  We demonstrate a precision frequency measurement using a phase-stabilized
120-km optical fiber link over a physical distance of 50 km. The transition
frequency of the 87Sr optical lattice clock at the University of Tokyo is
measured to be 429228004229874.1(2.4) Hz referenced to international atomic
time (TAI). The measured frequency agrees with results obtained in Boulder and
Paris at a 6*10^-16 fractional level, which matches the current best
evaluations of Cs primary frequency standards. The results demonstrate the
excellent functions of the intercity optical fibre link, and the great
potential of optical lattice clocks for use in the redefinition of the second.


  We derive stellar masses from SED fitting to rest-frame optical and UV fluxes
for 401 star-forming galaxies at z 4, 5, and 6 from Hubble-WFC3/IR observations
of the ERS combined with the deep GOODS-S Spitzer/IRAC data (and include a
previously-published z 7 sample). A mass-luminosity relation with strongly
luminosity-dependent M/Luv ratios is found for the largest sample (299
galaxies) at z 4. The relation M \propto L_{UV,1500}^(1.7+/-0.2) has a
well-determined intrinsic sample variance of 0.5 dex. This relation is also
consistent with the more limited samples at z 5-7. This z 4 mass-luminosity
relation, and the well-established faint UV luminosity functions at z 4-7, are
used to derive galaxy mass functions (MF) to masses M~10^8 at z 4-7. A bootstap
approach is used to derive the MFs to account for the large scatter in the
M--Luv relation and the luminosity function uncertainties, along with an
analytical crosscheck. The MFs are also corrected for the effects of
incompleteness. The incompleteness-corrected MFs are steeper than previously
found, with slopes \alpha_M-1.4 to -1.6 at low masses. These slopes are,
however, still substantially flatter than the MFs obtained from recent
hydrodynamical simulations. We use these MFs to estimate the stellar mass
density (SMD) of the universe to a fixed M_{UV,AB}<-18 as a function of
redshift and find a SMD growth \propto(1+z)^{-3.4 +/-0.8} from z 7 to z 4. We
also derive the SMD from the completeness-corrected MFs to a mass limit
M~10^{8} Msun. Such completeness-corrected MFs and the derived SMDs will be
particularly important for model comparisons as future MFs reach to lower
masses.


  In this paper, we describe the irreducible spherical functions of fundamental
$K$-types associated with the pair
$(G,K)=({\mathrm{SO}}(n+1),{\mathrm{SO}}(n))$ in terms of matrix hypergeometric
functions. The output of this description is that the irreducible spherical
functions of the same $K$-fundamental type are encoded in new examples of
classical sequences of matrix-valued orthogonal polynomials, of size $2$ and
$3$, with respect to a matrix-weight $W$ supported on $[0,1]$. Moreover, we
show that $W$ has a second order symmetric hypergeometric operator $D$.


  This work presents our ongoing research of unsupervised pretraining in neural
machine translation (NMT). In our method, we initialize the weights of the
encoder and decoder with two language models that are trained with monolingual
data and then fine-tune the model on parallel data using Elastic Weight
Consolidation (EWC) to avoid forgetting of the original language modeling
tasks. We compare the regularization by EWC with the previous work that focuses
on regularization by language modeling objectives. The positive result is that
using EWC with the decoder achieves BLEU scores similar to the previous work.
However, the model converges 2-3 times faster and does not require the original
unlabeled training data during the fine-tuning stage. In contrast, the
regularization using EWC is less effective if the original and new tasks are
not closely related. We show that initializing the bidirectional NMT encoder
with a left-to-right language model and forcing the model to remember the
original left-to-right language modeling task limits the learning capacity of
the encoder for the whole bidirectional context.


  A recently developed reduced activation ferritic/martensitic steel MNHS was
irradiated with 200keV He ions to a fluence of 1E21ions/m^2 at 450 celsius
degree and 1E20ions/m^2 at 300 celsius degree and 450 celsius degree,
respectively. The irradiation hardening of the steel was investigated by
nanoindentation measurements combined with transmission electron microscopy
(TEM) analysis. Dispersed barrier-hardening (DBH) model was applied to predict
the hardness increments based on TEM analysis. The predicted hardness
increments are consistent with the values obtained by nanoindentation tests. It
is found that dislocation loops and He bubbles are hard barriers against
dislocation motion and they are the main contributions to He
irradiation-induced hardening of MNHS steel. The obstacle strength of He
bubbles is stronger than the obstacle strength of dislocation loops.


  The recent catalog of spectral types of Galactic O-type stars by
Mai'z-Apella'niz et al. has been used to study the differences between the
frequencies of various subtypes of O-type stars in the field, in OB
associations and among runaway stars. At a high level of statistical
significance the data show that O-stars in clusters and associations have
earlier types (and hence presumably larger masses and/or younger ages) than
those that are situated in the general field. Furthermore it is found that the
distribution of spectral subtypes among runaway O-stars is indistinguishable
from that among field stars, and differs significantly from that of the O-type
stars that are situated in clusters and associations. The difference is in the
sense that runaway O-stars, on average, have later subtypes than do those that
are still located in clusters and associations.


  Recently, deep networks have achieved impressive semantic segmentation
performance, in particular thanks to their use of larger contextual
information. In this paper, we show that the resulting networks are sensitive
not only to global attacks, where perturbations affect the entire input image,
but also to indirect local attacks where perturbations are confined to a small
image region that does not overlap with the area that we aim to fool. To this
end, we introduce several indirect attack strategies, including adaptive local
attacks, aiming to find the best image location to perturb, and universal local
attacks. Furthermore, we propose attack detection techniques both for the
global image level and to obtain a pixel-wise localization of the fooled
regions. Our results are unsettling: Because they exploit a larger context,
more accurate semantic segmentation networks are more sensitive to indirect
local attacks.


  We present new radial velocities and photometry of the short-period Algol TT
Herculis. Previous attempts to model the light curves of the system have met
with limited success, primarily because of the lack of a reliable mass ratio.
Our spectroscopic observations are the first to result in radial velocities for
the secondary star, and thus provide a spectroscopic mass ratio. Simultaneous
analysis of the radial velocities and new photometry shows that the system is a
double contact binary, with a rapidly rotating primary that fills its limiting
lobe.


  We study two models having an infinite-disorder critical point --- the zero
temperature random transverse-field Ising model and the random contact process
--- on a star-like network composed of $M$ semi-infinite chains connected to a
common central site. By the strong disorder renormalization group method, the
scaling dimension $x_M$ of the local order parameter at the junction is
calculated. It is found to decrease rapidly with the number $M$ of arms, but
remains positive for any finite $M$. This means that, in contrast with the pure
transverse-field Ising model, where the transition becomes of first order for
$M>2$, it remains continuous in the disordered models, although, for not too
small $M$, it is hardly distinguishable from a discontinuous one owing to a
close-to-zero $x_M$. The scaling behavior of the order parameter in the
Griffiths-McCoy phase is also analyzed.


  This is a book to be published in 2020 by Cambridge University Press (Tracts
in Mathematics Series). It focuses on the Assouad dimension of sets and
measures in Euclidean space, as well as many variants on the Assouad dimension,
including the lower dimension and Assouad spectrum. It considers these notions
in the setting of fractal geometry and topics covered include: weak tangents,
self-similar sets, self-affine sets, Mandelbrot percolation, limit sets of
Kleinian groups, orthogonal projections, distance sets, and Kakeya sets. It
also considers applications of these ideas to other areas, including: embedding
theory, number theory, probability theory and functional analysis. It ends with
a list of open problems.


  Ordered blueprints are algebraic objects that generalize monoids and ordered
semirings, and $\mathbb{F}_1^{\pm}$-algebras are ordered blueprints that have
an element $\epsilon$ that acts as $-1$. In this work we introduce an analogue
of the exterior algebra for $\mathbb{F}_1^{\pm}$-algebras that provides a new
cryptomorphism for matroids. We also show how to recover the usual exterior
algebra if the $\mathbb{F}_1^{\pm}$-algebra comes from a ring, and the
Giansiracusa Grassmann algebra if the $\mathbb{F}_1^{\pm}$-algebra comes from
an idempotent semifield.


  NORD (Neural Operations Research & Development) is an open source distributed
deep learning architectural research framework, based on PyTorch, MPI and
Horovod. It aims to make research of deep architectures easier for experts of
different domains, in order to accelerate the process of finding better
architectures, as well as study the best architectures generated for different
datasets. Although currently under heavy development, the framework aims to
allow the easy implementation of different design and optimization method
families (optimization algorithms, meta-heuristics, reinforcement learning
etc.) as well as the fair comparison between them. Furthermore, due to the
computational resources required in order to optimize and evaluate network
architectures, it leverage the use of distributed computing, while aiming to
minimize the researcher's overhead required to implement it. Moreover, it
strives to make the creation of architectures more intuitive, by implementing
network descriptors, allowing to separately define the architecture's nodes and
connections. In this paper, we present the framework's current state of
development, while presenting its basic concepts, providing simple examples as
well as their experimental results.


  We complete the recalculation of the available two-loop expressions for the
reaction \gamma\gamma->\pi\pi in the framework of chiral perturbation theory.
Here, we present the results for charged pions. The cross section and the
values of the dipole polarizabilities agree very well with the earlier
calculation, provided the same set of low-energy constants (LECs) is used. With
updated values for the LECs at order p^4, we find for the dipole
polarizabilities (\alpha_1-\beta_1)_{\pi^\pm} = (5.7\pm 1.0) 10^{-4} fm^3,
which is in conflict with the experimental result recently reported by the MAMI
Collaboration.


  This paper studies the influence of perturbations of conjugate priors in
Bayesian inference. A perturbed prior is defined inside a larger family, local
mixture models, and the effect on posterior inference is studied. The
perturbation, in some sense, generalizes the linear perturbation studied in
\cite{Gustafson1996}. It is intuitive, naturally normalized and is flexible for
statistical applications. Both global and local sensitivity analyses are
considered. A geometric approach is employed for optimizing the sensitivity
direction function, the difference between posterior means and the divergence
function between posterior predictive models. All the sensitivity measure
functions are defined on a convex space with non-trivial boundary which is
shown to be a smooth manifold.


  The increased availability of data in recent years has led several authors to
ask whether it is possible to use data as a {\em computational} resource. That
is, if more data is available, beyond the sample complexity limit, is it
possible to use the extra examples to speed up the computation time required to
perform the learning task?
  We give the first positive answer to this question for a {\em natural
supervised learning problem} --- we consider agnostic PAC learning of
halfspaces over $3$-sparse vectors in $\{-1,1,0\}^n$. This class is
inefficiently learnable using $O\left(n/\epsilon^2\right)$ examples. Our main
contribution is a novel, non-cryptographic, methodology for establishing
computational-statistical gaps, which allows us to show that, under a widely
believed assumption that refuting random $\mathrm{3CNF}$ formulas is hard, it
is impossible to efficiently learn this class using only
$O\left(n/\epsilon^2\right)$ examples. We further show that under stronger
hardness assumptions, even $O\left(n^{1.499}/\epsilon^2\right)$ examples do not
suffice. On the other hand, we show a new algorithm that learns this class
efficiently using $\tilde{\Omega}\left(n^2/\epsilon^2\right)$ examples. This
formally establishes the tradeoff between sample and computational complexity
for a natural supervised learning problem.


  In this paper, we classify projective toric birational morphisms from
Gorenstein toric 3-folds onto the 3-dimensional affine space with relatively
ample anti-canonical divisors.


  Massive machine-type communications (mMTC) is one of the main three focus
areas in the 5th generation (5G) of mobile standards to enable connectivity of
a massive number of internet of things (IoT) devices with little or no human
intervention. In conventional human-type communications (HTC), due to the
limited number of available radio resources and orthogonal/non-overlapping
nature of existing resource allocation techniques, users need to compete for
connectivity through a random access (RA) process, which may turn into a
performance bottleneck in mMTC. In this context, non-orthogonal multiple access
(NOMA) has emerged as a potential technology that allows overlapping of
multiple users over a radio resource, thereby creating an opportunity to enable
more autonomous and grant-free communication, where devices can transmit data
whenever they need. The existing literature on NOMA schemes majorly considers
centralized scheduling based HTC, where users are already connected, and
various system parameters like spreading sequences, interleaving patterns,
power control, etc., are predefined. Contrary to HTC, mMTC traffic is different
with mostly uplink communication, small data size per device, diverse quality
of service, autonomous nature, and massive number of devices. Hence, the
signaling overhead and latency of centralized scheduling becomes a potential
performance bottleneck. To tackle this, grant-free access is needed, where mMTC
devices can autonomously transmit their data over randomly chosen radio
resources. This article, in contrast to existing surveys, comprehensively
discusses the recent advances in NOMA from a grant-free connectivity
perspective. Moreover, related practical challenges and future directions are
discussed.


  We consider M-theory compactification on Calabi-Yau threefolds. The recently
discovered connection between the BPS states of wrapped M2 branes and the
topological string amplitudes on the threefold is used both as a tool to
compute topological string amplitudes at higher genera as well as to unravel
the degeneracies and quantum numbers of BPS states. Moduli spaces of $k$-fold
symmetric products of the wrapped M2 brane play a crucial role. We also show
that the topological string partition function is the Calabi-Yau version of the
elliptic genus of the symmetric product of $K3$'s and use the macroscopic
entropy of spinning black holes in 5 dimensions to obtain new predictions for
the asymptotic growth of the topological string amplitudes at high genera.


  Let C be a locally convex subset of a negatively curved Riemannian manifold
M. We define the skinning measure on the outer unit normal bundle to C in M by
pulling back the Patterson-Sullivan measures at infinity, and give a finiteness
result of skinning measures, generalising the work of Oh and Shah, with
different methods. We prove that the skinning measures, when finite, of the
equidistant hypersurfaces to C equidistribute to the Bowen-Margulis measure on
the unit tangent bundle of M, assuming only that the Bowen-Margulis measure is
finite and mixing for the geodesic flow. Under additional assumptions on the
rate of mixing, we give a control on the rate of equidistribution.


  In this article, we explicitly compute in momentum space the three and
four-point correlation functions involving scalar and spinning operators in the
free bosonic and the free fermionic theory in three dimensions. We also
evaluate the five-point function of the scalar operator in the free bosonic
theory. We discuss techniques which are more efficient than the usual PV
reduction to evaluate one loop integrals. Our techniques can be easily
generalised to momentum space correlators of complicated spinning operators and
to higher point functions. The three dimensional fermionic theory has the
interesting feature that the scalar operator $\bar\psi\psi$ is odd under
parity. To account for this, we develop a parity odd basis which is useful to
write correlation functions involving spinning operators and an odd number of
$\bar\psi\psi$ operators. We further study higher spin (HS) equations in
momentum space which are algebraic in nature and hence simpler than their
position space counterparts. We use them to solve for three-point functions
involving spinning operators without invoking conformal invariance. However, at
the level of four-point functions, solving the HS equation requires additional
constraints that come from conformal invariance and we could only verify that
our explicit results solve the HS equation.


  The scattering effects are studied in nanometer-scaled double-gate MOSFET,
using Monte Carlo simulation. The non-equilibrium transport in the channel is
analyzed with the help of the spectroscopy of the number of scatterings
experienced by electrons. We show that the number of ballistic electrons at the
drain end, even in terms of flux, is not the only relevant characteristic of
ballistic transport. Then the drive current in the 15 nm-long channel
transistor generations should be very close to the value obtained in the
ballistic limit even if all electrons are not ballistic. Additionally, most
back-scattering events which deteriorates the ON current, take place in the
first half of the channel and in particular in the first low field region.
However, the contribution of the second half of the channel can not be
considered as negligible in any studied case i.e. for a channel length below 25
nm. Furthermore, the contribution of the second half of the channel tends to be
more important as the channel length is reduced. So, in ultra short channel
transistors, it becomes very difficult to extract a region of the channel which
itself determine the drive current Ion.


  We provide some variations on the Greene-Krammer's identity which involve
q-Catalan numbers. Our method reveals a curious analogy between these new
identities and some congruences modulo a prime.


  Fiducial and differential measurements of $W^+W^-$ production in events with
at least one hadronic jet are presented. These cross-section measurements are
sensitive to the properties of electroweak-boson self-interactions and provide
a test of perturbative quantum chromodynamics and the electroweak theory. The
analysis is performed using proton$-$proton collision data collected at
$\sqrt{s}=13~$TeV with the ATLAS experiment, corresponding to an integrated
luminosity of 139$~$fb$^{-1}$. Events are selected with exactly one oppositely
charged electron$-$muon pair and at least one hadronic jet with a transverse
momentum of $p_{\mathrm{T}}>30~$GeV and a pseudorapidity of $|\eta|<4.5$. After
subtracting the background contributions and correcting for detector effects,
the jet-inclusive $W^+W^-+\ge 1~$jet fiducial cross-section and $W^+W^-+$ jets
differential cross-sections with respect to several kinematic variables are
measured, thus probing a previously unexplored event topology at the LHC. These
measurements include leptonic quantities, such as the lepton transverse momenta
and the transverse mass of the $W^+W^-$ system, as well as jet-related
observables such as the leading jet transverse momentum and the jet
multiplicity. Limits on anomalous triple-gauge-boson couplings are obtained in
a phase space where interference between the Standard Model amplitude and the
anomalous amplitude is enhanced.


  Sampling-based kinodynamic motion planners (SKMPs) are powerful in finding
collision-free trajectories for high-dimensional systems under differential
constraints. Time-informed set (TIS) can provide the heuristic search domain to
accelerate their convergence to the time-optimal solution. However, existing
TIS approximation methods suffer from the curse of dimensionality,
computational burden, and limited system applicable scope, e.g., linear and
polynomial nonlinear systems. To overcome these problems, we propose a method
by leveraging deep learning technology, Koopman operator theory, and random set
theory. Specifically, we propose a Deep Invertible Koopman operator with
control U model named DIKU to predict states forward and backward over a long
horizon by modifying the auxiliary network with an invertible neural network. A
sampling-based approach, ASKU, performing reachability analysis for the DIKU is
developed to approximate the TIS of nonlinear control systems online.
Furthermore, we design an online time-informed SKMP using a direct sampling
technique to draw uniform random samples in the TIS. Simulation experiment
results demonstrate that our method outperforms other existing works,
approximating TIS in near real-time and achieving superior planning performance
in several time-optimal kinodynamic motion planning problems.


  Robots are becoming everyday devices, increasing their interaction with
humans. To make human-machine interaction more natural, cognitive features like
Visual Voice Activity Detection (VVAD), which can detect whether a person is
speaking or not, given visual input of a camera, need to be implemented. Neural
networks are state of the art for tasks in Image Processing, Time Series
Prediction, Natural Language Processing and other domains. Those Networks
require large quantities of labeled data. Currently there are not many datasets
for the task of VVAD. In this work we created a large scale dataset called the
VVAD-LRS3 dataset, derived by automatic annotations from the LRS3 dataset. The
VVAD-LRS3 dataset contains over 44K samples, over three times the next
competitive dataset (WildVVAD). We evaluate different baselines on four kinds
of features: facial and lip images, and facial and lip landmark features. With
a Convolutional Neural Network Long Short Term Memory (CNN LSTM) on facial
images an accuracy of 92% was reached on the test set. A study with humans
showed that they reach an accuracy of 87.93% on the test set.


  The prototypical diffuse-interface model that describes multi-component flows
is the Navier-Stokes Cahn-Hilliard model (NSCH). Over the last decades many
NSCH models have appeared that claim to describe the same physical phenomena,
yet are distinct from one another. In a recent article [M.F.P. ten Eikelder,
K.G. van der Zee, I. Akkerman, and D. Schillinger, Math. Mod. Meth. Appl. S.
33, pp 175-221, 2023.] we have established a unified framework of virtually all
NSCH models. The framework reveals that there is only a single consistent NSCH
model that naturally emanates from the underlying mixture theory. In the
current article we present, verify and validate this novel consistent NSCH
model by means of numerical simulation. To this purpose we discretize a
divergence-free velocity formulation of the NSCH model using
divergence-conforming isogeometric spaces. We compare computations of our
consistent model to results of existing models from literature. The predictive
capability of the numerical methodology is demonstrated via three-dimensional
computations of a rising bubble and the contraction of a liquid filament that
compare well with experimental data.


  This paper studies the Graph-Connected Clique-Partitioning Problem (GCCP), a
clustering optimization model in which units are characterized by both
individual and relational data. This problem, introduced by Benati et al.
(2017) under the name of Connected Partitioning Problem, shows that the
combination of the two data types improves the clustering quality in comparison
with other methodologies. Nevertheless, the resulting optimization problem is
difficult to solve; only small-sized instances can be solved exactly,
large-sized instances require the application of heuristic algorithms. In this
paper we improve the exact and the heuristic algorithms previously proposed.
Here, we provide a new Integer Linear Programming (ILP) formulation, that
solves larger instances, but at the cost of using an exponential number of
variables. In order to limit the number of variables necessary to calculate the
optimum, the new ILP formulation is solved implementing a branch-and-price
algorithm. The resulting pricing problem is itself a new combinatorial model:
the Maximum-weighted Graph-Connected Single-Clique problem (MGCSC), that we
solve testing various Mixed Integer Linear Programming (MILP) formulations and
proposing a new fast "random shrink" heuristic. In this way, we are able to
improve the previous algorithms: The branch-and-price method outperforms the
computational times of the previous MILP algorithms and the new random shrink
heuristic, when applied to GCCP, is both faster and more accurate than the
previous heuristic methods. Moreover, the combination of column generation and
random shrink is itself a new MILP-relaxed matheuristic that can be applied to
large instances too. Its main advantage is that all heuristic local optima are
combined together in a restricted MILP, consisting in the application of the
exact branch-and-price method but solving heuristically the pricing problem.


  We study the beta functions for the dimensionless couplings in quadratic
curvature gravity, and find that there is a simple argument to restrict the
possible form of the beta functions as derived from the counterterms at an
arbitrary loop. The relation to the recent different results on beta functions
is also commented on.


  This is a cornucopia of types of algebras with some of their properties from
the operadic point of view.


  Differential privacy (DP) quantifies privacy loss by analyzing noise injected
into output statistics. For non-trivial statistics, this noise is necessary to
ensure finite privacy loss. However, data curators frequently release
collections of statistics where some use DP mechanisms and others are released
as-is, i.e., without additional randomized noise. Consequently, DP alone cannot
characterize the privacy loss attributable to the entire collection of
releases. In this paper, we present a privacy formalism, $(\epsilon, \{
\Theta_z\}_{z \in \mathcal{Z}})$-Pufferfish ($\epsilon$-TP for short when $\{
\Theta_z\}_{z \in \mathcal{Z}}$ is implied), a collection of Pufferfish
mechanisms indexed by realizations of a random variable $Z$ representing public
information not protected with DP noise. First, we prove that this definition
has similar properties to DP. Next, we introduce mechanisms for releasing
partially private data (PPD) satisfying $\epsilon$-TP and prove their desirable
properties. We provide algorithms for sampling from the posterior of a
parameter given PPD. We then compare this inference approach to the alternative
where noisy statistics are deterministically combined with Z. We derive mild
conditions under which using our algorithms offers both theoretical and
computational improvements over this more common approach. Finally, we
demonstrate all the effects above on a case study on COVID-19 data.


  In quantum theory of the free Dirac field on spatially flat FLRW spacetimes
we introduce a new type of vacuum able to separate the positive and negative
frequencies in the rest frames. This is refereed as the rest frame vacuum
shoving that this differs from the adiabatic vacuum apart from the Minkowski
spacetime where these two vacua coincide.


  Quantum dot-superconductor arrays have emerged as a new and promising
material platform for realizing Kitaev chains with Majorana zero modes. So far,
experiments have implemented a two-site chain with limited protection. We
propose a protocol for scaling up the Kitaev chain that is accessible to
current experiments and optimizes the Majorana protection. To this end, we make
use of the fact that the relative sign of normal and superconducting hoppings
mediated by an Andreev bound state can be changed by electrostatic gates. In
this way, our method only relies on the use of individual electrostatic gates
on hybrid regions, quantum dots, and tunnel barriers, respectively, without the
need for individual magnetic flux control, greatly simplifying the device
design. Our work provides guidance for realizing a topologically protected
Kitaev chain, which is the building block of error-resilient topological
quantum computation.


  The unique feature of surface states in topological insulators is the
so-called "spin-momentum locking", which means that electron spin is oriented
along a fixed direction for a given momentum and forms a texture in the
momentum space. In this work, we study spin textures of two typical topological
insulators in Hg-Based Chalcogenides, namely HgTe and HgS, based on both the
first principles calculation and the eight band Kane model. We find opposite
helicities of spin textures between these two materials, originating from the
opposite signs of spin-orbit couplings. Furthermore, we reveal that different
mirror Chern numbers between HgTe and HgS characterize different topological
natures of the systems with opposite spin textures and guarantee the existence
of gapless interface states.


  The unit ball $B_p^n(\mathbb{R})$ of the finite-dimensional Schatten trace
class $\mathcal S_p^n$ consists of all real $n\times n$ matrices $A$ whose
singular values $s_1(A),\ldots,s_n(A)$ satisfy $s_1^p(A)+\ldots+s_n^p(A)\leq
1$, where $p>0$. Saint Raymond [Studia Math.\ 80, 63--75, 1984] showed that the
limit $$ \lim_{n\to\infty} n^{1/2 + 1/p} \big(\text{Vol}\,
B_p^n(\mathbb{R})\big)^{1/n^2} $$ exists in $(0,\infty)$ and provided both
lower and upper bounds. In this paper we determine the precise limiting
constant based on ideas from the theory of logarithmic potentials with external
fields. A similar result is obtained for complex Schatten balls. As an
application we compute the precise asymptotic volume ratio of the Schatten
$p$-balls, as $n\to\infty$, thereby extending Saint Raymond's estimate in the
case of the nuclear norm ($p=1$) to the full regime $1\leq p \leq \infty$ with
exact limiting behavior.


  A thin dark thread is observed in a UV/EUV solar jet in the 171A, 193A and
211A and partially in 304A. The dark thread appears to originate in the
chromosphere but its temperature does not appear to lie within the passbands of
the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory
(SDO). We therefore implement solar magnetoseismology to estimate the plasma
parameters of the dark thread. A propagating fast kink (transverse) wave is
observed to travel along the dark thread. The wave is tracked over a range of
~7000km by placing multiple slits along the axis of the dark thread. The phase
speed and amplitude of the wave are estimated and magnetoseismological theory
is employed to determine the plasma parameters. We are able to estimate the
plasma temperature, density gradient, magnetic field gradient and
sub-resolution expansion of the dark thread. The dark thread is found to be
cool, T~3x10^4$ with both strong density and magnetic field gradients. The
expansion of the flux tube along its length is ~300-400km.


  Though QCD Factorization(QCDF) could produce sufficiently large $B\to K\pi$
branching ratios close to experiments, the predicted direct CP asymmetry in
${\bar B}^{0}\to K^{+}\pi^{-}$ decay is however still quite below experiment,
even with a large negative phase in the annihilation term, according to
existing calculations. This suggests the presence of an additional strong phase
in the decay amplitude which could come from the long-distance final state
interactions(FSI) like charming penguin. In this paper, we show that, by adding
to the $B\to K\pi$ decay QCDF amplitude, a real part and an absorptive part
with a strength 10% and 30% of the penguin amplitude, respectively, we could
bring the
  $B\to K\pi$ branching ratios and the ${\bar B}^{0}\to K^{-}\pi^{+}$ CP
asymmetry close to the measured values. We also find that the color-allowed
electroweak penguin is appreciable and that from the QCDF electroweak-strong
penguin interference terms and the measured $B^{-}\to {\bar K}^{0}\pi^{-}$ we
obtain $(9.0\pm 0.3)\times 10^{-6}$ for the ${\bar B}^{0}\to {\bar
K}^{0}\pi^{0}$ branching ratio, a bit lower than experiment. Similarly, the
predicted value for $B^{-}\to K^{-}\pi^{0}$ in terms of the ${\bar B}^{0}\to
K^{-}\pi^{+}$ branching ratio agrees well with experiment. This suggests that
the measured value for ${\bar B}^{0}\to {\bar K}^{0}\pi^{0}$ in fact should be
lower than the current measured value.


  Explicit results for various quantum thermodynamic function (QTF) of a
charged magneto-oscillator coupled to a heat bath at arbitrary temperature are
demonstrated in this paper. Discernible expressions for different QTF in the
two limits of very low and very high temperatures are presented for three
popular heat bath models : Ohmic, single relaxation time and blackbody
radiation. The central result is that the effect of magnetic field turns out to
be important at low temperatures yet crucial at high temperatures. It is
observed that the dissipation parameter, $\gamma$, and the cyclotron frequency,
$\omega_c$, affect the decaying or rising behaviour of various QTF in just the
opposite way to each other at low temperatures. In the high temperature regime,
the effect of $\gamma$ is much pronounced than that of $\omega_c$.


  The nature of the QCD chiral phase transition in the limit of vanishing quark
masses has remained elusive for a long time, since it cannot be simulated
directly on the lattice and is strongly cutoff-dependent. We report on a
comprehensive ongoing study using unimproved staggered fermions with
$N_\text{f}\in[2,8]$ mass-degenerate flavours on $N_\tau\in\{4,6,8\}$ lattices,
in which we locate the chiral critical surface separating regions with
first-order transitions from crossover regions in the bare parameter space of
the lattice theory. Employing the fact that it terminates in a tricritical
line, this surface can be extrapolated to the chiral limit using tricritical
scaling with known exponents. Knowing the order of the transitions in the
lattice parameter space, conclusions for approaching the continuum chiral limit
in the proper order can be drawn. While a narrow first-order region cannot be
ruled out, we find initial evidence consistent with a second-order chiral
transition in all massless theories with $N_\text{f}\leq 6$, and possibly up to
the onset of the conformal window at $9\lesssim N_\text{f}^*\lesssim 12$. A
reanalysis of already published $\mathcal{O}(a)$-improved $N_\text{f}=3$ Wilson
data on $N_\tau\in[4,12]$ is also consistent with tricritical scaling, and the
associated change from first to second-order on the way to the continuum chiral
limit. We discuss a modified Columbia plot and a phase diagram for many-flavour
QCD that reflect these possible features.


  We study the magnetic, structural, and electronic properties of the recently
discovered iron- based superconductor BaFe2S3 based on density functional
theory with the generalized gradient approximation. The calculations show that
the magnetic alignment in which the spins are coupled ferromagnetically along
the rung and antiferromagnetically along the leg is the most stable in the
possible magnetic structure within an Fe-ladder and is further stabilized with
the periodicity char- acterized by the wave vector Q=(pi,pi,0), leading to the
experimentally observed magnetic ground state. The magnetic exchange
interaction between the Fe-ladders creates a tiny energy gap, whose size is in
excellent agreement with the experiments. Applied pressure suppresses the
energy gap and leads to an insulator-metal transition. Finally, we also discuss
what type of orbitals can play crucial roles on the magnetic and
insulator-metal transition.


  A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron
electronic structure within a uniform magnetic field in three dimensions is
presented. The one-electron system is used to demonstrate the utility of this
new methodology and is a first step in laying the foundation for further
development of many-electron atomic and molecular methodology. It is shown in
this manuscript how to effectively calculate all basis set integrals, which
includes the mixed Gaussian-Sinc integrals, with a fast and accurate method.
The Sinc basis is invariant to the choice of the position of the Coulomb
potential, as opposed to traditional grid based methods. This invariance
guarantees that the choice of the grids origin has no effect on the electronic
structure calculation. This is because the Coulomb potential is treated
properly in this methodology, as opposed to DVR methodologies. The off-diagonal
terms are sparse but very important around the Coulomb singularity. In general,
five to six significant digits of accuracy on all converged results without the
linear dependency problems of the Gaussian methodologies are achievable. This
methodology is applied to calculate the ground state energy of H atom,
$H_2^{+}$ ion and $H_3^{2+}$ ion in magnetic fields up to a magnetic field
strength of 2.35x$10^13$ G (10,000 au). From these calculations it is shown
that $H_3^{2+}$ ion is unstable without relativistic considerations.


  The photon emission from a non-equilibrium quark-gluon plasma (QGP) is
analyzed. We derive an integral equation that describes photon production
through quark-antiquark annihilation and quark bremsstrahlung. It includes
coherence between different scattering sites, also known as the
Landau-Pomeranchuk-Migdal effect. These leading-order processes are studied for
the first time together in an out-of-equilibrium field theoretical treatment
that enables the inclusion of viscous corrections to the calculation of
electromagnetic emission rates. In the special case of an isotropic, viscous,
plasma the integral equation only depends on three constants which capture the
non-equilibrium nature of the medium.


  We analyze the accretion properties of 21 low mass T Tauri stars using a
dataset of contemporaneous near ultraviolet (NUV) through optical observations
obtained with the Hubble Space Telescope Imaging Spectrograph (STIS) and the
ground based Small and Medium Aperture Research Telescope System (SMARTS), a
unique dataset because of the nearly simultaneous broad wavelength coverage.
Our dataset includes accreting T Tauri stars (CTTS) in Taurus, Chamaeleon I,
$\eta$ Chamaeleon and the TW Hydra Association. For each source we calculate
the accretion rate by fitting the NUV and optical excesses above the
photosphere, produced in the accretion shock, introducing multiple accretion
components characterized by a range in energy flux (or density) for the first
time. This treatment is motivated by models of the magnetospheric geometry and
accretion footprints, which predict that high density, low filling factor
accretion spots co-exist with low density, high filling factor spots. By
fitting the UV and optical spectra with multiple accretion components, we can
explain excesses which have been observed in the near infrared. Comparing our
estimates of the accretion rate to previous estimates, we find some
discrepancies; however, they may be accounted for when considering assumptions
for the amount of extinction and variability in optical spectra. Therefore, we
confirm many previous estimates of the accretion rate. Finally, we measure
emission line luminosities from the same spectra used for the accretion rate
estimates, to produce correlations between accretion indicators (H$\beta$, Ca
II K, C II] and Mg II) and accretion properties obtained simultaneously.


  To quantify how well natural language understanding models can capture
consistency in a general conversation, we introduce the DialoguE COntradiction
DEtection task (DECODE) and a new conversational dataset containing both
human-human and human-bot contradictory dialogues. We then compare a structured
utterance-based approach of using pre-trained Transformer models for
contradiction detection with the typical unstructured approach. Results reveal
that: (i) our newly collected dataset is notably more effective at providing
supervision for the dialogue contradiction detection task than existing NLI
data including those aimed to cover the dialogue domain; (ii) the structured
utterance-based approach is more robust and transferable on both analysis and
out-of-distribution dialogues than its unstructured counterpart. We also show
that our best contradiction detection model correlates well with human
judgments and further provide evidence for its usage in both automatically
evaluating and improving the consistency of state-of-the-art generative
chatbots.


  We design a receiver assembling several photomultipliers (PMTs) as an array
to increase the field of view (FOV) of the receiver and adapt to multiuser
situation over None-line-of-sight (NLOS) ultraviolet (UV) channels. Channel
estimation and signal detection have been investigated according to the space
division characteristics of the structure. Firstly, we adopt the balanced
structure on the pilot matrix, analyze the channel estimation mean square error
(MSE), and optimize the structure parameters. Then, with the estimated
parameters, an analytical threshold detection rule is proposed as a preliminary
work of multiuser detection. The detection rule can be optimized by analyzing
the separability of two users based on the Gaussian approximation of Poisson
weighted sum. To assess the effect of imperfect estimation, the sensitivity
analysis of channel estimation error on two-user signal detection is performed.
Moreover, we propose a successive elimination method for on-off keying (OOK)
modulated multiuser symbol detection based on the previous threshold detection
rule. A closed-form upper bound on the detection error rate is calculated,
which turns out to be a good approximation of that of multiuser
maximum-likelihood (ML) detection. The proposed successive elimination method
is twenty times faster than the ML detection with negligible detection error
rate degradation.


  We analyze the structure of DNA molecules of different organisms by using the
additive Markov chain approach. Transforming nucleotide sequences into binary
strings, we perform statistical analysis of the corresponding "texts". We
develop the theory of N-step additive binary stationary ergodic Markov chains
and analyze their differential entropy. Supposing that the correlations are
weak we express the conditional probability function of the chain by means of
the pair correlation function and represent the entropy as a functional of the
pair correlator. Since the model uses two point correlators instead of
probability of block occurring, it makes possible to calculate the entropy of
subsequences at much longer distances than with the use of the standard
methods. We utilize the obtained analytical result for numerical evaluation of
the entropy of coarse-grained DNA texts. We believe that the entropy study can
be used for biological classification of living species.


  We study a model for social influence in which the agents' opinion is a
continuous variable [G. Weisbuch et al., Complexity \textbf{7}, 2, 55 (2002)].
The convergent opinion adjustment process takes place as a result of random
binary encounters whenever the difference between agents' opinions is below a
given threshold. The inhomogeneity in the dynamics gives rise to a complex
steady state structure, which is also highly dependent on the threshold and on
the convergence parameter of the model.


  We have performed a comparative study of rubrene single-crystal field-effect
transistors fabricated using different materials as gate insulator. For all
materials, highly reproducible device characteristics are obtained. The
achieved reproducibility permits to observe that the mobility of the charge
carriers systematically decreases with increasing the dielectric constant of
the gate insulator, the decrease being proportional to (epsilon)-1. This
finding demonstrates that the mobility of carriers in organic single-crystal
field-effect transistors is an intrinsic property of the crystal/dielectric
interface and that it does not only depend on the specific molecule used.


  The moduli space of holomorphic fiber bundles ${\cal M}_n(\Si)$ over a
compact Riemann surface $\Si$ is considered.
  A formula for the regularised determinant and an other for the symplectic
form at trivial bundle are proposed.


  The epitaxial growth of complex oxides enables the production of high-quality
films, yet substrate choice is restricted to certain symmetry and lattice
parameters, thereby limiting the technological applications of epitaxial
oxides. In comparison, the development of free-standing oxide membranes gives
opportunities to create novel heterostructures by non-epitaxial stacking of
membranes, opening new possibilities for materials design. Here, we introduce a
method for writing, with atomic precision, ionically bonded crystalline
material across the gap between an oxide membrane and a carrier substrate. The
process involves a thermal pre-treatment, followed by localized exposure to the
raster scan of a scanning transmission electron microscopy (STEM) beam. STEM
imaging and electron energy-loss spectroscopy show that we achieve atomically
sharp interface reconstructions between a 30 nm-thick SrTiO${_3}$ membrane and
a niobium-doped SrTiO${_3}$(001)-oriented carrier substrate. These findings
indicate new strategies for fabricating synthetic heterostructures with novel
structural and electronic properties.


  The notion of holonomy $R$-matrices is introduced. It is shown how to define
invariants of tangles with flat connections in a principle $G$-bundle of the
complement of a tangle using holonomy $R$-matrices.


  Quantum inequalities are lower bounds for local averages of quantum
observables that have positive classical counterparts, such as the energy
density or the Wick square. We establish such inequalities in general (possibly
interacting) quantum field theories on Minkowski space, using nonperturbative
techniques. Our main tool is a rigorous version of the operator product
expansion.


  Superfluid-to-superfluid phase transitions in a Fermi-liquid leading to the
emergence of two-gap superfluid states have been studied.
  There are considered the systems of fermions of one and two (nuclear matter)
sorts. The self-consistent equations describing new two-gap superfluid states
have been obtained. These equations differ essentially from the equations of
the BCS theory. The solutions of the self-consistent equations corresponding to
one-gap and two-gap superfluid states have been found.


  In the context of weak-field metric-affine (i.e. Palatini) gravity near
Minkowski spacetime, we compute the particle spectra in the simultaneous
presence of all independent contractions quadratic in Ricci-type tensors. Apart
from the full metric-affine geometry, we study kinematic limits with vanishing
torsion (i.e. a symmetric connection) and vanishing non-metricity (i.e. a
metric connection, which is physically indistinguishable from Poincar\'e gauge
theory at the level of the particle spectrum). We present a detailed report on
how spin-parity projection operators can be used to derive systematically and
unambiguously the character of the propagating states. The unitarity
constraints derived from the requirements of tachyon- and ghost-freedom are
obtained. We show that, even in the presence of all Ricci-type operators, only
a narrow selection of viable theories emerges by a tuning.


  We study the collision of a brane with a black hole. Our aim is to explore
the topology changing process of perforation of a brane. The brane is described
as a field theoretical domain wall in the context of an axion-like model
consisting of a complex scalar effective field theory with approximate U(1)
symmetry. We simulate numerically the dynamics of the collision and illustrate
the transition from the configuration without a hole to the pierced one with
the aid of a phase diagram. The process of perforation is found to depend on
the collisional velocity, and, contrary to our expectation, we observe that
above a critical value of the velocity, the black hole has no chance to
perforate the wall. That is: high energy collisions do not assist piercing. We
also show that, only when the model parameters are fine-tuned so that the
energy scale of the string is very close to that of the domain wall, the
collision of the wall with the black hole has a possibility to provide a
mechanism to erase domain walls, if the hole expands. However, in such cases,
domain walls will form with many holes edged by a string and therefore
disappear eventually. Therefore this mechanism is unlikely to be a solution to
the cosmological domain wall problem, although it may cause some minor effects
on the evolution of a domain wall network.


  Beta-decay into broad resonances gives a distorted lineshape in the observed
energy spectrum. Part of the distortion arises from the phase space factor, but
we show that the beta-decay matrix element may also contribute. Based on a
schematic model for p-wave continuum neutron states it is argued that
beta-decay directly to the continuum should be considered as a possible
contributing mechanism in many decays close to the driplines. The signatures in
R-matrix fits for such decays directly to continuum states are discussed and
illustrated through an analysis of the beta-decay of $^8$B into $2^+$ states in
$^8$Be.


  Nematic phase is the most fundamental mesophase exhibited by most of the rod
shaped anisotropic liquid crystalline molecules. Nematics are orientationally
ordered fluids whose average orientation direction can be manipulated on
application of electric and magnetic fields. Carbon nanotube (CNT), a highly
shape anisotropic object can find numerous industrial application because of
its interesting electronic and mechanical properties. The self-organizing
properties of nematics can be used to align CNTs dispersed in them. We have
dispersed functionalized CNTs in nematic liquid crystal and carried out many
experimental studies. We will present results of electro-optic switching and
dielectric measurements on some CNT-LC dispersion. We have observed that
addition of functionalized CNTs in a liquid crystal (LC) has led to improvement
in the nematic ordering which is evidential from enhancement in dielectric
anisotropy (De) measurement. These results indicate that the anchoring energy
at alignment layers has been influenced by presence of FCNT in the LC host. The
anchoring enhancement can be attributed to p-p electron stacking between the
FCNT, LC and the alignment layer.


  In this work we numerically explore the quantum behavior of a classically
unstable relativistic Bose-Einstein condensate (BEC). The main goal is to study
the phenomenon of so-called quantum break time which amounts to a significant
departure from a semiclassical mean-field description. It has been suggested
previously that the existence of Lyapunov instability is crucial for a fast
quantum breaking, chaos, and scrambling. In order to clarify the issue, we work
within the 2-PI effective action formalism and introduce a simple and very
widely applicable dynamical criterion for identifying the timescale of
quantumbreaking. We indeed observe that the fast quantum break time is
controlled by the Lyapunov exponent of the unstable BEC.


  The observation of a non-classical rotation inertia (NCRI) fraction in bulk
solid 4He by M. Chan and E. Kim attracted significant interest as a possible
manifestation of supersolid state of matter. Despite numerous experimental and
theoretical studies inspired by this observation, an explicit explanation for
this phenomenon is still missing. Neutron scattering experiments on solid elium
may help to shed light on the physical grounds of NCRI and answer the question
on whether this phenomenon could be caused by Bose-Einstein Condensation. In
this paper we are going to discuss the results obtained in experiments
involving neutron scattering on solid 4He. Microscopic quantitative data such
as mean kinetic energy, mean square momentum and mean square displacement of
helium atoms as well as the lattice parameter have been obtained for the first
time for solid 4He in temperature range 70 mK - 500 mK. No change was seen in
the single atom kinetic energy within statistical error better than 1per cent
as well as change in the lattice parameter within 0.03 per cent. The mean
square displacement did not change in the region of expected supersolid
transition either. All these results suggest that the NCRI transition is quite
different from the superfluid transition in liquid 4He.


  For a (right and left) coherent ring $A$, we show that there exists a duality
between homotopy categories ${\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A^{{\rm
op}})$ and ${\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A)$. If $A=\Lambda$ is
an artin algebra of finite global dimension, this duality restricts to a
duality between their subcategories of acyclic complexes,
${\mathbb{K}}^{{\rm{b}}}_{\rm ac}({\rm mod}{\mbox{-}}\Lambda^{\rm op})$ and
${\mathbb{K}}^{{\rm{b}}}_{\rm ac}({\rm mod}{\mbox{-}}\Lambda).$ As a result, it
will be shown that, in this case, ${\mathbb{K}}_{\rm ac}^{{\rm{b}}}({\rm
mod}{\mbox{-}}\Lambda)$ admits a Serre functor and hence has Auslander-Reiten
triangles.


  We investigate the luminous X-ray sources in the Lockman Hole (LH) and the
Extended Groth Strip (EGS) detected at 24microns using MIPS and also with IRAC
on board Spitzer. We assemble optical/infrared spectral energy distributions
(SEDs) for 45 X-ray/24micron sources in the EGS and LH. Only about 1/4 of the
hard X-ray/24micron sources show pure type 1 AGN SEDs. More than half of the
X-ray/24micron sources have stellar-emission-dominated or obscured SEDs,
similar to those of local type 2 AGN and spiral/starburst galaxies. One-third
of the sources detected in hard X-rays do not have a 24micron counterpart. Two
such sources in the LH have SEDs resembling those of S0/elliptical galaxies.
The broad variety of SEDs in the optical-to-Spitzer bands of X-ray selected AGN
means that AGN selected according to the behavior in the optical/infrared will
have to be supplemented by other kinds of data (e.g., X-ray) to produce
unbiased samples of AGN.


  Terahertz (THz) radiation is a powerful tool with widespread applications
ranging from imaging, sensing, and broadband communications to spectroscopy and
nonlinear control of materials. Future progress in THz technology depends on
the development of efficient, structurally simple THz emitters that can be
implemented in advanced miniaturized devices. Here we show how the natural
electronic anisotropy of layered conducting transition metal oxides enables the
generation of intense terahertz radiation via the transverse thermoelectric
effect. In thin films grown on offcut substrates, femtosecond laser pulses
generate ultrafast out-of-plane temperature gradients, which in turn launch
in-plane thermoelectric currents, thus allowing efficient emission of the
resulting THz field out of the film structure. We demonstrate this scheme in
experiments on thin films of the layered metals PdCoO2 and La1.84Sr0.16CuO4,
and present model calculations that elucidate the influence of the material
parameters on the intensity and spectral characteristics of the emitted THz
field. Due to its simplicity, the method opens up a promising avenue for the
development of highly versatile THz sources and integrable emitter elements.


  Despite the striking success of general protein folding models such as
AlphaFold2(AF2, Jumper et al. (2021)), the accurate computational modeling of
antibody-antigen complexes remains a challenging task. In this paper, we first
analyze AF2's primary loss function, known as the Frame Aligned Point Error
(FAPE), and raise a previously overlooked issue that FAPE tends to face
gradient vanishing problem on high-rotational-error targets. To address this
fundamental limitation, we propose a novel geodesic loss called Frame Aligned
Frame Error (FAFE, denoted as F2E to distinguish from FAPE), which enables the
model to better optimize both the rotational and translational errors between
two frames. We then prove that F2E can be reformulated as a group-aware
geodesic loss, which translates the optimization of the residue-to-residue
error to optimizing group-to-group geodesic frame distance. By fine-tuning AF2
with our proposed new loss function, we attain a correct rate of 52.3\% (DockQ
$>$ 0.23) on an evaluation set and 43.8\% correct rate on a subset with low
homology, with substantial improvement over AF2 by 182\% and 100\%
respectively.


  Optically levitated rotors are prime candidates for torque sensors whose
precision is limited by the fluctuationsof the rotation frequency. In this work
we investigate an optically levitated rotor at its fundamental thermal limitof
frequency stability, where rotation-frequency fluctuations arise solely due to
coupling to the thermal bath.


  We discuss time complexity of The Conjugacy Problem in HNN-extensions of
groups, in particular, in Miller's groups. We show that for "almost all", in
some explicit sense, elements, the Conjugacy Problem is decidable in cubic
time. It is worth noting that the Conjugacy Problem in a Miller group may have
be undecidable. Our results show that "hard" instances of the problem comprise
a negligibly small part of the group.


  We review critically the concepts and the applications of Cayley Trees and
Bethe Lattices in statistical mechanics in a tentative effort to remove
widespread misuse of these simple, but yet important - and different - ideal
graphs. We illustrate, in particular, two rigorous techniques to deal with
Bethe Lattices, based respectively on self-similarity and on the Kolmogorov
consistency theorem, linking the latter with the Cavity and Belief Propagation
methods, more known to the physics community.


  We continue the study of the d=2,4,6 pure-spinor superstring models
introduced in [1]. By explicitly solving the pure-spinor constraint we show
that these theories have vanishing central charge and work out the (covariant)
current algebra for the Lorentz currents. We argue that these super-Poincare
covariant models may be thought of as compactifications of the superstring on
CY_{4,3,2}, and take some steps toward making this precise by constructing a
map to the RNS superstring variables. We also discuss the relation to the so
called hybrid superstrings, which describe the same type of compactifications.


  For an operator $T$ in the class ${\mathrm B}_n(\Omega)$, introduced in
\cite{CD}, the simultaneous unitary equivalence class of the curvature and the
covariant derivatives up to a certain order of the corresponding bundle $E_T$
determine the unitary equivalence class of the operator $T$. In the paper
\cite{CD2}, the authors ask if there exists some pair of inequivalent oprators
$T_1$ and $T_2$ for which the simultaneous unitary equivalence class of the
curvature along with all the covariant derivatives coincide except for the
derivative of the highest order. Here we show that some of the covariant
derivatives are necessary to determine the unitary equivalence class of the
operators in ${\mathrm B}_n(\Omega)$. Our examples consist of homogeneous
operators. For homogeneous operators, the simultaneous unitary equivalence
class of the curvature and all its covariant derivatives are determined from
the simultaneous unitary equivalence class of these at 0. This shows that it is
enough to calculate all the invariants and compare them at just one point, say
0. These calculations are then carried out in number of examples.


  This paper provides a comprehensive examination of a Brazilian corporate tax
reform targeted at the sector and product level. Difference-in-differences
estimates instrumented by sector eligibility show that a 20 percentage point
cut on payroll tax rates caused a 9% employment increase at the firm level,
mostly driven by small firms. This expansion is not driven by formalization of
existing workers, and it is explained by reduction on separations rather than
additional hires. In terms of earnings, there is a significant 4% earnings
increase in the long run, which is concentrated at leadership positions. The
unequal pass-through worsen within-firm wage inequality. I exploit the
exogenous variation on labor cost to document substantial labor market power in
Brazil, where wages are marked down by 36%. Consistent with the empirical
findings, I develop a model of factor demand with imperfect competition in the
goods and labor market to shed light on the mechanism through which imperfect
competition drives corporate tax incidence. The model is identified by the
reduced form elasticities, and allows me to structurally estimate the
capital-labor elasticity of substitution, which differs from the benchmark case
of perfect competition.


  The status of RHIC theory and phenomenology is reviewed with an emphasis on
the indications for the creation of a new deconfined state of matter. The
critical role of high energy nuclear physics in the development of theoretical
tools that address various aspects of the QCD many body dynamics is
highlighted. The perspectives for studying nuclear matter under even more
extreme conditions at the LHC and the overlap with high energy physics is
discussed.


  After Mayers (1996, 2001) gave a proof of the security of the
Bennett-Brassard 1984 (BB84) quantum key distribution protocol, Shor and
Preskill (2000) made a remarkable observation that a Calderbank-Shor-Steane
(CSS) code had been implicitly used in the BB84 protocol, and suggested its
security could be proven by bounding the fidelity, say F(n), of the
incorporated CSS code of length n in the form 1-F(n) <= exp[-n E+o(n)] for some
positive number E. This work presents such a number E=E(R) as a function of the
rate of a code R, and a threshold R' such that E(R)>0 whenever R < R', which is
larger than the achievable rate based on the Gilbert-Varshamov bound that is
essentially due to Shor and Preskill (2000). The codes in the present work are
robust against fluctuations of channel parameters, which fact is needed to
establish the security rigorously and was not proved for rates above the
Gilbert-Varshamov rate before in the literature. As a byproduct, the security
of a modified BB84 protocol against any joint (coherent) attacks is proved
quantitatively.


  We consider a pair of isoperimetric problems arising in physics. The first
concerns a Schr\"odinger operator in $L^2(\mathbb{R}^2)$ with an attractive
interaction supported on a closed curve $\Gamma$, formally given by
$-\Delta-\alpha \delta(x-\Gamma)$; we ask which curve of a given length
maximizes the ground state energy. In the second problem we have a loop-shaped
thread $\Gamma$ in $\mathbb{R}^3$, homogeneously charged but not conducting,
and we ask about the (renormalized) potential-energy minimizer. Both problems
reduce to purely geometric questions about inequalities for mean values of
chords of $\Gamma$. We prove an isoperimetric theorem for $p$-means of chords
of curves when $p \leq 2$, which implies in particular that the global extrema
for the physical problems are always attained when $\Gamma$ is a circle. The
article finishes with a discussion of the $p$--means of chords when $p > 2$.


  One of the important unknowns of current cosmology concerns the effects of
the large scale distribution of matter on the formation and evolution of dark
matter haloes and galaxies. One main difficulty in answering this question lies
in the absence of a robust and natural way of identifying the large scale
environments and their characteristics. This work summarizes the NEXUS+
formalism which extends and improves our multiscale scale-space MMF method. The
new algorithm is very successful in tracing the Cosmic Web components, mainly
due to its novel filtering of the density in logarithmic space. The method, due
to its multiscale and hierarchical character, has the advantage of detecting
all the cosmic structures, either prominent or tenuous, without preference for
a certain size or shape. The resulting filamentary and wall networks can easily
be characterized by their direction, thickness, mass density and density
profile. These additional environmental properties allows to us to investigate
not only the effect of environment on haloes, but also how it correlates with
the environment characteristics.


  We analyze potential violations of causality in Unruh DeWitt-type detector
models in relativistic quantum information. We proceed by first studying the
relation between faster-than-light signaling and the causal factorization of
the dynamics for multiple detector-field interactions. We show in what way
spatially extended non-relativistic detector models predict superluminal
propagation of the field's initial conditions. We draw parallels between this
characteristic of detector models, stemming from their non-relativistic
dynamics, and Sorkin's "impossible measurements on quantum fields"
arXiv:gr-qc/9302018. Based on these features, we discuss the validity of
measurements in QFT when performed with non-relativistic particle detectors.


  Recently there has been an intense effort to understand measurement induced
transitions, but we still lack a good understanding of non-Markovian effects on
these phenomena. To that end, we consider two coupled chains of free fermions,
one acting as the system of interest, and one as a bath. The bath chain is
subject to Markovian measurements, resulting in an effective non-Markovian
dissipative dynamics acting on the system chain which is still amenable to
numerical studies in terms of quantum trajectories. Within this setting, we
study the entanglement within the system chain, and use it to characterize the
phase diagram depending on the ladder hopping parameters and on the measurement
probability. For the case of pure state evolution, the system is in an area law
phase when the internal hopping of the bath chain is small, while a non-area
law phase appears when the dynamics of the bath is fast. The non-area law
exhibits a logarithmic scaling of the entropy compatible with a conformal
phase, but also displays linear corrections for the finite system sizes we can
study. For the case of mixed state evolution, we instead observe regions with
both area, and non-area scaling of the entanglement negativity. We quantify the
non-Markovianity of the system chain dynamics and find that for the regimes of
parameters we study, a stronger non-Markovianity is associated to a larger
entanglement within the system.


  Those experiencing strokes, traumatic brain injuries, and drug complications
can often end up hospitalized and diagnosed with coma or locked-in syndrome.
Such mental impediments can permanently alter the neurological pathways in work
and significantly decrease the quality of life (QoL). It is critical to
translate brain signals into images to gain a deeper understanding of the
thoughts of a comatose patient. Traditionally, brain signals collected by an
EEG could only be translated into text, but with the novel method of an
open-source model available on GitHub, DreamDiffusion can be used to convert
brain waves into images directly. DreamDiffusion works by extracting features
from EEG signals and then using the features to create images through
StableDiffusion. Upon this, we made further improvements that could make
StableDiffusion the forerunner technology in waves to media translation. In our
study, we begin by modifying the existing DreamDiffusion codebase so that it
does not require any prior setup, avoiding any confusing steps needed to run
the model from GitHub. For many researchers, the incomplete setup process,
errors in the existing code, and a lack of directions made it nearly impossible
to run, not even considering the model's performance. We brought the code into
Google Colab so users could run and evaluate problems cell-by-cell, eliminating
the specific file and repository dependencies. We also provided the original
training data file so users do not need to purchase the necessary computing
power to train the model from the given dataset. The second change is utilizing
the mutability of the code and optimizing the model so it can be used to
generate images from other given inputs, such as sleep data. Additionally, the
affordability of EEG technology allows for global dissemination and creates the
opportunity for those who want to work on the shared DreamDiffusion model.


  By fibering the duality between the $E_{8}\times E_{8}$ heterotic string on
$T^{3}$ and M-theory on K3, we study heterotic duals of M-theory compactified
on $G_{2}$ orbifolds of the form $T^{7}/\mathbb{Z}_{2}^{3}$. While the
heterotic compactification space is straightforward, the description of the
gauge bundle is subtle, involving the physics of point-like instantons on
orbifold singularities. By comparing the gauge groups of the dual theories, we
deduce behavior of a "half-$G_{2}$" limit, which is the M-theory analog of the
stable degeneration limit of F-theory. The heterotic backgrounds exhibit
point-like instantons that are localized on pairs of orbifold loci, similar to
the "gauge-locking" phenomenon seen in Ho\v{r}ava-Witten compactifications. In
this way, the geometry of the $G_{2}$ orbifold is translated to bundle data in
the heterotic background. While the instanton configuration looks surprising
from the perspective of the $E_{8}\times E_{8}$ heterotic string, it may be
understood as T-dual $\text{Spin}(32)/\mathbb{Z}_{2}$ instantons along with
winding shifts originating in a dual Type I compactification.


  The melting-like transition in sodium clusters Na_N, with N=55, 92, and 142
is studied by using constant-energy molecular dynamics simulations. An
orbital-free version of the Car-Parrinello technique is used which scales
linearly with system size allowing investigation of the thermal behaviour of
large clusters. The ground state isomer of Na_142 (an uncomplete three-shell
icosahedron) melts in two steps: the first one (at approx. 240 K) is
characterized by the high mobility of the atoms located on the cluster surface;
the second, homogeneous melting (at approx. 270 K), involves diffusive motion
of all the atoms across the cluster. For the case of Na_92, the icosahedral
structure has a larger number of surface vacancies, and melts in two well
separated steps, surface melting at approx. 130 K and homogeneous melting at
approx. 240 K. Na_55, a complete two-shell icosahedron, melts in a single stage
at approx. 190 K. Our results on homogeneous melting for Na_142 and Na_92 are
in excellent agreement with recent experimental determinations of melting
temperatures and latent heats. However, the experimentally observed enhancement
of the melting temperature around N=55 is not reproduced by the calculations.


  The derived category $D[C,V]$ of the Grothendieck category of enriched
functors $[C,V]$, where $V$ is a closed symmetric monoidal Grothendieck
category and $C$ is a small $V$-category, is studied. We prove that if the
derived category $D(V)$ of $V$ is a compactly generated triangulated category
with certain reasonable assumptions on compact generators or $K$-injective
resolutions, then the derived category $D[C,V]$ is also compactly generated
triangulated. Moreover, an explicit description of these generators is given.


  A new two-dimensional model for blood flows in arteries with arbitrary cross
sections is derived. The model consists of a system of balance laws for
conservation of mass and balance of momentum in the axial and angular
directions. The equations are derived by applying asymptotic analysis to the
incompressible Navier-Stokes equations in narrow, large vessels and integrating
in the radial direction in each cross section. The main properties of the
system are discussed and a positivity-preserving well-balanced central-upwind
scheme is presented. The merits of the scheme will be tested in a variety of
scenarios. In particular, numerical results of simulations using an idealized
aorta model are shown. We analyze the time evolution of the blood flow under
different initial conditions such as perturbations to steady states consisting
of a bulging in the vessel's wall. We consider different situations given by
distinct variations in the vessel's elasticity.


  This paper proposes the algorithm NOWPAC (Nonlinear Optimization With
Path-Augmented Constraints) for nonlinear constrained derivative-free
optimization. The algorithm uses a trust region framework based on fully linear
models for the objective function and the constraints. A new
constraint-handling scheme based on an inner boundary path allows for the
computation of feasible trial steps using models for the constraints. We prove
that the iterates computed by NOWPAC converge to a first-order critical point.
We also discuss the convergence of NOWPAC in situations where evaluations of
the objective function or the constraints are inexact, e.g., corrupted by
numerical errors. We determine a rate of decay that the magnitude of these
numerical errors must satisfy, while approaching the critical point, to
guarantee convergence. In settings where adjusting the accuracy of the
objective or constraint evaluations is not possible, as is often the case in
practical applications, we introduce an error indicator to detect these regimes
and prevent deterioration of the optimization results.


  We develop a convex integration scheme for constructing nonunique weak
solutions to the hydrostatic Euler equations (also known as the inviscid
primitive equations of oceanic and atmospheric dynamics) in both two and three
dimensions. We also develop such a scheme for the construction of nonunique
weak solutions to the three-dimensional viscous primitive equations, as well as
the two-dimensional Prandtl equations.
  While in [D.W. Boutros, S. Markfelder and E.S. Titi, Calc. Var. Partial
Differential Equations, 62 (2023), 219] the classical notion of weak solution
to the hydrostatic Euler equations was generalised, we introduce here a further
generalisation. For such generalised weak solutions we show the existence and
nonuniqueness for a large class of initial data. Moreover, we construct
infinitely many examples of generalised weak solutions which do not conserve
energy. The barotropic and baroclinic modes of solutions to the hydrostatic
Euler equations (which are the average and the fluctuation of the horizontal
velocity in the $z$-coordinate, respectively) that are constructed have
different regularities.


  Mueller matrices provide a complete description of a medium's response to
excitation by polarized light, and their characterization is important across a
broad range of applications from ellipsometry in material science to
polarimetry in biochemistry, medicine and astronomy. Here we introduce
single-shot Mueller matrix polarimetry based on generalized measurements
performed with a Poincar\'e beam. We determine the Mueller matrix of a
homogeneous medium with unknown optical activity by detecting its optical
response to a Poincar\'e beam, which across its profile contains all
polarization states, and analyze the resulting polarization pattern in terms of
four generalized measurements, which are implemented as a path-displaced Sagnac
interferometer. We illustrate the working of our Mueller matrix polarimetry on
the example of tilted and rotated wave plates and find excellent agreement with
predictions as well as alternative Stokes measurements. After initial
calibration, the alignment of the device stays stable for up to 8 hours,
promising suitability for the dynamic characterization of Mueller matrices that
change in time.


  Although many methods have been designed for ranking universities, there is
no suitable system that focuses on the ranking of countries based on the
performance of their universities. The overall ranking of the universities in a
region can indicate the growth of interests in science among the people of that
land. This paper introduces a novel ranking mechanism based on the rankings of
universities. Firstly, we introduce and discuss two new rankings of countries,
based on the rank of their universities. Secondly, we create rankings of
countries according to the selected method, based on the top 12000 universities
in webometrics.info (January 2012) and compare rankings of countries in 4
editions (January 2012 to July 2013). Firstly, we introduce two new methods of
ranking countries based on their university rankings, Weighted Ranking (WR) and
Average Ranking (AR). Secondly, we discuss how the introduced ranking systems,
perform in ranking countries based on the two years of data. Thirdly, we choose
QS (http://www.topuniversities.com) and webometrics.info as two different
classification systems for comparing rankings of countries, based on the top
500 universities in these rankings. Results indicate that the methodology can
be used to show the quality of the whole universities of each country used to
compare rankings of countries in practice compare to other countries in the
world.


  A smooth spatial disturbance of the Fermi surface in a Fermi gas inevitably
becomes sharp. This phenomenon, called {\it the gradient catastrophe}, causes
the breakdown of a Fermi sea to disconnected parts with multiple Fermi points.
We study how the gradient catastrophe effects probing the Fermi system via a
Fermi edge singularity measurement. We show that the gradient catastrophe
transforms the single-peaked Fermi-edge singularity of the tunneling (or
absorption) spectrum to a set of multiple asymmetric singular resonances. Also
we gave a mathematical formulation of FES as a matrix Riemann-Hilbert problem.


  A survey is presented on the current status of 3D nucleon tomography. Several
research frontiers are addressed that dominate modern physics from theory to
current and future experiments. We have now a much more detailed spatial image
of the nucleon thanks to various theoretical concepts and methods to describe
its charge distribution and spin decomposition which are highlighted here. The
progress of lattice computations of these quantities is reported and the
prospects of what we can come to expect in the near future are discussed.
Multi-dimensional maps of the nucleon's partonic structure appear now within
reach of forthcoming experiments.


  We consider the effective conformal field theory with symmetry W-infinity x
W-infinity that describes the thermodynamic limit of the Calogero-Sutherland
model. In the repulsive regime of the free fermion formulation, we identify an
attractive interaction between opposite moving particle-hole pairs that
dominates the short distance behavior and that is proposed as responsible for
the destabilization of the ground state, leading to a new one of bosonic
nature. The process is described by a Bogoliubov transformation of the free
fermion bilinear operators into bosonic ones, preserving the form of the
W-infinity algebra but decoupling the opposite chirality terms in the
hamiltonian, as expected in the low energy limit. In coordinate space this
interaction has a short range component that arises due to the quantum
regularization of the theory. The described dynamical process may be considered
as a mechanism of the emergence of the known charge and quantum statistics
fractionalization of the low lying excitations of the theory, as predicted in
both first and second quantization studies.


  We study the properties of the Green's functions of the fermions in the
extremal charged dilatonic black hole proposed by Gubser and Rocha [Phys. Rev.
D \textbf{81}, 046001 (2010)]. We find that many properties seem to be in
agreement with that of Fermi liquid. Especially, the dispersion relation is
linear. It is very different from that found in the extremal
Reissner-Nordstr$\ddot{o}$m (RN) black hole for massless fermion, which is
obviously non-Fermi liquid due to a nonlinear dispersion relation. However, for
another scaling behavior of the height of $ImG_{11}$ at the maximum, the
scaling exponent is not one, which is at odds with that found in the RN black
hole.


  We investigate modified steepest descent methods coupled with a loping
Kaczmarz strategy for obtaining stable solutions of nonlinear systems of
ill-posed operator equations. We show that the proposed method is a convergent
regularization method. Numerical tests are presented for a linear problem
related to photoacoustic tomography and a non-linear problem related to the
testing of semiconductor devices.


  Mechanical Properties of Ni-Ti-Nb alloys with these conditions of
cold-drawing, non-vacuum heat treatment and vacuum heat treatment were measured
at low temperature, and Mechanical Properties of Ni47Ti44Nb9 alloys of
restricting recover was compared with the one of alloys of non-restricting
recover, and these rules of the mechanical performance between them was
analyzed. Experiment indicates that, mechanical Properties of vacuum heat
treatment's alloys was more excellent than the other two (non-vacuum heat
treatment and cold-drawing), and the stress curves of alloys of restricting
recover haven't the evident yield band, and the stress of alloys of restricting
recover was higher than the ones of alloys of non-restricting recover, but the
stress of alloys of restricting recover was lower than the ones of alloys of
non-restricting recover.


  In this paper, we propose and analyse a family of generalised stochastic
composite mirror descent algorithms. With adaptive step sizes, the proposed
algorithms converge without requiring prior knowledge of the problem. Combined
with an entropy-like update-generating function, these algorithms perform
gradient descent in the space equipped with the maximum norm, which allows us
to exploit the low-dimensional structure of the decision sets for
high-dimensional problems. Together with a sampling method based on the
Rademacher distribution and variance reduction techniques, the proposed
algorithms guarantee a logarithmic complexity dependence on dimensionality for
zeroth-order optimisation problems.


  We predict that an interplay between isotropic and anisotropic exchange
interactions in a honeycomb lattice structure can lead to topological edge
conduction when the anisotropic interaction is at least twice the strength of
the isotropic interaction. For materials like Na$_2$IrO$_3$, such a strong
anisotropic exchange interaction simultaneously induces a zigzag type of
antiferromagnetic order that breaks the time-reversal symmetry of the
topological edge conductor. We show that the electronic transport in such
topological conductors will exhibit a quantized Hall conductance without any
external magnetic field when the Fermi energy lies within a particular energy
range.


  Cloud computing has become the leading paradigm for deploying large-scale
infrastructures and running big data applications, due to its capacity of
achieving economies of scale. In this work, we focus on one of the most
prominent advantages of cloud computing, namely the on-demand resource
provisioning, which is commonly referred to as elasticity. Although a lot of
effort has been invested in developing systems and mechanisms that enable
elasticity, the elasticity decision policies tend to be designed without
guaranteeing or quantifying the quality of their operation. This work aims to
make the development of elasticity policies more formalized and dependable. We
make two distinct contributions. First, we propose an extensible approach to
enforcing elasticity through the dynamic instantiation and online quantitative
verification of Markov Decision Processes (MDP) using probabilistic model
checking. Second, we propose concrete elasticity models and related elasticity
policies. We evaluate our decision policies using both real and synthetic
datasets in clusters of NoSQL databases. According to the experimental results,
our approach improves upon the state-of-the-art in significantly increasing
user-defined utility values and decreasing user-defined threshold violations.


  The first motivation of our paper is to explore further the idea that, in
risk control problems, it may be profitable to base decisions both on the
position of the underlying process Xt and on its supremum Xt := sup
0$\le$s$\le$t Xs. Strongly connected to Azema-Yor/generalized
draw-down/trailing stop time (see [AY79]), this framework provides a natural
unification of draw-down and classic first passage times. We illustrate here
the potential of this unified framework by solving a variation of the De
Finetti problem of maximizing expected discounted cumulative
dividends/consumption gained under a barrier policy, until an optimally chosen
Azema-Yor time, with a general spectrally negative Markov model. While
previously studied cases of this problem [APP07, SLG84, AS98, AVZ17, AH18,
WZ18] assumed either L{\'e}vy or diffusion models, and the draw-down function
to be fixed, we describe, for a general spectrally negative Markov model, not
only the optimal barrier but also the optimal draw-down function. This is
achieved by solving a variational problem tackled by Pontryaghins maximum
principle. As a by-product we show that in the L{\'e}vy case the classic first
passage solution is indeed optimal; in the diffusion case, we obtain the
optimality equations, but the existence of solutions improving the classic ones
is left for future work.


  Conventional thermo-statistics address infinite homogeneous systems within
the canonical ensemble. However, some 170 years ago the original motivation of
thermodynamics was the description of steam engines, i.e. boiling water. Its
essential physics is the separation of the gas phase from the liquid. Of
course, boiling water is inhomogeneous and as such cannot be treated by
conventional thermo-statistics. Then it is not astonishing, that a phase
transition of first order is signaled canonically by a Yang-Lee singularity.
Thus it is only treated correctly by microcanonical Boltzmann-Planck
statistics. This was elaborated in the talk presented at this conference. It
turns out that the Boltzmann-Planck statistics is much richer and gives
fundamental insight into statistical mechanics and especially into entropy.
This can be done to a far extend rigorously and analytically. The deep and
essential difference between ``extensive'' and ``intensive'' control
parameters, i.e. microcanonical and canonical statistics, was exemplified by
rotating, self-gravitating systems. In the present paper the necessary
appearance of a convex entropy $S(E)$ and the negative heat capacity at phase
separation in small as well macroscopic systems independently of the range of
the force is pointed out.


  An important topic of interest in imaging is the construction of protocols
that are not diffraction limited. This can be achieved in a variety of ways,
including classical superresolution techniques or quantum entanglement-based
protocols. Here, we consider superresolving imaging in the far field using
higher-order intensity correlations. We show that third and fourth order
correlations can improve upon the first and second order correlations that are
traditionally used in classical optics and Hanbury Brown and Twiss type
experiments. The improvement is achieved entirely by post-processing of the
data. As a demonstrator, we simulate the far field intensity distribution of a
circular aperture that emits thermal light and use maximum likelihood
estimation to determine the radius of the aperture. We compare the achieved
precision to the Cram\'er-Rao lower bound and find that the variance of
measurements for the third and fourth order correlation functions are indeed
closer to the Cram\'er-Rao bound than that of the second order correlation
function. The method presented here is general, and can be used for all kinds
of incoherent emitters, geometries, and types of noise.


  We study the effect of finite 't Hooft coupling corrections on the imaginary
potential and the thermal width of a moving heavy quarkonium from the AdS/CFT
correspondence. To study these corrections, we consider $\mathcal{R}^4$ terms
and Gauss$-$Bonnet gravity. We conclude that the imaginary potential of a
moving or static heavy quarkonium starts to be generated for smaller distances
of quark and antiquark. Similar to the case of static heavy quarkonium, it is
shown that by considering the corrections the thermal width becomes effectively
smaller. The results are compared with analogous calculations in a weakly
coupled plasma.


  Information-theoretic formulations of the private information retrieval (PIR)
problem have been investigated under a variety of scenarios. Symmetric private
information retrieval (SPIR) is a variant where a user is able to privately
retrieve one out of $K$ messages from $N$ non-colluding replicated databases
without learning anything about the remaining $K-1$ messages. However, the goal
of perfect privacy can be too taxing for certain applications. In this paper,
we investigate if the information-theoretic capacity of SPIR (equivalently, the
inverse of the minimum download cost) can be increased by relaxing both user
and DB privacy definitions. Such relaxation is relevant in applications where
privacy can be traded for communication efficiency. We introduce and
investigate the Asymmetric Leaky PIR (AL-PIR) model with different privacy
leakage budgets in each direction. For user privacy leakage, we bound the
probability ratios between all possible realizations of DB queries by a
function of a non-negative constant $\epsilon$. For DB privacy, we bound the
mutual information between the undesired messages, the queries, and the
answers, by a function of a non-negative constant $\delta$. We propose a
general AL-PIR scheme that achieves an upper bound on the optimal download cost
for arbitrary $\epsilon$ and $\delta$. We show that the optimal download cost
of AL-PIR is upper-bounded as $D^{*}(\epsilon,\delta)\leq
1+\frac{1}{N-1}-\frac{\delta e^{\epsilon}}{N^{K-1}-1}$. Second, we obtain an
information-theoretic lower bound on the download cost as
$D^{*}(\epsilon,\delta)\geq
1+\frac{1}{Ne^{\epsilon}-1}-\frac{\delta}{(Ne^{\epsilon})^{K-1}-1}$. The gap
analysis between the two bounds shows that our AL-PIR scheme is optimal when
$\epsilon =0$, i.e., under perfect user privacy and it is optimal within a
maximum multiplicative gap of $\frac{N-e^{-\epsilon}}{N-1}$ for any
$(\epsilon,\delta)$.


  The emergent nature of quantum mechanics is shown to follow from a precise
correspondence with the classical theory of irreversible thermodynamics.


  In the classical Drossel-Schwabl forest fire process, vertices of a lattice
become occupied at rate $1$, and they are hit by lightning at some tiny rate
$\zeta > 0$, which causes entire connected components to burn. In this paper,
we study a variant where fires are coming from the boundary of the forest
instead.
  In particular we prove that, for the case without recoveries where the forest
is an $N \times N$ box in the triangular lattice, the probability that the
center of the box gets burnt tends to $0$ as $N \rightarrow \infty$ (but
substantially slower than the one-arm probability of critical Bernoulli
percolation). And, for the case where the forest is the upper-half plane, we
show (still for the version without recoveries) that no infinite occupied
cluster emerges. We also discuss analogs of some of these results for the
corresponding models with recoveries, and explain how our results and proofs
give valuable insight on a process considered earlier by Graf.


  The cross section of the $^{23}$Na($n, \gamma$)$^{24}$Na reaction has been
measured via the activation method at the Karlsruhe 3.7 MV Van de Graaff
accelerator. NaCl samples were exposed to quasistellar neutron spectra at
$kT=5.1$ and 25 keV produced via the $^{18}$O($p, n$)$^{18}$F and $^{7}$Li($p,
n$)$^{7}$Be reactions, respectively. The derived capture cross sections
$\langle\sigma\rangle_{\rm kT=5 keV}=9.1\pm0.3$ mb and
$\langle\sigma\rangle_{\rm kT=25 keV}=2.03 \pm 0.05$ mb are significantly lower
than reported in literature. These results were used to substantially revise
the radiative width of the first $^{23}$Na resonance and to establish an
improved set of Maxwellian average cross sections. The implications of the
lower capture cross section for current models of $s$-process nucleosynthesis
are discussed.


  We consider monopoles with singularities of Dirac type on quasiregular
Sasakian three-folds fibering over a compact Riemann surface $\Sigma$, for
example the Hopf fibration $S^3\longrightarrow S^2$. We show that these
correspond to holomorphic objects on $\Sigma$, which we call twisted bundle
triples. These are somewhat similar to Murray's bundle gerbes. A spectral curve
construction allows us to classify these structures, and, conjecturally,
monopoles.


  With the high collision energies at the LHC, the contributions to particle
production from hard-QCD processes increase, but it remains dominated by
soft-QCD processes. Such processes challenge the theoretical models, since they
are described by non-perturbative phenomenology. A selection of the most recent
ALICE measurements of charged-particle multiplicities and the Underlying Event
will be presented, focusing on model comparisons. A summary of the current
understanding of soft-QCD processes will be discussed, evaluating possible ways
to further constrain theory.


  We study the three-body problem for both fermionic and bosonic cold atom
gases in a parabolic transverse trap of lengthscale $a_\perp$. For this
quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for
any sign of the 3D scattering length $a$, and a confinement-induced scattering
resonance. The fermionic three-body problem is universal and characterized by
two atom-dimer scattering lengths, $a_{ad}$ and $b_{ad}$. In the tightly bound
`dimer limit', $a_\perp/a\to\infty$, we find $b_{ad}=0$, and $a_{ad}$ is linked
to the 3D atom-dimer scattering length. In the weakly bound `BCS limit',
$a_\perp/a\to-\infty$, a connection to the Bethe Ansatz is established, which
allows for exact results. The full crossover is obtained numerically. The
bosonic three-body problem, however, is non-universal: $a_{ad}$ and $b_{ad}$
depend both on $a_\perp/a$ and on a parameter $R^*$ related to the sharpness of
the resonance. Scattering solutions are qualitatively similar to fermionic
ones. We predict the existence of a single confinement-induced three-body bound
state (trimer) for bosons.


  This paper considers a class of two-player zero-sum games on directed graphs
whose vertices are equipped with random payoffs of bounded support known by
both players.
  Starting from a fixed vertex, players take turns to move a token along the
edges of the graph.
  On the one hand, for acyclic directed graphs of bounded degree and
sub-exponential expansion, we show that the value of the game converges almost
surely to a constant at an exponential rate dominated in terms of the
expansion.
  On the other hand, for the infinite $d$-ary tree that does not fall into the
previous class of graphs, we show convergence at a double-exponential rate in
terms of the expansion.


  Galaxies in dense environments, such as groups and clusters, experience
various processes by which galaxies gain and lose gas. Using data from the
SDSS-IV MaNGA survey, we previously reported the discovery of a giant (6 -- 8
kpc in diameter) H$\alpha$ blob, Totoro, about 8 kpc away from a pair of
galaxies (Satsuki and Mei) residing in a galaxy group which is experiencing a
group-group merger. Here, we combine interferometric $^{12}$CO(1--0) molecular
gas data, new wide-field H$\alpha$, $u$-band data, and published X-ray data to
determine the origin of the blob. Several scenarios are discussed to account
for its multi-wavelength properties, including (1) H$\alpha$ gas being stripped
from galaxy Satsuki by ram-pressure; (2) a separated low-surface-brightness
galaxy; (3) gas being ejected or ionized by an active galactic nucleus (AGN);
and (4) a cooling intra-group medium (IGM). Scenarios (1) and (2) are less
favored by the present data. Scenario (3) is also less likely as there is no
evidence for an active ongoing AGN in the host galaxy. We find that the CO
(cold) and H$\alpha$ (warm) gas coexist with X-ray (hot) structures; moreover,
the derived cooling time is within the regime where molecular and H$\alpha$ gas
are expected. The coexistence of gas with different temperatures also agrees
with that of cooling gas in other systems. Our multi-wavelength results
strongly suggest that the CO and H$\alpha$ gas are the product of cooling from
the IGM at its current location, i.e., cooling has occurred, and may be
ongoing, well outside the host-galaxy core.


  We present here a manifestly gauge invariant calculation of vacuum
polarization to fermions in the presence of a constant Maxwell and a constant
Kalb-Ramond field in four dimensions. The formalism is a generalisation of the
one used by Schwinger in his famous paper on gauge invariance and vacuum
polarization. We get an explicit expression for the vacuum polarization induced
effective Lagrangian for a constant Maxwell field interacting with a constant
Kalb-Ramond field. In the weak field limit we get the coupling between the
Maxwell field and the Kalb-Ramond field to be $(\tilde{H}.\tilde{F})^2$, where
${\tilde H}_{\mu}= {1\over
{3!}}\epsilon_{\mu\alpha\beta\lambda}H^{\alpha\beta\lambda}$ and $\tilde F$ is
the dual of $F_{\mu\nu}$.


  Suppose that a transcendental meromorphic function in the plane has finitely
many critical values, while its multiple points have bounded multiplicities,
and its inverse function has finitely many transcendental singularities. Using
the Wiman-Valiron method it is shown that the Schwarzian derivative does not
have a direct transcendental singularity over infinity, and does not have
infinity as a Borel exceptional value.