  We investigate a pilot allocation problem in wireless networks over Markovian
fading channels. In wireless systems, the Channel State Information (CSI) is
collected at the Base Station (BS), in particular, this paper considers a
pilot-aided channel estimation method (TDD mode). Typically, there are less
available pilots than users, hence at each slot the scheduler needs to decide
an allocation of pilots to users with the goal of maximizing the long-term
average throughput. There is an inherent tradeoff in how the limited pilots are
used: assign a pilot to a user with up-to-date CSI and good channel condition
for exploitation, or assign a pilot to a user with outdated CSI for
exploration. As we show, the arising pilot allocation problem is a restless
bandit problem and thus its optimal solution is out of reach. In this paper, we
propose an approximation that, through the Lagrangian relaxation approach,
provides a low-complexity heuristic, the Whittle index policy. We prove this
policy to be asymptotically optimal in the many users regime (when the number
of users in the system and the available pilots for channel sensing grow
large). We evaluate the performance of Whittle's index policy in various
scenarios and illustrate its remarkably good performance.


  A class of models describing the flow of information within networks via
routing processes is proposed and investigated, concentrating on the effects of
memory traces on the global properties. The long-term flow of information is
governed by cyclic attractors, allowing to define a measure for the information
centrality of a vertex given by the number of attractors passing through this
vertex. We find the number of vertices having a non-zero information centrality
to be extensive/sub-extensive for models with/without a memory trace in the
thermodynamic limit. We evaluate the distribution of the number of cycles, of
the cycle length and of the maximal basins of attraction, finding a complete
scaling collapse in the thermodynamic limit for the latter. Possible
implications of our results on the information flow in social networks are
discussed.


  We provide a systematic study of the problem of finding the source of a rumor
in a network. We model rumor spreading in a network with a variant of the
popular SIR model and then construct an estimator for the rumor source. This
estimator is based upon a novel topological quantity which we term
\textbf{rumor centrality}. We establish that this is an ML estimator for a
class of graphs. We find the following surprising threshold phenomenon: on
trees which grow faster than a line, the estimator always has non-trivial
detection probability, whereas on trees that grow like a line, the detection
probability will go to 0 as the network grows. Simulations performed on
synthetic networks such as the popular small-world and scale-free networks, and
on real networks such as an internet AS network and the U.S. electric power
grid network, show that the estimator either finds the source exactly or within
a few hops of the true source across different network topologies. We compare
rumor centrality to another common network centrality notion known as distance
centrality. We prove that on trees, the rumor center and distance center are
equivalent, but on general networks, they may differ. Indeed, simulations show
that rumor centrality outperforms distance centrality in finding rumor sources
in networks which are not tree-like.


  We present a discussion of the linear thermoelectric response of an
interacting electron gas in a quantizing magnetic field. Boundary currents can
carry a significant fraction of the net current passing through the system. We
derive general expressions for the bulk and boundary components of the number
and energy currents. We show that the local current density may be described in
terms of ``transport'' and ``internal magnetization'' contributions. The latter
carry no net current and are not observable in standard transport experiments.
We show that although Onsager relations cannot be applied to the local current,
they are valid for the transport currents and hence for the currents observed
in standard transport experiments. We relate three of the four thermoelectric
response coefficients of a disorder-free interacting two-dimensional electron
gas to equilibrium thermodynamic quantities. In particular, we show that the
diffusion thermopower is proportional to the entropy per particle, and we
compare this result with recent experimental observations.


  The relation between galaxy stellar mass and gas-phase metallicity is a
sensitive diagnostic of the main processes that drive galaxy evolution, namely
cosmological gas inflow, metal production in stars, and gas outflow via
galactic winds. We employed the direct method to measure the metallicities of
~200,000 star-forming galaxies from the SDSS that were stacked in bins of (1)
stellar mass and (2) both stellar mass and star formation rate (SFR) to
significantly enhance the signal-to-noise ratio of the weak [O III] 4363 and [O
II] 7320, 7330 auroral lines required to apply the direct method. These
metallicity measurements span three decades in stellar mass from
log(Mstar/Msun) = 7.4-10.5, which allows the direct method mass-metallicity
relation to simultaneously capture the high-mass turnover and extend a full
decade lower in mass than previous studies that employed more uncertain strong
line methods. The direct method mass-metallicity relation rises steeply at low
mass (O/H ~ Mstar^{1/2}) until it turns over at log(Mstar/Msun) = 8.9 and
asymptotes to 12 + log(O/H) = 8.8 at high mass. The direct method
mass-metallicity relation has a steeper slope, a lower turnover mass, and a
factor of two to three greater dependence on SFR than strong line
mass-metallicity relations. Furthermore, the SFR-dependence appears monotonic
with stellar mass, unlike strong line mass-metallicity relations. We also
measure the N/O abundance ratio, an important tracer of star formation history,
and find the clear signature of primary and secondary nitrogen enrichment. N/O
correlates tightly with oxygen abundance, and even more so with stellar mass.


  Addressing the feasibilty of quantum communication with electrons we consider
entangled spin states of electrons in a double-dot which is weakly coupled to
in--and outgoing leads. We show that the entanglement of two electrons in the
double-dot can be detected in mesoscopic transport and noise measurements. In
the Coulomb blockade and cotunneling regime the singlet and triplet states lead
to phase-coherent current and noise contributions of opposite signs and to
Aharonov-Bohm and Berry phase oscillations in response to magnetic fields.
These oscillations are a genuine two-particle effect and provide a direct
measure of non-locality in entangled states. We show that the ratio of
zero-frequency noise to current (Fano factor) is universal and equal to the
electron charge.


  In this article we present a numerical method for the Stokes flow of an
Oldroyd-B fluid. The viscoelastic stress evolves according to a constitutive
law formulated in terms of the upper convected time derivative. A finite
difference method is used to discretise along fluid trajectories to approximate
the advection and deformation terms of the upper convected derivative in a
simple, cheap and cohesive manner, as well as ensuring that the discrete
conformation tensor is positive definite. A full implementation with coupling
to the fluid flow is presented, along with detailed discussion of the issues
that arise with such schemes. We demonstrate the performance of this method
with detailed numerical experiments in a lid-driven cavity setup. Numerical
results are benchmarked against published data, and the method is shown to
perform well in this challenging case.


  We present a three-dimensional cubic lattice spin model, anisotropic in the
$\hat{z}$ direction, that exhibits fracton topological order. The latter is a
novel type of topological order characterized by the presence of immobile
pointlike excitations, named fractons, residing at the corners of an operator
with two-dimensional support. As other recent fracton models, ours exhibits a
subextensive ground state degeneracy: On an $L_x\times L_y\times L_z$
three-torus, it has a $2^{2L_z}$ topological degeneracy, and an additional
non-topological degeneracy equal to $2^{L_xL_y-2}$. The fractons can be
combined into composite excitations that move either in a straight line along
the $\hat{z}$ direction, or freely in the $xy$ plane at a given height $z$.
While our model draws inspiration from the toric code, we demonstrate that it
cannot be adiabatically connected to a layered toric code construction.
Additionally, we investigate the effects of imposing open boundary conditions
on our system. We find zero energy modes on the surfaces perpendicular to
either the $\hat{x}$ or $\hat{y}$ directions, and their absence on the surfaces
normal to $\hat{z}$. This result can be explained using the properties of the
two kinds of composite two-fracton mobile excitations.


  Deep learning has shown high performances in various types of tasks from
visual recognition to natural language processing, which indicates superior
flexibility and adaptivity of deep learning. To understand this phenomenon
theoretically, we develop a new approximation and estimation error analysis of
deep learning with the ReLU activation for functions in a Besov space and its
variant with mixed smoothness. The Besov space is a considerably general
function space including the Holder space and Sobolev space, and especially can
capture spatial inhomogeneity of smoothness. Through the analysis in the Besov
space, it is shown that deep learning can achieve the minimax optimal rate and
outperform any non-adaptive (linear) estimator such as kernel ridge regression,
which shows that deep learning has higher adaptivity to the spatial
inhomogeneity of the target function than other estimators such as linear ones.
In addition to this, it is shown that deep learning can avoid the curse of
dimensionality if the target function is in a mixed smooth Besov space. We also
show that the dependency of the convergence rate on the dimensionality is tight
due to its minimax optimality. These results support high adaptivity of deep
learning and its superior ability as a feature extractor.


  We consider the problem of computing reachable sets directly from noisy data
without a given system model. Several reachability algorithms are presented for
different types of systems generating the data. First, an algorithm for
computing over-approximated reachable sets based on matrix zonotopes is
proposed for linear systems. Constrained matrix zonotopes are introduced to
provide less conservative reachable sets at the cost of increased computational
expenses and utilized to incorporate prior knowledge about the unknown system
model. Then we extend the approach to polynomial systems and, under the
assumption of Lipschitz continuity, to nonlinear systems. Theoretical
guarantees are given for these algorithms in that they give a proper
over-approximate reachable set containing the true reachable set. Multiple
numerical examples and real experiments show the applicability of the
introduced algorithms, and comparisons are made between algorithms.


  We construct a two-current model. It includes two gauge fields, which
introduce the doping effect, and a neutral scalar field. And then we
numerically construct an AdS black brane geometry with scalar hair. Over this
background, we study the fermionic system with the pseudoscalar Yukawa
coupling. Some universal properties from the pseudoscalar Yukawa coupling are
revealed. In particular, as the coupling increases, there is a transfer of the
spectral weight from the low energy band to the high energy band. The transfer
is over low energy scales but not over all energy scales. The peculiar
properties are also explored. The study shows that with the increase of the
doping, the gap opens more difficult. It indicates that there is a competition
between the pseudoscalar Yukawa coupling and the doping.


  The main result of this note, Theorem 2, is the following: a Borel measure on
the space of infinite Hermitian matrices, that is invariant under the action of
the infinite unitary group and that admits well-defined projections onto the
quotient space of "corners" of finite size, must be finite. A similar result,
Theorem 1, is also established for unitarily invariant measures on the space of
all infinite complex matrices. These results, combined with the ergodic
decomposition theorem of [3], imply that the infinite Hua-Pickrell measures of
Borodin and Olshanski [2] have finite ergodic components.
  The proof is based on the approach of Olshanski and Vershik [6]. First, it is
shown that if the sequence of orbital measures assigned to almost every point
is weakly precompact, then our ergodic measure must indeed be finite. The
second step, which completes the proof, shows that if a unitarily-invariant
measure admits well-defined projections onto the quotient space of finite
corners, then for almost every point the corresponing sequence of orbital
measures is indeed weakly precompact.


  Motivated in part by the modular properties of enumerative invariants of
K3-fibered Calabi-Yau threefolds, we introduce a family of 39 Calabi-Yau mirror
pairs $(X,Y)$ with $h_{1,1}(X)=h_{2,1}(Y)=2$, labelled by certain integer
quadruples $(m,i,j,s)$ with $m\leq 11$. On the A-model side, $X$ arises as a
complete intersection in a projective bundle over a Fano fourfold
$V_m^{[i,j]}$, and admits a Tyurin degeneration into a pair of degree $m$ Fano
threefolds $F_m^{[i]}\cup F_m^{[j]}$ intersecting on an anticanonical K3
divisor of degree $2m$. On the B-model side, $Y$ is fibered by
$M_{m}$-polarized K3-surfaces of Picard rank 19, and determined by a branched
covering of $\mathbb{P}^1$, consistent with the Doran-Harder-Thompson mirror
conjecture. When $s=0$, $Y$ itself acquires a Tyurin degeneration, and
correspondingly $X$ acquires a fibration by degree $2m$ K3 surfaces, such that
the two K\"ahler moduli control the size of the K3-fiber and base
$\mathbb{P}^1$. While the mirror pairs with $m\leq 4$ can be realized as
complete intersections in products of projective spaces or as hypersurfaces in
toric varieties, the examples with $m\geq 5$ are intrinsically non-toric. We
obtain uniform formulae for the genus 0 and 1 topological free energies near
the Tyurin degeneration (mirror to the large base limit), exhibiting modular
properties under the Fricke-extended congruence group $\Gamma_0(m)^+$. We use
these results to compute the vertical Gopakumar-Vafa and Noether-Lefschetz
invariants and check that their generating functions satisfy the expected
modular properties. We also compute generating series of Gopakumar-Vafa
invariants with fixed non-zero base degree and exhibit their modular
properties.


  Coherent electron spin dynamics in 10-nm-wide InGaAs/InAlAs quantum wells is
studied from 10 K to room temperature using time-resolved Kerr rotation. The
spin lifetime exceeds 1 ns at 10 K and decreases with temperature. By varying
the spatial overlap between pump and probe pulses, a diffusive velocity is
imprinted on the measured electron spins and a spin precession in the
spin-orbit field is measured. A Rashba symmetry of the SOI is determined. By
comparing the spatial precession frequency gradient with the spin decay rate,
an upper limit for the Rashba coefficients $\alpha$ of 2$\times$10$^{-12}$ eVm
is estimated.


  This is a preface introducing a Special Issue on the topic of "Guided-Wave
Optics" published by Applied Sciences. The Special Issue is a collection of 20
original and review articles dealing with various fundamental and applied
aspects of the topic.


  We study the class of one-dimensional equations driven by a stochastic
measure $\mu$. For $\mu$ we assume only $\sigma$-additivity in probability.
This class of equations include the Burgers equation and the heat equation. The
existence and uniqueness of the solution are proved, and the averaging
principle for the equation is studied.


  Medical image segmentation has seen significant improvements with transformer
models, which excel in grasping far-reaching contexts and global contextual
information. However, the increasing computational demands of these models,
proportional to the squared token count, limit their depth and resolution
capabilities. Most current methods process D volumetric image data
slice-by-slice (called pseudo 3D), missing crucial inter-slice information and
thus reducing the model's overall performance. To address these challenges, we
introduce the concept of \textbf{Deformable Large Kernel Attention (D-LKA
Attention)}, a streamlined attention mechanism employing large convolution
kernels to fully appreciate volumetric context. This mechanism operates within
a receptive field akin to self-attention while sidestepping the computational
overhead. Additionally, our proposed attention mechanism benefits from
deformable convolutions to flexibly warp the sampling grid, enabling the model
to adapt appropriately to diverse data patterns. We designed both 2D and 3D
adaptations of the D-LKA Attention, with the latter excelling in cross-depth
data understanding. Together, these components shape our novel hierarchical
Vision Transformer architecture, the \textit{D-LKA Net}. Evaluations of our
model against leading methods on popular medical segmentation datasets
(Synapse, NIH Pancreas, and Skin lesion) demonstrate its superior performance.
Our code implementation is publicly available at the:
https://github.com/mindflow-institue/deformableLKA


  We consider fair allocation of a set $M$ of indivisible goods to $n$
equally-entitled agents, with no monetary transfers. Every agent $i$ has a
valuation $v_i$ from some given class of valuation functions. A share $s$ is a
function that maps a pair $(v_i,n)$ to a value, with the interpretation that if
an allocation of $M$ to $n$ agents fails to give agent $i$ a bundle of value at
least equal to $s(v_i,n)$, this serves as evidence that the allocation is not
fair towards $i$. For such an interpretation to make sense, we would like the
share to be feasible, meaning that for any valuations in the class, there is an
allocation that gives every agent at least her share. The maximin share was a
natural candidate for a feasible share for additive valuations. However,
Kurokawa, Procaccia and Wang [2018] show that it is not feasible.
  We initiate a systematic study of the family of feasible shares. We say that
a share is \emph{self maximizing} if truth-telling maximizes the implied
guarantee. We show that every feasible share is dominated by some
self-maximizing and feasible share. We seek to identify those self-maximizing
feasible shares that are polynomial time computable, and offer the highest
share values. We show that a SM-dominating feasible share -- one that dominates
every self-maximizing (SM) feasible share -- does not exist for additive
valuations (and beyond). Consequently, we relax the domination property to that
of domination up to a multiplicative factor of $\rho$ (called
$\rho$-dominating). For additive valuations we present shares that are
feasible, self-maximizing and polynomial-time computable. For $n$ agents we
present such a share that is $\frac{2n}{3n-1}$-dominating. For two agents we
present such a share that is $(1 - \epsilon)$-dominating. Moreover, for these
shares we present poly-time algorithms that compute allocations that give every
agent at least her share.


  We propose an atomistic model for correlated particle dynamics in liquids and
glasses predicting both slow stretched-exponential relaxation (SER) and fast
compressed-exponential relaxation (CER). The model is based on the key concept
of elastically interacting local relaxation events. SER is related to slowing
down of dynamics of local relaxation events as a result of this interaction,
whereas CER is related to the avalanche-like dynamics in the low-temperature
glass state. The model predicts temperature dependence of SER and CER seen
experimentally and recovers the simple, Debye, exponential decay at high
temperature. Finally, we reproduce SER to CER crossover across the glass
transition recently observed in metallic glasses.


  We show that the Schur polynomials in all primitive $n$th roots of unity are
$1$, $0$, or $-1$, if $n$ has at most two distinct odd prime factors. This
result can be regarded as a generalization of properties of the coefficients of
the cyclotomic polynomial and its multiplicative inverse. The key to the proof
is the notion of a unimodular system of vectors. Namely, this result is reduced
in turn to four propositions on the unimodularity of vector systems, and the
last proposition is proved by using graph theory.


  In this paper, we present the current progress of the project Verif.ai, an
open-source scientific generative question-answering system with referenced and
verified answers. The components of the system are (1) an information retrieval
system combining semantic and lexical search techniques over scientific papers
(PubMed), (2) a fine-tuned generative model (Mistral 7B) taking top answers and
generating answers with references to the papers from which the claim was
derived, and (3) a verification engine that cross-checks the generated claim
and the abstract or paper from which the claim was derived, verifying whether
there may have been any hallucinations in generating the claim. We are
reinforcing the generative model by providing the abstract in context, but in
addition, an independent set of methods and models are verifying the answer and
checking for hallucinations. Therefore, we believe that by using our method, we
can make scientists more productive, while building trust in the use of
generative language models in scientific environments, where hallucinations and
misinformation cannot be tolerated.


  The problematic divergence of the $q$-partition function of the harmonic
oscillator recently considered in \cite{plastino} is a particular case of the
non-normalizabilty of the distribution function of classical Hamiltonian
systems in non-extensive thermostatistics as discussed previously in
\cite{lutsko-boon}.


  The recent proposal of theories with compactified large extra dimensions is
reviewed. We pay especial attention to brane world models with low tension
where the only relevant degrees of freedom at low energies are the Standard
Model (SM) particles and the branons, which are transversal brane oscillations.
By using an effective Lagrangian, we study some phenomenological consequences
of these scenarios in a model independent way.


  We present an approach for reconstructing networks of pulse-coupled
neuron-like oscillators from passive observation of pulse trains of all nodes.
It is assumed that units are described by their phase response curves and that
their phases are instantaneously reset by incoming pulses. Using an iterative
procedure, we recover the properties of all nodes, namely their phase response
curves and natural frequencies, as well as strengths of all directed
connections.


  Robustness of the solutions to the inflaton potential inverse problem based
on the slow-roll approximation is addressed. With that aim it is introduced a
measure of the difference of the outputs obtained using first and second order
respectively in the horizon-flow expansion. The evolution of this measure is
determined by a second order linear non-autonomous non-homogeneous differential
equation. Boundedness of the general solutions to this equation is analyzed. It
is shown that they diverge for most of the physically meaningful cases.
Examples for typical inflationary models are presented. It is argued that this
lack of robustness is due to the limitations of the slow-roll expansion for
probing the scale-dependence of the inflationary spectra.


  A comprehensive understanding of Gamma Ray Bursts (GRBs) has been elusive due
to the variety of questions surrounding the radiation mechanism at play in
these events. Polarization measurements of GRBs can heavily constrain the
relevant radiation mechanisms and the structure of the GRB jet; however, there
is a limited number of theoretical predictions that observed GRB polarizations
can be compared against. Here, we conduct radiative transfer calculations of a
set of two dimensional relativistic hydrodynamic long GRB (LGRB) jet
simulations, of a constant and a variable jet, using the Monte Carlo Radiation
Transport (MCRaT) code. MCRaT has been enhanced by the inclusion of
polarization; it has been first verified by reproducing a variety of results in
the literature and then used to obtain the time integrated and resolved
polarization degrees and angles of the synthetic LGRBs. While the obtained
time-integrated polarization degrees {($\lesssim 1$\%)} are consistent with the
constraints from the POLAR experiment, they are lower than other theoretical
studies due to the lack of strong gradients in the model jet profiles that we
use. The time resolved results suggests that GRBs with wide jets observed on
axis will have small polarization degrees ($\lesssim 2\%$) and {constant
polarization angles}, during the brightest portion of the light curve. GRBs
observed off axis will have larger polarization degrees and polarization angles
that change with the temporal structure of radiating shells in the outflow. We
then place our results in the context of GRB prompt emission models and future
LEAP and POLAR-2 GRB polarimetry detections.


  [abridged] Three years of optical monitoring of the low-mass X-ray binary
(LMXB) 4U 1957+11 is presented. The source was observed in V, R and i-bands
using the Faulkes Telescopes North and South. The light curve is dominated by
long-term variations which are correlated (at the > 3 sigma level) with the
RXTE ASM soft X-ray flux. The variations span one magnitude in all three
filters. We find no evidence for periodicities in our light curves, contrary to
a previous short-timescale optical study in which the flux varied on a 9.3-hour
sinusoidal period by a smaller amplitude. The optical spectral energy
distribution is blue and typical of LMXBs in outburst, as is the power law
index of the correlation beta = 0.5, where F_{nu,OPT} propto F_X^beta. The
discrete cross-correlation function reveals a peak at an X-ray lag of 2 - 14
days, which could be the viscous timescale. However, adopting the least squares
method the strongest correlation is at a lag of 0 +/- 4 days, consistent with
X-ray reprocessing on the surface of the disc. We therefore constrain the
optical lag behind X-ray to be between -14 and +4 days. In addition, we use the
optical - X-ray luminosity diagram for LMXBs as a diagnostic tool to constrain
the nature of the compact object in 4U 1957+11, since black hole (BH) and
neutron star (NS) sources reside in different regions of this diagram. If the
system contains a BH (as is the currently favoured hypothesis), its distance
must exceed ~ 20 kpc for the optical and X-ray luminosities to be consistent
with other soft state BH systems. For distances < 20 kpc, the data lie in a
region of the diagram populated only by NS sources. 4U 1957+11 is unique: it is
either the only BH LMXB to exist in an apparent persistent soft state, or it is
a NS LMXB which behaves like a black hole.


  During the "WISE at 5: Legacy and Prospects" conference in Pasadena, CA --
which ran from February 10 - 12, 2015 -- attendees were invited to engage in an
interactive session exploring the future uses of the Wide-field Infrared Survey
Explorer (WISE) data. The 65 participants -- many of whom are extensive users
of the data -- brainstormed the top questions still to be answered by the
mission, as well as the complementary current and future datasets and
additional processing of WISE/NEOWISE data that would aid in addressing these
most important scientific questions. The results were mainly bifurcated between
topics related to extragalactic studies (e.g. AGN, QSOs) and substellar mass
objects. In summary, participants found that complementing WISE/NEOWISE data
with cross-correlated multiwavelength surveys (e.g. SDSS, Pan-STARRS, LSST,
Gaia, Euclid, etc.) would be highly beneficial for all future mission goals.
Moreover, developing or implementing machine-learning tools to comb through and
understand cross-correlated data was often mentioned for future uses. Finally,
attendees agreed that additional processing of the data such as co-adding WISE
and NEOWISE and extracting a multi-epoch photometric database and parallax and
proper motion catalog would greatly improve the scientific results of the most
important projects identified. In that respect, a project such as MaxWISE which
would execute the most important additional processing and extraction as well
as make the data and catalogs easily accessible via a public portal was deemed
extremely important.


  We revisit the problem of approximating minimizers of certain convex
functionals subject to a convexity constraint by solutions of fourth order
equations of Abreu type. This approximation problem was studied in previous
works of Carlier-Radice (Approximation of variational problems with a convexity
constraint by PDEs of Abreu type. Calc. Var. Partial Differential Equations. 58
(2019), no. 5, Art. 170) and the author (Singular Abreu equations and
minimizers of convex functionals with a convexity constraint,
arXiv:1811.02355v3, Comm. Pure Appl. Math., to appear), under the uniform
convexity of both the Lagrangian and constraint barrier. By introducing a new
approximating scheme, we completely remove the uniform convexity of both the
Lagrangian and constraint barrier. Our analysis is applicable to variational
problems motivated by the original 2D Rochet-Chon\'e model in the monopolist's
problem in Economics, and variational problems arising in the analysis of
wrinkling patterns in floating elastic shells in Elasticity.


  A Slavnov-Taylor identity is derived for the gluon polarization tensor in hot
QCD. We evaluate its implications for damping of gluonic modes in the plasma.
Applying the identity to next to the leading order in hard-thermal-loop
resummed perturbation theory, we derive the expected equality of damping rates
for static transverse and longitudinal (soft) gluons. This is of interest also
in view of deviating recent reports of $\gamma_t(p=0)\neq\gamma_l(p=0)$ based
on a direct calculation of $\gamma_l(p=0)$.


  Classical, i.e. non-quantum, communications include configurations with
multiple-input multiple-output (MIMO) channels. Some associated signal
processing tasks consider these channels in a symmetric way, i.e. by assigning
the same role to all channel inputs, and similarly to all channel outputs.
These tasks especially include channel identification/estimation and channel
equalization, tightly connected with source separation. Their most challenging
version is the blind one, i.e. when the receivers have (almost) no prior
knowledge about the emitted signals. Other signal processing tasks consider
classical communication channels in an asymmetric way. This especially includes
the situation when data are sent by Emitter 1 to Receiver 1 through a main
channel, and an "intruder" (including Receiver 2) interferes with that channel
so as to extract information, thus performing so-called eavesdropping, while
Receiver 1 may aim at detecting that intrusion. Part of the above processing
tasks have been extended to quantum channels, including those that have several
quantum bits (qubits) at their input and output. For such quantum channels,
beyond previously reported work for symmetric scenarios, we here address
asymmetric (blind and non-blind) ones, with emphasis on intrusion detection and
additional comments about eavesdropping. To develop fundamental concepts, we
first consider channels with exchange coupling as a toy model. We especially
use the general quantum information processing framework that we recently
developed, to derive new attractive intrusion detection methods based on a
single preparation of each state. Finally, we discuss how the proposed methods
might be extended, beyond the specific class of channels analyzed here.


  The prototypical network is a prototype classifier based on meta-learning and
is widely used for few-shot learning because it classifies unseen examples by
constructing class-specific prototypes without adjusting hyper-parameters
during meta-testing. Interestingly, recent research has attracted a lot of
attention, showing that training a new linear classifier, which does not use a
meta-learning algorithm, performs comparably with the prototypical network.
However, the training of a new linear classifier requires the retraining of the
classifier every time a new class appears. In this paper, we analyze how a
prototype classifier works equally well without training a new linear
classifier or meta-learning. We experimentally find that directly using the
feature vectors, which is extracted by using standard pre-trained models to
construct a prototype classifier in meta-testing, does not perform as well as
the prototypical network and training new linear classifiers on the feature
vectors of pre-trained models. Thus, we derive a novel generalization bound for
a prototypical classifier and show that the transformation of a feature vector
can improve the performance of prototype classifiers. We experimentally
investigate several normalization methods for minimizing the derived bound and
find that the same performance can be obtained by using the L2 normalization
and minimizing the ratio of the within-class variance to the between-class
variance without training a new classifier or meta-learning.


  Gravitational wave observations can be used to accurately measure the Hubble
constant $H_0$ and could help understand the present discrepancy between
constraints from Type Ia supernovae and the cosmic microwave background.
Neutron star mergers are primarily used for this purpose as their
electromagnetic emission can be used to greatly reduce measurement
uncertainties. Here we estimate $H_0$ using the recently observed black hole
merger GW190521 and its candidate electromagnetic counterpart found by ZTF
using a highly eccentric explanation of the properties of GW190521. We find
that the reconstructed distance of GW190521 and the redshift of the candidate
host galaxy are more consistent with standard cosmology for our eccentric model
than if we reconstruct the source parameters assuming no eccentricity. We
obtain $H_0=88.6^{+17.1}_{-34.3}$\,km\,s$^{-1}$Mpc$^{-1}$ for GW190521, and
$H_0=73.4^{+6.9}_{-10.7}$\,km\,s$^{-1}$Mpc$^{-1}$ in combination with the
results of the neutron star merger GW170817. Our results indicate that future
$H_0$ computations using black hole mergers will need to account for possible
eccentricity. For extreme cases, the orbital velocity of binaries in AGN disks
can represent a significant systematic uncertainty.


  The quantum energy-momentum tensor ${\hat T}^{\mu\nu}(x)$ is computed for
strings in Minkowski space-time. We compute its expectation value for different
physical string states both for open and closed bosonic strings. The states
considered are described by normalizable wave-packets in the center of mass
coordinates. We find in particular that ${\hat T}^{\mu\nu}(x)$ is {\bf finite}
which could imply that the classical divergence that occurs in string theory as
we approach the string position is removed at the quantum level as the string
position is smeared out by quantum fluctuations. For massive string states the
expectation value of ${\hat T}^{\mu\nu}(x)$ vanishes at leading order (genus
zero). For massless string states it has a non-vanishing value which we
explicitly compute and analyze for both spherically and cylindrically symmetric
wave packets. The energy-momentum tensor components propagate outwards as a
massless lump peaked at $ r = t $.


  We study the frog model on $\mathbb{Z}^d$ with drift in dimension $d \geq 2$
and establish the existence of transient and recurrent regimes depending on the
transition probabilities. We focus on a model in which the particles perform
nearest neighbour random walks which are balanced in all but one direction.
This gives a model with two parameters. We present conditions on the parameters
for recurrence and transience, revealing interesting differences between
dimension $d=2$ and dimension $d \geq 3$. Our proofs make use of (refined)
couplings with branching random walks for the transience, and with percolation
for the recurrence.


  The article by Bouwmeester et al. on experimental quantum teleportation
constitutes an important advance in the burgeoning field of quantum
information. The experiment was motivated by the proposal of Bennett et al. in
which an unknown quantum state is `teleported' by Alice to Bob. As illustrated
in Fig. 1, in the implementation of this procedure, by Bouwmeester et al., an
input quantum state is `disembodied' into quantum and classical components, as
in the original protocol. However, in contrast to the original scheme,
Bouwmeester et al.'s procedure necessarily destroys the state at Bob's
receiving terminal, so a `teleported' state can never emerge as a freely
propagating state for subsequent examination or exploitation. In fact,
teleportation is achieved only as a postdiction.


  We conducted a high-sensitivity radio detection survey for forty narrow-line
Seyfert 1 (NLS1) galaxies using very-long-baseline interferometry (VLBI) at 22
GHz through phase-referencing long-time integration and using a newly
developing recorder with a data rate of 8 Gbps, which is a candidate of the
next generation VLBI data recording systems for the Japanese VLBI Network. The
baseline sensitivity was typically a few mJy. The observations resulted in a
detection rate of 12/40 for our radio-selected NLS1 sample; 11 out of the
detected 12 NLS1s showed inverted radio spectra between 1.4 and 22 GHz on the
basis of the Very Large Array flux densities and the VLBI detections. These
high fractions suggest that a compact radio core with a high brightness
temperature is frequently associated with NLS1 nuclei. On the other hand, at
least half of the sample indicated apparently steep spectra even with the
limited VLBI sensitivity. Both the inverted and steep spectrum radio sources
are included in the NLS1 population.


  Phantom fields with negative kinetic energy are often plagued by the vacuum
quantum instability in the ultraviolet region. We present a Lorentz-violating
dark energy model free from this problem and show that the crossing of the
cosmological constant boundary w=-1 to the phantom equation of state is
realized before reaching a de Sitter attractor. Another interesting feature is
a peculiar time-dependence of the effective Newton's constant; the magnitude of
this effect is naturally small but may be close to experimental limits. We also
derive momentum scales of instabilities at which tachyons or ghosts appear in
the infrared region around the present Hubble scale and clarify the conditions
under which tachyonic instabilities do not spoil homogeneity of the
present/future Universe.


  We propose two functions to distinguish fission-like events from
quasi-elastic (QE) scattering and deep inelastic collisions (DIC), for a better
analysis of the measured mass-total kinetic energy distributions of binary
fragments formed in fusion-fission reactions. We note that the ratio of capture
to DIC events evidently decreases with the decreasing of the depth of the
capture pocket predicted from the Skyrme energy density functional, with which
the capture pocket could be extracted from the measured mass-energy
distributions. Together with the improved quantum molecular dynamics
simulations, in which the typical contact time of the reaction partners is
smaller than 200 fm/c for QE and is larger than 600 fm/c for fission-like
events, we find that the ratio of capture to touching cross section
systematically increases with the pocket depth.


  Excitonic insulators conduct neither electrons nor holes but bound
electron-hole pairs, excitons. Unfortunately, it is not possible to inject and
detect the electron and hole currents independently within a single
semiconducting layer. However, interlayer excitonic insulators provide a
spatial separation of electrons and holes enabling exciton current
measurements. The problem is that the spatial separation weakens electron-hole
pairing and may lead to interlayer exciton disassociation. Here we develop an
explicitly solvable model to determine an interlayer separation that is strong
enough to prevent electron and hole hopping across the layers but still allows
for electron-hole pairing sufficient for transition into an interlayer
excitonic insulator state. An ideal junction to realize such a state would
comprise a pair of identical narrow-gap two-dimensional semiconductors
separated by a wide-gap dielectric layer with low dielectric permittivity. The
present study quantifies parameters of such a junction by taking into account
interlayer coherence effects.


  We report on the kinetic inductance detector (KID) array focal plane assembly
design for the Terahertz Intensity Mapper (TIM). Each of the 2 arrays consists
of 4 wafer-sized dies (quadrants), and the overall assembly must satisfy
thermal and mechanical requirements, while maintaining high optical efficiency
and a suitable electromagnetic environment for the KIDs. In particular, our
design manages to strictly maintain a 50 $\mathrm{\mu m}$ air gap between the
array and the horn block. We have prototyped and are now testing a sub-scale
assembly which houses a single quadrant for characterization before integration
into the full array. The initial test result shows a $>$95% yield, indicating a
good performance of our TIM detector packaging design.


  The early history of the development of Quantum Mechanics is surveyed to
discern the arguments leading to the introduction of the notions of `irreal'
wave functions and `nonlocal' correlations. It is argued that the assumption
that Quantum Mechanics is `complete', i.e., not just a variant of Statistical
Mechanics, is the feature compelling the introduction of these otherwise
problematic properties. Additionally, a consequence of the error first found by
Jaynes in proofs of Bell's ``theorem'', is illustrated. Finally, speculation on
the practical consequences of recognising that ``entanglement'' is a feature of
all hyperbolic differential equations is proposed.


  Observations of quasi-periodic oscillations (QPOs) in X-ray binaries hold a
key to understanding many aspects of these enigmatic systems. Complex
appearance of the Fourier phase lags related to QPOs is one of the most
puzzling observational effects in accreting black holes. In this Letter we show
that QPO properties, including phase lags, can be explained in a framework of a
simple scenario, where the oscillating media provides a feedback on the
emerging spectrum. We demonstrate that the QPO waveform is presented by the
product of a perturbation and a time delayed response factors, where the
response is energy dependent. The essential property of this effect is its
non-linear and multiplicative nature. Our multiplicative reverberation model
successfully describes the QPO components in energy dependent power spectra as
well as the appearance of the phase lags between signal in different energy
bands. We apply our model to QPOs observed by Rossi X-ray Timing Explorer in BH
candidate XTE J1550-564. We briefly discuss the implications of the observed
energy dependence of the QPO reverberation times and amplitudes to the nature
of the power law spectral component and its variability.


  Phone sensors could be useful in assessing changes in gait that occur with
alcohol consumption. This study determined (1) feasibility of collecting
gait-related data during drinking occasions in the natural environment, and (2)
how gait-related features measured by phone sensors relate to estimated blood
alcohol concentration (eBAC). Ten young adult heavy drinkers were prompted to
complete a 5-step gait task every hour from 8pm to 12am over four consecutive
weekends. We collected 3-xis accelerometer, gyroscope, and magnetometer data
from phone sensors, and computed 24 gait-related features using a sliding
window technique. eBAC levels were calculated at each time point based on
Ecological Momentary Assessment (EMA) of alcohol use. We used an artificial
neural network model to analyze associations between sensor features and eBACs
in training (70% of the data) and validation and test (30% of the data)
datasets. We analyzed 128 data points where both eBAC and gait-related sensor
data was captured, either when not drinking (n=60), while eBAC was ascending
(n=55) or eBAC was descending (n=13). 21 data points were captured at times
when the eBAC was greater than the legal limit (0.08 mg/dl). Using a Bayesian
regularized neural network, gait-related phone sensor features showed a high
correlation with eBAC (Pearson's r > 0.9), and >95% of estimated eBAC would
fall between -0.012 and +0.012 of actual eBAC. It is feasible to collect
gait-related data from smartphone sensors during drinking occasions in the
natural environment. Sensor-based features can be used to infer gait changes
associated with elevated blood alcohol content.


  We present observations of the Vela X region at 31 GHz using the Cosmic
Background Imager (CBI). We find a strong compact radio source (5.9'x4.1',
FWHM) about the Vela pulsar, which we associate with the Vela pulsar wind
nebula (PWN) recently discovered at lower radio-frequencies. The CBI's 4'
resolution for a 45' field of view allows the PWN to be studied in the
large-scale context of Vela X. Filamentary structure in Vela X, which stands
out in lower frequency maps, is very low-level at 31 GHz. By combining the 10
CBI channels, which cover 26-36 GHz, and 8.4 GHz archive data, we study the
spectral energy distribution (SED) of the PWN and the brightest filaments. Our
results show that the spectral index alpha (F_{nu} propto nu^alpha) of the PWN
is flat, or even marginally positive, with a value of
alpha_{8.4}^{31}=0.10+-0.06, while the Vela X filamentary structure has a
negative spectral index of alpha_{8.4}^{31}=-0.28+-0.09. The SED inhomogeneity
observed in Vela X suggests different excitation processes between the PWN and
the filaments. We investigate whether the PWN's flat spectrum is a consequence
of variability or truly reflects the SED of the object. The peak of the PWN at
31 GHz is 80''+-20'' south-west of the peak at 8.4 GHz. This shift is confirmed
by comparing the 31 GHz CBI image with higher resolution 5 GHz Australia
Telescope Compact Array observations, and is likely to be due to SED variations
within the PWN. We also investigate the nature of the Vela X filamentary
structure.


  Exposure to a $^{51}$Cr neutrino source as that used in Gallex will provide
an excellent overall performance test of Borexino, which should collect about
1400 source induced events, with an initial rate of about 35 counts per day.
This will be particularly important if MSW-small-angle turns out to be the
solution of the solar neutrino problem. In addition, if an independent,
accurate calibration is available, one will have an interesting experiment on
neutrino properties: as an example, a neutrino magnetic moment of the order
$5\cdot10^{-11}\mu_B$could be detected/excluded at the 90\% C.L.


  We show that the next-to-leading order perturbative prediction, matched with
the next-to-leading logarithmic approximation for predicting both two-, three-
and four-jet rates using the Durham jet-clustering algorithm, in the 0.001 <
ycut < 0.1 range gives a very accurate description of the data obtained at the
Large Electron Positron collider. This information can be utilized either for
simultaneous measurement of the strong coupling and the QCD colour charges, or
for improving the QCD background prediction in new particle searches at LEP2.


  Given the abstract evolution equation \[ y'(t)=Ay(t),\ t\in \mathbb{R}, \]
with scalar type spectral operator $A$ in a complex Banach space, found are
conditions necessary and sufficient for all weak solutions of the equation,
which a priori need not be strongly differentiable, to be strongly infinite
differentiable on $\mathbb{R}$. The important case of the equation with a
normal operator $A$ in a complex Hilbert space is obtained immediately as a
particular case. Also, proved is the following inherent smoothness improvement
effect explaining why the case of the strong finite differentiability of the
weak solutions is superfluous: if every weak solution of the equation is
strongly differentiable at $0$, then all of them are strongly infinite
differentiable on $\mathbb{R}$.


  We present here results of high resolution synchrotron x-ray diffraction
(SXRD) and dielectric studies in conjunction with Landau theory considerations
on (Pb0.94Sr0.06)(ZrxTi1-x)O3 compositions in the vicinity of the morphotropic
phase boundary (MPB) to find evidence for the flattening of the free energy
surface at the MPB proposed in recent ab-initio studies on strongly
piezoelectric ceramics. SXRD results reveal that the tetragonal and
pseudorhombohedral monoclinic compositions with x=0.515 and 0.550 transform
directly into the cubic paraelectric phase, whereas for 0.520<x<0.545, the
pseudotetragonal as well as pseudorhombohedral monoclinic compositions first
transform to the tetragonal phase and then to the cubic phase. Our results
reveal the existence of a triple point at x~0.550. It is shown that the
tetragonal to cubic transition, irrespective of the composition, upto x~0.545
is accompanied with a discontinuous change in the unit cell volume and thermal
hysteresis confirming first order nature of this transition. The
pseudorhombohedral monoclinic composition for x=0.550, on the other hand,
transforms directly into the cubic phase in a second order manner. Our
experimental results thus reveal a crossover from first order to second order
phase transition through a tricritical point around x=0.550. Landau theory
calculations also confirm gradual flattening of the free energy surface on
approaching the tricritical composition x=0.550. We conclude that the triple
point in the PZT phase diagram is indeed a tricritical point.


  Recent works on end-to-end trainable neural network based approaches have
demonstrated state-of-the-art results on dialogue state tracking. The best
performing approaches estimate a probability distribution over all possible
slot values. However, these approaches do not scale for large value sets
commonly present in real-life applications and are not ideal for tracking slot
values that were not observed in the training set. To tackle these issues,
candidate-generation-based approaches have been proposed. These approaches
estimate a set of values that are possible at each turn based on the
conversation history and/or language understanding outputs, and hence enable
state tracking over unseen values and large value sets however, they fall short
in terms of performance in comparison to the first group. In this work, we
analyze the performance of these two alternative dialogue state tracking
methods, and present a hybrid approach (HyST) which learns the appropriate
method for each slot type. To demonstrate the effectiveness of HyST on a
rich-set of slot types, we experiment with the recently released MultiWOZ-2.0
multi-domain, task-oriented dialogue-dataset. Our experiments show that HyST
scales to multi-domain applications. Our best performing model results in a
relative improvement of 24% and 10% over the previous SOTA and our best
baseline respectively.


  Bacterial plant pathogens rely on a battalion of transcription factors to
fine-tune their response to changing environmental conditions and marshal the
genetic resources required for successful pathogenesis. Prediction of
transcription factor binding sites represents an important tool for elucidating
regulatory networks, and has been conducted in multiple genera of plant
pathogenic bacteria for the purpose of better understanding mechanisms of
survival and pathogenesis. The major categories of transcription factor binding
sites that have been characterized are reviewed here with emphasis on in silico
methods used for site identification and challenges therein, their
applicability to different types of sequence datasets, and insights into
mechanisms of virulence and survival that have been gained through binding site
mapping. An improved strategy for establishing E value cutoffs when using
existing models to screen uncharacterized genomes is also discussed.


  We derive the free Osp(8|4) singleton action by sending the M2brane to the
Minkowski boundary of an AdS_4x{\cal M}_7 background. We do this by means of
the solvable Lie algebra parametrization of the coset space. We also give some
comments on singleton actions from membranes on AdS_4xG/H backgrounds.


  In recent years, neural models have often outperformed rule-based and classic
Machine Learning approaches in NLG. These classic approaches are now often
disregarded, for example when new neural models are evaluated. We argue that
they should not be overlooked, since, for some tasks, well-designed non-neural
approaches achieve better performance than neural ones. In this paper, the task
of generating referring expressions in linguistic context is used as an
example. We examined two very different English datasets (WEBNLG and WSJ), and
evaluated each algorithm using both automatic and human evaluations. Overall,
the results of these evaluations suggest that rule-based systems with simple
rule sets achieve on-par or better performance on both datasets compared to
state-of-the-art neural REG systems. In the case of the more realistic dataset,
WSJ, a machine learning-based system with well-designed linguistic features
performed best. We hope that our work can encourage researchers to consider
non-neural models in future.


  We have investigated polyyne and cumulene prototypes based on the
density-functional theory. Our independent-particle spectra show that the
various carbynes can be distinguished by optical properties comparing the
low-energy spectral structure as well as using very general considerations. The
latter conclusion is supported by results based on the random-phase
approximation including local-field effects.


  We show that the topological Majorana modes in nanowires much longer than the
superconducting coherence length are adiabatically connected with discrete
zero-energy states generically occurring in short nanowires. We demonstrate
that these zero-energy crossings can be tuned by an external magnetic field and
are protected by the particle-hole symmetry. We study the evolution of the
low-energy spectrum and the splitting oscillations as a function of magnetic
field, wire length, and chemical potential, manifestly establishing that the
low-energy physics of short wires is related to that occurring in long wires.
This physics, which represents a hallmark of spinless p-wave superconductivity,
can be observed in tunneling conductance measurements.


  A variation of Dirac equation based on SO(2,1) group is suggested for
treating low dimensional systems in the three dimensional x,y,t space.
Non-unitary representations are developed in an analogous way to those used in
the ordinary Dirac equations and quantum field theory is developed for the
present SO(2,1) relativistic equation. The theory is applied for low
dimensional systems including especially holes-electrons pairs, or other
two-particle states, in the low dimensional space.


  Constraining cosmology using weak gravitational lensing consists of comparing
a measured feature vector of dimension $N_b$ with its simulated counterpart. An
accurate estimate of the $N_b\times N_b$ feature covariance matrix $\mathbf{C}$
is essential to obtain accurate parameter confidence intervals. When
$\mathbf{C}$ is measured from a set of simulations, an important question is
how large this set should be. To answer this question, we construct different
ensembles of $N_r$ realizations of the shear field, using a common
randomization procedure that recycles the outputs from a smaller number
$N_s\leq N_r$ of independent ray-tracing $N$--body simulations. We study
parameter confidence intervals as a function of ($N_s,N_r$) in the range $1\leq
N_s\leq 200$ and $1\leq N_r\lesssim 10^5$. Previous work has shown that
Gaussian noise in the feature vectors (from which the covariance is estimated)
lead, at quadratic order, to an $O(1/N_r)$ degradation of the parameter
confidence intervals. Using a variety of lensing features measured in our
simulations, including shear-shear power spectra and peak counts, we show that
cubic and quartic covariance fluctuations lead to additional $O(1/N_r^2)$ error
degradation that is not negligible when $N_r$ is only a factor of few larger
than $N_b$. We study the large $N_r$ limit, and find that a single, 240Mpc$/h$
sized $512^3$-particle $N$--body simulation ($N_s=1$) can be repeatedly
recycled to produce as many as $N_r={\rm few}\times10^4$ shear maps whose power
spectra and high-significance peak counts can be treated as statistically
independent. As a result, a small number of simulations ($N_s=1$ or $2$) is
sufficient to forecast parameter confidence intervals at percent accuracy.


  Hopf algebra structures on rooted trees are by now a well-studied object,
especially in the context of combinatorics. In this work we consider a Hopf
algebra H by introducing a coproduct on a (commutative) algebra of rooted
forests, considering each tree of the forest (which must contain at least one
edge) as a Feynman-like graph without loops. The primitive part of the graded
dual is endowed with a pre-Lie product defined in terms of insertion of a tree
inside another. We establish a surprising link between the Hopf algebra H
obtained this way and the well-known Connes-Kreimer Hopf algebra of rooted
trees by means of a natural H-bicomodule structure on the latter. This enables
us to recover recent results in the field of numerical methods for differential
equations due to Chartier, Hairer and Vilmart as well as Murua.


  In this paper, we introduce the category of quasi-tempered automorphic
D-modules, which is a rather natural class of D-modules from the point of view
of geometric Langlands. We provide a characterization of this category in terms
of singular support, and as a consequence, we obtain certain microlocal
categorical K\"unneth formulas.


  We undertake a systematic comparison between implied volatility, as
represented by VIX (new methodology) and VXO (old methodology), and realized
volatility. We compare visually and statistically distributions of realized and
implied variance (volatility squared) and study the distribution of their
ratio. We find that the ratio is best fitted by heavy-tailed -- lognormal and
fat-tailed (power-law) -- distributions, depending on whether preceding or
concurrent month of realized variance is used. We do not find substantial
difference in accuracy between VIX and VXO. Additionally, we study the variance
of theoretical realized variance for Heston and multiplicative models of
stochastic volatility and compare those with realized variance obtained from
historic market data.


  The J-function in Gromov-Witten theory is a generating function for one-point
genus zero Gromov-Witten invariants with descendants. Here we give formulas for
the quantum K-theoretic J-functions of type A flag manifolds and conjectural
formulas for other types. Some K-theoretic tools for computation are also
provided. As an application, we prove the quantum K-theoretic J-function
version of the abelian-nonabelian correspondence for Grassmannians and products
of projective space.


  We present squeezing and anti-squeezing spectra of the output from a
degenerate optical parametric oscillator (OPO) network arranged in different
coherent quantum feedback configurations. One OPO serves as a quantum plant,
the other as a quantum controller. The addition of coherent feedback enables
shaping of the output squeezing spectrum of the plant, and is found to be
capable of pushing the frequency of maximum squeezing away from the optical
driving frequency and broadening the spectrum over a wider frequency band. The
experimental results are in excellent agreement with the developed theory, and
illustrate the use of coherent quantum feedback to engineer the quantum-optical
properties of the plant OPO output.


  The ultracompact low-mass X-ray binary 4U 1820-30 situated in the globular
cluster NGC 6624 has an orbital period of only $\approx$11.4 min which likely
implies a white dwarf companion. The observed X-ray bursts demonstrate a
photospheric radius expansion phase and therefore are believed to reach the
Eddington luminosity allowing us to estimate the mass and the radius of the
neutron star (NS) in this binary. Here we re-analyse all Rossi X-ray Timing
Explorer observations of the system and confirm that almost all the bursts took
place during the hard persistent state of the system. This allows us to use the
recently developed direct cooling tail method to estimate the NS mass and
radius. However, because of the very short, about a second, duration of the
cooling tail phases that can be described by the theoretical atmosphere models,
the obtained constraints on the NS radius are not very strict. Assuming a pure
helium NS atmosphere we found that the NS radius is in the range 10-12 km, if
the NS mass is below 1.7 $M_\odot$, and in a wider range of 8-12 km for a
higher 1.7-2.0 $M_\odot$ NS mass. The method also constrains the distance to
the system to be 6.5$\pm$0.5 kpc, which is consistent with the distance to the
cluster. For the solar composition atmosphere, the NS parameters are in strong
contradiction with the generally accepted range of possible NS masses and
radii.


  In this article, we show that four sets of differential Fay identities of an
$N$-component KP hierarchy derived from the bilinear relation satisfied by the
tau function of the hierarchy are sufficient to derive the auxiliary linear
equations for the wave functions. From this, we derive the Lax representation
for the $N$-component KP hierarchy, which are equations satisfied by some
pseudodifferential operators with matrix coefficients. Besides the Lax
equations with respect to the time variables proposed in \cite{2}, we also
obtain a set of equations relating different charge sectors, which can be
considered as a generalization of the modified KP hierarchy proposed in
\cite{3}.


  Stock management should be guided by assessment models that, among others,
need to be fed by reliable data of catch and effort. However, precise data are
difficult to obtain in heterogeneous fisheries. Specifically, small scale,
multi gear, multispecies fisheries are dynamic systems where fishers may lively
change fishing strategy conditioned by multiple drivers. Provided that some
stocks can be shared by several metiers, a precise categorization of metiers
should be the first step toward metier specific estimates of catch and effort,
which in turn would allow a better understanding of the system dynamics. Here
we propose an approach for predicting the metier of any given fishing trip from
its landing records. This approach combines the knowledge of expert fishers
with the existing sales register of landings in Mallorca. It successfully
predicts metiers for all the 162815 small scale fishery fishing trips from
Mallorca between 2004 and 2015. The largest effort is invested in the metiers
Cuttlefish Fish and Spiny lobster, landings peak for Cuttlefish Fish and
Dolphinfish and revenues for Spiny lobster and Dolphinfish. Metier predictions
also allowed us to describe the temporal trends experienced by each metier and
to characterize the species that are specific to each metier. Seasonal
variability is by far more relevant than between year variability, which
confirms that at least some fishers are adopting a rotation cycle of metiers
along the year. Effort, landings and gross revenues decreased in the last 12
years. The approach proposed is also applicable to any other fishery for which
the metier for a fishing trip sample is known, but relying on fishers expertise
points more directly to fishers intention. Thus, metier predictions produced
with the proposed approach are closer to the actual uses of fishers, providing
better grounds for an improved management.


  The orbital dynamics of a test particle moving in the non-spherically
symmetric field of a rotating oblate primary is impacted also by certain
indirect, mixed effects arising from the interplay of the different Newtonian
and post-Newtonian accelerations which induce known direct perturbations. We
systematically calculate the indirect gravitoelectromagnetic shifts per orbit
of the Keplerian orbital elements of the test particle arising from the
crossing among the first even zonal harmonic $J_2$ of the central body and the
post-Newtonian static and stationary components of its gravitational field. We
also work out the Newtonian shifts per orbit of order $J_2^2$, and the direct
post-Newtonian gravitoelectric effects of order $J_2 c^{-2}$ arising from the
equations of motion. In the case of both the indirect and direct
gravitoelectric $J_2 c^{-2}$ shifts, our calculation holds for an arbitrary
orientation of the symmetry axis of the central body. We yield numerical
estimates of their relative magnitudes for systems ranging from Earth
artificial satellites to stars orbiting supermassive black holes.


  Recent studies have pointed out that natural language processing (NLP) models
are vulnerable to backdoor attacks. A backdoored model produces normal outputs
on the clean samples while performing improperly on the texts with triggers
that the adversary injects. However, previous studies on textual backdoor
attack pay little attention to stealthiness. Moreover, some attack methods even
cause grammatical issues or change the semantic meaning of the original texts.
Therefore, they can easily be detected by humans or defense systems. In this
paper, we propose a novel stealthy backdoor attack method against textual
models, which is called \textbf{PuncAttack}. It leverages combinations of
punctuation marks as the trigger and chooses proper locations strategically to
replace them. Through extensive experiments, we demonstrate that the proposed
method can effectively compromise multiple models in various tasks. Meanwhile,
we conduct automatic evaluation and human inspection, which indicate the
proposed method possesses good performance of stealthiness without bringing
grammatical issues and altering the meaning of sentences.


  This paper presents a new method to solve keypoint detection and instance
association by using Transformer. For bottom-up multi-person pose estimation
models, they need to detect keypoints and learn associative information between
keypoints. We argue that these problems can be entirely solved by Transformer.
Specifically, the self-attention in Transformer measures dependencies between
any pair of locations, which can provide association information for keypoints
grouping. However, the naive attention patterns are still not subjectively
controlled, so there is no guarantee that the keypoints will always attend to
the instances to which they belong. To address it we propose a novel approach
of supervising self-attention for multi-person keypoint detection and instance
association. By using instance masks to supervise self-attention to be
instance-aware, we can assign the detected keypoints to their corresponding
instances based on the pairwise attention scores, without using pre-defined
offset vector fields or embedding like CNN-based bottom-up models. An
additional benefit of our method is that the instance segmentation results of
any number of people can be directly obtained from the supervised attention
matrix, thereby simplifying the pixel assignment pipeline. The experiments on
the COCO multi-person keypoint detection challenge and person instance
segmentation task demonstrate the effectiveness and simplicity of the proposed
method and show a promising way to control self-attention behavior for specific
purposes.


  The European Research Council has recently funded HOLMES, a new experiment to
directly measure the neutrino mass. HOLMES will perform a calorimetric
measurement of the energy released in the decay of 163Ho. The calorimetric
measurement eliminates systematic uncertainties arising from the use of
external beta sources, as in experiments with beta spectrometers. This
measurement was proposed in 1982 by A. De Rujula and M. Lusignoli, but only
recently the detector technological progress allowed to design a sensitive
experiment. HOLMES will deploy a large array of low temperature
microcalorimeters with implanted 163Ho nuclei. The resulting mass sensitivity
will be as low as 0.4 eV. HOLMES will be an important step forward in the
direct neutrino mass measurement with a calorimetric approach as an alternative
to spectrometry. It will also establish the potential of this approach to
extend the sensitivity down to 0.1 eV. We outline here the project with its
technical challenges and perspectives.


  An approach, based on the Smith Normal Form, is introduced to study the
spectra of symmetric matrices with a given graph. The approach serves well to
explain how the path cover number (resp. diameter of a tree T) is related to
the maximum multiplicity occurring for an eigenvalue of a symmetric matrix
whose graph is T (resp. the minimum number q(T) of distinct eigenvalues over
the symmetric matrices whose graphs are T). The approach is also applied to a
more general class of connected graphs G, not necessarily trees, in order to
establish a lower bound on q(G).


  Let N be the set of non-negative integer numbers, T the circle group and c
the cardinality of the continuum. Given an abelian group G of size at most 2^c
and a countable family F of infinite subsets of G, we construct "Baire many"
monomorphisms p: G --> T^c such that p(E) is dense in {y in T^c : ny=0}
whenever n in N, E in F, nE={0} and {x in E: mx=g} is finite for all g in G and
m such that n=mk for some k in N--{1}. We apply this result to obtain an
algebraic description of countable potentially dense subsets of abelian groups,
thereby making a significant progress towards a solution of a problem of Markov
going back to 1944. A particular case of our result yields a positive answer to
a problem of Tkachenko and Yaschenko. Applications to group actions and
discrete flows on T^c, diophantine approximation, Bohr topologies and Bohr
compactifications are also provided.


  This note presents an extension to the adaptive control strategy presented in
[1] able to counter eventual instability due to disturbances at the input of an
otherwise $\mathcal{L}_2$ stable closed-loop system. These disturbances are due
to the presence of affine terms in the plant and reference model. The existence
of a common Lyapunov function is used to prove global convergence of the error
system, even in the presence of sliding solutions, as well as boundedness of
all the adaptive gains.


  We present an accurate and efficient algorithm to calculate the electrostatic
interaction of charged point particles with partially periodic boundary
conditions that are confined along the nonperiodic direction by two metallic
parallel plates. The method preserves the original boundary conditions and
hence, it does not introduce any kind of artifacts. In addition, it enjoys the
quasilinear complexity of $\mathcal{O}(N\ln(N))$, where $N$ being the number of
particles in the simulation box. In fact, based on the superposition principle
in electrostatics, the problem is split into two electrostatic problems where
each one can be calculated by the appropriate Poisson solver. In this paper we
apply the method to sodium chloride ultrathin films and investigate its
dielectric response with respect to external bias voltage. We show how
accurately in this method one can obtain the total charge induced on metallic
boundaries to an arbitrary precision.


  In this paper we give an example of a noncongruence subgroup whose
three-dimensional space of cusp forms of weight 3 has the following properties.
For each of the four residue classes of odd primes modulo 8 there is a basis
whose Fourier coefficients at infinity satisfy a three-term Atkin and
Swinnerton-Dyer congruence relation, which is the $p$-adic analogue of the
three-term recursion satisfied by the coefficients of classical Hecke eigen
forms. We also show that there is an automorphic $L$-function over $\mathbb Q$
whose local factors agree with those of the $l$-adic Scholl representations
attached to the space of noncongruence cusp forms.


  The current cosmological model includes cold dark matter, which consists of
massive nonrelativistic particles. There are also some observational and
theoretical evidences for warm dark matter. The existence of warm DM can be
examined by measuring of the galaxy clusters density profiles and accurate
counting of dwarf galaxies. In this work I suppose that DM haloes are well
traced by X-ray gas in clusters, groups, pairs and even single galaxies. The
type of DM is inspected with the Xgal sample of 5021 X-ray emitting galaxies
observed by XMM-Newton. The selection bias of this sample is also analyzed.


  Repeatedly-monitored quantum walks with a rate $1/\tau$ yield discrete-time
trajectories which are inherently random. With these paths the first-hitting
time with sharp restart is studied. We find an instability in the optimal mean
hitting time, which is not found in the corresponding classical random walk
process. This instability implies that a small change in parameters can lead to
a rather large change of the optimal restart time. We show that the optimal
restart time versus $\tau$, as a control parameter, exhibits sets of staircases
and plunges. The plunges, are due to the mentioned instability, which in turn
is related to the quantum oscillations of the first-hitting time probability,
in the absence of restarts. Furthermore, we prove that there are only two
patterns of staircase structures, dependent on the parity of the distance
between the target and the source in units of lattice constant. The global
minimum of the hitting time, is controlled not only by the restart time, as in
classical problems, but also by the sampling time $\tau$. We provide numerical
evidence that this global minimum occurs for the $\tau$ minimizing the mean
hitting time, given restarts taking place after each measurement. Last but not
least, we numerically show that the instability found in this work is
relatively robust against stochastic perturbations in the sampling time $\tau$.


  Background: Recent theoretical and experimental researches using
proton-induced $\alpha$-knockout reactions provide direct manifestation of
$\alpha$-cluster formation in nuclei. In recent and future experiments,
$\alpha$-knockout data are available for neutron-rich beryllium isotopes. In
$^{12}$Be , rich phenomena are induced by the formation of $\alpha$-clusters
surrounded by neutrons, for instance, breaking of the neutron magic number
$N=8$.
  Purpose: Our objective is to provide direct probing of the $\alpha$-cluster
formation in the $^{12}$Be target through associating the structure information
obtained by a microscopic theory with the experimental observables of
$\alpha$-knockout reactions.
  Method: We formulate a new wave function of the
Tohsaki-Horiuchi-Schuck-R{\"o}pke (THSR) type for the structure calculation of
${}^{12}$Be nucleus and integrate it with the distorted wave impulse
approximation framework for the $\alpha$-knockout reaction calculation of
$^{12}$Be$(p,p\alpha)^{8}$He.
  Results: We reproduce the low-lying spectrum of the $^{12}$Be nucleus using
the THSR wave function and discuss the cluster structure of the ground state.
Based on the microscopic wave function, the optical potentials and
$\alpha$-cluster wave function are determined and utilized in the calculation
of ${}^{12}$Be($p,p\alpha$)${}^{8}$He reaction at 250 MeV. The possibility of
probing the clustering state of $^{12}$Be through this reaction is demonstrated
by analysis of the triple differential cross sections that are sensitively
dependent on the $\alpha$-cluster amplitude at the nuclear surface.
  Conclusions: This study provides a feasible approach to validate directly the
theoretical predictions of clustering features in the $^{12}$Be nucleus through
the $\alpha$-knockout reaction.


  Uniform timeslicing of dynamic graphs has been used due to its convenience
and uniformity across the time dimension. However, uniform timeslicing does not
take the data set into account, which can generate cluttered timeslices with
edge bursts and empty timeslices with few interactions. The graph mining filed
has explored nonuniform timeslicing methods specifically designed to preserve
graph features for mining tasks. In this paper, we propose a nonuniform
timeslicing approach for dynamic graph visualization. Our goal is to create
timeslices of equal visual complexity. To this end, we adapt histogram
equalization to create timeslices with a similar number of events, balancing
the visual complexity across timeslices and conveying more important details of
timeslices with bursting edges. A case study has been conducted, in comparison
with uniform timeslicing, to demonstrate the effectiveness of our approach.


  The goal of this paper is to study the family of singular perturbations of
Blaschke products given by
$B_{a,\lambda}(z)=z^3\frac{z-a}{1-\overline{a}z}+\frac{\lambda}{z^2}$. We focus
on the study of these rational maps for parameters $a$ in the punctured disk
$\mathbb{D}^*$ and $|\lambda|$ small. We prove that, under certain conditions,
all Fatou components of a singularly perturbed Blaschke product $B_{a,\lambda}$
have finite connectivity but there are components of arbitrarily large
connectivity within its dynamical plane. Under the same conditions we prove
that the Julia set is the union of countably many Cantor sets of quasicircles
and uncountably many point components.


  We prove that in any recurrent reversible random rooted graph, two
independent simple random walks started at the same vertex collide infinitely
often almost surely. This applies to the Uniform Infinite Planar Triangulation
and Quadrangulation and to the Incipient Infinite Cluster in $\mathbb{Z}^2$.


  In the last couple of years, the role of Open Access (OA) publishing has
become central in science management and research policy. In the UK and the
Netherlands, national OA mandates require the scientific community to seriously
consider publishing research outputs in OA forms. At the same time, other
elements of Open Science are becoming also part of the debate, thus including
not only publishing research outputs but also other related aspects of the
chain of scientific knowledge production such as open peer review and open
data. From a research management point of view, it is important to keep track
of the progress made in the OA publishing debate. Until now, this has been
quite problematic, given the fact that OA as a topic is hard to grasp by
bibliometric methods, as most databases supporting bibliometric data lack
exhaustive and accurate open access labelling of scientific publications. In
this study, we present a methodology that systematically creates OA labels for
large sets of publications processed in the Web of Science database. The
methodology is based on the combination of diverse data sources that provide
evidence of publications being OA


  We study relation between Chiral Separation Effect (CSE) and Chiral Anomaly,
and argue that CSE does not inherit the immutability of Chiral Anomaly. For QED
in the leading order in electric charge, with point-splitting regularization in
real-time formalism, we demontrate, in regularization-dependent way though,
that CSE is an infrared (IR) effect, while the Anomaly is an ultra-violet (UV)
phenomena. Thus, CSE in general is sensitive to non-perturbative interactions
that alter the theory IR properties, while the Anomaly is fixed by Lorentz
symmetry. The simplest example of such an interaction is the Yukawa-like
fermion mass.


  In this paper we consider the numerical solution of fractional differential
equations. In particular, we study a step-by-step graded mesh procedure based
on an expansion of the vector field using orthonormal Jacobi polynomials. Under
mild hypotheses, the proposed procedure is capable of getting spectral
accuracy. A few numerical examples are reported to confirm the theoretical
findings.


  We evaluate the next-to-next-to-leading order soft function for the
production of a massive color octet state at rest in the collision of two
massless colored partons in either the fundamental or the adjoint
representation. The main application of our result is the determination of the
threshold expansion of the heavy-quark pair-production cross sections in the
quark annihilation and gluon fusion channels. We discuss the factorization
necessary for this purpose and explain the relationship between hard functions
and virtual amplitudes.


  A new method to constrain gravitational theories depending on the Ricci
scalar is presented. It is based on the weak energy condition and yields limits
on the parameters of a given theory through the current values of the
derivatives of the scale factor of the Friedmann-Robertson-Walker geometry. A
further constraint depending on the current value of the snap is also given.
Actual constraints (and the corresponding error propagation analysis) are
calculated for two examples, which show that the method is useful in limiting
the possible $f(R)$ theories.


  Here we report results of a density-matrix-renormalization-group (DMRG)
calculation of the charge, spin, and pairing properties of a two-leg CuO
Hubbard ladder. The outer oxygen atoms as well as the rung and leg oxygen atoms
are included along with near-neighbor and oxygen-hopping matrix elements. This
system allows us to study the effects of hole and electron doping on a system
which is a charge transfer insulator at a filling of one hole per Cu and
exhibits power law, d-wave-like pairing correlations when doped. In particular,
we focus on the differences between doping with holes or electrons.


  Ambiguities have recently been found in the definition of the partial
derivative (in the case of presence of both explicit and implicit dependencies
of the function subjected to differentiation). We investigate the possible
influence of this subject on quantum mechanics and the classical/quantum field
theory. Surprisingly, some commutators of operators of space-time 4-coordinates
and those of 4-momenta are not equal to zero.
  Notes added in the Abstract: Two iterated limits are not equal each other, in
general. Thus, we present an example when the massless limit of the function of
E, p, m does not exist in some calculations within quantum field theory.


  Subduction zones transport water into Earth's deep interior through slab
subduction. Serpentine minerals, the primary hydration product of ultramafic
peridotite, are abundant in most subduction zones. Characterization of their
high-temperature elasticity, particularly their anisotropy, will help us better
estimate the extent of mantle serpentinization and the Earth's deep water
cycle. Lizardite, the low-temperature polymorph of serpentine, is stable under
the P-T conditions of cold subduction slabs (< 260{\deg}C at 2 GPa), and its
high-temperature elasticity remains unknown. Here we report ab initio
elasticity and acoustic wave velocities of lizardite at P-T conditions of
subduction zones. Our static results agree with previous studies. Its
high-temperature velocities are much higher than previous experimental-based
lizardite estimates with chrysotile but closer to antigorite velocities. The
elastic anisotropy of lizardite is much larger than that of antigorite and
could better account for the observed large shear-wave splitting in some cold
slabs such as Tonga.


  Strong external difference families (SEDFs) have applications to cryptography
and are rich combinatorial structures in their own right; until now, all SEDFs
have been in abelian groups. In this paper, we consider SEDFs in both abelian
and non-abelian groups. We characterize the order of groups possessing
admissible parameters for non-trivial SEDFs, develop non-existence and
existence results, several of which extend known results, and present the first
family of non-abelian SEDFs. We introduce the concept of equivalence for EDFs
and SEDFs, and begin the task of enumerating SEDFs. Complete results are
presented for all groups up to order $24$, underpinned by a computational
approach.


  Segre embedding was introduced by C. Segre (1863--1924) in his famous 1891
article \cite{segre}. The Segre embedding plays an important roles in algebraic
geometry as well as in differential geometry, mathematical physics, and coding
theory. In this article, we survey main results on Segre embedding in
differential geometry. Moreover, we also present recent differential geometric
results on maps and immersions which are constructed in ways similar to Segre
embedding.


  We derive the matrix elements of Coulomb interaction between states with
different number of electrons and holes in a semiconductor nanocrystal within
the 8-band $\mathbf{k}\cdot\mathbf{p}$ theory. These matrix elements are
responsible for multiple exciton generation which may contribute to the
enhancement of the efficiency of solar cells. Our calculations are performed
within the multi band envelope function formalism based on the states resulting
from diagonalization of the 8-band $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian. We
study in detail and compare two contributions to the inter-band Coulomb
coupling: the mesoscopic one, which involves only the envelope functions and
relies on band mixing, and the microscopic one, that relies on the Bloch parts
of the wave functions and is non-zero even between single- band states. We show
that these two contributions are of a similar order of magnitude. We study also
the statistical distribution of the magnitudes of the inter-band Coulomb matrix
elements and show that the overall coupling to remote states decays according
to a power law favorable for the convergence of numerical computations.


  We use recently introduced three-point dynamic susceptibilities to obtain an
experimental determination of the temperature evolution of the number of
molecules, N_corr, that are dynamically correlated during the structural
relaxation of supercooled liquids. We first discuss in detail the physical
content of three-point functions that relate the sensitivity of the averaged
two-time dynamics to external control parameters (such as temperature or
density), as well as their connection to the more standard four-point dynamic
susceptibility associated with dynamical heterogeneities. We then demonstrate
that these functions can be experimentally determined with a good precision. We
gather available data to obtain the temperature dependence of N_corr for a
large number of supercooled liquids over a wide range of relaxation timescales
from the glass transition up to the onset of slow dynamics. We find that N_corr
systematically grows when approaching the glass transition. It does so in a
modest manner close to the glass transition, which is consistent with an
activation-based picture of the dynamics in glassforming materials. For higher
temperatures, there appears to be a regime where N_corr behaves as a power-law
of the relaxation time. Finally, we find that the dynamic response to density,
while being smaller than the dynamic response to temperature, behaves
similarly, in agreement with theoretical expectations.


  We prove {\em sign equidistribution} of Legendre polynomials: the ratio
between the lengths of the regions in the interval $[-1, 1]$ where the Legendre
polynomial assumes positive versus negative values, converges to one as the
degree grows. The proof method also has application to the symmetry conjecture
for a basis of eigenfunctions in the sphere.


  In this paper, we study the well-posedness and regularity of non-autonomous
stochastic differential algebraic equations (SDAEs) with nonlinear, locally
Lipschitz and monotone (2) coefficients of the form (1). The main difficulty is
the fact that the operator A(.) is non-autonomous, i.~e. depends on t and the
matrix $A(t)$ is singular for all $t\in \left[0,T\right]$. Our interest is in
SDAE of index-1. This means that in order to solve the problem, we can
transform the initial SDAEs into an ordinary stochastic differential equation
with algebraic constraints. Under appropriate hypothesizes, the main result
establishes the existence and uniqueness of the solution in
$\mathcal{M}^p(\left[0, T\right], \mathbb{R}^n)$, $p\geq 2$, $p\in \mathbb{N}$.
Several strong estimations and regularity results are also provided. Note that,
in this paper, we use various techniques such as It\^o's lemma,
Burkholder-Davis-Gundy inequality, and Young inequality.


  In this paper, we compare the structural features of Ca modified Ba(Ti, Sn)O3
with that of its Ca-free counterpart to understand why the Ca-modified variant
of this lead-free piezoelectric gives a much higher piezoelectric response. We
found that in spite of the reduced spontaneous lattice strain, the polarization
of the Ca-modified variant is higher. We, therefore, demonstrate that the very
large piezoelectric response of (Ba, Ca)(Ti, Sn)O3 is associated with the
decoupling of the polarization and lattice strain by Ca-modification.


  The model of holographic dark energy in which dark energy interacts with dark
matter is investigated in this paper. In particular, we consider the
interacting holographic dark energy model in the context of a perturbed
universe, which was never investigated in the literature. To avoid the
large-scale instability problem in the interacting dark energy cosmology, we
employ the generalized version of the parameterized post-Friedmann approach to
treat the dark energy perturbations in the model. We use the current
observational data to constrain the model. Since the cosmological perturbations
are considered in the model, we can then employ the redshift-space distortions
(RSD) measurements to constrain the model, in addition to the use of the
measurements of expansion history, which was either never done in the
literature. We find that, for both the cases with $Q=\beta H\rho_{\rm c}$ and
$Q=\beta H_0\rho_{\rm c}$, the interacting holographic dark energy model is
more favored by the current data, compared to the holographic dark energy model
without interaction. It is also found that, with the help of the RSD data, a
positive coupling $\beta$ can be detected at the $2.95\sigma$ statistical
significance for the case of $Q=\beta H_0\rho_{\rm c}$.


  We investigate Gamma-cohomology of some commutative cooperation algebras E_*E
associated with certain periodic cohomology theories. For KU and E(1), the
Adams summand at a prime p, and for KO we show that Gamma-cohomology vanishes
above degree 1. As these cohomology groups are the obstruction groups in the
obstruction theory developed by Alan Robinson we deduce that these spectra
admit unique E infinity structures. As a consequence we obtain an E infinity
structure for the connective Adams summand. For the Johnson-Wilson spectrum
E(n) with n > 0 we establish the existence of a unique E infinity structure for
its I_n-adic completion.


  Differential cross sections and decay asymmetries for coherent $\phi$-meson
photoproduction from deuterons were measured for the first time at forward
angles using linearly polarized photons at $E_{\gamma}$= 1.5-2.4 GeV. This
reaction offers a unique way to directly access natural-parity Pomeron dynamics
and gluon exchange at low energies. The cross sections at zero degrees increase
with increasing photon energy. The decay asymmetries demonstrate a complete
dominance of natural-parity exchange processes, showing that isovector
unnatural-parity $\pi$-meson exchange is small. Nevertheless the deduced cross
sections of $\phi$-mesons from nucleons contributed by isoscalar t-channel
exchange processes are not well described by the conventional Pomeron model.


  We investigate what it means to apply the solution, proposed to the firewall
paradox by Harlow and Hayden, to the famous quantum paradoxes of Sch\"odinger's
Cat and Wigner's Friend if ones views these as posing a thermodynamic decoding
problem (as does Hawking radiation in the firewall paradox). The implications
might point to a relevance of the firewall paradox for the axiomatic and set
theoretic foundations underlying mathematics. We reconsider in this context the
results of Benioff on the foundational challenges posed by the randomness
postulate of quantum theory. A central point in our discussion is that one can
mathematically not naturally distinguish between computational complexity (as
central to the approach of Harlow and Hayden and further developed by Susskind)
and proof theoretic complexity (since they represent the same concept on a
Turing machine), with the latter being related to a finite bound on Kolmogorov
entropy (due to Chaitin incompleteness).


  6-dimensional superconformal field theories are exotic and fascinating. They
emerge from compactifications of F-theory on Calabi-Yau elliptic fibrations,
which grants them a rich array of dualities with various other formulations of
string and M-theory. In this thesis, we consider extended families of elliptic
fibrations, giving rise to 6d theories connected by Higgs transitions. These
families not only encompass the moduli space of a specific manifold but also
include other manifolds with different topologies.
  Our investigation focuses on rank 1 6D superconformal field theories from two
distinct angles. In Chapter 4, we employ modularity, which arises from the
holomorphic anomaly equations, to compute the topological string partition
function in terms of Jacobi modular forms. We also provide a prescription for
obtaining the topological partition function of a Higgsed theory from its
parent. Through this approach, we can explain numerous symmetry enhancements
that we observed in our study.
  On the other hand, in Chapter 5, we explore the 2D soliton of the 6D theory,
the non-critical string. The elliptic genus of this non-critical string
coincides with a part of the topological string partition function. By
carefully studying this non-critical string, we propose an ansatz for the
elliptic genera expressed in terms of characters of the associated current
algebras. We present compelling evidence supporting the validity of this ansatz
and unveil novel closed form expressions for the elliptic genera of these
non-critical strings.
  Through these investigations, we hope to shed light on the intriguing world
of 6D superconformal field theories and uncover new insights into their
remarkable properties and connections.


  We present a consistent model for the UV and supersoft X-ray emission from
the symbiotic nova SMC3 (=RX J0048.4-7332). Following the present picture of
symbiotic stars, the model consists of radiation from a hot star and an
emission nebula excited by that star. The observations were compared to
theoretical models in which the hot star's emission is calculated with the help
of hydrostatic and Wolf-Rayet-type non-LTE model atmospheres. Our analysis
clearly shows evidence for mass loss rates of several 10^{-6} Msolar/yr. The
minimum effective temperature compatible with both the observed UV and X-ray
flux is about 260000K, which is higher than in any other star analyzed with
sophisticated NLTE model atmospheres.
  Since the hydrostatic surface is hidden by the stellar wind no upper limit
for the temperature can be determined. However, we were able to determine the
total luminosity of a symbiotic nova with reasonable accuracy
L_SMC3=10^{4.05\pm 0.05} Lsun. This value is well below the Eddington limit
(approx. 50000~Lsun). In order to reproduce the observed energy distribution a
carbon-to-helium ratio >2 10^{-4} --- leading to an absorption edge at
0.39\,keV --- is necessary.


  The present PhD dissertation focuses on modern random access (RA) techniques.
In the first part an slot- and frame-asynchronous RA scheme adopting replicas,
successive interference cancellation and combining techniques is presented and
its performance analysed. The comparison of both slot-synchronous and
asynchronous RA at higher layer, follows. Next, the optimization procedure, for
slot-synchronous RA with irregular repetitions, is extended to the Rayleigh
block fading channel. Finally, random access with multiple receivers is
considered.


  The flavor vortex operator $V_\alpha$ is a local disorder operator defined by
coupling a two-dimensional $\mathcal{N}=(2,2)$ chiral multiplet to a
non-dynamical gauge field with vortex singularity of holonomy $2\pi\alpha$. We
show that it is related to the mirror-dual twisted chiral multiplet, with
bottom component $y$, as $V_\alpha=e^{-\alpha y}$.


  We describe a technique for probing the statistical properties of cosmic
magnetic fields based on radio polarimetry data. Second-order magnetic field
statistics like the power spectrum cannot always distinguish between magnetic
fields with essentially different spatial structure. Synchrotron polarimetry
naturally allows certain 4th-order magnetic field statistics to be inferred
from observational data, which lifts this degeneracy and can thereby help us
gain a better picture of the structure of the cosmic fields and test
theoretical scenarios describing magnetic turbulence. In this work we show that
a 4th-order correlator of physical interest, the tension-force spectrum, can be
recovered from the polarized synchrotron emission data. We develop an estimator
for this quantity based on polarized-emission observations in the
Faraday-rotation-free frequency regime. We consider two cases: a statistically
isotropic field distribution, and a statistically isotropic field superimposed
on a weak mean field. In both cases the tension force power spectrum is
measurable; in the latter case, the magnetic power spectrum may also be
obtainable. The method is exact in the idealized case of a homogeneous
relativistic-electron distribution that has a power-law energy spectrum with a
spectral index p=3, and assumes statistical isotropy of the turbulent field. We
carry out tests of our method using synthetic data generated from numerically
simulated magnetic fields. We show that the method is valid, that it is not
prohibitively sensitive to the value of the electron spectral index, and that
the observed tension-force spectrum allows one to distinguish between, e.g., a
randomly tangled magnetic field (a default assumption in many studies) and a
field organized in folded flux sheets or filaments.