. In this paper, we
firstly point out that such phenomenon can bring severe safety hazards to
device-free sensing systems, and then propose a novel learning framework,
SecureSense, to defend common attacks. SecureSense aims to achieve consistent
predictions regardless of whether there exists an attack on its input or not,
alleviating the negative effect of distribution perturbation caused by
adversarial attacks. Extensive experiments demonstrate that our proposed method
can significantly enhance the model robustness of existing deep models,
overcoming possible attacks. The results validate that our method works well on
wireless human activity recognition and person identification systems. To the
best of our knowledge, this is the first work to investigate adversarial
attacks and further develop a novel defense framework for wireless human
activity recognition in mobile computing research.


  (lecture delivered at the Congress of the Romanian mathematicians, Brasov,
June 2011) Using graph representations a new class of computable topological
invariants associated with a tame real or angle valued map were recently
introduced, providing a theory which can be viewed as an alternative to
Morse-Novicov theory for real or angle valued Morse maps. The invariants are
"barcodes" and "Jordan cells". From them one can derive all familiar
topological invariants which can be derived via Morse-Novikov theory, like the
Betti numbers and in the case of angle valued maps also the Novikov Betti
numbers and the monodromy. Stability results for (some) bar codes and the
homotopy invariance of the Jordan cells are the key results, and two new
polynomials for any nonnegative integer (up to the dimension of the source)
associated to a continuous nonzero complex valued map provide potentially
interesting refinements of the Betti numbers and of the Novikov Betti numbers.
In our theory the bar codes which are intervals with ends critical
values/angles, the Jordan cells and the " canonical long exact sequence" of a
tame map are the analogues of instantons between rest points, closed
trajectories and of the Morse-Smale complex of the gradient of a Morse function
in the Morse-Novikov theory.


  We show that Bernstein polynomials are related to the Lebesgue measure on [0,
1] in a manner similar as Chebyshev polynomials are related to the equilibrium
measure of [--1, 1]. We also show that Pell's polynomial equation satisfied by
Chebyshev polynomials, provides a partition of unity of [--1, 1], the analogue
of the partition of unity of [0, 1] provided by Bernstein polynomials. Both
partitions of unity are interpreted as a specific algebraic certificate that
the constant polynomial ''1'' is positive-on [--1, 1] via Putinar's certificate
of positivity (for Chebyshev), and-on [0, 1] via Handeman's certificate of
positivity (for Bernstein). Then in a second step, one combines this partition
of unity with an interpretation of a duality result of Nesterov in convex conic
optimization to obtain an explicit connection with the equilibrium measure on
[--1, 1] (for Chebyshev) and Lebesgue measure on [0, 1] (for Bernstein).
Finally this connection is also partially established for the ''d''-dimensional
simplex.


  Graphene, a unique two-dimensional material of carbon in a honeycomb lattice,
has brought remarkable breakthroughs across the domains of electronics,
mechanics, and thermal transport, driven by the quasiparticle Dirac fermions
obeying a linear dispersion. Here we demonstrate a counter-pumped all-optical
difference frequency process to coherently generate and control THz plasmons in
atomic layer graphene with an octave tunability and high efficiency. We
leverage the inherent surface asymmetry of graphene for a strong second-order
nonlinear polarizability chi(2), which together with tight plasmon field
confinement, enables a robust difference frequency signal at THz frequencies.
The counter-pumped resonant process on graphene uniquely achieves both energy
and momentum conservation. Consequently we demonstrate a dual-layer graphene
heterostructure that achieves the charge- and gate-tunability of the THz
plasmons over an octave, from 9.4 THz to 4.7 THz, bounded only by the pump
amplifier optical bandwidth. Theoretical modeling supports our
single-volt-level gate tuning and optical-bandwidth-bounded 4.7 THz
phase-matching measurements, through the random phase approximation with phonon
coupling, saturable absorption, and below the Landau damping, to predict and
understand the graphene carrier plasmon physics.


  Conventional quantization of two-dimensional diffeomorphism and Weyl
invariant theories sacrifices the latter symmetry to anomalies, while
maintaining the former. When alternatively Weyl invariance is preserved by
abandoning diffeomorphism invariance, we find that some invariance against
coordinate redefinition remains: one can still perform at will transformations
possessing a constant Jacobian. The alternate approach enjoys as much ``gauge''
symmetry as the conventional formulation.


  We prove the first $\chi$-bounding function for circle graphs that is optimal
up to a constant factor. To be more precise, we prove that every circle graph
with clique number at most $\omega$ has chromatic number at most $2\omega
\log_2 (\omega) +2\omega \log_2(\log_2 (\omega)) + 10\omega$.


  Addressing the charged particle beam diagnostics in accelerators poses a
formidable challenge, demanding high-fidelity simulations in limited
computational time. Machine learning (ML) based surrogate models have emerged
as a promising tool for non-invasive charged particle beam diagnostics. Trained
ML models can make predictions much faster than computationally expensive
physics simulations. In this work, we have proposed a temporally structured
variational autoencoder model to autoregressively forecast the spatiotemporal
dynamics of the 15 unique 2D projections of 6D phase space of charged particle
beam as it travels through the LANSCE linear accelerator. In the model, VAE
embeds the phase space projections into a lower dimensional latent space. A
long-short-term memory network then learns the temporal correlations in the
latent space. The trained network can evolve the phase space projections across
further modules provided the first few modules as inputs. The model predicts
all the projections across different modules with low mean squared error and
high structural similarity index.


  We present a construction method for mappings between generalized
connections, comprising, e.g., the action of gauge transformations,
diffeomorphisms and Weyl transformations. Moreover, criteria for continuity and
measure preservation are stated.


  We present a new method for statistical process control (SPC) of a discrete
part manufacturing system based on intrinsic geometrical properties of the
parts, estimated from three-dimensional sensor data. An intrinsic method has
the computational advantage of avoiding the difficult part registration
problem, necessary in previous SPC approaches of three-dimensional geometrical
data, but inadequate if noncontact sensors are used. The approach estimates the
spectrum of the Laplace-Beltrami (LB) operator of the scanned parts and uses a
multivariate nonparametric control chart for online process control. Our
proposal brings SPC closer to computer vision and computer graphics methods
aimed to detect large differences in shape (but not in size). However, the SPC
problem differs in that small changes in either shape or size of the parts need
to be detected, keeping a controllable false alarm rate and without completely
filtering noise. An online or "Phase II" method and a scheme for starting up in
the absence of prior data ("Phase I") are presented. Comparison with earlier
approaches that require registration shows the LB spectrum method to be more
sensitive to rapidly detect small changes in shape and size, including the
practical case when the sequence of part datasets is in the form of large,
unequal size meshes. A post-alarm diagnostic method to investigate the location
of defects on the surface of a part is also presented. While we focus in this
article on surface (triangulation) data, the methods can also be applied to
point cloud and voxel metrology data.


  We consider a one-dimensional diffusion which solves a stochastic
differential equation with Borel-measurable coefficients in an open interval.
We allow for the endpoints to be inaccessible or absorbing. Given a
Borel-measurable function $r$ that is uniformly bounded away from 0, we
establish a new analytic representation of the $r$-potential of a continuous
additive functional of the diffusion. We also characterize the value function
of an optimal stopping problem with general reward function as the unique
solution of a variational inequality (in the sense of distributions) with
appropriate growth or boundary conditions. Furthermore, we establish several
other characterisations of the solution to the optimal stopping problem,
including a generalisation of the so-called "principle of smooth fit".


  This paper describes BomJi, a supervised system for capturing discriminative
attributes in word pairs (e.g. yellow as discriminative for banana over
watermelon). The system relies on an XGB classifier trained on carefully
engineered graph-, pattern- and word embedding based features. It participated
in the SemEval- 2018 Task 10 on Capturing Discriminative Attributes, achieving
an F1 score of 0:73 and ranking 2nd out of 26 participant systems.


  We construct 4d $\mathcal{N}=1$ quantum field theories by compactifying the
(2,0) theories on a Riemann surface with genus $g$ and $n$ punctures, where the
normal bundle decomposes into a sum of two line bundles with possibly negative
degrees $p$ and $q$. Until recently, the only available field-theoretic
constructions required the line bundle degrees to be nonnegative, although
supergravity solutions were constructed in the literature for the zero-puncture
case for all $p$ and $q$. Here, we provide field-theoretic constructions and
computations of the central charges of 4d $\mathcal{N}=1$ SCFTs that are the IR
limit of M5-branes wrapping a surface with general $p$ or $q$ negative, for
general genus $g$ and number of maximal punctures $n$.


  Under a suitable bunching condition, we establish that stable holonomies
inside center-stable manifolds for $C^{1+\beta}$ diffeomorphisms are uniformly
bi-Lipschitz and in fact $C^{1+\text{H\"older}}$. This verifies that the
Pugh-Shub theory for ergodicity holds for suitably center-bunched,
$C^{1+\beta}$, essentially accessible, partially hyperbolic diffeomorphism and
verifies that the Ledrappier-Young entropy formulas hold for $C^{1+\beta}$
diffeomorphisms of compact manifolds.


  We introduce the program MAVKA for determination of characteristics of
extrema using observations in the adjacent data intervals, with intended
applications to variable stars, but it may be used for signals of arbitrary
nature. We have used a dozen of basic functions, some of them use the interval
near extremum without splitting the interval (algebraic polynomial in general
form, "Symmetrical" algebraic polynomial using only even degrees of time
(phase) deviation from the position of symmetry argument), others split the
interval into 2 subintervals (a Taylor series of the "New Algol Variable", "the
function of Prof. Z. Mikul\'a\v{s}ek"), or even 3 parts ("Asymptotic Parabola",
"Wall-Supported Parabola", "Wall-Supported Line", "Wall-Supported Asymptotic
Parabola", "Parabolic Spline of defect 1"). The variety of methods allows to
choose the "best" (statistically optimal) approximation for a given data
sample. As the criterion, we use the accuracy of determination of the extremum.
For all parameters, the statistical errors are determined. The methods are
illustrated by applications to observations of pulsating and eclipsing variable
stars, as well as to the exoplanet transits. They are used for the
international campaigns "Inter-Longitude Astronomy", "Virtual Observatory" and
"AstroInformatics". The program may be used for studies of individual objects,
also using ground-based (NSVS, ASAS, WASP, CRTS et al.) and space (GAIA,
KEPLER, HIPPARCOS/TYCHO, WISE et al.) surveys.


  We study an impurity Anderson model to describe an iron phthalocyanine (FePc)
molecule on Au(111), motivated by previous results of scanning tunneling
spectroscopy (STS) and theoretical studies. The model hybridizes a spin doublet
consisting in one hole at the $3d_{z^2}$ orbital of iron and two degenerate
doublets corresponding to one hole either in the $3d_{xz}$ or in the $3d_{yz}$
orbital (called $\pi$ orbitals) with two degenerate Hund-rule triplets with one
hole in the $3d_{z}$ orbital and another one in a $\pi$ orbital. We solve the
model using a slave-boson mean-field approximation (SBMFA). For reasonable
parameters we can describe very well the observed STS spectrum between sample
bias -60 mV to 20 mV. For these parameters the Kondo stage takes place in two
stages, with different energy scales $T_K^z > T_K^\pi$ corresponding to the
Kondo temperatures related with the hopping of the $z^2$ and $\pi$ orbitals
respectively. There is a strong interference between the different channels and
the Kondo temperatures, particularly the lowest one is strongly reduced
compared with the value in the absence of the competing channel.


  Nearly all circadian clocks maintain a period that is insensitive to
temperature changes, a phenomenon known as temperature compensation (TC). Yet,
it is unclear whether there is any common feature among different systems that
exhibit TC. From a general timescale invariance, we show that TC relies on
existence of certain period-lengthening reactions wherein the period of the
system increases strongly with the rates in these reactions. By studying
several generic oscillator models, we show that this counter-intuitive
dependence is nonetheless a common feature of oscillators in the nonlinear
(far-from-onset) regime where the oscillation can be separated into fast and
slow phases. The increase of the period with the period-lengthening reaction
rates occurs when the amplitude of the slow phase in the oscillation increases
with these rates while the progression-speed in the slow phase is controlled by
other rates of the system. The positive dependence of the period on the
period-lengthening rates balances its inverse dependence on other kinetic rates
in the system, which gives rise to robust TC in a wide range of parameters. We
demonstrate the existence of such period-lengthening reactions and their
relevance for TC in all four model systems we considered. Theoretical results
for a model of the Kai system are supported by experimental data. A study of
the energy dissipation also shows that better TC performance requires higher
energy consumption. Our study unveils a general mechanism by which a
biochemical oscillator achieves TC by operating at regimes far from the onset
where period-lengthening reactions exist.


  Replacing linear diffusion by a degenerate diffusion of porous medium type is
known to regularize the classical two-dimensional parabolic-elliptic
Keller-Segel model. The implications of nonlinear diffusion are that solutions
exist globally and are uniformly bounded in time. We analyse the stationary
case showing the existence of a unique, up to translation, global minimizer of
the associated free energy. Furthermore, we prove that this global minimizer is
a radially decreasing compactly supported continuous density function which is
smooth inside its support, and it is characterized as the unique compactly
supported stationary state of the evolution model. This unique profile is the
clear candidate to describe the long time asymptotics of the diffusion
dominated classical Keller-Segel model for general initial data.


  While the performance of mmWave links has been thoroughly investigated by
simulations or testbeds, the behavior of this technology in real-world
commercial setups has not yet been thoroughly documented. In this paper, we
address this gap and present the results of an empirical study to determine the
actual performance of a commercial 5G mmWave cell through on-field
measurements. We evaluate the signal and beam coverage map of an operational
network as well as the end-to-end communication performance of a 5G mmWave
connection, considering various scenarios, including human body blockage
effects, foliage-caused and rain-induced attenuation, and water surface
effects. To the best of our knowledge, this paper is the first to report on a
commercial deployment while not treating the radio as a black box. Measurement
results are compared with 3GPP's statistical channel models for mmWave to check
the possible gaps between simulated and actual performance. This measurement
analysis provides valuable information for researchers and 5G verticals to
fully understand how a 5G mmWave commercial access network operates in
real-world, under various operational conditions, with buildings, humans,
trees, water surfaces, etc.


  Recent work in adversarial robustness suggests that natural data
distributions are localized, i.e., they place high probability in small volume
regions of the input space, and that this property can be utilized for
designing classifiers with improved robustness guarantees for $\ell_2$-bounded
perturbations. Yet, it is still unclear if this observation holds true for more
general metrics. In this work, we extend this theory to $\ell_0$-bounded
adversarial perturbations, where the attacker can modify a few pixels of the
image but is unrestricted in the magnitude of perturbation, and we show
necessary and sufficient conditions for the existence of $\ell_0$-robust
classifiers. Theoretical certification approaches in this regime essentially
employ voting over a large ensemble of classifiers. Such procedures are
combinatorial and expensive or require complicated certification techniques. In
contrast, a simple classifier emerges from our theory, dubbed Box-NN, which
naturally incorporates the geometry of the problem and improves upon the
current state-of-the-art in certified robustness against sparse attacks for the
MNIST and Fashion-MNIST datasets.


  We study the problem of extending partial isomorphisms for hypertournaments,
which are relational structures generalizing tournaments. This is a generalized
version of an old question of Herwig and Lascar. We show that the generalized
problem has a negative answer, and we provide a positive answer in a special
case. As a corollary, we show that the extension property holds for tournaments
in case the partial isomorphisms have pairwise disjoint ranges and pairwise
disjoint domains.


  In this work, we obtain closed expressions for the transfer matrix and the
transmittance of electromagnetic waves propagating in finite 1D anisotropic
periodic stratified media with an arbitrary number of cells. By invoking the
Cayley-Hamilton theorem on the transfer matrix for the electromagnetic field in
a periodic stratified media formed by N cells, we obtain a fourth-degree
recursive relation for the matrix coefficients that defines the so-called
Tetranacci Polynomials. In the symmetric case, corresponding to a unit-cell
transfer matrix with a characteristic polynomial where the coefficients of the
linear and cubic terms are equal, closed expressions for the solutions to the
recursive relation, known as symmetric Tetranacci Polynomials, have recently
been derived, allowing us to write the transfer matrix and transmittance in a
closed form. We show as sufficient conditions that the $4\times4$ differential
propagation matrix of each layer in the binary unit cell, $\Delta$, a) has
eigenvalues of the form $\pm p_1$, $\pm p_2$, with $p_1\ne p_2$, and b) its
off-diagonal $2\times2$ block matrices possess the same symmetric structure in
both layers. Otherwise, the recursive relations are still solvable for any
$4\times4$-matrix and provide an algorithm to compute the N-th power of the
transfer matrix without carrying out explicitly the matrix multiplication of N
matrices. We obtain analytical expressions for the dispersion relation and
transmittance, in closed form, for two finite periodic systems: the first one
consists of two birefringent uniaxial media with their optical axis
perpendicular to the z-axis, and the second consists of two isotropic media
subject to an external magnetic field oriented along the z-axis and exhibiting
the Faraday effect. Our formalism applies also to lossy media, magnetic
anisotropy or optical activity.


  Unconventional superconductors host a plethora of interesting physical
phenomena. However, the standard theory of superconductivity suggests that
unconventional pairing is highly sensitive to disorder, and hence can only be
observed in ultraclean systems. We find that due to an emergent chiral
symmetry, spin-orbital locking can parametrically suppress pair decoherence
introduced by impurity scattering in odd-parity superconductors. Our work
demonstrates that disorder is not an obstacle to realize odd-parity
superconductivity in materials with strong spin-orbit coupling.


  A new procedure to capture the shocks has been proposed and is demonstrated
for the solutions of two-dimensional Euler equations using discontinuous
Galerkin method and overset grids. A discontinuous Galerkin solver using a
coarse grid provides the troubled cell data that is used to determine the
location of the shock. An overset grid aligned to the shock is constructed
based on this information. The solver is run again with the coarse grid
solution as the initial condition with limiting occurring only in the overset
grid to give a solution with the shock aligned to the grid line. Results for
supersonic flow over a ramp, shock reflecting off a flat plate and the
supersonic flow over a circular cylinder are presented. For the flow over a
circular cylinder, the results obtained are validated using an existing
analytical method for calculating the shock offset distance.


  The CASH problem has been widely studied in the context of automated
configurations of machine learning (ML) pipelines and various solvers and
toolkits are available. However, CASH solvers do not directly handle black-box
constraints such as fairness, robustness or other domain-specific custom
constraints. We present our recent approach [Liu, et al., 2020] that leverages
the ADMM optimization framework to decompose CASH into multiple small problems
and demonstrate how ADMM facilitates incorporation of black-box constraints.


  Nesterov SGD is widely used for training modern neural networks and other
machine learning models. Yet, its advantages over SGD have not been
theoretically clarified. Indeed, as we show in our paper, both theoretically
and empirically, Nesterov SGD with any parameter selection does not in general
provide acceleration over ordinary SGD. Furthermore, Nesterov SGD may diverge
for step sizes that ensure convergence of ordinary SGD. This is in contrast to
the classical results in the deterministic scenario, where the same step size
ensures accelerated convergence of the Nesterov's method over optimal gradient
descent.
  To address the non-acceleration issue, we introduce a compensation term to
Nesterov SGD. The resulting algorithm, which we call MaSS, converges for same
step sizes as SGD. We prove that MaSS obtains an accelerated convergence rates
over SGD for any mini-batch size in the linear setting. For full batch, the
convergence rate of MaSS matches the well-known accelerated rate of the
Nesterov's method.
  We also analyze the practically important question of the dependence of the
convergence rate and optimal hyper-parameters on the mini-batch size,
demonstrating three distinct regimes: linear scaling, diminishing returns and
saturation.
  Experimental evaluation of MaSS for several standard architectures of deep
networks, including ResNet and convolutional networks, shows improved
performance over SGD, Nesterov SGD and Adam.


  In this paper, we consider a K-user interference channel where interference
among the users is neither too strong nor too weak, a scenario that is
relatively underexplored in the literature. We propose a novel deep
learning-based approach to design the encoder and decoder functions that aim to
maximize the sumrate of the interference channel for discrete constellations.
We first consider the MaxSINR algorithm, a state-of-the-art linear scheme for
Gaussian inputs, as the baseline and then propose a modified version of the
algorithm for discrete inputs. We then propose a neural network-based approach
that learns a constellation mapping with the objective of maximizing the
sumrate. We provide numerical results to show that the constellations learned
by the neural network-based approach provide enhanced alignments, not just in
beamforming directions but also in terms of the effective constellation at the
receiver, thereby leading to improved sum-rate performance.


  Recent advances in deep learning for sequential data have given rise to fast
and powerful models that produce realistic videos of talking humans. The state
of the art in talking face generation focuses mainly on lip-syncing, being
conditioned on audio clips. However, having the ability to synthesize talking
humans from text transcriptions rather than audio is particularly beneficial
for many applications and is expected to receive more and more attention,
following the recent breakthroughs in large language models. For that, most
methods implement a cascaded 2-stage architecture of a text-to-speech module
followed by an audio-driven talking face generator, but this ignores the highly
complex interplay between audio and visual streams that occurs during speaking.
In this paper, we propose the first, to the best of our knowledge, text-driven
audiovisual speech synthesizer that uses Transformers and does not follow a
cascaded approach. Our method, which we call NEUral Text to ARticulate Talk
(NEUTART), is a talking face generator that uses a joint audiovisual feature
space, as well as speech-informed 3D facial reconstructions and a lip-reading
loss for visual supervision. The proposed model produces photorealistic talking
face videos with human-like articulation and well-synced audiovisual streams.
Our experiments on audiovisual datasets as well as in-the-wild videos reveal
state-of-the-art generation quality both in terms of objective metrics and
human evaluation.


  Connected and autonomous vehicles (CAVs) will revolutionize tomorrow's
intelligent transportation systems, being considered promising to improve
transportation safety, traffic efficiency, and mobility. In fact, envisioned
use cases of CAVs demand very high throughput, lower latency, highly reliable
communications, and precise positioning capabilities. The availability of a
large spectrum at millimeter-wave (mmWave) band potentially promotes new
specifications in spectrum technologies capable of supporting such service
requirements. In this article, we specifically focus on how mmWave
communications are being approached in vehicular standardization activities,
CAVs use cases and deployment challenges in realizing the future fully
connected settings. Finally, we also present a detailed performance assessment
on mmWave-enabled vehicle-to-vehicle (V2V) cooperative perception as an example
case study to show the impact of different configurations.


  First-order `Bogomol'nyi' equations are found for dilaton domain walls of
D-dimensional gravity with the general dilaton potential admitting a stable
anti-de Sitter vacuum. Implications for renormalization group flow in the
holographically dual field theory are discussed.


  We find a solution for exponential inflation in a Brans-Dicke generalized
model, where the coupling "constant " is variable. While in General Relativity
the equation of state is p is equal to minus rho, here we find p proportional
to rho, where the proportionality constant is smaller than -2/3. The negativity
of cosmic pressure implies acceleration of the expansion, even with lambda < 0
>.


  The cascade-emitted biphotons generated from the alkali metal atomic
ensembles are an excellent entanglement resource which enables long-distance
quantum communication. The communication of quantum information between distant
locations can be realized by utilizing the low-loss telecom bandwidth in the
upper transition of the cascaded photons in a fiber-based quantum network.
Meanwhile, the infrared photon from the lower transition of this highly
directional and frequency-correlated biphoton can be created under the
four-wave mixing process and can be stored locally as a collective spin wave.
Here we theoretically investigate the frequency entanglement of this biphoton
and propose two approaches to remove their mutual correlations in frequency
spaces. The first approach applies an optical cavity which modulates the
biphoton spectrum into a more symmetric and narrow spectral function by
multiplexing multiple atomic ensembles with phase compensation. The purity of
single photon reaches up to $0.999$ and the entanglement entropy $S$ of the
biphoton reduces to $0.006$, which is $200$ times smaller than the one without
multiplexing. The other approach employs a symmetric pumping of the laser
fields in two atomic ensembles, which leads to a moderate reduction of $S\sim
0.3$ when non-discrimination detection devices are used for both photons. An
extremely low frequency entanglement implies an almost indistinguishable single
photon source, which offers a potential resource for photonic quantum
simulation and computation.


  Non-collinear magnetic order arises for various reasons in several magnetic
systems and exhibits interesting spin dynamics. Despite its ubiquitous
presence, little is known of how magnons, otherwise stable quasiparticles,
decay in these systems, particularly in metallic magnets. Using inelastic
neutron scattering, we examine the magnetic excitation spectra in a metallic
non-collinear antiferromagnet CrB$_{2}$, in which Cr atoms form a triangular
lattice and display incommensurate magnetic order. Our data show intrinsic
magnon damping and continuum-like excitations that cannot be explained by
linear spin wave theory. The intrinsic magnon linewidth $\Gamma(q,E_{q})$ shows
very unusual momentum dependence, which our analysis shows to originate from
the combination of two-magnon decay and the Stoner continuum. By comparing the
theoretical predictions with the experiments, we identify where in the momentum
and energy space one of the two factors becomes more dominant. Our work
constitutes a rare comprehensive study of the spin dynamics in metallic
non-collinear antiferromagnets. It reveals, for the first time, definite
experimental evidence of the higher-order effects in metallic antiferromagnets.


  We propose a local, past-oriented fragment of propositional dynamic logic to
reason about concurrent scenarios modelled as Mazurkiewicz traces, and prove it
to be expressively complete with respect to regular trace languages. Because of
locality, specifications in this logic are efficiently translated into
asynchronous automata, in a way that reflects the structure of formulas. In
particular, we obtain a new proof of Zielonka's fundamental theorem and we
prove that any regular trace language can be implemented by a cascade product
of localized asynchronous automata, which essentially operate on a single
process.
  These results refine earlier results by Adsul et al. which involved a larger
fragment of past propositional dynamic logic and used Mukund and Sohoni's
gossip automaton. Our new results avoid using this automaton, or Zielonka's
timestamping mechanism and, in particular, they show how to implement a gossip
automaton as a cascade product.


  It is shown that the data on the pion charge form factor admit the
possibility for a substantial sea-quark components in the pion wave function.
If the charge form factor is calculated with instant form kinematics in a
constituent quark model that is extended to include explicit $(q\bar q)^2$
components in the pion wave function, that component will give the dominant
contribution to the calculated $\pi^+$ charge form factor at large values of
momentum transfer. The present experimental values $Q^2$ can be described well
with $(q\bar q)^2$ component admixtures of up to 50%. The sensitivity of the
calculated $\pi^+$ charge form factor to whether one of the quarks or one of
the antiquarks is taken to be in the P-state is small.


  Three-dimensional studies of convection in deep spherical shells have been
used to test the hypothesis that the strong jet streams on Jupiter, Saturn,
Uranus, and Neptune result from convection throughout the molecular envelopes.
Due to computational limitations, these simulations must adopt viscosities and
heat fluxes many orders of magnitude larger than the planetary values. Several
numerical investigations have identified trends for how the mean jet speed
varies with heat flux and viscosity, but no previous theories have been
advanced to explain these trends. Here, we show using simple arguments that if
convective release of potential energy pumps the jets and viscosity damps them,
the mean jet speeds split into two regimes. When the convection is weakly
nonlinear, the equilibrated jet speeds should scale approximately with F/nu,
where F is the convective heat flux and nu is the viscosity. When the
convection is strongly nonlinear, the jet speeds are faster and should scale
approximately as (F/nu)^{1/2}. We demonstrate how this regime shift can
naturally result from a shift in the behavior of the jet-pumping efficiency
with heat flux and viscosity. Moreover, the simulations hint at a third regime
where, at sufficiently small viscosities, the jet speed becomes independent of
the viscosity. We show based on mixing-length estimates that if such a regime
exists, mean jet speeds should scale as heat flux to the 1/4 power. Our
scalings provide a good match to the mean jet speeds obtained in previous
Boussinesq and anelastic, three-dimensional simulations of convection within
giant planets over a broad range of parameters. When extrapolated to the real
heat fluxes, these scalings suggest that the mass-weighted jet speeds in the
molecular envelopes of the giant planets are much weaker--by an order of
magnitude or more--than the speeds measured at cloud level.


  In this paper I provide a general framework based on $\delta N$ formalism to
study the features of unavoidable higher dimensional non-renormalizable
K\"ahler operators for ${\cal N}=1$ supergravity (SUGRA) during primordial
inflation from the combined constraint on non-Gaussianity, sound speed and CMB
dipolar asymmetry as obtained from the recent Planck data. In particular I
study the nonlinear evolution of cosmological perturbations on large scales
which enables us to compute the curvature perturbation, $\zeta$, without
solving the exact perturbed field equations. Further I compute the non-Gaussian
parameters $f_{NL}$, $\tau_{NL}$ and $g_{NL}$ for local type of
non-Gaussianities and CMB dipolar asymmetry parameter, $ A_{CMB}$, using the
$\delta N$ formalism for a generic class of sub-Planckian models induced by the
Hubble-induced corrections for a minimal supersymmetric D-flat direction where
inflation occurs at the point of inflection within the visible sector. Hence by
using multi parameter scan I constrain the non-minimal couplings appearing in
non-renormalizable K\"ahler operators within, ${\cal O}(1)$, for the speed of
sound, $0.02\leq c_s\leq 1$, and tensor to scalar, $10^{-22} \leq r_{\star}
\leq 0.12$. Finally applying all of these constraints I will fix the lower as
well as the upper bound of the non-Gaussian parameters within, ${\cal
O}(1-5)\leq f_{NL}\leq 8.5$, ${\cal O}(75-150)\leq\tau_{NL}\leq 2800$ and
${\cal O}(17.4-34.7)\leq g_{NL}\leq 648.2$, and CMB dipolar asymmetry parameter
within the range, $0.05\leq A_{CMB}\leq 0.09$.


  Adaptation in a fluctuating environment is a process of fueling environmental
information to gain fitness. Living systems have gradually developed strategies
for adaptation from random and passive diversification of the phenotype to more
proactive decision making, in which environmental information is sensed and
exploited more actively and effectively. Understanding the fundamental relation
between fitness and information is therefore crucial to clarify the limits and
universal properties of adaptation. In this work, we elucidate the underlying
stochastic and information-thermodynamic structure in this process, by deriving
causal fluctuation relations (FRs) of fitness and information. Combined with a
duality between phenotypic and environmental dynamics, the FRs reveal the limit
of fitness gain, the relation of time reversibility with the achievability of
the limit, and the possibility and condition for gaining excess fitness due to
environmental fluctuation. The loss of fitness due to causal constraints and
the limited capacity of real organisms is shown to be the difference between
time-forward and time-backward path probabilities of phenotypic and
environmental dynamics. Furthermore, the FRs generalize the concept of
evolutionary stable state (ESS) for fluctuating environment by giving the
probability that the optimal strategy on average can be invaded by a suboptimal
one owing to rare environmental fluctuation. These results clarify the
information thermodynamic structures in adaptation and evolution.


  Spin qubits composed of either one or three electrons are realized in a
quantum dot formed at a Si/SiO_2-interface in isotopically enriched silicon.
Using pulsed electron spin resonance, we perform coherent control of both types
of qubits, addressing them via an electric field dependent g-factor. We perform
randomized benchmarking and find that both qubits can be operated with high
fidelity. Surprisingly, we find that the g-factors of the one-electron and
three-electron qubits have an approximately linear but opposite dependence as a
function of the applied dc electric field. We develop a theory to explain this
g-factor behavior based on the spin-valley coupling that results from the sharp
interface. The outer "shell" electron in the three-electron qubit exists in the
higher of the two available conduction-band valley states, in contrast with the
one-electron case, where the electron is in the lower valley. We formulate a
modified effective mass theory and propose that inter-valley spin-flip
tunneling dominates over intra-valley spin-flips in this system, leading to a
direct correlation between the spin-orbit coupling parameters and the g-factors
in the two valleys. In addition to offering all-electrical tuning for
single-qubit gates, the g-factor physics revealed here for one-electron and
three-electron qubits offers potential opportunities for new qubit control
approaches.


  We report two-photon resonance fluorescence of an individual semiconductor
artificial atom. By non-linearly driving a single quantum dot via a two-photon
transition, we probe the linewidth of the two-photon processes and show that,
similar to their single-photon counterparts, they are close to being Fourier
limited at low temperatures. The evolution of the population of excitonic
states with the Rabi frequency exhibits a clear s-shaped behavior, indicative
of the non-linear response via the two-photon excitation process. We model the
non-linear response using a 4-level atomic system representing the manifold of
excitonic and biexcitonic states of the quantum dot and show that quantitative
agreement is obtained only by including the interaction with LA-phonons in the
solid state environment. Finally, we demonstrate the formation of dressed
states emerging from a two-photon interaction between the artificial atom and
the excitation field. The non-linear optical dressing induces a mixing of all
four excitonic states that facilitates the tuning of the polarization selection
rules of the artificial atom.


  We study the late time evolution of flat and negatively curved
Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source and
a scalar field arising in the conformal frame of $f(R)$ theories nonminimally
coupled to matter. Under mild assumptions on the potential V we prove that
equilibria corresponding to non-negative local minima for V are asymptotically
stable, as well as horizontal asymptotes approached from above by V. We
classify all cases of the flat model where one of the matter components
eventually dominates. In particular for a nondegenerate minimum of the
potential with zero critical value we prove in detail that if the parameter of
the equation of state is larger than one, then there is a transfer of energy
from the fluid to the scalar field and the later eventually dominates in a
generic way.


  We present the stellar mass-size relations for elliptical, lenticular, and
spiral galaxies in the field and cluster environments using HST/ACS imaging and
data from the Space Telescope A901/2 Galaxy Evolution Survey (STAGES). We use a
large sample of ~1200 field and cluster galaxies, and a sub-sample of cluster
core galaxies, and quantify the significance of any putative environmental
dependence on the stellar mass-size relation. For elliptical, lenticular, and
high-mass (log M*/M_sun > 10) spiral galaxies we find no evidence to suggest
any such environmental dependence, implying that internal drivers are governing
their size evolution. For intermediate/low-mass spirals (log M*/M_sun < 10) we
find evidence, significant at the 2-sigma level, for a possible environmental
dependence on galaxy sizes: the mean effective radius a_e for lower-mass
spirals is ~15-20 per cent larger in the field than in the cluster. This is due
to a population of low-mass large-a_e field spirals that are largely absent
from the cluster environments. These large-a_e field spirals contain extended
stellar discs not present in their cluster counterparts. This suggests the
fragile extended stellar discs of these spiral galaxies may not survive the
environmental conditions in the cluster. Our results suggest that internal
physical processes are the main drivers governing the size evolution of
galaxies, with the environment possibly playing a role affecting only the discs
of intermediate/low-mass spirals.


  We use a rigid axisymetric microfluidic flow focusing device to produce
monodisperse bubbles, dispersed in a surfactant solution. The gas volume
fraction of the dispersion collected out of this device can be as large as 90%,
demonstrating that foam with solid-like viscoelastic properties can be produced
in this way. The polydispersity of the bubbles is so low that we observe
crystallization of our foam. We measure the diameter of the bubbles and compare
these data to recent theoretical predictions. The good control over bubble size
and foam gas volume fraction shows that our device is a flexible and promising
tool to produce calibrated foam at a high flow rate.


  Chaos presents complex dynamics arising from nonlinearity and a sensitivity
to initial states. These characteristics suggest a depth of expressivity that
underscores their potential for advanced computational applications. However,
strategies to effectively exploit chaotic dynamics for information processing
have largely remained elusive. In this study, we reveal that the essence of
chaos can be found in various state-of-the-art deep neural networks. Drawing
inspiration from this revelation, we propose a novel method that directly
leverages chaotic dynamics for deep learning architectures. Our approach is
systematically evaluated across distinct chaotic systems. In all instances, our
framework presents superior results to conventional deep neural networks in
terms of accuracy, convergence speed, and efficiency. Furthermore, we found an
active role of transient chaos formation in our scheme. Collectively, this
study offers a new path for the integration of chaos, which has long been
overlooked in information processing, and provides insights into the
prospective fusion of chaotic dynamics within the domains of machine learning
and neuromorphic computation.


  Simulation of time dynamical physical problems has been a challenge for
classical computers due to their time-complexity. To demonstrate the dominance
of quantum computers over classical computers in this regime, here we simulate
a semi-empirical model where two neutral particles interact through
Lennard-Jones potential in a one-dimensional system. We implement the above
scenario on the IBM quantum experience platform using a 5-qubit real device. We
construct the Hamiltonian and then efficiently map it to quantum operators onto
quantum gates using the time-evolutionary unitary matrix obtained from the
Hamiltonian. We verify the results collected from the QASM-simulator and
compare it with that of the 5-qubit real chip ibmqx2.


  This paper is concerned with the inverse spectral problem for the third-order
differential equation with distribution coefficient. The inverse problem
consists in the recovery of the differential expression coefficients from the
spectral data of two boundary value problems with separated boundary
conditions. For this inverse problem, we solve the most fundamental question of
the inverse spectral theory about the necessary and sufficient conditions of
solvability. In addition, we prove the local solvability and stability of the
inverse problem. Furthermore, we obtain very simple sufficient conditions of
solvability in the self-adjoint case. The main results are proved by a
constructive method that reduces the nonlinear inverse problem to a linear
equation in the Banach space of bounded infinite sequences. In the future, our
results can be generalized to various classes of higher-order differential
operators with integrable or distribution coefficients.


  We study the problem of repeated two-sided matching with uncertain
preferences (two-sided bandits), and no explicit communication between agents.
Recent work has developed algorithms that converge to stable matchings when one
side (the proposers or agents) must learn their preferences, but the
preferences of the other side (the proposees or arms) are common knowledge, and
the matching mechanism uses simultaneous proposals at each round. We develop
new algorithms that converge to stable matchings for two more challenging
settings: one where the arm preferences are no longer common knowledge, and a
second, more general one where the arms are also uncertain about their own
preferences. In our algorithms, agents start with optimistic beliefs about
arms' preferences, updating these preferences over time, and combining beliefs
about preferences with beliefs about the value of matching when choosing whom
to propose to.


  Finding shortest distance between two vertices in a graph is an important
problem due to its numerous applications in diverse domains, including
geo-spatial databases, social network analysis, and information retrieval.
Classical algorithms (such as, Dijkstra) solve this problem in polynomial time,
but these algorithms cannot provide real-time response for a large number of
bursty queries on a large graph. So, indexing based solutions that pre-process
the graph for efficiently answering (exactly or approximately) a large number
of distance queries in real-time is becoming increasingly popular. Existing
solutions have varying performance in terms of index size, index building time,
query time, and accuracy. In this work, we propose T OP C OM , a novel
indexing-based solution for exactly answering distance queries. Our experiments
with two of the existing state-of-the-art methods (IS-Label and TreeMap) show
the superiority of T OP C OM over these two methods considering scalability and
query time. Besides, indexing of T OP C OM exploits the DAG (directed acyclic
graph) structure in the graph, which makes it significantly faster than the
existing methods if the SCCs (strongly connected component) of the input graph
are relatively small.


  Segmentation algorithms for medical images are widely studied for various
clinical and research purposes. In this paper, we propose a new and efficient
method for medical image segmentation under noisy labels. The method operates
under a deep learning paradigm, incorporating four novel contributions.
Firstly, a residual interconnection is explored in different scale encoders to
transfer gradient information efficiently. Secondly, four copy-and-crop
connections are replaced by residual-block-based concatenation to alleviate the
disparity between encoders and decoders. Thirdly, convolutional attention
modules for feature refinement are studied on all scale decoders. Finally, an
adaptive denoising learning strategy (ADL) is introduced into the training
process to avoid too much influence from the noisy labels. Experimental results
are illustrated on a publicly available benchmark database of spine CTs. Our
proposed method achieves competitive performance against other state-of-the-art
methods over a variety of different evaluation measures.


  The first investigation is made of designs for screening experiments where
the response variable is approximated by a generalised linear model. A Bayesian
information capacity criterion is defined for the selection of designs that are
robust to the form of the linear predictor. For binomial data and logistic
regression, the effectiveness of these designs for screening is assessed
through simulation studies using all-subsets regression and model selection via
maximum penalised likelihood and a generalised information criterion. For
Poisson data and log-linear regression, similar assessments are made using
maximum likelihood and the Akaike information criterion for minimally-supported
designs that are constructed analytically. The results show that effective
screening, that is, high power with moderate type I error rate and false
discovery rate, can be achieved through suitable choices for the number of
design support points and experiment size. Logistic regression is shown to
present a more challenging problem than log-linear regression. Some areas for
future work are also indicated.


  This paper uses observations of dusty debris discs, including a growing
number of gas detections in these systems, to test our understanding of the
origin and evolution of this gaseous component. It is assumed that all debris
discs with icy planetesimals create second generation CO, C and O gas at some
level, and the aim of this paper is to predict that level and assess its
observability. We present a new semi-analytical equivalent of the numerical
model of Kral et al. (2016) allowing application to large numbers of
systems.That model assumes CO is produced from volatile-rich solid bodies at a
rate that can be predicted from the debris disc's fractional luminosity. CO
photodissociates rapidly into C and O that then evolve by viscous spreading.
This model provides a good qualitative explanation of all current observations,
with a few exceptional systems that likely have primordial gas. The radial
location of the debris and stellar luminosity explain some non-detections, e.g.
close-in debris (like HD 172555) is too warm to retain CO, while high stellar
luminosities (like $\eta$ Tel) result in short CO lifetimes. We list the most
promising targets for gas detections, predicting $>15$ CO detections and $>30$
CI detections with ALMA, and tens of CII and OI detections with future far-IR
missions. We find that CO, CI, CII and OI gas should be modelled in non-LTE for
most stars, and that CO, CI and OI lines will be optically thick for the most
gas-rich systems. Finally, we find that radiation pressure, which can blow out
CI around early-type stars, can be suppressed by self-shielding.


  We aim to reduce the social cost of congestion in many smart city
applications. In our model of congestion, agents interact over limited
resources after receiving signals from a central agent that observes the state
of congestion in real time. Under natural models of agent populations, we
develop new signalling schemes and show that by introducing a non-trivial
amount of uncertainty in the signals, we reduce the social cost of congestion,
i.e., improve social welfare. The signalling schemes are efficient in terms of
both communication and computation, and are consistent with past observations
of the congestion. Moreover, the resulting population dynamics converge under
reasonable assumptions.


  We consider three equilibrium concepts proposed in the literature for
time-inconsistent stopping problems, including mild equilibria, weak equilibria
and strong equilibria. The discount function is assumed to be log sub-additive
and the underlying process is one-dimensional diffusion. We first provide
necessary and sufficient conditions for the characterization of weak
equilibria. The smooth-fit condition is obtained as a by-product. Next, based
on the characterization of weak equilibria, we show that an optimal mild
equilibrium is also weak. Then we provide conditions under which a weak
equilibrium is strong. We further show that an optimal mild equilibrium is also
strong under a certain condition. Finally, we provide several examples
including one shows a weak equilibrium may not be strong, and another one shows
a strong equilibrium may not be optimal mild.


  While the maximum entropy (MaxEnt) reinforcement learning (RL) framework --
often touted for its exploration and robustness capabilities -- is usually
motivated from a probabilistic perspective, the use of deep probabilistic
models has not gained much traction in practice due to their inherent
complexity. In this work, we propose the adoption of latent variable policies
within the MaxEnt framework, which we show can provably approximate any policy
distribution, and additionally, naturally emerges under the use of world models
with a latent belief state. We discuss why latent variable policies are
difficult to train, how naive approaches can fail, then subsequently introduce
a series of improvements centered around low-cost marginalization of the latent
state, allowing us to make full use of the latent state at minimal additional
cost. We instantiate our method under the actor-critic framework, marginalizing
both the actor and critic. The resulting algorithm, referred to as Stochastic
Marginal Actor-Critic (SMAC), is simple yet effective. We experimentally
validate our method on continuous control tasks, showing that effective
marginalization can lead to better exploration and more robust training. Our
implementation is open sourced at
https://github.com/zdhNarsil/Stochastic-Marginal-Actor-Critic.


  In this paper, by proving a simple local trace formula for real reductive
groups, we prove a multiplicity formula of K-types for all irreducible
representations of real reductive groups. This multiplicity formula expresses
the K-characters in terms of the Harish-Chandra characters.


  This paper presents the development of a density-based solver suitable for
cavitating flows in the OpenFOAM framework. In this solver, the thermodynamic
equilibrium mixture approach is adopted to model the presence of and the phase
transition between liquid and vapor phases. Using this approach, two cavitation
models are implemented in a separate library, although more cavitation models
can be easily added. The two are a temperature-dependent cavitation model and a
barotropic cavitation model developed by Egerer et al. (2014). One of the main
advantages of the solver is that it considers the compressibility of all
phases. This feature combined with using the density-based approach enables
capturing shock-waves created upon the collapse of cavitating structures which
are known to be one of the main mechanisms of cavitation erosion. The
implementation also includes a post-processing tool which detects aggressive
collapse-induced shock-waves based on the method proposed by Mihatsch et al.
(2015) and identifies the areas with a high risk of cavitation erosion. In
order to validate the implemented solver and post-processing tool, four cases
with progressively increasing complexity are simulated. The results from
simulation of these cases are compared with analytical solution, similar
numerical simulations as well as available experimental results. All of these
comparisons show that the numerical results obtained by the implemented solver
agree well with the reference analytical solution and numerical and
experimental results.


  In this paper, Meyer wavelets with an arbitrary integer scaling factor $N>2$
are defined using wavelets with multiple scaling factors $MN>2$. Expressions
for frequency functions of wavelets and corresponding filters are obtained.


  We address the effects of natural three-qubit interactions on the
computational power of one-way quantum computation (\QC). A benefit of using
more sophisticated entanglement structures is the ability to construct compact
and economic simulations of quantum algorithms with limited resources. We show
that the features of our study are embodied by suitably prepared optical
lattices, where effective three-spin interactions have been theoretically
demonstrated. We use this to provide a compact construction for the Toffoli
gate. Information flow and two-qubit interactions are also outlined, together
with a brief analysis of relevant sources of imperfection.


  Correlations, highly important in low--dimensional systems, are known to
decrease the plasmon dispersion of two-dimensional electron liquids. Here we
calculate the plasmon properties, applying the 'Dynamic Many-Body Theory',
accounting for correlated two-particle--two-hole fluctuations. These dynamic
correlations are found to significantly lower the plasmon's energy. For the
data obtained numerically, we provide an analytic expression that is valid
across a wide range both of densities and of wave vectors. Finally, we
demonstrate how this can be invoked in determining the actual electron
densities from measurements on an AlGaAs quantum well.


  The visibility of graphene sheets on different types of substrates has been
investigated both theoretically and experimentally. Although single layer
graphene is observable on various types of dielectrics under an optical
microscope, it is invisible when it is placed directly on most of the
semiconductor and metallic substrates. We show that coating of a resist layer
with optimum thickness is an effective way to enhance the contrast of graphene
on various types of substrates and makes single layer graphene visible on most
semiconductor and metallic substrates. Experiments have been performed to
verify the results on quartz and NiFe-coated Si substrates. The results
obtained will be useful for fabricating graphene-based devices on various types
of substrates for electronics, spintronics and optoelectronics applications.


  Indirect detection of dark matter via its annihilation products is a key
technique in the search for dark matter in the form of weakly interacting
massive particles (WIMPs). Strong constraints exist on the annihilation of
WIMPs to highly visible Standard Model final states such as photons or charged
particles. In the case of s-wave annihilation, this typically eliminates
thermal relic cross sections for dark matter of mass below $\cal{O}$(10) GeV.
However, such limits typically neglect the possibility that dark matter may
annihilate to assumed invisible or hard-to-detect final states, such as
neutrinos. This is a difficult paradigm to probe due to the weak neutrino
interaction cross section. Considering dark matter annihilation in the Galactic
halo, we study the prospects for indirect detection using the Hyper-Kamiokande
(HyperK) neutrino experiment, for dark matter of mass below 1 GeV. We undertake
a dedicated simulation of the HyperK detector, which we benchmark against
results from the similar Super-Kamiokande experiment and HyperK physics
projections. We provide projections for the annihilation cross-sections that
can be probed by HyperK for annihilation to muon or neutrino final states, and
discuss uncertainties associated with the dark matter halo profile. For
neutrino final states, we find that HyperK is sensitive to thermal annihilation
cross-sections for dark matter with mass around 20 MeV, assuming an NFW halo
profile. We also discuss the effects of neutron tagging, and prospects for
improving the reach at low mass.


  We present a generalization of the discrete Lehmann representation (DLR) to
three-point correlation and vertex functions in imaginary time and Matsubara
frequency. The representation takes the form of a linear combination of
judiciously chosen exponentials in imaginary time, and products of simple poles
in Matsubara frequency, which are universal for a given temperature and energy
cutoff. We present a systematic algorithm to generate compact sampling grids,
from which the coefficients of such an expansion can be obtained by solving a
linear system. We show that the explicit form of the representation can be used
to evaluate diagrammatic expressions involving infinite Matsubara sums, such as
polarization functions or self-energies, with controllable, high-order
accuracy. This collection of techniques establishes a framework through which
methods involving three-point objects can be implemented robustly, with a
substantially reduced computational cost and memory footprint.


  Thermodynamic Casimir forces of film systems in the O$(n)$ universality
classes with Dirichlet boundary conditions are studied below bulk criticality.
Substantial progress is achieved in resolving the long-standing problem of
describing analytically the pronounced minimum of the scaling function observed
experimentally in $^4$He films $(n=2)$ by R. Garcia and M.H.W. Chan, Phys. Rev.
Lett. ${\bf 83}, 1187 \;(1999)$ and in Monte Carlo simulations for the
three-dimensional Ising model ($n=1$) by O. Vasilyev et al., EPL ${\bf 80},
60009 \;(2007)$. Our finite-size renormalization-group approach yields
excellent agreement with the depth and the position of the minimum for $n=1$
and semiquantitative agreement with the minimum for $n=2$. Our theory also
predicts a pronounced minimum for the $n=3$ Heisenberg universality class.


  We develop a bosonization approach for one-dimensional models based on Bethe
ansatz equations. The operator formalism of the exact soluble models in the low
energy limit provides a systematic method to calculate the asymptotic
correlation functions. As examples with and without internal degrees of
freedom, the Calogero-Sutherland (C-S) model and the repulsive Hubbard model
are considered respectively. We verify that the low energy behavior of the C-S
model is controlled by two classes of c=1 conformal field theories, depending
on whether the C-S interactions are among bosons or among fermions. For the
Hubbard model, we show the explicit charge-spin separation at low energy for
arbitrary U>0. The low energy behavior of the system is described by the
(semi-) direct product of two independent Virasoro algebras with c=1.


  For practical quantum communications, the efficiency of the entire system
(source, quantum channel and detectors) must be taken into account. In many
urban environments, the quantum channel in the form of telecommunication
optical fiber (confirming to ITU G.652D standards) are available, but the
detectors in this range typically have low efficiency. We investigate the
possibility that for campus-type communications, entangled photons prepared in
the Near-Infrared Range (NIR) can be transmitted successfully while preserving
polarization entanglement. We demonstrate the distribution of degenerate and
non-degenerate entangled photon pairs of wavelength around 810 nm through
standard telecommunication fiber. This technique benefits from the high
efficiency of the NIR single photon detectors and the mature design of setups
around 810 nm.. In this work, we obtain high quality entanglement (visibility
is 94.8\% based on the raw data) after an overall distance of 12 km,
corresponding to about -36 dB of fiber induced loss.


  The flow field studied was eight strongly impinging, radially injected jets,
into a non-swirling mainstream flow in a cylindrical duct. Our previous paper
(Heat Mass Transf. (2020) 56:2285-2302), showed that asymmetry in the solution
is very likely to be an indication of the flow unsteadiness. Also, if the flow
is asymmetric, even a time dependent flow solver would not represent the flow
correctly if the computational domain is less than the complete cylindrical
duct. Thus, the current numerical and topological study was conducted in a 360
degree (complete cylindrical duct) computational domain using a time dependent
Unsteady Reynolds-Averaged Navier-Stokes URANS code. Results of this study
confirm that the flow of strongly impinging jets is unsteady and asymmetric
after the establishment of a regular flow pattern. The asymmetry appears to be
cyclic at a frequency of < 2 Hz. Also, the computational fluid dynamics (CFD)
results agree with the rules of topological analysis from applied mathematics.


  We propose a neural-network based model for coordination boundary prediction.
The network is designed to incorporate two signals: the similarity between
conjuncts and the observation that replacing the whole coordination phrase with
a conjunct tends to produce a coherent sentences. The modeling makes use of
several LSTM networks. The model is trained solely on conjunction annotations
in a Treebank, without using external resources. We show improvements on
predicting coordination boundaries on the PTB compared to two state-of-the-art
parsers; as well as improvement over previous coordination boundary prediction
systems on the Genia corpus.


  The chromatic number $\overrightarrow{\chi}(D)$ of a digraph $D$ is the
minimum number of colors needed to color the vertices of $D$ such that each
color class induces an acyclic subdigraph of $D$. A digraph $D$ is $k$-critical
if $\overrightarrow{\chi}(D) = k$ but $\overrightarrow{\chi}(D') < k$ for all
proper subdigraphs $D'$ of $D$. We examine methods for creating infinite
families of critical digraphs, the Dirac join and the directed and bidirected
Haj\'os join. We prove that a digraph $D$ has chromatic number at least $k$ if
and only if it contains a subdigraph that can be obtained from bidirected
complete graphs on $k$ vertices by (directed) Haj\'os joins and identifying
non-adjacent vertices. Building upon that, we show that a digraph $D$ has
chromatic number at least $k$ if and only if it can be constructed from
bidirected $K_k$'s by using directed and bidirected Haj\'os joins and
identifying non-adjacent vertices (so called Ore joins), thereby transferring a
well-known result of Urquhart to digraphs. Finally, we prove a Gallai-type
theorem that characterizes the structure of the low vertex subdigraph of a
critical digraph, that is, the subdigraph, which is induced by the vertices
that have in-degree $k-1$ and out-degree $k-1$ in $D$.


  V347 Aurigae is associated with the small dark cloud L1438 and appears to be
an isolated pre-main sequence star located at distance $d\approx$200 pc.
Multi-epoch, archival photometry reveals periodic brightness variations with
amplitude $V\approx2.0$ magnitudes occurring on timescales of $\sim$160 days
that have persisted for decades. Regular cadence, optical imaging of the source
with the Zwicky Transient Facility shows that a small reflection nebula
illuminated by V347 Aur also fluctuates in brightness, at times fading
completely. Multi-epoch, Keck/HIRES data suggests the presence of two distinct
spectral components: a prominent emission-line dominated spectrum with a
heavily veiled continuum correlated with the bright photometric state, and an
M-type absorption line spectrum associated with quiescence. All spectra exhibit
strong Balmer and He I line emission, consistent with accretion, as well as
high velocity emission arising from the forbidden transitions of [O I], [N II],
and [S II] that are generally associated with collimated jets and disk winds.
There is no evidence in existing high dispersion spectroscopy or high
resolution imaging for binarity of V347 Aur. The repeating outburst events are
possibly linked to accretion instabilities induced by an undetected companion
or a structure within the circumstellar disk that periodically increases the
mass accretion rate. V347 Aur is perhaps analogous to an EXor-type variable,
though more regularly recurring.


  We consider weak solutions for a diffuse interface model of two non-Newtonian
viscous, incompressible fluids of power-law type in the case of different
densities in a bounded, sufficiently smooth domain. This leads to a coupled
system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard
equation. For the Cahn-Hilliard part a smooth free energy density and a
constant, positive mobility is assumed. Using the $L^\infty$-truncation method
we prove existence of weak solutions for a power-law exponent
$p>\frac{2d+2}{d+2}$, $d=2,3$.


  The resonance-like signal with axial-vector quantum numbers $J^{PC}=1^{++}$
at a mass of $1420\,$MeV and a width of $140\,$MeV, recently observed by the
COMPASS and VES experiments in the $f_0(980)\pi$ final state and tentatively
called $a_1(1420)$, is discussed. Instead of a genuine new meson, we interpret
this signal as a dynamical effect due to a singularity (branching point) in the
triangle diagram formed by the processes $a_1(1260) \to K^\star \bar{K}$,
$K^\star\to K\pi$, and $K \bar{K} \to f_0(980)$ (+ c.c). The amplitude for this
diagram is calculated. The result exhibits a peak in the intensity with a sharp
phase motion with respect to the dominant $a_1(1260) \to \rho \pi$ $S$-wave
decay, in good agreement with the data. The branching ratio of $a_1(1260)\to
f_0(980)\pi$ via the triangle diagram is estimated and compared to the dominant
decay $a_1(1260)\to\rho\pi$.


  We prove the meridional rank conjecture for twisted links and arborescent
links associated to bipartite trees with even weights. These links are
substantial generalizations of pretzels and two-bridge links, respectively.
Lower bounds on meridional rank are obtained via Coxeter quotients of the
groups of link complements. Matching upper bounds on bridge number are found
using the Wirtinger numbers of link diagrams, a combinatorial tool developed by
the authors.


  Since the spectrogram does not preserve phase information contained in the
original data, any algorithm based on the spectrogram is not likely to be
optimum for detection. In this paper, we present the Short Time Fourier
Transform detector to detect marine mammals in the time-frequency plane. The
detector uses phase information for detection. We evaluate this detector by
comparing it to the existing spectrogram based detectors for different SNRs and
various environments including a known ocean, uncertain ocean, and mean ocean.
The results show that this detector outperforms the spectrogram based detector.
Simulations are presented using the polynomial phase signal model of the North
Atlantic Right Whale (NARW), along with the bellhop ray tracing model.


  Anomalous diffusion is a common phenomenon observed in underground solute
transport, soil water infiltration and sediment movement, etc. Time and space
fractional derivative advection-dispersion equation (FADE) has been widely
employed as the governing equation to characterize above mentioned anomalous
diffusion related processes. However, a main problem in application of time and
space FADE model to describe the real-world mass transport processes, is its
low computation efficiency for long-time range and large irregular domain
cases. This study offers a new algorithm in which the Kansa method is used for
vector space fractional derivative term discretization and then analytical
approach for resulted time fractional ordinary system. The influence of node
distribution mode and node numbers on accuracy and convergence rate are
analysed through the numerical examples in one and two dimensional cases. To
test the application potentials of present methods, we offer the numerical
results of two dimensional time and space FADE models in continuous and
discrete cases. It shows that the solute plumes in heterogeneous and
anisotropic media, can be well simulated by using present method compared with
the previous time-consumed particle Monte-Carlo methods.


  Self-similarity may stem from two origins: the process' increments infinite
variance and/or process' memory. The $b$-value of the Gutenberg-Richter law
comes from the first origin. In the frame of natural time analysis of
earthquake data, a fall of the b-value observed before large earthquakes
reflects an increase of the order parameter fluctuations upon approaching the
critical point (mainshock). The increase of these fluctuations, however, is
also influenced from the second origin of self-similarity, i.e., temporal
correlations between earthquake magnitudes. This is supported by observations
and simulations of an earthquake model.


  The magnetic and electronic properties of Eu2Ru2O7 are discussed in terms of
the local ruthenium and europium coordinations, electronic band structure
calculations and molecular orbital energy levels. A preliminary electronic
structure was calculated within the LDA and LSDA+U approximations. The
molecular orbital energy level diagrams have been used to interpret the Eu-Ru
ligand spectrum and the ensuing magnetic properties. The orbital hybridizations
and bonds are discussed.


  We continue our analysis of Ising models on the (directed) Erd\H{o}s-R\'enyi
random graph. This graph is constructed on $N$ vertices and every edge has
probability $p$ to be present. These models were introduced by Bovier and
Gayrard [J. Stat. Phys., 1993] and analyzed by the authors in a previous note,
in which we consider the case of $p=p(N)$ satisfying $p^3N^2\to +\infty$ and
$\beta <1$. In the current note we prove a quenched Central Limit Theorem for
the magnetization for $p$ satisfying $pN \to \infty$ in the high-temperature
regime $\beta<1$. We also show a non-standard Central Limit Theorem for $p^4N^3
\to \infty$ at the critical temperature $\beta=1$. For $p^4N^3 \to 0$ we obtain
a Gaussian limiting distribution for the magnetization. Finally, on the
critical line $p^4N^3 \to c$ the limiting distribution for the magnetization
contains a quadratic component as well as a $x^4$-term. Hence, at $\beta=1$ we
observe a phase transition in $p$ for the fluctuations of the magnetization.


  Given a positive and unitarily invariant Lagrangian L defined in the algebra
of Hermitian matrices, and a fixed interval $[a,b]\subset\mathbb R$, we study
the action defined in the Lie group of $n\times n$ unitary matrices
$\mathcal{U}(n)$ by $$ S(\alpha)=\int_a^b L(\dot\alpha(t))\,dt\,, $$ where
$\alpha:[a,b]\to\mathcal{U}(n)$ is a rectifiable curve. We prove that the
one-parameter subgroups of $\mathcal{U}(n)$ are the optimal paths, provided the
spectrum of the exponent is bounded by $\pi$. Moreover, if L is strictly
convex, we prove that one-parameter subgroups are the unique optimal curves
joining given endpoints. Finally, we also study the connection of these results
with unitarily invariant metrics in $\mathcal{U}(n)$ as well as angular metrics
in the Grassmann manifold


  I give a review of existing frameworks, which are designed to analyse lattice
data in the three-particle sector. A particular emphasis is laid on the
foundations of the theory, where the separation of the short- and long-range
effects plays a central role. It is shown that the use of the effective field
theory approach enables one to carry out this separation in a natural and
efficient way. In conclusion, a few examples of the analysis of lattice data
are considered for illustration.


  Many dynamical systems are subjected to stochastic influences, such as random
excitations, noise, and unmodeled behavior. Tracking the system's state and
parameters based on a physical model is a common task for which filtering
algorithms, such as Kalman filters and their non-linear extensions, are
typically used. However, many of these filters use assumptions on the
transition probabilities or the covariance model, which can lead to
inaccuracies in non-linear systems. We will show the application of a
stochastic coupling filter that can approximate arbitrary transition densities
under non-Gaussian noise. The filter is based on transport maps, which couple
the approximation densities to a user-chosen reference density, allowing for
straightforward sampling and evaluation of probabilities.


  In this paper, using a quasi-classical statistical approach based on the
Langevin equation, we simulate the fission dynamics of selected even-even $\rm
U$, $\rm Pu$, $\rm Cm$, $\rm Cf$ and $\rm Fm$ actinide nuclei. As a preparatory
part of the work, before solving the Langevin equations, the determination of
transport parameters such as inertia and friction tensors within the
hydrodynamic model is performed. Potential energy surfaces are calculated
within a macroscopic-microscopic approach in a three-dimensional space of
deformation parameters defined within the Fourier decomposition of the surface
radius function in cylindrical coordinates. Using the Lublin-Strasbourg drop
model, Strutinsky shell correction and BCS-like pairing energy model with the
projection onto good particle number, we calculate the nuclear total potential
energy surfaces (PES). The restoration of the particle number in the superfluid
approach is realized within the Generator Coordinate Method (GCM) with the so
called Gaussian Overlap Approximation (GOA). The final study is concerned with
the effect of the starting point of the stochastic Langevin trajectory on its
time evolution and, more importantly, the conditions for judging whether such a
trajectory for a given time moment describes an already passed fission nucleus
or not. Collecting a large number of such stochastic trajectories allows us to
assess the resulting fragment mass distributions, which appear to be in good
agreement with their experimental counterparts for light and intermediate
actinides. More serious discrepancies are observed for single isotopes of
californium and fermium.


  Reliable measurement routines are crucial for power rating and yield
prediction of photovoltaic emerging thinfilm technologies.
Copper-Zinc-Tin-Sulfur-Selenium (CZTSSe) thin-film photovoltaic devices are an
emerging technology made of abundant elements. Still, sufficient stabilization
methods prior to electric power measurement are missing in the international
standardization, while existing standards for other thin-film technologies do
not work properly for CZTSSe. This study investigated methods for achieving
power stabilization of the CZTSSe solar devices. Three complementary
stabilization routines for the kesterite-based solar devices were investigated
as an alternative to the existing international device testing standards: rapid
annealing, dark electric biasing and different operating points under
illumination. The typical number of stabilization cycles for power
stabilization was between 3 and 6 cycles of rapid annealing, dark electric bias
and illumination with a power loss of -19.5%, -11.4%, and -1.9%, for the
respective methods. The dark electric bias method was found to provide the most
reliable average result for power stabilization. All stabilization methods
proved to have the potential to work sufficiently in stabilizing the CZTSSe
devices for standardized power measurement.