  A word is "crucial" with respect to a given set of "prohibited words" (or
simply "prohibitions") if it avoids the prohibitions but it cannot be extended
to the right by any letter of its alphabet without creating a prohibition. A
"minimal crucial word" is a crucial word of the shortest length. A word W
contains an "abelian k-th power" if W has a factor of the form X_1X_2...X_k
where X_i is a permutation of X_1 for 2<= i <= k. When k=2 or 3, one deals with
"abelian squares" and "abelian cubes", respectively.
  In 2004 (arXiv:math/0205217), Evdokimov and Kitaev showed that a minimal
crucial word over an n-letter alphabet A_n = {1,2,..., n} avoiding abelian
squares has length 4n-7 for n >= 3. In this paper we show that a minimal
crucial word over A_n avoiding abelian cubes has length 9n-13 for n >= 5, and
it has length 2, 5, 11, and 20 for n=1, 2, 3, and 4, respectively. Moreover,
for n >= 4 and k >= 2, we give a construction of length k^2(n-1)-k-1 of a
crucial word over A_n avoiding abelian k-th powers. This construction gives the
minimal length for k=2 and k=3. For k >= 4 and n >= 5, we provide a lower bound
for the length of crucial words over A_n avoiding abelian k-th powers.


  We consider a large $- N, $ two-family Calogero model in the Hamiltonian,
collective-field approach. The Bogomol'nyi limit appears and the corresponding
solutions are given by the static-soliton configurations. Solitons from
different families are localized at the same place. They behave like a paired
hole and lump on the top of the uniform vacuum condensates, depending on the
values of the coupling strengths. When the number of particles in the first
family is much larger than that of the second family, the hole solution goes to
the vortex profile already found in the one-family Calogero model.


  A framework for the theoretical and analytical understanding of the impact
crater-size frequency distribution is developed and applied to observed data
from Mars and Earth. The analitical model derived gives the crater
population,N, as a function of crater diameter,D, and age, taking into
consideration the reduction in crater number as a function of time, cause by
the elimination of craters due to effects, such as erosion, obliteration by
other impacts, and tectonic changes. We are also able to estimate the rate of
impacts as a function of D and the kinetic energy, E, of the impactors. In
particular, for energies of one megaton or larger we find near one impact every
three years for Mars, an interesting and concerning result for future Mars
explorations. The corresponding calculations for our planet give a probability
of one impact per 15 years, while for a Tunguska like event, of about E=10
megatons, an estimate of one per century is obtained for Earth. The model
allows the derivation of an expression that gives the number of craters
observed today as a function of D and age. The application of this expression
to the Earth`s crater data shows a remarkable agreement between theory and
observations.


  This paper summarizes the how the unique knowledge of accelerator operators
has contributed to the success of the Jefferson Lab Control System.


  This paper reconsiders refinements which introduce actions on the concrete
level which were not present at the abstract level. It draws a distinction
between concrete actions which are "perspicuous" at the abstract level, and
changes of granularity of actions between different levels of abstraction.
  The main contribution of this paper is in exploring the relation between
these different methods of "action refinement", and the basic refinement
relation that is used. In particular, it shows how the "refining skip" method
is incompatible with failures-based refinement relations, and consequently some
decisions in designing Event-B refinement are entangled.


  We review a class of dynamical models in which top condensation occurs at the
weak scale, giving rise to the large top quark mass and other phenomena. This
typically requires a color embedding, $SU(3)_c \rightarrow SU(3)_1\times
SU(3)_2$. These models imply many signatures addressable in near term
experiments at colliders and in fixed target mode.


  We present magnetometry and muon spin rotation ($\mu$SR) measurements of the
superconducting dichalcogenide Ir$_{0.95}$Pt$_{0.05}$Te$_2$. From both sets of
measurements we calculate the penetration depth and thence superfluid density
as a function of temperature. The temperature dependence of the superfluid
densities from both sets of data indicate fully gapped superconductivity that
can be fit to a conventional s-wave model and yiel fitting parameters
consistent with a BCS weak coupling superconductor. We therefore see no
evidence for exotic superconductivity in Ir$_{0.95}$Pt$_{0.05}$Te$_2$.


  We have performed Density Functional Theory (DFT) based calculations to
investigate the effects of stacking patterns on the electronic and magnetic
properties of several Nitride MXenes. MXenes, a relatively new addition to the
family of two-dimensional materials, have exhibited fascinating properties on
several occasions, primarily due to their compositional flexibility. However,
compared to Carbide MXenes, Nitride MXenes are much less explored. Moreover,
the structural aspects of MXenes and the tunability it may offer have not been
explored until recently. In this work, we have combined these two less-explored
aspects to examine the structure-property relations in the field of magnetism.
We find that in the family of M$_{2}$NT$_{2}$ (M=Sc, Ti, V, Cr, Mn; T=O, F)
MXenes, the stacking of transition metal planes has a substantial effect on the
ground state and finite temperature magnetic properties. We also find that the
electronic ground states can be tuned by changing the stacking pattern in these
compounds, making the materials appropriate for applications as magnetic
devices. Through a detailed analysis, we have connected the unconventional
stacking pattern-driven tunability of these compounds with regard to electronic
and magnetic properties to the local symmetry, inhomogeneity (or lack of it) of
structural parameters, and electronic structures.


  The wall shear stress is a quantity of profound importance for clinical
diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable
numerical method of solving the flow problems, but it suffers from errors of
the velocity field near the boundaries which leads to errors in the wall shear
stress and normal vectors computed from the velocity. In this work we present a
simple formula to calculate the wall shear stress in the lattice Boltzmann
model and propose to compute wall normals, which are necessary to compute the
wall shear stress, by taking the weighted mean over boundary facets lying in a
vicinity of a wall element. We carry out several tests and observe an increase
of accuracy of computed normal vectors over other methods in two and three
dimensions. Using the scheme we compute the wall shear stress in an inclined
and bent channel fluid flow and show a minor influence of the normal on the
numerical error, implying that that the main error arises due to a corrupted
velocity field near the staircase boundary. Finally, we calculate the wall
shear stress in the human abdominal aorta in steady conditions using our method
and compare the results with a standard finite volume solver and experimental
data available in the literature. Applications of our ideas in a simplified
protocol for data preprocessing in medical applications are discussed.


  We develop a renormalization group (RG) procedure that includes important
system-specific features. The key ingredient is to systematize the coarse
graining procedure that generates the RG flow. The coarse graining technology
comes from control and operator theoretic model reduction. The resulting
"generalized" RG is a consistent generalization of the Wilsonian RG. We derive
the form of the projection operator from the dynamics of a nonlinear wave
equation and renormalize the distribution of initial conditions. The
probability density of the initial conditions is chosen to be the Boltzmann
weight for a standard $\phi^4$-theory. In our calculation, we find that in
contrast to conventional implementations of the RG, na\"ive power counting
breaks down. The RG-equations that we derive are different from those derived
from the conventional RG.


  Few-shot image classification aims to classify unseen classes with limited
labelled samples. Recent works benefit from the meta-learning process with
episodic tasks and can fast adapt to class from training to testing. Due to the
limited number of samples for each task, the initial embedding network for
meta-learning becomes an essential component and can largely affect the
performance in practice. To this end, most of the existing methods highly rely
on the efficient embedding network. Due to the limited labelled data, the scale
of embedding network is constrained under a supervised learning(SL) manner
which becomes a bottleneck of the few-shot learning methods. In this paper, we
proposed to train a more generalized embedding network with self-supervised
learning (SSL) which can provide robust representation for downstream tasks by
learning from the data itself. We evaluate our work by extensive comparisons
with previous baseline methods on two few-shot classification datasets ({\em
i.e.,} MiniImageNet and CUB) and achieve better performance over baselines.
Tests on four datasets in cross-domain few-shot learning classification show
that the proposed method achieves state-of-the-art results and further prove
the robustness of the proposed model. Our code is available at
\hyperref[https://github.com/phecy/SSL-FEW-SHOT.]{https://github.com/phecy/SSL-FEW-SHOT.}


  We calculate the dislocation glide mobility in solid $^4$He within a model
that assumes the existence of a superfluid field associated with dislocation
lines. Prompted by the results of this mobility calculation, we study within
this model the role that such a superfluid field may play in the motion of the
dislocation line when a stress is applied to the crystal. To do this, we relate
the damping of dislocation motion, calculated in the presence of the assumed
superfluid field, to the shear modulus of the crystal. As the temperature
increases, we find that a sharp drop in the shear modulus will occur at the
temperature where the superfluid field disappears. We compare the drop in shear
modulus of the crystal arising from the temperature dependence of the damping
contribution due to the superfluid field, to the experimental observation of
the same phenomena in solid $^4$He and find quantitative agreement. Our results
indicate that such a superfluid field plays an important role in dislocation
pinning in a clean solid $^4$He at low temperatures and in this regime may
provide an alternative source for the unusual elastic phenomena observed in
solid $^4$He.


  The goal of this paper is to introduce one of the versions of the
electromagnetic Lagrangian on a causal set in such a way that would address the
non-locality issues inherent to causal set theory. The key idea is that
Lagrangian density is assigned to the edges rather than points, and there is a
way of defining the concept of "neighboring edges" of a given edge in such a
way that each edge has only finitely many neighboring edges which would
ultimately allow for the theory to be local. That is to be contrasted with
points where every point has infinitely many direct neighbors which is a source
of non-locality. The edges are needed in order to define electromagnetic
Lagrangian anyway, regardless of the consideration of locality; the novelty of
this paper is to assign Lagrangian density to the edges as well. Also, in the
other papers edges were both spacelike and timelike, while in this paper they
are only timelike. This makes calculations considerably more complicated, but
it is crucial in preserving locality since the Lorentz group in a hyperplane
perpendicular to the edge is compact only if the edge is timelike.


  We aim to collect buried lemmas that are useful for proofs. In particular, we
try to provide self-contained proofs for those lemmas and categorise them
according to their usage.


  The use of dielectric microstructures driven by solid state lasers to
accelerate charged particles or to transversely deflect them is a growing area
of scientific interest with an international collaboration of researchers
working to develop this concept. Many experimental efforts and new designs use
a planar symmetric geometry with sub-micron apertures for the particle beam. We
provide a general theoretical framework for the electromagnetic fields in this
type of geometry, including derivation of the TE and TM modes supported, and
examine the transverse force components exerted on the beam, which may be used
for focusing or for deflection of the particles.


  The measurements of $R_K^{(*)}$ and $R_{D}^{(*)}$ by BaBar, Belle and the
LHCb collaborations could be showing a hint of lepton flavor universality
violation that can be accommodated by the presence of suitable leptoquarks at
the TeV scale. We consider an effective description, with leptoquarks arising
as composite pseudo Nambu-Goldstone bosons, as well as anarchic partial
compositeness of the SM fermions. Considering the $R_K^{(*)}$ anomaly within
this framework, we study pair production of $S_3\sim(\bar 3,3)_{1/3}$ at the
LHC. We focus on the component $S_3^{1/3}$ of the triplet, which decays
predominantly into $t\tau$ and $b\nu$, and study the bounds from existing
searches at $\sqrt{s}=13$ TeV at the LHC. We find that sbottom searches in the
$b\bar{b}$+MET final state best explore the region in parameter space preferred
by our model and currently exclude $S_3^{1/3}$ masses up to $\sim$1 TeV.
Additional searches, considering the $t\tau$ and $t\mu$ decay modes, are
required to probe the full physical parameter space. In this paper we also
recast existing studies on direct leptoquark searches in the $t\tau t\tau$
channel and SM $t\bar{t}t\bar{t}$ searches, and obtain the regions in parameter
space currently excluded. Practically the whole physical parameter space is
currently excluded for masses up to $\sim$0.8 TeV, which could be extended up
to $\sim$1 TeV with the full Run 3 dataset. We conclude that pair production
searches for this leptoquark can benefit from considering the final state $t
\tau b$ +MET, where the largest branching ratio is expected. We appraise that
future explorations of leptoquarks explaining the B-anomalies with masses
beyond the TeV should also consider single and non-resonant production in order
to extend the mass reach.


  We present a description of "the Conductor", an automated software package
which handles all observations at the first Stellar Observations Network Group
(SONG) node telescope at the Teide Observatory on the island of Tenerife. The
idea was to provide a complete description on the automated procedures for
target selection and execution of observations and to demonstrate how the SONG
robotic telescope is being operated. The Conductor is a software package
developed in Python and running on a server in Aarhus which makes use of a
large set of database tables through which it communicates with the SONG nodes.
Based on a number of selection criteria the Conductor is able to identify the
optimum target to be observed at any given moment taking into account local
weather conditions and technical constraints. The Conductor has made it
possible for the Hertzsprung SONG telescope to become a highly sophisticated
and efficient robotic telescopic facility without human interaction. It can
handle everything from Principal Investigators submitting their proposed
targets with specific settings to the data being available for download after
the observations has been carried out. At present, and thanks to the
availability of the Conductor, the first node of the SONG project can be
considered a world leading robotic telescope with respect to needed human
interactions, efficiency and flexibility in observing strategy.


  The burgeoning integration of Artificial Intelligence (AI) into
Environmental, Social, and Governance (ESG) initiatives within the financial
sector represents a paradigm shift towards more sus-tainable and equitable
financial practices. This paper surveys the industrial landscape to delineate
the necessity and impact of AI in bolstering ESG frameworks. With the advent of
stringent regulatory requirements and heightened stakeholder awareness,
financial institutions (FIs) are increasingly compelled to adopt ESG criteria.
AI emerges as a pivotal tool in navigating the complex in-terplay of financial
activities and sustainability goals. Our survey categorizes AI applications
across three main pillars of ESG, illustrating how AI enhances analytical
capabilities, risk assessment, customer engagement, reporting accuracy and
more. Further, we delve into the critical con-siderations surrounding the use
of data and the development of models, underscoring the importance of data
quality, privacy, and model robustness. The paper also addresses the imperative
of responsible and sustainable AI, emphasizing the ethical dimensions of AI
deployment in ESG-related banking processes. Conclusively, our findings suggest
that while AI offers transformative potential for ESG in banking, it also poses
significant challenges that necessitate careful consideration. The final part
of the paper synthesizes the survey's insights, proposing a forward-looking
stance on the adoption of AI in ESG practices. We conclude with recommendations
with a reference architecture for future research and development, advocating
for a balanced approach that leverages AI's strengths while mitigating its
risks within the ESG domain.


  An order--disorder phase transition is observed for Ising-like systems even
for arbitrarily chosen probabilities of spins flips [K. Malarz et al, Int. J.
Mod. Phys. C 22, 719 (2011)]. For such athermal dynamics one must define
$(z+1)$ spin flips probabilities $w(n)$, where $z$ is a number of the
nearest-neighbours for given regular lattice and $n=0,\cdots,z$ indicates the
number of nearest spins with the same value as the considered spin. Recently,
such dynamics has been successfully applied for the simulation of a cooperative
and competitive strategy selection by pedestrians in crowd [P. Gawro\'nski et
al, Acta Phys. Pol. A 123, 522 (2013)]. For the triangular lattice ($z=6$) and
flips probabilities dependence on a single control parameter $x$ chosen as
$w(0)=1$, $w(1)=3x$, $w(2)=2x$, $w(3)=x$, $w(4)=x/2$, $w(5)=x/4$, $w(6)=x/6$
the ordered phase (where most of pedestrians adopt the same strategy) vanishes
for $x>x_C\approx 0.429$. In order to introduce long-range interactions between
pedestrians the bonds of triangular lattice are randomly rewired with the
probability $p$. The amount of rewired bonds can be interpreted as the
probability of communicating by mobile phones. The critical value of control
parameter $x_C$ increases monotonically with the number of rewired links
$M=pzN/2$ from $x_C(p=0)\approx 0.429$ to $x_C(p=1)\approx 0.81$.


  We consider the motion of small bodies in general relativity. The key result
captures a sense in which such bodies follow timelike geodesics (or, in the
case of charged bodies, Lorentz-force curves). This result clarifies the
relationship between approaches that model such bodies as distributions
supported on a curve, and those that employ smooth fields supported in small
neighborhoods of a curve. This result also applies to "bodies" constructed from
wave packets of Maxwell or Klein-Gordon fields. There follows a simple and
precise formulation of the optical limit for Maxwell fields.


  Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt, and Giulia Sarfatti
recently gave the proof of a bi-parameter Carleson embedding theorem. Their
proof uses heavily the notion of capacity on bi-tree. In this note we give one
more proof of a bi-parameter Carleson embedding theorem that avoids the use of
bi-tree capacity. Unlike the proof on a simple tree (in a pervious paper of the
authors) that used the Bellman function technique, the proof here is based on
some rather subtle comparison of energies of measures on bi-tree.


  (Abridged) We have recently proposed that the ultra-high energy cosmic rays
(UHECRs) observed above the GZK limit could be mostly protons accelerated in
reconnection sites just above the magnetosphere of newborn millisecond pulsars
originated by accretion induced collapse (AIC-pulsars). Although the expected
rate of AIC sources in our own Galaxy is very small, our estimates have shown
that the observed total flux of UHECRs could be obtained from the integrated
contribution from AIC-pulsars of the whole distribution of galaxies located
within a distance which is unaffected by the GZK cutoff ($\sim 50 $ Mpc). We
presently examine the potential acceleration mechanisms in the magnetic
reconnection site and find that first-order Fermi acceleration cannot provide
sufficient efficiency (due to synchrotron losses). This leaves the one-shot
acceleration via an induced electric field within the reconnection region as
the only viable process for UHECR acceleration. We formulate the constraints on
both the magnetic field topology and strength in order to accelerate the
particles and allow them to freely escape from the system. Under fast
reconnection, we find that AIC-pulsars with surface B-fields $10^{12} $ G $<
B_{\star} \lesssim $ $10^{15}$ G and spin periods 1 ms $\lesssim P_{\star} < $
60 ms, are able to accelerate particles to energies $\geq 10^{20} $ eV, but the
magnetic field just above the Alfv\'en surface must be predominantly toroidal
for the particles to be allowed to escape from the acceleration zone without
being deflected. Synchrotron losses bring potentially important constraints on
the B-field geometry of $any$ UHECR accelerators involving compact sources with
strong magnetic fields.


  In this paper, we report about recent findings in the numerical solution of
Hamiltonian Partial Differential Equations (PDEs), by using energy-conserving
line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class.
In particular, we consider the semilinear wave equation, the nonlinear
Schr\"odinger equation, and the Korteweg-de Vries equation, to illustrate the
main features of this novel approach.


  In this paper, an incommensurate fractional order (FO) model has been
proposed to generate ECG like waveforms. Earlier investigation of ECG like
waveform generation is based on two identical Van-der Pol (VdP) family of
oscillators which are coupled by time delays and gains. In this paper, we
suitably modify the three state equations corresponding to the nonlinear
cross-product of states, time delay coupling of the two oscillators and
low-pass filtering, using the concept of fractional derivatives. Our results
show that a wide variety of ECG like waveforms can be simulated from the
proposed generalized models, characterizing heart conditions under different
physiological conditions. Such generalization of the modelling of ECG waveforms
may be useful to understand the physiological process behind ECG signal
generation in normal and abnormal heart conditions. Along with the proposed FO
models, an optimization based approach is also presented to estimate the VdP
oscillator parameters for representing a realistic ECG like signal.


  A polynomial algorithm for graphs' isomorphism testing is constructed in
assumption that there exists a corresponding polynomial algorithm for graphs
with trivial automorphism group.


  For functors $L:\A\to \B$ and $R:\B\to \A$ between any categories $\A$ and
$\B$, a {\em pairing} is defined by maps, natural in $A\in \A$ and $B\in \B$,
$$\xymatrix{\Mor_\B (L(A),B<EMAIL_ADDRESS>& \Mor_\A
<EMAIL_ADDRESS>  $(L,R)$ is an {\em adjoint pair} provided $\alpha$ (or $\beta$) is a
bijection. In this case the composition $RL$ defines a monad on the category
$\A$, $LR$ defines a comonad on the category $\B$, and there is a well-known
correspondence between monads (or comonads) and adjoint pairs of functors.
  For various applications it was observed that the conditions for a unit of a
monad was too restrictive and weakening it still allowed for a useful
generalised notion of a monad. This led to the introduction of {\em weak
monads} and {\em weak comonads} and the definitions needed were made without
referring to this kind of adjunction. The motivation for the present paper is
to show that these notions can be naturally derived from pairings of functors
$(L,R,\alpha,\beta)$ with $\alpha = \alpha\dcirc \beta\dcirc \alpha$ and $\beta
= \beta \dcirc\alpha\dcirc\beta$. Following closely the constructions known for
monads (and unital modules) and comonads (and counital comodules), we show that
any weak (co)monad on $\A$ gives rise to a regular pairing between $\A$ and the
category of {\em compatible (co)modules}.


  Studies of the properties of the inner Galactic Bulge depend strongly on the
assumptions about the interstellar extinction. Most of the extinction maps
available in the literature lack the information about the distance.
  We combine the observations with the Besancon model of the Galaxy to
investigate the variations of extinction along different lines of sight towards
the inner Galactic bulge as a function of distance. In addition we study the
variations in the extinction law in the Bulge. We construct color-magnitude
diagrams with the following sets of colors: H-Ks and J-Ks from the VVV
catalogue as well as Ks-[3.6], Ks-[4.5], Ks-[5.8] and Ks-[8.0] from GLIMPSE-II
catalogue matched with 2MASS. Using the newly derived temperature-color
relation for M giants that match better the observed color-magnitude diagrams
we then use the distance-color relations to derive the extinction as a function
of distance. The observed colors are shifted to match the intrinsic colors in
the Besan\c{c}on model, as a function of distance, iteratively thereby creating
an extinction map with three dimensions: two spatial and one distance dimension
along each line of sight towards the bulge. Colour excess maps are presented at
a resolution of 15' x 15' for 6 different combinations of colors, in distance
bins of 1 kpc. The high resolution and depth of the photometry allows to derive
extinction maps to 10 kpc distance and up to 35 magnitudes of extinction in Av
(3.5 mag in Aks). Integrated maps show the same dust features and consistent
values with the other 2D maps. Starting from the color excess between the
observations and the model we investigate the extinction law in near-infrared
and its variation along different lines of sight.


  We present a scalable algorithm for solving the collisionless Boltzmann
equation in two and three spatial dimensions for variable grid sizes and
discrete velocities on a fault-tolerant universal quantum computer. As a proof
of concept of our collisionless quantum Boltzmann method (CQBM), we describe a
full-circuit start-to-end implementation in Qiskit and present numerical
results for 2D flows. Our CQBM is based on a novel streaming approach which
leads to a reduction in the amount of CNOT gates required in comparison to
state-of-the-art quantum streaming methods. As a second highlight we present a
novel object encoding method, that reduces the complexity of the amount of CNOT
gates required to encode walls, which now becomes independent of the size of
the wall. Finally we present a novel quantum encoding of the particles'
discrete velocities that enables a linear speed-up in the costs of reflecting
the velocity of a particle, which now becomes independent of the amount of
velocities encoded. Our main contribution is a detailed description of a
fail-safe implementation of a quantum algorithm for the reflection step of the
collisionless Boltzmann equation that can be readily implemented on a physical
quantum computer. This fail-safe implementation allows for a variety of initial
conditions and particle velocities and leads to physically correct behavior
around the walls, edges and corners of obstacles. Combining these results we
present a novel and fail-safe start-to-end quantum algorithm for the
collisionless Boltzmann equation that can be used for a multitude of flow
configurations. We finally show that our approach is quadratic in the amount of
qubits necessary to encode the grid and the amount of qubits necessary to
encode the discrete velocities in a single spatial dimension, which makes our
approach superior to state-of-the-art approaches known in the literature.


  Divergence From Randomness (DFR) ranking models assume that informative terms
are distributed in a corpus differently than non-informative terms. Different
statistical models (e.g. Poisson, geometric) are used to model the distribution
of non-informative terms, producing different DFR models. An informative term
is then detected by measuring the divergence of its distribution from the
distribution of non-informative terms. However, there is little empirical
evidence that the distributions of non-informative terms used in DFR actually
fit current datasets. Practically this risks providing a poor separation
between informative and non-informative terms, thus compromising the
discriminative power of the ranking model. We present a novel extension to DFR,
which first detects the best-fitting distribution of non-informative terms in a
collection, and then adapts the ranking computation to this best-fitting
distribution. We call this model Adaptive Distributional Ranking (ADR) because
it adapts the ranking to the statistics of the specific dataset being processed
each time. Experiments on TREC data show ADR to outperform DFR models (and
their extensions) and be comparable in performance to a query likelihood
language model (LM).


  Let $Y$ be a stochastic process on $[0,1]$ satisfying $dY(t) = n^{1/2} f(t)
dt + dW(t)$, where $n \ge 1$ is a given scale parameter (``sample size''), $W$
is standard Brownian motion and $f$ is an unknown function. Utilizing suitable
multiscale tests we construct confidence bands for $f$ with guaranteed given
coverage probability, assuming that $f$ is isotonic or convex. These confidence
bands are computationally feasible and shown to be asymptotically sharp optimal
in an appropriate sense.


  We develop a simulation tool to support policy-decisions about healthcare for
chronic diseases in defined populations. Incident disease-cases are generated
in-silico from an age-sex characterised general population using standard
epidemiological approaches. A novel disease-treatment model then simulates
continuous life courses for each patient using discrete event simulation.
Ideally, the discrete event simulation model would be inferred from complete
longitudinal healthcare data via a likelihood or Bayesian approach. Such data
is seldom available for relevant populations, therefore an innovative approach
to evidence synthesis is required. We propose a novel entropy-based approach to
fit survival densities. This method provides a fully flexible way to
incorporate the available information, which can be derived from arbitrary
sources. Discrete event simulation then takes place on the fitted model using a
competing hazards framework. The output is then used to help evaluate the
potential impacts of policy options for a given population.


  In the present paper we study the oscillations of fast rotating neutron stars
with realistic equations of state (EoS) within the Cowling approximation. We
derive improved empirical relations for gravitational wave asteroseismology
with f-modes and for the first time we consider not only quadrupolar
oscillations but also modes with higher spherical order (l=|m|=3,4). After
performing a systematic comparison with polytropic EoS, it is shown that the
empirical relations found in this case approximately also hold for realistic
EoS. Even more, we show that these relations will not change significantly even
if the Cowling approximation is dropped and the full general relativistic case
is considered, although the normalization used here(frequencies and damping
times in the nonrotating limit) could differ considerably. We also address the
inverse problem, i.e. we investigate in detail what kind of observational data
is required in order to determine characteristical neutron star parameters. It
is shown that masses, radii and rotation rates can be estimated quite
accurately using the derived asteroseismology relations. We also compute the
instability window for certain models, i.e. the limiting curve in a
T-\Omega-plane where the secular Chandrasekhar-Friedman-Schutz(CFS) instability
overcomes dissipative effects, and show that some of the modern realistic EoS
will lead to a larger instability window compared to all of the polytropic ones
presented so far in the literature. Additionally, we calculate the r-mode
instability window and compare it with the f-mode-case. The overall results for
the instability window suggest that it is vital to take into account
oscillations with l=3,4 when considering gravitational wave asteroseismology
using the f-mode in rapidly rotating neutron stars, as these modes can become
CFS unstable for a much larger range of parameters than pure quadrupolar
oscillations.


  We present a time-dependent radiative model of the atmosphere of HD209458b
and investigate its thermal structure and chemical composition. In a first
step, the stellar heating profile and radiative timescales were calculated
under planet-averaged insolation conditions. We find that 99.99% of the
incoming stellar flux has been absorbed before reaching the 7 bar level.
Stellar photons cannot therefore penetrate deeply enough to explain the large
radius of the planet. We derive a radiative time constant which increases with
depth and reaches about 8 hr at 0.1 bar and 2.3 days at 1 bar. Time-dependent
temperature profiles were also calculated, in the limit of a zonal wind that is
independent on height (i.e. solid-body rotation) and constant absorption
coefficients. We predict day-night variations of the effective temperature of
\~600 K, for an equatorial rotation rate of 1 km/s, in good agreement with the
predictions by Showman &Guillot (2002). This rotation rate yields day-to-night
temperature variations in excess of 600 K above the 0.1-bar level. These
variations rapidly decrease with depth below the 1-bar level and become
negligible below the ~5--bar level for rotation rates of at least 0.5 km/s. At
high altitudes (mbar pressures or less), the night temperatures are low enough
to allow sodium to condense into Na2S. Synthetic transit spectra of the visible
Na doublet show a much weaker sodium absorption on the morning limb than on the
evening limb. The calculated dimming of the sodium feature during planetary
transites agrees with the value reported by Charbonneau et al. (2002).


  Reservoir computing (RC) is a special recurrent neural network which consists
of a fixed high dimensional feature mapping and trained readout weights. In
this paper, we introduce a new RC structure for multiple-input, multiple-output
orthogonal frequency-division multiplexing (MIMO-OFDM) symbol detection, namely
windowed echo state network (WESN). The theoretical analysis shows that adding
buffers in input layers can bring an enhanced short-term memory (STM) to the
underlying neural network. Furthermore, a unified training framework is
developed for the WESN MIMO-OFDM symbol detector using both comb and scattered
pilot patterns that are compatible with the structure adopted in 3GPP
LTE/LTE-Advanced systems. Complexity analysis suggests the advantages of WESN
based symbol detector over state-of-the-art symbol detectors such as the linear
minimum mean square error (LMMSE) detection and the sphere decoder, when the
system is employed with a large number of OFDM sub-carriers. Numerical
evaluations illustrate the advantage of the introduced WESN-based symbol
detector and demonstrate that the improvement of STM can significantly improve
symbol detection performance as well as effectively mitigate model mismatch
effects compared to existing methods.


  We present robust, model-marginalized limits on both the total neutrino mass
($\sum m_\nu$) and abundance ($N_{\rm eff}$) to minimize the role of
parameterizations, priors and models when extracting neutrino properties from
cosmology. The cosmological observations we consider are CMB temperature
fluctuation and polarization measurements, Supernovae Ia luminosity distances,
BAO observations and determinations of the growth rate parameter from the Data
Release 16 of the Sloan Digital Sky Survey IV. The degenerate neutrino mass
spectrum (which implies $\sum m_\nu>0$) is weakly (moderately) preferred over
the normal and inverted hierarchy possibilities, which imply the priors $\sum
m_\nu>0.06$ and $\sum m_\nu>0.1$ eV respectively. Concerning the underlying
cosmological model, the $\Lambda$CDM minimal scenario is almost always strongly
preferred over the possible extensions explored here. The most constraining
$95\%$ CL bound on the total neutrino mass in the $\Lambda$CDM+$\sum m_\nu$
picture is $\sum m_\nu< 0.087$ eV. The parameter $N_{\rm eff}$ is restricted to
$3.08\pm 0.17$ ($68\%$ CL) in the $\Lambda$CDM+$N_{\rm eff}$ model. These
limits barely change when considering the $\Lambda$CDM+$\sum m_\nu$+$N_{\rm
eff}$ scenario. Given the robustness and the strong constraining power of the
cosmological measurements employed here, the model-marginalized posteriors
obtained considering a large spectra of non-minimal cosmologies are very close
to the previous bounds, obtained within the $\Lambda$CDM framework in the
degenerate neutrino mass spectrum. Future cosmological measurements may improve
the current Bayesian evidence favouring the degenerate neutrino mass spectra,
challenging therefore the consistency between cosmological neutrino mass bounds
and oscillation neutrino measurements, and potentially suggesting a more
complicated cosmological model and/or neutrino sector.


  This paper studies a notion of enumerative invariants for stable $A$-branes,
and discusses its relation to invariants defined by spectral and exponential
networks. A natural definition of stable $A$-branes and their counts is
provided by the string theoretic origin of the topological $A$-model. This is
the Witten index of the supersymmetric quantum mechanics of a single $D3$ brane
supported on a special Lagrangian in a Calabi-Yau threefold. Geometrically,
this is closely related to the Euler characteristic of the $A$-brane moduli
space. Using the natural torus action on this moduli space, we reduce the
computation of its Euler characteristic to a count of fixed points via
equivariant localization. Studying the $A$-branes that correspond to fixed
points, we make contact with definitions of spectral and exponential networks.
We find agreement between the counts defined via the Witten index, and the BPS
invariants defined by networks. By extension, our definition also matches with
Donaldson-Thomas invariants of $B$-branes related by homological mirror
symmetry.


  Abundance observations indicate the presence of often surprisingly large
amounts of neutron capture (i.e., s- and r-process) elements in old Galactic
halo and globular cluster stars. These observations provide insight into the
nature of the earliest generations of stars in the Galaxy -- the progenitors of
the halo stars -- responsible for neutron-capture synthesis. Comparisons of
abundance trends can be used to understand the chemical evolution of the Galaxy
and the nature of heavy element nucleosynthesis. In addition age
determinations, based upon long-lived radioactive nuclei abundances, can now be
obtained. These stellar abundance determinations depend critically upon atomic
data. Improved laboratory transition probabilities have been recently obtained
for a number of elements. These new gf values have been used to greatly refine
the abundances of neutron-capture elemental abundances in the solar photosphere
and in very metal-poor Galactic halo stars. The newly determined stellar
abundances are surprisingly consistent with a (relative) Solar System r-process
pattern, and are also consistent with abundance predictions expected from such
neutron-capture nucleosynthesis.


  SIDE (Super Ifu Deployable Experiment) is proposed as second-generation,
common-user instrument for the GTC. It will be a low and intermediate
resolution fiber fed spectrograph, highly efficient in multi-object and 3D
spectroscopy. The low resolution part (R = 1500, 4000) is called Dual VIS-NIR
because it will observe in the VIS and NIR bands (0.4 ~V 1.7 microns)
simultaneously. Because of the large number of fibers, a set of ~10 identical
spectrographs is needed, each with a mirror collimator, a dichroic and two
refractive cameras. The cameras are optimized for 0.4 - 0.95 microns (VIS) and
0.95 - 1.7 microns (NIR) respectively.


  Most surrogate models for computer experiments are interpolators, and the
most common interpolator is a Gaussian process (GP) that deliberately omits a
small-scale (measurement) error term called the nugget. The explanation is that
computer experiments are, by definition, "deterministic", and so there is no
measurement error. We think this is too narrow a focus for a computer
experiment and a statistically inefficient way to model them. We show that
estimating a (non-zero) nugget can lead to surrogate models with better
statistical properties, such as predictive accuracy and coverage, in a variety
of common situations.


  In relativistic potential model of heavy-light mesons it is essential to
incorporate the chiral radiative corrections before comparing the model
predictions with data. Once the radiative corrections are taken into account
the potential model can explain the unusual mass spectra and absence of the
spin orbit-inversion in P-wave states.


  Contextualized word embeddings (CWE) such as provided by ELMo (Peters et al.,
2018), Flair NLP (Akbik et al., 2018), or BERT (Devlin et al., 2019) are a
major recent innovation in NLP. CWEs provide semantic vector representations of
words depending on their respective context. Their advantage over static word
embeddings has been shown for a number of tasks, such as text classification,
sequence tagging, or machine translation. Since vectors of the same word type
can vary depending on the respective context, they implicitly provide a model
for word sense disambiguation (WSD). We introduce a simple but effective
approach to WSD using a nearest neighbor classification on CWEs. We compare the
performance of different CWE models for the task and can report improvements
above the current state of the art for two standard WSD benchmark datasets. We
further show that the pre-trained BERT model is able to place polysemic words
into distinct 'sense' regions of the embedding space, while ELMo and Flair NLP
do not seem to possess this ability.


  Considered here is one quite general problem about description of extremal
configurations maximizing the product of inner radii non-overlapping domains.


  This paper proposes a new logic RoCTL* to model robustness in concurrent
systems. RoCTL* extends CTL* with the addition of Obligatory and Robustly
operators, which quantify over failure-free paths and paths with one more
failure respectively. We present a number of examples of problems to which
RoCTL* can be applied. The core result of this paper is to show that RoCTL* is
expressively equivalent to CTL* but is non-elementarily more succinct. We
present a translation from RoCTL* into CTL* that preserves truth but may result
in non-elementary growth in the length of the translated formula as each nested
Robustly operator may result in an extra exponential blowup. However, we show
that this translation is optimal in the sense that any equivalence preserving
translation will require an extra exponential growth per nested Robustly. We
also compare RoCTL* to Quantified CTL* (QCTL*) and hybrid logics.


  We introduce a multiscale framework which combines time-dependent
nonequilibrium Green function (TD-NEGF) algorithms, scaling linearly in the
number of time steps and describing quantum-mechanically conduction electrons
in the presence of time-dependent fields of arbitrary strength or frequency,
with classical time evolution of localized magnetic moments described by the
Landau-Lifshitz-Gilbert (LLG) equation. The TD-NEGF+LLG framework can be
applied to a variety of problems where current-driven spin torque induces
dynamics of magnetic moments as the key resource for next generation
spintronics. Using magnetic domain wall (DW) as an example, we predict that its
motion will pump time-dependent spin and charge currents (on the top of
unpolarized DC charge current injected through normal metal leads to drive the
DW motion). The conversion of AC components of spin current, whose amplitude
increases (decreases) as the DW approaches (distances from) the normal metal
lead, into AC voltage via the inverse spin Hall effect offers a tool to
precisely track the DW position along magnetic nanowire. We also quantify the
DW transient inertial displacement due to its acceleration and deceleration by
pulse current and the entailed spin and charge pumping. Finally, TD-NEGF+LLG as
a nonperturbative (i.e., numerically exact) framework allows us to establish
the limits of validity of the so-called spin-motive force (SMF) theory for
pumped charge current by time-dependent magnetic textures---the perturbative
analytical formula of SMF theory becomes inapplicable for large frequencies
(but unrealistic in magnetic system) and, more importantly, for increasing
noncollinearity when the angles between neighboring magnetic moments exceed
$\simeq 10^\circ$.


  A systematic approach is presented to construct non-homogeneous two- and
three-qubit Bell-type inequalities. When projector-like terms are subtracted
from homogeneous two-qubit CHSH polynomial, non-homogeneous inequalities are
attained and the maximal quantum mechanical violation asymptotically equals a
constant with the subtracted terms becoming sufficiently large. In the case of
three-qubit system, it is found that most significant three-qubit inequalities
presented in literature can be recovered in our framework. We aslo discuss the
behavior of such inequalities in the loophole-free Bell test and obtain
corresponding thresholds of detection efficiency.


  The second author's $\omega$, $\Delta$, $\chi$ conjecture proposes that every
graph satisties $\chi \leq \lceil \frac 12 (\Delta+1+\omega)\rceil$. In this
paper we prove that the conjecture holds for all claw-free graphs. Our approach
uses the structure theorem of Chudnovsky and Seymour.
  Along the way we discuss a stronger local conjecture, and prove that it holds
for claw-free graphs with a three-colourable complement. To prove our results
we introduce a very useful $\chi$-preserving reduction on homogeneous pairs of
cliques, and thus restrict our view to so-called "skeletal" graphs.


  We investigate the effects of static electric and magnetic fields on the
differential ac Stark shifts for microwave transitions in ultracold bosonic
$^{87}$Rb$^{133}$Cs molecules, for light of wavelength $\lambda =
1064~\mathrm{nm}$. Near this wavelength we observe unexpected two-photon
transitions that may cause trap loss. We measure the ac Stark effect in
external magnetic and electric fields, using microwave spectroscopy of the
first rotational transition. We quantify the isotropic and anisotropic parts of
the molecular polarizability at this wavelength. We demonstrate that a modest
electric field can decouple the nuclear spins from the rotational angular
momentum, greatly simplifying the ac Stark effect. We use this simplification
to control the ac Stark shift using the polarization angle of the trapping
laser.


  We present the results of a photometric and spectroscopic study of the white
dwarf candidate members of the intermediate age open clusters NGC3532 and
NGC2287. Of the nine objects investigated, it is determined that six are
probable members of the clusters, four in NGC3532 and two in NGC2287. For these
six white dwarfs we use our estimates of their cooling times together with the
cluster ages to constrain the lifetimes and masses of their progenitor stars.
We examine the location of these objects in initial mass-final mass space and
find that they now provide no evidence for substantial scatter in initial
mass-final mass relation as suggested by previous investigations. Instead, we
demonstrate that, when combined with current data from other solar metalicity
open clusters and the Sirius binary system, they hint at an IFMR that is
steeper in the initial mass range 3M$_{\odot}$$\simless$M$_{\rm
init}$$\simless$4M$_{\odot}$ than at progenitor masses immediately lower and
higher than this. This form is generally consistent with the predictions of
stellar evolutionary models and can aid population synthesis models in
reproducing the relatively sharp drop observed at the high mass end of the main
peak in the mass distribution of white dwarfs.


  In this paper, the finite volume method is developed to analyze coupled
dynamic problems of nonlinear thermoelasticity. The major focus is given to the
description of martensitic phase transformations essential in the modelling of
shape memory alloys. Computational experiments are carried out to study the
thermo-mechanical wave interactions in a shape memory alloy rod, and a patch.
Both mechanically and thermally induced phase transformations, as well as
hysteresis effects, in a one-dimensional structure are successfully simulated
with the developed methodology. In the two-dimensional case, the main focus is
given to square-to-rectangular transformations and examples of martensitic
combinations under different mechanical loadings are provided.


  Living cells need a constant availability of certain resources to have a
sustained gene expression process. Limited availability of cellular resources
for gene expression, like ribosomes, along with a variation of resource
affinity, significantly modifies the system dynamics. Factors like the
variation in rate of binding, or variation in efficiency of the recruited
resource have the potential to affect crucial dynamical phenomena like cell
fate determination. In this paper, we have taken a very important motif, a
bistable genetic toggle switch, and explored the effect of resource imbalance
in this circuit in terms of the bifurcations taking place. We show that initial
asymmetric biasing to resource via resource affinity or gene copy number,
significantly modifies the cell fate transition, both in pitchfork and saddle
node type bifurcation. Our study establishes that in a limited resource
environment, controlled resource allocation can be an important factor for
robust functioning of the synthetic or cellular genetic switches.


  Self-calibration methods with the CLEAN algorithm have been widely employed
in Very Long Baseline Interferometry (VLBI) data processing in order to correct
antenna-based amplitude and phase corruptions present in the data. However,
human interaction during the conventional CLEAN self-calibration process can
impose a strong effective prior, which in turn may produce artifacts within the
final image and hinder the reproducibility of final results. In this work, we
aim to demonstrate a combined self-calibration and imaging method for VLBI data
in a Bayesian inference framework. The method corrects for amplitude and phase
gains for each antenna and polarization mode by inferring the temporal
correlation of the gain solutions. We use Stokes I data of M87 taken with the
Very Long Baseline Array (VLBA) at 43GHz, pre-calibrated using the rPICARD
CASA-based pipeline. For antenna-based gain calibration and imaging, we use the
Bayesian imaging software resolve. To estimate gain and image uncertainties, we
use a Variational Inference method. We obtain a high-resolution M87 Stokes I
image at 43GHz in conjunction with antenna-based gain solutions using our
Bayesian self-calibration and imaging method. The core with counter-jet
structure is better resolved, and extended jet emission is better described
compared to the CLEAN reconstruction. Furthermore, uncertainty estimation of
the image and antenna-based gains allows us to quantify the reliability of the
result. Our Bayesian self-calibration and imaging method is able to reconstruct
robust and reproducible Stokes I images and gain solutions with uncertainty
estimation by taking into account the uncertainty information in the data.


  We present a revised analysis of the photometric reverberation mapping
campaign of the narrow-line Seyfert 1 galaxy PKS 0558-504 carried out with the
Swift Observatory during 2008--2010. Previously, Gliozzi et al.\ found using
the Discrete Correlation Function (DCF) method that the short-wavelength
continuum variations lagged behind variations at longer wavelengths, the
opposite of the trend expected for thermal reprocessing of X-rays by the
accretion disc, and they interpreted their results as evidence against the
reprocessing model. We carried out new DCF measurements that demonstrate that
the inverted lag-wavelength relationship found by Gliozzi et al.\ resulted from
their having interchanged the order of the driving and responding light curves
when measuring the lags. To determine the inter-band lags and uncertainties
more accurately, we carried out new measurements with four independent methods.
These give consistent results showing time delays increasing as a function of
wavelength, as expected for the disc reprocessing scenario. The slope of the
re-analysed delay spectrum appears to be roughly compatible with the predicted
$\tau \propto \lambda^{4/3}$ relationship for reprocessing by an optically
thick and geometrically thin accretion disc, although the data points exhibit a
large scatter about the fitted power-law trend.


  Magnetic tunnel junction (MTJ) based on CoFeB/MgO/CoFeB structures is of
great interest due to its application in the spin-transfer-torque magnetic
random access memory (STT-MRAM). Large interfacial perpendicular magnetic
anisotropy (PMA) is required to achieve high thermal stability. Here we use
first-principles calculations to investigate the magnetic anisotropy energy
(MAE) of MgO/CoFe/capping layer structures, where the capping materials include
5d metals Hf, Ta, Re, Os, Ir, Pt, Au and 6p metals Tl, Pb, Bi. We demonstrate
that it is feasible to enhance PMA by using proper capping materials.
Relatively large PMA is found in the structures with capping materials of Hf,
Ta, Os, Ir and Pb. More importantly, the MgO/CoFe/Bi structure gives rise to
giant PMA (6.09 mJ/m2), which is about three times larger than that of the
MgO/CoFe/Ta structure. The origin of the MAE is elucidated by examining the
contributions to MAE from each atomic layer and orbital. These findings provide
a comprehensive understanding of the PMA and point towards the possibility to
achieve advanced-node STT-MRAM with high thermal stability.


  Let $\mathbb{H}^{n}=\mathbb{C}^{n}\times\mathbb{R}$ be the $n$-dimensional
Heisenberg group, $Q=2n+2$ be the homogeneous dimension of $\mathbb{H}^{n}$. We
extend the well-known concentration-compactness principle on finite domains in
the Euclidean spaces of \ P. L. Lions to the setting of the Heisenberg group
$\mathbb{H}^{n}$. Furthermore, we also obtain the corresponding
concentration-compactness principle for the Sobolev space $HW^{1,Q}\left(
\mathbb{H}^{n}\right) $ on the entire Heisenberg group $\mathbb{H}^{n}$.
  Our results improve the sharp Trudinger-Moser inequality on domains of finite
measure in $\mathbb{H}^{n}$ by Cohn and the second author [8] and the
corresponding one on the whole space $\mathbb{H}^n$ by Lam and the second
author [21]. All the proofs of the concentration-compactness principles in the
literature even in the Euclidean spaces use the rearrangement argument and the
Poly\'a-Szeg\"{o} inequality. Due to the absence of the Poly\'a-Szeg\"{o}
inequality on the Heisenberg group, we will develop a different argument. Our
approach is surprisingly simple and general and can be easily applied to other
settings where symmetrization argument does not work. As an application of the
concentration-compactness principle, we establish the existence of ground state
solutions for a class of $Q$- Laplacian subelliptic equations on
$\mathbb{H}^{n}$ with nonlinear terms $f$ of maximal exponential growth
$\exp\left( \alpha t^{\frac{Q}{Q-1}}\right) $ as $t\rightarrow+\infty$.


  Using the Model of the Stochastic Vacuum many diffractive processes have been
calculated by investigating the dipole-dipole scattering at a cm-energy of 20
GeV. In this work we extend the calculation to larger energies and small
dipoles. We assume that there are two pomerons, the hard- and the soft-pomeron,
which cause the different energy dependence for processes dominated by small or
large dipoles. The physical processes are obtained by smearing the
dipole-dipole amplitude with wavefunctions. For small dipoles the leading
perturbative contribution is taken into account. By that way we can describe in
addition to the already calculated low energy results (20 GeV) also the HERA
data for the considered processes in nearly the whole energy and Q^2 range.


  Xu introduced a family of root-tree-diagram nilpotent Lie algebras of
differential operators, in connection with evolution partial differential
equations. We generalized his notion to more general oriented tree diagrams.
These algebras are natural analogues of the maximal nilpotent Lie subalgebras
of finite-dimensional simple Lie algebras. In this paper, we use Hodge
Laplacian to study the cohomology of these Lie algebras. The "total rank
conjecture" and "$b_2$-conjecture" for the algebras are proved. Moreover, we
find the generating functions of the Betti numbers by means of Young tableaux
for the Lie algebras associated with certain tree diagrams of single branch
point. By these functions and Euler-Poincare principle, we obtain analogues of
the denominator identity for finite-dimensional simple Lie algebras. The result
is a natural generalization of the Bott's classical result in the case of
special linear Lie algebras.


  The jet-jet profile, or detailed manner, in which transverse energy and mass
are distributed around the jet-jet system resulting from the hadronic decay of
a $Z$ boson in the process Higgs$\to ZZ$ at a proton-proton collider energy of
$40\tev$ is carefully examined. Two observables are defined that can be used to
help distinguish the $\ell^+\ell^-$-jet-jet signal from Higgs decay from the
``ordinary'' QCD background arising from the large transverse momentum
production of single $Z$ bosons plus the associated jets. By making cuts on
these observables, signal to background enhancement factors greater than $100$
can be obtained.


  Designing for manufacturing poses significant challenges in part due to the
computation bottleneck of Computer-Aided Manufacturing (CAM) simulations.
Although deep learning as an alternative offers fast inference, its performance
is dependently bounded by the need for abundant training data. Representation
learning, particularly through pre-training, offers promise for few-shot
learning, aiding in manufacturability tasks where data can be limited. This
work introduces VIRL, a Volume-Informed Representation Learning approach to
pre-train a 3D geometric encoder. The pretrained model is evaluated across four
manufacturability indicators obtained from CAM simulations: subtractive
machining (SM) time, additive manufacturing (AM) time, residual von Mises
stress, and blade collisions during Laser Power Bed Fusion process. Across all
case studies, the model pre-trained by VIRL shows substantial enhancements on
demonstrating improved generalizability with limited data and superior
performance with larger datasets. Regarding deployment strategy, case-specific
phenomenon exists where finetuning VIRL-pretrained models adversely affects AM
tasks with limited data but benefits SM time prediction. Moreover, the efficacy
of Low-rank adaptation (LoRA), which balances between probing and finetuning,
is explored. LoRA shows stable performance akin to probing with limited data,
while achieving a higher upper bound than probing as data size increases,
without the computational costs of finetuning. Furthermore, static
normalization of manufacturing indicators consistently performs well across
tasks, while dynamic normalization enhances performance when a reliable task
dependent input is available.


  Bulk heterojunction (BHJ) organic solar cells have made remarkable inroads
towards 20% efficiency, yet nonradiative recombination losses ({\Delta}Vnr)
remain high compared to silicon and perovskite photovoltaics. Interfaces buried
within BHJ blends hold the key to recombination losses but access to their
energetic landscape underpinning charge transfer (CT) states and their disorder
remain elusive. Here, we reveal the energetic landscape and CT state manifold
of modern BHJs with both spatial and energetic resolutions and link the offset
between singlet (ES1) and CT energy (ES1-CT) and interfacial energetic disorder
with {\Delta}Vnr. We do so by locally mapping the energy distributions of
modern PM6-based BHJs with IT4F, Y6 and PC71BM acceptors and combine it, for
the first time, with sensitive EQE measurements, to visualize and quantify
donor (D) and acceptor (A) energetics at interfaces and associated them with CT
states within a modified Marcus framework. A key new ability is the
identification of the specific BHJ interfaces associated with the CT manifold,
including where the lowest energy CT states reside. Moreover, we quantify
energy levels and electronic disorders directly at these and other interfaces
and connect these contributions to the energy losses. We delineate the
influences of S1-CT offset and interfacial energetic disorder on {\Delta}Vnr
across morphologically varied BHJs. Our results show both factors influencing
energy losses in different ways. We demonstrate that PM6:Y6 can achieve low
{\Delta}Vnr by forming a nominally sharp D/A interface with exceptionally low
interfacial disorder via judicious processing combined with a low S1 to CT
offset. This provides a design rule to minimize {\Delta}Vnr for modern NFAs:
sharp D/A interfaces with low S1 to CT offset exhibiting minimal interfacial
disorder.


  Continuing our inquiry into the conditions when fluctuation-dissipation
relations (FDR) may appear in the context of nonequilibrium dynamics of open
quantum systems (over and beyond the conventional FDR from linear response
theory) we turn to nonGaussian systems and consider this issue for an
anharmonic oscillator interacting with a scalar quantum field bath. We present
the general {nonperturbative} expressions for the rate of energy (power)
exchange between the anharmonic oscillator and the thermal bath. For the cases
that a stable final equilibrium state exists, and the nonstationary components
of the two-point functions of the anharmonic oscillator have negligible
contributions to the evaluation of the power balance, we can show
nonperturbatively that equilibration implies an FDR for the anharmonic
oscillator. We then use a weakly anharmonic oscillator as an example to
illustrate that those two assumptions indeed are satisfied according to our
first-order perturbative results: that the net energy exchange vanishes after
relaxation in the open system dynamics and an equilibrium state exists at late
times.


  The formation of metallic nanofilaments bridging two electrodes across an
insulator is a mechanism for resistive switching. Examples of such phenomena
include atomic synapses, which constitute a distinct class of memristive
devices whose behavior is closely tied to the properties of the filament. Until
recently, experimental investigation of the low-temperature regime and quantum
transport effects has been limited. However, with growing interest in
understanding the true impacts of the filament on device conductance,
comprehending quantum effects has become crucial for quantum neuromorphic
hardware. We discuss quantum transport resulting from filamentary switching in
a narrow region where the continuous approximation of the contact is not valid,
and only a few atoms are involved. In this scenario, the filament can be
represented by a graph depicting the adjacency of atoms and the overlap between
atomic orbitals. Using quantum graphs, we calculate the scattering amplitude of
charge carriers on this graph and explore the interplay between filamentary
formation and quantum transport effects.


  Four sets of global average temperature anomalies, altered so that they refer
to pre-industrial temperature levels (baseline), as recommended by the
Intergovernmental Panel on Climate Change, are analysed in this study.
Expectation values of the time, at which the crossing of the $1.5^\circ$C
threshold above the baseline will occur, are extracted from the two datasets
which are accompanied by meaningful uncertainties; the two estimates are in the
2030s and differ by about four years: mid-2032 and mid-2036.


  This paper offers a comprehensive overview of recent technological
advancements concerning the critical point of chiral phase transition, with a
particular focus on Effective Field. Theories in Quantum Chromodynamics (QCD).
It delves into the intricacies of these pivotal points, utilizing theoretical
tools to explore associated phenomena.


  We model the effects of a large number of zero and near-zero modes in the QCD
partition function by using sparse chiral matrix models with an emphasis on the
quenched topological susceptibility in the choice of the measure. At finite
temperature, the zero modes are not affected by temperature but are allowed to
pair into topologically neutral near-zero modes which are gapped at high
temperature. In equilibrium, chiral and U(1) symmetry are simultaneously
restored for total pairing, evading mean-field arguments. We analyze a number
of susceptibilities versus the light quark masses. At the transition point the
topological susceptibility vanishes, and the dependence on the vacuum angle
$\theta$ drops out. Our results are briefly contrasted with recent lattice
simulations.


  In a recent work [JNT \textbf{129}, 2154 (2009)], Gun and co-workers have
claimed that the number $\,\log{\Gamma(x)} + \log{\Gamma(1-x)}\,$, $x$ being a
rational number between $0$ and $1$, is transcendental with at most \emph{one}
possible exception, but the proof presented there in that work is
\emph{incorrect}. Here in this paper, I point out the mistake they committed
and I present a theorem that establishes the transcendence of those numbers
with at most \emph{two} possible exceptions. As a consequence, I make use of
the reflection property of this function to establish a criteria for the
transcendence of $\,\log{\pi}$, a number whose irrationality is not proved yet.
This has an interesting consequence for the transcendence of the product $\,\pi
\cdot e$, another number whose irrationality remains unproven.


  We introduce an entropy function for supersymmetric accelerating black holes
in $AdS_4$, that uplift on general Sasaki-Einstein manifolds $X_7$ to solutions
of M-theory. This allows one to compute the black hole entropy without knowing
the explicit solutions. A dual holographic microstate counting would follow
from computing certain supersymmetric partition functions of
Chern-Simons-matter theories compactified on a spindle. We make a general
prediction for a class of such partition functions in terms of ``blocks'', with
each block being constructed from the partition function on a three-sphere.


  We address a challenging tank blending and scheduling problem regarding
operations for a chemical plant. We model the problem as a nonconvex MIQCP,
then approximate this model as a MILP using a discretization-based approach. We
combine a rolling horizon approach with the discretization of individual
chemical property specifications to deal with long scheduling horizons,
time-varying quality specifications, and multiple suppliers with discrete
arrival times. This approach has been evaluated using industry-representative
data sets from the specialty chemical industry.
  We demonstrate that the proposed approach supports fast planning cycles.


  In this work we study the existence and the asymptotic behaviour of the
asymptotically almost periodic mild solutions of the vectorial parabolic
equations on the real hyperbolic manifold $\mathbb{H}^d(\mathbb{R})$ ($d
\geqslant 2$). We will consider the vectorial laplace operator in the sense of
Ebin-Marsden's laplace operator. Our method is based on certain dispertive and
smoothing estimates of the semigroup generated by the linearized vectorial heat
equation and the fixed point argument. First, we prove the existence and the
uniqueness of the asymptotically almost periodic mild solution for the
linearized equations. Next, using the fixed point argument, we can pass from
linearized equations to semilinear equations to prove the existence,
uniqueness, exponential decay and stability of the solutions. Our abstract
results will be applied to the incompressible Navier-Stokes equation and the
semilinear vectorial heat equation.


  We show that models for screening of nuclear reactions in the Sun can be
tested by means of helioseismology. As well known, solar models using the weak
screening factors are in agreement with data. We find that the solar model
calculated with the anti screening factors of Tsytovitch is not consistent with
helioseismology, both for the sound speed profile and for the depth of the
convective envelope. Moreover, the difference between the no-screening and weak
screening model is significant in comparison with helioseismic uncertainty. In
other words, the existence of screening can be proved by means of
helioseismology.


  This paper reports on some new inequalities of
Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution
between two orthogonal pure states. The clear determinant of the qualitative
behavior of this time scale is the statistics of the energy spectrum. An
often-overlooked correspondence between the real-time behavior of a quantum
system and the statistical mechanics of a transformed (imaginary-time)
thermodynamic system appears promising as a source of qualitative insights into
the quantum dynamics.


  Sterile neutrinos with various masses could be participated in astrophysical
and cosmological processes including mixing with active neutrinos, if exist. It
is considered the possible effects of mixing of active and sterile neutrinos
with masses of the order or less than 1 eV. For oscillation processes involving
electron and muon neutrinos, as well as for beta decay and neutrinoless double
beta decay processes, the contributions of light sterile neutrinos in the
characteristics of these processes are calculated. For this purpose the
estimates of the mixing parameters in the model with three active and three
sterile neutrinos are made taking into account experimental data. Two cases of
sterile neutrinos masses distribution are considered in detail. The results
obtained can be used for interpretation of available experimental data, and
also for predictions of subsequent experimental results.


  We consider the simplest identical-fermion system that exhibits the
phenomenon of entanglement (beyond exchange correlations) to analyze its speed
of evolution towards an orthogonal state, and revisit the relation between this
latter and the amount of fermionic entanglement. A characterization of the
quantum speed limit and the orthogonality times is performed, throwing light
into the general structure of the faster and the slower states. Such
characterization holds not only for fermionic composites, but apply more
generally to a wide family of 6-dimensional states, irrespective of the
specific nature of the system. Further, it is shown that the connection between
speed of evolution and entanglement in the fermionic system, though more subtle
than in composites of distinguishable parties, may indeed manifest for certain
classes of states.


  Electromagnetic effects play an important role in many phenomena such as
isospin-symmetry breaking in the hadron spectrum and the hadronic contributions
to g-2. We have generalized the MILC QCD code to include the electromagnetic
field. In this work, we focus on simulations including charged sea quarks using
the RHMC algorithm. We show details of the dynamical QCD+QED simulation
algorithm with compact QED. We analyze the code performance and results for
hadron-spectrum observables.


  We use the LEP/SLD data to place constraints on Topcolor Assisted Technicolor
Models. We find that due to a large negative shift in R_b induced by charged
top-pion exchange, it is difficult to make the models compatible with
experiment.


  The effect of focusing and defocusing nonlinearities on Anderson localization
in highly nonlocal media is theoretically and numerically investigated. A
perturbative approach is developed to solve the nonlocal nonlinear Schroedinger
equation in the presence of a random potential, showing that nonlocality
stabilizes Anderson states.


  Accurate workload forecasting is critical for efficient resource management
in cloud computing systems, enabling effective scheduling and autoscaling.
Despite recent advances with transformer-based forecasting models, challenges
remain due to the non-stationary, nonlinear characteristics of workload time
series and the long-term dependencies. In particular, inconsistent performance
between long-term history and near-term forecasts hinders long-range
predictions. This paper proposes a novel framework leveraging self-supervised
multiscale representation learning to capture both long-term and near-term
workload patterns. The long-term history is encoded through multiscale
representations while the near-term observations are modeled via temporal flow
fusion. These representations of different scales are fused using an attention
mechanism and characterized with normalizing flows to handle
non-Gaussian/non-linear distributions of time series. Extensive experiments on
9 benchmarks demonstrate superiority over existing methods.


  In this paper, firstly we study the continuity of the core-EP inverse without
explicit error bounds by virtue of two methods. One is the rank equality,
followed from the classical generalized inverse. The other one is matrix
decomposition. The continuity of the core inverse can be derived as a
particular case. Secondly, we study perturbation bounds for the core-EP inverse
under prescribed conditions. Perturbation bounds for the core inverse can be
derived as a particular case. Also, as corollaries, the sufficient (and
necessary) conditions for the continuity of the core-EP inverse are obtained.
Thirdly, a numerical example is illustrated to compare the derived upper
bounds. Finally, an application to semistable matrices is provided.


  We show exactly that the $\alpha$th power of Bures measure of entanglement
and geometric measure of entanglement, as special case of entanglement measures
based on fidelity, obey a class of general monogamy inequalities in an
arbitrary multiqubit mixed state for $\alpha\geq1$.


  The Hepp method is the coherent state approach to the mean field dynamics for
bosons or to the semiclassical propagation. A key point is the asymptotic
evolution of Wick observables under the evolution given by a time-dependent
quadratic Hamiltonian. This article provides a complete expansion with respect
to the small parameter \epsilon > 0 which makes sense within the
infinite-dimensional setting and fits with finite-dimensional formulae.


  We study heat transport in a Weyl semimetal with broken time-reversal
symmetry in the hydrodynamic regime. At the neutrality point, the longitudinal
heat conductivity is governed by the momentum relaxation (elastic) time, while
longitudinal electric conductivity is controlled by the inelastic scattering
time. In the hydrodynamic regime this leads to a large longitudinal Lorenz
ratio. As the chemical potential is tuned away from the neutrality point, the
longitudinal Lorenz ratio decreases because of suppression of the heat
conductivity by the Seebeck effect. The Seebeck effect (thermopower) and the
open circuit heat conductivity are intertwined with the electric conductivity.
The magnitude of Seebeck tensor is parametrically enhanced, compared to the
non-interacting model, in a wide parameter range. While the longitudinal
component of Seebeck response decreases with increasing electric anomalous Hall
conductivity $\sigma_{xy}$, the transverse component depends on $\sigma_{xy}$
in a non-monotonous way. Via its effect on the Seebeck response, large
$\sigma_{xy}$ enhances the longitudinal Lorenz ratio at a finite chemical
potential. At the neutrality point, the transverse heat conductivity is
determined by the Wiedemann-Franz law. Increasing the distance from the
neutrality point, the transverse heat conductivity is enhanced by the
transverse Seebeck effect and follows its non-monotonous dependence on
$\sigma_{xy}$.


  We consider dynamics of fluctuations in transonically accelerating
Bose-Einstein condensates and luminous liquids (coherent light propagating in a
Kerr nonlinear medium) using the hydrodynamic approach. It is known that
neglecting the quantum potential (QP) leads to a singular behavior of quantum
and classical fluctuations in the vicinity of the Mach (sonic) horizon, which
in turn gives rise to the Hawking radiation. The neglect of QP is well founded
at not too small distances $|x| \gg l_h$ from the horizon, where $l_h$ is the
healing length. Taking the QP into account we show that a second characteristic
length $l_r > l_h$ exists, such that the linear fluctuation modes become
regularized for $|x| \ll l_r$. At $|x| \gg l_r$ the modes keep their singular
behavior, which however is influenced by the QP. As a result we find a
deviation of the high frequency tail of the spectrum of Hawking radiation from
Planck's black body radiation distribution. Similar results hold for the wave
propagation in Kerr nonlinear media where the length $l_h$ and $l_r$ exist due
to the nonlinearity.


  The galactose network is a complex system responsible for galactose
metabolism. It has been extensively studied experimentally and mathematically
at the unicellular level to broaden our understanding of its regulatory
mechanisms at higher order species. Although the key molecular players involved
in the metabolic and regulatory processes underlying this system have been
known for decades, their interactions and chemical kinetics remain incompletely
understood. Mathematical models can provide an alternative method to study the
dynamics of this network from a quantitative and a qualitative perspective.
Here, we employ such approaches to unravel the main properties of the galactose
network, including equilibrium binary and temporal responses, as a way to
decipher its adaptation to actively-changing inputs. We combine the two main
components of the network; namely, the genetic branch which allows for bistable
responses, and a metabolic branch, encompassing the relevant metabolic
processes and glucose repressive reactions. We use both computational tools to
estimate model parameters based on published experimental data, as well as
bifurcation analysis to decipher the properties of the system in various
parameter regimes. Our model analysis reveals that the interplay between the
inducer (galactose) and the repressor (glucose) creates the bistability regime
which dictates the temporal responses of the system. Based on the same
bifurcation techniques, we can also explain why the system is robust to genetic
mutations and molecular instabilities. These findings may provide
experimentalists with a theoretical framework upon which they can determine how
the galactose network functions under various conditions.


  Quantum convolutional code was introduced recently as an alternative way to
protect vital quantum information. To complete the analysis of quantum
convolutional code, I report a way to decode certain quantum convolutional
codes based on the classical Viterbi decoding algorithm. This decoding
algorithm is optimal for a memoryless channel. I also report three simple
criteria to test if decoding errors in a quantum convolutional code will
terminate after a finite number of decoding steps whenever the Hilbert space
dimension of each quantum register is a prime power. Finally, I show that
certain quantum convolutional codes are in fact stabilizer codes. And hence,
these quantum stabilizer convolutional codes have fault-tolerant
implementations.


  The polarized images of a synchrotron emitting ring are studied in the
spacetime of a rotating black hole in the Scalar-Tensor-Vector-Gravity (STVG)
theory. The black hole owns an additional dimensionless MOG parameter described
its deviation from Kerr black hole. The effects of the MOG parameter on the
observed polarization vector and Strokes $Q-U$ loops depend heavily on the spin
parameter, the magnetic field configuration, the fluid velocity and the
observation inclination angle. For the fixed MOG parameter, the changes of the
polarization vector in the image plane are similar to those in the Kerr black
hole case. The comparison of the polarization images between Kerr-MOG black
hole and M87* implies that there remains some possibility for the STVG-MOG
theory.


  We numerically study a directed small-world network consisting of
attractively coupled, identical phase oscillators. While complete
synchronization is always stable, it is not always reachable from random
initial conditions. Depending on the shortcut density and on the asymmetry of
the phase coupling function, there exists a regime of persistent chaotic
dynamics. By increasing the density of shortcuts or decreasing the asymmetry of
the phase coupling function, we observe a discontinuous transition in the
ability of the system to synchronize. Using a control technique, we identify
the bifurcation scenario of the order parameter. We also discuss the relation
between dynamics and topology and remark on the similarity of the
synchronization transition to directed percolation.


  A fundamental question in learning to classify 3D shapes is how to treat the
data in a way that would allow us to construct efficient and accurate geometric
processing and analysis procedures. Here, we restrict ourselves to networks
that operate on point clouds. There were several attempts to treat point clouds
as non-structured data sets by which a neural network is trained to extract
discriminative properties. The idea of using 3D coordinates as class
identifiers motivated us to extend this line of thought to that of shape
classification by comparing attributes that could easily account for the shape
moments. Here, we propose to add polynomial functions of the coordinates
allowing the network to account for higher order moments of a given shape.
Experiments on two benchmarks show that the suggested network is able to
provide state of the art results and at the same token learn more efficiently
in terms of memory and computational complexity.


  In this work we show how the inclusion of dark matter (DM) direct detection
upper bounds in a theoretically consistent manner can affect the allowed
parameter space of a DM model. Traditionally, the limits from DM direct
detection experiments on the elastic scattering cross section of DM particles
as a function of their mass are extracted under simplifying assumptions.
Relaxing the assumptions related to the DM particle nature, such as the neutron
to proton ratio of the interactions, or the possibility of having similar
contributions from the spin independent (SI) and spin dependent (SD)
interactions can vary significantly the upper limits. Furthermore, it is known
that astrophysical and nuclear uncertainties can also affect the upper bounds.
To exemplify the impact of properly including all these factors, we have
analysed two well motivated and popular DM scenarios: neutralinos in the NMSSM
and a Z' portal with Dirac DM. We have found that the allowed parameter space
of these models is subject to important variations when one includes both the
SI and SD interactions at the same time, realistic neutron to proton ratios, as
well as using different self-consistent speed distributions corresponding to
popular DM halo density profiles, and distinct SD structure functions. Finally,
we provide all the necessary information to include the upper bounds of
SuperCDMS and LUX taking into account all these subtleties in the investigation
of any particle physics model. The data for each experiment and example codes
are available at this site http://goo.gl/1CDFYi, and their use is detailed in
the appendices of this work.


  We accept the implicit challenge of A. Uhlmann in his 1994 paper, "Parallel
Lifts and Holonomy along Density Operators: Computable Examples Using
O(3)-Orbits," by, in fact, computing the holonomy invariants for rotations of
certain n-level Gibbsian density matrices (n = 2,...,11). From these, we
derive, by the tracing operation, the associated geometric phases and
visibilities, which we analyze and display. We then proceed analogously,
implementing the alternative methodology presented by E. Sjoqvist et al in
their letter, "Geometric Phases for Mixed States in Interferometry" (Phys. Rev.
Lett. 85, 2845 [2000]). For the Uhlmann case, we are able to also compute
several higher-order invariants. We compare the various geometric phases and
visibilities for different values of n, and also directly compare the two forms
of analysis. By setting one parameter (a) in the Uhlmann analysis to zero, we
find that the so-reduced form of the first-order holonomy invariant is simply
equal to (-1)^{n+1} times the holonomy invariant in the Sj\"oqvist et al
method. Additional phenomena of interest are reported too.


  We represent a general procedure for calculating the partition function of an
Ising model on a one dimensional Fibonacci lattice in presence of magnetic
field.This partition function can be written as a sum of partition functions of
usual open Ising chains in presence of magnetic field with coefficients having
Fibonacci symmetries.An exact expression for the partition function of the
usual open Ising model is found.We observe that "Mirror Symmetry" is a
characteristic property of all Fibonacci generations.Further nth and (n+6)th
generations have the same topology.We have also established a recurrence
relation among partition functions of different Fibonacci generations from nth
to (n+6)th.


  LiSrAlF$_6$ crystals doped with $^{229}$Th are used in a laser-based search
for the nuclear isomeric transition. Two spectroscopic features near the
nuclear transition energy are observed. The first is a broad excitation feature
that produces red-shifted fluorescence that decays with a timescale of a few
seconds. The second is a narrow, laser-linewidth-limited spectral feature at
$148.38219(4)_{\textrm{stat}}(20)_{\textrm{sys}}$ nm
($2020407.3(5)_{\textrm{stat}}(30)_{\textrm{sys}}$ GHz) that decays with a
lifetime of $568(13)_{\textrm{stat}}(20)_{\textrm{sys}}$ s. This feature is
assigned to the excitation of the $^{229}$Th nuclear isomeric state, whose
energy is found to be $8.355733(2)_{\textrm{stat}}(10)_{\textrm{sys}}$ eV in
$^{229}$Th:\thor:LiSrAlF$_6$.


  It is well known that a continuous piecewise monotone interval map with
positive topological entropy is semiconjugate to a map of a constant slope and
the same entropy, and if it is additionally transitive then this semiconjugacy
is actually a conjugacy. We generalize this result to piecewise continuous
piecewise monotone interval maps, and as a consequence, get it also for
piecewise monotone graph maps. We show that assigning to a continuous
transitive piecewise monotone map of positive entropy a map of constant slope
conjugate to it defines an operator, and show that this operator is not
continuous.


  Cellular ingredient concentrations can be stabilized by adjusting generation
and consumption rates through multiple pathways. To explore the portion of
cellular metabolism equipped with multiple pathways, we categorize individual
metabolic reactions and compounds as viable or inviable: A compound is viable
if processed by two or more reactions, and a reaction is viable if all of its
substrates and products are viable. Using this classification, we identify the
maximal subnetwork of viable nodes, referred to as the {\it viable core}, in
bipartite metabolic networks across thousands of species. The obtained viable
cores are remarkably larger than those in degree-preserving randomized
networks, while their broad degree distributions commonly enable the viable
cores to shrink gradually as reaction nodes are deleted. We demonstrate that
the positive degree-degree correlations of the empirical networks may underlie
the enlarged viable cores compared to the randomized networks. By investigating
the relation between degree and cross-species frequency of metabolic compounds
and reactions, we elucidate the evolutionary origin of the correlations.


  Time series forecasting plays an increasingly important role in modern
business decisions. In today's data-rich environment, people often aim to
choose the optimal forecasting model for their data. However, identifying the
optimal model requires professional knowledge and experience, making accurate
forecasting a challenging task. To mitigate the importance of model selection,
we propose a simple and reliable algorithm to improve the forecasting
performance. Specifically, we construct multiple time series with different
sub-seasons from the original time series. These derived series highlight
different sub-seasonal patterns of the original series, making it possible for
the forecasting methods to capture diverse patterns and components of the data.
Subsequently, we produce forecasts for these multiple series separately with
classical statistical models (ETS or ARIMA). Finally, the forecasts are
combined. We evaluate our approach on widely-used forecasting competition data
sets (M1, M3, and M4) in terms of both point forecasts and prediction
intervals. We observe performance improvements compared with the benchmarks.
Our approach is particularly suitable and robust for the data with higher
frequency. To demonstrate the practical value of our proposition, we showcase
the performance improvements from our approach on hourly load data that exhibit
multiple seasonal patterns.


  A finite set $X$ in the $d$-dimensional Euclidean space is called an
$s$-distance set if the set of distances between any two distinct points of $X$
has size $s$. In 1977, Larman-Rogers-Seidel proved that if the cardinality of
an two-distance set is large enough, then there exists an integer $k$ such that
the two distances $\alpha$, $\beta$ $(\alpha < \beta)$ having the integer
condition, namely, $\frac{\alpha^2}{\beta^2}=\frac{k-1}{k}$. In 2011, Nozaki
generalized Larman-Rogers-Seidel's theorem to the case of $s$-distance sets,
i.e. if the cardinality of an $s$-distance set $|X|\geqslant 2N$ with distances
$\alpha_1,\alpha_2,\cdots,\alpha_s$, where
$N=\binom{d+s-1}{s-1}+\binom{d+s-2}{s-2}$, then the numbers
$k_i=\prod_{j=1,2,\cdots,s,\text{ }j\neq
i}\frac{\alpha_{j}^{2}}{\alpha_{j}^{2}-\alpha_{i}^{2}}$ are integers. In this
note, we reduce the lower bound of the requirement of integer condition of
$s$-distance sets in $\mathbb{R}^d$. Furthermore, we can show that there are
only finitely many $s$-distance sets $X$ in $\mathbb{R}^d$ with $|X|\geqslant
2\binom{d+s-1}{s-1}.$


  Quantum key distribution, initialized in 1984, is a commercialized secure
communication method which enables two parties to produce shared random secret
key by the nature of quantum mechanics. We propose QQUIC (Quantum assisted
Quick UDP Internet Connections) transport protocol, which modifies the famous
QUIC transport protocol by employing the quantum key distribution instead of
the original classical algorithms in the key exchanging stage. Thanks to the
provable security of quantum key distribution, the security of QQUIC key does
not depend on computational assumptions. Maybe surprisingly, QQUIC can reduce
the network latency in some circumstance even comparing with QUIC. To achieve
this, the attached quantum connections are used as the dedicated lines for key
generation.


  Under certain integrability and geometric conditions, we prove division
theorems for the exact sequences of holomorphic vector bundles and improve the
results in the case of Koszul complex. By introducing a singular Hermitian
structure on the trivial bundle, our results recover Skoda's division theorem
for holomorphic functions on pseudoconvex domains in complex Euclidean spaces.


  Weak gravitational lensing is a powerful tool for precision tests of
cosmology. As the expected deflection angles are small, predictions based on
non-linear N-body simulations are commonly computed with the Born
approximation. Here we examine this assumption using ${\small DORIAN}$, a newly
developed full-sky ray-tracing scheme applied to high-resolution mass-shell
outputs of the two largest simulations in the MillenniumTNG suite, each with a
3000 Mpc box containing almost 1.1 trillion cold dark matter particles in
addition to 16.7 billion particles representing massive neutrinos. We examine
simple two-point statistics like the angular power spectrum of the convergence
field, as well as statistics sensitive to higher order correlations such as
peak and minimum statistics, void statistics, and Minkowski functionals of the
convergence maps. Overall, we find only small differences between the Born
approximation and a full ray-tracing treatment. While these are negligibly
small at power-spectrum level, some higher order statistics show more sizable
effects; ray-tracing is necessary to achieve percent level precision. At the
resolution reached here, full-sky maps with 0.8 billion pixels and an angular
resolution of 0.43 arcmin, we find that interpolation accuracy can introduce
appreciable errors in ray-tracing results. We therefore implemented an
interpolation method based on nonuniform fast Fourier transforms (NUFFT) along
with more traditional methods. Bilinear interpolation introduces significant
smoothing, while nearest grid point sampling agrees well with NUFFT, at least
for our fiducial source redshift, $z_s=1.0$, and for the 1 arcmin smoothing we
use for higher-order statistics.


  Attention mechanisms have attracted considerable interest in image captioning
because of its powerful performance. Existing attention-based models use
feedback information from the caption generator as guidance to determine which
of the image features should be attended to. A common defect of these attention
generation methods is that they lack a higher-level guiding information from
the image itself, which sets a limit on selecting the most informative image
features. Therefore, in this paper, we propose a novel attention mechanism,
called topic-guided attention, which integrates image topics in the attention
model as a guiding information to help select the most important image
features. Moreover, we extract image features and image topics with separate
networks, which can be fine-tuned jointly in an end-to-end manner during
training. The experimental results on the benchmark Microsoft COCO dataset show
that our method yields state-of-art performance on various quantitative
metrics.


  We demonstrate how to map out the phase diagram of a two dimensional quantum
many body system with no prior physical knowledge by applying deep
\textit{anomaly detection} to ground states from infinite projected entangled
pair state simulations. As a benchmark, the phase diagram of the 2D frustrated
bilayer Heisenberg model is analyzed, which exhibits a second-order and two
first-order quantum phase transitions. We show that in order to get a good
qualitative picture of the transition lines, it suffices to use data from the
cost-efficient simple update optimization. Results are further improved by
post-selecting ground-states based on their energy at the cost of contracting
the tensor network once. Moreover, we show that the mantra of ``more training
data leads to better results'' is not true for the learning task at hand and
that, in principle, one training example suffices for this learning task. This
puts the necessity of neural network optimizations for these learning tasks in
question and we show that, at least for the model and data at hand, a simple
geometric analysis suffices.


  We compute the integrated doublon production rate in response to a lattice
modulation for two component fermions in an optical lattice. We derive a
general formula for the integrated intensity, valid in the presence of
inhomogeneous potentials such as the trap, which gives the integrated intensity
in terms of equal time correlation functions only. Such a formula is thus well
suited for direct numerical calculations. We show that, in the limit of large
repulsion for commensurate fillings, or for temperature ranges for which the
hopping is incoherent, the integrated doublon spectrum is directly related to
the nearest neighbor spin-spin correlation function. We compute its temperature
dependence in this regime using finite temperature quantum Monte Carlo
calculation.


  We consider the problem of localizing and segmenting individual teeth inside
3D Cone-Beam Computed Tomography (CBCT) images. To handle large image sizes we
approach this task with a coarse-to-fine framework, where the whole volume is
first analyzed as a 33-class semantic segmentation (adults have up to 32 teeth)
in coarse resolution, followed by binary semantic segmentation of the cropped
region of interest in original resolution. To improve the performance of the
challenging 33-class segmentation, we first train the Coarse step model on a
large weakly labeled dataset, then fine-tune it on a smaller precisely labeled
dataset. The Fine step model is trained with precise labels only. Experiments
using our in-house dataset show significant improvement for both
weakly-supervised pretraining and for the addition of the Fine step.
Empirically, this framework yields precise teeth masks with low localization
errors sufficient for many real-world applications.


  We study medium access control layer random access under the assumption that
the receiver can perform successive interference cancellation, without
feedback. During recent years, a number of protocols with impressive error
performance have been suggested for this channel model. However, the random
nature of these protocols causes an error floor which limits their usability
when targeting ultra-reliable communications. In very recent works by Paolini
et al. and Boyd et. al., it was shown that if each user employs predetermined
combinatorial access patterns, this error floor disappears. In this paper, we
develop code design criteria for deterministic random access protocols in the
ultra-reliability region, and build codes based on these principles. The
suggested design methods are supported by simulations.