  This document provides a comprehensive guide to hyperparameter tuning using
spotPython for scikit-learn, PyTorch, and river. The first part introduces
spotPython's surrogate model-based optimization process, while the second part
focuses on hyperparameter tuning. Several case studies are presented, including
hyperparameter tuning for sklearn models such as Support Vector Classification,
Random Forests, Gradient Boosting (XGB), and K-nearest neighbors (KNN), as well
as a Hoeffding Adaptive Tree Regressor from river. The integration of
spotPython into the PyTorch and PyTorch Lightning training workflow is also
discussed. With a hands-on approach and step-by-step explanations, this
cookbook serves as a practical starting point for anyone interested in
hyperparameter tuning with Python. Highlights include the interplay between
Tensorboard, PyTorch Lightning, spotPython, and river. This publication is
under development, with updates available on the corresponding webpage.


  An unsupervised learning classification model is described. It achieves
classification error probability competitive with that of popular supervised
learning classifiers such as SVM or kNN. The model is based on the incremental
execution of small step shift and rotation operations upon selected
discriminative hyperplanes at the arrival of input samples. When applied, in
conjunction with a selected feature extractor, to a subset of the ImageNet
dataset benchmark, it yields 6.2 % Top 3 probability of error; this exceeds by
merely about 2 % the result achieved by (supervised) k-Nearest Neighbor, both
using same feature extractor. This result may also be contrasted with popular
unsupervised learning schemes such as k-Means which is shown to be practically
useless on same dataset.


  We look for long-living topological solutions of classical nonlinear $(1+1)-$
dimensional $\varphi^4$ field theory. To that effect we use the well-known
cut-and-match method. In this framework, new long-living states are obtained in
both topological sectors. In particular, in one case a highly excited state of
a kink is found. We discover several ways of energy reset. In addition to the
expected emission wave packets (with small amplitude), for some selected
initial conditions the production of kink-antikink pairs results in a large
energy reset. Also, the topological number of a kink in the central region
changes in the contrast of saving full topological number. At lower excitation
energies there is a long-living excited vibrational state of the kink; this
phenomenon is the final stage of all considered initial states. Over time this
excited state of the kink changes to a well-known linearized solution - a
discrete kink excitation mode. This method yields a qualitatively new way to
describe the large-amplitude bion, which was detected earlier in the
kink-scattering processes in the nontopological sector.


  In this paper, we propose an online speaker diarization system based on
Relation Network, named RenoSD. Unlike conventional diariztion systems which
consist of several independently-optimized modules, RenoSD implements
voice-activity-detection (VAD), embedding extraction, and speaker identity
association using a single deep neural network. The most striking feature of
RenoSD is that it adopts a meta-learning strategy for speaker identity
association. In particular, the relation network learns to learn a deep
distance metric in a data-driven way and it can determine through a simple
forward pass whether two given segments belong to the same speaker. As such,
RenoSD can be performed in an online manner with low latency. Experimental
results on AMI and CALLHOME datasets show that the proposed RenoSD system
achieves consistent improvements over the state-of-the-art x-vector baseline.
Compared with an existing online diarization system named UIS-RNN, RenoSD
achieves a better performance using much fewer training data and at a lower
time complexity.


  A quantum superintegrable model with reflections on the three-sphere is
presented. Its symmetry algebra is identified with the rank-two Bannai-Ito
algebra. It is shown that the Hamiltonian of the system can be constructed from
the tensor product of four representations of the superalgebra
$\mathfrak{osp}(1|2)$ and that the superintegrability is naturally understood
in that setting. The exact separated solutions are obtained through the Fischer
decomposition and a Cauchy-Kovalevskaia extension theorem.


  Motion artifacts are a primary source of magnetic resonance (MR) image
quality deterioration with strong repercussions on diagnostic performance.
Currently, MR motion correction is carried out either prospectively, with the
help of motion tracking systems, or retrospectively by mainly utilizing
computationally expensive iterative algorithms. In this paper, we utilize a new
adversarial framework, titled MedGAN, for the joint retrospective correction of
rigid and non-rigid motion artifacts in different body regions and without the
need for a reference image. MedGAN utilizes a unique combination of
non-adversarial losses and a new generator architecture to capture the textures
and fine-detailed structures of the desired artifact-free MR images.
Quantitative and qualitative comparisons with other adversarial techniques have
illustrated the proposed model performance.


  We consider a $\phi$-mixing shift $T$ on a sequence space $\Om$ and study the
number $\cN_N$ of returns $\{ T^{q_N(n)}\om\in A^a_n\}$ at times $q_N(n)$ to a
cylinder $A^a_n$ constructed by a sequence $a\in\Om$ where $n$ runs either
until a fixed integer $N$ or until a time $\tau_N$ of the first return $\{
T^{q_N(n)}\om\in A^b_m\}$ to another cylinder $A^b_m$ constructed by $b\in\Om$.
Here $q_N(n)$ are certain functions of $n$ taking on nonnegative integer values
when $n$ runs from 0 to $N$ and the dependence on $N$ is the main
generalization here which requires certain conditions under which we obtain
Poisson distributions limits of $\cN_N$ when counting is until $N$ as
$N\to\infty$ and geometric distributions limits when counting is until $\tau_N$
as $N\to\infty$.


  We present a determination of the QCD coupling constant, $\alpha_s$, obtained
by fitting lattice results for the flavour $ud$ hadronic vacuum polarisation
function to continuum perturbation theory. We use $n_f=2+1$ flavours of Domain
Wall fermions generated by the RBC/UKQCD collaboration and three lattice
spacings $a^{-1}=1.79,\, 2.38$ and $3.15\ \text{GeV}$. Several sources of
potential systematic error are identified and dealt with. After fitting and
removing expected leading cut-off effects, we find for the five-flavour
$\overline{\text{MS}}$ coupling the value
$\alpha_s(M_Z)=0.1181(27)^{+8}_{-22}$, where the first error is statistical and
the second systematic.


  We obtain a complete classification of hypercomplex manifolds, on which a
compact group of automorphisms acts transitively.
  The description of the spaces as well as the proofs of our results use only
the structure theory of reductive groups, in particular the notion of "stem" of
a reduced root system, introduced in the first paper of this series.


  We demonstrate that the ability to polarize the photons produced by
back-scattering laser beams at a TeV scale linear $\epem$ collider could make
it possible to determine whether or not a neutral Higgs boson produced in
photon-photon collisions is a CP eigenstate. The relative utility of different
types of polarization is discussed. Asymmetries that are only non-zero if the
Higgs boson is a CP mixture are defined, and their magnitudes illustrated for a
two-doublet Higgs model with CP-violating neutral sector.


  Rhe Fast Radio Burst FRB121102 has been observed to repeat in an irregular
fashion. Using published timing data of the observed bursts, we show that
Poissonian statistics are not a good description of this random process. As an
alternative we suggest to describe the intervals between bursts with a Weibull
distribution with a shape parameter smaller than one, which allows for the
clustered nature of the bursts. We quantify the amount of clustering using the
parameters of the Weibull distribution and discuss the consequences that it has
for the detection probabilities of future observations and for the optimization
of observing strategies. \new{Allowing for this generalization, we find a mean
repetition rate of r=5.7^{+3.0}_{-2.0} per day and index k=0.34^{+0.06}_{-0.05}
for a correlation function \xi(t)=(t/t_0)^{k-1}.


  We describe a collection of acoustic and language modeling techniques that
lowered the word error rate of our English conversational telephone LVCSR
system to a record 6.6% on the Switchboard subset of the Hub5 2000 evaluation
testset. On the acoustic side, we use a score fusion of three strong models:
recurrent nets with maxout activations, very deep convolutional nets with 3x3
kernels, and bidirectional long short-term memory nets which operate on FMLLR
and i-vector features. On the language modeling side, we use an updated model
"M" and hierarchical neural network LMs.


  By numerical integration, we study the relaxation dynamics of degenerate
harmonic oscillator modes dispersively coupled to particle positions. Depending
on whether the effective inertial potential induced by the oscillators keep the
particles confined, or if the particle trajectories traverse the system, the
local oscillator energy dissipation rate changes drastically. The inertial
trapping, release and retrapping of particles results in a characteristic
step-wise relaxation process, with alternating regions of fast and slow
dissipation. To demonstrate this phenomenon we consider first a one-dimensional
minimal prototype model which displays these characteristics. We then treat the
effect of dispersive interaction in a model corresponding to an adsorbate
diffusing on a circular membrane interacting with its three lowest vibrational
modes. In the latter model, stepwise relaxation appears only in the presence of
thermal noise, which also causes a slow-in-time stochastic precession of the
mixing angle between the degenerate eigenmodes.


  We investigate the spreading of damage in Ising models with Kawasaki
spin-exchange dynamics which conserves the magnetization. We first modify a
recent master equation approach to account for dynamic rules involving more
than a single site. We then derive an effective-field theory for damage
spreading in Ising models with Kawasaki spin-exchange dynamics and solve it for
a two-dimensional model on a honeycomb lattice. In contrast to the cases of
Glauber or heat-bath dynamics, we find that the damage always spreads and never
heals. In the long-time limit the average Hamming distance approaches that of
two uncorrelated systems. These results are verified by Monte-Carlo
simulations.


  This paper studies the formal adiabatic limit of coassociative K3 fibred
torsion free $G_2$ manifolds fibred over a contractible base, shows how to put
this structure on a different fibration obtained by fibrewise performing Mukai
duality of K3 surfaces, and furthermore relates the gauge theories on both
fibrations by a Nahm transform. This gives a mathematical interpretation to the
physical speculations of Gukov, Yau and Zaslow.


  Encoder-decoder networks are popular for modeling sequences probabilistically
in many applications. These models use the power of the Long Short-Term Memory
(LSTM) architecture to capture the full dependence among variables, unlike
earlier models like CRFs that typically assumed conditional independence among
non-adjacent variables. However in practice encoder-decoder models exhibit a
bias towards short sequences that surprisingly gets worse with increasing beam
size.
  In this paper we show that such phenomenon is due to a discrepancy between
the full sequence margin and the per-element margin enforced by the locally
conditioned training objective of a encoder-decoder model. The discrepancy more
adversely impacts long sequences, explaining the bias towards predicting short
sequences.
  For the case where the predicted sequences come from a closed set, we show
that a globally conditioned model alleviates the above problems of
encoder-decoder models. From a practical point of view, our proposed model also
eliminates the need for a beam-search during inference, which reduces to an
efficient dot-product based search in a vector-space.


  We investigate measures of chaos in the measurement record of a quantum
system which is being observed. Such measures are attractive because they can
be directly connected to experiment. Two measures of chaos in the measurement
record are defined and investigated numerically for the case of a quantum
kicked top. A smooth transition between chaotic and regular behavior is found.


  In the current versions of the Dempster-Shafer theory, the only essential
restriction on the validity of the rule of combination is that the sources of
evidence must be statistically independent. Under this assumption, it is
permissible to apply the Dempster-Shafer rule to two or mere distinct
probability distributions.


  Out-of-distribution generalization in neural networks is often hampered by
spurious correlations. A common strategy is to mitigate this by removing
spurious concepts from the neural network representation of the data. Existing
concept-removal methods tend to be overzealous by inadvertently eliminating
features associated with the main task of the model, thereby harming model
performance. We propose an iterative algorithm that separates spurious from
main-task concepts by jointly identifying two low-dimensional orthogonal
subspaces in the neural network representation. We evaluate the algorithm on
benchmark datasets for computer vision (Waterbirds, CelebA) and natural
language processing (MultiNLI), and show that it outperforms existing concept
removal methods


  We prove by an explicit construction that solutions to incompressible 3D
Euler equations defined in the periodic cube can be mapped bijectively to a new
system of equations whose solutions are globally regular. We establish that the
usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a
solution to the 3D Euler system is equivalent to a condition on the
corresponding \emph{regular} solution of the new system. In the hypothetical
case of Euler finite-time singularity, we provide an explicit formula for the
blowup time in terms of the regular solution of the new system. The new system
is amenable to being integrated numerically using similar methods as in Euler
equations. We propose a method to simulate numerically the new regular system
and describe how to use this to draw robust and reliable conclusions on the
finite-time singularity problem of Euler equations, based on the conservation
of quantities directly related to energy and circulation. The method of mapping
to a regular system can be extended to any fluid equation that admits a
Beale-Kato-Majda type of theorem, e.g. 3D Navier-Stokes, 2D and 3D
magnetohydrodynamics, and 1D inviscid Burgers. We discuss briefly the case of
2D ideal magnetohydrodynamics. In order to illustrate the usefulness of the
mapping, we provide a thorough comparison of the analytical solution versus the
numerical solution in the case of 1D inviscid Burgers equation.


  We have been trying to get software engineering researchers and practitioners
to talk to one another for over a decade. This paper describes what we have
done, assesses our impact, and recommends an approach that we hope will have
greater success.


  Different dynamics, described by kinetic equation and clipping method is
shown as well as a role of approximate resonances in wave turbulence theory.
Applications of clipping method are sketched for gravity-capillary and drift
waves. Brief discussion of possible transition from continuous spectrum (=
kinetic equation) to discrete spectrum (= clipping) is given at the end.


  We show that the geometric realisation of the poset of proper parabolic
subgroups of a large-type Artin group has a systolic geometry. We use this
geometry to show that the set of parabolic subgroups of a large-type Artin
group is stable under arbitrary intersections and forms a lattice for the
inclusion. As an application, we show that parabolic subgroups of large-type
Artin groups are stable under taking roots and we completely characterise the
parabolic subgroups that are conjugacy stable.
  We also use this geometric perspective to recover and unify results
describing the normalisers of parabolic subgroups of large-type Artin groups.


  We introduce an extension of the dynamical mean field approximation (DMFA)
which retains the causal properties and generality of the DMFA, but allows for
systematic inclusion of non-local corrections. Our technique maps the problem
to a self-consistently embedded cluster. The DMFA (exact result) is recovered
as the cluster size goes to one (infinity). As a demonstration, we study the
Falicov-Kimball model using a variety of cluster sizes. We show that the sum
rules are preserved, the spectra are positive definite, and the non-local
correlations suppress the CDW transition temperature. \


  In 1980, Burr conjectured that every directed graph with chromatic number
$2k-2$ contains any oriented tree of order $k$ as a subdigraph. Burr showed
that chromatic number $(k-1)^2$ suffices, which was improved in 2013 to
$\frac{k^2}{2} - \frac{k}{2} + 1$ by Addario-Berry et al. We give the first
subquadratic bound for Burr's conjecture, by showing that every directed graph
with chromatic number $8\sqrt{\frac{2}{15}} k \sqrt{k} + O(k)$ contains any
oriented tree of order $k$. Moreover, we provide improved bounds of
$\sqrt{\frac{4}{3}} k \sqrt{k}+O(k)$ for arborescences, and $(b-1)(k-3)+3$ for
paths on $b$ blocks, with $b\ge 2$.


  The Tokai to Kamioka (T2K) experiment uses a beam of muon neutrinos, produced
at the J-PARC facility on the east coast of Japan, to study neutrino
oscillations driven by the $\Delta m_{\textrm{atm}}^{2}$ mass splitting. A
suite of near detectors located 280~m from the secondary beam source samples
the unoscillated beam, and the Super-Kamiokande water Cherenkov detector
samples the beam at a baseline of 295~km, and at a point $2.5^\circ$ off the
beam axis, giving a narrow-band beam centred around 600~MeV. Analyses of the
oscillation channels $\nu_\mu \to \nu_e$ and $\nu_\mu \to \nu_\mu$ allow
measurements to be made of $\theta_{13}$, $\theta_{23}$ and $\Delta
m^2_{\textrm{atm}}$, and, ultimately, for weak constraints to be placed on the
CP-violating phase $\delta_{CP}$.
  In addition to these analyses, T2K has made world-leading neutrino
cross-section measurements in the sub-GeV energy range, utilising both the near
and far detectors. The present work will discuss both the most recent
measurements of the oscillation parameters, and these cross section analyses.


  The joint distribution of two off-diagonal Wishart matrix elements was useful
in recent work on geometric probability [Finch 2010]. Not finding such formulas
in the literature, we report these here.


  A rigorous mathematical model and an efficient computational method are
proposed to solving the inverse elastic surface scattering problem which arises
from the near-field imaging of periodic structures. We demonstrate how an
enhanced resolution can be achieved by using more easily measurable far-field
data. The surface is assumed to be a small and smooth perturbation of an
elastically rigid plane. By placing a rectangular slab of a homogeneous and
isotropic elastic medium with larger mass density above the surface, more
propagating wave modes can be utilized from the far-field data which
contributes to the reconstruction resolution. Requiring only a single
illumination, the method begins with the far-to-near (FtN) field data
conversion and utilizes the transformed field expansion to derive an analytic
solution for the direct problem, which leads to an explicit inversion formula
for the inverse problem. Moreover, a nonlinear correction scheme is developed
to improve the accuracy of the reconstruction. Results show that the proposed
method is capable of stably reconstructing surfaces with resolution controlled
by the slab's density.


  In this work, we present a lightweight pipeline for robust behavioral cloning
of a human driver using end-to-end imitation learning. The proposed pipeline
was employed to train and deploy three distinct driving behavior models onto a
simulated vehicle. The training phase comprised of data collection, balancing,
augmentation, preprocessing and training a neural network, following which, the
trained model was deployed onto the ego vehicle to predict steering commands
based on the feed from an onboard camera. A novel coupled control law was
formulated to generate longitudinal control commands on-the-go based on the
predicted steering angle and other parameters such as actual speed of the ego
vehicle and the prescribed constraints for speed and steering. We analyzed
computational efficiency of the pipeline and evaluated robustness of the
trained models through exhaustive experimentation during the deployment phase.
We also compared our approach against state-of-the-art implementation in order
to comment on its validity.


  Hermitian tensors are natural generalizations of Hermitian matrices, while
possessing rather different properties. A Hermitian tensor is separable if it
has a Hermitian decomposition with only positive coefficients, i.e., it is a
sum of rank-1 psd Hermitian tensors. This paper studies how to detect
separability of Hermitian tensors. It is equivalent to the long-standing
quantum separability problem in quantum physics, which asks to tell if a given
quantum state is entangled or not. We formulate this as a truncated moment
problem and then provide a semidefinite relaxation algorithm to solve it.
Moreover, we study psd decompositions of separable Hermitian tensors. When the
psd rank is low, we first flatten them into cubic order tensors and then apply
tensor decomposition methods to compute psd decompositions. We prove that this
method works well if the psd rank is low. In computation, this flattening
approach can detect separability for much larger sized Hermitian tensors. This
method is a good start on determining psd ranks of separable Hermitian tensors.


  We present what we believe is the first example of a "$\lambda$-line" phase
transition in black hole thermodynamics. This is a line of (continuous) second
order phase transitions which in the case of liquid $^4$He marks the onset of
superfluidity. The phase transition occurs for a class of asymptotically AdS
hairy black holes in Lovelock gravity where a real scalar field is conformally
coupled to gravity. We discuss the origin of this phase transition and outline
the circumstances under which it (or generalizations of it) could occur.


  In this paper we consider a modified version of the classical optimal
dividends problem of de Finetti in which the dividend payments subject to a
penalty at ruin. We assume that the risk process is modeled by a general
spectrally positive Levy process before dividends are deducted. Using the
fluctuation theory of spectrally positive Levy processes we give an explicit
expression of the value function of a barrier strategy. Subsequently we show
that a barrier strategy is the optimal strategy among all admissible ones. Our
work is motivated by the recent work of Bayraktar, Kyprianou and Yamazaki
(2013).


  Consider a totally ordered set $S$ of $n$ elements; as an example, a set of
tennis players and their rankings. Further assume that their ranking is a total
order and thus satisfies transitivity and anti-symmetry. Following Frances Yao
(1974), an element (player) is said to be $(i,j)$-\emph{mediocre} if it is
neither among the top $i$ nor among the bottom $j$ elements of $S$. Finding a
mediocre element is closely related to finding the median element. More than
$40$ years ago, Yao suggested a very simple and elegant algorithm for finding
an $(i,j)$-mediocre element: Pick $i+j+1$ elements arbitrarily and select the
$(i+1)$-th largest among them. She also asked: "Is this the best algorithm?" No
one seems to have found a better algorithm ever since. We first provide a
deterministic algorithm that beats the worst-case comparison bound in Yao's
algorithm for a large range of values of $i$ (and corresponding suitable
$j=j(i)$) even if the current best selection algorithm is used. We then repeat
the exercise for randomized algorithms; the average number of comparisons of
our algorithm beats the average comparison bound in Yao's algorithm for another
large range of values of $i$ (and corresponding suitable $j=j(i)$) even if the
best selection algorithm is used; the improvement is most notable in the
symmetric case $i=j$. Moreover, the tight bound obtained in the analysis of
Yao's algorithm allows us to give a definite answer for this class of
algorithms. In summary, we answer Yao's question as follows: (i)~"Presently
not" for deterministic algorithms and (ii)~"Definitely not" for randomized
algorithms. (In fairness, it should be said however that Yao posed the question
in the context of deterministic algorithms.)


  We present a study of the extreme O-type supergiant He 3-759 using new
high-resolution FEROS data, revealing that it is a near spectroscopic twin of
HD 151804 (O8 Iaf). We investigate the extinction towards He 3-759 using a
variety of methods, revealing A_V ~ 4.7 mag. If we assume He 3-759 has an
identical absolute K-band magnitude to HD 151804 we find that it lies in the
Sagittarius-Carina spiral arm at a distance of ~6.5 kpc. We derive the physical
and wind properties for He 3-759, revealing T* = 30.5 kK, log L/L(sun) = 5.9
and dM/dt = 10^-5.17 M(sun)/yr for a clumped wind whose terminal velocity is
estimated at 1000 km/s. The atmosphere of He 3-759 is enriched in helium (X_He
= 49%) and nitrogen (X_N = 0.3%). A reanalysis of HD 151804 and HD 152408
(WN9ha) reveals similar parameters except that the WN9ha star possesses a
stronger wind and reduced surface hydrogen content. HD 151804 and HD 152408 lie
within the Sco OB1 association, with initial masses of ~60 M(sun) and ages ~2.7
Myr, consistent with NGC 6231 cluster members using standard Geneva isochrones.
Improved agreement with observed surface abundances are obtained for similar
initial masses with more recent Geneva group predictions from which higher ages
of ~3.75 Myr are obtained. No young, massive star cluster is known to be
associated with He 3-759.


  Reopening strategies are crucial to balance efforts of economic
revitalization and bringing back a sense of normalcy while mitigating outbreaks
and effectively flattening the infection curve. This paper proposes practical
reopening, monitoring and testing strategies for institutions to reintroduce
physical meetings based on SIR simulations run on a student friendship network
collected pre-Covid-19. These serve as benchmarks to assess several testing
strategies that can be applied in physical classes. Our simulations show that
the best outbreak mitigation results are obtained with full knowledge of
contact, but are also robust to non-compliance of students to new social
interaction guidelines, simulated by partial knowledge of the interactions.
These results are not only applicable to institutions but also for any
organization or company wanting to navigate the Covid-19 ravaged world.


  In this paper we will be examining impartial scoring play games. We first
give the basic definitions for what impartial scoring play games are and look
at their general structure under the disjunctive sum. We will then examine the
game of nim and all octal games, and define a function that can help us analyse
these games. We will finish by looking at the properties this function has and
give many conjectures about the behaviour this function exhibits.


  We study the resolvent for nontrapping obstacles on manifolds with Euclidean
ends. It is well known that for such manifolds, the outgoing resolvent
satisfies $\|\chi R(k) \chi\|_{L^2\to L^2}\leq C{k}^{-1}$ for ${k}>1$, but the
constant $C$ has been little studied. We show that, for high frequencies, the
constant is bounded above by $2/\pi$ times the length of the longest
generalized bicharacteristic of $|\xi|_g^2-1$ remaining in the support of
$\chi.$ We show that this estimate is optimal in the case of manifolds without
boundary. We then explore the implications of this result for the numerical
analysis of the Helmholtz equation.


  To study systematically the evolution on the angular extents of the galaxy,
ICM, and dark matter components in galaxy clusters, we compiled the optical and
X-ray properties of a sample of 340 clusters with redshifts $<0.5$, based on
all the available data with the Sloan Digital Sky Survey (SDSS) and {\it
Chandra}/{\it XMM-Newton}. For each cluster, the member galaxies were
determined primarily with photometric redshift measurements. The radial ICM
mass distribution, as well as the total gravitational mass distribution, were
derived from a spatially-resolved spectral analysis of the X-ray data. When
normalizing the radial profile of galaxy number to that of the ICM mass, the
relative curve was found to depend significantly on the cluster redshift; it
drops more steeply towards outside in lower redshift subsamples. The same
evolution is found in the galaxy-to-total mass profile, while the ICM-to-total
mass profile varies in an opposite way. We interpret that the galaxies, the
ICM, and the dark matter components had similar angular distributions when a
cluster was formed, while the galaxies travelling interior of the cluster have
continuously fallen towards the center relative to the other components, and
the ICM has slightly expanded relative to the dark matter although it suffers
strong radiative loss. This cosmological galaxy infall, accompanied by an ICM
expansion, can be explained by considering that the galaxies interact strongly
with the ICM while they are moving through it. The interaction is considered to
create a large energy flow of $10^{44-45}$ erg $\rm s^{-1}$ per cluster from
the member galaxies to their environment, which is expected to continue over
cosmological time scales.


  We prove a version of the tamely ramified geometric Langlands correspondence
in positive characteristic for $GL_n(k)$. Let $k$ be an algebraically closed
field of characteristic $p> n$. Let $X$ be a smooth projective curve over $k$
with marked points, and fix a parabolic subgroup of $GL_n(k)$ at each marked
point. We denote by $\text{Bun}_{n,P}$ the moduli stack of (quasi-)parabolic
vector bundles on $X$, and by $\mathcal{L}oc_{n,P}$ the moduli stack of
parabolic flat connections such that the residue is nilpotent with respect to
the parabolic reduction at each marked point. We construct an equivalence
between the bounded derived category
$D^{b}(\text{Qcoh}({\mathcal{L}oc_{n,P}^{0}}))$ of quasi-coherent sheaves on an
open substack $\mathcal{L}oc_{n,P}^{0}\subset\mathcal{L}oc_{n,P}$, and the
bounded derived category
$D^{b}(\mathcal{D}^{0}_{{\text{Bun}}_{n,P}}\text{-mod})$ of
$\mathcal{D}^{0}_{{\text{Bun}}_{n,P}}$-modules, where
$\mathcal{D}^0_{\text{Bun}_{n,P}}$ is a localization of
$\mathcal{D}_{\text{Bun}_{n,P}}$ the sheaf of crystalline differential
operators on $\text{Bun}_{n,P}$. Thus we extend the work of
Bezrukavnikov-Braverman to the tamely ramified case. We also prove a
correspondence between flat connections on $X$ with regular singularities and
meromorphic Higgs bundles on the Frobenius twist $X^{(1)}$ of $X$ with first
order poles .


  With the growing ubiquity of wearable devices, sensed physiological responses
provide new means to connect with others. While recent research demonstrates
the expressive potential for biosignals, the value of sharing these personal
data remains unclear. To understand their role in communication, we created
Significant Otter, an Apple Watch/iPhone app that enables romantic partners to
share and respond to each other's biosignals in the form of animated otter
avatars. In a one-month study with 20 couples, participants used Significant
Otter with biosignals sensing OFF and ON. We found that while sensing OFF
enabled couples to keep in touch, sensing ON enabled easier and more authentic
communication that fostered social connection. However, the addition of
biosignals introduced concerns about autonomy and agency over the messages they
sent. We discuss design implications and future directions for communication
systems that recommend messages based on biosignals.


  We have developed a numerical MHD model of the propeller candidate star AE
Aqr using axisymmetric magneto-hydrodynamic (MHD) simulations. We suggest that
AE Aqr is an intermediate polar-type star, where the magnetic field is
relatively weak and an accretion disc may form around the white dwarf. The star
is in the propeller regime, and many of its observational properties are
determined by the disc-magnetosphere interaction. Comparisons of the
characteristics of the observed versus modelled AE Aqr star show that the model
can explain many observational properties of AE Aqr. In a representative model,
the magnetic field of the star is B\approx 3.3x10^5 G and the time averaged
accretion rate in the disc is 5.5\times 10^{16} g/s. Most of this matter is
ejected into conically-shaped winds. The numerical model explains the rapid
spin-down of AE Aqr through the outflow of angular momentum from the surface of
the star to the wind, corona and disc. The energy budget in the outflows,
9x10^{33} erg/s, is sufficient for explaining the observed flaring radiation in
different wavebands. The time scale of ejections into the wind matches the
short time scale variability in the light curves of AE Aqr.


  In this paper, we study the problem of latency and reliability trade-off in
ultra-reliable low-latency communication (URLLC) in the presence of decoding
complexity constraints. We consider linear block encoded codewords transmitted
over a binary-input AWGN channel and decoded with order-statistic (OS) decoder.
We first investigate the performance of OS decoders as a function of decoding
complexity and propose an empirical model that accurately quantifies the
corresponding trade-off. Next, a consistent way to compute the aggregate
latency for complexity constrained receivers is presented, where the latency
due to decoding is also included. It is shown that, with strict latency
requirements, decoding latency cannot be neglected in complexity constrained
receivers. Next, based on the proposed model, several optimization problems,
relevant to the design of URLLC systems, are introduced and solved. It is shown
that the decoding time has a drastic effect on the design of URLLC systems when
constraints on decoding complexity are considered. Finally, it is also
illustrated that the proposed model can closely describe the performance versus
complexity trade-off for other candidate coding solutions for URLLC such as
tail-biting convolutional codes, polar codes, and low-density parity-check
codes.


  Although deep face recognition benefits significantly from large-scale
training data, a current bottleneck is the labelling cost. A feasible solution
to this problem is semi-supervised learning, exploiting a small portion of
labelled data and large amounts of unlabelled data. The major challenge,
however, is the accumulated label errors through auto-labelling, compromising
the training. This paper presents an effective solution to semi-supervised face
recognition that is robust to the label noise aroused by the auto-labelling.
Specifically, we introduce a multi-agent method, named GroupNet (GN), to endow
our solution with the ability to identify the wrongly labelled samples and
preserve the clean samples. We show that GN alone achieves the leading accuracy
in traditional supervised face recognition even when the noisy labels take over
50\% of the training data. Further, we develop a semi-supervised face
recognition solution, named Noise Robust Learning-Labelling (NRoLL), which is
based on the robust training ability empowered by GN. It starts with a small
amount of labelled data and consequently conducts high-confidence labelling on
a large amount of unlabelled data to boost further training. The more data is
labelled by NRoLL, the higher confidence is with the label in the dataset. To
evaluate the competitiveness of our method, we run NRoLL with a rough condition
that only one-fifth of the labelled MSCeleb is available and the rest is used
as unlabelled data. On a wide range of benchmarks, our method compares
favorably against the state-of-the-art methods.


  This paper proposes a general unplanned incident analysis framework for
public transit systems from the supply and demand sides using automated fare
collection (AFC) and automated vehicle location (AVL) data. Specifically, on
the supply side, we propose an incident-based network redundancy index to
analyze the network's ability to provide alternative services under a specific
rail disruption. The impacts on operations are analyzed through the headway
changes. On the demand side, the analysis takes place at two levels: aggregate
flows and individual response. We calculate the demand changes of different
rail lines, rail stations, bus routes, and bus stops to better understand the
passenger flow redistribution under incidents. Individual behavior is analyzed
using a binary logit model based on inferred passengers' mode choices and
socio-demographics using AFC data. The public transit system of the Chicago
Transit Authority is used as a case study. Two rail disruption cases are
analyzed, one with high network redundancy around the impacted stations and the
other with low. Results show that the service frequency of the incident line
was largely reduced (by around 30% ~ 70%) during the incident time. Nearby rail
lines with substitutional functions were also slightly affected. Passengers
showed different behavioral responses in the two incident scenarios. In the low
redundancy case, most of the passengers chose to use nearby buses to move,
either to their destinations or to the nearby rail lines. In the high
redundancy case, most of the passengers transferred directly to nearby lines.
Corresponding policy implications and operating suggestions are discussed.


  We discuss supersymmetric Yang-Mills theory dimensionally reduced to zero
dimensions and evaluate the SU(2) and SU(3) partition functions by Monte Carlo
methods. The exactly known SU(2) results are reproduced to very high precision.
Our calculations for SU(3) agree closely with an extension of a conjecture due
to Green and Gutperle concerning the exact value of the SU(N) partition
functions.


  The Long Term Evolution (LTE) broadcast is a promising solution to cope with
exponentially increasing user traffic by broadcasting common user requests over
the same frequency channels. In this paper, we propose a novel network
framework provisioning broadcast and unicast services simultaneously. For each
serving file to users, a cellular base station determines either to broadcast
or unicast the file based on user demand prediction examining the file's
content specific characteristics such as: file size, delay tolerance, price
sensitivity. In a network operator's revenue maximization perspective while not
inflicting any user payoff degradation, we jointly optimize resource
allocation, pricing, and file scheduling. In accordance with the state of the
art LTE specifications, the proposed network demonstrates up to 32% increase in
revenue for a single cell and more than a 7-fold increase for a 7 cell
coordinated LTE broadcast network, compared to the conventional unicast
cellular networks.


  Using precise lattice QCD computations of the baryon spectrum, we present the
first direct evidence for the presence of contributions to the baryon masses
which are non-analytic in the light quark masses; contributions which are often
denoted "chiral logarithms". We isolate the poor convergence of SU(3) baryon
chiral perturbation theory to the flavor-singlet mass combination. The
flavor-octet baryon mass splittings, which are corrected by chiral logarithms
at next to leading order in SU(3) chiral perturbation theory, yield baryon-pion
axial coupling constants D, F, C and H consistent with QCD values; the first
evidence of chiral logarithms in the baryon spectrum. The Gell-Mann--Okubo
relation, a flavor-27 baryon mass splitting, which is dominated by chiral
corrections from light quark masses, provides further evidence for the presence
of non-analytic light quark mass dependence in the baryon spectrum; we
simultaneously find the GMO relation to be inconsistent with the first few
terms in a taylor expansion in m_s - m_l, which must be valid for small values
of this SU(3) breaking parameter. Additional, more definitive tests of SU(3)
chiral perturbation theory will become possible with future, more precise,
lattice calculations.


  For an arbitrary positive integer n, we construct infinitely many one-cusped
hyperbolic 3-manifolds where each manifold's A-polynomial detects every n-th
root of unity. This answers a question of Cooper, Culler, Gillet, Long, and
Shalen as to which roots of unity arise in this manner.


  We show how the Jaynes--Cummings--Rabi model of cavity quantum
electrodynamics can be realized via an isomorphism to the Hamiltonian of a
qubit inside a parametric amplifier cavity. This realization clears the way to
observe the full spectrum of the Rabi model via a probe applied to a parametric
amplifier cavity containing a qubit and a parametric oscillator operating below
threshold. An important outcome of the isomorphism is that the actual
frequencies are replaced by detunings which make it feasible to reach the
ultra-strong coupling regime. We find that inside this regime the probed
spectrum displays a narrow resonance peak that is traced back to the transition
between ground and first excited states. The exact form of these states is
given at an energy crossing and then extended numerically. At the crossing, the
eigenstates are entangled states of field and atom where the field is found
inside squeezed cat states.


  Terahertz (THz) tomography is a rather novel technique for nondestructive
testing that is particularly suited for the testing of plastics and ceramics.
Previous publications showed a large variety of conventional algorithms adapted
from computed tomography or ultrasound tomography which were directly applied
to THz tomography. Conventional algorithms neglect the specific nature of THz
radiation, i.e. refraction at interfaces, reflection losses and the beam
profile (Gaussian beam), which results in poor reconstructions. The aim is the
efficient reconstruction of the complex refractive index, since it indicates
inhomogeneities in the material. A hybrid algorithm has been developed based on
the algebraic reconstruction technique (ART). ART is adapted by including
refraction (Snell's law) and reflection losses (Fresnel equations). Our method
uses a priori information about the interface and layer geometry of the sample.
This results in the 'Modified ART for THz tomography', which reconstructs
simultaneously the complex refractive index from transmission coefficient and
travel time measurements.


  A brief experimental overview on the close-to-threshold eta meson production
in proton-proton interactions is presented and the available observables in
measurements with unpolarized and polarized beam and target are discussed.


  In this set of lectures, we review briefly some of the recent developments in
the study of the chaotic dynamics of nonlinear oscillators, particularly of
damped and driven type. By taking a representative set of examples such as the
Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain
the various bifurcations and chaos phenomena associated with these systems. We
use numerical and analytical as well as analogue simulation methods to study
these systems. Then we point out how controlling of chaotic motions can be
effected by algorithmic procedures requiring minimal perturbations. Finally we
briefly discuss how synchronization of identically evolving chaotic systems can
be achieved and how they can be used in secure communications.


  Medium-Mn steels exhibit excellent mechanical properties and lower production
costs compared to high-Mn steels, which makes them a potential material for
future application in the automotive industry. Intercritical annealing (ICA)
after cold rolling allows to control the stacking fault energy (SFE) of
austenite, the fraction of ferrite and reverted austenite, and the element
partitioning (especially Mn). Although Mn deteriorates the corrosion behavior
of Fe-Mn-Al alloys, the influence of austenite fraction and element
partitioning of Mn on the electrochemical corrosion behavior has not been
investigated yet. Therefore, the electrochemical corrosion behavior in 0.1 M
H2SO4 of X6MnAl12-3, which was intercritically annealed for 2 h at 550 {\deg}C,
600 {\deg}C and 700 {\deg}C, was investigated by potentiodynamic polarization
(PDP), electrochemical impedance spectroscopy (EIS) and mass spectroscopy with
inductively coupled plasma (ICP-MS). Additionally, specimens after 1 h and 24 h
of immersion were examined via SEM to visualize the corrosion damage. The ICA
specimens showed a selective dissolution of reverted austenite due to its
micro-galvanic coupling with the adjacent ferrite. The severity of the
micro-galvanic coupling can be reduced by decreasing the interface area as well
as the chemical gradient of mainly Mn between ferrite and reverted austenite by
ICA.


  In this paper, we primarily consider the following semilinear elliptic
equation
  \begin{eqnarray*}
  \arraycolsep=1pt\left\{
  \begin{array}{lll}
  \displaystyle -\Delta u= h(x,u)\quad \
  &{\rm in}\ \Omega,\\[1.5mm]
  \phantom{ -\Delta }
  \displaystyle u\ge 0\qquad &{\rm on}\ \partial{\Omega},
  \end{array}\right.
  \end{eqnarray*} where $\Omega$ is an exterior domain in $R^N$ with $N\ge 3$,
and derive optimal nonexistence results of positive supersolution. Our argument
is based on a nonexistence result of positive supersolution of a linear
elliptic problem with Hardy potential. We also establish sharp nonexistence
results of positive supersolution to an elliptic system.


  We are revisiting the topic of travelling fronts for the food-limited (FL)
model with spatio-temporal nonlocal reaction. These solutions are crucial for
understanding the whole model dynamics. Firstly, we prove the existence of
monotone wavefronts. In difference with all previous results formulated in
terms of `sufficiently small parameters', our existence theorem indicates a
reasonably broad and explicit range of the model key parameters allowing the
existence of monotone waves. Secondly, numerical simulations realized on the
base of our analysis show appearance of non-oscillating and non-monotone
travelling fronts in the FL model. These waves were never observed before.
Finally, invoking a new approach developed recently by Solar $et\ al$, we prove
the uniqueness (for a fixed propagation speed, up to translation) of each
monotone front.


  Federated Learning is emerging as a privacy-preserving model training
approach in distributed edge applications. As such, most edge deployments are
heterogeneous in nature i.e., their sensing capabilities and environments vary
across deployments. This edge heterogeneity violates the independence and
identical distribution (IID) property of local data across clients and produces
biased global models i.e. models that contribute to unfair decision-making and
discrimination against a particular community or a group. Existing bias
mitigation techniques only focus on bias generated from label heterogeneity in
non-IID data without accounting for domain variations due to feature
heterogeneity and do not address global group-fairness property.
  Our work proposes a group-fair FL framework that minimizes group-bias while
preserving privacy and without resource utilization overhead. Our main idea is
to leverage average conditional probabilities to compute a cross-domain group
\textit{importance weights} derived from heterogeneous training data to
optimize the performance of the worst-performing group using a modified
multiplicative weights update method. Additionally, we propose regularization
techniques to minimize the difference between the worst and best-performing
groups while making sure through our thresholding mechanism to strike a balance
between bias reduction and group performance degradation. Our evaluation of
human emotion recognition and image classification benchmarks assesses the fair
decision-making of our framework in real-world heterogeneous settings.


  This paper considers incremental few-shot learning, which requires a model to
continually recognize new categories with only a few examples provided. Our
study shows that existing methods severely suffer from catastrophic forgetting,
a well-known problem in incremental learning, which is aggravated due to data
scarcity and imbalance in the few-shot setting. Our analysis further suggests
that to prevent catastrophic forgetting, actions need to be taken in the
primitive stage -- the training of base classes instead of later few-shot
learning sessions. Therefore, we propose to search for flat local minima of the
base training objective function and then fine-tune the model parameters within
the flat region on new tasks. In this way, the model can efficiently learn new
classes while preserving the old ones. Comprehensive experimental results
demonstrate that our approach outperforms all prior state-of-the-art methods
and is very close to the approximate upper bound. The source code is available
at https://github.com/moukamisama/F2M.


  The charmless three-body decays $B^0_{(s)} \to K_{\mathrm{\scriptscriptstyle
S}}^0 h^+ h^{\prime -}$ (where $h^{(\prime)} = \pi, K$) are analysed using a
sample of $pp$ collision data recorded by the LHCb experiment, corresponding to
an integrated luminosity of $3\mbox{fb}^{-1}$. The branching fractions are
measured relative to that of the $B^0 \to K_{\mathrm{\scriptscriptstyle S}}^0
\pi^{+} \pi^{-}$ decay, and are determined to be: \begin{eqnarray*}
  \frac{{\cal B}(B^0\rightarrow K^0_{\rm S}K^{\pm}\pi^{\mp})}{{\cal
B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})}
  = {} & 0.123 \pm 0.009 \; \mathrm{\,(stat)}\; \pm 0.015 \;
\mathrm{\,(syst)}\,,
  \frac{{\cal B}(B^0\rightarrow K^0_{\rm S}K^{+}K^{-})} {{\cal
B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})}
  = {} & 0.549 \pm 0.018 \; \mathrm{\,(stat)}\; \pm 0.033 \;
\mathrm{\,(syst)}\,,
  \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})}{{\cal
B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})}
  = {} & 0.191 \pm 0.027 \; \mathrm{\,(stat)}\; \pm 0.031 \;
\mathrm{\,(syst)}\; \pm 0.011 \; (f_s/f_d) \,,
  \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}K^{\pm}\pi^{\mp})} {{\cal
B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})}
  = {} & 1.70\phantom{0} \pm 0.07\phantom{0} \; \mathrm{\,(stat)} \; \pm
0.11\phantom{0} \; \mathrm{\,(syst)}\; \pm 0.10\phantom{0} \; (f_s/f_d) \,,
  \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}K^{+}K^{-})}{{\cal
B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} \in {} & [0.008 - 0.051] \rm
~at~90\%~confidence~level,
  \end{eqnarray*} where $f_s/f_d$ represents the ratio of hadronisation
fractions of the $B^0_s$ and $B^0$ mesons.


  Integrated Information Theory is one of the leading models of consciousness.
It aims to describe both the quality and quantity of the conscious experience
of a physical system, such as the brain, in a particular state. In this
contribution, we propound the mathematical structure of the theory, separating
the essentials from auxiliary formal tools. We provide a definition of a
generalized IIT which has IIT 3.0 of Tononi et. al., as well as the Quantum IIT
introduced by Zanardi et. al. as special cases. This provides an axiomatic
definition of the theory which may serve as the starting point for future
formal investigations and as an introduction suitable for researchers with a
formal background.


  Aims: A near-infrared study of the main ionizing star of the ultracompact HII
region G23.96+0.15 (IRAS 18317-0757) is presented, along with a re-evaluation
of the distance to this source, and a re-assessment of H- and K-band
classification diagnostics for O dwarfs; Methods: We have obtained near-IR
VLT/ISAAC imaging and spectroscopy of G23.96+0.15, plus archival imaging from
UKIRT/UFTI. A spectroscopic analysis was carried out using a non-LTE model
atmosphere code; Results: A quantitative H- and K-band classification scheme
for O dwarfs is provided, from which we establish an O7.5V spectral subtype for
the central star of G23.96+0.15. We estimate an effective temperature of Teff ~
38 kK from a spectral analysis; Conclusions: A spectroscopic distance of 2.5
kpc is obtained for G23.96+0.15, substantially lower than the kinematic
distance of 4.7 kpc, in common with recent studies of other Milky way HII
regions. Such discrepancies would be alleviated if sources are unresolved
binaries or clusters.


  Given a graph $G$, a cost function on the non-edges of $G$, and an integer
$d$, the problem of finding a cheapest globally rigid supergraph of $G$ in
$\mathbb{R}^d$ is NP-hard for $d\geq 1$. For this problem, which is a common
generalization of several well-studied graph augmentation problems, no
approximation algorithm has previously been known for $d\geq 2$. Our main
algorithmic result is a 5-approximation algorithm in the $d=2$ case. We achieve
this by proving numerous new structural results on rigid graphs and globally
linked vertex pairs. In particular, we show that every rigid graph in
$\mathbb{R}^2$ has a tree-like structure, which conveys all the information
regarding its globally rigid augmentations. Our results also yield a new,
simple solution to the minimum cardinality version (where the cost function is
uniform) for rigid input graphs, a problem which is known to be solvable in
polynomial time.


  We introduce the structured projection of intermediate gradients optimization
technique (SPIGOT), a new method for backpropagating through neural networks
that include hard-decision structured predictions (e.g., parsing) in
intermediate layers. SPIGOT requires no marginal inference, unlike structured
attention networks (Kim et al., 2017) and some reinforcement learning-inspired
solutions (Yogatama et al., 2017). Like so-called straight-through estimators
(Hinton, 2012), SPIGOT defines gradient-like quantities associated with
intermediate nondifferentiable operations, allowing backpropagation before and
after them; SPIGOT's proxy aims to ensure that, after a parameter update, the
intermediate structure will remain well-formed.
  We experiment on two structured NLP pipelines: syntactic-then-semantic
dependency parsing, and semantic parsing followed by sentiment classification.
We show that training with SPIGOT leads to a larger improvement on the
downstream task than a modularly-trained pipeline, the straight-through
estimator, and structured attention, reaching a new state of the art on
semantic dependency parsing.


  We apply the perturbative QCD factorization theorem developed recently for
nonleptonic heavy meson decays to the radiative decay $B\to K^*\gamma$. In this
formalism the evolution of the Wilson coefficients from the $W$ boson mass down
to the characteristic scale of the decay process is governed by the effective
weak Hamiltonian. The evolution from the characteristic scale to a lower
hadronic scale is formulated by the Sudakov resummation. Besides computing the
dominant contribution arising from the magnetic-penguin operator $O_7$, we also
calculate the contributions of four-quark operators. By fitting our prediction
for the branching ratio of the $B\to K^*\gamma$ decay to the CLEO data, we
determine the $B$ meson wave function, that possesses a sharp peak at a low
momentum fraction.


  Motivated by the recent discovery of quantized spin Hall effect in InAs/GaSb
quantum wells\cite{du2013}$^,$\cite{xu2014}, we theoretically study the effects
of in-plane magnetic field and strain effect to the quantization of charge
conductance by using Landauer-Butikker formalism. Our theory predicts a
robustness of the conductance quantization against the magnetic field up to a
very high field of 20 tesla. We use a disordered hopping term to model the
strain and show that the strain may help the quantization of the conductance.
Relevance to the experiments will be discussed.


  we calculate the new physics contributions to seven measured decays $B \to
\pi^+ \pi^-, K \pi$ and $ K \etap$ in the general two-Higgs-doublet model
(Model III). Within the considered parameter space, we find that: (a) the
CLEO/BaBar measurement of $B\to \pi^+ \pi^-$ decay prefers a small
$F_0^{B\pi}(0)$: $F_0^{B\pi}(0)=0.25 \pm 0.03$; (b) the new physics
enhancements to the penguin-dominated $B \to K\pi$ and $B\to K \etap$ decays
are significant in size, $\sim (40-70)%$ $w.r.t$ the standard model
predictions; and (c) the new physics enhancements can boost the branching
ratios ${\cal B}(B \to K^+ \etap)$ and ${\cal B}(B \to K^0 \etap)$ to be
consistent with the data within one standard deviation, and hence lead to a
simple and plausible new physics interpretation for the $\etap K$ puzzle.


  It is proved that the Heisenberg group $\operatorname*{Nil}\nolimits_{3}$
with a balanced metric, the sum of the left and right invariant metrics, splits
as a Riemannian product $\mathbb{T\times Z}$, where $\mathbb{T}$ is a totally
geodesic surface and $\mathbb{Z}$ the center of $\operatorname*{Nil}%
\nolimits_{3}.$ It is then proved the existence of complete properly embedded
minimal surfaces in $\operatorname*{Nil}\nolimits_{3}$ by solving the
asymptotic Dirichlet problem for the minimal surface equation on $\mathbb{T}$.
It is also proved the existence of complete properly embedded minimal surfaces
foliating an open set of $\operatorname*{Nil}\nolimits_{3}$ having as boundary
a given curve $\Gamma$ in $\mathbb{T},$ satisfying the exterior circle
condition, by solving the exterior Dirichlet problem for the minimal surface
equation in the unbounded connected component of $\mathbb{T}\backslash\Gamma$.


  Postulates of the quantum atomistic solid-state theory (QUASST) have been
presented. QUASST is an extension of the crystal-field theory and is applicable
to compounds containing open-shell 3d, 4f and 5f atoms. QUASST points out the
existence in a solid of the atomic-like discrete electronic structure
determined by the crystal- field and spin-orbit interactions. This approach
unifies the description of 3d and 4f ions and allows to bridge the atomic
physics and the solid-state physics.


  The integration of pretrained language models (PLMs) like BERT and GPT has
revolutionized NLP, particularly for English, but it has also created
linguistic imbalances. This paper strategically identifies the need for
linguistic equity by examining several knowledge editing techniques in
multilingual contexts. We evaluate the performance of models such as Mistral,
TowerInstruct, OpenHathi, Tamil-Llama, and Kan-Llama across languages including
English, German, French, Italian, Spanish, Hindi, Tamil, and Kannada. Our
research identifies significant discrepancies in normal and merged models
concerning cross-lingual consistency. We employ strategies like 'each language
for itself' (ELFI) and 'each language for others' (ELFO) to stress-test these
models. Our findings demonstrate the potential for LLMs to overcome linguistic
barriers, laying the groundwork for future research in achieving linguistic
inclusivity in AI technologies.


  The magnetization and hole distribution of Mn clusters in (Ga,Mn)As are
investigated by all-electron total energy calculations using the projector
augmented wave method within the density-functional formalism. It is found that
the energetically most favorable clusters consist of Mn atoms surrounding one
center As atom. As the Mn cluster grows the hole band at the Fermi level splits
increasingly and the hole distribution gets increasingly localized at the
center As atom. The hole distribution at large distances from the cluster does
not depend significantly on the cluster size. As a consequence, the spin-flip
energy differences of distant clusters are essentially independent of the
cluster size. The Curie temperature $T_C$ is estimated directly from these
spin-flip energies in the mean field approximation. When clusters are present
estimated $T_C$ values are around 250 K independent of Mn concentration whereas
for a uniform Mn distribution we estimate a $T_C$ of about 600 K.


  In this article, a new mathematical model of human population growth as an
autonomous non-Markov queuing system with an unlimited number of servers and
two types of applications is proposed. The research of this system was carried
out a virtual phase method and a modified method of asymptotic analysis of a
stochastic age-specific density for a number of applications served in the
system at time t and was proofed that the asymptotic distribution is Gaussian.
The main probabilistic characteristics of this distribution are found. The
mathematical model and methods of its research can be applied to the analysis
of the population growth both in a single country and around the world.


  We study the efficiency of a single particle Szilard and Carnot engine.
Within a first order correction to the quasi-static limit, the work
distribution is found to be Gaussian and the correction factor to average work
and efficiency only depends on the piston speed. The stochastic efficiency is
studied for both models and the recent findings on efficiency fluctuations are
confirmed numerically. Special features are revealed in the zero temperature
limit.


  We calculate repulsive Casimir forces between metallic and magnetic plates
and quantitatively probe the magnetic plate's properties as tuning knobs for
the repulsion. Namely, the plate's thickness and its low-frequency permittivity
and permeability. For a thin magnetic plate ($\leq 10\,\text{nm}$), we find
that repulsion can exist as long as $\mu(0) \geq \epsilon(0)$. We also explore
the effect of temperature on the repulsion and transition distance between
attractive and repulsive interactions. We show how the parameters can be tuned
to allow repulsion at sub-micron separation regimes, making it potentially
accessible to known high-resolution measurement techniques using magnetic van
der Waals materials.


  We present a numerical strategy to efficiently estimate bipartite
entanglement measures, and in particular the Entanglement of Formation, for
many-body quantum systems on a lattice. Our approach exploits the Tree Tensor
Operator tensor network ansatz, a positive loopless representation for density
matrices which, as we demonstrate, efficiently encodes information on bipartite
entanglement, enabling the up-scaling of entanglement estimation. Employing
this technique, we observe a finite-size scaling law for the entanglement of
formation in 1D critical lattice models at finite temperature for up to 128
spins, extending to mixed states the scaling law for the entanglement entropy.


  Earthwork-related locations (ERLs), such as construction sites, earth dumping
ground, and concrete mixing stations, are major sources of urban dust pollution
(particulate matters). The effective management of ERLs is crucial and requires
timely and efficient tracking of these locations throughout the city. This work
aims to identify and classify urban ERLs using GPS trajectory data of over
16,000 construction waste hauling trucks (CWHTs), as well as 58 urban features
encompassing geographic, land cover, POI and transport dimensions. We compare
several machine learning models and examine the impact of various
spatial-temporal features on classification performance using real-world data
in Chengdu, China. The results demonstrate that 77.8% classification accuracy
can be achieved with a limited number of features. This classification
framework was implemented in the Alpha MAPS system in Chengdu, which has
successfully identified 724 construction cites/earth dumping ground, 48
concrete mixing stations, and 80 truck parking locations in the city during
December 2023, which has enabled local authority to effectively manage urban
dust pollution at low personnel costs.


  We present a fast and spectrally accurate method for efficient computation of
the three dimensional Coulomb potential with periodicity in one direction. The
algorithm is FFT-based and uses the so-called Ewald decomposition, which is
naturally most efficient for the triply periodic case. In this paper, we show
how to extend the triply periodic Spectral Ewald method to the singly periodic
case, such that the cost of computing the singly periodic potential is only
marginally larger than the cost of computing the potential for the
corresponding triply periodic system.
  In the Fourier space contribution of the Ewald decomposition, a Fourier
series is obtained in the periodic direction with a Fourier integral over the
non periodic directions for each discrete wave number. We show that upsampling
to resolve the integral is only needed for modes with small wave numbers. For
the zero wave number, this Fourier integral has a singularity. For this mode,
we effectively need to solve a free-space Poisson equation in two dimensions. A
very recent idea by Vico et al. makes it possible to use FFTs to solve this
problem, allowing us to unify the treatment of all modes. An adaptive 3D FFT
can be established to apply different upsampling rates locally. The
computational cost for other parts of the algorithm is essentially unchanged as
compared to the triply periodic case, in total yielding only a small increase
in both computational cost and memory usage for this singly periodic case.


  In order to apply nonstandard methods to questions of algebraic geometry we
continue our investigation from "Enlargements of categories" (Theory Appl.
Categ. 14 (2005), No. 16, 357--398) and show how important homotopical
constructions behave under enlargements.


  The initial state recurrence in numerical simulations of the Vlasov-Poisson
system is a well-known phenomenon. Here we study the effect on recurrence of
artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard
and I. B. Bernstein, Phys. Rev. 112, 1456-1459 (1958)]. By decomposing the
linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence
problem is investigated in the linear regime of the damping of a Langmuir wave
and of the onset of the bump-on-tail instability. The analysis is then
confirmed and extended to the nonlinear regime through a Eulerian collisional
Vlasov-Poisson code. It is found that, despite being routinely used, an
artificial collisionality is not a viable way of preventing recurrence in
numerical simulations without compromising the kinetic nature of the solution.
Moreover, it is shown how numerical effects associated to the generation of
fine velocity scales, can modify the physical features of the system evolution
even in nonlinear regime. This means that filamentation-like phenomena, usually
associated with low amplitude fluctuations contexts, can play a role even in
nonlinear regime.


  The asymptotic behaviour of massless spin-0 fields close to spatial and null
infinity in Minkowski spacetime is studied by means of Friedrich's cylinder at
spatial infinity. The results are applied to a system of equations called the
good-bad-ugly which serves as a model for the Einstein field equations in
generalised harmonic gauge. The relation between the logarithmic terms
(polyhomogeneity) appearing in the solution obtained using conformal methods
and those obtained by means of a heuristic method based on H\"ormander's
asymptotic system is discussed. This review article is based on Class. Quantum
Grav. 40 055002 and arXiv:2304.11950.


  We prove a quantitative structure theorem for metrics on $\mathbf{R}^n$ that
are conformal to the flat metric, have almost constant positive scalar
curvature, and cannot concentrate more than one bubble. As an application of
our result, we show a quantitative rate of convergence in relative entropy for
a fast diffusion equation in $\mathbf{R}^n$ related to the Yamabe flow.


  We show that the estimating equations for quantile regression can be solved
using a simple EM algorithm in which the M-step is computed via weighted least
squares, with weights computed at the E-step as the expectation of independent
generalized inverse-Gaussian variables. We compute the variance-covariance
matrix for the quantile regression coefficients using a kernel density
estimator that results in more stable standard errors than those produced by
existing software. A natural modification of the EM algorithm that involves
fitting a linear mixed model at the M-step extends the methodology to mixed
effects quantile regression models. In this case, the fitting method can be
justified as a generalized alternating minimization algorithm. Obtaining
quantile regression estimates via the weighted least squares method enables
model diagnostic techniques similar to the ones used in the linear regression
setting. The computational approach is compared with existing software using
simulated data, and the methodology is illustrated with several case studies.


  In order to fully function in human environments, robot perception will need
to account for the uncertainty caused by translucent materials. Translucency
poses several open challenges in the form of transparent objects (e.g.,
drinking glasses), refractive media (e.g., water), and diffuse partial
occlusions (e.g., objects behind stained glass panels). This paper presents
Plenoptic Monte Carlo Localization (PMCL) as a method for localizing object
poses in the presence of translucency using plenoptic (light-field)
observations. We propose a new depth descriptor, the Depth Likelihood Volume
(DLV), and its use within a Monte Carlo object localization algorithm. We
present results of localizing and manipulating objects with translucent
materials and objects occluded by layers of translucency. Our PMCL
implementation uses observations from a Lytro first generation light field
camera to allow a Michigan Progress Fetch robot to perform grasping.


  We present MIPS observations of the cluster A3266. About 100 spectroscopic
cluster members have been detected at 24 micron. The IR luminosity function in
A3266 is very similar to that in the Coma cluster down to the detection limit
L_IR~10^43 ergs/s, suggesting a universal form of the bright end IR LF for
local rich clusters with M~10^15 M_sun. The shape of the bright end of the
A3266-Coma composite IR LF is not significantly different from that of nearby
field galaxies, but the fraction of IR-bright galaxies (SFR > 0.2M_sun/yr) in
both clusters increases with cluster-centric radius. The decrease of the blue
galaxy fraction toward the high density cores only accounts for part of the
trend; the fraction of red galaxies with moderate SFRs (0.2 < SFR < 1 M_sun/yr)
also decreases with increasing galaxy density. These results suggest that for
the IR bright galaxies, nearby rich clusters are distinguished from the field
by a lower star-forming galaxy fraction, but not by a change in L*_IR. The
composite IR LF of Coma and A3266 shows strong evolution when compared with the
composite IR LF of two z~0.8 clusters, MS 1054 and RX J0152, with L*_IR \propto
(1+z)^{3.2+/-0.7},Phi*_IR \propto (1+z)^{1.7+/-1.0}. This L*_IR evolution is
indistinguishable from that in the field, and the Phi*_IR evolution is
stronger, but still consistent with that in the field. The similarity of the
evolution of bright-end IR LF in very different cluster and field environments
suggests either this evolution is driven by the mechanism that works in both
environments, or clusters continually replenish their star-forming galaxies
from the field, yielding an evolution in the IR LF that is similar to the
field. The mass-normalized integrated star formation rates (SFRs) of clusters
within 0.5R_200 also evolve strongly with redshift, as (1+z)^5.3.


  With the increase in Artificial Intelligence driven approaches, researchers
are requesting unprecedented volumes of medical imaging data which far exceed
the capacity of traditional on-premise client-server approaches for making the
data research analysis-ready. We are making available a flexible solution for
on-demand de-identification that combines the use of mature software
technologies with modern cloud-based distributed computing techniques to enable
faster turnaround in medical imaging research. The solution is part of a
broader platform that supports a secure high performance clinical data science
platform.


  The central result of classical game theory states that every finite normal
form game has a Nash equilibrium, provided that players are allowed to use
randomized (mixed) strategies. However, in practice, humans are known to be bad
at generating random-like sequences, and true random bits may be unavailable.
Even if the players have access to enough random bits for a single instance of
the game their randomness might be insufficient if the game is played many
times.
  In this work, we ask whether randomness is necessary for equilibria to exist
in finitely repeated games. We show that for a large class of games containing
arbitrary two-player zero-sum games, approximate Nash equilibria of the
$n$-stage repeated version of the game exist if and only if both players have
$\Omega(n)$ random bits. In contrast, we show that there exists a class of
games for which no equilibrium exists in pure strategies, yet the $n$-stage
repeated version of the game has an exact Nash equilibrium in which each player
uses only a constant number of random bits.
  When the players are assumed to be computationally bounded, if cryptographic
pseudorandom generators (or, equivalently, one-way functions) exist, then the
players can base their strategies on "random-like" sequences derived from only
a small number of truly random bits. We show that, in contrast, in repeated
two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then
$\Omega(n)$ random bits remain necessary for equilibria to exist.


  Recent research has identified interactions between networks as crucial for
the outcome of evolutionary games taking place on them. While the consensus is
that interdependence does promote cooperation by means of organizational
complexity and enhanced reciprocity that is out of reach on isolated networks,
we here address the question just how much interdependence there should be.
Intuitively, one might assume the more the better. However, we show that in
fact only an intermediate density of sufficiently strong interactions between
networks warrants an optimal resolution of social dilemmas. This is due to an
intricate interplay between the heterogeneity that causes an asymmetric
strategy flow because of the additional links between the networks, and the
independent formation of cooperative patterns on each individual network.
Presented results are robust to variations of the strategy updating rule, the
topology of interdependent networks, and the governing social dilemma, thus
suggesting a high degree of universality.


  The confinement transition from the quark and gluon degrees of freedom
appropriate in perturbation theory to the hadrons observed by real world
experiments is poorly understood. In this strongly interacting transition
regime we presently rely on models, which to varying degrees reflect possible
scenarios for the QCD dynamics. Because of the absence of beam and target
remnants, and the clean experimental conditions and high event rates, e+e-
annihilation to hadrons at the Z0 provides a unique laboratory, both
experimentally and theoretically, for the study of parton hadronization. This
review discusses current theoretical understanding of the hadronization of
partons, with particular emphasis on models of the non-perturbative phase, as
implemented in Monte Carlo simulation programs. Experimental results at LEP and
SLC are summarised and considered in the light of the models. Suggestions are
given for further measurements which could help to produce more progress in
understanding hadronization.


  Let $E$ be an elliptic curve over $\Q$ without complex multiplication, and
which is not isogenous to a curve with non-trivial rational torsion. For each
prime $p$ of good reduction, let $|E(\F_p)|$ be the order of the group of
points of the reduced curve over $\F_p$. We prove in this paper that, under the
GRH, there are at least $2.778 C_E^{\rm twin} x / (\log{x})^2$ primes $p$ such
that $|E(\F_p)|$ has at most 8 prime factors, counted with multiplicity. This
improves previous results of Steuding & Weng and Murty & Miri. This is also the
first result where the dependence on the conjectural constant $C_E^{\rm twin}$
appearing in the twin prime conjecture for elliptic curves (also known as
Koblitz's conjecture) is made explicit. This is achieved by sieving a slightly
different sequence than the one used by previous authors. By sieving the same
sequence and using Selberg's linear sieve, we can also improve the constant
appearing in the upper bound for the number of primes $p$ such that $|E(\F_p)|$
is prime. Finally, we remark that our results still hold under an hypothesis
weaker than the GRH.


  Steady-state observables, such as occupation numbers and currents, are
crucial experimental signatures in open quantum systems. The
time-convolutionless (TCL) master equation, which is both exact and time-local,
is an ideal candidate for the perturbative computation of such observables. We
develop a diagrammatic approach to evaluate the steady-state TCL generator
based on operators rather than superoperators. We obtain the steady-state
occupation numbers, extend our formulation to the calculation of currents, and
provide a simple physical interpretation of the diagrams. We further benchmark
our method on a single non-interacting level coupled to Fermi reservoirs, where
we recover the exact expansion to next-to-leading order. The low number of
diagrams appearing in our formulation makes the extension to higher orders
accessible. Combined, these properties make the steady-state
time-convolutionless master equation an effective tool for the calculation of
steady-state properties in open quantum systems.


  We perform Hochschild homology calculations in the algebro-geometric setting
of motives. The motivic Hochschild homology coefficient ring contains torsion
classes which arise from the mod-$p$ motivic Steenrod algebra and from
generating functions on the natural numbers with finite non-empty support.
Under the Betti realization, we recover B\"okstedt's calculation of the
topological Hochschild homology of finite prime fields.


  The continuation of point vortex dynamics after a vortex collapse is
investigated by means of a regularization procedure consisting in introducing a
small stochastic diffusive term, that corresponds to a vanishing viscosity. In
contrast with deterministic regularization, in which a cutoff interaction
selects in the limit a single trajectory of the system after collapse, the
zero-noise method produces a probability distribution supported by trajectories
satisfying relevant conservation laws of the point vortex system.


  Detection of human body and its parts has been intensively studied. However,
most of CNNs-based detectors are trained independently, making it difficult to
associate detected parts with body. In this paper, we focus on the joint
detection of human body and its parts. Specifically, we propose a novel
extended object representation integrating center-offsets of body parts, and
construct an end-to-end generic Body-Part Joint Detector (BPJDet). In this way,
body-part associations are neatly embedded in a unified representation
containing both semantic and geometric contents. Therefore, we can optimize
multi-loss to tackle multi-tasks synergistically. Moreover, this representation
is suitable for anchor-based and anchor-free detectors. BPJDet does not suffer
from error-prone post matching, and keeps a better trade-off between speed and
accuracy. Furthermore, BPJDet can be generalized to detect body-part or
body-parts of either human or quadruped animals. To verify the superiority of
BPJDet, we conduct experiments on datasets of body-part (CityPersons,
CrowdHuman and BodyHands) and body-parts (COCOHumanParts and Animals5C). While
keeping high detection accuracy, BPJDet achieves state-of-the-art association
performance on all datasets. Besides, we show benefits of advanced body-part
association capability by improving performance of two representative
downstream applications: accurate crowd head detection and hand contact
estimation. Project is available in https://hnuzhy.github.io/projects/BPJDet.


  Exponential growth occurs when the growth rate of a given quantity is
proportional to the quantity's current value. Surprisingly, when exponential
growth data is plotted as a simple histogram disregarding the time dimension, a
remarkable fit to the positively skewed k/x distribution is found, where the
small is numerous and the big is rare. Such quantitative preference for the
small has a corresponding digital preference known as Benford's Law which
predicts that the first significant digit on the left-most side of numbers in
typical real-life data is proportioned between all possible 1 to 9 digits
approximately as in LOG(1 + 1/digit), so that low digits occur much more
frequently than high digits in the first place. Exponential growth series with
high growth rate are nearly perfectly Benford given that plenty of elements are
considered. An additional constraint is that the logarithm of the growth factor
must be an irrational number. Since the irrationals vastly outnumber the
rationals, on the face of it, this constraint seems to constitute the
explanation of why almost all growth series are Benford, yet, in reality this
is all too simplistic, and the real and more complex explanation is provided in
this article. Empirical examinations of close to a half a million growth series
via computerized programs almost perfectly match the prediction of the
theoretical study on rational versus irrational occurrences, thus in a sense
confirming both, the empirical work as well as the theoretical study. In
addition, a rigorous mathematical proof is provided in the continuous growth
case showing that it exactly obeys Benford's Law. A non-rigorous proof is given
in the discrete case via uniformity of mantissa argument. Finally cases of
discrete series embedded within continuous series are studied, detailing the
degree of deviation from the ideal Benford configuration.


  The solutions of trigonometric Scarf potential, PT/non-PT-symmetric and
non-Hermitian q-deformed hyperbolic Scarf and Manning-Rosen potentials are
obtained by solving the Schrodinger equation. The Nikiforov-Uvarov method is
used to obtain the real energy spectra and corresponding eigenfunctions.


  Some of the more promising ideas about the origin of the high frequency
variability (kHz QPOs) in the observed X-ray emissions of low-mass X-ray
binaries are contrasted with less promising ones.


  We report on molecular dynamics simulations of spacetime correlations of the
Toda lattice in thermal equilibrium. The correlations of stretch, momentum, and
energy are computed numerically over a wide range of pressure and temperature.
Our numerical results are compared with the predictions from linearized
generalized hydrodynamics on the Euler scale. The system size is N=3000,4000
and time t =600, at which ballistic scaling is well confirmed. With no
adjustable parameters, the numerically obtained scaling functions agree with
the theory within a precision of less than 3.5%.


  The main focus of this paper is the characterization and exploitation of the
asymptotic spectrum of the saddle--point matrix sequences arising from the
discretization of optimization problems constrained by elliptic partial
differential equations. We uncover the existence of a hidden structure in these
matrix sequences, namely, we show that these are indeed an example of
Generalized Locally Toeplitz (GLT) sequences. We show that this enables a
sharper characterization of the spectral properties of such sequences than the
one that is available by using only the fact that we deal with saddle--point
matrices. Finally, we exploit it to propose an optimal preconditioner strategy
for the GMRES, and Flexible-GMRES methods.


  We exhibit some explicit co-adapted couplings for n-dimensional Brownian
motion and all its Levy stochastic areas. In the two-dimensional case we show
how to derive exact asymptotics for the coupling time under various mixed
coupling strategies, using Dufresne's formula for the distribution of
exponential functionals of Brownian motion. This yields quantitative
asymptotics for the distributions of random times required for certain
simultaneous couplings of stochastic area and Brownian motion. The approach
also applies to higher dimensions, but will then lead to upper and lower bounds
rather than exact asymptotics.


  Conventional methods of assessing attitudes towards climate change are
limited in capturing authentic opinions, primarily stemming from a lack of
context-specific assessment strategies and an overreliance on simplistic
surveys. Game-based Assessments (GBA) have demonstrated the ability to overcome
these issues by immersing participants in engaging gameplay within carefully
crafted, scenario-based environments. Concurrently, advancements in AI and
Natural Language Processing (NLP) show promise in enhancing the gamified
testing environment, achieving this by generating context-aware, human-like
dialogues that contribute to a more natural and effective assessment. Our study
introduces a new technique for probing climate change attitudes by actualizing
a GPT-driven chatbot system in harmony with a game design depicting a
futuristic climate scenario. The correlation analysis reveals an assimilation
effect, where players' post-game climate awareness tends to align with their
in-game perceptions. Key predictors of pro-climate attitudes are identified as
traits like 'Openness' and 'Agreeableness', and a preference for democratic
values.


  The US Census Bureau will implement a new privacy-preserving disclosure
avoidance system (DAS), which includes application of differential privacy, on
the public-release 2020 census data. There are concerns that the DAS may bias
small-area and demographically-stratified population counts, which play a
critical role in public health research and policy, serving as denominators in
estimation of disease/mortality rates. Employing three DAS demonstration
products, we quantify errors attributable to reliance on DAS-protected
denominators in standard small-area disease mapping models for characterizing
health inequities. We conduct simulation studies and real data analyses of
inequities in premature mortality at the census tract level in Massachusetts.
Results show that overall patterns of inequity by racialized group and economic
deprivation level are not compromised by the DAS. While early versions of DAS
induce errors in mortality rate estimation that are larger for Black than for
non-Hispanic white populations, this issue is ameliorated in newer DAS
versions.


  Strongly-interacting nanomagnetic systems are pivotal across next-generation
technologies including reconfigurable magnonics and neuromorphic computation.
Controlling magnetisation state and local coupling between neighbouring
nanoelements allows vast reconfigurable functionality and a host of associated
functionalities. However, existing designs typically suffer from an inability
to tailor inter-element coupling post-fabrication and nanoelements restricted
to a pair of Ising-like magnetisation states. Here, we propose a new class of
reconfigurable magnonic crystal incorporating nanodisks as the functional
element. Magnetic nanodisks are crucially bistable in macrospin and vortex
states, allowing inter-element coupling to be selectively activated (macrospin)
or deactivated (vortex). Through microstate engineering, we leverage the
distinct coupling behaviours and magnonic band structures of bistable nanodisks
to achieve reprogrammable magnonic waveguiding, bending, gating and
phase-shifting across a 2D network. The potential of nanodisk-based magnonics
for wave-based computation is demonstrated via an all-magnon interferometer
exhibiting XNOR logic functionality. Local microstate control is achieved here
via topological magnetic writing using a magnetic force microscope tip.


  The dark matter velocity distribution in the Solar neighbourhood is an
important astrophysical input which enters in the predicted event rate of dark
matter direct detection experiments. It has been recently suggested that the
local dark matter velocity distribution can be inferred from that of old or
metal-poor stars in the Milky Way. We investigate this potential relation using
six high resolution magneto-hydrodynamical simulations of Milky Way-like
galaxies of the Auriga project. We do not find any correlation between the
velocity distributions of dark matter and old stars in the Solar neighbourhood.
Likewise, there are no strong correlations between the local velocity
distributions of dark matter and metal-poor stars selected by applying
reasonable cuts on metallicity. In some simulated galaxies, extremely
metal-poor stars have a velocity distribution that is statistically consistent
with that of the dark matter, but the sample of such stars is so small that we
cannot draw any strong conclusions.


  In recent years, observational $\gamma$-ray astronomy has seen a remarkable
range of exciting new results in the high-energy and very-high energy regimes.
Coupled with extensive theoretical and phenomenological studies of non-thermal
processes in the Universe these observations have provided a deep insight into
a number of fundamental problems of high energy astrophysics and astroparticle
physics. Although the main moti- vations of $\gamma$-ray astronomy remain
unchanged, recent observational results have contributed significantly towards
our understanding of many related phenomena. This article aims to review the
most important results in the young and rapidly developing field of
$\gamma$-ray astrophysics.


  Asteroseismology has revealed that cores of red giants rotate about one order
of magnitude faster than their convective envelopes. This paper attempts an
explanation for this rotational state in terms of the theory of angular
momentum transport in stellar convection zones. A differential rotation model
based on the theory is applied to a sequence of evolutionary states of a red
giant of one solar mass. The model computations show a rotation of about ten
times faster in the cores compared to the stellar surface. This rotational
state is caused by the non-diffusive downward convective transport of angular
momentum. The contrast in rotational rates between core and envelope increases
with the radius (age) of the star. Seismologically detected scaling for the
spindown of the giants' cores is also reproduced.


  In many synthesis problems, it can be essential to generate implementations
which not only satisfy functional constraints but are also randomized to
improve variety, robustness, or unpredictability. The recently-proposed
framework of control improvisation (CI) provides techniques for the
correct-by-construction synthesis of randomized systems subject to hard and
soft constraints. However, prior work on CI has focused on qualitative
specifications, whereas in robotic planning and other areas we often have
quantitative quality metrics which can be traded against each other. For
example, a designer of a patrolling security robot might want to know by how
much the average patrol time needs to be increased in order to ensure that a
particular aspect of the robot's route is sufficiently diverse and hence
unpredictable. In this paper, we enable this type of application by
generalizing the CI problem to support quantitative soft constraints which
bound the expected value of a given cost function, and randomness constraints
which enforce diversity of the generated traces with respect to a given label
function. We establish the basic theory of labelled quantitative CI problems,
and develop efficient algorithms for solving them when the specifications are
encoded by finite automata. We also provide an approximate improvisation
algorithm based on constraint solving for any specifications encodable as
Boolean formulas. We demonstrate the utility of our problem formulation and
algorithms with experiments applying them to generate diverse near-optimal
plans for robotic planning problems.


  We propose a new type of interferometry, based on geometric phases
accumulated by a periodically driven two-level system undergoing multiple
Landau-Zener transitions. As a specific example, we study its implementation in
a superconducting charge pump. We find that interference patterns appear as a
function of the pumping frequency and the phase bias, and clearly manifest
themselves in the pumped charge. We also show that the effects described should
persist in the presence of realistic decoherence.


  In this paper we derive the tail asymptotics of a Kotz Type III elliptical
random vector. As an application of our asymptotic expansion we derive an
approximation for the conditional excess distribution. Furthermore, we discuss
the asymptotic dependence of Kotz Type III triangular arrays and provide some
details on the estimation of conditional excess distribution and survivor
function.


  In this article, we give some existence and smoothness results for the law of
the solution to a stochastic heat equation driven by a finite dimensional
fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on
recent tools of Young integration for convolutional integrals combined with
stochastic analysis methods for the study of laws of random variables defined
on a Wiener space.


  We consider an antiferromagnetic four leg spin-1/2 tube using abelian and
non-abelian bosonization. We show that in the limit of weak interchain
coupling, the most relevant interaction gives rise to an emergent SU(3)}
symmetry, broken only by marginal interactions that can be canceled by diagonal
interchain couplings. We discuss the low energy spectrum in the semiclassical
limit and using a mapping to a trimerized SU(3) spin chain. We establish that
the correlation functions of ferroquadrupolar operators can be used to reveal
the emergent symmetry.


  We prove that every limit group acts geometrically on a CAT(0) space with the
isolated flats property.


  Inclusive Higgs boson production at large transverse momentum is induced by
different production channels. We focus on the leading production through gluon
fusion, and perform a consistent combination of the state of the art
calculations obtained in the infinite-top-mass effective theory at
next-to-next-to-leading order (NNLO) and in the full Standard Model (SM) at
next-to-leading order (NLO). We thus present approximate QCD predictions for
this process at NNLO, and a study of the corresponding perturbative
uncertainties. This calculation is then compared with those obtained with
commonly used event generators, and we observe that the description of the
considered kinematic regime provided by these tools is in good agreement with
state of the art calculations. Finally, we present accurate predictions for
other production channels such as vector boson fusion, and associated
production with a gauge boson, and with a $t\bar{t}$ pair. We find that, at
large transverse momentum, the contribution of other production modes is
substantial, and therefore must be included for a precise theory prediction of
this observable.


  In this paper, we study the trending behaviour of COVID-19 data at country
level, and draw attention to some existing econometric tools which are
potentially helpful to understand the trend better in future studies. In our
empirical study, we find that European countries overall flatten the curves
more effectively compared to the other regions, while Asia & Oceania also
achieve some success, but the situations are not as optimistic elsewhere.
Africa and America are still facing serious challenges in terms of managing the
spread of the virus, and reducing the death rate, although in Africa the virus
spreads slower and has a lower death rate than the other regions. By comparing
the performances of different countries, our results incidentally agree with Gu
et al. (2020), though different approaches and models are considered. For
example, both works agree that countries such as USA, UK and Italy perform
relatively poorly; on the other hand, Australia, China, Japan, Korea, and
Singapore perform relatively better.


  The major challenge in designing a discriminative learning algorithm for
predicting structured data is to address the computational issues arising from
the exponential size of the output space. Existing algorithms make different
assumptions to ensure efficient, polynomial time estimation of model
parameters. For several combinatorial structures, including cycles, partially
ordered sets, permutations and other graph classes, these assumptions do not
hold. In this thesis, we address the problem of designing learning algorithms
for predicting combinatorial structures by introducing two new assumptions: (i)
The first assumption is that a particular counting problem can be solved
efficiently. The consequence is a generalisation of the classical ridge
regression for structured prediction. (ii) The second assumption is that a
particular sampling problem can be solved efficiently. The consequence is a new
technique for designing and analysing probabilistic structured prediction
models. These results can be applied to solve several complex learning problems
including but not limited to multi-label classification, multi-category
hierarchical classification, and label ranking.