  Accurate brain tumor segmentation in the early stages of the disease is
crucial for the treatment's effectiveness, avoiding exhaustive visual
inspection of a qualified specialist on 3D MR brain images of multiple
protocols (e.g., T1, T2, T2-FLAIR, T1-Gd). Several networks exist for Glioma
segmentation, being nnU-Net one of the best. In this work, we evaluate
self-calibrated convolutions in different parts of the nnU-Net network to
demonstrate that self-calibrated modules in skip connections can significantly
improve the enhanced-tumor and tumor-core segmentation accuracy while
preserving the wholetumor segmentation accuracy.


  Palliative medicine is an interdisciplinary specialty focusing on improving
quality of life (QOL) for patients with serious illness and their families.
Palliative care programs are available or under development at over 80% of
large US hospitals (300+ beds). Palliative care clinical trials present unique
analytic challenges relative to evaluating the palliative care treatment
efficacy which is to improve patients diminishing QOL as disease progresses
towards end of life (EOL). A unique feature of palliative care clinical trials
is that patients will experience decreasing QOL during the trial despite
potentially beneficial treatment. Often longitudinal QOL and survival data are
highly correlated which, in the face of censoring, makes it challenging to
properly analyze and interpret longitudinal QOL trajectory. To address these
issues, we propose a novel semiparametric statistical approach to jointly model
longitudinal QOL and survival data. There are two sub-models in our approach: a
semiparametric mixed effects model for longitudinal QOL and a Cox model for
survival. We use regression splines method to estimate the nonparametric curves
and AIC to select knots. We assess the model through simulation and application
to establish a novel modeling approach that could be applied in future
palliative care treatment research trials.


  It is well-known that any matrix $A$ has an LU decomposition. Less well-known
is the fact that it has a 'Toeplitz decomposition' $A = T_1 T_2 \cdots T_r$
where $T_i$'s are Toeplitz matrices. We will prove that any continuous function
$f : \mathbb{R}^n \to \mathbb{R}^m$ has an approximation to arbitrary accuracy
by a neural network that takes the form $L_1 \sigma_1 U_1 \sigma_2 L_2 \sigma_3
U_2 \cdots L_r \sigma_{2r-1} U_r$, i.e., where the weight matrices alternate
between lower and upper triangular matrices, $\sigma_i(x) := \sigma(x - b_i)$
for some bias vector $b_i$, and the activation $\sigma$ may be chosen to be
essentially any uniformly continuous nonpolynomial function. The same result
also holds with Toeplitz matrices, i.e., $f \approx T_1 \sigma_1 T_2 \sigma_2
\cdots \sigma_{r-1} T_r$ to arbitrary accuracy, and likewise for Hankel
matrices. A consequence of our Toeplitz result is a fixed-width universal
approximation theorem for convolutional neural networks, which so far have only
arbitrary width versions. Since our results apply in particular to the case
when $f$ is a general neural network, we may regard them as LU and Toeplitz
decompositions of a neural network. The practical implication of our results is
that one may vastly reduce the number of weight parameters in a neural network
without sacrificing its power of universal approximation. We will present
several experiments on real data sets to show that imposing such structures on
the weight matrices sharply reduces the number of training parameters with
almost no noticeable effect on test accuracy.


  If you are predicting the label $y$ of a new object with $\hat y$, how
confident are you that $y = \hat y$? Conformal prediction methods provide an
elegant framework for answering such question by building a $100 (1 -
\alpha)\%$ confidence region without assumptions on the distribution of the
data. It is based on a refitting procedure that parses all the possibilities
for $y$ to select the most likely ones. Although providing strong coverage
guarantees, conformal set is impractical to compute exactly for many regression
problems. We propose efficient algorithms to compute conformal prediction set
using approximated solution of (convex) regularized empirical risk
minimization. Our approaches rely on a new homotopy continuation technique for
tracking the solution path with respect to sequential changes of the
observations. We also provide a detailed analysis quantifying its complexity.


  How can we explain the predictions of a black-box model? In this paper, we
use influence functions -- a classic technique from robust statistics -- to
trace a model's prediction through the learning algorithm and back to its
training data, thereby identifying training points most responsible for a given
prediction. To scale up influence functions to modern machine learning
settings, we develop a simple, efficient implementation that requires only
oracle access to gradients and Hessian-vector products. We show that even on
non-convex and non-differentiable models where the theory breaks down,
approximations to influence functions can still provide valuable information.
On linear models and convolutional neural networks, we demonstrate that
influence functions are useful for multiple purposes: understanding model
behavior, debugging models, detecting dataset errors, and even creating
visually-indistinguishable training-set attacks.


  We study the phase space of the spherically symmetric solutions of the system
obtained from the dimensional reduction of the six-dimensional
Einstein-Gauss-Bonnet action with a cosmological constant. We show that all the
physical solutions have anti-de Sitter asymptotic behavior.


  There are several standard procedures used to create new sequences from a
given sequence or from a given pair of sequences. In this paper I discuss the
most popular of these procedures. For each procedure, I give a definition and
provide examples based on three famous sequences: the natural numbers, the
prime numbers and the Fibonacci numbers. I also add my thoughts on what makes a
sequence interesting. My goal is to help my readers invent new sequences,
differentiate interesting sequences from boring ones, and better understand
sequences they encounter.


  In this paper we present a novel method to connect data on the visualization
level. In general, visualizations are a dead end, when it comes to reusability.
Yet, users prefer to work with visualizations as evidenced by WYSIWYG editors.
To enable users to work with their data in a way that is intuitive to them, we
have created Vizgr. Vizgr.com offers basic visualization methods, like graphs,
tag clouds, maps and time lines. But unlike normal data visualizations, these
can be re-used, connected to each other and to web sites. We offer a simple
opportunity to combine diverse data structures, such as geo-locations and
networks, with each other by a mouse click. In an evaluation, we found that
over 85 % of the participants were able to use and understand this technology
without any training or explicit instructions.


  We suggest a simple algebraic approach to fix the elements of the $\{ \beta
\}$-expansion for renormalization group invariant quantities, which uses
additional degrees of freedom. The approach is discussed in detail for N$^2$LO
calculations in QCD with the MSSM gluino -- an additional degree of freedom. We
derive the formulae of the $\{ \beta \}$-expansion for the nonsinglet Adler
$D$-function and Bjorken polarized sum rules in the actual N$^3$LO within this
quantum field theory scheme with the MSSM gluino and the scheme with the second
additional degree of freedom. We discuss the properties of the $\{ \beta
\}$-expansion for higher orders considering the N$^4$LO as an example.


  First the fluctuation energy is derived from the adiabatic random
fluctuations due to the second-order perturbation theory, and the evolutionary
relation for it is expressed in the form of rho_f = rho_f (rho), where rho and
rho_f are the densities of ordinary dust and the fluctuation energy,
respectively. The pressureless matter as a constituent of the universe at the
later stage is assumed to consist of ordinary dust and the fluctuation energy.
Next, cosmological models including the fluctuation energy as a kind of dark
matter are derived using the above relation, and it is found that the Hubble
parameter and the other model parameters in the derived models can be
consistent with the recent observational values. Moreover, the perturbations of
rho and rho_f are studied.


  Thin-film lithium niobate (TFLN) based frequency doublers have been widely
recognized as essential components for both classical and quantum optical
communications. Nonetheless, the efficiency of these devices is hindered by
imperfections present in the quasi-phase matching (QPM) spectrum. In this
study, we present a thorough analysis of the spectral imperfections in TFLN
frequency doublers with varying lengths, ranging from 5 mm to 15 mm. Employing
a non-destructive diagnostic method based on scattered light imaging, we
identify the sources and waveguide sections that contribute to the
imperfections in the QPM spectrum. Furthermore, by mapping the TFLN film
thickness across the entire waveguiding regions, we successfully reproduce the
QPM spectra numerically, thus confirming the prominent influence of film
thickness variations on the observed spectral imperfections. This comprehensive
investigation provides valuable insights into the identification and mitigation
of spectral imperfections in TFLN-based frequency doublers, paving the way
toward the realization of nonlinear optical devices with enhanced efficiency
and improved spectral fidelity.


  We study forward scattering of 2D massless Dirac electrons at Fermi energy
{\varepsilon} > 0 in single layer graphene through a 1D rectangular barrier of
height {u_0} in the presence of uniform Rashba spin-orbit coupling (of strength
{\lambda}). The role of the Klein paradox in graphene spintronics is thereby
exposed. It is shown that (1) For {\varepsilon} - 2{\lambda} < {u_0}<
{\varepsilon} + 2{\lambda} there is partial Klein tunneling, wherein the
transmission is bounded by 1 and, quite remarkably, for small {\lambda} >
{\lambda_0} {\approx} 0.1 meV, the transmission nearly vanishes when the
scattering energy equals the barrier height, {\varepsilon}={u_0}. (2) Spin
density and spin-current density are shown to be remarkably different than
these observables predicted in bulk single layer graphene. In particular, they
are sensitive to {\lambda} and {u_0}. (3) Spin current densities are space
dependent, implying the occurrence of non-zero spin torque density. Such a
system may serve as a graphene based spintronic device without the use of an
external magnetic field or magnetic materials.


  In this paper, we consider Kirchhoff-Schrodinger equations with singular
exponential nonlinearities in R^4,using singular Adams inequality and
variational techniques, we get the existence of ground state solutions.
Moreover, we also get the same results without the Ambrosetti-Rabinowitz (AR)
condition.


  The synthesis of heavy, proton rich isotopes in the astrophysical
gamma-process proceeds through photodisintegration reactions. For the improved
understanding of the process, the rates of the involved nuclear reactions must
be known. The reaction 128Ba(g,a)124Xe was found to affect the abundance of the
p nucleus 124Xe. Since the stellar rate for this reaction cannot be determined
by a measurement directly, the aim of the present work was to measure the cross
section of the inverse 124Xe(a,g)128Ba reaction and to compare the results with
statistical model predictions. Of great importance is the fact that data below
the (a,n) threshold was obtained. Studying simultaneously the 124Xe(a,n)127Ba
reaction channel at higher energy allowed to further identify the source of a
discrepancy between data and prediction. The 124Xe + alpha cross sections were
measured with the activation method using a thin window 124Xe gas cell. The
studied energy range was between E = 11 and 15 MeV close above the
astrophysically relevant energy range. The obtained cross sections are compared
with statistical model calculations. The experimental cross sections are
smaller than standard predictions previously used in astrophysical
calculations. As dominating source of the difference, the theoretical alpha
width was identified. The experimental data suggest an alpha width lower by at
least a factor of 0.125 in the astrophysical energy range. An upper limit for
the 128Ba(g,a)124Xe stellar rate was inferred from our measurement. The impact
of this rate was studied in two different models for core-collapse supernova
explosions of 25 solar mass stars. A significant contribution to the 124Xe
abundance via this reaction path would only be possible when the rate was
increased above the previous standard value. Since the experimental data rule
this out, they also demonstrate the closure of this production path.


  We present an elegant derivation of the Doppler factor in the
Lienard-Wiechert potentials of an extended particle, based on a theorem
authored by J. L. Synge and dealing with cross-sections through worldtubes.


  We analyse various properties of stochastic Markov processes with
multiplicative white noise. We take a single-variable problem as a simple
example, and we later extend the analysis to the Landau-Lifshitz-Gilbert
equation for the stochastic dynamics of a magnetic moment. In particular, we
focus on the non-equilibrium transfer of angular momentum to the magnetization
from a spin-polarised current of electrons, a technique which is widely used in
the context of spintronics to manipulate magnetic moments. We unveil two hidden
dynamical symmetries of the generating functionals of these Markovian
multiplicative white-noise processes. One symmetry only holds in equilibrium
and we use it to prove generic relations such as the fluctuation-dissipation
theorems. Out of equilibrium, we take profit of the symmetry-breaking terms to
prove fluctuation theorems. The other symmetry yields strong dynamical
relations between correlation and response functions which can notably simplify
the numerical analysis of these problems. Our construction allows us to clarify
some misconceptions on multiplicative white-noise stochastic processes that can
be found in the literature. In particular, we show that a first-order
differential equation with multiplicative white noise can be transformed into
an additive-noise equation, but that the latter keeps a non-trivial memory of
the discretisation prescription used to define the former.


  In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.


  We consider horofunction compactifications of symmetric spaces with respect
to invariant Finsler metrics. We show that any (generalized) Satake
compactification can be realized as a horofunction compactification with
respect to a polyhedral Finsler metric.


  Recently, Deep Neural Networks (DNNs) have made remarkable progress for text
classification, which, however, still require a large number of labeled data.
To train high-performing models with the minimal annotation cost, active
learning is proposed to select and label the most informative samples, yet it
is still challenging to measure informativeness of samples used in DNNs. In
this paper, inspired by piece-wise linear interpretability of DNNs, we propose
a novel Active Learning with DivErse iNterpretations (ALDEN) approach. With
local interpretations in DNNs, ALDEN identifies linearly separable regions of
samples. Then, it selects samples according to their diversity of local
interpretations and queries their labels. To tackle the text classification
problem, we choose the word with the most diverse interpretations to represent
the whole sentence. Extensive experiments demonstrate that ALDEN consistently
outperforms several state-of-the-art deep active learning methods.


  We study a class of filters -- discrete finite-state transition systems
employed as incremental stream transducers -- that have application to
robotics: e.g., to model combinatorial estimators and also as concise encodings
of feedback plans/policies. The present paper examines their minimization
problem under some new assumptions. Compared to strictly deterministic filters,
allowing nondeterminism supplies opportunities for compression via re-use of
states. But this paper suggests that the classic automata-theoretic concept of
nondeterminism, though it affords said opportunities for reduction in state
complexity, is problematic in many robotics settings. Instead, we argue for a
new constrained type of nondeterminism that preserves input-output behavior for
circumstances when, as for robots, causation forbids 'rewinding' of the world.
We identify problem instances where compression under this constrained form of
nondeterminism results in improvements over all deterministic filters. In this
new setting, we examine computational complexity questions for the problem of
reducing the state complexity of some given input filter. A hardness result for
general deterministic input filters is presented, as well as for checking
specific, narrower requirements, and some special cases. These results show
that this class of nondeterminism gives problems of the same complexity class
as classical nondeterminism, and the narrower questions help give a more
nuanced understanding of the source of this complexity.


  We show that Mellin moments of generalized parton distributions, given as
even polynomials in the skewness parameter, are obtained from the Taylor
expansion of light front wave functions. Furthermore, we derive non-standard
versions of the inverse Radon transform to obtain the double distribution from
the parton number conserved light front wave function overlap. These
transformations are utilized to extend a generalized parton distribution from
the outer region to the central one. We exemplify the formalism for a light
front wave function that arises from an AdS/QCD duality conjecture.


  This paper presents an experimental and numerical investigation of
solid-liquid fluidized beds consisting of bonded spheres in very narrow tubes,
i.e., when the ratio between the tube and grain diameters is small. In narrow
beds, high confinement effects have proved to induce crystallization, jamming
and different patterns, which can be intensified or modified if some grains are
bonded together. In order to investigate that, we produced duos and trios of
bonded aluminum spheres with diameter of 4.8 mm, and formed beds consisting
either of 150-300 duos or 100-200 trios in a 25.4 mm-ID pipe, which were
submitted to water velocities above those necessary for fluidization. For the
experiments, we filmed the bed with high-speed and conventional cameras and
processed the images, obtaining measurements at both the bed and grain scales.
For the numerical part, we computed the bed evolution for the same conditions
with a CFD-DEM (computational fluid dynamics - discrete element method) code.
Our results show distinct motions for individual duos and trios, and different
structures within the bed. We also found that jamming may occur suddenly for
trios, where even the microscopic motion (fluctuation at the grain scale)
stops, calling into question the fluidization conditions for those cases.


  Fitch graphs $G=(X,E)$ are digraphs that are explained by $\{\emptyset,
1\}$-edge-labeled rooted trees $T$ with leaf set $X$: there is an arc $(x,y)
\in E$ if and only if the unique path in $T$ that connects the last common
ancestor $\mathrm{lca}(x,y)$ of $x$ and $y$ with $y$ contains at least one edge
with label "1". In practice, Fitch graphs represent xenology relations, i.e.,
pairs of genes $x$ and $y$ for which a horizontal gene transfer happened along
the path from $\mathrm{lca}(x,y)$ to $y$.
  In this contribution, we generalize the concept of Fitch graphs and consider
trees $T$ that are equipped with edge-labeling $\lambda: E\to \mathcal{P}(M)$
that assigns to each edge a subset $M'\subseteq M$ of colors. Given such a
tree, we can derive a map $\varepsilon_{(T,\lambda)}$ (or equivalently a set of
not necessarily disjoint binary relations), such that $i\in
\varepsilon_{(T,\lambda)}(x,y)$ (or equivalently $(x,y)\in R_i$) with $x,y\in
X$, if and only if there is at least one edge with color $i$ from
$\mathrm{lca}(x,y)$ to $y$.
  The central question considered here: Is a given map $\varepsilon$ a Fitch
map, i.e., is there there an edge-labeled tree $(T,\lambda)$ with
$\varepsilon_{(T,\lambda)} = \varepsilon$, and thus explains $\varepsilon$?
Here, we provide a characterization of Fitch maps in terms of certain
neighborhoods and forbidden submaps. Further restrictions of Fitch maps are
considered. Moreover, we show that the least-resolved tree explaining a Fitch
map is unique (up to isomorphism). In addition, we provide a polynomial-time
algorithm to decide whether $\varepsilon$ is a Fitch map and, in the
affirmative case, to construct the (up to isomorphism) unique least-resolved
tree $(T^*,\lambda^*)$ that explains $\varepsilon$.


  We have obtained intermediate resolution optical spectra of the black-hole
candidate Nova Sco 1994 in June 1996, when the source was in an X-ray/optical
active state (R~15.05). We measure the radial velocity curve of the secondary
star and obtain a semi-amplitude of 279+/-10 km/s; a value which is 30 per cent
larger than the value obtained when the source is in quiescence. Our large
value for K_2 is consistent with 60 +9,-7 per cent of the secondary star's
surface being heated; compared to 35 per cent, which is what one would expect
if only the inner face of the secondary star were irradiated. Effects such as
irradiation-induced flows on the secondary star may be important in explaining
the observed large value for K_2.


  We report conductance measurements on multiwall carbon nanotubes in a
perpendicular magnetic field. A gate electrode with large capacitance is used
to considerably vary the nanotube Fermi level. This enables us to search for
signatures of the unique electronic band structure of the nanotubes in the
regime of diffusive quantum transport. We find an unusual quenching of the
magnetoconductance and the zero bias anomaly in the differential conductance at
certain gate voltages, which can be linked to the onset of
quasi-one-dimensional subbands.


  We investigate the effect of helium on hydrogen reionisation using a
hydrodynamical simulation combined with the cosmological radiative transfer
code CRASH. The simulations are run in a 35.12/h comoving Mpc box using a
variety of assumptions for the amplitude and power-law extreme-UV (EUV)
spectral index, alpha, of the ionising emissivity. We use an empirically
motivated prescription for ionising sources which ensures all of the models are
consistent with constraints on the Thomson scattering optical depth and the
hydrogen photo-ionisation rate at z=6. The inclusion of helium slightly delays
reionisation due to the small number of ionising photons which reionise neutral
helium instead of hydrogen. However, helium has a significant impact on the
thermal state of the IGM. Models with alpha=3 produce IGM temperatures at the
mean density at z=6 which are about 20 % higher compared to models without
helium photo-heating. Harder EUV indices produce even larger IGM temperature
boosts. A comparison to recent observational estimates of the IGM temperature
at z=5 - 6 suggests that hydrogen reionisation was primarily driven by pop-II
stellar sources with a soft EUV index, alpha<3. We also find that faint, as yet
undetected galaxies, characterised by a luminosity function with a steepening
faint-end slope and an increasing Lyman continuum escape fraction (fesc=0.5),
are required to reproduce the ionising emissivity used in our simulations at
z>6. Finally, we note there is some tension between recent observational
constraints which indicate the IGM is > 10% neutral by volume z=7, and
estimates of the ionising emissivity at z=6 which indicate only between 1 and 3
ionising photons are emitted per hydrogen atom over a Hubble time. This tension
may be alleviated by either a lower neutral fraction at z=7 or an IGM which
still remains a few % neutral by volume at z=6.


  We study perturbation of holographic dark energy and find it be stable. We
study the fate of the universe when interacting holographic dark energy is
present, and discuss a simple phenomenological classification of the
interacting holographic dark energy models. We also discuss the cosmic
coincidence problem in the context of holographic dark energy. We find that the
coincidence problem can not be completely solved by adding an interacting term.
Inflation may provide a better solution of the coincidence problem.


  In this paper we prove the Pohozaev identity for the weighted anisotropic
$p$-Laplace operator. As an application of our identity, we deduce the
nonexistence of nontrivial solutions of the Dirichlet problem for the weighted
anisotropic $p$-Laplacian in star-shaped domains of $\mathbb{R}^n$. We also
provide an upper bound estimate for the first Dirichet eigenvalue of the
anisotropic $p$-Laplacian on bounded domains of $\mathbb{R}^n$, some sharp
estimates for the torsion function of compact manifolds with boundary and a
nonexistence result for the solutions of the Laplace equation on closed
Riemannian manifolds.


  This work examines the economic benefits of learning a new skill from a
different domain: cross-skilling. To assess this, a network of skills from the
job profiles of 14,790 online freelancers is constructed. Based on this skill
network, relationships between 3,480 different skills are revealed and marginal
effects of learning a new skill can be calculated via workers' wages. The
results indicate that learning in-demand skills, such as popular programming
languages, is beneficial in general, and that diverse skill sets tend to be
profitable, too. However, the economic benefit of a new skill is individual, as
it complements the existing skill bundle of each worker. As technological and
social transformation is reshuffling jobs' task profiles at a fast pace, the
findings of this study help to clarify skill sets required for designing
individual re-skilling pathways. This can help to increase employability and
reduce labour market shortages.


  We develop and apply methods to extract planet masses and eccentricities from
observed transit time variations (TTVs). First, we derive simple analytic
expressions for the TTV that include the effects of both first- and
second-order resonances. Second, we use N-body Markov chain Monte Carlo (MCMC)
simulations, as well as the analytic formulae, to measure the masses and
eccentricities of ten planets discovered by Kepler that have not previously
been analyzed. Most of the ten planets have low densities. Using the analytic
expressions to partially circumvent degeneracies, we measure small
eccentricities of a few percent or less.


  The exponential increase in the use of the Internet and social media over the
last two decades has changed human interaction. This has led to many positive
outcomes, but at the same time it has brought risks and harms. While the volume
of harmful content online, such as hate speech, is not manageable by humans,
interest in the academic community to investigate automated means for hate
speech detection has increased. In this study, we analyse six publicly
available datasets by combining them into a single homogeneous dataset and
classify them into three classes, abusive, hateful or neither. We create a
baseline model and we improve model performance scores using various
optimisation techniques. After attaining a competitive performance score, we
create a tool which identifies and scores a page with effective metric in
near-real time and uses the same as feedback to re-train our model. We prove
the competitive performance of our multilingual model on two langauges, English
and Hindi, leading to comparable or superior performance to most monolingual
models.


  In this paper, we introduce a new framework for robust multiple signal
classification (MUSIC). The proposed framework, called robust
measure-transformed (MT) MUSIC, is based on applying a transform to the
probability distribution of the received signals, i.e., transformation of the
probability measure defined on the observation space. In robust MT-MUSIC, the
sample covariance is replaced by the empirical MT-covariance. By judicious
choice of the transform we show that: 1) the resulting empirical MT-covariance
is B-robust, with bounded influence function that takes negligible values for
large norm outliers, and 2) under the assumption of spherically contoured noise
distribution, the noise subspace can be determined from the eigendecomposition
of the MT-covariance. Furthermore, we derive a new robust measure-transformed
minimum description length (MDL) criterion for estimating the number of
signals, and extend the MT-MUSIC framework to the case of coherent signals. The
proposed approach is illustrated in simulation examples that show its
advantages as compared to other robust MUSIC and MDL generalizations.


  Most time-series models assume that the data come from observations that are
equally spaced in time. However, this assumption does not hold in many diverse
scientific fields, such as astronomy, finance, and climatology, among others.
There are some techniques that fit unequally spaced time series, such as the
continuous-time autoregressive moving average (CARMA) processes. These models
are defined as the solution of a stochastic differential equation. It is not
uncommon in astronomical time series, that the time gaps between observations
are large. Therefore, an alternative suitable approach to modeling astronomical
time series with large gaps between observations should be based on the
solution of a difference equation of a discrete process. In this work we
propose a novel model to fit irregular time series called the complex irregular
autoregressive (CIAR) model that is represented directly as a discrete-time
process. We show that the model is weakly stationary and that it can be
represented as a state-space system, allowing efficient maximum likelihood
estimation based on the Kalman recursions. Furthermore, we show via Monte Carlo
simulations that the finite sample performance of the parameter estimation is
accurate. The proposed methodology is applied to light curves from periodic
variable stars, illustrating how the model can be implemented to detect poor
adjustment of the harmonic model. This can occur when the period has not been
accurately estimated or when the variable stars are multiperiodic. Last, we
show how the CIAR model, through its state space representation, allows
unobserved measurements to be forecast.


  We propose an exactly solvable lattice Hamiltonian model of topological
phases in $3+1$ dimensions, based on a generic finite group $G$ and a
$4$-cocycle $\omega$ over $G$. We show that our model has topologically
protected degenerate ground states and obtain the formula of its ground state
degeneracy on the $3$-torus. In particular, the ground state spectrum implies
the existence of purely three-dimensional looplike quasi-excitations specified
by two nontrivial flux indices and one charge index. We also construct other
nontrivial topological observables of the model, namely the $SL(3,\mathbb{Z})$
generators as the modular $S$ and $T$ matrices of the ground states, which
yield a set of topological quantum numbers classified by $\omega$ and
quantities derived from $\omega$. Our model fulfills a Hamiltonian extension of
the $3+1$-dimensional Dijkgraaf-Witten topological gauge theory with a gauge
group $G$. This work is presented to be accessible for a wide range of
physicists and mathematicians.


  It is shown that the nonperturbative effects due to hadronization play a
crucial role in low-energy strong interaction processes. Specifically, such
effects impose a stringent constraint on the infrared behavior of the Adler
function and play an essential role in the theoretical analysis of inclusive
tau lepton decay.


  The CIII] and CIV rest-frame UV emission lines are powerful probes of the
ionizations states of galaxies. They have furthermore been suggested as
alternatives for spectroscopic redshift confirmation of objects at the epoch of
reionization ($z>6$), where the most frequently used redshift indicator,
Ly$\alpha$, is attenuated by the high fraction of neutral hydrogen in the
inter-galactic medium. However, currently only very few confirmations of carbon
UV lines at these high redshifts exist, making it challenging to quantify these
claims. Here, we present the detection of CIV$\lambda\lambda$1548,1551\AA\ in
\HST\ slitless grism spectroscopy obtained by GLASS of a Ly$\alpha$ emitter at
$z=6.11$ multiply imaged by the massive foreground galaxy cluster RXJ2248. The
CIV emission is detected at the 3--5$\sigma$ level in two images of the source,
with marginal detection in two other images. We do not detect significant
CIII]$\lambda\lambda$1907,1909\AA\ emission implying an equivalent width
EW$_\textrm{CIII]}<20$\AA\ (1$\sigma$) and $\textrm{CIV/CIII}>0.7$ (2$\sigma$).
Combined with limits on the rest-frame UV flux from the HeII$\lambda$1640\AA\
emission line and the OIII]$\lambda\lambda$1661,1666\AA\ doublet, we put
constraints on the metallicity and the ionization state of the galaxy. The
estimated line ratios and equivalent widths do not support a scenario where an
AGN is responsible for ionizing the carbon atoms. SED fits including nebular
emission lines imply a source with a mass of log(M/M$_\odot)\sim9$, SFR of
around 10M$_\odot$/yr, and a young stellar population $<50$Myr old. The source
shows a stronger ionizing radiation field than objects with detected CIV
emission at $z<2$ and adds to the growing sample of low-mass
(log(M/M$_\odot)\lesssim9$) galaxies at the epoch of reionization with strong
radiation fields from star formation.


  An Engel manifold is a 4-manifold with a completely non-integrable
2-distribution called Engel structure. I research the functorial relation
between Engel manifolds and Contact 3-orbifolds. And I construct an Engel
manifold that the automorphism group is trivial.


  In a covariant quark-diquark model, we investigate the rare decay of
$\Lambda_b \rightarrow n l^+ l^-$ and $\Lambda_b \rightarrow n \gamma$ in the
Bethe-Salpeter equation approach. In this model the baryons are treated as
bound states of a constituent quark and a diquark interacting via a gluon
exchange and the linear confinement. We find that the ratio of form factors $R$
is varies from $-0.90$ to $-0.25$ and the branching ratios $Br(\Lambda_b
\rightarrow n l^+ l^-)\times 10^{8}$ are $6.79(l=e),~4.08 ~ (l=\mu),~2.9
~(l=\tau) $ and the branching ratio $Br(\Lambda_b \rightarrow \gamma)\times
10^{7} )=3.69$ in central values of parameters.


  This paper presents an improved system based on our prior work, designed to
create explanations for autonomous robot actions during Human-Robot Interaction
(HRI). Previously, we developed a system that used Large Language Models (LLMs)
to interpret logs and produce natural language explanations. In this study, we
expand our approach by incorporating Vision-Language Models (VLMs), enabling
the system to analyze textual logs with the added context of visual input. This
method allows for generating explanations that combine data from the robot's
logs and the images it captures. We tested this enhanced system on a basic
navigation task where the robot needs to avoid a human obstacle. The findings
from this preliminary study indicate that adding visual interpretation improves
our system's explanations by precisely identifying obstacles and increasing the
accuracy of the explanations provided.


  In this paper we present a lower bound for the domination number of the
Cartesian product of a path and a cycle, that is tight if the length of the
cycle is a multiple of five. This bound improves the natural lower bound
obtained by using the domination number of the Cartesian product of two paths,
that is the best one known so far.


  In comparing geodesics induced by different metrics, Audenaert formulated the
following determinantal inequality
  $$\det(A^2+|BA|)\le \det(A^2+AB),$$ where $A, B$ are $n\times n$ positive
semidefinite matrices. We complement his result by proving
  $$\det(A^2+|AB|)\ge \det(A^2+AB).$$ Our proofs feature the fruitful interplay
between determinantal inequalities and majorization relations. Some related
questions are mentioned.


  We study generalized variants of the Burgers equation and the KdV equation on
the circle. The main goal of the paper is to show that both extensions can be
recast as geodesic equations on a suitable diffeomorphism group of the circle
and the corresponding Bott-Virasoro group respectively. As a consequence we
obtain that the initial value problem for the Burgers equation with an
additional quadratic term is well-posed on a scale of Sobolev spaces on the
circle.


  Map-based methods for autonomous racing estimate the vehicle's location,
which is used to follow a high-level plan. While map-based optimisation methods
demonstrate high-performance results, they are limited by requiring a map of
the environment. In contrast, mapless methods can operate in unmapped contexts
since they directly process raw sensor data (often LiDAR) to calculate
commands. However, a major limitation in mapless methods is poor performance
due to a lack of optimisation. In response, we propose the local map framework
that uses easily extractable, low-level features to build local maps of the
visible region that form the input to optimisation-based controllers. Our local
map generation extracts the visible racetrack boundaries and calculates a
centreline and track widths used for planning. We evaluate our method for
simulated F1Tenth autonomous racing using a two-stage trajectory optimisation
and tracking strategy and a model predictive controller. Our method achieves
lap times that are 8.8% faster than the Follow-The-Gap method and 3.22% faster
than end-to-end neural networks due to the optimisation resulting in a faster
speed profile. The local map planner is 3.28% slower than global methods that
have access to an entire map of the track that can be used for planning.
Critically, our approach enables high-speed autonomous racing on unmapped
tracks, achieving performance similar to global methods without requiring a
track map.


  We find the general conditions for viable cosmological solution at the
background level in bigravity models. Furthermore, we constrain the parameters
by comparing to the Union 2.1 supernovae catalog and identify, in some cases
analytically, the best fit parameter or the degeneracy curve among pairs of
parameters. We point out that a bimetric model with a single free parameter
predicts a simple relation between the equation of state and the density
parameter, fits well the supernovae data and is a valid and testable
alternative to $\Lambda$CDM. Additionally, we identify the conditions for a
phantom behavior and show that viable bimetric cosmologies cannot cross the
phantom divide.


  The goal of this project is to create an inexpensive, lightweight, wearable
assistive device that can measure hand or finger movements accurately enough to
identify a range of hand gestures. One eventual application is to provide
assistive technology and sign language detection for the hearing impaired. My
system, called LiTe (Light-based Technology), uses optical fibers embedded into
a wristband. The wrist is an optimal place for the band since the light
propagation in the optical fibers is impacted even by the slight movements of
the tendons in the wrist when gestures are performed. The prototype
incorporates light dependent resistors to measure these light propagation
changes. When creating LiTe, I considered a variety of fiber materials, light
frequencies, and physical shapes to optimize the tendon movement detection so
that it can be accurately correlated with different gestures. I implemented and
evaluated two approaches for gesture recognition. The first uses an algorithm
that combines moving averages of sensor readings with gesture sensor reading
signatures to determine the current gesture. The second uses a neural network
trained on a labelled set of gesture readings to recognize gestures. Using the
signature-based approach, I was able to achieve a 99.8% accuracy at recognizing
distinct gestures. Using the neural network the recognition accuracy was 98.8%.
This shows that high accuracy is feasible using both approaches. The results
indicate that this novel method of using fiber optics-based sensors is a
promising first step to creating a gesture recognition system.


  We consider the problem of finding a desired item out of $N$ items arranged
on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$.
The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to
solve this problem, and it is an open question whether the performance can be
improved. We present a new algorithm which solves the problem in $O(\sqrt{N\log
N})$ steps, thus giving an $O(\sqrt{\log N})$ improvement over the known
algorithms. The improvement is achieved by controlling the quantum walk on the
lattice using an ancilla qubit.


  This article focuses on the connection between the possibility of quantum
computers, the predictability of complex quantum systems in nature, and the
issue of free will.


  We use near-infrared observations obtained as part of the {\sl Visible and
Infrared Survey Telescope for Astronomy} (VISTA) Survey of the Magellanic
Clouds (VMC), as well as two complementary {\sl Hubble Space Telescope} ({\sl
HST}) data sets, to study the luminosity and mass functions as a function of
clustercentric radius of the main-sequence stars in the Galactic globular
cluster 47 Tucanae. The {\sl HST} observations indicate a relative deficit in
the numbers of faint stars in the central region of the cluster compared with
its periphery, for $18.75\leq m_{\rm F606W}\leq 20.9$ mag (corresponding to a
stellar mass range of $0.55<m_\ast/{M_\odot}<0.73$). The stellar number counts
at $6.7'$ from the cluster core show a deficit for $17.62\leq m_{\rm F606W}\leq
19.7$ mag (i.e., $0.65<m_\ast/{M_\odot}<0.82$), which is consistent with
expectations from mass segregation. The VMC-based stellar mass functions
exhibit power-law shapes for masses in the range $0.55<m_\ast/{M_\odot}< 0.82$.
These power laws are characterized by an almost constant slope, $\alpha$. The
radial distribution of the power-law slopes $\alpha$ thus shows evidence of the
importance of both mass segregation and tidal stripping, for both the first-
and second-generation stars in 47 Tuc.


  We obtain constraints on first- and second-generation scalar leptoquarks
using the available data on dilepton (Drell-Yan) and monojet searches at the
CERN Large Hadron Collider. Assuming that the leptoquark interactions respect
the Standard Model gauge symmetries as well as lepton and baryon numbers, we
show that the study of dilepton production enlarges the exclusion region on the
mass and coupling plane with respect to the pair production searches for
first-generation leptoquarks. Moreover, the monojet channel leads to a larger
excluded parameter region for moderate to large values of the leptoquark Yukawa
coupling than the presently available experimental results.


  We study dynamical error suppression from the perspective of reducing
sequencing complexity, in order to facilitate efficient semi-autonomous
quantum-coherent systems. With this aim, we focus on digital sequences where
all interpulse time periods are integer multiples of a minimum clock period and
compatibility with simple digital classical control circuitry is intrinsic,
using so-called em Walsh functions as a general mathematical framework. The
Walsh functions are an orthonormal set of basis functions which may be
associated directly with the control propagator for a digital modulation
scheme, and dynamical decoupling (DD) sequences can be derived from the
locations of digital transitions therein. We characterize the suite of the
resulting Walsh dynamical decoupling (WDD) sequences, and identify the number
of periodic square-wave (Rademacher) functions required to generate a Walsh
function as the key determinant of the error-suppressing features of the
relevant WDD sequence. WDD forms a unifying theoretical framework as it
includes a large variety of well-known and novel DD sequences, providing
significant flexibility and performance benefits relative to basic
quasi-periodic design. We also show how Walsh modulation may be employed for
the protection of certain nontrivial logic gates, providing an implementation
of a dynamically corrected gate. Based on these insights we identify Walsh
modulation as a digital-efficient approach for physical-layer error
suppression.


  We study the behavior of zeros and mass of holomorphic Hecke cusp forms on
$SL_2(\mathbb Z) \backslash \mathbb H$ at small scales. In particular, we
examine the distribution of the zeros within hyperbolic balls whose radii
shrink sufficiently slowly as $k \rightarrow \infty$. We show that the zeros
equidistribute within such balls as $k \rightarrow \infty$ as long as the radii
shrink at a rate at most a small power of $1/\log k$. This relies on a new,
effective, proof of Rudnick's theorem on equidistribution of the zeros and on
an effective version of Quantum Unique Ergodicity for holomorphic forms, which
we obtain in this paper.
  We also examine the distribution of the zeros near the cusp of $SL_2(\mathbb
Z) \backslash \mathbb H$. Ghosh and Sarnak conjectured that almost all the
zeros here lie on two vertical geodesics. We show that for almost all forms a
positive proportion of zeros high in the cusp do lie on these geodesics. For
all forms, we assume the Generalized Lindel\"of Hypothesis and establish a
lower bound on the number of zeros that lie on these geodesics, which is
significantly stronger than the previous unconditional results.


  Highly degenerate chaotic radiation has a Gaussian density matrix and a large
occupation number of modes $f $. If it is passed through a weakly transmitting
barrier, its counting statistics is close to Poissonian. We show that a second
identical barrier, in series with the first, drastically modifies the
statistics. The variance of the photocount is increased above the mean by a
factor $f$ times a numerical coefficient. The photocount distribution reaches a
limiting form with a Gaussian body and highly asymmetric tails. These are
general consequences of the combination of weak transmission and multiple
scattering.


  We investigate the possible production of a MeV-scale sterile fermion through
the up-scattering of neutrinos on nuclei and atomic electrons at different
facilities. We consider a phenomenological model that adds a new fermion to the
particle content of the Standard Model and we allow for all possible
Lorentz-invariant non-derivative interactions (scalar, pseudoscalar, vector,
axial-vector and tensor) of neutrinos with electrons and first-generation
quarks. We first explore the sensitivity of the DUNE experiment to this
scenario, by simulating elastic neutrino-electron scattering events in the near
detector. We consider both options of a standard and a tau-optimized neutrino
beams, and investigate the impact of a mobile detector that can be moved
off-axis with respect to the beam. Next, we infer constraints on the typical
coupling, new fermion and mediator masses from elastic neutrino-electron
scattering events induced by solar neutrinos in two current dark matter direct
detection experiments, XENONnT and LZ. Under the assumption that the new
mediators couple also to first-generation quarks, we further set constraints on
the up-scattering production of the sterile fermion using coherent elastic
neutrino-nucleus scattering data from the COHERENT experiment. Moreover, we set
additional constraints assuming that the sterile fermion may decay within the
detector. We finally compare our results and discuss how these facilities are
sensitive to different regions of the relevant parameter space due to
kinematics arguments and can hence provide complementary information on the
up-scattering production of a sterile fermion.


  Let $p$ be an odd prime. For a number field $K$, we let $K_\infty$ be the
maximal unramified pro-$p$ extension of $K$; we call the group
$\mathrm{Gal}(K_\infty/K)$ the $p$-class tower group of $K$. In a previous
work, as a non-abelian generalization of the work of Cohen and Lenstra on ideal
class groups, we studied how likely it is that a given finite $p$-group occurs
as the $p$-class tower group of an imaginary quadratic field. Here we do the
same for an arbitrary real quadratic field $K$ as base. As before, the action
of $\mathrm{Gal}(K/\mathbb{Q})$ on the $p$-class tower group of $K$ plays a
crucial role; however, the presence of units of infinite order in the ground
field significantly complicates the possibilities for groups that can occur. We
also sharpen our results in the imaginary quadratic field case by removing a
certain hypothesis, using ideas of Boston and Wood. In an appendix, we show how
the probabilities introduced for finite $p$-groups can be extended in a
consistent way to the infinite pro-$p$ groups which can arise in both the real
and imaginary quadratic settings.}


  We study spin-1 bosons in an optical lattice under a magnetic field by the
Gutzwiller approximation. Our results thus obtained join the discontinuous
phase boundary curves obtained by perturbative studies through a first-order
transition. On the phase boundary curve, we also find a peculiar cusp structure
originating from the degeneracy between different spin Mott states under a
magnetic field. The magnetic field dependence of both fluctuation in the total
number of bosons and the spin magnetization clarifies that the superfluid phase
is divided into two regions reflecting the coexisting first- and second-order
superfluid transitions.


  New spectral line polarisation observations of 7 bright Ap stars have been
obtained with the ESPaDOnS and Narval high resolution spectropolarimeters
(Silvester et al. 2012). The aim of this data set is produce a series of
surface magnetic field and surface chemistry maps for these Ap stars. We
present new magnetic maps for the Ap star $\alpha^2$ CVn using these new data
and the MDI inversion code INVERS10. $\alpha^2$ CVn is the first Ap star to be
observed during two separate epochs using high resolution phase resolved
spectropolarimetric $IQUV$ observations and as such allows us an insight into
how stable the surface magnetic structure is over a decade timescale. We show
that the new maps give a magnetic field structure consistent with the previous
maps obtained by Kochukhov and Wade (2010) from lower quality MuSiCoS spectra
taken a decade ago and that the field topology cannot be described by a dipolar
or quadrupolar field.


  We present the first 2+1 flavour lattice QCD calculations of pseudoscalar
flavour-singlet propagators using improved staggered fermions. We explore the
relevant techniques and discuss prospects for the larger scale studies now in
progress. The disconnected correlator is shown to have a highly non-Gaussian
distribution and reliable estimates of the errors require care.


  We report on one of the brightest flux levels of the Seyfert 2 galaxy NGC
2992 ever observed in X-rays, on May 2019. The source has been monitored every
few days from March 26, 2019 to December 14, 2019 by Swift-XRT, and
simultaneous XMM-Newton (250 ks) and NuSTAR (120 ks) observations were
triggered on May 6, 2019. The high count rate of the source (its 2-10 keV flux
ranged between 0.7 and $1.0\times10^{-10}$ erg cm$^{-2}$ s$^{-1}$) allows us to
perform a time-resolved spectroscopy, probing spatial scales of tens of
gravitational radii from the central black hole. By constructing a map of the
excess emission over the primary continuum, we find several emission structures
in the 5.0-7.2 keV energy band. From fitting the 50 EPIC pn spectral slices of
$\sim$5 ks duration, we interpret them as a constant narrow iron K$\alpha$ line
and three variable components in the iron K complex. When a self-consistent
model accounting for the accretion disk emission is considered (KYNrline), two
of these features (in the 5.0-5.8 keV and 6.8-7.2 keV bands) can be ascribed to
a flaring region of the accretion disk located at ${r_{in}}\simeq15$-40
r$_{g\rm }$ from the black hole. The third one (6.5-6.8 keV) is likely produced
at much larger radii ($r_{in}>50$ r$_{g\rm }$). The inner radius and the
azimuthal extension retrieved from the coadded spectra of the flaring states
are ${ r_{in}}=15\pm3$ r$_{g\rm }$ and $\phi=165^{\circ}-330^{\circ}$,
suggesting that the emitting region responsible for the broad iron K component
is a relatively compact annular sector within the disk. Our findings support a
physical scenario in which the accretion disk in NGC 2992 becomes more active
at high accretion rates ($L_{\rm bol}/L_{\rm Edd}\geq4\%$).


  In this paper we propose a primal-dual proximal extragradient algorithm to
solve the generalized Dantzig selector (GDS) estimation problem, based on a new
convex-concave saddle-point (SP) reformulation. Our new formulation makes it
possible to adopt recent developments in saddle-point optimization, to achieve
the optimal $O(1/k)$ rate of convergence. Compared to the optimal non-SP
algorithms, ours do not require specification of sensitive parameters that
affect algorithm performance or solution quality. We also provide a new
analysis showing a possibility of local acceleration to achieve the rate of
$O(1/k^2)$ in special cases even without strong convexity or strong smoothness.
As an application, we propose a GDS equipped with the ordered $\ell_1$-norm,
showing its false discovery rate control properties in variable selection.
Algorithm performance is compared between ours and other alternatives,
including the linearized ADMM, Nesterov's smoothing, Nemirovski's mirror-prox,
and the accelerated hybrid proximal extragradient techniques.


  We measure the coherent nonlinear response of excitons in a single-layer of
molybdenum disulphide embedded in hexagonal boron nitride, forming a
$h$-BN/MoS$_2$/$h$-BN heterostructure. Using four-wave mixing microscopy and
imaging, we correlate the exciton homogeneous and inhomogeneous broadenings. We
find that the exciton dynamics is governed by microscopic disorder on top of
the ideal crystal properties. Analyzing the exciton ultra-fast density dynamics
using amplitude and phase of the response, we investigate the relaxation
pathways of the resonantly driven exciton population. The surface protection
via encapsulation provides stable monolayer samples with low disorder, avoiding
surface contaminations and the resulting exciton broadening and modifications
of the dynamics. We identify areas localized to a few microns where the optical
response is totally dominated by homogeneous broadening. Across the sample of
tens of micrometers, weak inhomogeneous broadening and strain effects are
observed, attributed to the remaining interaction with the $h$-BN and
imperfections in the encapsulation process.


  Normal ideals on regular uncountable cardinals are familiar objects. We
investigate ideals that are pleasant--while a normal ideal is closed under
arbitrary diagonal unions, a pleasant ideal is closed only under diagonal
unions indexed by sets that are elements of the ideal. We show any selective
ideal extending the nonstationary ideal must be normal.


  The character of star formation is intimately related to the supersonic
magnetohydrodynamic (MHD) turbulent dynamics of the molecular clouds in which
stars form. A significant amount of the turbulent energy dissipates in low
velocity shocks. Fast and slow MHD shocks differ in how they compress and heat
the molecular gas, and so their radiative signatures reveal distinct physical
conditions.
  We use a two-fluid model to compare one-dimensional fast and slow MHD shocks
propagating at low speeds (a few km/s). Fast shocks are magnetically driven,
forcing ion species to stream through the neutral gas ahead of the shock front.
This magnetic precursor heats the gas sufficiently to create a large, warm
transition zone where all the fluid variables smoothly change in the shock
front. In contrast, slow shocks are driven by gas pressure, and neutral species
collide with ion species in a thin hot slab that closely resembles an ordinary
gas dynamic shock.
  We consider shocks at velocities $v_s = 2$-$4$ km/s and preshock Hydrogen
nuclei densities $n_\mathrm{H} = 10^2$-$10^4$ cm$^{-3}$. We include a simple
oxygen chemistry and cooling by CO, H$_2$ and H$_2$O. CO rotational lines above
$J = 6\to 5$ are more strongly excited in slow shocks. These slow shock
signatures may have already been observed in infrared dark clouds in the Milky
Way.


  Modern application domains such as Composite Event Recognition (CER) and
real-time Analytics require the ability to dynamically refresh query results
under high update rates. Traditional approaches to this problem are based
either on the materialization of subresults (to avoid their recomputation) or
on the recomputation of subresults (to avoid the space overhead of
materialization). Both techniques have recently been shown suboptimal: instead
of materializing results and subresults, one can maintain a data structure that
supports efficient maintenance under updates and can quickly enumerate the full
query output, as well as the changes produced under single updates.
Unfortunately, these data structures have been developed only for
aggregate-join queries composed of equi-joins, limiting their applicability in
domains such as CER where temporal joins are commonplace. In this paper, we
present a new approach for dynamically evaluating queries with multi-way
theta-joins under updates that is effective in avoiding both materialization
and recomputation of results, while supporting a wide range of applications. To
do this we generalize Dynamic Yannakakis, an algorithm for dynamically
processing acyclic equi-join queries. In tandem, and of independent interest,
we generalize the notions of acyclicity and free-connexity to arbitrary
theta-joins and show how to compute corresponding join trees. We instantiate
our framework to the case where theta-joins are only composed of equalities and
inequalities and experimentally compare our algorithm to state of the art CER
systems as well as incremental view maintenance engines. Our approach performs
consistently better than the competitor systems with up to two orders of
magnitude improvements in both time and memory consumption.


  The multihadron production in nucleus-nucleus collisions and its
interrelation with that in (anti)proton-proton interactions are studied by
exploring the charged particle mean multiplicity collision-energy and
centrality dependencies in the measurements to date. The study is performed in
the framework of the recently proposed effective-energy approach which, under
the proper scaling of the collision energy, combines the constituent quark
picture with Landau relativistic hydrodynamics counting for the
centrality-defined effective energy of participants and relating different
types of collisions. Within this approach, the multiplicity energy dependence
and the pseudorapidity spectra from the most central nuclear collisions are
well reproduced. The study of the multiplicity centrality dependence reveals a
new scaling between the measured pseudorapidity spectra and the calculations.
By means of this scaling, called the energy balanced limiting fragmentation
scaling, one reproduces the pseudorapidity spectra for all centralities. The
scaling elucidates some differences in the multiplicity and midrapidity density
centrality dependence obtained at RHIC and LHC. These findings reveal an
inherent similarity in the multiplicity energy dependence from the most central
collisions and centrality data. A new regime in heavy-ion collisions to occur
at about a TeV energy is indicated, similar to that observed in the earlier
studies of the midrapidity densities. Predictions are made for the mean
multiplicities to be measured in proton-proton and heavy-ion collisions at the
LHC.


  We study a warped extra-dimension scenario where the Standard Model fields
lie in the bulk, with the addition of a fourth family of fermions. We
concentrate on the flavor structure of the Higgs couplings with fermions in the
flavor anarchy ansatz. Even without a fourth family, these couplings will be
generically misaligned with respect to the SM fermion mass matrices. The
presence of the fourth family typically enhances the misalignment effects and
we show that one should expect them to be highly non-symmetrical in the
${(34)}$ inter-generational mixing. The radiative corrections from the new
fermions and their flavor violating couplings to the Higgs affect negligibly
known experimental precision measurements such as the oblique parameters and
$Z\to b {\bar b}$ or $Z \to \mu^+ \mu^-$. On the other hand, $\Delta F=1,2$
processes, mediated by tree-level Higgs exchange, as well as radiative
corrections to $b \to s \gamma$ and $\mu \to e\gamma$ put some generic pressure
on the allowed size of the flavor violating couplings. But more importantly,
these couplings will alter the Higgs decay patterns as well as those of the new
fermions, and produce very interesting new signals associated to Higgs
phenomenology in high energy colliders. These might become very important
indirect signals for these type of models as they would be present even when
the KK mass scale is high and no heavy KK particle is discovered.


  This paper concerns the problem of matrix completion, which is to estimate a
matrix from observations in a small subset of indices. We propose a calibrated
spectrum elastic net method with a sum of the nuclear and Frobenius penalties
and develop an iterative algorithm to solve the convex minimization problem.
The iterative algorithm alternates between imputing the missing entries in the
incomplete matrix by the current guess and estimating the matrix by a scaled
soft-thresholding singular value decomposition of the imputed matrix until the
resulting matrix converges. A calibration step follows to correct the bias
caused by the Frobenius penalty. Under proper coherence conditions and for
suitable penalties levels, we prove that the proposed estimator achieves an
error bound of nearly optimal order and in proportion to the noise level. This
provides a unified analysis of the noisy and noiseless matrix completion
problems. Simulation results are presented to compare our proposal with
previous ones.


  Medical images are often used to detect and characterize pathology and
disease; however, automatically identifying and segmenting pathology in medical
images is challenging because the appearance of pathology across diseases
varies widely. To address this challenge, we propose a Bayesian deep learning
method that learns to translate healthy computed tomography images to magnetic
resonance images and simultaneously calculates voxel-wise uncertainty. Since
high uncertainty occurs in pathological regions of the image, this uncertainty
can be used for unsupervised anomaly segmentation. We show encouraging
experimental results on an unsupervised anomaly segmentation task by combining
two types of uncertainty into a novel quantity we call scibilic uncertainty.


  It is shown that the Confluent Heun Equation (CHEq) reduces for certain
conditions of the parameters to a particular class of Quasi-Exactly Solvable
models, associated with the Lie algebra $sl (2,{\mathbb R})$. As a consequence
it is possible to find a set of polynomial solutions of this quasi-exactly
solvable version of the CHEq. These finite solutions encompass previously known
polynomial solutions of the Generalized Spheroidal Equation, Razavy Eq.,
Whittaker-Hill Eq., etc. The analysis is applied to obtain and describe special
eigen-functions of the quantum Hamiltonian of two fixed Coulombian centers in
two and three dimensions.


  The NA48/2 experiment at CERN collected two data samples with minimum bias
trigger conditions in 2003 and 2004. A measurement of the rate and dynamic
properties of the rare decay $K^\pm\to\pi^\pm\gamma\gamma$ from these data sets
based on 149 decay candidates with an estimated background of $15.5\pm0.7$
events is reported. The model-independent branching ratio in the kinematic
range $z=(m_{\gamma\gamma}/m_K)^2>0.2$ is measured to be ${\cal B}_{\rm
MI}(z>0.2) = (0.877 \pm 0.089) \times 10^{-6}$, and the branching ratio in the
full kinematic range assuming a particular Chiral Perturbation Theory
description to be ${\cal B}(K_{\pi\gamma\gamma}) = (0.910 \pm 0.075) \times
10^{-6}$.


  We present a method for a non-linear asteroseismic inversion suitable for
gravity-mode pulsators and apply it to slowly pulsating B-type (SPB) stars. Our
inversion method is based on the iterative improvement of a parameterised
static stellar structure model, which in turn is based on constraints from the
observed oscillation periods. We present tests to demonstrate that the method
is successful in recovering the properties of artificial targets both inside
and outside the parameter space. We also present a test of our method on the
well-studied SPB star KIC 7760680. We believe that this method is promising for
carrying out detailed analyses of observations of SPB and $\gamma$ Dor stars
and will provide complementary information to evolutionary models.


  The tri-hypercharge proposal introduces a separate gauged weak hypercharge
assigned to each fermion family as the origin of flavour. This is arguably one
of the simplest setups for building "gauge non-universal theories of flavour"
or "flavour deconstructed theories". In this paper we propose and study two
minimal but ultraviolet complete and renormalisable tri-hypercharge models. We
show that both models, which differ only by the heavy messengers that complete
the effective theory, are able to explain the observed patterns of fermion
masses and mixings (including neutrinos) with all fundamental coefficients
being of $\mathcal{O}(1)$. In fact, both models translate the complicated
flavour structure of the Standard Model into three simple physical scales above
electroweak symmetry breaking, completely correlated with each other, that
carry meaningful phenomenology. In particular, the heavy messenger sector
determines the origin and size of fermion mixing, which controls the size and
nature of the flavour-violating currents mediated by the two heavy $Z'$ gauge
bosons of the theory. The phenomenological implications of the two minimal
models are compared. In both models the lightest $Z'$ remains discoverable in
dilepton searches at the LHC Run 3.


  We analyze the dynamics and steady state of a linear ion array when some of
the ions are continuously laser cooled. We calculate the ions' local
temperature measured by its position fluctuation under various trapping and
cooling configurations, taking into account background heating due to the noisy
environment. For a large system, we demonstrate that by arranging the cooling
ions evenly in the array, one can suppress the overall heating considerably. We
also investigate the effect of different cooling rates and find that the
optimal cooling efficiency is achieved by an intermediate cooling rate. We
discuss the relaxation time for the ions to approach the steady state, and show
that with periodic arrangement of the cooling ions, the cooling efficiency does
not scale down with the system size.


  We propose a new scheme to express the uncertainty principle in form of
inequality of the bipartite correlation functions for a given multipartite
state, which provides an experimentally feasible and model-independent way to
verify various uncertainty and measurement disturbance relations. By virtue of
this scheme the implementation of experimental measurement on the measurement
disturbance relation to a variety of physical systems becomes practical. The
inequality in turn also imposes a constraint on the strength of correlation,
i.e. it determines the maximum value of the correlation function for two-body
system and a monogamy relation of the bipartite correlation functions for
multipartite system.


  We find that diverse nonlinear waves, such as soliton, Akhmediev breather,
and rogue waves (RWs), can emerge and interplay with each other in a two-mode
coupled system. It provides a good platform to study interaction between
different kinds of nonlinear waves. In particular, we obtain dark RWs
analytically for the first time in the coupled system, and find that two RWs
can appear in the temporal-spatial distribution. Possible ways to observe these
nonlinear waves are discussed.


  We study geometries occurring in Feynman integrals that contribute to the
scattering of black holes in the post-Minkowskian expansion. These geometries
become relevant to gravitational-wave production during the inspiralling phase
of binary black hole mergers through the classical conservative potential. At
fourth post-Minkowskian order, a K3 surface is known to occur in a three-loop
integral, leading to elliptic integrals in the result. In this letter, we
identify a Calabi-Yau three-fold in a four-loop integral, contributing at fifth
post-Minkowskian order. The presence of this Calabi-Yau geometry indicates that
completely new functions occur in the full analytical results at this order.


  This paper studies the structure of downlink sum-rate maximizing selective
decentralized feedback policies for opportunistic beamforming under finite
feedback constraints on the average number of mobile users feeding back.
Firstly, it is shown that any sum-rate maximizing selective decentralized
feedback policy must be a threshold feedback policy. This result holds for all
fading channel models with continuous distribution functions. Secondly, the
resulting optimum threshold selection problem is analyzed in detail. This is a
non-convex optimization problem over finite dimensional Euclidean spaces. By
utilizing the theory of majorization, an underlying Schur-concave structure in
the sum-rate function is identified, and the sufficient conditions for the
optimality of homogenous threshold feedback policies are obtained. Applications
of these results are illustrated for well known fading channel models such as
Rayleigh, Nakagami and Rician fading channels, along with various engineering
and design insights. Rather surprisingly, it is shown that using the same
threshold value at all mobile users is not always a rate-wise optimal feedback
strategy, even for a network with identical mobile users experiencing
statistically the same channel conditions. For the Rayleigh fading channel
model, on the other hand, homogenous threshold feedback policies are proven to
be rate-wise optimal if multiple orthonormal data carrying beams are used to
communicate with multiple mobile users simultaneously.


  Sentiment analysis consists of evaluating opinions or statements from the
analysis of text. Among the methods used to estimate the degree in which a text
expresses a given sentiment, are those based on Gaussian Processes. However,
traditional Gaussian Processes methods use a predefined kernel with
hyperparameters that can be tuned but whose structure can not be adapted. In
this paper, we propose the application of Genetic Programming for evolving
Gaussian Process kernels that are more precise for sentiment analysis. We use
use a very flexible representation of kernels combined with a multi-objective
approach that simultaneously considers two quality metrics and the
computational time spent by the kernels. Our results show that the algorithm
can outperform Gaussian Processes with traditional kernels for some of the
sentiment analysis tasks considered.


  We show that for critical site percolation on the triangular lattice two new
observables have conformally invariant scaling limits. In particular the
expected number of clusters separating two pairs of points converges to an
explicit conformal invariant. Our proof is independent of earlier results and
$SLE$ techniques, and in principle should provide a new approach to
establishing conformal invariance of percolation.


  The work of Braginsky introduced radiation pressure dynamical backaction, in
which a mechanical oscillator that is parametrically coupled to an
electromagnetic mode can experience a change in its rigidity and its damping
rate. The finite cavity electromagnetic decay rate can lead to either
amplification or cooling of the mechanical oscillator, and lead in particular
to a parametric oscillatory instability, associated with regenerative
oscillations of the mechanical oscillator, an effect limiting the circulating
power in laser gravitational wave interferometers. These effects implicitly
rely on an electromagnetic cavity whose dissipation rate vastly exceeds that of
the mechanical oscillator, a condition naturally satisfied in most
optomechanical systems. Here we consider the opposite limit, where the
mechanical dissipation is engineered to dominate over the electromagnetic one,
essentially reversing role of electromagnetic and mechanical degree of freedom.
As a result, the electromagnetic field is now subject to dynamical backaction:
the mechanical oscillator provides a feedback mechanism which modifies the
damping rate of the electromagnetic cavity. We describe this phenomenon in the
spirit of Braginsky's original description, invoking finite cavity delay and
highlighting the role of dissipation. Building on previous experimental work,
we demonstrate this dynamical backaction on light in a superconducting
microwave optomechanical circuit. In particular, we drive the system above the
parametric instability threshold of the microwave mode, leading to maser action
and demonstrate injection locking of the maser, which stabilizes its frequency
and reduces its noise.


  In this work, we perform observational data analysis on Einsteinian cubic
gravity and $f(P)$ gravity to constrain the parameter space of the theories. We
use the 30-point $z-H(z)$ cosmic chronometer data as the observational tool for
our analysis along with the BAO and the CMB peak parameters. The $\chi^2$
statistic is used for the fitting analysis and it is minimized to obtain the
best fit values for the free model parameters. We have used the Markov chain
Monte Carlo algorithm to obtain bounds for the free parameters. To achieve this
we used the publicly available CosmoMC code to put parameter bounds and
subsequently generate contour plots for them with different confidence
intervals. Besides finding the Hubble parameter $H$ in terms of the redshift
$z$ theoretically from our gravity models, we have exercised correlation
coefficients and two machine learning models, namely the linear regression (LR)
and artificial neural network (ANN), for the estimation of $H(z)$. For this
purpose, we have developed a Python package for finding the parameter space and
performing the subsequent statistical analysis and prediction analysis using
machine learning. We compared both our theoretical and estimated values of
$H(z)$ with the observations. It is seen that our theoretical and estimated
models from machine learning performed significantly well when compared with
the observations.


  Two-dimensional (2D) honeycomb ferromagnets, such as monolayer
chromium-trihalides, are predicted to behave as topological magnon insulators -
characterized by an insulating bulk and topologically protected edge states,
giving rise to a thermal magnon Hall effect. Here we report the behavior of the
topological magnons in monolayer CrI$_3$ under external stimuli, including
biaxial and uniaxial strain, electric gating, as well as in-plane and
out-of-plane magnetic field, revealing that one can thereby tailor the magnetic
states as well as the size and the topology of the magnonic bandgap. These
findings broaden the perspective of using 2D magnetic materials to design
topological magnonic devices.


  The unique physics found in moir\'e superlattices of twisted or
lattice-mismatched atomic layers hold great promise for future quantum
technologies. However, twisted configurations are typically thermodynamically
unfavorable, making the accurate twist angle control in direct growth
implausible. While rotationally aligned moir\'e superlattices based on
lattice-mismatched layers such as WSe2/WS2 can be synthesized, they lack the
critical tunability of the moir\'e period and the moir\'e formation mechanisms
are not well-understood. Here, we report the scalable, thermodynamically driven
van der Waals epitaxy of stable moir\'es with tunable period from 10 to 45
nanometers, based on lattice mismatch engineering in two WSSe layers with
adjustable chalcogens ratios. Contrarily to conventional epitaxy, where lattice
mismatch induced stress hinders high-quality growth, we reveal the key role of
bulk stress in moir\'e formation, as well as its unique interplay with edge
stress in shaping the moir\'e growth modes. Moreover, the synthesized
superlattices display tunable interlayer, and moir\'e intralayer excitons. Our
studies unveil the unique epitaxial science of moir\'e synthesis and lay the
foundations for moir\'e-based technologies.


  In this paper, we describe a method to determine the power sum of the
elements of the rows in the hyperbolic Pascal triangles corresponding to
$\{4,q\}$ with $q\ge5$. The method is based on the theory of linear
recurrences, and the results are demonstrated by evaluating the $k^{th}$ power
sum in the range $2\le k\le 11$.


  This paper reviews the existing literature on input device evaluation and
design in human-computer interaction (HCI) and discusses possible applications
of this knowledge to the design and evaluation of new interfaces for musical
expression. Specifically, a set of musical tasks is suggested to allow the
evaluation of different existing controllers.


  Unlike many deterministic PDEs, stochastic equations are not amenable to the
classical variational theory of Euler-Lagrange. In this paper, we show how
self-dual variational calculus leads to solutions of various stochastic partial
differential equations driven by monotone vector fields. We construct weak
solutions as minima of suitable non-negative and self-dual energy functionals
on It\^o spaces of stochastic processes. We deal with both additive and
non-additive noise. The equations considered in this paper have already been
resolved by other methods, starting with the celebrated thesis of Pardoux, and
many other subsequent works. This paper is about presenting a new variational
approach to this type of problems, hoping it will lead to progress on other
still unresolved situations.


  We aim to investigate mass loss and luminosity in a large sample of evolved
stars in several Local Group galaxies with a variety of metalliticies and
star-formation histories: the Small and Large Magellanic Cloud, and the Fornax,
Carina, and Sculptor dwarf spheroidal galaxies. Dust radiative transfer models
are presented for 225 carbon stars and 171 oxygen-rich evolved stars for which
spectra from the Infrared Spectrograph on Spitzer are available. The spectra
are complemented with available optical and infrared photometry to construct
spectral energy distributions. A minimization procedure was used to determine
luminosity and mass-loss rate (MLR). Pulsation periods were derived for a large
fraction of the sample based on a re-analysis of existing data. New deep K-band
photometry from the VMC survey and multi-epoch data from IRAC and
AllWISE/NEOWISE have allowed us to derive pulsation periods longer than 1000
days for some of the most heavily obscured and reddened objects. We derive
(dust) MLRs and luminosities for the entire sample. The estimated MLRs can
differ significantly from estimates for the same objects in the literature due
to differences in adopted optical constants (up to factors of several) and
details in the radiative transfer modelling. Updated parameters for the
super-AGB candidate MSX SMC 055 (IRAS 00483-7347) are presented. Its current
mass is estimated to be 8.5 +- 1.6 \msol, suggesting an initial mass well above
8~\msol. Using synthetic photometry, we present and discuss colour-colour and
colour-magnitude diagrams which can be expected from the James Webb Space
Telescope.


  In this work we completely describe the dynamics of triangle tiling
billiards. In the first part of this work, we propose a geometric approach of
dynamics by introducing natural foliations associated to it. In the second
part, we exploit the relationship between triangle tiling billiards and a
family of fully flipped $3$-interval exchange transformations on the circle. We
give a combinatorial approach of dynamics via renormalization. By uniting the
two approaches, we prove several conjectures on the dynamics of triangle tiling
billiards. First, we prove the Tree Conjecture and the 4n+2 Conjecture, both
concerning the symbolic dynamics of periodic trajectories, and both stated by
Baird-Smith, Davis, Fromm and Iyer. Second, we study a family of exceptional
trajectories which are closely related to the orbits of minimal Arnoux-Rauzy
maps. We prove that all of these exceptional trajectories pass by all tiles,
which confirms our own conjecture with P. Hubert on their non-linear escape.
Moreover, we use tiling billiards to prove the convergence, up to rescaling, of
arithmetic orbits of the Arnoux-Yoccoz map to the Rauzy fractal, conjectured by
Hooper and Weiss. All of these conjectures have been stated in print in the
last three years.


  Contrary to a widely spread believe, we have demonstrated that strongly
coupled electroweak models including both a light Higgs-like boson and massive
spin-1 resonances are not in conflict with experimental constraints on the
oblique S and T parameters. We use an effective Lagrangian implementing the
chiral symmetry breaking SU(2)_L x SU(2)_R -> SU(2)_{L+R} that contains the
Standard Model gauge bosons coupled to the electroweak Goldstones, one
Higgs-like scalar state h with mass m_h=126 GeV and the lightest vector and
axial-vector resonance multiplets V and A. We have considered the one-loop
calculation of S and T in order to study the viability of these
strongly-coupled scenarios, being short-distance constraints and dispersive
relations the main ingredients of the calculation. Once we have constrained the
resonance parameters, we do a first approach to the determination of the low
energy constants of the electroweak effective theory at low energies (without
resonances). We show this determination in the case of the purely Higgsless
bosonic Lagrangian.


  We report the serendipitous discovery of a flare star observed with the ROSAT
X-ray observatory. From optical spectra, which show strong and variable
emission lines of the hydrogen Balmer series and neutral helium, we classify
this object as a M3.0Ve star, and estimate a distance of 52 pc from published
photometry. Due to the star's close proximity (13.6') to the calibration source
and RS CVn binary AR Lacertae, long term X-ray coverage is available in the
ROSAT archive (~50 hours spanning 6.5 years). Two large flare events occurred
early in the mission (6-7/1990), and the end of a third flare was detected in
6/1996. One flare, observed with the Position Sensitive Proportional Counter
(PSPC), had a peak luminosity Lx=1.1x10^{30} erg/s, an e-folding rise time of
2.2 hours and a decay time of 7 hours. This decay time is one of the longest
detected on a dMe star, providing evidence for the possibility of additional
heating during the decay phase. A large HRI flare (peak Lx=2.9x10^{30} erg/s)
is also studied. The "background" X-ray emission is also variable - evidence
for low-level flaring or microflaring. We find that >=59% of the HRI counts and
>=68% of the PSPC counts are due to flares. At least 41% of the HRI exposure
time and 47% of the PSPC are affected by detectable flare enhancement.


  To completely understand a document, the use of textual information is not
enough. Understanding visual cues, such as layouts and charts, is also
required. While the current state-of-the-art approaches for document
understanding (both OCR-based and OCR-free) work well, a thorough analysis of
their capabilities and limitations has not yet been performed. Therefore, in
this work, we addresses the limitation of current VisualQA models when applied
to charts and plots. To investigate shortcomings of the state-of-the-art
models, we conduct a comprehensive behavioral analysis, using ChartQA as a case
study. Our findings indicate that existing models particularly underperform in
answering questions related to the chart's structural and visual context, as
well as numerical information. To address these issues, we propose three simple
pre-training tasks that enforce the existing model in terms of both
structural-visual knowledge, as well as its understanding of numerical
questions. We evaluate our pre-trained model (called MatCha-v2) on three chart
datasets - both extractive and abstractive question datasets - and observe that
it achieves an average improvement of 1.7% over the baseline model.


  We have investigated $D^{+}\pi^{-}$ and $D^{*+}\pi^{-}$ final states and
observed the two established $L=1$ charmed mesons, the $D_1(2420)^0$ with mass
$2421^{+1+2}_{-2-2}$ MeV/c$^{2}$ and width $20^{+6+3}_{-5-3}$ MeV/c$^{2}$ and
the $D_2^*(2460)^0$ with mass $2465 \pm 3 \pm 3$ MeV/c$^{2}$ and width
$28^{+8+6}_{-7-6}$ MeV/c$^{2}$. Properties of these final states, including
their decay angular distributions and spin-parity assignments, have been
studied. We identify these two mesons as the $j_{light}=3/2$ doublet predicted
by HQET. We also obtain constraints on {\footnotesize $\Gamma_S/(\Gamma_S +
\Gamma_D)$} as a function of the cosine of the relative phase of the two
amplitudes in the $D_1(2420)^0$ decay.


  Detecting breast lesion in videos is crucial for computer-aided diagnosis.
Existing video-based breast lesion detection approaches typically perform
temporal feature aggregation of deep backbone features based on the
self-attention operation. We argue that such a strategy struggles to
effectively perform deep feature aggregation and ignores the useful local
information. To tackle these issues, we propose a spatial-temporal deformable
attention based framework, named STNet. Our STNet introduces a spatial-temporal
deformable attention module to perform local spatial-temporal feature fusion.
The spatial-temporal deformable attention module enables deep feature
aggregation in each stage of both encoder and decoder. To further accelerate
the detection speed, we introduce an encoder feature shuffle strategy for
multi-frame prediction during inference. In our encoder feature shuffle
strategy, we share the backbone and encoder features, and shuffle encoder
features for decoder to generate the predictions of multiple frames. The
experiments on the public breast lesion ultrasound video dataset show that our
STNet obtains a state-of-the-art detection performance, while operating twice
as fast inference speed. The code and model are available at
https://github.com/AlfredQin/STNet.


  The Witt group of nondegenerate braided fusion categories $\mathcal{W}$
contains a subgroup $\mathcal{W}_\text{un}$ consisting of Witt equivalence
classes of pseudo-unitary nondegenerate braided fusion categories. For each
finite-dimensional simple Lie algebra $\mathfrak{g}$ and positive integer $k$
there exists a pseudo-unitary category $\mathcal{C}(\mathfrak{g},k)$ consisting
of highest weight integerable $\hat{g}$-modules of level $k$ where
$\hat{\mathfrak{g}}$ is the corresponding affine Lie algebra. Relations between
the classes $[\mathcal{C}(\mathfrak{sl}_2,k)]$, $k\geq1$ have been completely
described in the work of Davydov, Nikshych, and Ostrik. Here we give a complete
classification of relations between the classes
$[\mathcal{C}(\mathfrak{sl}_3,k)]$, $k\geq1$ with a view toward extending these
methods to arbitrary simple finite dimensional Lie algebras $\mathfrak{g}$ and
positive integer levels $k$.


  Hierarchical application of Triple-Modular Redundancy (TMR) increases fault
tolerance of digital Integrated Circuit (IC). In this paper, a simple
probabilistic model was proposed for analysis of fault masking performance of
hierarchical TMR networks. Performance improvements obtained by second order
TMR network were theoretically compared with first order TMR network.


  Despite attaining high empirical generalization, the sharpness of models
trained with sharpness-aware minimization (SAM) do not always correlate with
generalization error. Instead of viewing SAM as minimizing sharpness to improve
generalization, our paper considers a new perspective based on SAM's training
dynamics. We propose that perturbations in SAM perform perturbed forgetting,
where they discard undesirable model biases to exhibit learning signals that
generalize better. We relate our notion of forgetting to the information
bottleneck principle, use it to explain observations like the better
generalization of smaller perturbation batches, and show that perturbed
forgetting can exhibit a stronger correlation with generalization than
flatness. While standard SAM targets model biases exposed by the steepest
ascent directions, we propose a new perturbation that targets biases exposed
through the model's outputs. Our output bias forgetting perturbations
outperform standard SAM, GSAM, and ASAM on ImageNet, robustness benchmarks, and
transfer to CIFAR-{10,100}, while sometimes converging to sharper regions. Our
results suggest that the benefits of SAM can be explained by alternative
mechanistic principles that do not require flatness of the loss surface.


  This paper presents a tutorial overview of path integral (PI) control
approaches for stochastic optimal control and trajectory optimization. We
concisely summarize the theoretical development of path integral control to
compute a solution for stochastic optimal control and provide algorithmic
descriptions of the cross-entropy (CE) method, an open-loop controller using
the receding horizon scheme known as the model predictive path integral (MPPI),
and a parameterized state feedback controller based on the path integral
control theory. We discuss policy search methods based on path integral
control, efficient and stable sampling strategies, extensions to multi-agent
decision-making, and MPPI for the trajectory optimization on manifolds. For
tutorial demonstrations, some PI-based controllers are implemented in Python,
MATLAB and ROS2/Gazebo simulations for trajectory optimization. The simulation
frameworks and source codes are publicly available at
https://github.com/INHA-Autonomous-Systems-Laboratory-ASL/An-Overview-on-Recent-Advances-in-Path-Integral-Control.


  Evolutionary game dynamics with two 2-strategy games in a finite population
has been investigated in this study. Traditionally, frequency-dependent
evolutionary dynamics are modeled by deterministic replicator dynamics under
the assumption that the population size is infinite. However, in reality,
population sizes are finite. Recently, stochastic processes in finite
populations have been introduced into evolutionary games in order to study
finite size effects in evolutionary game dynamics. However, most of these
studies focus on populations playing only single games. In this study, we
investigate a finite population with two games and show that a finite
population playing two games tends to evolve toward a specific direction to
form particular linkages between the strategies of the two games.


  In this paper, we study the desingularization problem in the first $q$-Weyl
algebra. We give an order bound for desingularized operators, and thus derive
an algorithm for computing desingularized operators in the first $q$-Weyl
algebra. Moreover, an algorithm is presented for computing a generating set of
the first $q$-Weyl closure of a given $q$-difference operator. As an
application, we certify that several instances of the colored Jones polynomial
are Laurent polynomial sequences by computing the corresponding desingularized
operator.


  We address the topological nature of electronic states of step edges of
Bi(111) films by first principles band structure calculations. We confirm that
the dispersion of step edge states reflects the topological nature of
underlying films. This result unambiguously denies recent claims that the step
edge state on the surface of a bulk Bi(111) crystal or a sufficiently thick
Bi(111) films represents non-trivial edge states of the two dimensional
topologcial insulator phase expected for a very thin Bi(111) film. The trivial
step edge states have a gigantic spin splitting of one dimensional Rashba bands
and the substantial intermixing with electronic states of the bulk, which might
be exploited further.


  This paper introduces DONUT-hole, a sparse OCR-free visual document
understanding (VDU) model that addresses the limitations of its predecessor
model, dubbed DONUT. The DONUT model, leveraging a transformer architecture,
overcoming the challenges of separate optical character recognition (OCR) and
visual semantic understanding (VSU) components. However, its deployment in
production environments and edge devices is hindered by high memory and
computational demands, particularly in large-scale request services. To
overcome these challenges, we propose an optimization strategy based on
knowledge distillation and model pruning. Our paradigm to produce DONUT-hole,
reduces the model denisty by 54\% while preserving performance. We also achieve
a global representational similarity index between DONUT and DONUT-hole based
on centered kernel alignment (CKA) metric of 0.79. Moreover, we evaluate the
effectiveness of DONUT-hole in the document image key information extraction
(KIE) task, highlighting its potential for developing more efficient VDU
systems for logistic companies.


  As current gravitational wave (GW) detectors increase in sensitivity, and
particularly as new instruments are being planned, there is the possibility
that ground-based GW detectors will observe GWs from highly eccentric neutron
star binaries. We present the first detailed study of highly eccentric BNS
systems with full (3+1)D numerical relativity simulations using consistent
initial conditions, i.e., setups which are in agreement with the Einstein
equations and with the equations of general relativistic hydrodynamics in
equilibrium. Overall, our simulations cover two different equations of state
(EOSs), two different spin configurations, and three to four different initial
eccentricities for each pairing of EOS and spin. We extract from the simulated
waveforms the frequency of the f-mode oscillations induced during close
encounters before the merger of the two stars. The extracted frequency is in
good agreement with f-mode oscillations of individual stars for the
irrotational cases, which allows an independent measure of the supranuclear
equation of state not accessible for binaries on quasi-circular orbits. The
energy stored in these f-mode oscillations can be as large as $10^{-3}M_\odot
\sim 10^{51}$ erg, even with a soft EOS. In order to estimate the stored
energy, we also examine the effects of mode mixing due to the stars' offset
from the origin on the f-mode contribution to the GW signal. While in general
(eccentric) neutron star mergers produce bright electromagnetic counterparts,
we find that the luminosity decreases when the eccentricity becomes too large,
due to a decrease of the ejecta mass. Finally, the use of consistent initial
configurations also allows us to produce high-quality waveforms for different
eccentricities which can be used as a testbed for waveform model development of
highly eccentric binary neutron star systems.


  The Prisoner's Dilemma (PD) game is used in several fields due to the
emergence of cooperation among selfish players. Here, we have considered a
one-dimensional lattice, where each cell represents a player, that can
cooperate or defect. This one-dimensional geometry allows us to retrieve the
results obtained for regular lattices and to keep track of the system
spatio-temporal evolution. Players play PD with their neighbors and update
their state using the Pavlovian Evolutionary Strategy. If the players receive a
positive payoff greater than an aspiration level, they keep their states and
switch them, otherwise. We obtain analitycally the critical temptation values,
we present the cluster patterns that emerge from the players local interaction
and we perform an exploration of paramater space. The numerical results are in
accordance to the critical temptation analitycal results, it confirms that the
Pavlovian strategy foment the cooperation among the players and avoid the
defection. The system also presented a new phase in the steady state, the
quasi-regular phase, where several players switch their states during round to
round, but the proportion of cooperators does not alter significantly.