  In the classic version of the game of firefighter, on the first turn a fire
breaks out on a vertex in a graph $G$ and then $k$ firefighters protect $k$
vertices. On each subsequent turn, the fire spreads to the collective unburnt
neighbourhood of all the burning vertices and the firefighters again protect
$k$ vertices. Once a vertex has been burnt or protected it remains that way for
the rest of the game. A common objective with respect to some infinite graph
$G$ is to determine how many firefighters are necessary to stop the fire from
spreading after a finite number of turns, commonly referred to as containing
the fire. We introduce the concept of distance-restricted firefighting where
the firefighters' movement is restricted so they can only move up to some fixed
distance $d$ per turn rather than being able to move without restriction. We
establish some general properties of this new game in contrast to properties of
the original game, and we investigate specific cases of the distance-restricted
game on the infinite square, strong, and hexagonal grids. We conjecture that
two firefighters are insufficient on the square grid when $d = 2$, and we pose
some questions about how many firefighters are required in general when $d =
1$.


  Based on the assumption that the standard Schr\"odinger equation becomes
gravitationally modified for massive macroscopic objects, two independent
proposals has survived from the nineteen-eighties. The Schr\"odinger--Newton
equation (1984) provides well-localized solitons for free macro-objects but
lacks the mechanism how extended wave functions collapse on solitons. The
gravity-related stochastic Schr\"odinger equation (1989) provides the
spontaneous collapse but the resulting solitons undergo a tiny diffusion
leading to an inconvenient steady increase of the kinetic energy. We propose
the stochastic Schr\"odinger--Newton equation which contains the above two
gravity-related modifications together. Then the wave functions of free
macroscopic bodies will gradually and stochastically collapse to solitons which
perform inertial motion without the momentum diffusion: conservation of
momentum and energy is restored.


  In this article, a biallelic reversible mutation model with linear and
quadratic selection is analyzed. The approach reconnects to one proposed by
Kimura ( Possibility of extensive neutral evolution under stabilizing selection
with special reference to nonrandom use of codons (PNAS,1981)), who starts from
a diffusion model and derives its equilibrium distribution up to a constant. We
use a boundary-mutation Moran model, which approximates a general mutation
model for small effective mutation rates, and derive its equilibrium
distribution for polymorphic and monomorphic variants in small to moderately
sized populations. Using this model, we show that biased mutation rates and
linear selection alone can cause patterns of polymorphism rates within and
substitution rates between populations that are usually ascribed to balancing
or overdominant selection. We illustrate this using a data set of short introns
and fourfold degenerate sites from Drosophila simulans and Drosophila
melanogaster.


  We classify general square systems of polynomial equations solvable in
radicals. Expectedly, they are almost in a 1-to-1 correspondence with tuples of
lattice polytopes of mixed volume not exceeding 4. The proof is based on the
computation of the monodromy group for a general system of equations, which may
be of independent interest.


  This paper proposes a novel approach to pre-train encoder-decoder
sequence-to-sequence (seq2seq) model with unpaired speech and transcripts
respectively. Our pre-training method is divided into two stages, named
acoustic pre-trianing and linguistic pre-training. In the acoustic pre-training
stage, we use a large amount of speech to pre-train the encoder by predicting
masked speech feature chunks with its context. In the linguistic pre-training
stage, we generate synthesized speech from a large number of transcripts using
a single-speaker text to speech (TTS) system, and use the synthesized paired
data to pre-train decoder. This two-stage pre-training method integrates rich
acoustic and linguistic knowledge into seq2seq model, which will benefit
downstream automatic speech recognition (ASR) tasks. The unsupervised
pre-training is finished on AISHELL-2 dataset and we apply the pre-trained
model to multiple paired data ratios of AISHELL-1 and HKUST. We obtain relative
character error rate reduction (CERR) from 38.24% to 7.88% on AISHELL-1 and
from 12.00% to 1.20% on HKUST. Besides, we apply our pretrained model to a
cross-lingual case with CALLHOME dataset. For all six languages in CALLHOME
dataset, our pre-training method makes model outperform baseline consistently.


  Atomic deexcitation emitting a neutrino pair and a photon is expected to
provide a novel method of neutrino physics if it is enhanced by quantum
coherence in a macroscopic target. However, the same enhancement mechanism may
also lead to a serious problem of enhanced QED background process. We show that
the QED background can be suppressed enough in the photonic crystal waveguide
by using the spatial phase that is imprinted in the process of initial
coherence generation in the target at excitation.


  We present a computation of the k-string tension in the large N limit of the
two dimensional lattice Yang-Mills theory. It is well known that the problems
of computing the partition function and the Wilson loop can be both reduced to
a unitary matrix integral which has a third order phase transition separating
weak and strong coupling. We give an explicit computation of the interaction
energy for k-strings in the large N limit when k/N is held constant and
non-zero. In this limit, the interaction energy is finite and attractive. We
show that, in the strong coupling phase, the k -> N - k duality is realized as
a first order phase transition. We also show that the lattice k-string tension
reduces to the expected Casimir scaling in the continuum limit.


  This is the text of my speech at the Logica Universalis webinar, which took
place on May 11, 2022.
  I discuss two ways to implement a semantic approach to nonmonotonic
consequence relations in an arbitrary propositional language. For one
particular language, we also discuss the proof-theoretic framework that we
connect with this semantic approach.


  Transfer learning plays a key role in modern data analysis when: (1) the
target data are scarce but the source data are sufficient; (2) the
distributions of the source and target data are heterogeneous. This paper
develops an interpretable unified transfer learning model, termed as UTrans,
which can detect both transferable variables and source data. More
specifically, we establish the estimation error bounds and prove that our
bounds are lower than those with target data only. Besides, we propose a source
detection algorithm based on hypothesis testing to exclude the nontransferable
data. We evaluate and compare UTrans to the existing algorithms in multiple
experiments. It is shown that UTrans attains much lower estimation and
prediction errors than the existing methods, while preserving interpretability.
We finally apply it to the US intergenerational mobility data and compare our
proposed algorithms to the classical machine learning algorithms.


  We are responding to the comment of Tyshetskiy and Vladimirov
[arXiv:1212.4286] on a recently published paper by Shukla and Eliasson
[arXiv:1112.5556], regarding the discovery of a novel attractive force on
stationary test ion charges of the same sign shielded by degenerate electrons
in a dense quantum plasma.


  In this work a method of spectroscopy without monochromators for the
undulator radiation (UR) source is proposed. This method is based of changing
the magnetic field in the undulator. Different variations of field modulations
and corresponding object reaction for the case of a dipole regime of UR
exitation were considered. The results of a numerical experiment are shown and
possibilites of this method for an undulator consisting of two blocks and
rearranging by changing the distance between the blocks were estimated.


  Radiology report generation (RRG) aims to describe automatically a radiology
image with human-like language and could potentially support the work of
radiologists, reducing the burden of manual reporting. Previous approaches
often adopt an encoder-decoder architecture and focus on single-modal feature
learning, while few studies explore cross-modal feature interaction. Here we
propose a Cross-modal PROtotype driven NETwork (XPRONET) to promote cross-modal
pattern learning and exploit it to improve the task of radiology report
generation. This is achieved by three well-designed, fully differentiable and
complementary modules: a shared cross-modal prototype matrix to record the
cross-modal prototypes; a cross-modal prototype network to learn the
cross-modal prototypes and embed the cross-modal information into the visual
and textual features; and an improved multi-label contrastive loss to enable
and enhance multi-label prototype learning. XPRONET obtains substantial
improvements on the IU-Xray and MIMIC-CXR benchmarks, where its performance
exceeds recent state-of-the-art approaches by a large margin on IU-Xray and
comparable performance on MIMIC-CXR.


  We explore the quantum-classical crossover in the behaviour of a quantum
field mode. The quantum behaviour of a two-state system - a qubit - coupled to
the field is used as a probe. Collapse and revival of the qubit inversion form
the signature for quantum behaviour of the field and continuous Rabi
oscillations form the signature for classical behaviour of the field. We
demonstrate both limits in a single model for the full coupled system, for
states with the same average field strength, and so for qubits with the same
Rabi frequency.


  Having its origin in a successful mapping technique, the Fock-Tani formalism,
the corrected 3P0 model (C3P0) retains the basic aspects of the 3P0 predictions
with the inclusion of bound-state corrections. Evaluation of the decay
amplitudes has be performed for open-flavor strong decays in the light meson
sector. The bound-state corrections introduce a fine-tuning for the former 3P0
model, in particular, the adjustment of the D/S ratios in $b_{1}\to\omega\pi$,
$a_{1}\to\rho\pi$ and $h_1\to\rho\pi$ decays.


  We give a few observations on different types of bounded operators on a
topological vector space X and their relations with compact operators on X. In
particular, we investigate when these bounded operators coincide with compact
operators. We also consider similar types of bounded bilinear mappings between
topological vector spaces. Some properties of tensor product operators between
locally convex spaces are established. In the last part of the paper we deal
with operators on topological Riesz spaces.


  Multi-modal image registration is a crucial pre-processing step in many
medical applications. However, it is a challenging task due to the complex
intensity relationships between different imaging modalities, which can result
in large discrepancy in image appearance. The success of multi-modal image
registration, whether it is conventional or learning based, is predicated upon
the choice of an appropriate distance (or similarity) measure. Particularly,
deep learning registration algorithms lack in accuracy or even fail completely
when attempting to register data from an "unseen" modality. In this work, we
present Modality Agnostic Distance (MAD), a deep image distance}] measure that
utilises random convolutions to learn the inherent geometry of the images while
being robust to large appearance changes. Random convolutions are
geometry-preserving modules which we use to simulate an infinite number of
synthetic modalities alleviating the need for aligned paired data during
training. We can therefore train MAD on a mono-modal dataset and successfully
apply it to a multi-modal dataset. We demonstrate that not only can MAD
affinely register multi-modal images successfully, but it has also a larger
capture range than traditional measures such as Mutual Information and
Normalised Gradient Fields.


  The effect of light refraction in a galaxy halo of dark matter, described by
profiles of Navarro-Frenk-White and Burkett, was considered. Powers of the
Cherenkov radiation for the refractive indexes of gravitational fields with
these profiles were calculated. It was shown that correspondent radiation
temperature in the X-rays range have the magnitude about some microKelvins. It
was also marked that its detection may be the criteria on choosing the
preferable dark matter density distribution in a galaxy.


  The paper is devoted to the problem of mapping affine loop nests onto
distributed memory parallel computers. A method to find affine transformations
of loop nests for parallel execution and distribution of data over processors
is presented. The method tends to minimize the number of communications between
processors and to improve locality of data within one processor. A problem of
determination of data exchange sequence is investigated. Conditions to
determine the ability to arrange broadcast is presented.


  In this note the Polyakov equation [Phys. Rev. E {\bf 52} (1995) 6183] for
the velocity-difference PDF, with the exciting force correlation function
$\kappa (y)\sim1-y^{\alpha}$ is analyzed. Several solvable cases are
considered, which are in a good agreement with available numerical results.
Then it is shown how the method developed by A. Polyakov can be applied to
turbulence with short-scale-correlated forces, a situation considered in models
of self-organized criticality.


  We prove that there are no strictly shod algebras in hereditary gentle
algebras by geometric models.


  We study a problem on edge percolation on product graphs $G\times K_2$. Here
$G$ is any finite graph and $K_2$ consists of two vertices $\{0,1\}$ connected
by an edge. Every edge in $G\times K_2$ is present with probability $p$
independent of other edges. The Bunkbed conjecture states that for all $G$ and
$p$ the probability that $(u,0)$ is in the same component as $(v,0)$ is greater
than or equal to the probability that $(u,0)$ is in the same component as
$(v,1)$ for every pair of vertices $u,v\in G$.
  We generalize this conjecture and formulate and prove similar statements for
randomly directed graphs. The methods lead to a proof of the original
conjecture for special classes of graphs $G$, in particular outerplanar graphs.


  Experimental observations indicate that chemically active droplets suspended
in a surfactant-laden fluid can self-propel spontaneously. The onset of this
motion is attributed to a symmetry-breaking Marangoni instability resulting
from the nonlinear advective coupling of the distribution of surfactant to the
hydrodynamic flow generated by Marangoni stresses at the droplet's surface.
Here, we use weakly nonlinear analysis to characterize the self-propulsion near
the instability threshold and the influence of the droplet's deformability. We
report that in vicinity of the threshold, deformability enhances
self-propulsion of viscous droplets, but hinders propulsion of drops that are
roughly less viscous than the surrounding fluid. Our asymptotics further
reveals that droplet deformability may alter the type of bifurcation leading to
symmetry breaking: for moderately deformable droplets the onset of
self-propulsion is transcritical and a regime of steady self-propulsion is
stable; while in the case of highly deformable drops, no steady flows can be
found within the asymptotic limit considered in this paper suggesting that the
bifurcation is subcritical.


  An SU(2) slave boson formulation of bond-type spin nematic orders is
developed in frustrated ferromagnets, where the spin nematic states are
described as the resonating spin-triplet valence bond (RVB) states. The
d-vectors of spin-triplet pairing ansatzes play the role of the directors in
the bond-type spin quadrupolar states. The low-energy excitations around such
spin-triplet RVB ansatzes generally comprise the (potentially massless) gauge
bosons, massless Goldstone bosons, and spinon individual excitations. Extending
the projective symmetry group argument to the spin-triplet ansatzes, we show
how to identify the number of massless gauge bosons efficiently. Applying this
formulation, we next (i) enumerate possible mean field solutions for the S=1/2
ferromagnetic J1-J2 Heisenberg model on the square lattice, with ferromagnetic
nearest neighbor J1 and competing antiferromagnetic next-nearest neighbor J2,
and (ii) argue their stability against small gauge fluctuations. As a result,
two stable spin-triplet RVB ansatzes are found in the intermediate coupling
regime around J1:J2 \simeq 1:0.4. One is the Z_2 Balian-Werthamer (BW) state
stabilized by the Higgs mechanism and the other is the SU(2) chiral p-wave
(Anderson-Brinkman-Morel) state stabilized by the Chern-Simon mechanism. The
former Z_2 BW state in fact shows the same bond-type spin quadrupolar order as
found in the previous exact diagonalization study [N. Shannon et al., Phys.
Rev. Lett. 96, 027213 (2006)].


  Classical transport properties of an electron, moving in plain, in an array
of magnetic antidot has been calculated. The homogeneous magnetic field in
z-direction fills the whole space except of cylinders of radius r_0. The
magnetoresistance shows additional peak and minimum according to pinned orbits
at antidots and to propagating orbits in transport direction, respectively.


  A new learning scheme called time divergence-convergence (TDC) is proposed
for two-layer dynamic synapse neural networks (DSNN). DSNN is an artificial
neural network model, in which the synaptic transmission is modeled by a
dynamic process and the information between neurons are transmitted through
spike timing. In TDC, the intra-layer neurons of a DSNN are trained to map
input spike trains to a higher dimension of spike trains called a
feature-domain, and the output neurons are trained to build the desired spike
trains by processing the spike timing of intralayer neurons. The DSNN
performance was examined in a jittered spike train classification task which
shows more than 92\% accuracy in classifying different spike trains. The DSNN
performance is comparable with the recurrent multi-layer neural networks and
surpasses a single-layer DSNN with a 22\% margin. Synaptic dynamics have been
proposed as the neural substrate for sub-second temporal processing; we can
utilize TDC to train a DSNN to perform diverse forms of sub-second temporal
processing. The TDC learning proposed here is scalable in terms of the synaptic
adaptation of deeper layers of multi-layer DSNNs. The DSNN along with TDC
learning proposed here can be used in to replicate the processing observed in
neural circuitry and in pattern recognition tasks.


  Distributed learning has become a necessity for training ever-growing models
by sharing calculation among several devices. However, some of the devices can
be faulty, deliberately or not, preventing the proper convergence. As a matter
of fact, the baseline distributed SGD algorithm does not converge in the
presence of one Byzantine adversary. In this article we focus on the more
robust SignSGD algorithm derived from SGD. We provide an upper bound for the
convergence rate of SignSGD proving that this new version is robust to
Byzantine adversaries. We implemented SignSGD along with Byzantine strategies
attempting to crush the learning process. Therefore, we provide empirical
observations from our experiments to support our theory. Our code is available
on GitHub https://github.com/jasonakoun/signsgd-fault-tolerance and our
experiments are reproducible by using the provided parameters.


  In the present work we illustrate that classical but nonlinear systems may
possess features reminiscent of quantum ones, such as memory, upon suitable
external perturbation. As our prototypical example, we use the two-dimensional
complex Ginzburg-Landau equation in its vortex glass regime. We impose an
external drive as a perturbation mimicking a quantum measurement protocol, with
a given "measurement rate" (the rate of repetition of the drive) and "mixing
rate" (characterized by the intensity of the drive). Using a variety of
measures, we find that the system may or may not retain its coherence,
statistically retrieving its original glass state, depending on the strength
and periodicity of the perturbing field. The corresponding parametric regimes
and the associated energy cascade mechanisms involving the dynamics of vortex
waveforms and domain boundaries are discussed.


  A tanglegram consists of two rooted binary trees and a perfect matching
between their leaves, and a planar tanglegram is one that admits a layout with
no crossings. We show that the problem of generating planar tanglegrams
uniformly at random reduces to the corresponding problem for irreducible planar
tanglegram layouts, which are known to be in bijection with pairs of disjoint
triangulations of a convex polygon. We extend the flip operation on a single
triangulation to a flip operation on pairs of disjoint triangulations.
Interestingly, the resulting flip graph is both connected and regular, and
hence a random walk on this graph converges to the uniform distribution. We
also show that the restriction of the flip graph to the pairs with a fixed
triangulation in either coordinate is connected, and give diameter bounds that
are near optimal. Our results furthermore yield new insight into the flip graph
of triangulations of a convex $n$-gon with a geometric interpretation on the
associahedron.


  The category $\mathbf{Rel}$ is the category of sets (objects) and relations
(morphisms). Equipped with the direct product of sets, $\mathbf{Rel}$ is a
monoidal category. Moreover, $\mathbf{Rel}$ is a locally posetal 2-category,
since every homset $\mathbf{Rel}(A,B)$ is a poset with respect to inclusion. We
examine the 2-category of monoids $\mathbf{RelMon}$ in this category. The
morphism we use are lax.
  This category includes, as subcategories, various interesting classes:
hypergroups, partial monoids (which include various types of quantum logics,
for example effect algebras) and small categories. We show how the
2-categorical structure gives rise to several previously defined notions in
these categories, for example certain types of congruence relations on
generalized effect algebras. This explains where these definitions come from.


  In this paper the Stimulated radiation cooling (SRC) of ion beams and methods
of formation of the broadband laser beams with given spectral distribution are
discussed.


  With the proliferation of communication networks and mobile devices, the
privacy and security concerns on their information flow are raised. Given a
critical system that may leak confidential information, the problem consists of
verifying and also enforcing opacity by designing supervisors, to conceal
confidential information from unauthorized persons. To find out what the
intruder sees, it is required to construct an observer of the system. In this
paper, we consider incremental observer generation of modular systems, for
verification and enforcement of current state opacity. The synchronization of
the subsystems generate a large state space. Moreover, the observer generation
with exponential complexity adds even larger state space. To tackle the
complexity problem, we prove that observer generation can be done locally
before synchronizing the subsystems. The incremental local observer generation
along with an abstraction method lead to a significant state space reduction
compared to traditional monolithic methods. The existence of shared
unobservable events is also considered in the incremental approach. Moreover,
we present an illustrative example, where the results of verification and
enforcement of current state opacity are shown on a modular multiple
floor/elevator building with an intruder. Furthermore, we extend the current
state opacity, current state anonymity, and language based opacity formulations
for verification of modular systems.


  The quantization of the simple one-dimensional Hamiltonian H=xp is of
interest for its mathematical properties rather than for its physical
relevance. In fact, the Berry-Keating conjecture speculates that a proper
quantization of H=xp could yield a relation with the Riemann hypothesis.
Motivated by this, we study the so-called Wigner quantization of H=xp, which
relates the problem to representations of the Lie superalgebra osp(1|2). In
order to know how the relevant operators act in representation spaces of
osp(1|2), we study all unitary, irreducible star representations of this Lie
superalgebra. Such a classification has already been made by J.W.B. Hughes, but
we reexamine this classification using elementary arguments.


  The mass shift, width broadening, and spectral density for the $\omega$ meson
in a heat bath of nucleons and pions is calculated using a general formula
which relates the self-energy to the forward scattering amplitude. We use
experimental data to saturate the scattering amplitude at low energies with
resonances and include a background Pomeron term, while at high energies a
Regge parameterization is used. The peak of the spectral density is little
shifted from its vacuum position, but the width is considerably increased due
to collisional broadening. At normal nuclear matter density and a temperature
of 150 MeV the spectral density of the $\omega$ meson has a width of 140 MeV.
Zero temperature nuclear matter is also discussed.


  Recent studies on the phenomenology of ageing in certain many-particle
systems which are at a critical point of their non-equilibrium steady-states,
are reviewed. Examples include the contact process, the parity-conserving
branching-annihilating random walk, two exactly solvable particle-reaction
models and kinetic growth models. While the generic scaling descriptions known
from magnetic system can be taken over, some of the scaling relations between
the ageing exponents are no longer valid. In particular, there is no obvious
generalization of the universal limit fluctuation-dissipation ratio. The form
of the scaling function of the two-time response function is compared with the
prediction of the theory of local scale-invariance.


  The main goal of this manuscript is to prove the existence of insensitizing
controls for the fourth-order dispersive nonlinear Schr\"odinger equation with
cubic nonlinearity. To obtain the main result we prove a null controllability
property for a coupled fourth-order Schr\"odinger cascade type system with
zero-order coupling which is equivalent to the insensitizing control problem.
Precisely, employing a new Carleman estimate, we first obtain a null
controllability result for the linearized system around zero, and then the null
controllability for the nonlinear case is extended using an inverse mapping
theorem.


  We analyze 2+1 dimensional Yang-Mills theory regularized on a lattice with
twisted boundary conditions in the spatial directions. In previous work it was
shown that the observables in the non-zero electric flux sectors obey the
so-called $x$-scaling, i.e. depend only on the dimensionless variable $x\propto
NL/b$ and the angle $\tilde\theta$ given by the parameters of the twist ($L$
being the length of the spatial torus and $b$ the inverse 't Hooft coupling).
It is conjectured that this scaling is obeyed by all physical quantities. In
this work we extend the previous analyses to the zero electric flux (glueball)
sector. We study the mass of the lightest scalar glueball in two theories with
different $N$ but matching $x$ and $\tilde\theta$ in a wide range of couplings
from the perturbative small-volume regime to the non-perturbative one. We find
that the results are consistent with the $x$-scaling hypothesis.


  A signed probability distribution may extend a given traditional probability
from observable events to all events. We formalize and illustrate this
approach. We also illustrate its limitation. We argue that the right question
is not what negative probabilities are but what they are for.


  We introduce structured decompositions: category-theoretic generalizations of
many combinatorial invariants -- including tree-width, layered tree-width,
co-tree-width and graph decomposition width -- which have played a central role
in the study of structural and algorithmic compositionality in both graph
theory and parameterized complexity. Structured decompositions allow us to
generalize combinatorial invariants to new settings (for example decompositions
of matroids) in which they describe algorithmically useful structural
compositionality. As an application of our theory we prove an algorithmic meta
theorem for the Sub_P-composition problem which, when instantiated in the
category of graphs, yields compositional algorithms for NP-hard problems such
as: Maximum Bipartite Subgraph, Maximum Planar Subgraph and Longest Path.


  Large Language Models (LLMs) have revolutionized the field of Natural
Language Processing thanks to their ability to reuse knowledge acquired on
massive text corpora on a wide variety of downstream tasks, with minimal (if
any) tuning steps. At the same time, it has been repeatedly shown that LLMs
lack systematic generalization, which allows to extrapolate the learned
statistical regularities outside the training distribution. In this work, we
offer a systematic benchmarking of GPT-4, one of the most advanced LLMs
available, on three algorithmic tasks characterized by the possibility to
control the problem difficulty with two parameters. We compare the performance
of GPT-4 with that of its predecessor (GPT-3.5) and with a variant of the
Transformer-Encoder architecture recently introduced to solve similar tasks,
the Neural Data Router. We find that the deployment of advanced prompting
techniques allows GPT-4 to reach superior accuracy on all tasks, demonstrating
that state-of-the-art LLMs constitute a very strong baseline also in
challenging tasks that require systematic generalization.


  An explicit expression for the numbers $A(n,r;3)$ describing the refined
3-enumeration of alternating sign matrices is given. The derivation is based on
the recent results of Stroganov for the corresponding generating function. As a
result, $A(n,r;3)$'s are represented as 1-fold sums which can also be written
in terms of terminating ${}_4F_3$ series of argument 1/4.


  Human activity recognition (HAR) in wearable computing is typically based on
direct processing of sensor data. Sensor readings are translated into
representations, either derived through dedicated preprocessing, or integrated
into end-to-end learning. Independent of their origin, for the vast majority of
contemporary HAR, those representations are typically continuous in nature.
That has not always been the case. In the early days of HAR, discretization
approaches have been explored - primarily motivated by the desire to minimize
computational requirements, but also with a view on applications beyond mere
recognition, such as, activity discovery, fingerprinting, or large-scale
search. Those traditional discretization approaches, however, suffer from
substantial loss in precision and resolution in the resulting representations
with detrimental effects on downstream tasks. Times have changed and in this
paper we propose a return to discretized representations. We adopt and apply
recent advancements in Vector Quantization (VQ) to wearables applications,
which enables us to directly learn a mapping between short spans of sensor data
and a codebook of vectors, resulting in recognition performance that is
generally on par with their contemporary, continuous counterparts - sometimes
surpassing them. Therefore, this work presents a proof-of-concept for
demonstrating how effective discrete representations can be derived, enabling
applications beyond mere activity classification but also opening up the field
to advanced tools for the analysis of symbolic sequences, as they are known,
for example, from domains such as natural language processing. Based on an
extensive experimental evaluation on a suite of wearables-based benchmark HAR
tasks, we demonstrate the potential of our learned discretization scheme and
discuss how discretized sensor data analysis can lead to substantial changes in
HAR.


  A desirable property of an autocovariance estimator is to be robust to the
presence of additive outliers. It is well-known that the sample autocovariance,
being based on moments, does not have this property. Hence, the use of an
autocovariance estimator which is robust to additive outliers can be very
useful for time-series modeling. In this paper, the asymptotic properties of
the robust scale and autocovariance estimators proposed by Rousseeuw and Croux
(1993) and Genton and Ma (2000) are established for Gaussian processes, with
either short-range or long-range dependence. It is shown in the short-range
dependence setting that this robust estimator is asymptotically normal at the
rate $\sqrt{n}$, where $n$ is the number of observations. An explicit
expression of the asymptotic variance is also given and compared to the
asymptotic variance of the classical autocovariance estimator. In the
long-range dependence setting, the limiting distribution displays the same
behavior than that of the classical autocovariance estimator, with a Gaussian
limit and rate $\sqrt{n}$ when the Hurst parameter $H$ is less 3/4 and with a
non-Gaussian limit (belonging to the second Wiener chaos) with rate depending
on the Hurst parameter when $H \in (3/4,1)$. Some Monte-Carlo experiments are
presented to illustrate our claims and the Nile River data is analyzed as an
application. The theoretical results and the empirical evidence strongly
suggest using the robust estimators as an alternative to estimate the
dependence structure of Gaussian processes.


  Previously, self-dual codes have been constructed from weighing matrices, and
in particular from conference matrices (skew and symmetric). In this paper,
codes constructed from matrices of skew symmetric type whose determinants reach
the Ehlich-Wojtas' bound are presented. A necessary and sufficient condition
for these codes to be self-dual is given, and examples are provided for lengths
up to 52.


  The equilibrium properties of classical self-gravitating systems in the grand
canonical ensemble are studied by using the correspondence with an euclidean
field theory with infrared and ultraviolet cutoffs. It is shown that the system
developes a first order phase transition between a low and a high density
regime. In addition, due to the long range of the gravitational potential, the
system is close to criticality within each phase, with the exponents of mean
field theory. The coexistence of a sharp first order transition and critical
behavior can explain both the presence of voids in large regions of the
universe as well as the self-similar density correlations in terms of
self-gravity alone.


  Hypertree decompositions (HDs), as well as the more powerful generalized
hypertree decompositions (GHDs), and the yet more general fractional hypertree
decompositions (FHDs) are hypergraph decomposition methods successfully used
for answering conjunctive queries and for solving constraint satisfaction
problems. Every hypergraph $H$ has a width relative to each of these methods:
its hypertree width $hw(H)$, its generalized hypertree width $ghw(H)$, and its
fractional hypertree width $fhw(H)$, respectively. It is known that $hw(H)\leq
k$ can be checked in polynomial time for fixed $k$, while checking $ghw(H)\leq
k$ is NP-complete for $k \geq 3$. The complexity of checking $fhw(H)\leq k$ for
a fixed $k$ has been open for over a decade.
  We settle this open problem by showing that checking $fhw(H)\leq k$ is
NP-complete, even for $k=2$. The same construction allows us to prove also the
NP-completeness of checking $ghw(H)\leq k$ for $k=2$. After that, we identify
meaningful restrictions which make checking for bounded $ghw$ or $fhw$
tractable or allow for an efficient approximation of the $fhw$.


  We give formulas for the number of representations of non negative integers
by various quadratic forms. We also give evaluations in the case of sum of two
cubes (cubic case) and the quintic case, as well. We introduce a class of
generalized triangular numbers and give several evaluations. Finally, we
present a mean value asymptotic formula for the number of representations of an
integer as sum of two squares known as the Gauss circle problem.


  Event-by-event fluctuations of conserved charges - such as electric charge,
strangeness, and baryon number - in ultrarelativistic heavy-ion collisions
provide insight into the properties of the quark-gluon plasma and the QCD phase
diagram. They can be related to the higher moments of the multiplicity
distributions of identified particles, such as the $\Lambda$ baryon which
carries both strangeness and baryon number and is thus of particular interest.
We present the first measurement of net-$\Lambda$ fluctuations in Pb-Pb
collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV as a function of centrality
and the pseudorapidity acceptance of the measurement. The results are compared
to expectations of the effects of global baryon number conservation as well as
to predictions from the HIJING Monte Carlo event generator. In this analysis
the Identity Method is applied in a novel way to account for the combinatoric
background in the invariant mass distribution.


  Transport of scalar fields in compressible flow is investigated. The
effective equations governing the transport at scales large compared to those
of the advecting flow are derived by using multi-scale techniques. Ballistic
transport generally takes place when both the solenoidal and the potential
components of the velocity do not vanish, despite of the fact that it has zero
average value. The calculation of the effective ballistic velocity $V_b$ is
reduced to the solution of one auxiliary equation. An analytic expression for
$V_b$ is derived in some special instances, i.e. flows depending on a single
coordinate, random with short correlation times and slightly compressible
cellular flow. The effective mean velocity $V_b$ vanishes for velocity fields
which are either incompressible or potential and time-independent. For generic
compressible flow, the most general conditions ensuring the absence of
ballistic transport are isotropy and/or parity invariance. When $V_b$ vanishes
(or in the frame of reference moving with velocity $V_b$), standard diffusive
transport takes place. It is known that diffusion is always enhanced by
incompressible flow. On the contrary, we show that diffusion is depleted in the
presence of time-independent potential flow. Trapping effects due to potential
wells are responsible for this depletion. For time-dependent potential flow or
generic compressible flow, transport rates are enhanced or depleted depending
on the detailed structure of the velocity field.


  Introduced by Dal Lago and Hofmann, quantitative realizability is a technique
used to define models for logics based on Multiplicative Linear Logic. A
particularity is that functions are interpreted as bounded time computable
functions. It has been used to give new and uniform proofs of soundness of
several type systems with respect to certain time complexity classes. We
propose a reformulation of their ideas in the setting of Krivine's classical
realizability. The framework obtained generalizes Dal Lago and Hofmann's
realizability, and reveals deep connections between quantitative realizability
and a linear variant of Cohen's forcing.


  The Kazhdan-Lusztig polynomials for finite Weyl groups arise in the geometry
of Schubert varieties and representation theory. It was proved very soon after
their introduction that they have nonnegative integer coefficients, but no
completely combinatorial interpretation for them is known in general. Deodhar
(1990) has given a framework for computing the Kazhdan-Lusztig polynomials,
which generally involves recursion. We define embedded factor pattern avoidance
for general Coxeter groups and use it to characterize when Deodhar's algorithm
yields a simple combinatorial formula for the Kazhdan-Lusztig polynomials of
finite Weyl groups. Equivalently, if $(W, S)$ is a Coxeter system for a finite
Weyl group, we classify the elements $w \in W$ for which the Kazhdan-Lusztig
basis element $C'_w$ can be written as a monomial of $C'_s$ where $s \in S$.
This work generalizes results of Billey-Warrington (2001) which identified the
Deodhar elements in type $A$ as 321-hexagon-avoiding permutations, and
Fan-Green (1997) which identified the fully-tight Coxeter groups.


  Based on the multiband (BVRIJHKL) photometric observations of the active red
giant PZ Mon performed for the first time in the winter season of 2017-2018, we
have determined the main characteristics of the spotted stellar surface in a
parametric three-spot model. The unspotted surface temperature is Teff=4730 K,
the temperature of the cool spots is Tspot=3500 K, their relative area is about
41%, and the temperature of the warm spots is Twarm=4500 K with a maximum
relative area up to 20%. The distribution of spots over the stellar surface has
been modeled. The warm spots have been found to be distributed at various
longitudes in the hemisphere on the side of the secondary component and are
most likely a result of its influence.


  The finite range adiabatic wave approximation provides a practical method to
analyze (d,p) or (p,d) reactions, however until now the level of accuracy
obtained in the description of the reaction dynamics has not been determined.
In this work, we perform a systematic comparison between the finite range
adiabatic wave approximation and the exact Faddeev method. We include studies
of $^{11}$Be(p,d)$^{10}$Be(g.s.) at $E_p=$5, 10 and 35 MeV;
$^{12}$C(d,p)$^{13}$C(g.s.) at $E_d=$7, 12 and 56 MeV and
$^{48}$Ca(d,p)$^{49}$Ca(g.s.) at $E_d=$19, 56 and 100 MeV. Results show that
the two methods agree within $\approx 5%$ for a range of beam energies ($E_d
\approx 20-40$ MeV) but differences increase significantly for very low
energies and for the highest energies. Our tests show that ADWA agrees best
with Faddeev when the angular momentum transfer is small $\Delta l=0$ and when
the neutron-nucleus system is loosely bound.


  CAPTCHAs/HIPs are security mechanisms that try to prevent automatic abuse of
services. They are susceptible to learning attacks in which attackers can use
them as oracles. Kwon and Cha presented recently a novel algorithm that intends
to avoid such learning attacks and "detect all bots". They add uncertainties to
the grading of challenges, and also use trap images designed to detect bots.
The authors suggest that a major IT corporation is studying their proposal for
mainstream implementation. We present here two fundamental design flaws
regarding their trap images and uncertainty grading. These leak information
regarding the correct grading of images. Exploiting them, an attacker can use
an UTS-CAPTCHA as an oracle, and perform a learning attack. Our testing has
shown that we can increase any reasonable initial success rate up to 100%.


  This paper is an attempt to bring together two approaches to language
analysis. The possible use of probabilistic information in principle-based
grammars and parsers is considered, including discussion on some theoretical
and computational problems that arise. Finally a partial implementation of
these ideas is presented, along with some preliminary results from testing on a
small set of sentences.


  We present a variant of the Theory of Lorentzian (i. e. with a hyperbolic
generalized Cartan matrix) Kac-Moody algebras recently developed by V. A.
Gritsenko and the author. It is closely related with and strongly uses results
of R. Borcherds. This theory should generalize well-known Theories of finite
Kac-Moody algebras (i. e. classical semisimple Lie algebras corresponding to
positive generalized Cartan matrices) and affine Kac-Moody algebras
(corresponding to semi-positive generalized Cartan matrices).
  Main features of the Theory of Lorentzian Kac-Moody algebras are: One should
consider generalized Kac-Moody algebras introduced by Borcherds. Denominator
function should be an automorphic form on IV type Hermitian symmetric domain
(first example of this type related with Leech lattice was found by Borcherds).
The Kac-Moody algebra is graded by an integral hyperbolic lattice $S$. Weyl
group acts in the hyperbolic space related with $S$ and has a fundamental
polyhedron $\Cal M$ of finite (or almost finite) volume and a lattice Weyl
vector.
  There are results and conjectures which permit (in principle) to get a
``finite'' list of all possible Lorentzian Kac-Moody algebras. Thus, this
theory looks very similar to Theories of finite and affine Kac-Moody algebras
but is much more complicated. There were obtained some classification results
on Lorentzian Kac-Moody algebras and many of them were constructed.


  Convection that develops behind the shock front during the first second of a
core-collapse supernova explosion is believed to play a crucial role in the
explosion mechanism. We demonstrate that the resulting turbulent density
fluctuations may be directly observable in the neutrino signal starting at t>~
3-4 s after the onset of the explosion. The effect comes from the modulation of
the MSW flavor transformations by the turbulent density fluctuations. We derive
a simple and general criterion for neutrino flavor depolarization in a
Kolmogorov-type turbulence and apply it to the turbulence seen in modern
numerical simulations. The turbulence casts a "shadow", by making other
features, such as the shock front, unobservable in the density range covered by
the turbulence.


  We derive the optimal universal broadcasting for mixed states of qubits. We
show that the nobroadcasting theorem cannot be generalized to more than a
single input copy. Moreover, for four or more input copies it is even possible
to purify the input states while broadcasting. We name such purifying
broadcasting superbroadcasting.


  We describe local light-ray rotation in terms of complex refractive indices.
We show that Fermat's principle holds, and we derive an extended Snell's law.
The change in the angle of a light ray with respect to the normal to a
refractive-index interface is described by the modulus of the refractive-index
ratio, the rotation around the interface normal is described by the argument of
the refractive-index ratio.


  Within a spin-polarized LMTO approach in the Atomic-Sphere approximation we
calculate ab initio the magnetic properties of various binary and ternary
multilayers composed of Fe, Co, Ni, Cr, V and Cu. The emphasis lies on the
indirect exchange interaction of the magnetic sandwiches across the
antiferromagnetic or non-magnetic spacers, and on the profiles of the intrinsic
resp. induced magnetic moments. Among other results we find: (i) that Ni is
very sensitive on its neighborhood and that (ii) at the interface to Fe, V gets
almost as strongly polarized as Cr, whereas in the interiour layers, the V
sandwich remains nonpolarized.


  "Electromagnetic mass" where gravitational mass and other physical quantities
originate from the electromagnetic field alone has a century long distinguished
history. In the introductory chapter we have divided this history into three
broad categories -- classical, quantum mechanical and general relativistic.
Each of the categories has been described at a length to get the detailed
picture of the physical background. Recent developments on Repulsive
Electromagnetic Mass Models are of special interest in this introductory part
of the thesis. In this context we have also stated motivation of our work. In
the subsequent chapters we have presented our results and their physical
significances. It is concluded that the electromagnetic mass models which are
the sources of purely electromagnetic origin ``have not only heuristic flavor
associated with the conjecture of Lorentz but even a physics having
unconventional yet novel features characterizing their own contributions
independent of the rest of the physics".


  If X is a compact Hausdorff space, supplied with a homeomorphism, then a
crossed product involutive Banach algebra is naturally associated with these
data. If X consists of one point, then this algebra is the group algebra of the
integers. In this paper, we study spectral synthesis for the closed ideals of
this associated algebra in two versions, one modeled after C(X), and one
modeled after the group algebra of the integers. We identify the closed ideals
which are equal to (what is the analogue of) the kernel of their hull, and
determine when this holds for all closed ideals, i.e., when spectral synthesis
holds. In both models, this is the case precisely when the homeomorphism has no
periodic points.


  When using hexagonal boron-nitride (hBN) as a substrate for graphene, the
resulting moir\'e pattern creates secondary Dirac points. By encapsulating a
multilayer graphene within aligned hBN sheets the controlled moir\'e stacking
may offer even richer benefits. Using advanced tight-binding simulations on
atomistically-relaxed heterostructures, here we show that the gap at the
secondary Dirac point can be opened in selected moir\'e-stacking
configurations, and is independent of any additional vertical gating of the
heterostructure. On the other hand, gating can broadly tune the gap at the
principal Dirac point, and may thereby strongly compress the first moir\'e
mini-band in width against the moir\'e-induced gap at the secondary Dirac
point. We reveal that in hBN-encapsulated bilayer graphene this novel mechanism
can lead to isolated bands flatter than 10~meV under moderate gating, hence
presenting a convenient pathway towards electronically-controlled
strongly-correlated states on demand.


  The question of how network topology influences emergent synchronized
oscillations in excitable media is addressed. Coupled van der
Pol-FitzHugh-Nagumo elements arranged either on regular rings or on clusters of
the square lattice are investigated. Clustered and declustered rings are
constructed to have the same number of next-nearest-neighbors (four) and a
number of links twice that of nodes. The systems are chosen to be
close-to-threshold, allowing global oscillations to be triggered by a weak
diversity among the constituents that, by themselves, would be non-oscillating.
The results clearly illustrate the crucial role played by network topology. In
particular we found that network performance (oscillatory behavior and
synchronization) is mainly determined by the network average path length and by
the standard deviation of path lengths. The shorter the average path length and
the smaller the standard deviation, the better the network performance. Local
properties, as characterized by the clustering coefficient, are less important.
In addition we comment on the mechanisms that sustain synchronized oscillations
and on the transient times needed to reach these stationary regimes.


  In this letter, we improve the results in [5] by relaxing the symmetry
assumption and also taking the noise term into account. The author examines two
discrete-time autonomous linear systems whose motivation comes from a neural
network point of view in [5]. Here, we examine the following discrete-time
autonomous linear system: ${\mathbf x}(k+1) = {\mathbf A} {\mathbf x}(k) +
{\mathbf b}$ where ${\mathbf A}$ is any real square matrix with linearly
independent eigenvectors whose largest eigenvalue is real and its norm is
larger than 1, and vector ${\mathbf b}$ is constant. Using the same "SIR"
("Signal"-to-"Interference"-Ratio) concept as in [4] and [5], we show that the
ultimate "SIR" is equal to $\frac{a_{ii}}{\lambda_{max} - a_{ii}}$, $i=1, 2,
>..., N$, where $N$ is the number of states, $a_{ii}$ is the diagonal elements
of matrix ${\bf A}$, and $\lambda_{max}$ is the (single or multiple) eigenvalue
with maximum norm.


  It is well known that a closed loop of magnetic dipoles can give rise to the
rather elusive toroidal moment. However, artificial structures required to
generate the necessary magnetic moments are typically optically large, complex
to make and easily compromised by the kinetic inductance at high frequencies.
Instead of using magnetic dipoles, we propose a minimal model based on just
three aligned discrete electric dipoles in which the occurrence of resonant
toroidal modes is guaranteed by symmetry. The advantage of this model is its
simplicity and the same model supports toroidal moments from the microwave
regime up to optical frequencies as exemplified by a three-antenna array and a
system consisting of three nano-sized plasmonic particles. Both the microwave
and high-frequency configurations exhibit non-radiating "anapoles". Experiments
in the microwave regime confirm the theoretical predictions.


  The existence and uniqueness of fixed points of both the cyclic self-mapping
and its associate composite self-mappings on each of the subsets are
investigated if the subsets in the cyclic disposal are nonempty, bounded and of
nonempty convex intersection is investigated


  Let X be a smooth elliptic fibration over a smooth base B. Under mild
assumptions, we establish a Fourier-Mukai equivalence between the derived
categories of two objects, each of which is an O^* gerbe over a genus one
fibration which is a twisted form of X. The roles of the gerbe and the twist
are interchanged by our duality. We state a general conjecture extending this
to allow singular fibers, and we prove the conjecture when X is a surface. The
duality extends to an action of the full modular group. This duality is related
to the Strominger-Yau-Zaslow version of mirror symmetry, to twisted sheaves,
and to non-commutative geometry.


  We investigate ground state properties of spin-1 bosonic system trapped in
optical lattice with extended standard basis operator (SBO) method. For both
ferromagnetic ($U_2<0$) and antiferromagnetic ($U_2>0$) systems, we
analytically figure out the symmetry properties in Mott-insulator and
superfluid phases, which would provide a deeper insight into the MI-SF phase
transition process. Then by applying self-consistent approach to the method, we
include the effect of quantum and thermal fluctuations and derive the MI-SF
transition phase diagram, which is in quantitative agreement with recent
Monte-Carlo simulation at zero temperature, and at finite temperature, we find
the underestimation of finite-temperature-effect in the mean-field
approximation method. If we further consider the spin excitations in the
insulating states of spin-1 system in external field, distinct spin phases are
expected. Therefore, in the Mott lobes with $n=1$ and $n=2$ atoms per site, we
give analytical and numerical boundaries of the singlet, nematic, partially
magnetic and ferromagnetic phases in the magnetic phase diagrams.


  With the continuous growth of internet users and media content, it is very
hard to track down hateful speech in audio and video. Converting video or audio
into text does not detect hate speech accurately as human sometimes uses
hateful words as humorous or pleasant in sense and also uses different voice
tones or show different action in the video. The state-ofthe-art hate speech
detection models were mostly developed on a single modality. In this research,
a combined approach of multimodal system has been proposed to detect hate
speech from video contents by extracting feature images, feature values
extracted from the audio, text and used machine learning and Natural language
processing.


  We propose an observable for ultra-high energy cosmic ray (UHECR) physics:
the harmonic-space cross-correlation power spectrum between the arrival
directions of UHECRs and the large-scale cosmic structure mapped by galaxies.
This cross-correlation has not yet been considered in the literature, and it
permits a direct theoretical modelling of the main astrophysical components. We
describe the expected form of the cross-correlation and show how, if the
distribution of UHECR sources trace the large-scale cosmic structure, it could
be easier to detect with current data than the UHECR auto-correlation.
Moreover, the cross-correlation is more sensitive to UHECR anisotropies on
smaller angular scales, more robust to systematic uncertainties, and it could
be used to determine the redshift distribution of UHECR sources, making it a
valuable tool in determining their origins and properties.


  The equivariant CR minimal immersions from the round $3$-sphere $S^3$ into
the complex projective space $\mathbb CP^n$ have been classified by the third
author explicitly (J London Math Soc 68: 223-240, 2003). In this paper, by
employing the equivariant condition which implies that the induced metric is
left-invariant, and that all geometric properties of $S^3={\rm SU}(2)$ endowed
with a left-invariant metric can be expressed in terms of the structure
constants of the Lie algebra $\mathfrak{su}(2)$, we establish an extended
classification theorem for equivariant CR minimal immersions from the
$3$-sphere $S^3$ into $\mathbb CP^n$ without the assumption of constant
sectional curvatures.


  We extract J and K_s magnitudes from the 2MASS Point Source Catalog for
approximately 6 million stars with 8 < K_s < 13 in order to build an A_K
extinction map within 10 degrees of the Galactic centre. The extinction was
determined by fitting the upper giant branch of (K_s, J-K_s) colour-magnitude
diagrams to a dereddened upper giant branch mean locus built from previously
studied Bulge fields. The extinction values vary from A_K=0.05 in the edges of
the map up to A_K=3.2 close to the Galactic centre. The 2MASS extinction map
was compared to that recently derived from DENIS data. Both maps agree very
well up to A_K=1.0. The 2MASS extinction values were also compared to those
obtained from dust emission in the far infrared using DIRBE/IRAS. Several
systematic effects likely to bias this comparison were addressed, including the
presence of dust on the background of the bulk of 2MASS stars used in the
extinction determination. For the region with $3^{\circ}<|b|<5^{\circ}$, where
the dust contribution on the far side of the Galaxy is $\approx$ 5%, the two
extinction determinations correlate well, but the dust emission A_K values are
systematically higher than those from 2MASS. A calibration correction factor of
76% for the DIRBE/IRAS dust emission extinction is needed to eliminate this
systematic effect. Similar comparisons were also carried out for the
$1^{\circ}<|b|<3^{\circ}$ and $|b| < 0.5^{\circ}$ strips. An asymmetry relative
to the Galactic plane is observed in the dust maps, roughly in the sense that
A_K values are 60% smaller in the south than in the north for
$1^{\circ}<|b|<5^{\circ}$. This asymmetry is due to the presence of foreground
dust clouds mostly in the northern region of the Bulge.


  A surface-acoustic-wave (SAW) driven light-emitting-diode structure that can
implement a single-photon-source for quantum-cryptography applications is
demonstrated. Our lateral n-i-p junction is realized starting from an undoped
GaAs/AlGaAs quantum well by gating. It incorporates interdigitated transducers
for SAW generation and lateral gates for current control. We demonstrate
acoustoelectric transport and SAW-driven electroluminescence. The
acoustoelectric current can be controlled down to complete pinch-off by means
of the lateral gates.


  We investigate the decay of $a^+_1(1260) \to \pi^+ \pi^+ \pi^-$ with the
assumption that the $a_1(1260)$ is dynamically generated from the coupled
channel $\rho \pi$ and $\bar{K}K^*$ interactions. In addition to the tree level
diagrams that proceed via $a^+_1(1260) \to \rho^0 \pi^+ \to \pi^+\pi^+ \pi^-$,
we take into account also the final state interactions of $\pi\pi \to \pi \pi$
and $K \bar{K} \to \pi \pi$. We calculate the invariant $\pi^+ \pi^-$ mass
distribution and also the total decay width of $a^+_1(1260) \to \pi^+ \pi^+
\pi^-$ as a function of the mass of $a_1(1260)$. The calculated total decay
width of $a_1(1260)$ is significantly different from other model calculations
and tied to the dynamical nature of the $a_1(1260)$ resonance. The future
experimental observations could test of model calculations and would provide
vary valuable information on the relevance of the $\rho \pi$ component in the
$a_1(1260)$ wave function.


  This is the first work to investigate the effectiveness of BERT-based
contextual embeddings in active learning (AL) tasks on cold-start scenarios,
where traditional fine-tuning is infeasible due to the absence of labeled data.
Our primary contribution is the proposal of a more robust fine-tuning pipeline
- DoTCAL - that diminishes the reliance on labeled data in AL using two steps:
(1) fully leveraging unlabeled data through domain adaptation of the embeddings
via masked language modeling and (2) further adjusting model weights using
labeled data selected by AL. Our evaluation contrasts BERT-based embeddings
with other prevalent text representation paradigms, including Bag of Words
(BoW), Latent Semantic Indexing (LSI), and FastText, at two critical stages of
the AL process: instance selection and classification. Experiments conducted on
eight ATC benchmarks with varying AL budgets (number of labeled instances) and
number of instances (about 5,000 to 300,000) demonstrate DoTCAL's superior
effectiveness, achieving up to a 33% improvement in Macro-F1 while reducing
labeling efforts by half compared to the traditional one-step method. We also
found that in several tasks, BoW and LSI (due to information aggregation)
produce results superior (up to 59% ) to BERT, especially in low-budget
scenarios and hard-to-classify tasks, which is quite surprising.


  We study the influence of the relative size of the reservoir on the
adsorption isotherms of a fluid in disordered or inhomogeneous mesoporous
solids. We consider both an atomistic model of a fluid in a simple, yet
structured pore, whose adsorption isotherms are computed by molecular
simulation, and a coarse-grained model for adsorption in a disordered
mesoporous material, studied by a density functional approach in a local
mean-field approximation. In both cases, the fluid inside the porous solid
exchanges matter with a reservoir of gas that is at the same temperature and
chemical potential and whose relative size can be varied, and the control
parameter is the total number of molecules present in the porous sample and in
the reservoir. Varying the relative sizes of the reservoir and the sample may
change the shape of the hysteretic isotherms, leading to a "reentrant" behavior
compared to the grand-canonical isotherm when the latter displays a jump in
density. We relate these phenomena to the organization of the metastable states
that are accessible for the adsorbed fluid at a given chemical potential or
density.


  The outbreak of COVID-19 led to a record-breaking race to develop a vaccine.
However, the limited vaccine capacity creates another massive challenge: how to
distribute vaccines to mitigate the near-end impact of the pandemic? In the
United States in particular, the new Biden administration is launching mass
vaccination sites across the country, raising the obvious question of where to
locate these clinics to maximize the effectiveness of the vaccination campaign.
This paper tackles this question with a novel data-driven approach to optimize
COVID-19 vaccine distribution. We first augment a state-of-the-art
epidemiological model, called DELPHI, to capture the effects of vaccinations
and the variability in mortality rates across age groups. We then integrate
this predictive model into a prescriptive model to optimize the location of
vaccination sites and subsequent vaccine allocation. The model is formulated as
a bilinear, non-convex optimization model. To solve it, we propose a coordinate
descent algorithm that iterates between optimizing vaccine distribution and
simulating the dynamics of the pandemic. As compared to benchmarks based on
demographic and epidemiological information, the proposed optimization approach
increases the effectiveness of the vaccination campaign by an estimated $20\%$,
saving an extra $4000$ extra lives in the United States over a three-month
period. The proposed solution achieves critical fairness objectives -- by
reducing the death toll of the pandemic in several states without hurting
others -- and is highly robust to uncertainties and forecast errors -- by
achieving similar benefits under a vast range of perturbations.


  We employ a feed-forward artificial neural network to extrapolate at large
model spaces the results of {\it ab-initio} hypernuclear No-Core Shell Model
calculations for the $\Lambda$ separation energy $B_\Lambda$ of the lightest
hypernuclei, $^3_\Lambda$H, $^4_\Lambda$H and $^4_\Lambda$He, obtained in
computationally accessible harmonic oscillator basis spaces using chiral
nucleon-nucleon, nucleon-nucleon-nucleon and hyperon-nucleon interactions. The
overfitting problem is avoided by enlarging the size of the input dataset and
by introducing a Gaussian noise during the training process of the neural
network. We find that a network with a single hidden layer of eight neurons is
sufficient to extrapolate correctly the value of the $\Lambda$ separation
energy to model spaces of size $N_{max}=100$. The results obtained are in
agreement with the experimental data in the case of $^3_\Lambda$H and the $0^+$
state of $^4_\Lambda$He, although they are off of the experiment by about $0.3$
MeV for both the $0^+$ and $1^+$states of $^4_\Lambda$H and the $1^+$ state of
$^4_\Lambda$He. We find that our results are in excellent agreement with those
obtained using other extrapolation schemes of the No-Core Shell Model
calculations, showing this that an ANN is a reliable method to extrapolate the
results of hypernuclear No-Core Shell Model calculations to large model spaces.


  We give short proofs of two classical results about the position of the
extremal particle in a branching Brownian motion, one concerning the median
position and another the almost sure behaviour.


  Radio frequency (RF) wireless power transfer (WPT) is a key technology for
future low-power wireless systems. However, the inherently low end-to-end power
transfer efficiency (PTE) is challenging for practical applications. The main
factors contributing to it are the channel losses, transceivers' power
consumption, and losses related, e.g., to the digital-to-analog converter
(DAC), high-power amplifier, and rectenna. Optimizing PTE requires careful
consideration of these factors, motivating the current work. Herein, we
consider an analog multi-antenna power transmitter that aims to charge a single
energy harvester. We first provide a mathematical framework to calculate the
harvested power from multi-tone signal transmissions and the system power
consumption. Then, we formulate the joint waveform and analog beamforming
design problem to minimize power consumption and meet the charging
requirements. Finally, we propose an optimization approach relying on swarm
intelligence to solve the specified problem. Simulation results quantify the
power consumption reduction as the DAC, phase shifters resolution, and antenna
length are increased, while it is seen that increasing system frequency results
in higher power consumption.


  We present a simple and general procedure for calculating the thermal
radiation coming from any stationary metric. The physical picture is that the
radiation arises as the quasi--classical tunneling of particles through a
gravitational barrier. We show that our procedure can reproduce the results of
Hawking and Unruh radiation. We also show that under certain kinds of
coordinate transformations the temperature of the thermal radiation will change
in the case of the Schwarzschild black holes. In addition we apply our
procedure to a rotating/orbiting system and show that in this case there is no
radiation, which has experimental implications for the polarization of
particles in circular accelerators.


  We investigate the physical nature of active galactic nuclei (AGNs) using
machine learning (ML) tools. We show that the redshift, $z$, bolometric
luminosity, $L_{\rm Bol}$, central mass of the supermassive black hole (SMBH),
$M_{\rm BH}$, Eddington ratio, $\lambda_{\rm Edd}$, and AGN class (obscured or
unobscured) can be reconstructed through multi-wavelength photometric
observations only. We trained a random forest regressor (RFR) ML-model on 7616
spectroscopically observed AGNs from the SPIDERS-AGN survey, which had
previously been cross-matched with soft X-ray observations (from ROSAT or XMM),
WISE mid-infrared photometry, and optical photometry from SDSS \textit{ugriz}
filters. We built a catalog of 21050 AGNs that were subsequently reconstructed
with the trained RFR; for 9687 sources, we found archival redshift
measurements. All AGNs were classified as either type 1 or type 2 using a
random forest classifier (RFC) algorithm on a subset of known sources. All
known photometric measurement uncertainties were incorporated via a
simulation-based approach. We present the reconstructed catalog of 21050 AGNs
with redshifts ranging from $ 0 < z < 2.5$. We determined $z$ estimations for
11363 new sources, with both accuracy and outlier rates within 2%. The
distinction between type 1 or type 2 AGNs could be identified with respective
efficiencies of 94% and 89%. The estimated obscuration level, a proxy for AGN
classification, of all sources is given in the dataset. The $L_{\rm Bol}$,
$M_{\rm BH}$, and $\lambda_{\rm Edd}$ values are given for 21050 new sources
with their estimated error. These results have been made publicly available.
The release of this catalog will advance AGN studies by presenting key
parameters of the accretion history of 6 dex in luminosity over a wide range of
$z$.


  A new approach called NAF (the Neural Attention Forest) for solving
regression and classification tasks under tabular training data is proposed.
The main idea behind the proposed NAF model is to introduce the attention
mechanism into the random forest by assigning attention weights calculated by
neural networks of a specific form to data in leaves of decision trees and to
the random forest itself in the framework of the Nadaraya-Watson kernel
regression. In contrast to the available models like the attention-based random
forest, the attention weights and the Nadaraya-Watson regression are
represented in the form of neural networks whose weights can be regarded as
trainable parameters. The first part of neural networks with shared weights is
trained for all trees and computes attention weights of data in leaves. The
second part aggregates outputs of the tree networks and aims to minimize the
difference between the random forest prediction and the truth target value from
a training set. The neural network is trained in an end-to-end manner. The
combination of the random forest and neural networks implementing the attention
mechanism forms a transformer for enhancing the forest predictions. Numerical
experiments with real datasets illustrate the proposed method. The code
implementing the approach is publicly available.


  The Covid-19 pandemic introduces new challenges and constraints for return to
work business planning. We describe a space allocation problem that
incorporates social distancing constraints while optimising the number of
available safe workspaces in a return to work scenario. We propose and
demonstrate a graph based approach that solves the optimisation problem via
modelling as a bipartite graph of disconnected components over a graph of
constraints. We compare results obtained with a constrained random walk and a
linear programming approach.


  The BCS and HFB theories which can accommodate the pairing correlations in
the ground states of atomic nuclei are presented. As an application of the
pairing theories, we investigate the spatial extension of weakly bound Ne and C
isotopes by taking into account the pairing correlation with the
Hartree-Fock-Bogoliubov (HFB) method and a 3-body model, respectively. We show
that the odd-even staggering in the reaction cross sections of $^{30,31,32}$Ne
and $^{14,15,16}$C are successfully reproduced, and thus the staggering can be
attributed to the unique role of pairing correlations in nuclei far from the
stability line. A correlation between a one-neutron separation energy and the
anti-halo effect is demonstrated for $s$- and p-waves using the HFB wave
functions. We also propose effective density-dependent pairing interactions
which reproduce both the neutron-neutron ($nn$) scattering length at zero
density and the neutron pairing gap in uniform matter. Then, we apply these
interactions to study pairing gaps in semi-magic finite nuclei, such as Ca, Ni,
Sn and Pb isotopic chains.


  We consider two celebrated criteria for defining the non-classicality of
bipartite bosonic quantum systems, the first stemming from information
theoretic concepts and the second from physical constraints on the quantum
phase-space. Consequently, two sets of allegedly classical states are singled
out: i) the set C composed of the so called classical-classical (CC)
states---separable states that are locally distinguishable and do not possess
quantum discord; ii) the set P of states endowed with a positive
P-representation (P-classical states)---mixture of Glauber coherent states
that, e.g., fail to show negativity of their Wigner function. By showing that C
and P are almost disjoint, we prove that the two defining criteria are
maximally inequivalent. Thus, the notions of classicality that they put forward
are radically different. In particular, generic CC states show quantumness in
their P-representation and, viceversa, almost all P-classical states have
positive quantum discord, hence are not CC. This inequivalence is further
elucidated considering different applications of P-classical and CC states. Our
results suggest that there are other quantum correlations in nature than those
revealed by entanglement and quantum discord.


  ASTROSAT is India's first satellite fully devoted to astronomical
observations covering a wide spectral band from optical to hard X-rays by a
complement of 4 co-aligned instruments and a Scanning Sky X-ray Monitor. One of
the instruments is Large Area X-ray Proportional Counter with 3 identical
detectors. In order to assess the performance of this instrument, a balloon
experiment with two prototype Large Area X-ray Proportional Counters (LAXPC)
was carried out on 2008 April 14. The design of these LAXPCs was similar to
those on the ASTROSAT except that their field of view (FOV) was 3$^{\circ}$
$\times$ 3$^{\circ}$ versus FOV of 1$^{\circ}$ $\times$ 1$^{\circ}$ for the
LAXPCs on the ASTROSAT. The LAXPCs are aimed at the timing and spectral studies
of X-ray sources in 3-80 keV region. In the balloon experiment, the LAXPC,
associated electronics and support systems were mounted on an oriented platform
which could be pre-programmed to track any source in the sky. A brief
description of the LAXPC design, laboratory tests, calibration and the detector
characteristics is presented here. The details of the experiment and background
counting rates of the 2 LAXPCs at the float altitude of about 41 km are
presented in different energy bands. The bright black hole X-ray binary Cygnus
X-1 (Cyg X-1) was observed in the experiment for $\sim$ 3 hours. Details of Cyg
X-1 observations, count rates measured from it in different energy intervals
and the intensity variations of Cyg X-1 detected during the observations are
presented and briefly discussed.


  SMC$^2$ is an efficient algorithm for sequential estimation and state
inference of state-space models. It generates $N_{\theta}$ parameter particles
$\theta^{m}$, and, for each $\theta^{m}$, it runs a particle filter of size
$N_{x}$ (i.e. at each time step, $N_{x}$ particles are generated in the state
space $\mathcal{X}$). We discuss how to automatically calibrate $N_{x}$ in the
course of the algorithm. Our approach relies on conditional Sequential Monte
Carlo updates, monitoring the state of the pseudo random number generator and
on an estimator of the variance of the unbiased estimate of the likelihood that
is produced by the particle filters, which is obtained using nonparametric
regression techniques. We observe that our approach is both less CPU intensive
and with smaller Monte Carlo errors than the initial version of SMC$^2$.


  A multidimensional generalization of Bailey's very-well-poised bilateral
basic hypergeometric ${}_6\psi_6$ summation formula and its Dougall type
${}_5H_5$ hypergeometric degeneration for $q\to 1$ is studied. The multiple
Bailey sum amounts to an extension corresponding to the case of a nonreduced
root system of certain summation identities associated to the reduced root
systems that were recently conjectured by Aomoto and Ito and proved by
Macdonald. By truncation, we obtain multidimensional analogues of the
very-well-poised unilateral (basic) hypergeometric Rogers ${}_6\phi_5$ and
Dougall ${}_5F_4$ sums (both nonterminating and terminating). The terminating
sums may be used to arrive at product formulas for the norms of recently
introduced ($q$-)Racah polynomials in several variables.


  We give a holographic explanation how the renormalization group approach to
singular perturbations in non-linear differential equations proposed by Chen,
Goldenfeld and Oono is indeed equivalent to a renormalization group method in
quantum field theories proposed by Gell-Mann and Low via AdS/CFT
correspondence.


  Broadband light sources play essential roles in diverse fields, such as
high-capacity optical communications, optical coherence tomography, optical
spectroscopy, and spectrograph calibration. Though an ultrabroadband
nonclassical state from standard spontaneous parametric down-conversion may
serve as a quantum counterpart, its detection and quantum characterization have
been a challenging task. Here we demonstrate the quantitative characterization
of a multimode structure in such an ultrabroadband (150 nm FWHM) squeezed state
at telecom wavelength (1.5 \mu m). The nonclassical photon distribution of our
highly multimode state is directly observed using a superconducting
transition-edge sensor. From the observed photon correlation functions, we show
that several tens of different squeezers are coexisting in the same spatial
mode. We anticipate our results and technique open up a new possibility to
generate and characterize nonclassical light sources for a large-scale optical
quantum network in the frequency domain.


  Even and odd vector modes in optical fibers are represented with linear
combinations of orbital angular momentum modes, and considered as single-photon
spin-orbit entangled states. It renders generating such states with fiber
structures possible.


  By a Wigner-function calculation, we evaluate the trace of a certain Gaussian
operator arising in the theory of a boson system subject to both finite
temperature and (weak) interaction. Thereby we rederive (and generalize) a
recent result by Kocharovsky, Kocharovsky, and Scully [Phys. Rev. A, vol. 61,
art. 053606 (2000)] in a way that is technically much simpler. One step uses a
special case of the response of Wigner functions to linear transformations, and
we demonstrate the general case by simple means. As an application we extract
the counting statistics for each mode of the Bose gas.


  Deep learning for human action recognition in videos is making significant
progress, but is slowed down by its dependency on expensive manual labeling of
large video collections. In this work, we investigate the generation of
synthetic training data for action recognition, as it has recently shown
promising results for a variety of other computer vision tasks. We propose an
interpretable parametric generative model of human action videos that relies on
procedural generation and other computer graphics techniques of modern game
engines. We generate a diverse, realistic, and physically plausible dataset of
human action videos, called PHAV for "Procedural Human Action Videos". It
contains a total of 39,982 videos, with more than 1,000 examples for each
action of 35 categories. Our approach is not limited to existing motion capture
sequences, and we procedurally define 14 synthetic actions. We introduce a deep
multi-task representation learning architecture to mix synthetic and real
videos, even if the action categories differ. Our experiments on the UCF101 and
HMDB51 benchmarks suggest that combining our large set of synthetic videos with
small real-world datasets can boost recognition performance, significantly
outperforming fine-tuning state-of-the-art unsupervised generative models of
videos.


  Every measurable function f on the circle can be represented as a sum of
harmonics with positive spectrum, converging in measure. For convergence almost
everywhere this is not true. We discuss several other subsets of Z for which
one might get a Menshov type representation converging almost everywhere or in
measure.


  We analyze Keck HIRES observations of a Lyman limit system at z=2.652 toward
Q2231-00. These observations afford the most comprehensive study of the
physical properties of a LL system to date. By comparing the ionic column
densities for Fe^+, Fe^{++}, Si^+, and Si^{3+} against calculations derived
from the CLOUDY software package, we have strictly constrained the ionization
state of this system. This has enabled us to calculate accurate abundances of a
Lyman limit system for the first time at z > 2, e.g., [Fe/H] = -0.5 \pm 0.1. We
also derive a total hydrogen column density, log N(H) = 20.73 \pm 0.2, which is
comparable to values observed for the damped lya systems.
  The system is special for exhibiting CII* 1335 absorption, allowing an
estimate of the electron density, n_e = 6.5 \pm 1.3 x 10^{-2} cm^{-3}. Coupling
this measurement with our knowledge of the ionization state, we derive the
following physical properties: (1) hydrogen volume density, n_H = 5.9 \pm 1.2 x
10^{-2} cm^{-3}, (2) path length, l = 3 \pm 1.6 kpc, and (3) ionizing
intensity, log J_{912} = -20.22 \pm 0.21. We point out that a number of the
physical properties (e.g. [Fe/H], N(H), n_H) resemble those observed for the
damped lya systems, which suggests this system may be the photoionized analog
of a damped system. The techniques introduced in this Letter should be
applicable to a number of Lyman limit systems and therefore enable a survey of
their chemical abundances and other physical properties.


  Uncertainty quantification is a fundamental yet unsolved problem for deep
learning. The Bayesian framework provides a principled way of uncertainty
estimation but is often not scalable to modern deep neural nets (DNNs) that
have a large number of parameters. Non-Bayesian methods are simple to implement
but often conflate different sources of uncertainties and require huge
computing resources. We propose a new method for quantifying uncertainties of
DNNs from a dynamical system perspective. The core of our method is to view DNN
transformations as state evolution of a stochastic dynamical system and
introduce a Brownian motion term for capturing epistemic uncertainty. Based on
this perspective, we propose a neural stochastic differential equation model
(SDE-Net) which consists of (1) a drift net that controls the system to fit the
predictive function; and (2) a diffusion net that captures epistemic
uncertainty. We theoretically analyze the existence and uniqueness of the
solution to SDE-Net. Our experiments demonstrate that the SDE-Net model can
outperform existing uncertainty estimation methods across a series of tasks
where uncertainty plays a fundamental role.


  Langevin dynamics simulations are performed to investigate ejection dynamics
of spherically confined flexible polymers through a pore. By varying the chain
length $N$ and the initial volume fraction $\phi_0$ of the monomers, two
scaling behaviors for the ejection velocity $v$ on the monomer number $m$ in
the cavity are obtained: $v \sim m^{1.25}\phi_0^{1.25}/N^{1.6}$ for large $m$
and $v \sim m^{-1.4}$ as $m$ is small. A robust scaling theory is developed by
dividing the process into the confined and the non-confined stages, and the
dynamical equation is derived via the study of energy dissipation. After
trimming the prior stage related to the escape of the head monomer across the
pore, the evolution of $m$ is shown to be well described by the scaling theory.
The ejection time exhibits two proper scaling behaviors:
$N^{2/(3\nu)+y_1}\phi_0^{-2/(3\nu)}$ and $N^{2+y_2}$ under the large and small
$\phi_0$- or $N$-conditions, respectively, where $y_1=1/3$, $y_2=1-\nu$, and
$\nu$ is the Flory exponent.


  We have used the Hubble Space Telescope to directly measure the angular size
of the large Kuiper belt object 2003 UB313. By carefully calibrating the point
spread function of a nearby field star, we measure the size of 2003 UB313 to be
34.3$\pm$1.4 milliarcseconds, corresponding to a diameter of 2400$\pm$100 km or
a size $\sim5$% larger than Pluto. The V band geometric albedo of 2003 UB313 is
$86\pm7$%. The extremely high albedo is consistent with the frosty methane
spectrum, the lack of red coloring, and the lack of observed photometric
variation on the surface of 2003 UB313. Methane photolysis should quickly
darken the surface of 2003 UB313, but continuous evaporation and redeposition
of surface ices appears capable of maintaining the extreme alebdo of this body.


  We consider scalar Wilson operators of ${\cal N}=4$ SYM at high spin, $s$,
and generic twist in the multi-color limit. We show that the corresponding
(non)linear integral equations (originating from the asymptotic Bethe Ansatz
equations) respect certain 'reciprocity' and functional 'self-tuning' relations
up to all terms $\frac{1}{s(\ln s)^n}$ (inclusive) at any fixed 't Hooft
coupling $\lambda$. Of course, this relation entails straightforwardly the
well-known (homonymous) relations for the anomalous dimension at the same order
in $s$. On this basis we give some evidence that wrapping corrections should
enter the non-linear integral equation and anomalous dimension expansions at
the next order $\frac{(\ln s)^{2}}{s^2}$, at fixed 't Hooft coupling, in such a
way to re-establish the aforementioned relation (which fails otherwise).


  Symmetric multiple zeta values (SMZVs) are elements in the ring of all
multiple zeta values modulo the ideal generated by $\zeta(2)$ introduced by
Kaneko-Zagier as counterparts of finite multiple zeta values. It is known that
symmetric multiple zeta values satisfy double shuffle relations and duality
relations. In this paper, we construct certain lifts of SMZVs which live in the
ring generated by all multiple zeta values and $2\pi i$ as certain iterated
integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty\}$ along a certain closed
path. We call this lifted values as refined symmetric multiple zeta values
(RSMZVs). We show double shuffle relations and duality relations for RSMZVs.
These relations are refinements of the double shuffle relations and the duality
relations of SMZVs. Furthermore we compare RSMZVs to other variants of lifts of
SMZVs. Especially, we prove that RSMZVs coincide with
Bachmann-Takeyama-Tasaka's $\xi$-values.


  The effects of asymptotically anti-de Sitter wormholes in low-energy field
theory are calculated in full detail for three different matter contents: a
conformal scalar field, an electromagnetic field and gravitons. There exists a
close relation between the choice of vacuum for the matter fields and the
selection of a basis of the Hilbert space of anti-de Sitter wormholes. In the
presence of conformal matter (i.e., conformal scalar or electromagnetic
fields), this relation allows us to interpret the elements of these bases as
wormhole states containing a given number of particles. This interpretation is
subject to the same kind of ambiguity in the definition of particle as that
arising from quantum field theory in curved spacetime. In the case of
gravitons, owing to the non-conformal coupling, it is not possible to describe
wormhole states in terms of their particle content.


  This paper is concerned with the quantum Zakharov system. We prove that when
the ionic speed of sound goes to infinity, the solution to the fourth order
Schrodinger part of the quantum Zakharov system converges to the solution to
quantum modified nonlinear Schrodinger eqaution.


  Charge transfer excitations can be described within TD-DFT, not only by means
of long-range corrected exchange functionals but also with a combination of
wave function theory and TD-DFT based on range separation. The latter approach
enables a rigorous formulation of multi-determinantal TD-DFT schemes where
excitation classes, which are absent in conventional TD-DFT spectra (like for
example double excitations), can be addressed. This paper investigates the
combination of both the long-range MCSCF and SOPPA ans\"atze with a short-range
DFT (srDFT) description. We find that the combinations of SOPPA or MCSCF with
TD-DFT yield better results than could be expected from the pure wave function
schemes. For the Time-Dependent MCSCF short-range DFT ansatz (TD-MC-srDFT)
excitation energies calculated over a larger benchmark set of molecules with
predominantly single reference character yield good agreement with their
reference values, and are in general comparable to the long-range corrected
functional CAM-B3LYP. The SOPPA-srDFT scheme is tested for a subset of
molecules used for benchmarking TD-MC-srDFT and performs slightly better
against the reference data for this small subset. Beyond the proof-of-principle
calculations comprising the first part of this contribution, we additionally
studied the low-lying singlet excited states (S1 and S2) of the retinal
chromophore. The chromophore displays multireference character in the ground
state and both excited states exhibit considerable double excitation character,
which in turn cannot be described within standard TD-DFT, due to the adiabatic
approximation. However, a TD-MC-srDFT approach can account for the
multireference character, and excitation energies are obtained with accuracy
comparable to CASPT2, although using a much smaller active space.


  We present the results of a near-infrared (NIR) monitoring program carried
out between 1999 and 2005 to determine the variability properties of the
Arecibo sample of OH/IR stars. The sample consists of 385 IRAS-selected
Asymptotic Giant Branch (AGB) candidates, for which their O-rich chemistry has
been proven by the detection of 1612 MHz OH maser emission. The monitoring data
was complemented by data collected from public optical and NIR surveys. We
fitted the light curves obtained in the optical and NIR bands with a model
using an asymmetric cosine function, and derived a period for 345 sources (90%
of the sample). Based on their variability properties, most of the Arecibo
sources are classified as long-period large-amplitude variable stars (LPLAV),
4% as (candidate) post-AGB stars, and 3% remain unclassified although they are
likely post-AGB stars or highly obscured AGB stars. The period distribution of
the LPLAVs peaks at 400 days, with periods between 300 and 800 days for most of
the sources, and has a long tail up to 2100 days. Typically, the amplitudes are
between 1 and 3 mag in the NIR and between 2 and 6 mag in the optical. We find
correlations between periods and amplitudes, with larger amplitudes associated
to longer periods, as well as between the period and the infrared colours, with
the longer periods linked to the redder sources. Among the post-AGB stars, the
light curve of IRAS 19566+3423 was exceptional, showing a large systematic
increase in K-band brightness over 7 years.


  We show that the definition of proper time for Weyl-invariant space-times
given by Perlick naturally extends to spaces with arbitrary non-metricity. We
then discuss the relation between this generalized proper time and the
Ehlers-Pirani-Schild definition of time when there is arbitrary non-metricity.
Then we show how this generalized proper time suffers from a second clock
effect. Assuming that muons are a device to measure this proper time, we
constrain the non-metricity tensor on Earth's surface and then elaborate on the
feasibility of such assumption.


  The pion form factor calculation in the ``point-form'' of relativistic
quantum mechanics is re-considered. Particular attention is given to the
relation between the momentum of the system and the momentum transfer as well
as to the quark current.


  A microscopic study of proton elastic scattering from unstable nuclei at
intermediate energies using a relativistic formalism is presented. We have
employed both the original relativistic impulse approximation (IA1) and the
generalised impulse approximation (IA2) formalisms to calculate the
relativistic optical potentials, with target densities derived from
relativistic mean field (RMF) theory using the NL3 and FSUGold parameter sets.
Comparisons between the optical potentials computed using both IA1 and IA2
formalisms, and the different RMF Lagrangians are presented for both stable and
unstable targets. The comparisons are required to study the effect of using IA1
versus IA2 optical potentials, with different RMF parameter sets, on elastic
scattering observables for unstable targets at intermediate energies. We also
study the effect of full-folding versus the factorized form of the optical
potentials on elastic scattering observables. As with the case for stable
nuclei, we found that the use of the full-folding optical potential improves
the scattering observables (especially spin observables) at low intermediate
energy (e.g. 200MeV). No discernible difference is found at a projectile
incident energy of 500 MeV. To check the validity of using localized optical
potential, we calculate the scattering observables using non-local potentials
by solving the momentum space Dirac equation. The Dirac equation is transformed
to two coupled Lippmann-Schwinger equations, which are then numerically solved
to obtain elastic scattering observables. The results are discussed and
compared to calculations involving local coordinate-space optical potentials.


  The reaction-diffusion waves of proteins are known to be involved in
fundamental cellular functions, such as cell migration, cell division, and
vesicular transportation. In some of these phenomena, pattern formation on the
membranes is induced by the coupling between membrane deformation and the
reaction-diffusion system through curvature-inducing proteins that bend the
biological membranes. Although the membrane shape and the dynamics of the
curvature-inducing proteins affect each other in these systems, the effect of
such mechanochemical feedback loops on the waves has not been studied in
detail. In this study, reaction-diffusion waves coupled with membrane
deformation are investigated using simulations combining a dynamically
triangulated membrane model with the Brusselator model extended to include the
effect of membrane curvature. It is found that the propagating wave patterns
change into nonpropageting patterns and spiral wave patterns due to the
mechanochemical effects. Moreover, the wave speed is positively or negatively
correlated with the local membrane curvature depending on the spontaneous
curvature and bending rigidity. In addition, self-oscillation of the vesicle
shape occurs, associated with the reaction-diffusion waves of
curvature-inducing proteins. This agrees with the experimental observation of
liposomes with a reconstituted Min system, which plays a key role in the cell
division of Escherichia coli. The findings of this study demonstrate the
importance of mechanochemical coupling in biological phenomena.


  The inference of source parameters from gravitational-wave signals relies on
theoretical models that describe the emitted waveform. Different model
assumptions on which the computation of these models is based could lead to
biases in the analysis of gravitational-wave data. In this work, we sample
directly on four state-of-the-art binary black hole waveform models from
different families, in order to investigate these systematic biases from the 13
heaviest gravitational-wave sources with moderate to high signal-to-noise
ratios in the third Gravitational-Wave Transient Catalog (GWTC- 3). All models
include spin-precession as well as higher-order modes. Using the "hypermodels"
technique, we treat the waveform models as one of the sampled parameters,
therefore directly getting the odds ratio of one waveform model over another
from a single parameter estimation run. From the joint odds ratio over all 13
sources, we find the model NRSur7dq4 to be favoured over SEOBNRv4PHM, with an
odds ratio of 29.43; IMRPhenomXPHM and IMRPhenomTPHM have an odds ratio,
respectively, of 4.70 and 5.09 over SEOBNRv4PHM. However, this result is mainly
determined by three events that show a strong preference for some of the models
and that are all affected by possible data quality issues. If we do not
consider these potentially problematic events, the odds ratio do not exhibit a
significant preference for any of the models. Although further work studying a
larger set of signals will be needed for robust quantitative results, the
presented method highlights one possible avenue for future waveform model
development.


  We investigate the representation theory of the polynomial core of the
quantum Teichmuller space of a punctured surface S. This is a purely algebraic
object, closely related to the combinatorics of the simplicial complex of ideal
cell decompositions of S. Our main result is that irreducible
finite-dimensional representations of this polynomial core are classified, up
to finitely many choices, by group homomorphisms from the fundamental group of
the surface to the isometry group of the hyperbolic 3--space. We exploit this
connection between algebra and hyperbolic geometry to exhibit new invariants of
diffeomorphisms of S.