  In this paper we propose a computational approach to proving the Birkhoff
conjecture on the restricted three-body problem, which asserts the existence of
a disk-like global surface of section. Birkhoff had conjectured this surface of
section as a tool to prove existence of a direct periodic orbit. Using
techniques from validated numerics we prove the existence of an approximately
circular direct orbit for a wide range of mass parameters and Jacobi energies.
We also provide methods to rigorously compute the Conley-Zehnder index of
periodic Hamiltonian orbits using computational tools, thus giving some initial
steps for developing computational Floer homology and providing the means to
prove the Birkhoff conjecture via symplectic topology. We apply this method to
various symmetric orbits in the restricted three-body problem.


  We study the distribution of interstellar matter near the galactic plane on
the basis of open star clusters and reviewed the correlation of extinction with
different physical parameters of the clusters to understand the galactic
structure. It is seen from the extinction towards open clusters that about 90%
of the absorbing material lie within -5<b<5 deg of the galactic plane. The mean
thickness of the absorbing material, which is determined in terms of half-width
value \beta, is estimated to be about 125+/-21 pc. We show that the
interstellar absorption follows a sinusoidal variation with galactic longitude
and maximum and minimum absorptions occur at l ~ 48+/-4 deg and l ~ 228+/-4 deg
respectively. It is found that the galactic plane defined by the reddening
material is inclined by an angle of 0.6+/-0.4 deg to the formal galactic plane
and inclination is maximum at l ~ 54+/-6 deg. The reddening analysis has been
used to constrain the Solar offset which is found to be about 22.8+/-3.3 pc
above the reddening plane. We obtained a scale height of 53+/-5 pc for the
distribution of open clusters while it is 186+/-25 pc for the distribution of
reddening material from the reddening plane.


  Let $V$ be a projective variety defined over a number field $K$, let $S$ be a
polarized set of endomorphisms of $V$ all defined over $K$, and let $P\in
V(K)$. For each prime $\mathfrak{p}$ of $K$, let $m_{\mathfrak{p}}(S,P)$ denote
the number of points in the orbit of $P\bmod\mathfrak{p}$ for the semigroup of
maps generated by $S$. Under suitable hypotheses on $S$ and $P$, we prove an
analytic estimate for $m_{\mathfrak{p}}(S,P)$ and use it to show that the set
of primes for which $m_{\mathfrak{p}}(S,P)$ grows subexponentially as a
function of $\operatorname{\mathsf{N}}_{K/\mathbb{Q}}\mathfrak{p}$ is a set of
density zero. For $V=\mathbb{P}^1$ we show that this holds for a generic set of
maps $S$ provided that at least two of the maps in $S$ have degree at least
four.


  We study maximal families W of the Hilbert scheme, H(d,g)_{sc}, of smooth
connected space curves whose general curve C lies on a smooth surface S of
degree s. We give conditions on C under which W is a generically smooth
component of H(d,g)_{sc} and we determine dim W. If s=4 and W is an irreducible
component of H(d,g)_{sc}, then the Picard number of S is at most 2 and we
explicitly describe, also for s > 4, non-reduced and generically smooth
components in the case Pic(S) is generated by the classes of a line and a
smooth plane curve of degree s-1. For curves on smooth cubic surfaces the first
author finds new classes of non-reduced components of H(d,g)_{sc}, thus making
progress in proving a conjecture for such families.


  Recently, non-recurrent architectures (convolutional, self-attentional) have
outperformed RNNs in neural machine translation. CNNs and self-attentional
networks can connect distant words via shorter network paths than RNNs, and it
has been speculated that this improves their ability to model long-range
dependencies. However, this theoretical argument has not been tested
empirically, nor have alternative explanations for their strong performance
been explored in-depth. We hypothesize that the strong performance of CNNs and
self-attentional networks could also be due to their ability to extract
semantic features from the source text, and we evaluate RNNs, CNNs and
self-attention networks on two tasks: subject-verb agreement (where capturing
long-range dependencies is required) and word sense disambiguation (where
semantic feature extraction is required). Our experimental results show that:
1) self-attentional networks and CNNs do not outperform RNNs in modeling
subject-verb agreement over long distances; 2) self-attentional networks
perform distinctly better than RNNs and CNNs on word sense disambiguation.


  The theoretical determination of braking indices of pulsars is still an open
problem. In this paper we report results of a study concerning such
determination based on a modification of the canonical model, which admits that
pulsars are rotating magnetic dipoles, and on data from the seven pulsars with
known braking indices. In order to test the modified model we predict ranges
for the braking indices of other pulsars.


  Topological property in a spinning system should be directly associated with
its wavefunction. A complete decomposition formula of SU(2) gauge potential in
terms of spinning wavefunction is established rigorously. Based on the $\phi
$-mapping theory and this formula, one proves that the second Chern class is
inherent in the spinning system. It is showed that this topological invariant
is only determined by the Hopf index and Brouwer degree of the spinning
wavefunction.


  We report the identification of Lyman Break Galaxy (LBG) candidates around
the most luminous Hot Dust-Obscured Galaxy (Hot DOG) known, WISE
J224607.56$-$052634.9 (W2246$-$0526) at $z=4.601$, using deep \textit{r}-,
\textit{i}-, and \textit{z}-band imaging from the Gemini Multi-Object
Spectrograph South (GMOS-S). We use the surface density of LBGs to probe the
Mpc-scale environment of W2246$-$0526 to characterize its richness and
evolutionary state. We identify LBG candidates in the vicinity of W2246$-$0526
using the selection criteria developed by \cite{2004VOuchi} and
\cite{2006Yoshida} in the Subaru Deep Field and in the Subaru XMM-Newton Deep
Field, slightly modified to account for the difference between the filters
used, and we find 37 and 55 LBG candidates, respectively. Matching to the
$z$-band depths of those studies, this corresponds to $\delta =
5.8^{+2.4}_{-1.9}$ times the surface density of LBGs expected in the field.
Interestingly, the Hot DOG itself, as well as a confirmed neighbor, do not
satisfy either LBG selection criteria, suggesting we may be missing a large
number of companion galaxies. Our analysis shows that we are most likely only
finding those with higher-than-average IGM optical depth or moderately high
dust obscuration. The number density of LBG candidates is not concentrated
around W2246$-$0526, suggesting either an early evolutionary stage for the
proto-cluster or that the Hot DOG may not be the most massive galaxy, or that
the Hot DOG may be affecting the IGM transparency in its vicinity. The
overdensity around W2246$-$0526 is comparable to overdensities found around
other Hot DOGs and is somewhat higher than typically found for radio galaxies
and luminous quasars at a similar redshift.


  In this paper, we analyze the asymptotic behavior of $\kappa$-noncollapsed
and positively curved steady Ricci solitons and prove that any $n$-dimensional
$\kappa$-noncollapsed steady K\"ahler-Ricci soliton with non-negative sectional
curvature must be flat.


  As quantum parallelism allows the effective co-representation of classical
mutually exclusive states, the diagonalization method of classical recursion
theory has to be modified. Quantum diagonalization involves unitary operators
whose eigenvalues are different from one.


  We introduce a 3-Higgs Doublet Model (3HDM) with two Inert (or dark) scalar
doublets and an active Higgs one, hence termed I(2+1)HDM, in the presence of a
discrete $Z_3$ symmetry acting upon the three doublet fields. We show that such
a construct yields a Dark Matter (DM) sector with two mass-degenerate states of
opposite CP parity, both of which contribute to DM dynamics, which we call
\textit{Hermaphrodite DM}, distinguishable from a (single) complex DM
candidate. We show that the relic density contributions of both states are
equal, saturating the observed relic density compliant with (in)direct searches
for DM as well as other experimental data impinging on both the dark and Higgs
sectors of the model, chiefly, in the form of Electro-Weak Precision
Observables (EWPOs), Standard Model (SM)-like Higgs boson measurements at the
Large Hadron Collider (LHC) and void searches for additional (pseudo)scalar
states at the CERN machine and previous colliders.


  We study the loop and suspension functors on the category of augmented
$\mathbb{E}_n$-algebras. One application is to the formality of the cochain
algebra of the $n$-sphere. We show that it is formal as an
$\mathbb{E}_n$-algebra, also with coefficients in general commutative ring
spectra, but rarely $\mathbb{E}_{n+1}$-formal unless the coefficients are
rational. Along the way we show that the free functor from operads in spectra
to monads in spectra is fully faithful on a nice subcategory of operads which
in particular contains the stable $\mathbb{E}_n$-operads for finite $n$. We use
this to interpret our results on loop and suspension functors of augmented
algebras in operadic terms.


  We study the quantum and classical evolution of a system of three harmonic
modes interacting via a trilinear Hamiltonian. With the modes prepared in
thermal states of different temperatures, this model describes the working
principle of an absorption refrigerator that transfers energy from a cold to a
hot environment at the expense of free energy provided by a high-temperature
work reservoir. Inspired by a recent experimental realization with trapped
ions, we elucidate key features of the coupling Hamiltonian that are relevant
for the refrigerator performance. The coherent system dynamics exhibits rapid
effective equilibration of the mode energies and correlations, as well as a
transient enhancement of the cooling performance at short times. We find that
these features can be fully reproduced in a classical framework.


  Bidirectional attention $\unicode{x2013}$ composed of self-attention with
positional encodings and the masked language model (MLM) objective
$\unicode{x2013}$ has emerged as a key component of modern large language
models (LLMs). Despite its empirical success, few studies have examined its
statistical underpinnings: What statistical model is bidirectional attention
implicitly fitting? What sets it apart from its non-attention predecessors? We
explore these questions in this paper. The key observation is that fitting a
single-layer single-head bidirectional attention, upon reparameterization, is
equivalent to fitting a continuous bag of words (CBOW) model with
mixture-of-experts (MoE) weights. Further, bidirectional attention with
multiple heads and multiple layers is equivalent to stacked MoEs and a mixture
of MoEs, respectively. This statistical viewpoint reveals the distinct use of
MoE in bidirectional attention, which aligns with its practical effectiveness
in handling heterogeneous data. It also suggests an immediate extension to
categorical tabular data, if we view each word location in a sentence as a
tabular feature. Across empirical studies, we find that this extension
outperforms existing tabular extensions of transformers in out-of-distribution
(OOD) generalization. Finally, this statistical perspective of bidirectional
attention enables us to theoretically characterize when linear word analogies
are present in its word embeddings. These analyses show that bidirectional
attention can require much stronger assumptions to exhibit linear word
analogies than its non-attention predecessors.


  The possible associations between the microquasars LS 5039 and LS I +61 303
and the EGRET sources 3EG J1824-1514 and 3EG J0241+6103 suggest that
microquasars could also be sources of high-energy gamma-rays. In this work, we
present a detailed numerical inverse Compton (IC) model, based on a microquasar
scenario, that reproduces the high-energy gamma-ray spectra and variability
observed by EGRET for the mentioned sources. Our model considers a population
of relativistic electrons entrained in a cylindrical inhomogeneous jet that
interact through IC scattering with both the radiation and the magnetic fields.


  We study lightlike submanifolds of indefinite statistical manifolds. Contrary
to the classical theory of submanifolds of statistical manifolds, lightlike
submanifolds of indefinite statistical manifolds need not to be statistical
submanifold. Therefore we obtain some conditions for a lightlike submanifold of
indefinite statistical manifolds to be a lightlike statistical submanifold. We
derive the expression of statistical sectional curvature and finally obtain
some conditions for the induced statistical Ricci tensor on a lightlike
submanifold of indefinite statistical manifolds to be symmetric.


  Gradient-based algorithms are one of the methods of choice for the
optimisation of Markov Decision Processes. In this article we will present a
novel approximate Newton algorithm for the optimisation of such models. The
algorithm has various desirable properties over the naive application of
Newton's method. Firstly the approximate Hessian is guaranteed to be
negative-semidefinite over the entire parameter space in the case where the
controller is log-concave in the control parameters. Additionally the inference
required for our approximate Newton method is often the same as that required
for first order methods, such as steepest gradient ascent. The approximate
Hessian also has many nice sparsity properties that are not present in the
Hessian and that make its inversion efficient in many situations of interest.
We also provide an analysis that highlights a relationship between our
approximate Newton method and both Expectation Maximisation and natural
gradient ascent. Empirical results suggest that the algorithm has excellent
convergence and robustness properties.


  We study universal critical adsorption on a solid sphere and a solid cylinder
in a fluid at bulk criticality, where preferential adsorption occurs. We use a
local functional theory proposed by Fisher, de Gennes, and Au-Yang ($[$C. R.
Acad. Sci. Paris Ser. B {\bf 287}, 207 (1978)$]$ and $[$Physica {\bf 101}A, 255
(1980)$]$). We calculate the mean order parameter profile $\psi(r)$, where $r$
is the distance from the sphere center and the cylinder axis, respectively. The
resultant differential equation for $\psi(r)$ is solved exactly around a sphere
and numerically around a cylinder. A strong adsorption regime is realized
except for very small surface field $h_1$, where the surface order parameter
$\psi(a)$ is determined by $h_1$ and is independent of the radius $a$. If $r$
considerably exceeds $a$, $\psi(r)$ decays as $r^{-(1+\eta)} $ for a sphere and
$r^{-(1+\eta)/2} $ for a cylinder in three dimensions, where $\eta$ is the
critical exponent in the order parameter correlation at bulk criticality.


  We study theoretically reflection problem in the junction between a normal
metal and an insulator characterized by a parameter $M$, which is a usual
insulator for $M>0$ or a quantum spin Hall system for $M<0$. The spin rotation
angle $\alpha$ at the reflection is obtained in the plane of $M$ and the
incident angle $\theta$ measured from the normal to the interface. The $\alpha$
shows rich structures around the quantum critical point M=0 and $\theta=0$,
i.e., $\alpha$ can be as large as $\sim \pi$ at an incident angle in the quatum
spin Hall case $M<0$ because the helical edge modes resonantly enhance the spin
rotation, which can be used to map the energy dispersion of the helical edge
modes. As an experimentally relevant system, we also study spin rotation effect
in quantum spin Hall/normal metal/quantum spin Hall trilayer junction.


  This paper proposes a cake-cutting protocol using cryptography when the cake
is a heterogeneous good that is represented by an interval on a real line.
Although the Dubins-Spanier moving-knife protocol with one knife achieves
simple fairness, all players must execute the protocol synchronously. Thus, the
protocol cannot be executed on asynchronous networks such as the Internet. We
show that the moving-knife protocol can be executed asynchronously by a
discrete protocol using a secure auction protocol. The number of cuts is n-1
where n is the number of players, which is the minimum.


  The Large Magellanic Cloud (LMC) is widely considered a corner-stone of the
astronomical distance scale, however a difference of 0.2-0.3 mag exists in its
distance as predicted by the "short" and "long" distance scales. Distances to
the LMC from Population II objects are founded on the RR Lyrae variables. We
have undertaken an observational campaign devoted to the definition of the
average apparent luminosity and to the study of the mass-metallicity relation
for RR Lyraes in the bar of the LMC. These are compared with analogous
quantities for cluster RR Lyraes. The purpose is to see whether an intrinsic
difference in luminosity, possibly due to a difference in mass, might exist
between field and cluster RR Lyraes, which could be responsible for the
well-known dichotomy between "short" and "long" distance scales. Preliminary
results are presented on the V and B-V light curves, the average apparent
visual magnitude, and the pulsational properties of 102 RR Lyrae in the bar of
the LMC, observed at ESO in January 1999. The photometric data are accurately
tied to the Johnson photometric system. Comparison is presented with the
photometry of RR Lyraes in the bar of the LMC obtained by the MACHO
collaboration (Alcock et al. 1996). Our sample includes 9 double-mode RR Lyraes
selected from Alcock et al. (1997) for which an estimate of the metal abundance
from the DeltaS method is presented.


  Low rank matrix factorisation is often used in recommender systems as a way
of extracting latent features. When dealing with large and sparse datasets,
traditional recommendation algorithms face the problem of acquiring large,
unrestrained, fluctuating values over predictions especially for users/items
with very few corresponding observations. Although the problem has been
somewhat solved by imposing bounding constraints over its objectives, and/or
over all entries to be within a fixed range, in terms of gaining better
recommendations, these approaches have two major shortcomings that we aim to
mitigate in this work: one is they can only deal with one pair of fixed bounds
for all entries, and the other one is they are very time-consuming when applied
on large scale recommender systems. In this paper, we propose a novel algorithm
named Magnitude Bounded Matrix Factorisation (MBMF), which allows different
bounds for individual users/items and performs very fast on large scale
datasets. The key idea of our algorithm is to construct a model by constraining
the magnitudes of each individual user/item feature vector. We achieve this by
converting from the Cartesian to Spherical coordinate system with radii set as
the corresponding magnitudes, which allows the above constrained optimisation
problem to become an unconstrained one. The Stochastic Gradient Descent (SGD)
method is then applied to solve the unconstrained task efficiently. Experiments
on synthetic and real datasets demonstrate that in most cases the proposed MBMF
is superior over all existing algorithms in terms of accuracy and time
complexity.


  Evidence for relativistic quantum criticality of antiferromagnetism and
superconductivity in two-dimensional Dirac fermion systems has been found in
large-scale quantum Monte Carlo simulations. However, the corresponding
($2+1$)-dimensional Gross--Neveu--Yukawa field theory with $N_f=2$
four-component Dirac fermions coupled to two triplets of order parameters does
not exhibit a renormalization group fixed point at one-loop order. Instead, the
theory only features a critical point for a large or very small fractional
number of fermion flavors $N_f$, which disappears for a broad range of flavor
numbers around the physical case, $N_f=2$, due to fixed-point annihilation.
This raises the question on how to explain the observed scaling collapse in the
quantum Monte Carlo data. Here, we extend previous renormalization-group
analyses by studying a generalized model at two-loop order in $4-\epsilon$
spacetime dimensions. We determine the $\epsilon$ correction to the upper and
lower critical flavor numbers for the fixed-point annihilation and find that
they both go towards the physical case $N_f=2$. However, this only happens very
slowly, such that an extrapolation to $\epsilon=1$ still suggests the absence
of criticality in $2+1$ dimensions. Thereby, we consolidate the finding that
the continuum field theory does not feature a stable renormalization-group
fixed point and no true quantum criticality would be expected for the
considered system. We briefly discuss a possible reconciliation in terms of a
complex conformal field theory. Further, we also explore the fixed-point
structure in an enlarged theory space and identify a candidate stable
fixed-point solution.


  In this review I concentrate on describing the physical characteristics and
evolution of the nebular remnants of classical novae. I also refer as
appropriate to the relationship between the central binary and the ejected
nebula, particularly in terms of remnant shaping. Evidence for remnant
structure in the spectra of unresolved novae is reviewed before moving on to
discuss resolved remnants in the radio and optical domains. As cited in the
published literature, a total of 5 remnants have now been resolved in the radio
and 44 in the optical. This represents a significant increase since the time of
the last conference. We have also made great strides in understanding the
relationship of remnant shape to the evolution of the outburst and the
properties of the central binary. The results of various models are presented.
Finally, I briefly describe new results relating to the idiosyncratic remnant
of GK Per (1901) which help to explain the apparently unique nature of the
evolving ejecta before concluding with a discussion of outstanding problems and
prospects for future work.


  This paper concerns the two-dimensional border-collision normal form -- a
four-parameter family of piecewise-linear maps generalising the Lozi family and
relevant to diverse applications. The normal form was recently shown to exhibit
a chaotic attractor throughout an open region of parameter space. This was
achieved by constructing a trapping region in phase space and an invariant
expanding cone in tangent space, but only allowed parameter combinations for
which the normal form is invertible and orientation-preserving. This paper
generalises the construction to include the non-invertible and
orientation-reversing cases. This provides a more complete and unified picture
of robust chaos by revealing its presence to be disassociated from the global
topological properties of the map. We identify a region of parameter space in
which the map exhibits robust chaos, and show that part of the boundary of this
region consists of bifurcation points at which the chaotic attractor is
destroyed.


  Hate speech is commonly defined as any communication that disparages a target
group of people based on some characteristic such as race, colour, ethnicity,
gender, sexual orientation, nationality, religion, or other characteristic. Due
to the massive rise of user-generated web content on social media, the amount
of hate speech is also steadily increasing. Over the past years, interest in
online hate speech detection and, particularly, the automation of this task has
continuously grown, along with the societal impact of the phenomenon. This
paper describes a hate speech dataset composed of thousands of sentences
manually labelled as containing hate speech or not. The sentences have been
extracted from Stormfront, a white supremacist forum. A custom annotation tool
has been developed to carry out the manual labelling task which, among other
things, allows the annotators to choose whether to read the context of a
sentence before labelling it. The paper also provides a thoughtful qualitative
and quantitative study of the resulting dataset and several baseline
experiments with different classification models. The dataset is publicly
available.


  The Minnesota Supercomputing Institute has implemented Jupyterhub and the
Jupyter notebook server as a general-purpose point-of-entry to interactive high
performance computing services. This mode of operation runs counter to
traditional job-oriented HPC operations, but offers significant advantages for
ease-of-use, data exploration, prototyping, and workflow development. From the
user perspective, these features bring the computing cluster nearer to parity
with emerging cloud computing options. On the other hand, retreating from
fully-scheduled, job-based resource allocation poses challenges for resource
availability and utilization efficiency, and can involve tools and technologies
outside the typical core competencies of a supercomputing center's operations
staff. MSI has attempted to mitigate these challenges by adopting Jupyter as a
common technology platform for interactive services, capable of providing
command-line, graphical, and workflow-oriented access to HPC resources while
still integrating with job scheduling systems and using existing compute
resources. This paper will describe the mechanisms that MSI has put in place,
advantages for research and instructional uses, and lessons learned.


  Trilateration-based localization (TBL) has become a corner stone of modern
technology. This study formulates the concern on how wireless sensor networks
can take advantage of the computational intelligent techniques using both
single- and multi-objective particle swarm optimization (PSO) with an overall
aim of concurrently minimizing the required time for localization, minimizing
energy consumed during localization, and maximizing the number of nodes fully
localized through the adjustment of wireless sensor transmission ranges while
using TBL process. A parameter-study of the applied PSO variants is performed,
leading to results that show algorithmic improvements of up to 32% in the
evaluated objectives.


  We study the Futaki invariant and the Mabuchi K-energy of a K\"ahler manifold
$M$ using the Deligne pairing technique developed in earlier papers. We first
prove a rather simple characterization of the Futaki character: The Futaki
character on a Q-Fano variety is the eigenvalue of the action of $Aut(M)$ on
$Chow(M)$, the Chow point of $M$. We use this to give a new proof of Lu's
theorem on the Futaki invariant of a complete intersection. In the last
theorem, we prove a non-linear generalization of Lu's formula which expresses
the K-energy of a smooth complete intersection as a singular norm on the space
of defining polynomials.


  Digitally retouching images has become a popular trend, with people posting
altered images on social media and even magazines posting flawless facial
images of celebrities. Further, with advancements in Generative Adversarial
Networks (GANs), now changing attributes and retouching have become very easy.
Such synthetic alterations have adverse effect on face recognition algorithms.
While researchers have proposed to detect image tampering, detecting GANs
generated images has still not been explored. This paper proposes a supervised
deep learning algorithm using Convolutional Neural Networks (CNNs) to detect
synthetically altered images. The algorithm yields an accuracy of 99.65% on
detecting retouching on the ND-IIITD dataset. It outperforms the previous state
of the art which reported an accuracy of 87% on the database. For
distinguishing between real images and images generated using GANs, the
proposed algorithm yields an accuracy of 99.83%.


  The band structure of graphene ribbons with zigzag edges have two valleys
well separated in momentum space, related to the two Dirac points of the
graphene spectrum. The propagating modes in each valley contain a single chiral
mode originating from a partially flat band at band center. This feature gives
rise to a perfectly conducting channel in the disordered system, if the
impurity scattering does not connect the two valleys, i.e. for long-range
impurity potentials. Ribbons with short-range impurity potentials, however,
through inter-valley scattering display ordinary localization behavior. The two
regimes belong to different universality classes: unitary for long-range
impurities and orthogonal for short-range impurities.


  Emotion recognition and understanding is a vital component in human-machine
interaction. Dimensional models of affect such as those using valence and
arousal have advantages over traditional categorical ones due to the complexity
of emotional states in humans. However, dimensional emotion annotations are
difficult and expensive to collect, therefore they are not as prevalent in the
affective computing community. To address these issues, we propose a method to
generate synthetic images from existing categorical emotion datasets using face
morphing as well as dimensional labels in the circumplex space with full
control over the resulting sample distribution, while achieving augmentation
factors of at least 20x or more.


  We present a framework for intuitive robot programming by non-experts,
leveraging natural language prompts and contextual information from the Robot
Operating System (ROS). Our system integrates large language models (LLMs),
enabling non-experts to articulate task requirements to the system through a
chat interface. Key features of the framework include: integration of ROS with
an AI agent connected to a plethora of open-source and commercial LLMs,
automatic extraction of a behavior from the LLM output and execution of ROS
actions/services, support for three behavior modes (sequence, behavior tree,
state machine), imitation learning for adding new robot actions to the library
of possible actions, and LLM reflection via human and environment feedback.
Extensive experiments validate the framework, showcasing robustness,
scalability, and versatility in diverse scenarios, including long-horizon
tasks, tabletop rearrangements, and remote supervisory control. To facilitate
the adoption of our framework and support the reproduction of our results, we
have made our code open-source. You can access it at:
https://github.com/huawei-noah/HEBO/tree/master/ROSLLM.


  The area of the unitarity triangle is a measure of CP-violation. We introduce
the leptonic unitarity triangles and study their properties. We consider the
possibility of reconstructing the unitarity triangle in future oscillation and
non-oscillation experiments. A set of measurements is suggested which will, in
principle, allow us to measure all sides of the triangle, and consequently to
establish CP-violation. For different values of the CP-violating phase,
$\delta_D$, the required accuracy of measurements is estimated. The key
elements of the method include determination of $|U_{e3}|$ and studies of the
$\nu_{\mu} - \nu_{\mu}$ survival probability in oscillations driven by the
solar mass splitting $\Delta m^2_{sun}$. We suggest additional astrophysical
measurements which may help to reconstruct the triangle. The method of the
unitarity triangle is complementary to the direct measurements of CP-asymmetry.
It requires mainly studies of the {\it survival} probabilities and processes
where oscillations are averaged or the coherence of the state is lost.


  We give general intersecting brane solutions without assuming any restriction
on the metric in supergravity coupled to a dilaton and antisymmetric tensor
fields in arbitrary dimensions $D$. The result is a general class of
intersecting brane solutions which interpolate the non-extreme solutions of
type 1 and 2. We also discuss the relation of our solutions to the known single
brane solution.


  We study three different quasi-symmetry models and three different mixture
models of $n\times n\times n$ tensors for modeling rater agreement data. For
these models we give a geometric description of the associated varieties and we
study their invariants distinguishing between the case $n=2$ and the case
$n>2$. Finally, for the two models for pairwise agreement we state some results
about the pairwise Cohen's $\kappa$ coefficients.


  Recently, Chalermsook et al. [SODA'21(arXiv:2007.07862)] introduces a notion
of vertex sparsifiers for $c$-edge connectivity, which has found applications
in parameterized algorithms for network design and also led to exciting dynamic
algorithms for $c$-edge st-connectivity [Jin and Sun
FOCS'21(arXiv:2004.07650)]. We study a natural extension called vertex
sparsifiers for $c$-hyperedge connectivity and construct a sparsifier whose
size matches the state-of-the-art for normal graphs. More specifically, we show
that, given a hypergraph $G=(V,E)$ with $n$ vertices and $m$ hyperedges with
$k$ terminal vertices and a parameter $c$, there exists a hypergraph $H$
containing only $O(kc^{3})$ hyperedges that preserves all minimum cuts (up to
value $c$) between all subset of terminals. This matches the best bound of
$O(kc^{3})$ edges for normal graphs by [Liu'20(arXiv:2011.15101)]. Moreover,
$H$ can be constructed in almost-linear $O(p^{1+o(1)} + n(rc\log n)^{O(rc)}\log
m)$ time where $r=\max_{e\in E}|e|$ is the rank of $G$ and $p=\sum_{e\in E}|e|$
is the total size of $G$, or in $\text{poly}(m, n)$ time if we slightly relax
the size to $O(kc^{3}\log^{1.5}(kc))$ hyperedges.


  We prove two conjectures on weighted complete intersections and give the
complete classification of threefold weighted complete intersections in
weighted projective space that are canonically or anticanonically embedded.


  A study of convection in a circular two dimensional cell is presented. The
system is heated and cooled at two diametrically opposed points on the edge of
the circle, which are parallel or anti-parallel to gravity. The latter's role
in the plane of the cell can be changed by tilting the cell. When the system is
in a horizontal position, a non-trivial analytic solution for the temperature
distribution of the quiescent fluid can be found. For a slight inclination, the
projection of gravity in the plane of the cell is used as a perturbation
parameter in the full hydrodynamic description, as the Boussinesq approximation
is inadequate. To first order, the equations are solved for the stationary case
and four symmetrical rolls become apparent, showing that a purely conductive
state is impossible if gravity -however small- is present; an approximate
closed analytical expression is obtained, which describes the four convection
rolls. Further analysis is done by a direct numerical integration. Comparison
with preliminary observations is mentioned.


  We provide a simple mechanism for reconciling the direct dark matter
experimental results. We consider light asymmetric composite dark matter which
scatters off nuclei via Higgs and photon exchange. We demonstrate that the
interference between these two channels naturally accommodates the experimental
results. We discover that this happens for a compositeness scale of the order
of the electroweak. We also provide a model realization based on strong
dynamics at the electroweak scale.


  We calculate the nucleons' electromagnetic polarizabilities in heavy baryon
chiral perturbation theory including all terms to order ${\cal O} (q^4)$. The
chiral prediction of the electric polarizabilities for the neutron and the
proton are in good agreement with the data. In the case of the magnetic
polarizabilities the big positive contribution from the $\Delta(1232)$
resonance is largely cancelled by a non--analytic loop contribution of the $\ln
M_\pi$ type. This novel effect helps to understand the rather small empirical
value of the nucleons' magnetic polarizability.


  There is perfect state transfer between two vertices of a graph, if a single
excitation can travel with fidelity one between the corresponding sites of a
spin system modeled by the graph. When the excitation is back at the initial
site, for all sites at the same time, the graph is said to be periodic. A graph
is cubic if each of its vertices has a neighbourhood of size exactly three. We
prove that the 3-dimensional cube is the only periodic, connected cubic graph
with perfect state transfer. We conjecture that this is also the only connected
cubic graph with perfect state transfer.


  Let $f: A\rightarrow B$ and $g: A\rightarrow C$ be two commutative ring
homomorphisms and let $J$ and $J'$ be two ideals of $B$ and $C$, respectively,
such that $f^{-1}(J)=g^{-1}(J')$. The \emph{bi-amalgamation} of $A$ with $(B,
C)$ along $(J, J')$ with respect to $(f,g)$ is the subring of $B\times C$ given
by $$A\bowtie^{f,g}(J,J'):=\big\{(f(a)+j,g(a)+j') \mid a\in A, (j,j')\in
J\times J'\big\}.$$
  This paper investigates ring-theoretic properties of \emph{bi-amalgamations}
and capitalizes on previous works carried on various settings of pullbacks and
amalgamations. In the second and third sections, we provide examples of
bi-amalgamations and show how these constructions arise as pullbacks. The
fourth section investigates the transfer of some basic ring theoretic
properties to bi-amalgamations and the fifth section is devoted to the prime
ideal structure of these constructions. All new results agree with recent
studies in the literature on D'Anna-Finocchiaro-Fontana's amalgamations and
duplications.


  The massive neutron star (NS) or black hole (BH) accretion disk resulting
from NS--NS or NS--BH mergers is dense in neutrinos. We present the first study
on the role of angular distributions in the neutrino flavor conversion above
the remnant disk. In particular, we focus on "fast" pairwise conversions whose
rate depends on the local angular intensity of the electron lepton number
carried by neutrinos. Because of the emission geometry and the flux density of
$\bar{\nu}_e$ being larger than that of $\nu_e$, fast conversions prove to be a
generic phenomenon in NS--NS and NS--BH mergers for physically motivated
disturbances in the mean field of flavor coherence. Our findings suggest that,
differently from the core-collapse supernova case, fast flavor conversions seem
to be unavoidable in compact mergers and could have major consequences for the
jet dynamics and the synthesis of elements above the remnant disk.


  We prove that the Dirichlet problem for the Lane-Emden equation in a
half-space has no positive solutions which grow at most like the distance to
the boundary to a power given by the natural scaling exponent of the equation;
in other words, we rule out {\it type~I grow-up} solutions. Such a nonexistence
result was previously available only for bounded solutions, or under a
restriction on the power in the nonlinearity. Instrumental in the proof are
local pointwise bounds for the logarithmic gradient of the solution and its
normal derivative, which we also establish.


  We here propose a model to simulate the process of opinion formation, which
accounts for the mutual affinity between interacting agents. Opinion and
affinity evolve self-consistently, manifesting a highly non trivial interplay.
A continuous transition is found between single and multiple opinion states.
Fractal dimension and signature of critical behaviour are also reported. A rich
phenomenology is presented and discussed with reference to corresponding
psychological implications.


  Recently, a novel mechanism to address the hierarchy problem has been
proposed \cite{Graham:2015cka}, where the hierarchy between weak scale physics
and any putative `cutoff' $M$ is translated into a parametrically large field
excursion for the so-called relaxion field, driving the Higgs mass to values
much less than $M$ through cosmological dynamics. In its simplest incarnation,
the relaxion mechanism requires nothing beyond the standard model other than an
axion (the relaxion field) and an inflaton. In this note, we critically
re-examine the requirements for successfully realizing the relaxion mechanism
and point out that parametrically larger field excursions can be obtained for a
given number of e-folds by simply requiring that the background break exact de
Sitter invariance. We discuss several corollaries of this observation,
including the interplay between the upper bound on the scale $M$ and the order
parameter $\epsilon$ associated with the breaking of dS symmetry, and entertain
the possibility that the relaxion could play the role of a curvaton. We find
that a successful realization of the mechanism is possible with as few as
$\mathcal O (10^3)$ e-foldings, albeit with a reduced cutoff $M \sim 10^6$ GeV
for a dark QCD axion and outline a minimal scenario that can be made consistent
with CMB observations.


  Quantum thermometry exploits the high level of control in coherent devices to
offer enhanced precision for temperature estimation. This highlights the need
for constructing concrete estimation strategies. Of particular importance is
collisional thermometry, where a series of ancillas are sent sequentially to
probe the system's temperature. In this paper we put forth a complete framework
for analyzing collisional thermometry using Bayesian inference. The approach is
easily implementable and experimentally friendly. Moreover, it is guaranteed to
always saturate the Cramer-Rao bound in the long-time limit. Subtleties
concerning the prior information about the system's temperature are also
discussed, and analyzed in terms of a modified Cramer-Rao bound associated to
Van Trees and Sch\"utzenberger.


  The study focuses on the applicability of system identification to identify
building and system dynamics for climate control design. The main problem
regarding the simulation of the dynamic response of a building using building
simulation software is that (1) the simulation of a large complex building is
time consuming, and (2) simulation results often lack information regarding
fast dynamic behaviour (in the order of seconds), since most software uses a
discrete time step, usually fixed to one hour. The first objective is to study
the applicability of system identification to reduce computing time for the
simulation of large complex buildings. The second objective is to research the
applicability of system identification to identify building dynamics based on
discrete time data (one hour) for climate control design. The study illustrates
that system identification is applicable for the identification of building
dynamics with a frequency that is smaller as the maximum sample frequency as
used for identification. The research shows that system identification offers
good perspectives for the modelling of heat, air and moisture processes in a
building. The main advantages of system identification models compared to the
modelling of building dynamics using building simulation software are, that (1)
the computing time is reduced significantly, and (2) system identification
models run in a MATLAB environment, in which many building simulation tools
have been developed


  Generative AI holds the promise of enabling a range of sought-after
capabilities and revolutionizing workflows in various consumer and enterprise
verticals. However, putting a model in production involves much more than just
generating an output. It involves ensuring the model is reliable, safe,
performant and also adheres to the policy of operation in a particular domain.
Guardrails as a necessity for models has evolved around the need to enforce
appropriate behavior of models, especially when they are in production. In this
paper, we use education as a use case, given its stringent requirements of the
appropriateness of content in the domain, to demonstrate how a guardrail model
can be trained and deployed in production. Specifically, we describe our
experience in building a production-grade guardrail model for a K-12
educational platform. We begin by formulating the requirements for deployment
to this sensitive domain. We then describe the training and benchmarking of our
domain-specific guardrail model, which outperforms competing open- and closed-
instruction-tuned models of similar and larger size, on proprietary
education-related benchmarks and public benchmarks related to general aspects
of safety. Finally, we detail the choices we made on architecture and the
optimizations for deploying this service in production; these range across the
stack from the hardware infrastructure to the serving layer to language model
inference optimizations. We hope this paper will be instructive to other
practitioners looking to create production-grade domain-specific services based
on generative AI and large language models.


  If at least some Wheeler-DeWitt solutions can be interpreted as zero-energy
resonances then the total s-wave cross section of the corresponding quantum
universes is infinite


  The Quantum State Preparation problem aims to prepare an $n$-qubit quantum
state $|\psi_v\rangle =\sum_{k=0}^{2^n-1}v_k|k\rangle$ from the initial state
$|0\rangle^{\otimes n}$, for a given unit vector
$v=(v_0,v_1,v_2,\ldots,v_{2^n-1})^T\in \mathbb{C}^{2^n}$ with $\|v\|_2 = 1$.
The problem is of fundamental importance in quantum algorithm design,
Hamiltonian simulation and quantum machine learning, yet its circuit depth and
size complexity remain open when ancillary qubits are available. In this paper,
we study efficient constructions of quantum circuits with $m$ ancillary qubits
that can prepare $|\psi_v\rangle$ in depth $\tilde
O\left(\frac{2^n}{m+n}+n\right)$and size $O(2^n)$, achieving the optimal value
for both measures simultaneously. These results also imply a depth complexity
of $\Theta(4^n/(m+n))$ for quantum circuits implementing a general $n$-qubit
unitary using $m = O(2^n/n)$ ancillary qubits. This resolves the depth
complexity for circuits without ancillary qubits, and for circuits with
exponentially many ancillary qubits, this gives a quadratic saving from
$O(4^n)$ to $\tilde \Theta(2^n)$. Our circuits are deterministic, prepare the
state and carry out the unitary precisely, utilize the ancillary qubits tightly
and the depths are optimal in a wide range of parameter regime. The results can
be viewed as (optimal) time-space tradeoff bounds, which is not only
theoretically interesting, but also practically relevant in the current trend
that the number of qubits starts to take off, by showing a way to use a large
number of qubits to compensate the short qubit lifetime.


  Network epidemics is a ubiquitous model that can represent different
phenomena and finds applications in various domains. Among its various
characteristics, a fundamental question concerns the time when an epidemic
stops propagating. We investigate this characteristic on a SIS epidemic induced
by agents that move according to independent continuous time random walks on a
finite graph: Agents can either be infected (I) or susceptible (S), and
infection occurs when two agents with different epidemic states meet in a node.
After a random recovery time, an infected agent returns to state S and can be
infected again. The End of Epidemic (EoE) denotes the first time where all
agents are in state S, since after this moment no further infections can occur
and the epidemic stops.
  For the case of two agents on edge-transitive graphs, we characterize EoE as
a function of the network structure by relating the Laplace transform of EoE to
the Laplace transform of the meeting time of two random walks. Interestingly,
this analysis shows a separation between the effect of network structure and
epidemic dynamics. We then study the asymptotic behavior of EoE (asymptotically
in the size of the graph) under different parameter scalings, identifying
regimes where EoE converges in distribution to a proper random variable or to
infinity. We also highlight the impact of different graph structures on EoE,
characterizing it under complete graphs, complete bipartite graphs, and rings.


  Many basic properties in Tutte's flow theory for unsigned graphs do not have
their counterparts for signed graphs. However, signed graphs without long
barbells in many ways behave like unsigned graphs from the point view of flows.
In this paper, we study whether some basic properties in Tutte's flow theory
remain valid for this family of signed graphs. Specifically let $(G,\sigma)$ be
a flow-admissible signed graph without long barbells. We show that it admits a
nowhere-zero $6$-flow and that it admits a nowhere-zero modulo $k$-flow if and
only if it admits a nowhere-zero integer $k$-flow for each integer $k\geq 3$
and $k \not = 4$. We also show that each nowhere-zero positive integer $k$-flow
of $(G,\sigma)$ can be expressed as the sum of some $2$-flows. For general
graphs, we show that every nowhere-zero $\frac{p}{q}$-flow can be normalized in
such a way, that each flow value is a multiple of $\frac{1}{2q}$. As a
consequence we prove the equality of the integer flow number and the ceiling of
the circular flow number for flow-admissible signed graphs without long
barbells.


  Artificial Intelligence (AI) provides many opportunities to improve private
and public life. Discovering patterns and structures in large troves of data in
an automated manner is a core component of data science, and currently drives
applications in computational biology, finance, law and robotics. However, such
a highly positive impact is coupled with significant challenges: How do we
understand the decisions suggested by these systems in order that we can trust
them? How can they be held accountable for those decisions?
  In this short survey, we cover some of the motivations and trends in the area
that attempt to address such questions.


  In this paper we study the effect of a magnetic field on the fluctuation
spectrum of the cosmic microwave background. We find that upcoming measurements
might give interesting bounds on large scale magnetic fields in the early
Universe. If the effects are seen, it might be possible to establish the
presence of different fields in different patches of the sky. Absence of any
effect, will provide by one order of magnitude a better limit for a primordial
field, now given by nucleosynthesis.


  Innovations in computer vision algorithms for satellite image analysis can
enable us to explore global challenges such as urbanization and land use change
at the planetary level. However, domain shift problems are a common occurrence
when trying to replicate models that drive these analyses to new areas,
particularly in the developing world. If a model is trained with imagery and
labels from one location, then it usually will not generalize well to new
locations where the content of the imagery and data distributions are
different. In this work, we consider the setting in which we have a single
large satellite imagery scene over which we want to solve an applied problem --
building footprint segmentation. Here, we do not necessarily need to worry
about creating a model that generalizes past the borders of our scene but can
instead train a local model. We show that surprisingly few labels are needed to
solve the building segmentation problem with very high-resolution (0.5m/px)
satellite imagery with this setting in mind. Our best model trained with just
527 sparse polygon annotations (an equivalent of 1500 x 1500 densely labeled
pixels) has a recall of 0.87 over held out footprints and a R2 of 0.93 on the
task of counting the number of buildings in 200 x 200-meter windows. We apply
our models over high-resolution imagery in Amman, Jordan in a case study on
urban change detection.


  We introduce and study the problem of computing the similarity self-join in a
streaming context (SSSJ), where the input is an unbounded stream of items
arriving continuously. The goal is to find all pairs of items in the stream
whose similarity is greater than a given threshold. The simplest formulation of
the problem requires unbounded memory, and thus, it is intractable. To make the
problem feasible, we introduce the notion of time-dependent similarity: the
similarity of two items decreases with the difference in their arrival time. By
leveraging the properties of this time-dependent similarity function, we design
two algorithmic frameworks to solve the sssj problem. The first one, MiniBatch
(MB), uses existing index-based filtering techniques for the static version of
the problem, and combines them in a pipeline. The second framework, Streaming
(STR), adds time filtering to the existing indexes, and integrates new
time-based bounds deeply in the working of the algorithms. We also introduce a
new indexing technique (L2), which is based on an existing state-of-the-art
indexing technique (L2AP), but is optimized for the streaming case. Extensive
experiments show that the STR algorithm, when instantiated with the L2 index,
is the most scalable option across a wide array of datasets and parameters.


  Professional software developers spend a significant amount of time fixing
builds, but this has received little attention as a problem in automatic
program repair. We present a new deep learning architecture, called Graph2Diff,
for automatically localizing and fixing build errors. We represent source code,
build configuration files, and compiler diagnostic messages as a graph, and
then use a Graph Neural Network model to predict a diff. A diff specifies how
to modify the code's abstract syntax tree, represented in the neural network as
a sequence of tokens and of pointers to code locations. Our network is an
instance of a more general abstraction that we call Graph2Tocopo, which is
potentially useful in any development tool for predicting source code changes.
We evaluate the model on a dataset of over 500k real build errors and their
resolutions from professional developers. Compared to the approach of DeepDelta
(Mesbah et al., 2019), our approach tackles the harder task of predicting a
more precise diff but still achieves over double the accuracy.


  The future of the arts and artificial intelligence (AI) is promising as
technology advances. As the use of AI in design becomes more widespread, art
practice may not be a human-only art form and could instead become a digitally
integrated experience. With enhanced creativity and collaboration, arts and AI
could work together towards creating artistic outputs that are visually
appealing and meet the needs of the artist and viewer. While it is uncertain
how far the integration will go, arts and AI will likely influence one another.
This workshop pictorial puts forward first-person research that shares
interactions between an HCI researcher and AI as they try to escape the
creative block. The pictorial paper explores two questions: How can AI support
artists' creativity, and what does it mean to be explainable in this context?
HIs, ChatGPT and Midjourney were engaged; the result was a series of
reflections that require further discussion and explorations in the XAIxArts
community: Transparency of attribution, the creation process, ethics of asking,
and inspiration vs copying.


  Wind speed modelling and prediction has been gaining importance because of
its significant roles in various stages of wind energy management. In this
paper, we propose a hybrid model, based on wavelet transform to improve the
accuracy of the short-term forecast. The wind speed time series are split into
various frequency components using wavelet decomposition technique, and each
frequency components are modelled separately. Since the components associated
with the high- frequency range shows stochastic nature, we modelled them with
autoregressive (AR) method and rest of low-frequency components modelled with
support vector machine (SVM). The results of the hybrid method show a promising
improvement in accuracy of wind speed prediction compared to that of
stand-alone AR or SVM model.


  This paper presents a novel algorithm that utilizes a 2D floorplan to align
panorama RGBD scans. While effective panorama RGBD alignment techniques exist,
such a system requires extremely dense RGBD image sampling. Our approach can
significantly reduce the number of necessary scans with the aid of a floorplan
image. We formulate a novel Markov Random Field inference problem as a scan
placement over the floorplan, as opposed to the conventional scan-to-scan
alignment. The technical contributions lie in multi-modal image correspondence
cues (between scans and schematic floorplan) as well as a novel coverage
potential avoiding an inherent stacking bias. The proposed approach has been
evaluated on five challenging large indoor spaces. To the best of our
knowledge, we present the first effective system that utilizes a 2D floorplan
image for building-scale 3D pointcloud alignment. The source code and the data
will be shared with the community to further enhance indoor mapping research.


  We investigate string-phenomenological questions of Hull's exotic superstring
theories with Euclidean strings/branes and multiple times. These are known to
be plagued by pathologies like the occurrence of ghosts. On the other hand,
these theories exhibit de Sitter solutions. Our special focus lies on the
question of the coexistence of such de Sitter solutions and ghost-free brane
worlds. To this end, the world-sheet CFT description of Euclidean fundamental
strings is generalized to include also the open string/D-brane sector.
Demanding that in the "observable" gauge theory sector the gauge fields
themselves are non-ghosts, a generalization of the dS swampland conjecture is
found.


  We study a phase transition in parameter learning of Hidden Markov Models
(HMMs). We do this by generating sequences of observed symbols from given
discrete HMMs with uniformly distributed transition probabilities and a noise
level encoded in the output probabilities. By using the Baum-Welch (BW)
algorithm, an Expectation-Maximization algorithm from the field of Machine
Learning, we then try to estimate the parameters of each investigated
realization of an HMM. We study HMMs with n=4, 8 and 16 states. By changing the
amount of accessible learning data and the noise level, we observe a
phase-transition-like change in the performance of the learning algorithm. For
bigger HMMs and more learning data, the learning behavior improves tremendously
below a certain threshold in the noise strength. For a noise level above the
threshold, learning is not possible. Furthermore, we use an overlap parameter
applied to the results of a maximum-a-posteriori (Viterbi) algorithm to
investigate the accuracy of the hidden state estimation around the phase
transition.


  The main progresses in the multinucleon transfer reactions at energies close
to the Coulomb barrier are reviewed. After a short presentation of the
experimental progress and theoretical progress,the predicted production cross
sections for unknown neutron-rich heavy nuclei and the trans-uranium nuclei are
presented.


  A finite set $X \seq \RR^n$ with a weight function $w : X \longrightarrow
\RR_{>0}$ is called \emph{Euclidean $t$-design} in $\RR^n$ (supported by $p$
concentric spheres) if the following condition holds: \[ \sum_{i=1}^p
\frac{w(X_i)}{|S_i|}\int_{S_i} f(\boldsymbol x)d\sigma_i(\boldsymbol x)
=\sum_{\boldsymbol x \in X}w(\boldsymbol x) f(\boldsymbol x), \] for any
polynomial $f(\boldsymbol x) \in \mbox{Pol}(\RR^n)$ of degree at most $t$. Here
$S_i \seq \RR^n$ is a sphere of radius $r_i \geq 0,$ $X_i=X \cap S_i,$ and
$\sigma_i(\boldsymbol x)$ is an $O(n)$-invariant measure on $S_i$ such that
$|S_i|=r_i^{n-1}|S^{n-1}|$, with $|S_i|$ is the surface area of $S_i$ and
$|S^{n-1}|$ is a surface area of the unit sphere in $\RR^n$.
  Recently, Bajnok (2006) constructed tight Euclidean $t$-designs in the plane
($n=2$) for arbitrary $t$ and $p.$ In this paper we show that for case $t=6$
and $p=2,$ tight Euclidean $6$-designs constructed by Bajnok is the unique
configuration in $\RR^n$, for $2 \leq n \leq 8.$


  We present a detailed study of the stellar cluster M82F, using multi-band
high resolution HST imaging and deep ground based optical slit and integral
field spectroscopy. Using the imaging we create colour maps of the cluster and
surrounding region in order to search for substructure. We find a large amount
of substructure, which we interpret as the result of differential extinction
across the projected face of the cluster. With this interpretation, we are able
to construct a spatially resolved extinction map across the cluster which is
used to derive the intrinsic flux distribution. Fitting cluster profiles (King
and EFF) to the intrinsic images we find that the cluster is 15-30% larger than
previous estimates, and that no strong evidence of mass segregation in this
cluster exists. Using the optical spectra, we find that the age of M82F is
60-80 Myr and from its velocity conclude that the cluster is not physically
associated with a large HII region that it is projected upon, both in agreement
with previous studies. The reconstructed integral field maps show that that
majority of the line emission comes from a nearby HII region. The spatial
dependence of the line widths (implying the presence of multiple
components)measured corresponds to the extinction map derived from photometry,
indicating that the gas/dust clouds responsible for the extinction are also
partially ionised. Even with the wealth of observations presented here, we do
not find a conclusive solution to the problem of the high light-to-mass ratio
previously found for this cluster and its possible top-heavy stellar IMF.


  In wireless communications, electromagnetic theory and information theory
constitute a pair of fundamental theories, bridged by antenna theory and
wireless propagation channel modeling theory. Up to the fifth generation (5G)
wireless communication networks, these four theories have been developing
relatively independently. However, in sixth generation (6G)
space-air-ground-sea wireless communication networks, seamless coverage is
expected in the three-dimensional (3D) space, potentially necessitating the
acquisition of channel state information (CSI) and channel capacity calculation
at anywhere and any time. Additionally, the key 6G technologies such as
ultra-massive multiple-input multiple-output (MIMO) and holographic MIMO
achieves intricate interaction of the antennas and wireless propagation
environments, which necessitates the joint modeling of antennas and wireless
propagation channels. To address the challenges in 6G, the integration of the
above four theories becomes inevitable, leading to the concept of the so-called
electromagnetic information theory (EIT). In this article, a suite of 6G key
technologies is highlighted. Then, the concepts and relationships of the four
theories are unveiled. Finally, the necessity and benefits of integrating them
into the EIT are revealed.


  In a delightful article that recently appeared in Mathematics Magazine, David
and Lori Mccune analyze the board game "Count Your Chickens!", recommended to
children three and up. Alas, they use the advanced theory of Markov chains,
that presupposes a knowledge of linear algebra, that few three-years-olds are
likely to understand. Here we present a much simpler, more intuitive, approach,
that while unlikely to be understood by three-year-olds, will probably be
understood by a smart 14-year-old. Moreover, our approach accomplishes much
more, and is more efficient. It uses symbolic, rather than numeric computation.


  The paper presents a two-dimensional geometrically nonlinear formulation of a
beam element that can accommodate arbitrarily large rotations of cross
sections. The formulation is based on the integrated form of equilibrium
equations, which are combined with the kinematic equations and generalized
material equations, leading to a set of three first-order differential
equations. These equations are then discretized by finite differences and the
boundary value problem is converted into an initial value problem using a
technique inspired by the shooting method. Accuracy of the numerical
approximation is conveniently increased by refining the integration scheme on
the element level while the number of global degrees of freedom is kept
constant, which leads to high computational efficiency. The element has been
implemented into an open-source finite element code. Numerical examples show a
favorable comparison with standard beam elements formulated in the
finite-strain framework and with analytical solutions.


  AI-manipulated videos, commonly known as deepfakes, are an emerging problem.
Recently, researchers in academia and industry have contributed several
(self-created) benchmark deepfake datasets, and deepfake detection algorithms.
However, little effort has gone towards understanding deepfake videos in the
wild, leading to a limited understanding of the real-world applicability of
research contributions in this space. Even if detection schemes are shown to
perform well on existing datasets, it is unclear how well the methods
generalize to real-world deepfakes. To bridge this gap in knowledge, we make
the following contributions: First, we collect and present the largest dataset
of deepfake videos in the wild, containing 1,869 videos from YouTube and
Bilibili, and extract over 4.8M frames of content. Second, we present a
comprehensive analysis of the growth patterns, popularity, creators,
manipulation strategies, and production methods of deepfake content in the
real-world. Third, we systematically evaluate existing defenses using our new
dataset, and observe that they are not ready for deployment in the real-world.
Fourth, we explore the potential for transfer learning schemes and
competition-winning techniques to improve defenses.


  In this paper we study the universal properties of the baryon chemical
potential Fourier coefficients in Quantum Chromodynamics. We show that by
following a well-defined strategy, the Fourier coefficients can be used to
locate Yang-Lee edge singularities associated with chiral phase transition (and
by extension with the Roberge-Weiss) in the complex chemical potential plane.
We comment on the viability of performing this analysis using lattice QCD data.


  Atomic scale engineering of two-dimensional materials could create devices
with rich physical and chemical properties. External periodic potentials can
enable the manipulation of the electronic band structures of materials. A
prototypical system is 3x3-silicene/Ag(111), which has substrate-induced
periodic modulations. Recent angle-resolved photoemission spectroscopy
measurements revealed six Dirac cone pairs at the Brillouin zone boundary of
Ag(111), but their origin remains unclear [Proc. Natl. Acad. Sci. USA 113,
14656 (2016)]. We used linear dichroism angle-resolved photoemission
spectroscopy, the tight-binding model, and first-principles calculations to
reveal that these Dirac cones mainly derive from the original cones at the K
(K') points of free-standing silicene. The Dirac cones of free-standing
silicene are split by external periodic potentials that originate from the
substrate-overlayer interaction. Our results not only confirm the origin of the
Dirac cones in the 3x3-silicene/Ag(111) system, but also provide a powerful
route to manipulate the electronic structures of two-dimensional materials.


  The work considers the damped Pinney equation, defined as the model arising
when a linear in velocity damping term is included in the Pinney equation. In
the general case the resulting equation does not admit Lie point symmetries or
is reducible to a simpler form by any obvious coordinate transformation. In
this context the method of Kuzmak-Luke is applied to derive a perturbation
solution, for weak damping and slow time-dependence of the frequency function.
The perturbative and numerical solutions are shown to be in good agreement. The
results are applied to examine the time-evolution of Gaussian shaped
wave-functions in the Kostin formulation of dissipative quantum mechanics.


  Let $X$ be a del Pezzo surface of degree one over an algebraically closed
field $k$, and let $K_X$ be its canonical divisor. The morphism $\varphi$
induced by the linear system $|-2K_X|$ realizes $X$ as a double cover of a cone
in $\mathbb{P}^3$ that is ramified over a smooth curve of degree 6. The surface
$X$ contains 240 curves with negative self-intersection, called exceptional
curves. We prove that for a point~$P$ on the ramification curve of $\varphi$,
at most sixteen exceptional curves go through~$P$ in characteristic $2$, and at
most ten in all other characteristics. Moreover, we prove that for a point $Q$
outside the ramification curve of $\varphi$, at most twelve exceptional curves
go through $Q$ in characteristic $3$, and at most ten in all other
characteristics. We show that these upper bounds are sharp in all cases except
possibly in characteristic 5 outside the ramification curve.


  The problem of constrained reinforcement learning (CRL) holds significant
importance as it provides a framework for addressing critical safety
satisfaction concerns in the field of reinforcement learning (RL). However,
with the introduction of constraint satisfaction, the current CRL methods
necessitate the utilization of second-order optimization or primal-dual
frameworks with additional Lagrangian multipliers, resulting in increased
complexity and inefficiency during implementation. To address these issues, we
propose a novel first-order feasible method named Constrained Proximal Policy
Optimization (CPPO). By treating the CRL problem as a probabilistic inference
problem, our approach integrates the Expectation-Maximization framework to
solve it through two steps: 1) calculating the optimal policy distribution
within the feasible region (E-step), and 2) conducting a first-order update to
adjust the current policy towards the optimal policy obtained in the E-step
(M-step). We establish the relationship between the probability ratios and KL
divergence to convert the E-step into a convex optimization problem.
Furthermore, we develop an iterative heuristic algorithm from a geometric
perspective to solve this problem. Additionally, we introduce a conservative
update mechanism to overcome the constraint violation issue that occurs in the
existing feasible region method. Empirical evaluations conducted in complex and
uncertain environments validate the effectiveness of our proposed method, as it
performs at least as well as other baselines.


  Elemental calcium (Ca), a simple metal at ambient conditions, has attracted
huge interest because of its unusual high-pressure behavior in structural,
electrical, and melting properties whose origin remain unsolved. Here, using a
theoretical framework appropriate for describing electride phase formation,
i.e., the presence of anionic electrons, we establish electride formation in Ca
at a pressure as low as 8 GPa. Our analysis shows that under pressure the
valence electrons of Ca localize at octahedral holes and exhibit anionic
character which is responsible for its strange pressure behavior. Our
calculated enthalpy and electrical resistance indicate that Ca will directly
transform from an FCC-electride phase to an SC-electride phase near 30 GPa
thereby avoiding the intermediate BCC phase. These findings are not limited to
Ca but might hold a key to the understanding of host-guest type structures
which occur in other elemental solids though at much higher pressures.


  This paper presents a new stochastic preconditioning approach. For symmetric
diagonally-dominant M-matrices, we prove that an incomplete LDL factorization
can be obtained from random walks, and used as a preconditioner for an
iterative solver, e.g., conjugate gradient. It is argued that our factor
matrices have better quality, i.e., better accuracy-size tradeoffs, than
preconditioners produced by existing incomplete factorization methods.
Therefore the resulting preconditioned conjugate gradient (PCG) method requires
less computation than traditional PCG methods to solve a set of linear
equations with the same error tolerance, and the advantage increases for larger
and denser sets of linear equations. These claims are verified by numerical
tests, and we provide techniques that can potentially extend the theory to more
general types of matrices.


  Witten's linear sigma model for ADHM instantons possesses a natural $(0,4)$
supersymmetry. We study generalizations of the infrared limit of the model that
are invariant under $(4,4)$ supersymmetry. In the case of four space-time
dimensions a background with a conformally flat metric and torsion is required.
The geometry is specified by a single real scalar function satisfying Laplace's
equation. It gives rise to 't Hooft instantons for the gauge group $SU(2)$,
instead of the general ADHM instantons for an $SO(n)$ gauge group in the case
$(0,4)$.


  We present a far reaching generalization of a factorization theorem by Bhat,
Ramesh, and Sumesh (stated first by Asadi) and furnish a very quick proof.


  We prove that the number of immediate descendants of order $p^10$ of $G_p$ is
not PORC (Polynomial On Residue Classes) where $G_p$ is the $p$-group of order
$p^9$ defined by du Sautoy's nilpotent group encoding the elliptic curve
$y^2=x^3-x$. This has important implications for Higman's PORC conjecture.


  We introduce a simple functional language foetus (lambda calculus with
tuples, constructors and pattern matching) supplied with a termination checker.
This checker tries to find a well-founded structural order on the parameters on
the given function to prove termination. The components of the check algorithm
are: function call extraction out of the program text, call graph completion
and finding a lexical order for the function parameters.


  In the Galaxy, close binaries with compact objects are important
low-frequency gravitational wave (GW) sources. As potential low-frequency GW
sources, neutron star/white dwarf (WD) ultra-compact X-ray binaries (UCXBs)
have been investigated extensively. Using the MESA code, we systematically
explored the evolution of black hole (BH)-main sequence star (MS) binaries to
diagnose whether their descendants can be detected by space-borne GW detectors.
Our simulations show that BH-MS binaries with an initial orbital period less
than the bifurcation period can evolve into BH UCXBs that can be detected by
LISA. Such an evolutionary channel would form compact mass-transferring BH-WD
systems rather than detached BH-WD systems. The calculated X-ray luminosities
of BH UCXBs detected by LISA at a distance $d=1$ kpc are
$\sim10^{33}-10^{35}~\rm erg\,s^{-1}$ ($\sim10^{34}-10^{35}~\rm erg\,s^{-1}$
for $d=10$ kpc), hence it is possible to detect their electromagnetic
counterparts. It is worth emphasizing only some BH-MS systems with an initial
orbital period very close to the bifurcation period can evolve toward
low-frequency GW sources whose chirp masses can be measured. The maximum GW
frequency of BH UCXBs forming by BH-MS pathway is about 3 mHz, which is smaller
than the minimum GW frequency (6.4 mHz) of mass-transferring BH-WD originating
from a dynamic process. Furthermore, we obtain an initial parameter space
(donor-star masses and orbital periods) of progenitors of BH UCXB-GW sources,
which can be applied to future population synthesis simulations. By a rough
estimation, we predict that LISA could detect only a few BH UCXB-GW sources
forming by the BH-MS channel.


  A rich literature has explored the modeling of homophily and other forms of
nonuniform mixing associated with individual-level covariates within the
exponential family random graph (ERGM) framework. Such differential mixing does
not fully explain phenomena such as stigma, however, which involve the active
maintenance of social boundaries by ostracism of persons with out-group ties.
Here, we introduce a new statistic that allows for such effects to be captured,
making it possible to probe for the potential presence of boundary maintenance
above and beyond simple differences in nomination rates. We demonstrate this
statistic in the context of gender segregation in a school classroom.


  We develop a convenient framework for characterizing multipartite
entanglement in composite systems, based on relations between entropies of
various subsystems. This continues the program initiated in arXiv:1808.07871,
of using holography to effectively recast the geometric problem into an
algebraic one. We prove that, for an arbitrary number of parties, our procedure
identifies a finite set of entropic information quantities that we conveniently
represent geometrically in the form of an arrangement of hyperplanes. This
leads us to define the holographic entropy arrangement, whose algebraic and
combinatorial aspects we explore in detail. Using the framework, we derive
three new information quantities for four parties, as well as a new infinite
family for any number of parties. A natural construct from the arrangement is
the holographic entropy polyhedron which captures holographic entropy
inequalities describing the physically allowed region of entropy space. We
illustrate how to obtain the polyhedron by winnowing down the arrangement
through a sieve to pick out candidate sign-definite information quantities.
Comparing the polyhedron with the holographic entropy cone, we find perfect
agreement for 4 parties and corroborating evidence for the conjectured 5-party
entropy cone. We work with explicit configurations in arbitrary
(time-dependent) states leading to both simple derivations and an intuitive
picture of the entanglement pattern.


  A qualitative analysis of the chiral phase transition in QCD at non--zero
baryon density is performed. It is assumed that at zero baryonic density,
$\rho=0$, the temperature phase transition is of the second order and quark
condesate $\eta= \mid < 0\mid \bar{u} u\mid 0> \mid =\mid< 0 \mid \bar{d}d\mid
0 >\mid $ may be taken as order parameter of phase transition. It is
demonstrated, that the proportionality of baryon masses to quark condensate in
the power 1/3, $m_B \sim \mid < 0 \mid {\bar q} q \mid 0 > \mid^{1/3}$ is valid
in the wide interval of quark condensate values. By supposing, that such
specific dependence of baryon masses on quark condensate takes place up to
phase transition point, it is shown, that at finite baryon density $\rho$ the
phase transition becomes of the first order at the temperature
$T=T_{\mathrm{ph}}(\rho)$ for $\rho>0$. At temperatures
$T_{\mathrm{cont}}(\rho) > T > T_{\mathrm{ph}}(\rho)$ there is a mixed phase
consisting of the quark phase (stable) and the hadron phase (unstable). At the
temperature $T = T_{\mathrm{cont}}(\rho)$ the system experiences a continuous
transition to the pure chirally symmetric phase.


  Participating in demand response programs is a promising tool for reducing
energy costs in data centers by modulating energy consumption. Towards this
end, data centers can employ a rich set of resource management knobs, such as
workload shifting and dynamic server provisioning. Nonetheless, these knobs may
not be readily available in a cloud data center (CDC) that serves cloud
tenants/users, because workloads in CDCs are managed by tenants themselves who
are typically charged based on a usage-based or flat-rate pricing and often
have no incentive to cooperate with the CDC operator for demand response and
cost saving. Towards breaking such "split incentive" hurdle, a few recent
studies have tried market-based mechanisms, such as dynamic pricing, inside
CDCs. However, such mechanisms often rely on complex designs that are hard to
implement and difficult to cope with by tenants. To address this limitation, we
propose a novel incentive mechanism that is not dynamic, i.e., it keeps pricing
for cloud resources unchanged for a long period. While it charges tenants based
on a Usage-based Pricing (UP) as used by today's major cloud operators, it
rewards tenants proportionally based on the time length that tenants set as
deadlines for completing their workloads. This new mechanism is called
Usage-based Pricing with Monetary Reward (UPMR). We demonstrate the
effectiveness of UPMR both analytically and empirically. We show that UPMR can
reduce the CDC operator's energy cost by 12.9% while increasing its profit by
4.9%, compared to the state-of-the-art approaches used by today's CDC operators
to charge their tenants.


  Graph edit distance (GED) is a powerful and flexible graph matching paradigm
that can be used to address different tasks in structural pattern recognition,
machine learning, and data mining. In this paper, some new binary linear
programming formulations for computing the exact GED between two graphs are
proposed. A major strength of the formulations lies in their genericity since
the GED can be computed between directed or undirected fully attributed graphs
(i.e. with attributes on both vertices and edges). Moreover, a relaxation of
the domain constraints in the formulations provides efficient lower bound
approximations of the GED. A complete experimental study comparing the proposed
formulations with 4 state-of-the-art algorithms for exact and approximate graph
edit distances is provided. By considering both the quality of the proposed
solution and the efficiency of the algorithms as performance criteria, the
results show that none of the compared methods dominates the others in the
Pareto sense. As a consequence, faced to a given real-world problem, a
trade-off between quality and efficiency has to be chosen w.r.t. the
application constraints. In this context, this paper provides a guide that can
be used to choose the appropriate method.


  In Kac's classification of finite-dimensional Lie superalgebras, the
contragredient ones can be constructed from Dynkin diagrams similar to those of
the simple finite-dimensional Lie algebras, but with additional types of nodes.
For example, $A(n-1,0) = \mathfrak{sl}(1|n)$ can be constructed by adding a
"gray" node to the Dynkin diagram of $A_{n-1} = \mathfrak{sl}(n)$,
corresponding to an odd null root. The Cartan superalgebras constitute a
different class, where the simplest example is $W(n)$, the derivation algebra
of the Grassmann algebra on $n$ generators. Here we present a novel
construction of $W(n)$, from the same Dynkin diagram as $A(n-1,0)$, but with
additional generators and relations.


  We report a measurement of the branching fraction of inclusive semileptonic
$B$ meson decays $B\to X_c\ell\nu\ell$ in $\Upsilon(4S)\to B\bar B$~data
recorded by the Belle II experiment at the SuperKEKB asymmetric-energy $e^+e^-$
collider and corresponding to 62.8 fb$^{-1}$ of integrated luminosity. Only a
charged lepton (electon or muon) is reconstructed and the signal yield is
determined from a fit to the lepton momentum distribution in the center-of-mass
frame of the colliding beams. Averaging the result in the electron and muon
channels, we find ${\cal B}(B\to X_c\ell\nu_\ell) = (9.75\pm
0.03(\text{stat})\pm 0.47(\text{sys}))\%$.


  We present a procedure to solve the Schroedinger equation of two interacting
electrons in a quantum dot in the presence of an external magnetic field within
the context of quasi-exactly-solvable spectral problems. We show that the
symmetries of the Hamiltonian can be recovered for specific values of the
magnetic field, which leads to an exact determination of the eigenvalues and
eigenfunctions. We show that the problem possesses a hidden sl_2-algebraic
structure.


  A characterization of the C-projective vector fields on a Randers spaces is
presented in terms of a recently introduced non-Riemannian quantity defined by
Z. Shen and denoted by ${\bf\Xi}$; It is proved that the quantity ${\bf\Xi}$ is
invariant for C-projective vector fields. Therefore, the dimension of the
algebra of the C-projective vector fields on an $n$-dimensional Randers space
is at most $n(n+2)$. The generalized Funk metrics on the $n$-dimensional
Euclidean unit ball $\mathbb{B}^n(1)$ are shown to be explicit examples of the
Randers metrics with a C-projective algebra of maximum dimension $n(n+2)$.
Then, it is also proved that an $n$-dimensional Randers space has a
C-projective algebra of maximum dimension $n(n+2)$ if and only if it is locally
Minkowskian or (up to re-scaling) locally isometric to the generalized Funk
metric. A new projective invariant is also introduced.


  If $G=(V_G, E_G)$ is a graph, then $S\subseteq V_G$ is a global defensive
$k$-alliance in $G$ if (i) each vertex not in $S$ has a neighbor in $S$ and
(ii) each vertex of $S$ has at least $k$ more neighbors inside $S$ than outside
of it. The global defensive $k$-alliance number of $G$ is the minimum
cardinality among all global defensive $k$-alliance in $G$. In this paper this
concept is studied on the generalized hierarchical, the lexicographic, the
corona, and the edge corona product. For all of these products upper bounds
expressed with related invariants of the factors are given. Sharpness of the
bounds are also discussed.


  Let $k$ be a non-archimedean complete valued field and let X be a smooth
Berkovich analytic $k$-curve. Let $F$ be a finite locally constant \'{e}tale
sheaf on $k$ whose torsion is prime to the residue characteristic. We denote by
$|X|$ the underlying topological space and by $\pi$ the canonical map from the
\'{e}tale site to $|X|$. In this text we define a triangulation of $X$, we show
that it always exists and use it to compute $H^{0}(|X|,R^{q}\pi\_{*}F)$ and
$H^{1}(|X|,R^{q}\pi\_{*}F)$. If $X$ is the analytification of an algebraic
curve we give sufficient conditions so that those groups are isomorphic to
their algebraic counterparts ; if the cohomology of $k$ has a dualizing sheaf
in some degree $d$ (e.g $k$ is $p$-adic, or $k=C((t))$) then we prove a duality
theorem between $H^{0}(|X|,R^{q}\pi\_{*}F)$ and $H^{1}\_
{c}(|X|,R^{d+1}\pi\_{*}G)$ where $G$ is the tensor product of the dual sheaf of
$F$ with the dualizing sheaf and the sheaf of $n$-th roots of unity.


  We present a tight lower bound for the spanning tree congestion of Hamming
graphs.


  We study the invariant measures and fluctuation limits of discrete-time
harness processes in one spatial dimension. We construct one essential ergodic
(under spatial shifts) invariant measure of the increment process derived from
harness process, and all other ergodic invariant measures can be obtained by
adding constants. We also show that the weak limit of the one dimensional
height fluctuations starting from the increments under several
translation-invariant ergodic measures will obey Edwards-Wilkinson equation,
and the finite-dimensional marginal convergence can be extended to a process
level convergence.


  The equations of motion for the position and gauge invariant crystal momentum
are considered for multiband wave packets of Bloch electrons. For a localized
packet in a subset of bands well-separated from the rest of the band structure
of the crystal, one can construct an effective electromagnetic Hamiltonian with
respect to the center of the packet. We show that the equations of motion can
be obtained via a projection operator procedure, which is derived from the
adiabatic approximation within perturbation theory. These relations explicitly
contain information from each band captured in the expansion coefficients and
energy band structure of the Bloch states as well as non-Abelian features
originating from interband Berry phase properties. This general and transparent
Hamiltonian-based approach is applied to a wave packet spread over a single
band, a set of degenerate bands, and two linear crossing bands. The generalized
equations of motion hold promise for novel effects in transport currents and
Hall effect phenomena.


  We generalise and offer a different proof of a recent $L^2$ square function
estimate on UR sets by Hofmann, Mitrea, Mitrea and Morris. The proof is a short
argument using the $\alpha$-numbers of Tolsa.


  We first derive the relation between the eikonal approximation to the Maxwell
wave equations in an inhomogeneous anisotropic medium and geodesic motion in a
three dimensional Riemannian manifold using a method which identifies the
symplectic structure of the corresponding mechanics. We then apply an analogous
method to the five dimensional generalization of Maxwell theory required by the
gauge invariance of Stueckelberg's covariant classical and quantum dynamics to
demonstrate, in the eikonal approximation, the existence of geodesic motion for
the flow of mass in a four dimensional pseudo-Riemannian manifold. These
results provide a foundation for the geometrical optics of the five dimensional
radiation theory and establish a model in which there is mass flow along
geodesics. Finally we discuss the case of relativistic quantum theory in an
anisotropic medium as well. In this case the eikonal approximation to the
relativistic quantum mechanical current coincides with the geodesic flow
governed by the pseudo-Riemannian metric obtained from the eikonal
approximation to solutions of the Stueckelberg-Schr\"odinger equation. This
construction provides a model for an underlying quantum mechanical structure
for classical dynamical motion along geodesics on a pseudo-Riemannian manifold.
The locally symplectic structure which emerges is that of Stueckelberg's
covariant mechanics on this manifold.


  Dirac neutrino masses require two distinct neutral Weyl spinors per
generation, with a special arrangement of masses and interactions with charged
leptons. Once this arrangement is perturbed, lepton number is no longer
conserved and neutrinos become Majorana particles. If these lepton number
violating perturbations are small compared to the Dirac mass terms, neutrinos
are quasi-Dirac particles. Alternatively, this scenario can be characterized by
the existence of pairs of neutrinos with almost degenerate masses, and a lepton
mixing matrix which has 12 angles and 12 phases. In this work we discuss the
phenomenology of quasi-Dirac neutrino oscillations and derive limits on the
relevant parameter space from various experiments. In one parameter
perturbations of the Dirac limit, very stringent bounds can be derived on the
mass splittings between the almost degenerate pairs of neutrinos. However, we
also demonstrate that with suitable changes to the lepton mixing matrix, limits
on such mass splittings are much weaker, or even completely absent. Finally, we
consider the possibility that the mass splittings are too small to be measured
and discuss bounds on the new, non-standard lepton mixing angles from current
experiments for this case.


  Computing the determinant of a matrix with the univariate and multivariate
polynomial entries arises frequently in the scientific computing and
engineering fields. In this paper, an effective algorithm is presented for
computing the determinant of a matrix with polynomial entries using hybrid
symbolic and numerical computation. The algorithm relies on the Newton's
interpolation method with error control for solving Vandermonde systems. It is
also based on a novel approach for estimating the degree of variables, and the
degree homomorphism method for dimension reduction. Furthermore, the
parallelization of the method arises naturally.


  Generative AI has put many professional writers on the defensive; a major
negotiation point of the recent Writers Guild of America's strike concerned use
of AI. However, must AI threaten writers, their livelihoods or their
creativity? And under what conditions, if any, might AI assistance be invited
by different types of writers (from the amateur to the professional, from the
screenwriter to the novelist)? To explore these questions, we conducted a
qualitative study with 37 writers. We found that most writing occurs across
five stages and within one of three modes; we additionally map openness to AI
assistance to each intersecting stage-mode. We found that most writers were
interested in AI assistance to some degree, but some writers felt drawing firm
boundaries with an AI was key to their comfort using such systems. Designers
can leverage these insights to build agency-respecting AI products for writers.


  While machine learning (ML) has shown increasing effectiveness in optimizing
materials properties under known physics, its application in challenging
conventional wisdom and discovering new physics still remains challenging due
to its interpolative nature. In this work, we demonstrate the potential of
using ML for such applications by implementing an adaptive ML-accelerated
search process that can discover unexpected lattice thermal conductivity
($\kappa_l$) enhancement instead of reduction in aperiodic superlattices (SLs)
as compared to periodic superlattices. We use non-equilibrium molecular
dynamics (NEMD) simulations for high-fidelity calculations of $\kappa_l$ for a
small fraction of SLs in the search space, along with a convolutional neural
network (CNN) which can rapidly predict $\kappa_l$ for a large number of
structures. To ensure accurate prediction by the CNN for the target unknown
structures, we iteratively identify aperiodic SLs containing structural
features which lead to locally enhanced thermal transport, and include them as
additional training data for the CNN in each iteration. As a result, our CNN
can accurately predict the high $\kappa_l$ of aperiodic SLs that are absent
from the initial training dataset, which allows us to identify the previously
unseen exceptional structures. The identified RML structures exhibit increased
coherent phonon contribution to thermal conductivity owing to the presence of
closely spaced interfaces. Our work describes a general purpose machine
learning approach for identifying low-probability-of-occurrence exceptional
solutions within an extremely large subspace and discovering the underlying
physics.


  Over the past decade, non-Hermitian, $\mathcal{PT}$-symmetric Hamiltonians
have been investigated as candidates for both, a fundamental, unitary, quantum
theory, and open systems with a non-unitary time evolution. In this paper, we
investigate the implications of the former approach in the context of the
latter. Motivated by the invariance of the $\mathcal{PT}$ (inner) product under
time evolution, we discuss the dynamics of wave-function phases in a wide range
of $\mathcal{PT}$-symmetric lattice models. In particular, we numerically show
that, starting with a random initial state, a universal, gain-site location
dependent locking between wave function phases at adjacent sites occurs in the
$\mathcal{PT}$-symmetry broken region. Our results pave the way towards
understanding the physically observable implications of time-invariants in the
non-unitary dynamics produced by $\mathcal{PT}$-symmetric Hamiltonians.


  We report on an enhancement of the Curie temperature in GaMnAs/InGaMnAs
superlattices grown by low-temperature molecular beam epitaxy, which is due to
thin InGaMnAs or InGaAs films embedded into the GaMnAs layers. The pronounced
increase of the Curie temperature is strongly correlated to the In
concentration in the embedded layers. Curie temperatures up to 110 K are
observed in such structures compared to 60 K in GaMnAs single layers grown
under the same conditions. A further increase in T$_C$ up to 130 K can be
achieved using post-growth annealing at temperatures near the growth
temperature. Pronounced thickness fringes in the high resolution X-ray
diffraction spectra indicate good crystalline quality and sharp interfaces in
the structures.


  In this thesis we explore the implications of neutrino oscillations in the
context of the solar neutrino data, the atmospheric neutrino data and results
from the terrestrial accelerator/reactor neutrino oscillation experiments. We
perform comprehensive $\chi^2$ analysis for the global solar neutrino data
including SNO and present our results for two flavor $\nu_e-\nu_{active}$ and
$\nu_e-\nu_{sterile}$ oscillations. We explore the apparent conflict between
the flat SK spectrum and the non-monotonic energy dependence of the solar
neutrino survival probability inferred from the global data on total rates. We
analyze the SK atmospheric neutrino data in the framework of two and three
generations. For the three-generation analysis we simultaneously take into
account the results of the terrestrial neutrino experiments. We consider the
possibility of unstable neutrinos and explore the viability of this decay model
as a solution to the atmospheric neutrino anomaly. We make quantitative
predictions for the number of events recorded in the water Cerenkov detectors
due a galactic supernova and examine the signatures of neutrino mass and mixing
in the resultant neutrino signal.


  We extend the construction of the DAHA-Jones polynomials for any reduced root
systems and DAHA-superpolynomials in type A from the iterated torus knots (our
previous paper) to links, including arbitrary algebraic links. Such a passage
essentially corresponds to the usage of the products of Macdonald polynomials
and is directly connected to the so-called splice diagrams. The specialization
t=q of our superpolynomials conjecturally results in the HOMFLY-PT polynomials.
The relation of our construction to the stable Khovanov-Rozansky polynomials
and the so-called ORS-polynomials of the corresponding plane curve
singularities is expected for algebraic links in the uncolored case. These 2
connections are less certain, since the Khovanov-Rozansky theory for links is
not sufficiently developed and the ORS polynomials are quite involved. However
we provide some confirmations. For Hopf links, our construction produces the
DAHA-vertex, similar to the refined topological vertex, which is an important
part of our paper.


  A very short and direct proof along the lines of the Kamae-Katznelson-Weiss
approach.


  Elastic and inelastic properties of weakly bound s- and p-wave molecules of
fermionic atoms that collide with a third atom are investigated. Analysis of
calculated collisional properties of s-wave dimers of fermions in different
spin states permit us to compare and highlight the physical mechanisms that
determine the stability of s-wave and p-wave molecules. In contrast to s-wave
molecules, the collisional properties of p-wave molecules are found to be
largely insensitive to variations of the p-wave scattering length and that
these collisions will usually result in short molecular lifetimes. We also
discuss the importance of this result for both theories and experiments
involving degenerate Fermi gases.


  Particle aspects of two-dimensional conformal field theories are
investigated, using methods from algebraic quantum field theory. The results
include asymptotic completeness in terms of (counterparts of) Wigner particles
in any vacuum representation and the existence of (counterparts of)
infraparticles in any charged irreducible product representation of a given
chiral conformal field theory. Moreover, an interesting interplay between the
infraparticle's direction of motion and the superselection structure is
demonstrated in a large class of examples. This phenomenon resembles the
electron's momentum superselection expected in quantum electrodynamics.