  This work reports the performance evaluation of an SDR readout system based
on the latest generation (Gen3) of the AMD's Radio Frequency System-on-Chip
(RFSoC) processing platform, which integrates a full-stack processing system
and a powerful FPGA with up to 32 high-speed and high-resolution 14-bit
Digital-to-Analog Converters (DACs) and Analog-to-Digital Converters (ADCs).
The proposed readout system uses a previously developed multi-band,
double-conversion IQ RF-mixing board targeting a multiplexing factor of
approximately 1,000 bolometers in a bandwidth between 4 and 8 GHz, in line with
state-of-the-art microwave SQUID multiplexers ($\mu$MUX). The characterization
of the system was performed in two stages, under the conditions typically
imposed by the multiplexer and the cold readout circuit. First, in
transmission, showing that noise and spurious levels of the generated tones are
close to the values imposed by the cold readout. Second, in RF loopback,
presenting noise values better than -100 dBc/Hz totally in agreement with the
state-of-the-art readout systems. It was demonstrated that the RFSoC Gen3
device is a suitable enabling technology for the next generation of
superconducting detector readout systems, reducing system complexity,
increasing system integration, and achieving these goals without performance
degradation.


  Neural networks for multi-domain learning empowers an effective combination
of information from different domains by sharing and co-learning the
parameters. In visual tracking, the emerging features in shared layers of a
multi-domain tracker, trained on various sequences, are crucial for tracking in
unseen videos. Yet, in a fully shared architecture, some of the emerging
features are useful only in a specific domain, reducing the generalization of
the learned feature representation. We propose a semi-supervised learning
scheme to separate domain-invariant and domain-specific features using
adversarial learning, to encourage mutual exclusion between them, and to
leverage self-supervised learning for enhancing the shared features using the
unlabeled reservoir. By employing these features and training dedicated layers
for each sequence, we build a tracker that performs exceptionally on different
types of videos.


  Stability analysis and control of linear impulsive systems is addressed in a
hybrid framework, through the use of continuous-time time-varying discontinuous
Lyapunov functions. Necessary and sufficient conditions for stability of
impulsive systems with periodic impulses are first provided in order to set up
the main ideas. Extensions to stability of aperiodic systems under minimum,
maximum and ranged dwell-times are then derived. By exploiting further the
particular structure of the stability conditions, the results are
non-conservatively extended to quadratic stability analysis of linear uncertain
impulsive systems. These stability criteria are, in turn, losslessly extended
to stabilization using a particular, yet broad enough, class of state-feedback
controllers, providing then a convex solution to the open problem of robust
dwell-time stabilization of impulsive systems using hybrid stability criteria.
Relying finally on the representability of sampled-data systems as impulsive
systems, the problems of robust stability analysis and robust stabilization of
periodic and aperiodic uncertain sampled-data systems are straightforwardly
solved using the same ideas. Several examples are discussed in order to show
the effectiveness and reduced complexity of the proposed approach.


  In this paper, we present a novel and versatile method to study the dynamics
of resting-state fMRI brain connectivity with a high temporal sensitivity.
Whereas most existing methods often rely on dividing the time-series into
larger segments of data (i.e. so called sliding window techniques), the
point-based method (PBM) proposed here provides an estimate of brain
connectivity at the level of individual sampled time-points. The achieved
increase in temporal sensitivity, together with temporal graph network theory
allowed us to study functional integration between, as well as within,
resting-state networks. Our results show that functional integrations between
two resting-state networks predominately occurs in bursts of activity with
intermittent periods of less connectivity, whereas the functional connectivity
within resting-state networks is characterized by a tonic/periodic connectivity
pattern. Moreover, the point-based approach allowed us to estimate the
persistency of brain connectivity, i.e. the duration of the intrinsic trace or
memory of resting-state connectivity patterns. The described point-based method
of dynamic resting-state functional connectivity allows for a detailed and
expanded view on the temporal dynamics of resting-state connectivity that
provides novel insights into how neuronal information processing is integrated
in the human brain at the level of large-scale networks.


  We undertake the study of size-change analysis in the context of Reverse
Mathematics. In particular, we prove that the SCT criterion is equivalent to
$\Sigma^0_2$-induction over RCA$_0$.


  Afghanistan is responsible for the majority of the world's supply of poppy
crops, which are often used to produce illegal narcotics like heroin. This
paper presents an agent-based model that simulates policy scenarios to
characterize how the production of poppy can be dampened and replaced with
licit crops over time. The model is initialized with spatial data, including
transportation network and satellite-derived land use data. Parameters
representing national subsidies, insurgent influence, and trafficking blockades
are varied to represent different conditions that might encourage or discourage
poppy agriculture. Our model shows that boundary-level interventions, such as
targeted trafficking blockades at border locations, are critical in reducing
the attractiveness of growing this illicit crop. The principle of least effort
implies that interventions decrease to a minimal non-regressive point, leading
to the prediction that increases in insurgency or other changes are likely to
lead to worsening conditions, and improvements require substantial jumps in
intervention resources.


  The interaction between three localized vibrational modes is shown to be as
relevant for the lifetimes of localized modes as the interaction involving two
localized and one extended, and one localized and two extended modes. This
contrasts with previous views. I support my arguments by a numerical study of a
strongly disordered linear atomic chain.


  We consider streaming principal component analysis when the stochastic
data-generating model is subject to perturbations. While existing models assume
a fixed covariance, we adopt a robust perspective where the covariance matrix
belongs to a temporal uncertainty set. Under this setting, we provide
fundamental limits on convergence of any algorithm recovering principal
components. We analyze the convergence of the noisy power method and Oja's
algorithm, both studied for the stationary data generating model, and argue
that the noisy power method is rate-optimal in our setting. Finally, we
demonstrate the validity of our analysis through numerical experiments on
synthetic and real-world dataset.


  Electroplated Bismuth (Bi) is commonly used in Transition-Edge Sensors (TESs)
for X-rays because of its high stopping power and low heat capacity.
Electroplated Bi is usually grown on top of another metal that acts as seed
layer, typically gold (Au), making it challenging to extrapolate its
thermoelectric properties. In this work, we present four-wire resistance
measurement structures that allow us to measure resistance as a function of
temperature of electroplated Bi independently of Au. The results show that the
thermal conductivity of the Bi at 3 K is high enough to guarantee the correct
thermalization of X-ray photons when used as an absorber for TESs.


  Direct reciprocity is a well-known mechanism that could explain how
cooperation emerges and prevails in an evolving population. Numerous prior
researches have studied the emergence of cooperation in multiplayer games.
However, most of them use numerical or experimental methods, not theoretical
analysis. This lack of theoretical works on the evolution of cooperation is due
to the high complexity of calculating payoffs. In this paper, we propose a new
method, namely, the state-clustering method to calculate the long-term payoffs
in repeated games. Using this method, in an $n$-player repeated game, the
computing complexity is reduced from $O(2^n)$ to $O(n^2)$, which makes it
possible to compute a large-scale repeated game's payoff. We explore the
evolution of cooperation in both infinitely and finitely repeated public goods
games as an example to show the effectiveness of our method. In both cases, we
find that when the synergy factor is sufficiently large, the increasing number
of participants in a game is detrimental to the evolution of cooperation. Our
work provides a theoretical approach to study the evolution of cooperation in
repeated multiplayer games.


  Resistance functions for two spherical particles with the Navier slip
boundary condition in general linear flows, including rigid translation, rigid
rotation, and strain, at low Reynolds number are derived by the method of
reflections as well as twin multipole expansions. In the solutions, particle
radii and slip lengths can be chosen independently. In the course of
calculations, single-sphere problem with the slip boundary condition is solved
by Lamb's general solution and the expression of multipole expansions, and
Fax\'{e}n's laws of force, torque, and stresslet for slip particle are also
derived. The solutions of two-body problem are confirmed to recover the
existing results in the no-slip limit and for the case of equal scaled slip
lengths.


  As an experimental model to mimic the flow of bio-fluids in the cell and the
flow in tiny blood capillaries, we study the co-moving shear flow of dilute
polymeric solutions. An inflection point shear flow profile is created by
parallel streams moving at different speeds inside a pressure-driven Hele-Shaw
cell. The broad aim is to explore the possible instability mechanisms that lead
to Elastic Turbulence, discovered two decades ago (Groisman & Steinberg 2000).
The Reynolds number is kept very low ($Re < 0.1$) to eliminate any effects of
inertia, ensuring that any present instabilities are purely elastic in nature.
The interface is stable if the two co-moving fluids are Newtonian, but the
interface becomes wavy (Varshney & Steinberg 2019; David & Steinberg 2024) and
elastically turbulent with polymer solutions. Pressure spectra show clear
transitions, and the spectral decays have a well-defined form ($S(P) \sim
f^{-3.3}$), typical of Elastic Turbulence. Pressure drop measurements ($\Delta
P$) across the channel show an increase in drag up to 80% compared to the
purely viscous case and exhibit transitions consistent with pressure spectra
measurements. These measurements have led to an understanding that Elastic
Turbulence in dilute polymeric flows can be excited at Reynolds numbers as low
as 0.1, even with parallel shear flows and straight channels. This new finding
overturns the two-decade understanding, that Elastic Turbulence could be
achieved only in the presence of externally or internally imposed
curvature/perturbation in the flow and supports the recent growing body of
evidence (Steinberg 2022) which points to the presence of Elastic Turbulence in
straight channels with weak perturbations and no curvatures.


  We present a method for extracting the expected cosmological 21-cm signal
from the epoch of reionization, taking into account contaminating radiations
and random instrumental noise. The method is based on the maximum a-posteriori
probability (MAP) formalism and employs the coherence of the contaminating
radiation along the line-of-sight and the three-dimensional correlations of the
cosmological signal. We test the method using a detailed and comprehensive
modeling of the cosmological 21-cm signal and the contaminating radiation. The
signal is obtained using a high resolution N-body simulation where the gas is
assumed to trace the dark matter and is reionized by stellar radiation computed
from semi-analytic galaxy formation recipes. We model contaminations to the
cosmological signal from synchrotron and free-free galactic foregrounds and
extragalactic sources including active galactic nuclei, radio haloes and
relics, synchrotron and free-free emission from star forming galaxies, and
free-free emission from dark matter haloes and the intergalactic medium. We
provide tests of the reconstruction method for several rms values of
instrumental noise from $\sigma_{N}=1$ to 250 mK. For low instrumental noise,
the recovered signal, along individual lines-of-sight, fits the true
cosmological signal with a mean rms difference of $d_{rms}\approx 1.7\pm 0.6$
for $\sigma_{N}=1$ mK, and $d_{rms}\approx 4.2\pm 0.4$ for $\sigma_{N}=5$ mK.
The one-dimensional power spectrum is nicely reconstructed for all values of
$\sigma_{N}$ considered here, while the reconstruction of the two-dimensional
power spectrum and the Minkowski functionals is good only for noise levels of
the order of few mK.


  This is a point of view of the work of Herbert Busemann (1905-1994), seen as
a return to the geometry of Ancient Greece. The importance of this work, its
recognition and its relation with other works are discussed. The final version
of this paper will appear in the Handbook of the History and Philosophy of
Mathematical Practice, ed. Bharath Sriraman, Springer, 2024.


  We present a detailed account of the isomonodromic quantization of
dimensionally reduced Einstein gravity with two commuting Killing vectors. This
theory constitutes an integrable ``midi-superspace" version of quantum gravity
with infinitely many interacting physical degrees of freedom. The canonical
treatment is based on the complete separation of variables in the isomonodromic
sectors of the model. The Wheeler-DeWitt and diffeomorphism constraints are
thereby reduced to the Knizhnik-Zamolodchikov equations for $SL(2,R)$. The
physical states are shown to live in a well defined Hilbert space and are
manifestly invariant under the full diffeomorphism group. An infinite set of
independent observables \`a la Dirac exists both at the classical and the
quantum level. Using the discrete unitary representations of $SL(2,R)$, we
construct explicit quantum states. However, satisfying the additional
constraints associated with the coset space $SL(2,R)/SO(2)$ requires solutions
based on the principal series representations, which are not yet known. We
briefly discuss the possible implications of our results for string theory.


  The adiabatic approximation in open systems is formulated through the
effective Hamiltonian approach. By introducing an ancilla, we embed the open
system dynamics into a non-Hermitian quantum dynamics of a composite system,
the adiabatic evolution of the open system is then defined as the adiabatic
dynamics of the composite system. Validity and invalidity conditions for this
approximation are established and discussed. A High-order adiabatic
approximation for open systems is introduced. As an example, the adiabatic
condition for an open spin-$\frac 1 2$ particle in time-dependent magnetic
fields is analyzed.


  We review the calculation for Higgs production via the exclusive reaction pp
-> p+H+p. In the first part we review in some detail the calculation of the
Durham group and emphasise the main areas of uncertainty. Afterwards, we
comment upon other calculations.


  The design of mixed-criticality systems often involvespainful tradeoffs
between safety guarantees and performance.However, the use of more detailed
architectural modelsin the design and analysis of scheduling arrangements for
mixedcriticalitysystems can provide greater confidence in the analysis,but also
opportunities for better performance. Motivated by thisview, we propose an
extension of Vestal 19s model for mixedcriticalitymulticore systems that (i)
accounts for the per-taskpartitioning of the last-level cache and (ii) supports
the dynamicreassignment, for better schedulability, of cache portions
initiallyreserved for lower-criticality tasks to the higher-criticalitytasks,
when the system switches to high-criticality mode. Tothis model, we apply
partitioned EDF scheduling with Ekbergand Yi 19s deadline-scaling technique.
Our schedulability analysisand scalefactor calculation is cognisant of the
cache resourcesassigned to each task, by using WCET estimates that take
intoaccount these resources. It is hence able to leverage the
dynamicreconfiguration of the cache partitioning, at mode change, forbetter
performance, in terms of provable schedulability. We alsopropose heuristics for
partitioning the cache in low- and highcriticalitymode, that promote
schedulability. Our experimentswith synthetic task sets, indicate tangible
improvements inschedulability compared to a baseline cache-aware
arrangementwhere there is no redistribution of cache resources from low-
tohigh-criticality tasks in the event of a mode change.


  The frequent emergence of diseases with the potential to become threats at
local and global scales, such as influenza A(H1N1), SARS, MERS, and recently
COVID-19 disease, makes it crucial to keep designing models of disease
propagation and strategies to prevent or mitigate their effects in populations.
Since isolated systems are exceptionally rare to find in any context,
especially in human contact networks, here we examine the
susceptible-infected-recovered model of disease spreading in a multiplex
network formed by two distinct networks or layers, interconnected through a
fraction $q$ of shared individuals (overlap). We model the interactions through
weighted networks, because person-to-person interactions are diverse (or
disordered); weights represent the contact times of the interactions. Using
branching theory supported by simulations, we analyze a social distancing
strategy that reduces the average contact time in both layers, where the
intensity of the distancing is related to the topology of the layers. We find
that the critical values of the distancing intensities, above which an epidemic
can be prevented, increase with the overlap $q$. Also we study the effect of
the social distancing on the mutual giant component of susceptible individuals,
which is crucial to keep the functionality of the system. In addition, we find
that for relatively small values of the overlap $q$, social distancing policies
might not be needed at all to maintain the functionality of the system.


  In this paper, by minimizing the coherence quantifiers over all states in an
$\epsilon$ ball around a given state, we define a generalized smooth
quantifier, called the $\epsilon$-smooth measure of coherence. We use it to
estimate the difference between the expected state and the actually prepared
state and quantify quantum coherence contained in an actually prepared state,
and it can been interpreted as the minimal coherence guaranteed to present in
an $\epsilon$ ball around given quantum state. We find that the
$\epsilon$-smooth measure of any coherence monotone is still a coherence
monotone, but it does not satisfy monotonicity on average under incoherent
operations. We show the $\epsilon$-smooth measure of coherence is continuous
even if the original coherence quantifier is not. We also study the
$\epsilon$-smooth measure of distance-based coherence quantifiers, and some
interesting properties are given. Moreover, we discuss the dual form of the
$\epsilon$-smooth measure of coherence by maximizing over all states in an
$\epsilon$ ball around the given state and show that the dual $\epsilon$-smooth
measure of coherence provides an upper bound of one-shot coherence
distillation.


  Xenon scintillation has been widely used in rare event detection experiments
such as neutrinoless double beta decay, double electron captures and dark
matter searches. Nonetheless, experimental values for primary scintillation
yield in gaseous xenon (GXe) remain scarce and dispersed. The mean energy
required to produce a scintillation photon, wsc, in GXe in the absence of
recombination has been measured to be in the range of 34-111 eV. Lower values
were reported for alpha-particles when compared to electrons produced by gamma-
or x-rays. Since wsc is expected to be similar for x-, gamma-rays or electrons
and alpha-particles, the above difference cannot be understood. In addition,
one may pose the question of a dependence of wsc on photon energy. We carried
out a systematic study on the absolute primary scintillation yield in GXe for
electric fields in the 70-300 V/cm/bar range and for 1.2 bar supported by a
robust geometrical efficiency simulation model. We were able to clear-out the
above standing problems: we determined wsc for x/gamma-rays in the 5.9-60 keV
range and alpha-particles in the 1.5-2.5 MeV range; no significant dependency
neither on radiation type nor on energy was observed. Our values agree well
with both state-of-art simulations and literature data obtained for
alpha-particles. The discrepancy between our results and experimental values in
the literature for x/gamma-rays is discussed in this work and attributed to
unaddressed large systematic errors in previous studies. These findings can be
extrapolated to other gases and have impact on experiments such as double beta
decay, double electron capture and directional dark matter searches while also
on potential future detection systems such as DUNE-Gas. Neglecting the 3rd
continuum emission, as is the case of most of the literature values, a mean
wsc-value of 38.7 [+- 0.6 (sta.)] [(- 7.2) (+ 7.7) (sys.)] eV was obtained.


  We study properties of a helimagnetic thin film with quantum Heisenberg spin
model by using the Green's function method. Surface spin configuration is
calculated by minimizing the spin interaction energy. It is shown that the
angles between spins near the surface are strongly modified with respect to the
bulk configuration. Taking into account this surface spin reconstruction, we
calculate self-consistently the spin-wave spectrum and the layer magnetizations
as functions of temperature up to the disordered phase. The spin-wave spectrum
shows the existence of a surface-localized branch which causes a low surface
magnetization. We show that quantum fluctuations give rise to a crossover
between the surface magnetization and interior-layer magnetizations at low
temperatures. We calculate the transition temperature and show that it depends
strongly on the helical angle. Results are in agreement with existing
experimental observations on the stability of helical structure in thin films
and on the insensitivity of the transition temperature with the film thickness.
We also study effects of various parameters such as surface exchange and
anisotropy interactions. Monte Carlo simulations for the classical spin model
are also carried out for comparison with the quantum theoretical result.


  We study the interactions among phonons and the phonon lifetime in a
pair-condensed Fermi gas in the BEC-BCS crossover in the collisionless regime.
To compute the phonon-phonon coupling amplitudes we use a microscopic model
based on a generalized BCS Ansatz including moving pairs, which allows for a
systematic expansion around the mean field BCS approximation of the ground
state. We show that the quantum hydrodynamic expression of the amplitudes
obtained by Landau and Khalatnikov apply only on the energy shell, that is for
resonant processes that conserve energy. The microscopic model yields the same
excitation spectrum as the Random Phase Approximation, with a linear (phononic)
start and a concavity at low wave number that changes from upwards to downwards
in the BEC-BCS crossover. When the concavity of the dispersion relation is
upwards at low wave number, the leading damping mechanism at low temperature is
the Beliaev-Landau process 2 phonons $\leftrightarrow$ 1 phonon while, when the
concavity is downwards, it is the Landau-Khalatnikov process 2 phonons
$\leftrightarrow$ 2 phonons. In both cases, by rescaling the wave vectors to
absorb the dependence on the interaction strength, we obtain a universal
formula for the damping rate. This universal formula corrects and extends the
original analytic results of Landau and Khalatnikov [ZhETF {\bf 19}, 637
(1949)] for the $2\leftrightarrow2$ processes in the downward concavity case.
In the upward concavity case, for the Beliaev 1$\leftrightarrow$ 2 process for
the unitary gas at zero temperature, we calculate the damping rate of an
excitation with wave number $q$ including the first correction proportional to
$q^7$ to the $q^5$ hydrodynamic prediction, which was never done before in a
systematic way.


  The unusual and interesting physical properties of rare earth intemetallic
compounds have their origin in the combination of strongly correlated 4f states
and their hybridization with the conduction electron sea, which gives rise to
their complex low temperature Kondo behavior. In particular, Ce compounds are
very sensitive to the crystalline and chemical environment, as compared to
other rare earth systems. The interaction of the 4f state with the conduction
band plays an important role in the determination of the different magnetic,
structural and transport properties of these systems. Among the cerium
compounds, those of the type CeX, which crystallize in the rock salt structure,
exhibit extremely unusual magnetic properties. By making use of the mixed
LDA-NCA calculation technique we analyse the crystal-field splittings of CeX
compounds (X=N, P, As, Sb, Bi). The obtained ab-initio hybridization functions
are taken as imputs to calculate the crystal-field splittings within NCA (non
crossing approximation) and the tendencies are contrasted with experiments. KEY
WORDS: Highly correlated systems, crystal fields, p-electron.


  This paper is concerned with a Delsarte type extremal problem. Denote by
$\mathcal{P}(G)$ the set of positive definite continuous functions on a locally
compact abelian group $G$. We consider the function class, which was originally
introduced by Gorbachev, \begin{multline*} \mathcal{G}(W, Q)_G = \left\{ f \in
\mathcal{P}(G) \cap L^1(G) ~ : \right. ~ \left. f(0) = 1, ~ \text{supp}f_+
\subseteq W,~ \text{supp}\hat{f} \subseteq Q \right\} \end{multline*} where
$W\subseteq G$ is closed and of finite Haar measure and $Q\subseteq \hat{G}$ is
compact. We also consider the related Delsarte type problem of finding the
extremal quantity \begin{equation*} \mathcal{D}(W,Q)_G = \sup \left\{ \int_{G}
f(g) d\lambda_G(g) ~ : ~ f \in \mathcal{G}(W,Q)_G\right\}. \end{equation*} The
main objective of the current paper is to prove the existence of an extremal
function for the Delsarte type extremal problem $\mathcal{D}(W,Q)_G$. The
existence of the extremal function has recently been established by Berdysheva
and R\'ev\'esz in the most immediate case where $G=\mathbb{R}^d$. So the
novelty here is that we consider the problem in the general setting of locally
compact abelian groups. In this way our result provides a far reaching
generalization of the former work of Berdysheva and R\'ev\'esz.


  Text classification is one of the most frequent tasks for processing textual
data, facilitating among others research from large-scale datasets. Embeddings
of different kinds have recently become the de facto standard as features used
for text classification. These embeddings have the capacity to capture meanings
of words inferred from occurrences in large external collections. While they
are built out of external collections, they are unaware of the distributional
characteristics of words in the classification dataset at hand, including most
importantly the distribution of words across classes in training data. To make
the most of these embeddings as features and to boost the performance of
classifiers using them, we introduce a weighting scheme, Term
Frequency-Category Ratio (TF-CR), which can weight high-frequency,
category-exclusive words higher when computing word embeddings. Our experiments
on eight datasets show the effectiveness of TF-CR, leading to improved
performance scores over the well-known weighting schemes TF-IDF and KLD as well
as over the absence of a weighting scheme in most cases.


  Natural cooling, utilizing non-mechanical cooling, presents a low-carbon and
low-cost way to provide thermal comfort in residential buildings. However,
designing naturally cooled buildings requires a clear understanding of how
opening and closing windows affect occupants' comfort. Predicting when and why
occupants open windows is a challenging task, often relying on specialized
sensors and building-specific training data. This limits the scalability of
natural cooling solutions. Here, we, propose a novel unsupervised method that
utilizes easily deployable off-the-shelf temperature and humidity sensors to
detect window operations. The effectiveness of our approach is evaluated using
an empirical dataset and compared with a state-of-the-art support vector
machine (SVM) model. The results demonstrate that our proposed method
outperforms the SVM on key indicators, except when indoor and outdoor
temperatures have small differences. Unlike the SVM's sensitivity to time
series characteristics, our proposed method relies solely on indoor temperature
and exhibits robust performance in pilot studies, making it a promising
candidate for developing a highly scalable and generalizable window operation
detection model This work demonstrates the potential of unsupervised
data-driven methods for understanding window operations in residential
buildings. By enabling more accurate modeling of naturally cooled buildings,
our work aims to facilitate the widespread adoption of this low-cost and
low-carbon technology.


  Many species of phytoplankton migrate vertically near the surface of the
ocean, either in search of light or nutrients. These motile organisms are
affected by ocean waves at the surface. We derive a set of wave-averaged
equations to describe the motion of spheroidal microswimmers. We include
several possible effects, such as gyrotaxis, settling, and wind-driven shear.
In addition to the well-known Stokes drift, the microswimmer orbits depend on
their orientation in a way that can lead to trapping at a particular depth;
this in turn can affect transport of organisms, and may help explain observed
phytoplankton layers in the ocean.


  We present high spatial resolution (12pc) Atacama Large
Millimeter/sub-millimeter Array CO(J=3-2) observations of the nearby lenticular
galaxy NGC4429. We identify 217 giant molecular clouds within the 450pc radius
molecular gas disc. The clouds generally have smaller sizes and masses but
higher surface densities and observed linewidths than those of Milky Way disc
clouds. An unusually steep size - line width relation and large cloud internal
velocity gradients (0.05 - 0.91 km s^-1 pc^-1) and observed Virial parameters
(alpha_obs,vir = 4.0) are found, that appear due to internal rotation driven by
the background galactic gravitational potential. Removing this rotation, an
internal Virial equilibrium appears to be established between the
self-gravitational (Usg) and turbulent kinetic (Eturb) energies of each cloud,
i.e. alpha_sg,vir=Usg/Eturb = 1.3. However, to properly account for both self
and external gravity (shear and tidal forces), we formulate a modified Virial
theorem and define an effective Virial parameter alpha_eff,vir = alpha_sg,vir +
Usg/Eext (and associated effective velocity dispersion). The NGC4429 clouds
then appear to be in a critical state in which the self-gravitational energy
and the contribution of external gravity to the cloud's energy budget (Eext)
are approximately equal, i.e. Eext/Usg~1. As such, alpha_eff,vir = 2.2 and most
clouds are not virialised but remain marginally gravitationally bound. We show
this is consistent with the clouds having sizes similar to their tidal radii
and being generally radially elongated. External gravity is thus as important
as self-gravity to regulate the clouds of NGC4429.


  A connection between Maxwell's equations, Newton's laws, and the special
theory of relativity is established with a derivation that begins with Newton's
verbal enunciation of his first two laws. Derived equations are required to be
covariant, and a simplicity criterion requires that the four-vector force on a
charged particle be linearly related to the four-vector velocity. The
connecting tensor has derivable symmetry properties and contains the electric
and magnetic field vectors. The Lorentz force law emerges, and Maxwell's
equations for free space emerge with the assumption that the tensor and its
dual must both satisfy first order partial differential equations. The
inhomogeneous extension yields a charge density and a current density as being
the source of the field, and yields the law of conservation of charge. Newton's
third law is reinterpreted as a reciprocity statement, which requires that the
charge in the source term can be taken as the same physical entity as that of
the test particle and that both can be assigned the same units. Requiring
covariance under either spatial inversions or time reversals precludes magnetic
charge being a source of electromagnetic fields that exert forces on electric
charges.


  A reduced-density-matrix (RDM)-based approach to {\em ab initio} cavity
quantum electrodynamics (QED) is developed. The expectation value of the
Pauli-Fierz Hamiltonian is expressed in terms of one- and two-body electronic
and photonic RDMs, and the elements of these RDMs are optimized directly in
polynomial time by semidefinite programming techniques, without knowledge of
the full wave function. QED generalizations of important ensemble
$N$-representability conditions are derived and enforced in this procedure. The
resulting approach is applied to the description of classic ground-state strong
electron correlation problems, augmented by the presence of ultrastrong
light-matter coupling. First, we assess cavity-induced changes to the
singlet-triplet energy gap of the linear oligoacene series; for a heptacene
molecule, this gap can change by as much as 1.9 kcal mol$^{-1}$ (or 15\%) when
the molecule is aligned along the cavity mode polarization axis. We also
explore the metal-insulator transition in linear hydrogen chains and
demonstrate that strong electron-photon interactions increase the insulating
character of these systems under all coupling strengths considered.


  This paper provides an isomorphism $K_n (\mathscr{A}) \cong K_n
(\mathscr{A}_1) \times_{K_n(\mathscr{A}_0)} K_n(\mathscr{A}_2)$ of $K$-groups,
i.e., an exact sequence $0 \to K_n(\mathscr{A}) \to K_n(\mathscr{A}_1)\times
K_n(\mathscr{A}_2) \to K_n(\mathscr{A}_0)$ corresponding to a 2-fiber product
of abelian categories, taken with respect to exact functors. Using recent
patching results of D. Harbater, J. Hartmann and D. Krashen, given fields $F_1,
F_2 \leq F_0$ and $F= F_1 \cap F_2$ which satisfy a simple matrix factorization
criterion, our isomorphism relates the $K$-groups of the fields $F$ and $F_i$
($i$ = 0, 1, 2). In particular, we establish a local-global principle for
$K$-theory of function fields of curves defined over a complete discretely
valued field.


  Combining the thermal operator representation with the dispersion relation in
QED at finite temperature and chemical potential, we determine the complete
retarded photon self-energy only from its absorptive part at zero temperature.
As an application of this method, we show that, even for the case of a nonzero
chemical potential, the temperature dependent part of the one loop retarded
photon self-energy vanishes in $(1+1)$ dimensional massless QED.


  The flow field generated by a transom stern hull form is a complex,
broad-banded, three-dimensional system marked by a large breaking wave. This
unsteady multiphase turbulent flow feature is difficult to study experimentally
and simulate numerically. Recent model-scale experimental measurements and
numerical predictions of the wave-elevation topology behind a transom-sterned
hull form, Model 5673, are compared and assessed in this paper. The mean
height, surface roughness (RMS), and spectra of the breaking stern-waves were
measured by Light Detection And Ranging (LiDAR) and Quantitative Visualization
(QViz) sensors over a range of model speeds covering both wet- and dry-transom
operating conditions. Numerical predictions for this data set from two Office
of Naval Research (ONR) supported naval-design codes, Numerical Flow Analysis
(NFA) and CFDship-Iowa-V.4, have been performed. Comparisons of experimental
data, including LiDAR and QViz measurements, to the numerical predictions for
wet-transom and dry transom conditions are presented and demonstrate the
current state of the art in the simulation of ship generated breaking waves.
This work is part of an ongoing collaborative effort as part of the ONR Ship
Wave Breaking and Bubble Wake program, to assess, validate, and improve the
capability of Computational Fluid Dynamics (CFD).


  We show in this comment that the results obtained in a recent work by Yi et
al. [Phys. Rev. Lett. 92, 150406 (2004)] are quantitatively not correct and the
proposed subsystem Berry phase is not well-defined.


  The ground state of the solid solution of the two spin gap systems
(CH3)2CHNH3CuCl3 and (CH3)2CHNH3CuBr3 has been investigated by 1H-NMR. The
existence of a magnetic ordering in the sample with the Cl-content x=0.85 was
clearly demonstrated by a drastic splitting in a resonance line at low
temperatures below TN=13.5K. The observed NMR spectra in the ordered state was
qualitatively consistent with the simple antiferromagnetic state.


We analyze the three point Pick interpolation problem on the bidisk


  A general equation of state is used to model unified dark matter and dark
energy (dark fluid), and it has been proved that this model is equivalent to a
single fluid with time-dependent bulk viscosity. In this paper, we investigate
scalar perturbation of this viscosity dark fluid model. For particular
parameter selection, we find that perturbation quantity can be obtained exactly
in the future universe. We numerically solve the perturbation evolution
equations, and compare the results with those of $\Lambda$CDM model.
Gravitational potential and the density perturbation of the model studied here
have the similar behavior with the standard model, though there exists
significant value differences in the late universe.


  We have used the Very Long Baseline Array to measure the trigonometric
parallax of several member stars of the Orion Nebula Cluster showing
non-thermal radio emission. We have determined the distance to the cluster to
be 414 +/- 7 pc. Our distance determination allows for an improved calibration
of luminosities and ages of young stars. We have also measured the proper
motions of four cluster stars which, when accurate radial velocities are
measured, will put strong constraints on the origin of the cluster.


  We present a concrete theoretical proposal for detecting topological phase
transitions in double kicked atom-optics kicked rotors with internal spin-1/2
degree of freedom. The implementation utilizes a kicked Bose-Einstein
condensate evolving in one-dimensional momentum space. To reduce influence of
atom loss and phase decoherence we aim to keep experimental durations short
while maintaining a resonant experimental protocol. Experimental limitations
induced by phase noise, quasimomentum distributions, symmetries, and the
AC-Stark shift are considered. Our results thus suggest a feasible and
optimized procedure for observing topological phase transitions in quantum
kicked rotors.


  Radioactive decay of an unstable isotope is widely believed to be
exponential. This view is supported by experiments on rapidly decaying isotopes
but is more difficult to verify for slowly decaying isotopes. The decay of 14C
can be calibrated over a period of 12,550 years by comparing radiocarbon dates
with dates obtained from dendrochronology. It is well known that this approach
shows that radiocarbon dates of over 3,000 years are in error, which is
generally attributed to past variation in atmospheric levels of 14C. We note
that predicted atmospheric variation (assuming exponential decay) does not
agree with results from modelling, and that theoretical quantum mechanics does
not predict exact exponential decay. We give mathematical arguments that
non-exponential decay should be expected for slowly decaying isotopes and
explore the consequences of non-exponential decay. We propose an experimental
test of this prediction of non-exponential decay for 14C. If confirmed, a
foundation stone of current dating methods will have been removed, requiring a
radical reappraisal both of radioisotope dating methods and of currently
predicted dates obtained using these methods.


  The importance of explainability in machine learning continues to grow, as
both neural-network architectures and the data they model become increasingly
complex. Unique challenges arise when a model's input features become high
dimensional: on one hand, principled model-agnostic approaches to
explainability become too computationally expensive; on the other, more
efficient explainability algorithms lack natural interpretations for general
users. In this work, we introduce a framework for human-interpretable
explainability on high-dimensional data, consisting of two modules. First, we
apply a semantically meaningful latent representation, both to reduce the raw
dimensionality of the data, and to ensure its human interpretability. These
latent features can be learnt, e.g. explicitly as disentangled representations
or implicitly through image-to-image translation, or they can be based on any
computable quantities the user chooses. Second, we adapt the Shapley paradigm
for model-agnostic explainability to operate on these latent features. This
leads to interpretable model explanations that are both theoretically
controlled and computationally tractable. We benchmark our approach on
synthetic data and demonstrate its effectiveness on several
image-classification tasks.


  The Sun and sun-like stars commonly host the multi-million-Kelvin coronae and
the 10,000-Kelvin chromospheres. These extremely hot gases generate X-ray and
Extreme Ultraviolet emissions that may impact the erosion and chemistry of
(exo)planetary atmospheres, influencing the climate and conditions of
habitability. However, the mechanism of coronal and chromospheric heating is
still poorly understood. While the magnetic field most probably plays a key
role in driving and transporting energy from the stellar surface upwards, it is
not clear if the atmospheric heating mechanisms of the Sun and active sun-like
stars can be described in a unified manner. To this end, we report on a
systematic survey of the responses of solar and stellar atmospheres to surface
magnetic flux over a wide range of temperatures. By analyzing 10 years of
multi-wavelength synoptic observations of the Sun, we reveal that the
irradiance and magnetic flux show power-law relations with an exponent
decreasing from above- to sub-unity as the temperature decreases from the
corona to the chromosphere. Moreover, this trend indicating the efficiency of
atmospheric heating can be extended to sun-like stars. We also discover that
the power-law exponent has a solar cycle dependence, where it becomes smallest
at activity maximum, probably due to the saturation of atmospheric heating. Our
study provides observational evidence that the mechanism of atmospheric heating
is universal among the Sun and sun-like stars, regardless of age or activity.


  In this paper, we investigate building a sequence to sequence architecture
for motion to language translation and synchronization. The aim is to translate
motion capture inputs into English natural-language descriptions, such that the
descriptions are generated synchronously with the actions performed, enabling
semantic segmentation as a byproduct, but without requiring synchronized
training data. We propose a new recurrent formulation of local attention that
is suited for synchronous/live text generation, as well as an improved motion
encoder architecture better suited to smaller data and for synchronous
generation. We evaluate both contributions in individual experiments, using the
standard BLEU4 metric, as well as a simple semantic equivalence measure, on the
KIT motion language dataset. In a follow-up experiment, we assess the quality
of the synchronization of generated text in our proposed approaches through
multiple evaluation metrics. We find that both contributions to the attention
mechanism and the encoder architecture additively improve the quality of
generated text (BLEU and semantic equivalence), but also of synchronization.
Our code is available at
https://github.com/rd20karim/M2T-Segmentation/tree/main


  The complete charge-current density and field strength of an arbitrarily
accelerated relativistic point-charge are explicitly calculated. The current
density includes, apart from the well-established three-dimensional
delta-function which is sufficient for its global conservation, additional
delta-contributions depending on the second and third proper-time derivatives
of the position, which are necessary for its local conservation as required by
the internal consistency of classical electrodynamics which implies that local
charge-conservation is an {identity}. Similarly, the field strength includes an
additional delta-contribution which is necessary for obtaining this result. The
Lienard-Wiechert field and charge-current density must therefore be interpreted
as nonlinear generalized functions, i.e., not just as distributions, even
though only linear operations are necessary to verify charge-current
conservation. The four-potential from which this field and the conserved
charge-current density derive is found to be unique in the sense that it is the
only one reducing to an invariant scalar function in the instantaneous rest
frame of the point-charge that leads to a point-like locally-conserved
charge-current density.


  In principle, suppression of on-axis stellar light by a coronagraph is easier
on an unobscured aperture telescope than on one with an obscured aperture.
Recent designs such as the apodized pupil Lyot coronagraph, the `band-limited'
Lyot coronagraph, and several variants of phase mask coronagraphs work best on
unobscured circular aperture telescopes. These designs are developed to enable
the discovery and characterization of nearby jovian or even terrestrial
exoplanets. All of today's major space-based and adaptive optics-equipped
ground based telescopes are obscured aperture systems, with a secondary mirror
held in place by secondary support `spider' vanes. The presence of a secondary
obscuration can be dealt with by ingenious coronagraph designs, but the spider
vanes themselves cause diffracted light that can hamper the search for jovian
exoplanets around nearby stars. We look at the problem of suppressing spider
vane diffraction in Lyot coronagraphs, including apodized pupil and
band-limited designs. We show how spider vane diffraction can be reduced
drastically, and in fact contained, in the final coronagraphic image, within
one resolution element of the geometric image of the focal plane mask's
occulting spot. This makes adaptive optics coronagraphic searches for
exojupiters possible on the next generation of adaptive optics systems being
developed for 8-10 m class telescopes such as Gemini and the Very Large
Telescopes.


  An interesting feature of the finite-dimensional real spectral triple
(A,H,D,J) of the Standard Model is that it satisfies a ``second-order''
condition: conjugation by J maps the Clifford algebra Cl_D(A) into its
commutant, which in fact is isomorphic to the Clifford algebra itself (H is a
self-Morita equivalence Cl_D(A)-bimodule). This resembles a property of the
canonical spectral triple of a closed oriented Riemannian manifold: there is a
dense subspace of H which is a self-Morita equivalence Cl_D(A)-bimodule. In
this paper we argue that on manifolds, in order for the self-Morita equivalence
to be implemented by a reality operator J, one has to introduce a ``twist'' and
weaken one of the axioms of real spectral triples. We then investigate how the
above mentioned conditions behave under products of spectral triples.


  Exponential stochastic compression is the process when every second cell of
an infinite chain may increase its weight merging randomly with left, right, or
both neighboring cells. The total mass conservation is assumed. After that,
merged cells fill the empty space, compressing the chain twice. They may fill
empty spaces in two different ways: (I) using shifts only, i.e. preserving the
order; (II) using shifts and random permutations. Compressing the initial
homogeneous chain with cell weights $1$ many times, we compute final densities
$\rho_i$ of cells with weight $i=1,2,3,...$. The main result is that
$\rho_i/\rho_1=i$ in the ordered case (I), and
$\rho_i/\rho_1\approx1.464910...(i-1/4)$ in the disordered case (II). The
multiplier in the disordered case has a fractal nature. The compression of
initially inhomogeneous chains and rescaled continuous densities are also
discussed.


  Ubiquitous sensing devices frequently disseminate data among them. The use of
a distributed event-based system that decouples publishers from subscribers
arises as an ideal candidate to implement the dissemination process. In this
paper, we present a network architecture that merges the network and overlay
layers of typical structured event-based systems. Directional random walks are
used for the construction of this merged layer. Our strategy avoids using a
specific network protocol that provides point-to-point communication. This
implies that the topology of the network is not maintained, so that nodes not
involved in the system are able to save energy and computing resources. We
evaluate the performance of the overlay layer using directional random walks
and pure random walks for its construction. Our results show that directional
random walks are more efficient because: (1) they use less nodes of the network
for the establishment of the active path of the overlay layer and (2) they have
a more reliable performance. Furthermore, as the number of nodes in the network
increases, so do the number of nodes in the active path of the overlay layer
for the same number of publishers and subscribers. Finally, we discard any
correlation between the number of nodes that form the overlay layer and the
maximum Euclidean distance traversed by the walkers.


  This paper addresses the long standing and controversial issue of the origin
of superconductivity in cuprates. Their superconductivity can be attributed to
amphoteric defects associated with vacancy sites in copper oxide planes. A
local defect lattice relaxation results in a negative-$U$ energy binding two
holes on amphoteric defects in the donor configuration that act as preformed
boson pair. Thermodynamic equilibrium between defects in the donor and acceptor
configurations stabilizes Fermi energy at the amphoteric defect charge
transition state assuring resonant coupling between free holes and the
localized hole pairs. Model calculations show that the critical temperature is
primarily determined by the density of the amphoteric defects in the donor
configuration, explaining the ubiquity of dome-like dependence of the critical
temperature on the doping as well as its universal dependence on the superfluid
density. Intentional doping with chemical acceptors or donors is neither
necessary nor sufficient condition for superconductivity that is fully
determined by the amphoteric defects whose concentration can be controlled by
crystal nonstoichiometry. The only role of chemical doping is changing the
balance between concentrations of amphoteric defects in the donor and acceptor
configurations resulting in an increase of the superfluid density and thus also
the critical temperature for acceptor and a decrease for donor doping. This
accounts for the experimentally observed distinct asymmetry between the dome
structures for the chemical doping with acceptors and donors. The unusual
sensitivity of the critical temperature to external perturbations is explained
by the resonant nature of the coupling between free holes and preformed hole
pairs. The work has broader implications as it could be applicable to other
superconductors with dome-like dependence of the critical temperature on
doping.


  It is shown that a consistent application of Bayesian updating from a prior
probability density to a posterior using evidence in the form of expectation
constraints leads to exactly the same results as the application of the maximum
entropy principle, namely a posterior belonging to the exponential family. The
Bayesian updating procedure presented in this work is not expressed as a
variational principle, and does not involve the concept of entropy. Therefore
it conceptually constitutes a complete alternative to entropic methods of
inference.


  We obtain the analytical solutions to the Schr\"odinger equation for the
attractive inverse-square potential in an induced electric dipole moment system
under the influence of the harmonic oscillator. We show that bound states can
exist when the electric field configuration brings a cut-off point that imposes
a forbidden region for the neutral particle. Then, by dealing with $s$-waves,
we obtain the energy eigenvalues in the strong electric field regime and for
small values of the angular frequency of the harmonic oscillator. Further, we
extend our discussion about the energy eigenvalues beyond the $s$-waves.


  This paper studies source-free domain adaptive fundus image segmentation
which aims to adapt a pretrained fundus segmentation model to a target domain
using unlabeled images. This is a challenging task because it is highly risky
to adapt a model only using unlabeled data. Most existing methods tackle this
task mainly by designing techniques to carefully generate pseudo labels from
the model's predictions and use the pseudo labels to train the model. While
often obtaining positive adaption effects, these methods suffer from two major
issues. First, they tend to be fairly unstable - incorrect pseudo labels
abruptly emerged may cause a catastrophic impact on the model. Second, they
fail to consider the severe class imbalance of fundus images where the
foreground (e.g., cup) region is usually very small. This paper aims to address
these two issues by proposing the Class-Balanced Mean Teacher (CBMT) model.
CBMT addresses the unstable issue by proposing a weak-strong augmented mean
teacher learning scheme where only the teacher model generates pseudo labels
from weakly augmented images to train a student model that takes strongly
augmented images as input. The teacher is updated as the moving average of the
instantly trained student, which could be noisy. This prevents the teacher
model from being abruptly impacted by incorrect pseudo-labels. For the class
imbalance issue, CBMT proposes a novel loss calibration approach to highlight
foreground classes according to global statistics. Experiments show that CBMT
well addresses these two issues and outperforms existing methods on multiple
benchmarks.


  We present a method to efficiently compute the eigenfunctions of classically
chaotic systems. The key point is the definition of a modified Gram-Schmidt
procedure which selects the most suitable elements from a basis set of scar
functions localized along the shortest periodic orbits of the system. In this
way, one benefits from the semiclassical dynamical properties of such
functions. The performance of the method is assessed by presenting an
application to a quartic two dimensional oscillator whose classical dynamics
are highly chaotic. We have been able to compute the eigenfunctions of the
system using a small basis set. An estimate of the basis size is obtained from
the mean participation ratio. A thorough analysis of the results using
different indicators, such as eigenstate reconstruction in the local
representation, scar intensities, participation ratios, and error bounds, is
also presented.


  The rapid growth of the Industrial Internet of Things (IIoT) has brought
embedded systems into focus as major targets for both security analysts and
malicious adversaries. Due to the non-standard hardware and diverse software,
embedded devices present unique challenges to security analysts for the
accurate analysis of firmware binaries. The diversity in hardware components
and tight coupling between firmware and hardware makes it hard to perform
dynamic analysis, which must have the ability to execute firmware code in
virtualized environments. However, emulating the large expanse of hardware
peripherals makes analysts have to frequently modify the emulator for executing
various firmware code in different virtualized environments, greatly limiting
the ability of security analysis.
  In this work, we explore the problem of firmware re-hosting related to the
real-time operating system (RTOS). Specifically, developers create a Board
Support Package (BSP) and develop device drivers to make that RTOS run on their
platform. By providing high-level replacements for BSP routines and device
drivers, we can make the minimal modification of the firmware that is to be
migrated from its original hardware environment into a virtualized one. We show
that an approach capable of offering the ability to execute firmware at scale
through patching firmware in an automated manner without modifying the existing
emulators. Our approach, called static binary-level porting, first identifies
the BSP and device drivers in target firmware, then patches the firmware with
pre-built BSP routines and drivers that can be adapted to the existing
emulators. Finally, we demonstrate the practicality of the proposed method on
multiple hardware platforms and firmware samples for security analysis. The
result shows that the approach is flexible enough to emulate firmware for
vulnerability assessment and exploits development.


  Real-world optimization problems often do not just involve multiple
objectives but also uncertain parameters. In this case, the goal is to find
Pareto-optimal solutions that are robust, i.e., reasonably good under all
possible realizations of the uncertain data. Such solutions have been studied
in many papers within the last ten years and are called robust efficient.
However, solution methods for finding robust efficient solutions are scarce. In
this paper, we develop three algorithms for determining robust efficient
solutions to biobjective mixed-integer linear robust optimization problems. To
this end, we draw from methods for both multiobjective optimization and robust
optimization: dichotomic search for biobjective mixed-integer optimization
problems and an optimization-pessimization approach from (single-objective)
robust optimization, which iteratively adds scenarios and thereby increases the
uncertainty set. We propose two algorithms that combine dichotomic search with
the optimization-pessimization method as well as a dichotomic search method for
biobjective linear robust optimization that exploits duality. On the way we
derive some other results: We extend dichotomic search from biobjective linear
problems to biobjective linear minmax problems and generalize the
optimization-pessimization method from single-objective to multi-objective
robust optimization problems. We implemented and tested the three algorithms on
linear and integer linear instances and discuss their respective strengths and
weaknesses.


  The anomaly-induced inflation (modified Starobinsky model) is based on the
application of the effective quantum field theory approach to the Early
Universe. We present a brief general review of the model and show that it does
not require a fine-tuning for the parameters of the theory or initial data,
gives a real chance to meet a graceful exit to the FRW phase and also has
positive features with respect to the metric perturbations.


  Lin and Wang defined a model of random walks on knot diagrams and interprete
the Alexnader polynomials and the colored Jones polynomials as Ihara zeta
functions, i.e. zeta functions defined by counting cycles on the knot diagram.
Using this explanation, they gave a more conceptual proof for the Melvin-Morton
conjecture. In this paper, we give an analogous zeta function expression for
the twisted Alexander invariants.


  We describe measurements of the thermally-activated transitions between
fluxoid states of a single isolated superconducting ring. We compare these
measurements with theoretical predictions in which all of the relevant
parameters are determined via independent characterization of the same ring.
This no-free-parameters comparison shows qualitative agreement over a wide
range of temperatures. We discuss possible origins for the remaining
discrepancies between the data and theory, in particular the choice of model
for the superconducting order parameter's damping.


  Understanding structure-property relationships is essential for advancing
technologies based on thin films. X-ray pair distribution function (PDF)
analysis can access relevant atomic structure details spanning local-, mid-,
and long-range order. While X-ray PDF has been adapted for thin films on
amorphous substrates, measurements on single crystal substrates are necessary
to accurately determine structure origins for some thin film materials,
especially those for which the substrate changes the accessible structure and
properties. However, when measuring films on single crystal substrates, high
intensity anisotropic Bragg spots saturate 2D detector images, overshadowing
the thin films' isotropic scattering signal. This renders previous data
processing methods for films on amorphous substrates unsuitable for films on
single crystal substrates. To address this measurement need, we developed
IsoDAT2D, an innovative data processing approach using unsupervised machine
learning algorithms. The program combines non-negative matrix factorization and
hierarchical agglomerative clustering to separate thin film and single crystal
substrate X-ray scattering signals. We use SimDAT2D, a program we developed to
generate synthetic thin film data, to validate IsoDAT2D. We also use IsoDAT2D
to isolate X-ray total scattering signal from a thin film on a single crystal
substrate. The resulting PDF data are compared to similar data processed using
previous methods, demonstrating superior performance relative to substrate
subtraction with a single crystal substrate and similar performance to
substrate subtraction from an amorphous substrate. With IsoDAT2D, there are new
opportunities to expand PDF to a wider variety of thin films, including those
on single crystal substrates, with which new structure-property relationships
can be elucidated to enable fundamental understanding and technological
advances.


  Local robustness ensures that a model classifies all inputs within an
$\ell_2$-ball consistently, which precludes various forms of adversarial
inputs. In this paper, we present a fast procedure for checking local
robustness in feed-forward neural networks with piecewise-linear activation
functions. Such networks partition the input space into a set of convex
polyhedral regions in which the network's behavior is linear; hence, a
systematic search for decision boundaries within the regions around a given
input is sufficient for assessing robustness. Crucially, we show how the
regions around a point can be analyzed using simple geometric projections, thus
admitting an efficient, highly-parallel GPU implementation that excels
particularly for the $\ell_2$ norm, where previous work has been less
effective. Empirically we find this approach to be far more precise than many
approximate verification approaches, while at the same time performing multiple
orders of magnitude faster than complete verifiers, and scaling to much deeper
networks.


  In transportation, communication, social and other real complex networks,
some critical edges act a pivotal part in controlling the flow of information
and maintaining the integrity of the structure. Due to the importance of
critical edges in theoretical studies and practical applications, the
identification of critical edges gradually become a hot topic in current
researches. Considering the overlap of communities in the neighborhood of
edges, a novel and effective metric named subgraph overlap (SO) is proposed to
quantifying the significance of edges. The experimental results show that SO
outperforms all benchmarks in identifying critical edges which are crucial in
maintaining the integrity of the structure and functions of networks.


  The block-oriented models are usually based on linear dynamic and non-linear
static blocks that are connected in various sequential/parallel ways. Some
particular configurations of the involved blocks result in the well-known
Hammerstein, Wiener, Hammerstein-Wiener and generalised Hammerstein models. The
Urysohn model is a lesser-known model; it is represented by a single non-linear
dynamic block and can be approximated by a number of parallel Hammerstein
blocks. In this paper, it is shown that any block-oriented model can be
adequately replaced by a single Urysohn block followed by a single static
non-linear block. Furthermore, a method of the so-called non-parametric
identification of such object is introduced.


  Understanding player shooting profiles is an essential part of basketball
analysis: knowing where certain opposing players like to shoot from can help
coaches neutralize offensive gameplans from their opponents; understanding
where their players are most comfortable can lead them to developing more
effective offensive strategies. An automatic tool that can provide these
performance profiles in a timely manner can become invaluable for coaches to
maximize both the effectiveness of their game plan as well as the time
dedicated to practice and other related activities. Additionally, basketball is
dictated by many variables, such as playstyle and game dynamics, that can
change the flow of the game and, by extension, player performance profiles. It
is crucial that the performance profiles can reflect the diverse playstyles, as
well as the fast-changing dynamics of the game. We present a tool that can
visualize player performance profiles in a timely manner while taking into
account factors such as play-style and game dynamics. Our approach generates
interpretable heatmaps that allow us to identify and analyze how non-spatial
factors, such as game dynamics or playstyle, affect player performance
profiles.


  For Si and Ge nanocrystals (NCs) embedded in wide band-gap matrices, Auger
recombination (AR) and carrier multiplication (CM) lifetimes are computed
exactly in a three-dimensional real space grid using empirical pseudopotential
wave functions. Our results in support of recent experimental data offer new
predictions. We extract simple Auger constants valid for NCs. We show that both
Si and Ge NCs can benefit from photovoltaic efficiency improvement via CM due
to the fact that under an optical excitation exceeding twice the band gap
energy, the electrons gain lion's share from the total excess energy and can
cause a CM. We predict that CM becomes especially efficient for hot electrons
with an excess energy of about 1 eV above the CM threshold.


  The Visual Domain Adaptation (VisDA) 2021 Challenge calls for unsupervised
domain adaptation (UDA) methods that can deal with both input distribution
shift and label set variance between the source and target domains. In this
report, we introduce a universal domain adaptation (UniDA) method by
aggregating several popular feature extraction and domain adaptation schemes.
First, we utilize VOLO, a Transformer-based architecture with state-of-the-art
performance in several visual tasks, as the backbone to extract effective
feature representations. Second, we modify the open-set classifier of OVANet to
recognize the unknown class with competitive accuracy and robustness. As shown
in the leaderboard, our proposed UniDA method ranks the 2nd place with 48.56%
ACC and 70.72% AUROC in the VisDA 2021 Challenge.


  The two-dimensional (2D) orientation field transform has been proved to be
effective at enhancing 2D contours and curves in images by means of top-down
processing. It, however, has no counterpart in three-dimensional (3D) images
due to the extremely complicated orientation in 3D compared to 2D. Practically
and theoretically, the demand and interest in 3D can only be increasing. In
this work, we modularise the concept and generalise it to 3D curves. Different
modular combinations are found to enhance curves to different extents and with
different sensitivity to the packing of the 3D curves. In principle, the
proposed 3D orientation field transform can naturally tackle any dimensions. As
a special case, it is also ideal for 2D images, owning simpler methodology
compared to the previous 2D orientation field transform. The proposed method is
demonstrated with several transmission electron microscopy tomograms ranging
from 2D curve enhancement to, the more important and interesting, 3D ones.


  We investigate, theoretically and numerically, the spin dynamics of a
two-component exciton-polariton condensate created and sustained by
non-resonant spin-polarized optical pumping of a semiconductor microcavity.
Using the open-dissipative mean-field model, we show that the existence of well
defined phase-locked steady states of the condensate may lead to efficient
switching and control of spin (polarization) states with a non-resonant
excitation. Spatially inhomogeneous pulsed excitations can cause symmetry
breaking in the pseudo-spin structure of the condensate and lead to formation
of non-trivial spin textures. Our model is universally applicable to two weakly
coupled polariton condensates, and therefore can also describe the behaviour of
condensate populations and phases in 'double-well' type potentials.


  As a probe of the Yang-Mills vacuum, we study numerically the eigenmode
spectrum of the covariant lattice Laplacian operator. We find that the
eigenmodes at the low and high ends of the spectrum are localized in finite
regions whose volume is insensitive to the lattice volume. We also find that
the vacuum is seen very differently by localized modes of the covariant
Laplacian in different representations of the gauge group. In the fundamental
representation, the data suggests that the localization volume is finite in
physical units set by the string tension, and localization disappears when
center vortices are removed. In the adjoint and j=3/2 representations the low
and high-lying modes are far more localized, and the localization volume
appears to scale to zero, in physical units, in the continuum limit. The
adjoint Laplacian is insensitive to vortex removal, but we find that
exponential localization is absent for adjoint eigenmodes in the Higgs phase of
a gauge-Higgs theory. Localization is also absent in the spectrum of the
Coulomb gauge Faddeev-Popov operator, as required in Coulomb gauge confinement
scenarios.


  By using a variational Monte Carlo technique based upon Gutzwiller-projected
fermionic states, we investigate the dynamical structure factor of the
antiferromagnetic $S=1/2$ Heisenberg model on the honeycomb lattice, in
presence of first-neighbor ($J_1$) and second-neighbor ($J_2$) couplings, for
${J_2 < 0.5 J_1}$. The ground state of the system shows long-range
antiferromagnetic order for ${J_2/J_1 \lesssim 0.23}$, plaquette valence-bond
order for ${0.23 \lesssim J_2/J_1 \lesssim 0.36}$, and columnar dimer order for
${J_2/J_1 \gtrsim 0.36}$. Within the antiferromagnetic state, a well-defined
magnon mode is observed, whose dispersion is in relatively good agreement with
linear spin-wave approximation for $J_2=0$. When a nonzero second-neighbor
super-exchange is included, a roton-like mode develops around the $K$ point
(i.e., the corner of the Brillouin zone). This mode softens when $J_2/J_1$ is
increased and becomes gapless at the transition point, $J_2/J_1 \approx 0.23$.
Here, a broad continuum of states is clearly visible in the dynamical spectrum,
suggesting that nearly-deconfined spinon excitations could exist, at least at
relatively high energies. For larger values of $J_2/J_1$, valence-bond order is
detected and the spectrum of the system becomes clearly gapped, with a triplon
mode at low energies. This is particularly evident for the spectrum of the
dimer valence-bond phase, in which the triplon mode is rather well separated
from the continuum of excitations that appears at higher energies.


  3D simulations of magnetic flux emergence are carried out in a computational
domain spanning the upper layers of the convection zone to the lower corona. We
use the Oslo Staggered Code to solve the full MHD equations with non-grey and
NLTE radiative transfer and thermal conduction along the magnetic field lines.
In this paper we concentrate on the later stages of the simulations and study
the evolution of the structure of the rising flux in the upper chromosphere and
corona, the interaction between the emerging flux and the weak coronal magnetic
field initially present, and the associated dynamics.
  The flux tube injected at the bottom boundary rises to the photosphere where
it largely remains. However, some parts of the flux tube become unstable and
expand in patches into the upper chromosphere. The flux rapidly expands towards
the corona, pushing the coronal and transition region material aside, lifting
and maintaining the transition region at heights greater than 5 Mm above the
photosphere for extensive periods of time. The pre-existing magnetic field in
the corona and transition region is perturbed by the incoming flux and
reoriented by a series of high Joule heating events. Low density structures
form in the corona while at later times a high density filamentary structure
appears in the lower part of the expanding flux. The dynamics of these and
other structures is discussed. While Joule heating due to the expanding flux is
episodic, it increases in relative strength as fresh magnetic field rises and
becomes energetically important in the upper chromosphere and corona at later
times. Chromospheric, transition region and coronal lines are computed and
their response to the perturbation caused by the expanding emerging flux is
discussed.


  The Seyfert 1 nucleus of NGC 4395 is energized by a black hole of 360,000
Solar masses (Peterson et al.), making it one of only two nuclear black holes
of intermediate mass, one thousand to one million Solar masses, detected in the
radio regime. Building upon UV and X-ray evidence for outflows from this
Seyfert nucleus, the VLBI High Sensitivity Array was used at 1.4 GHz to search
for extended structure on scales greater than 5 mas (0.1 pc). Elongated
emission was discovered, extending over 15 mas (0.3 pc) and suggesting an
outflow on sub-parsec scales from this intermediate-mass black hole. The
Seyfert nucleus is located at the center of an elliptical star cluster, and the
elongation position angle of the sub-parsec radio structure is only 19 degrees
from the star cluster's minor axis.


  The Arcade Learning Environment (ALE) is proposed as an evaluation platform
for empirically assessing the generality of agents across dozens of Atari 2600
games. ALE offers various challenging problems and has drawn significant
attention from the deep reinforcement learning (RL) community. From Deep
Q-Networks (DQN) to Agent57, RL agents seem to achieve superhuman performance
in ALE. However, is this the case? In this paper, to explore this problem, we
first review the current evaluation metrics in the Atari benchmarks and then
reveal that the current evaluation criteria of achieving superhuman performance
are inappropriate, which underestimated the human performance relative to what
is possible. To handle those problems and promote the development of RL
research, we propose a novel Atari benchmark based on human world records
(HWR), which puts forward higher requirements for RL agents on both final
performance and learning efficiency. Furthermore, we summarize the
state-of-the-art (SOTA) methods in Atari benchmarks and provide benchmark
results over new evaluation metrics based on human world records. We concluded
that at least four open challenges hinder RL agents from achieving superhuman
performance from those new benchmark results. Finally, we also discuss some
promising ways to handle those problems.


  We present our experimental and theoretical studies of multi-dark-state
resonances (MDSRs) generated in a unique cold rubidium atomic system with only
one coupling laser beam. Such MDSRs are caused by different transition
strengths of the strong coupling beam connecting different Zeeman sublevels.
Controlling the transparency windows in such electromagnetically induced
transparency system can have potential applications in multi-wavelength optical
communication and quantum information processing.


  High-dimensional and sparse (HiDS) matrices are frequently adopted to
describe the complex relationships in various big data-related systems and
applications. A Position-transitional Latent Factor Analysis (PLFA) model can
accurately and efficiently represent an HiDS matrix. However, its involved
latent factors are optimized by stochastic gradient descent with the specific
gradient direction step-by-step, which may cause a suboptimal solution. To
address this issue, this paper proposes a Sequential-Group-Differential-
Evolution (SGDE) algorithm to refine the latent factors optimized by a PLFA
model, thereby achieving a highly-accurate SGDE-PLFA model to HiDS matrices. As
demonstrated by the experiments on four HiDS matrices, a SGDE-PLFA model
outperforms the state-of-the-art models.


  Using error diagrams, we quantify the forecasting of
characteristic-earthquake occurrence in a recently introduced minimalist model.
Initially we connect the earthquake alarm at a fixed time after the ocurrence
of a characteristic event. The evaluation of this strategy leads to a
one-dimensional numerical exploration of the loss function. This first strategy
is then refined by considering a classification of the seismic cycles of the
model according to the presence, or not, of some factors related to the
seismicity observed in the cycle. These factors, statistically speaking,
enlarge or shorten the length of the cycles. The independent evaluation of the
impact of these factors in the forecast process leads to two-dimensional
numerical explorations. Finally, and as a third gradual step in the process of
refinement, we combine these factors leading to a three-dimensional
exploration. The final improvement in the loss function is about 8.5%.


  Respondent-driven sampling (RDS) is currently widely used for the study of
HIV/AIDS-related high risk populations. However, recent studies have shown that
traditional RDS methods are likely to generate large variances and may be
severely biased since the assumptions behind RDS are seldom fully met in real
life. To improve estimation in RDS studies, we propose a new method to generate
estimates with ego network data, which is collected by asking RDS respondents
about the composition of their personal networks, such as "what proportion of
your friends are married?". By simulations on an extracted real-world social
network of gay men as well as on artificial networks with varying structural
properties, we show that the new estimator, RDSI^{ego} shows superior
performance over traditional RDS estimators. Importantly, RDSI^{ego} exhibits
strong robustness to the preference of peer recruitment and variations in
network structural properties, such as homophily, activity ratio, and community
structure. While the biases of traditional RDS estimators can sometimes be as
large as 10%~20%, biases of all RDSI^{ego} estimates are well restrained to be
less than 2%. The positive results henceforth encourage researchers to collect
ego network data for variables of interests by RDS, for both hard-to-access
populations and general populations when random sampling is not applicable. The
limitation of RDSI^{ego} is evaluated by simulating RDS assuming different
level of reporting error.


  Static correlation error(SCE) inevitably emerges when a dissociation of a
covalent bond is described with a conventional denstiy-functional theory (DFT)
for electrons. SCE gives rise to a serious overshoot in the potential energy at
the dissociation limit even in the simplest molecules. The error is attributed
to the basic framework of the approximate functional for the exchange
correlation energy Exc which refers only to local properties at coordinate r,
namely, the electron density n(r) and its derivatives. To solve the problem we
developed a functional Ee which uses xc the energy electron distribution ne(e)
as a fundamental variable in DFT. ne(e) is obtained by the projection of the
density n(r) onto an energy coordinate e defined with the external potential of
interest. The functional was applied to the dissociations of single, double,
and triple bonds in small molecules showing reasonable agreements with the
results given by a high level molecular orbitals theory. We also applied the
functional to the computation of the energy change associated with spin
depolarization and symmetrization in Carbon atom, which made an improvement
over the conventional functional. This work opens the way for development of
tougher functional that necessitates non-local properties of electrons such as
kinetic energy functional.


  Travel decisions are fundamental to understanding human mobility, urban
economy, and sustainability, but measuring it is challenging and controversial.
Previous studies of taxis are limited to taxi stands or hail markets at
aggregate spatial units. Here we estimate the dynamic demand and supply of
taxis in New York City (NYC) at street segment level, using in-vehicle Global
Positioning System (GPS) data which preserve individual privacy. To this end,
we model taxi demand and supply as non-stationary Poisson random fields on the
road network, and pickups result from income-maximizing drivers searching for
impatient passengers. With 868 million trip records of all 13,237 licensed
taxis in NYC in 2009 - 2013, we show that while taxi demand are almost the same
in 2011 and 2012, it declined about 2% in spring 2013, possibly caused by
transportation network companies (TNCs) and fare raise. Contrary to common
impression, street-hail taxis out-perform TNCs such as Uber in high-demand
locations, suggesting a taxi/TNC regulation change to reduce congestion and
pollution. We show that our demand estimates are stable at different supply
levels and across years, a property not observed in existing matching
functions. We also validate that taxi pickups can be modeled as Poisson
processes. Our method is thus simple, feasible, and reliable in estimating
street-hail taxi activities at a high spatial resolution; it helps quantify the
ongoing discussion on congestion charges to taxis and TNCs.


  A graph $\Gamma$ is called locally finite if, for each vertex $v$ of
$\Gamma$, the set $\Gamma(v)$ of all neighbors of $v$ in $\Gamma$ is finite.
For any locally finite graph $\Gamma$ with vertex set $V(\Gamma)$ and for any
field $F$, let $F^{V(\Gamma)}$ be the vector space over $F$ of all functions
$V(\Gamma) \to F$ (with natural componentwise operations) and let $A^{({\rm
alg})}_{\Gamma,F}$ be the linear operator $F^{V(\Gamma)} \to F^{V(\Gamma)}$
defined by $(A^{({\rm alg})}_{\Gamma,F}(f))(v) = \sum_{u \in \Gamma(v)}f(u)$
for all $f \in F^{V(\Gamma)}$, $v \in V(\Gamma)$. In the case of finite graph
$\Gamma$ the mapping $A^{({\rm alg})}_{\Gamma,F}$ is the well known operator
defined by the adjacency matrix of $\Gamma$ (over $F$), and the theory of
eigenvalues and eigenfunctions of such operator is a well-developed (at least
in the case $F = \mathbb{C}$) part of the theory of finite graphs. In this
paper we develope a theory of eigenvalues and eigenfunctions of $A^{({\rm
alg})}_{\Gamma,F}$ for arbitrary infinite locally finite graphs $\Gamma$
(although a few results may be of interest for finite graphs) and fields $F$
with a special emphasis on the case when $\Gamma$ is connected with uniformly
bounded vertex degrees and $F = \mathbb{C}$. By the author opinion, previous
attempts in this direction were not quite satisfactory since were limited by
consideration of rather special eigenfunctions and corresponding eigenvalues.


  We propose a new possibility to realize simultaneously the sufficient proton
stability and the interesting structure of neutrino mass matrix in superstring
inspired $E_6$ models. In this model the leptons and Higgs fields are assigned
to a fundamental representation {\bf 27} in the different way among
generations. Two pairs of Higgs doublets naturally remain light from three
generation ones by imposing certain discrete symmetries, although all extra
color triplets become sufficiently heavy. Under these symmetries suitable
$\mu$-terms to bring appropriate vacuum expectation values are prepared and the
dangerous FCNC is avoidable. Some related phenomena to this model, especially,
the structure of neutrino mass matrix are also discussed.


  This paper continues our study of the interconnection between controllability
and mixing properties of random dynamical systems. We begin with an abstract
result showing that the approximate controllability to a point and a local
stabilisation property imply the uniqueness of a stationary measure and
exponential mixing in the dual-Lipschitz metric. This result is then applied to
the 2D Navier-Stokes system driven by a random force acting through the
boundary. A by-product of our analysis is the local exponential stabilisation
of the boundary-driven Navier-Stokes system by a regular boundary control.


  We perform a detailed analysis of the next-to-minimal supersymmetric standard
model (NMSSM), imposing the constraints of two-loop gauge coupling unification,
universal soft supersymmetry breaking and the correct pattern of electroweak
symmetry breaking. We compare our results with those for the minimal
supersymmetric standard model (MSSM) using closely related techniques and, as
far as possible, a common set of input and output variables. In general, in the
constrained NMSSM, there are much stronger correlations between parameters than
in the constrained MSSM, and we map out the allowed parameter space. We also
give a detailed discussion of how to resolve the two models experimentally,
concentrating primarily on the prospects at LEPII.


  We study various aspects of the noncommutative residue for an algebra of
pseudodifferential operators whose symbols have an expansion $a\sim
\sum_{j=0}^\infty a_{m-j}, a_{m-j}(x,\xi)=\sum_{l=0}^k a_{m-j,l}(x,\xi)
\log^l|\xi|,$ where $a_{m-j,l}$ is homogeneous in $\xi$ of degree $m-j$. We
will explain why this algebra of pseudodifferential operators is natural.
  For a pseudodifferential operator in this class, $A$, and a classical
elliptic pseudodifferential operator, $P$, we show that the generalized
zeta-function $\Tr(AP^{-s})$ has a meromorphic continuation to the whole
complex plane, however possibly with higher order poles.
  Our algebra of operators has a bigrading given by the order and the highest
log-power occuring in the symbol expansion. We construct "higher"
noncommutative residue functionals on the subspaces given by the log-grading.
However, in contrast to the classical case we prove that the whole algebra does
not admit any nontrivial traces.
  Finally we show that the analogue of the Kontsevich-Vishik trace also exists
on our algebra. Our method also provides an alternative approach to the
Kontsevich-Vishik trace.


  We study the dynamical stability against bar-mode deformation of rapidly
spinning neutron stars with differential rotation. We perform fully
relativistic 3D simulations of compact stars with $M/R \geq 0.1$, where $M$ is
the total gravitational mass and $R$ the equatorial circumferential radius. We
adopt an adiabatic equation of state with adiabatic index $\Gamma=2$. As in
Newtonian theory, we find that stars above a critical value of $\beta \equiv
T/W$ (where $T$ is the rotational kinetic energy and $W$ the gravitational
binding energy) are dynamically unstable to bar formation. For our adopted
choices of stellar compaction and rotation profile, the critical value of
$\beta = \beta_{dGR}$ is $\sim 0.24-0.25$, only slightly smaller than the
well-known Newtonian value $\sim 0.27$ for incompressible Maclaurin spheroids.
The critical value depends only very weakly on the degree of differential
rotation for the moderate range we surveyed. All unstable stars form bars on a
dynamical timescale. Models with sufficiently large $\beta$ subsequently form
spiral arms and eject mass, driving the remnant to a dynamically stable state.
Models with moderately large $\beta \gtrsim \beta_{dGR}$ do not develop spiral
arms or eject mass but adjust to form dynamically stable ellipsoidal-like
configurations. If the bar-mode instability is triggered in supernovae collapse
or binary neutron star mergers, it could be a strong and observable source of
gravitational waves. We determine characteristic wave amplitudes and
frequencies.


  We investigate experimentally the diffusion properties of a bidimensional
bidisperse dry granular material under quasistatic cyclic shear.The comparison
of these properties with results obtained both in computer simulations of hard
spheres systems and Lenard-Jones liquids and experiments on colloidal systems
near the glass transition demonstrates a strong analogy between the behaviour
of granular matter and these systems. More specifically, we study in detail the
cage dynamics responsible for the subdiffusion in the slow relaxation regime,
and obtain the values of relevant time and length scales.


  We find exact exponentially expanding and contracting de Sitter solutions of
the spatially homogeneous TeVeS cosmological equations of motion in the vacuum
TeVeS model and a power law accelerated expanding solution in thepresence of an
additional ideal fluid with equation of state parameter $-5/3 < \omega < -1$. A
preliminary stability analysis shows that the expanding vacuum solution is
stable, while in the ideal fluid case stability depends on model parameter
values. These solutions might provide a basis for incorporating early-time
inflation or late-time accelerated expansion in TeVeS cosmology.


  The Fronsdal Lagrangians for free totally symmetric rank-s tensors rest on
suitable trace constraints for their gauge parameters and gauge fields. Only
when these constraints are removed, however, the resulting equations reflect
the expected free higher-spin geometry. We show that geometric equations, in
both their local and non-local forms, can be simply recovered from local
Lagrangians with only two additional fields, a rank-(s-3) compensator and a
rank-(s-4) Lagrange multiplier. In a similar fashion, we show that geometric
equations for unconstrained rank-n totally symmetric spinor-tensors can be
simply recovered from local Lagrangians with only two additional
spinor-tensors, a rank-(n-2) compensator and a rank-(n-3) Lagrange multiplier.


  We are concerned with the nonlinear Schr\"odinger equation with an $L^2$ mass
constraint on both finite and locally finite graphs and prove that the equation
has a normalized solution by employing variational methods. We also pay
attention to the behaviours of the normalized solution as the mass constraint
tends to $0^+$ or $+\infty$ and give clear descriptions of the limit equations.
Finally, we provide some numerical experiments on a finite graph to illustrate
our theoretical results.


  Two-dimensional conformal field theories with just Virasoro symmetry are
endowed with integrable structure. We review how to construct the integrable
charges in a two-dimensional conformal field theory and how to relate them to
the charges of quantum Sinh-Gordon theory when c>25. We then explicitly
calculate the single charge characters in the large c limit for all charges and
thereby reveal how their degeneracies grow within one module. This, in
particular, allows us to approximate the characters in the limit of small
chemical potential, which source the respective charges. The latter give us
insights into possible transformation properties of the characters. We also
comment on the full generalized Gibbs ensemble and approximations to pure
states.


  We present predictions for the abundance and nature of Extremely Red Objects
(EROs) in the Lambda cold dark matter model. EROs are red, massive galaxies
observed at z>= 1 and their numbers and properties pose a challenge to
hierarchical galaxy formation models. We compare the predictions from two
published models, one of which invokes a "superwind" to regulate star formation
in massive haloes and the other which suppresses gas cooling in haloes through
"radio-mode" AGN feedback. The superwind model underestimates the number counts
of EROs by an order of magnitude, whereas the radio-mode AGN feedback model
gives excellent agreement with the number counts and redshift distribution of
EROs. In the AGN feedback model the ERO population is dominated by old,
passively evolving galaxies, whereas observations favour an equal split between
old galaxies and dusty starbursts. Also, the model predicts a more extended
redshift distribution of passive galaxies than is observed. These comparisons
suggest that star formation may be quenched too efficiently in this model.


  All the realistic free fermionic models utilize a set of basis vectors, the
NAHE set, that correspond to $Z_2\times Z_2$ orbifold compactification with
nontrivial background fields. I argue that the realistic features of free
fermionic models, like the number of generations and the fermion mass spectrum
are due to the underlying $Z_2\times Z_2$ orbifold compactification.


  The main challenges of using electroencephalogram (EEG) signals to make
eye-tracking (ET) predictions are the differences in distributional patterns
between benchmark data and real-world data and the noise resulting from the
unintended interference of brain signals from multiple sources. Increasing the
robustness of machine learning models in predicting eye-tracking position from
EEG data is therefore integral for both research and consumer use. In medical
research, the usage of more complicated data collection methods to test for
simpler tasks has been explored to address this very issue. In this study, we
propose a fine-grain data approach for EEG-ET data collection in order to
create more robust benchmarking. We train machine learning models utilizing
both coarse-grain and fine-grain data and compare their accuracies when tested
on data of similar/different distributional patterns in order to determine how
susceptible EEG-ET benchmarks are to differences in distributional data. We
apply a covariate distributional shift to test for this susceptibility. Results
showed that models trained on fine-grain, vector-based data were less
susceptible to distributional shifts than models trained on coarse-grain,
binary-classified data.


  In this paper we study the rigidity of proper holomorphic maps $f\colon
\Omega\to\Omega'$ between irreducible bounded symmetric domains $\Omega$ and
$\Omega'$ with small rank differences: $2\leq \text{rank}(\Omega')<
2\,\text{rank}(\Omega)-1$. More precisely, if either $\Omega$ and $\Omega'$
have the same type or $\Omega$ is of type~III and $\Omega'$ is of type~I, then
up to automorphisms, $f$ is of the form $f=\imath\circ F$, where $F = F_1\times
F_2\colon \Omega\to \Omega_1'\times \Omega_2'$. Here $\Omega_1'$, $\Omega_2'$
are bounded symmetric domains, the map $F_1\colon \Omega \to \Omega_1'$ is a
standard embedding, $F_2: \Omega \to \Omega_2'$, and $\imath\colon
\Omega'_1\times \Omega'_2 \to \Omega'$ is a totally geodesic holomorphic
isometric embedding. Moreover we show that, under the rank condition above,
there exists no proper holomorphic map $f: \Omega \to \Omega'$ if $\Omega$ is
of type~I and $\Omega'$ is of type~III, or $\Omega$ is of type~II and $\Omega'$
is either of type~I or III. By considering boundary values of proper
holomorphic maps on maximal boundary components of $\Omega$, we construct
rational maps between moduli spaces of subgrassmannians of compact duals of
$\Omega$ and $\Omega'$, and induced CR-maps between CR-hypersurfaces of mixed
signature, thereby forcing the moduli map to satisfy strong local
differential-geometric constraints (or that such moduli maps do not exist), and
complete the proofs from rigidity results on geometric substructures modeled on
certain admissible pairs of rational homogeneous spaces of Picard number 1.


  Existence of wormholes can lead to a host of new effects like Misner-Wheeler
"charge without charge" effect, where without being generated by any source an
electric flux arrives from one "universe" and flows into the other "universe".
Here we show the existence of an intriguing opposite possibility. Namely, a
charged object (a charged lightlike brane in our case) sitting at the wormhole
"throat" expels all the flux it produces into just one of the "universes",
which turns out to be of compactified ("tube-like") nature. An outside observer
in the non-compact "universe" detects, therefore, a neutral object. This
charge-hiding effect takes place in a gravity/gauge-field system
self-consistently interacting with a charged lightlike brane as a matter
source, where the gauge field subsystem is of a special non-linear form
containing a square-root of the Maxwell term and which previously has been
shown to produce a QCD-like confining gauge field dynamics in flat space-time.


  We study the problem of detection of a high-dimensional signal function in
the white Gaussian noise model. As well as a smoothness assumption on the
signal function, we assume an additive sparse condition on the latter. The
detection problem is expressed in terms of a nonparametric hypothesis testing
problem and it is solved according to the asymptotical minimax approach. The
minimax test procedures are adaptive in the sparsity parameter for high
sparsity case. We extend to the functional case the known results in the
detection of sparse high-dimensional vectors. In particular, our asymptotic
detection boundaries are derived from the same asymptotic relations as in the
vector case.