  This paper studies the optimal dividend for a multi-line insurance group, in
which each subsidiary runs a product line and is exposed to some external
credit risk. The default contagion is considered such that one default event
may increase the default probabilities of all surviving subsidiaries. The total
dividend problem for the insurance group is investigated and we find that the
optimal dividend strategy is still of the barrier type. Furthermore, we show
that the optimal barrier of each subsidiary is modulated by the default state.
That is, how many and which subsidiaries have defaulted will determine the
dividend threshold of each surviving subsidiary. These conclusions are based on
the analysis of the associated recursive system of Hamilton-Jacobi-Bellman
variational inequalities (HJBVIs). The existence of the classical solution is
established and the verification theorem is proved. In the case of two
subsidiaries, the value function and optimal barriers are given in analytical
forms, allowing us to conclude that the optimal barrier of one subsidiary
decreases if the other subsidiary defaults.


  In this paper we show that the real differential of any injective slice
regular function is everywhere invertible. The result is a generalization of a
theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained
thanks, in particular, to some new information regarding the first coefficients
of a certain polynomial expansion for slice regular functions (called
\textit{spherical expansion}), and to a new general result which says that the
slice derivative of any injective slice regular function is different from
zero. A useful tool proven in this paper is a new formula that relates slice
and spherical derivatives of a slice regular function. Given a slice regular
function, part of its singular set is described as the union of surfaces on
which it results to be constant.


  We report on Chandra X-ray observations of SN 2016jae and SN 2018cqj, both
low luminosity Type Ia supernova that showed the presence of a H line in their
early optical spectrum. No X-ray emission is detected at the location of either
SN. Upper limits to the luminosity of up to 2 $\times 10^{40}\,$ erg s$^{-1}$
are calculated for each SN, depending on the assumed spectral model,
temperature and column density. This luminosity is comparable to that of
another low-luminosity Type Ia SN, SN 2018fhw, that was observed with Chandra.
It is generally lower than upper limits calculated for Type Ia-CSM SNe observed
in X-rays, and also below that of SN 2012ca, the only Type Ia-CSM SN to have
been detected in X-rays. Comparisons are made to other Type Ia SN with a H line
observed in X-rays. The observations suggest that while the density into which
the SN is expanding may have been high at the time the H$\alpha$ line was
detected, it had decreased considerably by the time of X-ray observations.


  A dynamical system of points moving along the edges of a graph could be
considered as a geometrical discrete dynamical system or as a discrete version
of a quantum graph with localized wave packets. We study the set of such
systems over metric graphs that can be constructed from a given set of
commensurable edges with fixed lengths. It is shown that there always exists a
system consisting of a bead graph with vertex degrees not greater than three
that demonstrates the longest stabilization time in such a set. The results are
extended to graphs with incommensurable edges using the notion of
$\varepsilon$-nets and, also, it is shown that dynamical systems of points on
linear graphs have the slowest growth of the number of dynamic points


  We extend to manifolds endowed with a general geometric structure, the
classical notions of gradient as well as Laplace operator, and provide some of
their natural properties.


  Tick-Borne diseases can be transmitted via non-systemic (NS) transmission.
This occurs when tick gets the infection by co-feeding with infected ticks on
the same host resulting in a direct pathogen transmission between the vectors,
without infecting the host. This transmission is peculiar, as it does not
require any systemic infection of the host. The NS transmission is the main
efficient transmission for the persistence of the Tick-Borne Encephalitis virus
in nature. By describing the heterogeneous ticks aggregation on hosts through a
\hyphenation{dynamical} bipartite graphs representation, we are able to
mathematically define the NS transmission and to depict the epidemiological
conditions for the pathogen persistence. Despite the fact that the underlying
network is largely fragmented, analytical and computational results show that
the larger is the variability of the aggregation, and the easier is for the
pathogen to persist in the population.


  We consider a Ginzburg-Landau type equation in $\R^2$ of the form $-\Delta u
= u J'(1-|u|^{2})$ with a potential function $J$ satisfying weak conditions
allowing for example a zero of infinite order in the origin. We extend in this
context the results concerning quantization of finite potential solutions of
H.Brezis, F.Merle, T.Rivi\`ere from \cite{BMR} who treat the case when $J$
behaves polinomially near 0, as well as a result of Th. Cazenave, found in the
same reference, and concerning the form of finite energy solutions.


  Bounding and predicting the generalization gap of overparameterized neural
networks remains a central open problem in theoretical machine learning. Neural
network optimization trajectories have been proposed to possess fractal
structure, leading to bounds and generalization measures based on notions of
fractal dimension on these trajectories. Prominently, both the Hausdorff
dimension and the persistent homology dimension have been proposed to correlate
with generalization gap, thus serving as a measure of generalization. This work
performs an extended evaluation of these topological generalization measures.
We demonstrate that fractal dimension fails to predict generalization of models
trained from poor initializations. We further identify that the $\ell^2$ norm
of the final parameter iterate, one of the simplest complexity measures in
learning theory, correlates more strongly with the generalization gap than
these notions of fractal dimension. Finally, our study reveals the intriguing
manifestation of model-wise double descent in persistent homology-based
generalization measures. This work lays the ground for a deeper investigation
of the causal relationships between fractal geometry, topological data
analysis, and neural network optimization.


  In this paper, we propose a 'full-stack' solution to designing high capacity
and low latency on-chip cache hierarchies by starting at the circuit level of
the hardware design stack. First, we propose a novel Gain Cell (GC) design
using FDSOI. The GC has several desirable characteristics, including ~50%
higher storage density and ~50% lower dynamic energy as compared to the
traditional 6T SRAM, even after accounting for peripheral circuit overheads. We
also exploit back-gate bias to increase retention time to 1.12 ms (~60x of
eDRAM) which, combined with optimizations like staggered refresh, makes it an
ideal candidate to architect all levels of on-chip caches. We show that
compared to 6T SRAM, for a given area budget, GC based caches, on average,
provide 29% and 36% increase in IPC for single- and multi-programmed workloads,
respectively on contemporary workloads including SPEC CPU2017. We also observe
dynamic energy savings of 42% and 34% for single- and multi-programmed
workloads, respectively.
  We utilize the inherent properties of the proposed GC, including decoupled
read and write bitlines to devise optimizations to save precharge energy and
architect GC caches with better energy and performance characteristics.
Finally, in a quest to utilize the best of all worlds, we combine GC with
STT-RAM to create hybrid hierarchies. We show that a hybrid hierarchy with GC
caches at L1 and L2, and an LLC split between GC and STT-RAM, with asymmetric
write optimization enabled, is able to provide a 54% benefit in energy-delay
product (EDP) as compared to an all-SRAM design, and 13% as compared to an
all-GC cache hierarchy, averaged across multi-programmed workloads.


  In this paper, a low complexity time domain semi-blind algorithm is proposed
to estimate and track the time varying MIMO OFDM channels. First, the proposed
least mean squares (LMS) based algorithm is developed for the training mode and
then is extended for the blind mode of the operation by combining with the
decision direction (DD) or adaptive Bussgang algorithm (ABA) techniques. In the
blind mode, because of decision errors, a smaller step size is considered for
the LMS algorithm and the channel estimation is run a few times to improve its
precision. In each round of the estimation in the blind mode, the step size is
decreased to form some kind of annealing. Both DD LMS and ABA LMS techniques
are simulated and compared to the full training case and MSE of channel
estimation error is considered as comparison criterion. It is shown for 2x4 DD
LMS and for 4x4 ABA LMS algorithms present near full training case estimation
error. Of course in some scenarios the former proposed technique performs
better and in other scenarios the latter is better and therefore combine of it
can be very interesting in all channel conditions.


  In this study, we propose an extended Watts model to examine the effect of
initiators on information cascades. The extended Watts model assumes that nodes
with connections to initiators have low adoption thresholds than other nodes,
due to the significant influence of initiators. We develop a tree approximation
to describe the active node fraction for the extended Watts model in random
networks and derive the cascade condition for a global cascade to occur with a
small fraction of initiators. By analyzing the active node fraction and the
cascade window of the extended Watts model on the Erdos-Renyi random graph, we
find that increasing the influence of initiators facilitates the possibility of
global cascades, i.e., how many nodes eventually become active is significantly
affected by the fraction of initiators and the threshold of nodes directly
connected to initiators, which determine cascade dynamics at early stages.


  In two-Higgs-doublet models with exact $Z_2$ symmetry, putting $m_h \simeq
125$ GeV at the alignment limit, the following limits on the heavy scalar
masses are obtained from the conditions of unitarity and stability of the
scalar potential: $m_H,~m_A,~m_{H^+} < 1$ TeV and $1/8 <\tan\beta <8$. The
constraints from $b \to s \gamma$ and neutral meson mass differences, when
superimposed on the unitarity constraints, put a tighter lower limit on
$\tan\beta$ depending on $m_{H^+}$. It has also been shown that larger values
of $\tan\beta$ can be allowed by introducing soft breaking term in the
potential at the expense of a correlation between $m_H$ and the soft breaking
parameter.


  We study random walks on $\mathbb{Z}$ which have a linear (or almost linear)
drift towards 0 in a range around 0. This drift leads to a metastable Gaussian
distribution centered at zero. We give specific, fast growing, time windows
where we can explicitely bound the distance of the distribution of the walk to
an appropriate Gaussian. In this way we give a solid theoretical foundation to
the notion of metastability. We show that the supercritical contact process on
the complete graph has a drift towards its equilibrium point which is locally
linear and that our results for random walks apply. This leads to the
conclusion that the infected fraction of the population in metastability (when
properly scaled) converges in distribution to a Gaussian, uniformly for all
times in a fast growing interval.


  We study scattering amplitudes in two-dimensional string theory on a black
hole bakground. We start with a simple derivation of the
Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation
functions of the sine-Liouville integrable model on the Riemann sphere to
tree-level string amplitudes on the Euclidean two-dimensional black hole. This
derivation of FZZ duality is based on perturbation theory, and it relies on a
trick originally due to Fateev, which involves duality relations between
different Selberg type integrals. This enables us to rewrite the correlation
functions of sine-Liouville theory in terms of a special set of correlators in
the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further
consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality.
In particular, we prove that n-point correlation functions in sine-Liouville
theory involving n-2 winding modes actually coincide with the correlation
functions in the SL(2,R)/U(1) gauged WZW model that include n-2 oscillator
operators of the type described by Giveon, Itzhaki and Kutasov in reference
arXiv:1603.05822. This proves the GFZZ duality for the case of tree level
maximally winding violating n-point amplitudes with arbitrary $n$. We also
comment on the connection between GFZZ and other marginal deformations
previously considered in the literature.


  According to the Heisenberg uncertainty principle of quantum mechanics,
particles which are localized in space by a bounding potential must have a
finite distribution of momenta. This leads, even in the lowest-possible energy
state, to vibrations, and thus, to the so-called zero-point energy. For
chemically bound hydrogen the zero-point energy can be quite substantial. For
example, for a free H_2 molecule it is 0.26 eV, a significant value in the
realm of chemistry, where often an energy of the order of 0.1 eV/atom (or 2.3
kcal/mol) decides whether or not a chemical reaction takes place with an
appreciable rate. Yet, in many theoretical studies the dynamics of chemical
reactions involving hydrogen has been treated classically or quasi-classically,
assuming that the quantum mechanical nature of H nuclei, i.e. the zero-point
effects, will not strongly affect the relevant physical or chemical properties.
In this paper we show that this assumption is not justified. We will
demonstrate that for very basic and fundamental catalytic-reaction steps,
namely the dissociative adsorption of molecular hydrogen at transition metal
surfaces and its time-reverse process, the associative desorption, zero-point
effects can not only quantitatively but even qualitatively affect the chemical
processes and rates. Our calculations (treating electrons as well as H nuclei
quantum-mechanically) establish the importance of additional zero-point effects
generated by the H_2-surface interaction and how energy of the H-H stretch
vibration is transferred into those and vice versa.


  This paper introduces a framework of gesture recognition operating on the
output of an event based camera using the computational resources of a mobile
phone. We will introduce a new development around the concept of time-surfaces
modified and adapted to run on the limited computational resources of a mobile
platform. We also introduce a new method to remove dynamically backgrounds that
makes full use of the high temporal resolution of event-based cameras. We
assess the performances of the framework by operating on several dynamic
scenarios in uncontrolled lighting conditions indoors and outdoors. We also
introduce a new publicly available event-based dataset for gesture recognition
selected through a clinical process to allow human-machine interactions for the
visually-impaired and the elderly. We finally report comparisons with prior
works that tackled event-based gesture recognition reporting comparable if not
superior results if taking into account the limited computational and memory
constraints of the used hardware.


  Metapopulation epidemic models describe epidemic dynamics in networks of
spatially distant patches connected with pathways for migration of individuals.
In the present study, we deal with a susceptible-infected-recovered (SIR)
metapopulation model where the epidemic process in each patch is represented by
an SIR model and the mobility of individuals is assumed to be a homogeneous
diffusion. Our study focuses on two types of patches including high-risk and
low-risk ones, in order to evaluate intervention strategies for epidemic
control. We theoretically analyze the intervention threshold, indicating the
critical fraction of low-risk patches for preventing a global epidemic
outbreak. We show that targeted intervention to high-degree patches is more
effective for epidemic control than random intervention. The theoretical
results are validated by Monte Carlo simulation for synthetic and realistic
scale-free patch networks. Our approach is useful for exploring better local
interventions aimed at containment of epidemics.


  We have embedded the classical theory of stochastic finance into a
differential geometric framework called Geometric Arbitrage Theory and show
that it is possible to:
  --Write arbitrage as curvature of a principal fibre bundle.
  --Parameterize arbitrage strategies by its holonomy.
  --Give the Fundamental Theorem of Asset Pricing a differential homotopic
characterization.
  --Characterize Geometric Arbitrage Theory by five principles and show they
they are consistent with the classical theory of stochastic finance.
  --Derive for a closed market the equilibrium solution for market portfolio
and dynamics in the cases where:
  -->Arbitrage is allowed but minimized.
  -->Arbitrage is not allowed.
  --Prove that the no-free-lunch-with-vanishing-risk condition implies the zero
curvature condition.


  In this paper we explain that the natural filtration of a continuous Hunt
process is continuous, and show that martingales over such a filtration are
continuous. We further establish a martingale representation theorem for a
class of continuous Hunt processes under certain technical conditions. In
particular we establish the martingale representation theorem for the
martingale parts of (reflecting) symmetric diffusions in a bounded domain with
a continuous boundary. Together with an approach put forward in Lyons et
al(2009), our martingale representation theorem is then applied to the study of
initial and boundary problems for quasi-linear parabolic equations by using
solutions to backward stochastic differential equations over the filtered
probability space determined by reflecting diffusions in a bounded domain with
only continuous boundary.


  Robustness is a significant constraint in machine learning models. The
performance of the algorithms must not deteriorate when training and testing
with slightly different data. Deep neural network models achieve awe-inspiring
results in a wide range of applications of computer vision. Still, in the
presence of noise or region occlusion, some models exhibit inaccurate
performance even with data handled in training. Besides, some experiments
suggest deep learning models sometimes use incorrect parts of the input
information to perform inference. Activate Image Augmentation (ADA) is an
augmentation method that uses interpretability methods to augment the training
data and improve its robustness to face the described problems. Although ADA
presented interesting results, its original version only used the Vanilla
Backpropagation interpretability to train the U-Net model. In this work, we
propose an extensive experimental analysis of the interpretability method's
impact on ADA. We use five interpretability methods: Vanilla Backpropagation,
Guided Backpropagation, GradCam, Guided GradCam, and InputXGradient. The
results show that all methods achieve similar performance at the ending of
training, but when combining ADA with GradCam, the U-Net model presented an
impressive fast convergence.


  Pre-transformed polar codes (PTPCs) form a class of codes that perform close
to the finite-length capacity bounds. The minimum distance and the number of
minimum weight codewords are two decisive properties for their performance. In
this work, we propose an efficient algorithm for determining the number of
minimum weight codewords of general PTPCs that eliminates all redundant visits
to nodes of the search tree, thus reducing the computational complexity
typically by several orders of magnitude compared to state-of-the-art
algorithms. This reduction in complexity allows, for the first time, the
minimum distance properties to be directly considered in the code design of
PTPCs. The algorithm is demonstrated for randomly pre-transformed Reed-Muller
(RM) codes and polarization-adjusted convolutional (PAC) codes. Furthermore, we
design optimal polynomials for PAC codes with this algorithm, minimizing the
number of minimum weight codewords.


  Beamforming design has been widely investigated for integrated sensing and
communication (ISAC) systems with full-duplex (FD) sensing and half-duplex (HD)
communication. To achieve higher spectral efficiency, in this paper, we extend
existing ISAC beamforming design by considering the FD capability for both
radar and communication. Specifically, we consider an ISAC system, where the BS
performs target detection and communicates with multiple downlink users and
uplink users reusing the same time and frequency resources. We jointly optimize
the downlink dual-functional transmit signal and the uplink receive beamformers
at the BS and the transmit power at the uplink users. The problems are
formulated under two criteria: power consumption minimization and sum rate
maximization. The downlink and uplink transmissions are tightly coupled due to
both the desired target echo and the undesired interference received at the BS,
making the problems challenging. To handle these issues in both cases, we first
determine the optimal receive beamformers, which are derived in closed forms
with respect to the BS transmit beamforming and the user transmit power, for
radar target detection and uplink communications, respectively. Subsequently,
we invoke these results to obtain equivalent optimization problems and propose
efficient iterative algorithms to solve them by using the techniques of rank
relaxation and successive convex approximation (SCA), where the adopted
relaxation is proven to be tight. In addition, we consider a special case under
the power minimization criterion and propose an alternative low complexity
design. Numerical results demonstrate that the optimized FD communication-based
ISAC brings tremendous improvements in terms of both power efficiency and
spectral efficiency compared to the conventional ISAC with HD communication.


  The 3D observed velocities of the Large and Small Magellanic Clouds(LMC and
SMC) provide an opportunity to probe the Galactic potential in the outskirt of
the Galactic halo. Based on a canonical NFW model of the Galactic potential,
Besla et al.(2007) reconstructed LMC and SMC's orbits and suggested that they
are currently on their first perigalacticon passage about the Galaxy. Motivated
by several recent revisions of the Sun's motion around the Galactic center, we
re-examine the LMC's orbital history and show that it depends sensitively on
the dark-matter's mass distribution beyond its present Galactic distance. We
utilize results of numerical simulations to consider a range of possible
structural and evolutionary models for the Galactic potentials. We find that
within the theoretical and observational uncertainties, it is possible for the
LMC to have had multiple perigalacticon passages on the Hubble time scale,
especially if the Galactic circular velocity at the location of the Sun is
greater than $\sim 228$km s$^{-1}$. Based on these models, a more accurate
determination of the LMC's motion may be used to determine the dark matter
distribution in the outskirt of the Galactic halo.


  We present a novel automated technique for parallelizing quantum circuits via
forward and backward translation to measurement-based quantum computing
patterns and analyze the trade off in terms of depth and space complexity. As a
result we distinguish a class of polynomial depth circuits that can be
parallelized to logarithmic depth while adding only polynomial many auxiliary
qubits. In particular, we provide for the first time a full characterization of
patterns with flow of arbitrary depth, based on the notion of influencing paths
and a simple rewriting system on the angles of the measurement. Our method
leads to insightful knowledge for constructing parallel circuits and as
applications, we demonstrate several constant and logarithmic depth circuits.
Furthermore, we prove a logarithmic separation in terms of quantum depth
between the quantum circuit model and the measurement-based model.


  The p-wave superfluid is characterized by nontrivial topological
characteristics essential for fault-tolerant quantum state manipulation.
However, the practical realization of the p-wave state remains a challenging
problem. We study the s- and p-wave superfluidity in mixtures of fermionic and
spinor bosonic gases and derive a general set of the gap equations for these
superfluid states. Numerically solving the gap equations for the s-wave state,
we quantify the physical conditions for the realization of the pure p-wave
state in a well-controlled environment of atomic physics in the absence of an
admixture of the s-wave state.


  We report on low-energy electron microscopy imaging of ferroelectric domains
with submicron resolution. Periodic strips of 'up' and 'down'-polarized
ferroelectric domains in bismuth ferrite -a room temperature multiferroic-
serve as a model system to compare low-energy electron microscopy with the
established piezoresponse force microscopy. The results confirm the possibility
of full-field imaging of ferroelectric domains with short acquisition times by
exploiting the sensitivity of ultraslow electrons to small variations of the
electric potential near surfaces in the "mirror" operation mode.


  Calorimetry experiments under high pressure were used to clarify the
interplay between different states such as superconductivity and
antiferromagnetism in CeRhIn5, spin density wave and large moment
antiferromagnetism in URu2Si2. Evidences are given on the re-entrance of
antiferromagnetism under magnetic field in the superconducting phase of CeRhIn5
up to pc = 2.5 GPa where the Neel temperature will collapse in the absence of
superconductivity. For URu2Si2 measurements up to 10 GPa support strongly the
coexistence of spin density wave and large moment antiferromagnetism at high
pressures.


  In this paper, we study the convergence properties of an algorithm that can
be viewed as an interpolation between two gradient based optimization methods,
Nesterov's acceleration method for strongly convex functions $(NAG$-$SC)$ and
Polyak's heavy ball method. Recent Progress has been made on using
High-Resolution ordinary differential equations (ODEs) to distinguish these two
fundamentally different methods. The key difference between them can be
attributed to the gradient correction term, which is reflected by the Hessian
term in the High-Resolution ODE. Our goal is to understand how this term can
affect the convergence rate and the choice of our step size. To achieve this
goal, we introduce the notion of $\beta$-High Resolution ODE, $0\leq \beta\leq
1$ and prove that within certain range of step size, there is a phase
transition happening at $\beta_c$. When $\beta_c\leq\beta\leq 1$, the algorithm
associated with $\beta$-High Resolution ODE have the same convergence rate as
NAG-SC. When $0\leq \beta\leq \beta_c$, this algorithm will have the slower
convergence rate than NAG-SC.


  The purpose of this article is to present a result on the existence of Cauchy
temporal functions invariant by the action of a compact group of conformal
transformations in arbitrary globally hyperbolic manifolds. Moreover, the
previous results about the existence of Cauchy temporal functions with
additional properties on arbitrary globally hyperbolic manifolds are unified in
a fully general theorem. The article is written as self-contained as possible,
no prior knowledge on Lorentzian geometry is assumed.


  By treating the order parameter as a stochastic thermal fluctuating variable
for small-large black hole phase transition, we investigate the kinetic process
of phase transition for the Kerr-AdS (anti-de Sitter) black holes on free
energy landscape. We find that the extremal points of the off shell Gibbs free
energy correspond to physical black holes. For small-large black hole phase
transition, the off shell Gibbs free energy exhibits a double well behavior
with the same depth. Contrary to previous research for the kinetics of phase
transition for the Kerr-Newman-AdS family black holes on a free energy
landscape, we find that there is a lower bound for the order parameter and the
lower bound corresponds to extremal black holes. In particular, the off shell
Gibbs free energy is zero instead of divergent as previous work suggested for
vanishing black hole horizon radius, which corresponds to the Gibbs free energy
of a thermal AdS space. The investigation for the evolution of the probability
distribution for the phase transition indicates that the initial stable small
(large) black hole tends to switch to stable large (small) black hole.
Increasing the temperature along the coexistence curve, the switching process
becomes faster and the probability distribution reaches the final stationary
Boltzmann distribution at a shorter time. The distribution of the first passage
time indicates the time scale of the small-large black hole phase transition,
and the peak of the distribution becomes sharper and shifts to the left with
the increase of temperature along the coexistence curve. This suggests that a
considerable first passage process occurs at a shorter time for higher
temperature. The investigation of the kinetics of phase transition might
provide us new insight into the underlying microscopic interactions.


  This is a survey of our results on the relation between perturbative
renormalization and motivic Galois theory. The main result is that all quantum
field theories share a common universal symmetry realized as a motivic Galois
group, whose action is dictated by the divergences and generalizes that of the
renormalization group. The existence of such a group was conjectured by P.
Cartier based on number theoretic evidence and on the Connes-Kreimer theory of
perturbative renormalization. The group provides a universal formula for
counterterms and is obtained via a Riemann-Hilbert correspondence classifying
equivalence classes of flat equisingular bundles, where the equisingularity
condition corresponds to the independence of the counterterms on the mass
scale.


  We report the electrical, magneto transport and specific heat of the layered
polycrystalline RECoPO (RE = La, Nd and Sm) samples. These compounds are
iso-structural to recently discovered superconductor LaFeAs(O/F). Bulk
polycrystalline samples are synthesized by solid state reaction route in an
evacuated sealed quartz tube. All these compounds are crystallized in a
tetragonal structure with space group P4/nmm. The Cobalt in these compounds is
in itinerant state with its paramagnetic moment above 1.4\muB and the same
orders ferromagnetically (FM) with saturation moment of around 0.20\muB below
say 80K. Though, LaCoPO shows single paramagnetic (PM) to ferromagnetic (FM)
transition near 35K, the NdCoPO and SmCoPO exhibit successive PM-FM-AFM
transitions. Both FM and AFM transition temperatures vary with applied field.
Although the itinerant ferromagnetism occurs with small saturation moment,
typical anti-ferromagnetic (AFM) transitions (TN1, TN2) are observed at 69K and
14K for Nd and 57K and 45K for Sm. This FM-AFM transition of Co spins in NdCoPO
and SmCoPO is both field and temperature dependent. The Magneto-transport of
NdCoPO and SmCoPO distinctly follows their successive PM-FM-AFM transitions. It
is clear that Sm/Nd (4f) interacts with the Co (3d) in first time synthesized
Sm/NdCoPO.


  Differential privacy (DP) has arisen as the gold standard in protecting an
individual's privacy in datasets by adding calibrated noise to each data
sample. While the application to categorical data is straightforward, its
usability in the context of images has been limited. Contrary to categorical
data the meaning of an image is inherent in the spatial correlation of
neighboring pixels making the simple application of noise infeasible.
Invertible Neural Networks (INN) have shown excellent generative performance
while still providing the ability to quantify the exact likelihood. Their
principle is based on transforming a complicated distribution into a simple one
e.g. an image into a spherical Gaussian. We hypothesize that adding noise to
the latent space of an INN can enable differentially private image
modification. Manipulation of the latent space leads to a modified image while
preserving important details. Further, by conditioning the INN on meta-data
provided with the dataset we aim at leaving dimensions important for downstream
tasks like classification untouched while altering other parts that potentially
contain identifying information. We term our method content-aware differential
privacy (CADP). We conduct experiments on publicly available benchmarking
datasets as well as dedicated medical ones. In addition, we show the
generalizability of our method to categorical data. The source code is publicly
available at https://github.com/Cardio-AI/CADP.


  We study the percolation properties of the nodal structures of random fields.
Lower bounds on crossing probabilities (RSW-type estimates) of quads by nodal
domains or nodal sets of Gaussian ensembles of smooth random functions are
established under the following assumptions: (i) sufficient symmetry; (ii)
smoothness and non-degeneracy; (iii) local convergence of the covariance
kernels; (iv) asymptotically non-negative correlations; and (v) uniform rapid
decay of correlations.
  The Kostlan ensemble is an important model of Gaussian homogeneous random
polynomials. An application of our theory to the Kostlan ensemble yields
RSW-type estimates that are uniform with respect to the degree of the
polynomials and quads of controlled geometry, valid on all relevant scales.
This extends the recent results on the local scaling limit of the Kostlan
ensemble, due to Beffara and Gayet.


  The experimental observation of traditional Zeeman-field induced
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by
various challenges, in particular, the requirement of low dimensional systems.
In 2D, finite temperature phase fluctuations lead to extremely small
Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO
superfluids, raising serious concerns regarding their experimental
observability. Recently, it was shown that FFLO superfluids can be realized
using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may
also support topological excitations such as Majorana fermions in 2D. Here we
address the finite temperature BKT transition issue in this system, which may
exhibit gapped, gapless, topological, and gapless topological FF phases. We
find a large BKT transition temperature due to large effective superfluid
densities, making it possible to observe 2D FF superfluids at finite
temperature. In addition, we show that gapless FF superfluids can be stable due
to their positive superfluid densities. These findings pave the way for the
experimental observation of 2D gapped and gapless FF superfluids and their
associated topological excitations at finite temperature.


  We show how to use Groebner bases for operads to prove various freeness
theorems: freeness of certain operads as nonsymmetric operads, freeness of an
operad Q as a P-module for an inclusion P into Q, freeness of a suboperad. This
gives new proofs of many known results of this type and helps to prove some new
results.


  In this note we study asymptotic isotopy of random real algebraic plane
curves. More precisely, we obtain a Kac-Rice type formula that gives the
expected number of two-sided components (i.e.\ ovals) of a random real
algebraic plane curve winding around a given point. In particular, we show that
expected number of such ovals for an even degree Kostlan polynomial is
$\frac{\sqrt{d}}{2}$ and independent of the given point.


  A necessary precondition for secure quantum key distribution (QKD) is that
sender and receiver can prove the presence of entanglement in a quantum state
that is effectively distributed between them. In order to deliver this
entanglement proof one can use the class of entanglement witness (EW) operators
that can be constructed from the available measurements results. This class of
EWs can be used to provide a necessary and sufficient condition for the
existence of quantum correlations even when a quantum state cannot be
completely reconstructed. The set of optimal EWs for two well-known
entanglement based (EB) schemes, the 6-state and the 4-state EB protocols, has
been obtained recently [M. Curty et al., Phys. Rev. Lett. 92, 217903 (2004)].
Here we complete these results, now showing specifically the analysis for the
case of prepare&measure (P&M) schemes. For this, we investigate the signal
states and detection methods of the 4-state and the 2-state P&M schemes. For
each of these protocols we obtain a reduced set of EWs. More importantly, each
set of EWs can be used to derive a necessary and sufficient condition to prove
that quantum correlations are present in these protocols.


  When a software transformation or software security task needs to analyze a
given program binary, the first step is often disassembly. Since many modern
disassemblers have become highly accurate on many binaries, we believe reliable
disassembler benchmarking requires standardizing the set of binaries used and
the disassembly ground truth about these binaries. This paper presents (i) a
first version of our work-in-progress disassembly benchmark suite, which
comprises 879 binaries from diverse projects compiled with multiple compilers
and optimization settings, and (ii) a novel disassembly ground truth generator
leveraging the notion of "listing files", which has broad support by Clang,
GCC, ICC, and MSVC. In additional, it presents our evaluation of four prominent
open-source disassemblers using this benchmark suite and a custom evaluation
system. Our entire system and all generated data are maintained openly on
GitHub to encourage community adoption.


  The density of states of the disordered s-wave superconductor is calculated
perturbatively. The effect of Coulomb interaction on diffusively moving
electrons in the normal state has been known before, but in the superconducting
state both diffuson and the screened Coulomb interaction are modified.
Therefore, the correction to the density of states in the superconducting state
exhibits an energy dependence different from that of the normal state. There is
a dip structure in the correction part because the interaction has a peak at
twice the energy of the superconducting gap. The Coulomb interaction and the
superconducting fluctuation cannot be treated separately because the density
fluctuation is coupled to the phase fluctuation in the superconducting state.
This coupling results in the absence of divergence around the gap edge in the
correction part, which suggests the validity of this perturbation calculation.


  The stellar encounter rate Gamma has been shown to be strongly correlated
with the number of X-ray binaries in clusters and also to the number of radio
pulsars. However, the pulsar populations in different clusters show remarkably
different characteristics: in some GCs the population is dominated by binary
systems, in others by single pulsars and exotic systems that result from
exchange encounters. In this paper, we describe a second dynamical parameter
for globular clusters, the encounter rate for a single binary, gamma. We find
that this parameter provides a good characterization of the differences between
the pulsar populations of different globular clusters. The higher gamma is for
any particular globular cluster the more isolated pulsars and products of
exchange interactions are observed. Furthermore, we also find that slow and
"young" pulsars are found almost exclusively in clusters with a high gamma;
this suggests that these kinds of objects are formed by the disruption of X-ray
binaries, thus halting the recycling of a previously dead neutron star. We
discuss the implications of this for the nature of young pulsars and for the
formation of neutron stars in globular clusters.


  We prove the non-existence of Shimura subvarieties of positive dimension
contained generically in the hyperelliptic Torelli locus for curves of genus at
least 8, which is an analogue of Oort's conjecture in the hyperelliptic case.


  Signed networks appear naturally in contexts where conflict or animosity is
apparent. In this book chapter we review some of the literature on signed
networks, especially in the context of partitioning. Most of the work is
founded in what is known as structural balance theory. We cover the basic
mathematical principles of structural balance theory. The theory yields a
natural formulation for partitioning. We briefly compare this to other
partitioning approaches based on community detection. Finally, we analyse an
international network of alliances and conflicts and discuss the implications
of our findings for structural balance theory.


  We study the use of truncated normal-ordered three-nucleon interactions in ab
initio nuclear structure calculations starting from chiral two- plus
three-nucleon Hamiltonians evolved consistently with the similarity
renormalization group (SRG). We present three key steps: (i) a rigorous
benchmark of the normal-ordering approximation in the importance-truncated
no-core shell model (IT-NCSM) for 4-He, 16-O, and 40-Ca; (ii) a direct
comparison of the IT-NCSM results with coupled-cluster calculations at the
singles and doubles level (CCSD) for 16-O; and (iii) first applications of
SRG-evolved chiral NN+3N Hamiltonians in CCSD for the medium-mass nuclei
16,24-O and 40,48-Ca. We show that the normal-ordered two-body approximation
works very well beyond the lightest isotopes and opens a path for ab initio
studies of medium-mass and heavy nuclei with chiral two- plus three-nucleon
interactions. At the same time we highlight the predictive power of chiral
Hamiltonians.


  Spectroscopic measurements of Mira variable stars, as a function of phase,
probe the stellar atmospheres and underlying pulsation mechanisms. For example,
measuring variations in TiO, VO, and ZrO with phase can be used to help
determine whether these molecular species are produced in an extended region
above the layers where Balmer line emission occurs or below this shocked
region. Using the same methods, the Balmer-line increment, where the strongest
Balmer line at phase zero is H-delta and not H-alpha can be measured and
explanations tested, along with another peculiarity, the absence of the
H-epsilon line in the spectra of Miras when other Balmer lines are strong. We
present new spectra covering the spectral range from 6200 Angstroms to 9000
Angstroms of 20 Mira variables. A relationship between variations in the CaII
IR triplet and H-alpha as a function of phase support the hypothesis that
H-epsilon's observational characteristics result from an interaction of
H-epsilon photons with the CaII H line. New periods and epochs of variability
are also presented for each star.


  The Levitated Sensor Detector (LSD) is a compact resonant gravitational-wave
(GW) detector based on optically trapped dielectric particles that is under
construction. The LSD sensitivity has more favorable frequency scaling at high
frequencies compared to laser interferometer detectors such as LIGO. We propose
a method to substantially improve the sensitivity by optically levitating a
multi-layered stack of dielectric discs. These stacks allow the use of a more
massive levitated object while exhibiting minimal photon recoil heating due to
light scattering. Over an order of magnitude of unexplored frequency space for
GWs above 10 kHz is accessible with an instrument 10 to 100 meters in size.
Particularly motivated sources in this frequency range are gravitationally
bound states of QCD axions with decay constant near the grand unified theory
(GUT) scale that form through black hole superradiance and annihilate to GWs.
The LSD is also sensitive to GWs from binary coalescence of sub-solar-mass
primordial black holes and as-yet unexplored new physics in the high-frequency
GW window.


  We present a thermodynamic theory of weakly excited two-dimensional granular
systems from the view point of elementary excitations of spinless Fermion
systems. We introduce a global temperature T that is associated with the
acceleration amplitude \Gamma in a vibrating bed. We show that the
configurational statistics of weakly excited granular materials in a vibrating
bed obey the Fermi statistics.


  We address the question how light the lightest MSSM neutralino can be as dark
matter candidate in a scenario where all supersymmetric scalar particles are
heavy. The hypothesis that the neutralino accounts for the observed dark matter
density sets strong requirements on the supersymmetric spectrum, thus providing
an handle for collider tests. In particular for a lightest neutralino below 100
GeV the relic density constraint translates into an upper bound on the Higgsino
mass parameter $\mu$ in case all supersymmetric scalar particles are heavy. One
can define a simplified model that highlights only the necessary features of
the spectrum and their observable consequences at the LHC. Reinterpreting
recent searches at the LHC we derive limits on the mass of the lightest
neutralino that, in many cases, prove to be more constraining than dark matter
experiments themselves.


  Using the adjoint action of the infinitesimal translations (with respect to
some (in)dependant variables) on specific finite-dimensional subspaces of the
space of generalized symmetries of some system of partial differential
equations, we explicitly determine the dependance of coefficients of
generalized symmetries from these subspaces on the above-mentioned variables.
We establish the connection of our results with the theory of quasiexactly
solvable models. Some generalizations of the approach proposed also are
discussed.


  ELECTRA pre-trains language models by detecting tokens in a sequence that
have been replaced by an auxiliary model. Although ELECTRA offers a significant
boost in efficiency, its potential is constrained by the training cost brought
by the auxiliary model. Notably, this model, which is jointly trained with the
main model, only serves to assist the training of the main model and is
discarded post-training. This results in a substantial amount of training cost
being expended in vain. To mitigate this issue, we propose Fast-ELECTRA, which
leverages an existing language model as the auxiliary model. To construct a
learning curriculum for the main model, we smooth its output distribution via
temperature scaling following a descending schedule. Our approach rivals the
performance of state-of-the-art ELECTRA-style pre-training methods, while
significantly eliminating the computation and memory cost brought by the joint
training of the auxiliary model. Our method also reduces the sensitivity to
hyper-parameters and enhances the pre-training stability.


  Radiology reporting is a crucial part of the communication between
radiologists and other medical professionals, but it can be time-consuming and
error-prone. One approach to alleviate this is structured reporting, which
saves time and enables a more accurate evaluation than free-text reports.
However, there is limited research on automating structured reporting, and no
public benchmark is available for evaluating and comparing different methods.
To close this gap, we introduce Rad-ReStruct, a new benchmark dataset that
provides fine-grained, hierarchically ordered annotations in the form of
structured reports for X-Ray images. We model the structured reporting task as
hierarchical visual question answering (VQA) and propose hi-VQA, a novel method
that considers prior context in the form of previously asked questions and
answers for populating a structured radiology report. Our experiments show that
hi-VQA achieves competitive performance to the state-of-the-art on the medical
VQA benchmark VQARad while performing best among methods without
domain-specific vision-language pretraining and provides a strong baseline on
Rad-ReStruct. Our work represents a significant step towards the automated
population of structured radiology reports and provides a valuable first
benchmark for future research in this area. Our dataset and code is available
at https://github.com/ChantalMP/Rad-ReStruct.


  We define the functors of specialization and microlocalization along a
quasi-smooth closed immersion using the theory of quasi-smooth blow-ups
developed in arXiv:1802.05702 [math.AG].
  Our first main result describes the entire microlocalization functor along
the inclusion of a derived zero fiber as the vanishing cycles with respect to a
certain function. The proof is based on the observation that the entire
Fourier-Sato transform may be written as a vanishing cycles. An equivalent
result in a slightly different setting was recently obtained by Tasuki Kinjo in
arXiv:2109.06468 [math.AG] using a different method of proof.
  Our second main result is an equivalence between the canonical twisted
vanishing cycles sheaf introduced by Brav, Bussi, Dupont, Joyce, Szendr\H{o}i,
and Sch\"urmann on the $-1$-shifted cotangent bundle of a quasi-smooth scheme
and the quasi-smooth microlocalization of the perverse constant sheaf.


  This paper focuses on Point-to-Point LoRa connections. We report on coverage
measurements performed in three distinct environments, i.e., coastal, forest
and urban. Our field experiments demonstrate coverage up to 1 km with antennas
at only 1.5 m height in an urban scenario. In free Line-of-Sight (LoS) this
coverage is extended to 4 km. Based on these results, we are developing a path
loss model in future work. The developed hardware and software including
measurements are open-source.


  We discuss the geometry of the moduli space of Prym varieties. The article is
based on series of lectures given in Bedlewo and Luminy. The first section of
the paper contains a detailed historical account of the lives of Friedrich Prym
and Friedrich Schottky.


  We show that a freshly sedimented granular bed settles and creeps forward
over extended periods of time under an applied hydrodynamic shear stress, which
is below the critical value for bedload transport. The rearrangements are found
to last over a time scale which is millions of times the sedimentation time
scale of a grain in the fluid. Compaction occurs uniformly throughout the bed,
but creep is observed to decay exponentially with depth, and decreases over
time. The granular volume fraction in the bed is found to increase
logarithmically, saturating at the random close packing value $\phi_{rcp}
\approx 0.64$, while the surface roughness is observed to remain essentially
unchanged. We demonstrate that an increasingly higher shear stress is required
to erode the bed after a sub-critical shear is applied which results in an
increase in its volume fraction. Thus, we find that bed armoring occurs due to
a deep shear-induced relaxation of the bed towards the volume fraction
associated with the glass transition.


  The performance of the Advanced GAmma Tracking Array (AGATA) at GANIL is
discussed, on the basis of the analysis of source and in-beam data taken with
up to 30 segmented crystals. Data processing is described in detail. The
performance of individual detectors are shown. The efficiency of the individual
detectors as well as the efficiency after $\gamma$-ray tracking are discussed.
Recent developments of $\gamma$-ray tracking are also presented. The
experimentally achieved peak-to-total is compared with simulations showing the
impact of back-scattered $\gamma$ rays on the peak-to-total in a $\gamma$-ray
tracking array. An estimate of the achieved position resolution using the
Doppler broadening of in-beam data is also given.
  Angular correlations from source measurements are shown together with
different methods to take into account the effects of $\gamma$-ray tracking on
the normalization of the angular correlations.


  After more than a decade of extensive research on the magnetic order
triggered by lattice defects in a wide range of nominally non-magnetic
materials, we report its application in a spintronic device. This device is
based on a spin-filter phenomenon we discovered at the interfaces between
defect-induced magnetic and non-magnetic regions, produced at the surface of a
Li doped ZnO microwire by low-energy proton implantation. Positive
magnetoresistance is observed at 300~K and scales with the number of interfaces
introduced along the wire.


  Motivated by the recent generalization of the Haldane conjecture to
$\mathrm{SU}(3)$ chains [M. Lajk\'o et al., Nucl. Phys. B924, 508 (2017)]
according to which a Haldane gap should be present for symmetric
representations if the number of boxes in the Young diagram is a multiple of
three, we develop a density matrix renormalization group algorithm based on
standard Young tableaus to study the model with three boxes directly in the
representations of the global $\mathrm{SU}(3)$ symmetry. We show that there is
a finite gap between the singlet and the symmetric $[3\,0\,0]$ sector
$\Delta_{[3\,0\,0]}/J = 0.040\pm0.006$ where $J$ is the antiferromagnetic
Heisenberg coupling, and we argue on the basis of the structure of the low
energy states that this is sufficient to conclude that the spectrum is gapped.


  In this paper, we present the LingOly benchmark, a novel benchmark for
advanced reasoning abilities in large language models. Using challenging
Linguistic Olympiad puzzles, we evaluate (i) capabilities for in-context
identification and generalisation of linguistic patterns in very low-resource
or extinct languages, and (ii) abilities to follow complex task instructions.
The LingOly benchmark covers more than 90 mostly low-resource languages,
minimising issues of data contamination, and contains 1,133 problems across 6
formats and 5 levels of human difficulty. We assess performance with both
direct accuracy and comparison to a no-context baseline to penalise
memorisation. Scores from 11 state-of-the-art LLMs demonstrate the benchmark to
be challenging, and models perform poorly on the higher difficulty problems. On
harder problems, even the top model only achieved 38.7% accuracy, 24.7%
improvement over the no-context baseline. Large closed models typically
outperform open models, and in general, the higher resource the language, the
better the scores. These results indicate, in absence of memorisation, true
multi-step out-of-domain reasoning remains a challenge for current language
models.


  What payoffs are positionally determined for deterministic two-player
antagonistic games on finite directed graphs? In this paper we study this
question for payoffs that are continuous. The main reason why continuous
positionally determined payoffs are interesting is that they include the
multi-discounted payoffs.
  We show that for continuous payoffs, positional determinacy is equivalent to
a simple property called prefix-monotonicity. We provide three proofs of it,
using three major techniques of establishing positional determinacy --
inductive technique, fixed point technique and strategy improvement technique.
A combination of these approaches provides us with better understanding of the
structure of continuous positionally determined payoffs as well as with some
algorithmic results.


  We study the time evolution of the quantum-classical correspondence (QCC) for
the well known model of quantised perturbed cat maps on the torus in the very
specific regime of semi-classically small perturbations. The quality of the QCC
is measured by the overlap of classical phase-space density and corresponding
Wigner function of the quantum system called quantum-classical fidelity (QCF).
In the analysed regime the QCF strongly deviates from the known general
behaviour in particular it decays faster then exponential. Here we study and
explain the observed behavior of the QCF and the apparent violation of the QCC
principle.


  We investigate properties of essential spectra of disjointness preserving
operators acting on Banach $C(K)$-modules. In particular, we prove that under
some very mild conditions the upper semi-Fredholm spectrum of such an operator
is rotation invariant. In the last part of the paper we provide a full
description of the spectrum and the essential spectra of operators acting on
Kaplansky modules of the form $T = wU$, where $w \in C(K)$, $U$ is a
$d$-isomorphism, and the spectrum of $U$ is a subset of the unit circle.


  We present results on the K*(892)+ production in proton-proton collisions at
a beam energy of E = 3.5 GeV, which is hitherto the lowest energy at which this
mesonic resonance has been observed in nucleon-nucleon reactions. The data are
interpreted within a two-channel model that includes the 3-body production of
K*(892)+ associated with the Lambda- or Sigma-hyperon. The relative
contributions of both channels are estimated. Besides the total cross section
sigma(p+p -> K*(892)+ + X) = 9.5 +- 0.9 +1.1 -0.9 +- 0.7 mub, that adds a new
data point to the excitation function of the K*(892)+ production in the region
of low excess energy, transverse momenta and angular spectra are extracted and
compared with the predictions of the two-channel model. The spin
characteristics of K*(892)+ are discussed as well in terms of the
spin-alignment.


  Activation Functions introduce non-linearity in the deep neural networks.
This nonlinearity helps the neural networks learn faster and efficiently from
the dataset. In deep learning, many activation functions are developed and used
based on the type of problem statement. ReLU's variants, SWISH, and MISH are
goto activation functions. MISH function is considered having similar or even
better performance than SWISH, and much better than ReLU. In this paper, we
propose an activation function named APTx which behaves similar to MISH, but
requires lesser mathematical operations to compute. The lesser computational
requirements of APTx does speed up the model training, and thus also reduces
the hardware requirement for the deep learning model.


  We present a new way of modeling turbulent thermonuclear deflagration fronts
in Chandrasekhar-mass white dwarfs, consisting of carbon and oxygen, undergoing
a type Ia supernova explosion. Our approach is a front capturing/tracking
hybrid scheme, based on a level set method, which treats the front as a
mathematical discontinuity and allows for full coupling between the front
geometry and the flow field. First results of the method applied to the problem
of type Ia supernovae are discussed. It will be shown that even in 2-D and even
with a physically motivated sub-grid model numerically ``converged'' results
are difficult to obtain.


  We construct a formula $\phi$ which axiomatizes non-narrow rectangular grids
without using any binary relations other than the grid neighborship relations.
As a corollary, we prove that a set $A \subseteq \mathbb{N}$ is a spectrum of a
formula which has only planar models if numbers $n \in A$ can be recognized by
a non-deterministic Turing machine (or a one-dimensional cellular automaton) in
time $t(n)$ and space $s(n)$, where $t(n)s(n) \leq n$ and $t(n),s(n) =
\Omega(\log(n))$.


  Formulas are derived for the average level density of deformed, or
transition, Gaussian orthogonal random matrix ensembles. After some general
considerations about Gaussian ensembles we derive formulas for the average
level density for (i) the transition from the Gaussian orthogonal ensemble
(GOE) to the Poisson ensemble and (ii) the transition from the GOE to $m$ GOEs.


  We show that important anomalous features of the normal-state thermoelectric
power S of high-Tc materials can be understood as being caused by doping
dependent short-range antiferromagnetic correlations. The theory is based on
the fluctuation-exchange approximation applied to Hubbard model in the
framework of the Kubo formalism. Firstly, the characteristic maximum of S as
function of temperature can be explained by the anomalous momentum dependence
of the single-particle scattering rate. Secondly, we discuss the role of the
actual Fermi surface shape for the occurrence of a sign change of S as a
function of temperature and doping.


  We theoretically investigate the use of quantum non-demolition measurement to
enhance the sensitivity of atom interferometry with Bose-condensed atoms. In
particular, we are concerned with enhancing existing high-precision atom
interferometry apparatuses, so restrict ourselves to dilute atomic samples, and
the use of free-propagating light, or optical cavities in the weak-coupling
regime. We find the optimum parameter regime that balances between spin
squeezing and atomic loss, and find that significant improvements in
sensitivity are possible. Finally, we consider the use of squeezed light, and
show that this can provide further boosts to sensitivity.


  The Muon Ionization Cooling Experiment (MICE) will demonstrate the principle
of muon beam phase-space reduction via ionization cooling. Muon beam cooling
will be required for the proposed Neutrino Factory or Muon Collider. The
phase-space before and after the cooling cell must be measured precisely. This
is achieved using two scintillating-fibre trackers, each placed in a solenoidal
magnetic field. This paper describes the software reconstruction for the fibre
trackers: the GEANT4 based simulation; the implementation of the geometry;
digitisation; space-point reconstruction; pattern recognition; and the final
track fit based on a Kalman filter. The performance of the software is
evaluated by means of Monte Carlo studies and the precision of the final track
reconstruction is evaluated.


  At the heart of systems chemistry lies the idea that supramolecular
interactions can give rise to complex and unexpected collective states that
emerge on a fundamentally different lengthscale to that of the interactions
themselves. While in certain cases - e.g. the self-assembly of virus-like
polyhedral cages from coordination building blocks - it is possible to control
emergence in a systematic manner, the development of general approaches remains
a fundamental challenge in the field. In the conceptually-related domain of
frustrated magnetism - where collective states give rise to exotic physics of
relevance to data storage and spintronics - the task of predicting emergent
behaviour is simplified through control over the geometry and form of the
magnetic interactions from which complexity arises. Seeking to combine
approaches from these two fields, we study here the solid phases of inorganic
polymer chains assembled from non-magnetic gold(I)/silver(I) cations and
cyanide anions. We show the periodic inter-chain potential encodes a
supramolecular interaction that can be tuned to mimic different magnetic
interactions between XY spins ("spin rotors"). Because the chains pack on a
triangular lattice, the crystal structures of gold(I)/silver(I) cyanides can be
interpreted in terms of the phase behaviour of triangular XY magnets. Complex
magnetic states predicted for this family - including hidden quadrupolar order
and emergent spin-vortex quasiparticles - are realised for the first time in
the structural chemistry of these cyanide polymers. In this way we demonstrate
both how simple inorganic materials might behave as structural analogues of
otherwise-unrealisable "toy" spin models, and also how a theoretical
understanding of those models might be used to predict and control emergent
phenomena in chemical systems.


  Pathogens drive changes in host immune systems that in turn exert pressure
for pathogens to evolve. Quantifying and understanding this constant
coevolutionary process has clear practical global health implications. Yet its
relatively easier accessibility compared to macroevolution makes it a
fascinating system to learn about the basic laws of evolution. Focusing on
immune-viral evolution, we present an overview of theoretical and experimental
approaches that have recently started coming together to build the foundations
for a quantitative and predictive co-evolutionary theory.


  We prove tight probabilistic bounds for the shortest vectors in module
lattices over number fields using the results of arXiv:2308.15275. Moreover,
establishing asymptotic formulae for counts of fixed rank matrices with
algebraic integer entries and bounded Euclidean length, we prove an approximate
Rogers integral formula for discrete sets of module lattices obtained from
lifts of algebraic codes. This in turn implies that the moment estimates of
arXiv:2308.15275 as well as the aforementioned bounds on the shortest vector
also carry through for large enough discrete sets of module lattices.


  Albeit great performance of Transformer-based speech selfsupervised learning
(SSL) models, their large parameter size and computational cost make them
unfavorable to utilize. In this study, we propose to compress the speech SSL
models by distilling speech temporal relation (STaR). Unlike previous works
that directly match the representation for each speech frame, STaR distillation
transfers temporal relation between speech frames, which is more suitable for
lightweight student with limited capacity. We explore three STaR distillation
objectives and select the best combination as the final STaR loss. Our model
distilled from HuBERT BASE achieves an overall score of 79.8 on SUPERB
benchmark, the best performance among models with up to 27 million parameters.
We show that our method is applicable across different speech SSL models and
maintains robust performance with further reduced parameters.


  In the framework of the gauge/gravity duality, and in particular of the
$AdS_3/CFT_2$ correspondence, we study one-dimensional superconductors
analyzing the dual (1+2)-dimensional gravity in the presence of the
Einstein-power-Maxwell non-linear Electrodynamics. In the probe limit we
compute the critical temperature of the transition as a function of the mass of
the scalar field. The computation is performed analytically employing the
Rayleigh-Ritz variational principle. The comparison with a power Maxwell field
in higher dimensions as well as with the (1+3)-dimensional Einstein-Maxwell
theory for two-dimensional superconductors is made as well.


  The properties of the orbit and the donor star in the high mass X-ray binary
microquasar LS 5039 indicate that accretion processes should mainly occur via a
radiatively driven wind. In such a scenario, significant X-ray variability
would be expected due to the eccentricity of the orbit. The source has been
observed at X-rays by several missions, although with a poor coverage that
prevents to reach any conclusion about orbital variability. Therefore, we
conducted RossiXTE observations of the microquasar system LS 5039 covering a
full orbital period of 4 days. Individual observations are well fitted with an
absorbed power-law plus a Gaussian at 6.7 keV, to account for iron line
emission that is probably a diffuse background feature. In addition, we have
taken into account that the continuum is also affected by significant diffuse
background contamination. Our results show moderate power-law flux variations
on timescales of days, as well as the presence of miniflares on shorter
timescales. The new orbital ephemeris of the system recently obtained by
Casares et al. have allowed us to show, for the first time, that an increase of
emission is seen close to the periastron passage, as expected in an accretion
scenario. Moreover, the detected orbital variability is a factor of ~4 smaller
than the one expected by using a simple wind accretion model, and we suggest
that an accretion disk around the compact object could be responsible for this
discrepancy. On the other hand, significant changes in the photon index are
also observed clearly anti-correlated with the flux variations. We interpret
the overall X-ray spectral characteristics of LS 5039 in the context of X-ray
radiation produced by inverse Compton and/or synchrotron processes in the jet
of this microquasar.


  We report the experimental emulation of trembling quantum motion, or
Zitterbewegung, of exciton polaritons in a perovskite microcavity at room
temperature. By introducing liquid crystal molecules into the microcavity, we
achieve spinor states with synthetic Rashba-Dresselhaus spin-orbit coupling and
tunable energy splitting. Under a resonant excitation, the polariton fluid
exhibits clear trembling motion perpendicular to its flowing direction,
accompanied by a unique spin pattern resembling interlocked fingers.
Furthermore, leveraging on the sizable tunability of energy gaps by external
electrical voltages, we observe the continuous transition of polariton
Zitterbewegung from relativistic (small gaps) to non-relativistic (large gaps)
regimes. Our findings pave the way for using exciton polaritons in the
emulation of relativistic quantum physics.


  A Petrov-Galerkin finite element method is constructed for a singularly
perturbed elliptic problem in two space dimensions. The solution contains a
regular boundary layer and two characteristic boundary layers. Exponential
splines are used as test functions in one coordinate direction and are combined
with bilinear trial functions defined on a Shishkin mesh. The resulting
numerical method is shown to be a stable parameter-uniform numerical method
that achieves a higher order of convergence compared to upwinding on the same
mesh.


  The Quasi-Frozen Spin (QFS) method was proposed by Yu. Senichev et al. in [1]
as an alternative to the Frozen Spin (FS) method [2] for the search of deuteron
electric dipole moment (dEDM). The QFS approach simplifies the design of the
lattice. In particular, small changes to the currently operating COSY storage
ring will satisfy the QFS condition. Spin decoherence and systematic errors
fundamentally limit EDM signal detection and measurement. Our QFS
implementation method includes measurement of spin precession in (1) the
horizontal plane to calibrate the magnetic field when changing field polarity
and (2) the vertical plane to search for EDM. To address systematic errors due
to element misalignments, we track particle bunches in forward and reverse
directions. We modeled and tracked two QFS and one FS lattice in COSY INFINITY.
The models include normally distributed random variate spin kicks in magnetic
dipoles and combined electrostatic and magnetic field elements. We used Wolfram
Mathematica programs to partially automate lattice input file generation and
tracking output data analysis. We observed indications that the QFS method is a
viable alternative to the FS method.
  [1] Y. Senichev, A. Lehrach, B. Lorentz, R. Maier, S. Andrianov, A. Ivanov,
S. Chekmenev, M. Berz, and E. Valetov (on behalf of the JEDI Collaboration), in
Proceedings of IPAC 2015, Richmond, VA (2015) MOPWA044. [2] D. Anastassopoulos
et al., AGS Proposal: Search for a Permanent Electric Dipole Moment of the
Deuteron Nucleus at the $10^{-29}\:e\cdot\mathrm{cm}$ Level, BNL Report,
Brookhaven National Laboratory, Upton, NY (2008).


  The interest in obtaining high-quality monolayer transition metal
dichalcogenides (TMDs) for optoelectronic device applications has been growing
dramatically. However, the prevalence of defects and unwanted doping in these
materials remains a challenge, as they both limit optical properties and device
performance. Surface chemical treatments of monolayer TMDs have been effective
in improving their photoluminescence yield and charge transport properties. In
this scenario, a systematic understanding of the underlying mechanism of
chemical treatments will lead to a rational design of passivation strategies in
future research, ultimately taking a step toward practical optoelectronic
applications. We will therefore describe in this review the strategies,
progress, mechanisms, and prospects of chemical treatments to passivate and
improve the optoelectronic properties of TMDs.


  The low-field electron mobility in rectangular silicon nanowire (SiNW)
transistors was computed using a self-consistent Poisson-Schr\"{o}dinger-Monte
Carlo solver. The behavior of the phonon-limited and surface-roughness-limited
components of the mobility was investigated by decreasing the wire width from
30 nm to 8 nm, the width range capturing a crossover between two-dimensional
(2D) and one-dimensional (1D) electron transport. The phonon-limited mobility,
which characterizes transport at low and moderate transverse fields, is found
to decrease with decreasing wire width due to an increase in the
electron-phonon wavefunction overlap. In contrast, the mobility at very high
transverse fields, which is limited by surface roughness scattering, increases
with decreasing wire width due to volume inversion. The importance of acoustic
phonon confinement is also discussed briefly.


  In this paper, we study some aspects of moduli stabilization using string
gases in the context of the Swampland. In the framework which we derive, the
matter Lagrangian for string gases yields a potential for the size moduli which
satisfies the de Sitter conjecture with the condition $\frac{|\nabla V|}{V}
\geq \frac{1}{\sqrt{p}}\frac{1}{M_p}$, where $p$ is the number of compactified
dimensions. Moreover, the moduli find themselves stabilized at the self-dual
radius, and gravity naturally emerges as the weakest force.


  Some problems in discrete-event systems (DES) model large, time-varying state
spaces with complex legal languages. To address these problems, Chung et al.
introduced limited lookahead policies (LLP) to provide online supervisory
control for discrete-event systems. This seminal paper, along with an addendum
of technical results, provided the field with a series of very important and
powerful results, but in a notationally- and conceptually-dense manner. In this
tutorial, we present Chung et al.'s problem formulation for online control and
unravel the formal definitions and proofs from their original work with the aim
of making the ideas behind limited lookahead accessible to all DES researchers.
Finally, we introduce the Air Traffic Control problem as an example of an
online control problem and demonstrate the synthesis of LLP supervisors.


  Second order buckling theory involves a one-way coupled coupled problem where
the stress tensor from a plane stress problem appears in an eigenvalue problem
for the fourth order Kirchhoff plate. In this paper we present an a posteriori
error estimate for the critical buckling load and mode corresponding to the
smallest eigenvalue and associated eigenvector. A particular feature of the
analysis is that we take the effect of approximate computation of the stress
tensor and also provide an error indicator for the plane stress problem. The
Kirchhoff plate is discretized using a continuous/discontinuous finite element
method which uses standard continuous piecewise polynomial finite element
spaces which can also be used to solve the plane stress problem.


  Recent thermal conductivity data on the heavy fermion superconductor $UPt_3$
have been interpreted as offering support for an $E_{2u}$ model of the order
parameter as opposed to an $E_{1g}$ model. In this paper, we analyze this issue
from a theoretical standpoint including the detailed effects of Fermi surface
and gap anisotropy. Our conclusion is that although current data put strong
constraints on the gap anisotropy, they cannot definitively distinguish between
these two models. Measurements on samples of varying quality could be decisive
in this regard, however.


  We consider a quantum system consisting of a regular chain of elementary
subsystems with nearest neighbor interactions and assume that the total system
is in a canonical state with temperature $T$. We analyze under what condition
the state factors into a product of canonical density matrices with respect to
groups of $n$ subsystems each, and when these groups have the same temperature
$T$. While in classical mechanics the validity of this procedure only depends
on the size of the groups $n$, in quantum mechanics the minimum group size
$n_{\text{min}}$ also depends on the temperature $T $! As examples, we apply
our analysis to a harmonic chain and an Ising spin chain. We discuss various
features that show up due to the characteristics of the models considered. For
the harmonic chain, which successfully describes thermal properties of
insulating solids, our approach gives a first quantitative estimate of the
minimal length scale on which temperature can exist: This length scale is found
to be constant for temperatures above the Debye temperature and proportional to
$T^{-3}$ below.


  We generalize the Bogoliubov quark-meson coupling model to also include
hyperons. The hyperon-$\sigma$-meson couplings are fixed by the model and the
hyperon-$\omega$-meson couplings are fitted to the hypreon potentials in
symmetric nuclear matter. The present model predicts neutron stars with masses
above 2$M_\odot$ and the radius of a 1.4$M_\odot$ star equal to 13.83 km.


  The corona is a layer of hot plasma that surrounds the Sun, traces out its
complex magnetic field, and ultimately expands into interplanetary space as the
supersonic solar wind. Although much has been learned in recent decades from
advances in observations, theory, and computer simulations, we still have not
identified definitively the physical processes that heat the corona and
accelerate the solar wind. In this review, we summarize these recent advances
and speculate about what else is required to finally understand the fundamental
physics of this complex system. Specifically: (1) We discuss recent
sub-arcsecond observations of the corona, some of which appear to provide
evidence for tangled and braided magnetic fields, and some of which do not. (2)
We review results from three-dimensional numerical simulations that, despite
limitations in dynamic range, reliably contain sufficient heating to produce
and maintain the corona. (3) We provide a new tabulation of scaling relations
for a number of proposed coronal heating theories that involve waves,
turbulence, braiding, nanoflares, and helicity conservation. An understanding
of these processes is important not only for improving our ability to forecast
hazardous space-weather events, but also for establishing a baseline of
knowledge about a well-resolved star that is relevant to other astrophysical
systems.


  We study matter-coupled $N=3$ gauged supergravity in four dimensions with
various semisimple gauge groups. When coupled to $n$ vector multiplets, the
gauged supergravity contains $3+n$ vector fields and $3n$ complex scalars
parametrized by $SU(3,n)/SU(3)\times SU(n)\times U(1)$ coset manifold.
Semisimple gauge groups take the form of $G_0\times H\subset SO(3,n)\subset
SU(3,n)$ with $H$ being a compact subgroup of $SO(n+3-\textrm{dim}(G_0))$. The
$G_0$ groups considered in this paper are of the form $SO(3)$, $SO(3,1)$,
$SO(2,2)$, $SL(3,\mathbb{R})$ and $SO(2,1)\times SO(2,2)$. We find that
$SO(3)\times SO(3)$, $SO(3,1)$ and $SL(3,\mathbb{R})$ gauge groups admit a
maximally supersymmetric $AdS_4$ critical point. The $SO(2,1)\times SO(2,2)$
gauge group admits a supersymmetric Minkowski vacuum while the remaining gauge
groups admit both half-supersymmetric domain wall vacua and $AdS_4$ vacua with
completely broken supersymmetry. For the $SO(3)\times SO(3)$ gauge group, there
exists another supersymmetric $N=3$ $AdS_4$ critical point with
$SO(3)_{\textrm{diag}}$ symmetry. We explicitly give a detailed study of
various holographic RG flows between $AdS_4$ critical points, flows to
non-conformal theories and supersymmetric domain walls in each gauge group. The
results provide gravity duals of $N=3$ Chern-Simons-Matter theories in three
dimensions.


  We report on the first measurement of the Breit-Wigner resonance of the
transition from {\it ortho-}positronium to {\it para-}positronium. We have
developed an optical system to accumulate a power of over 20 kW using a
frequency-tunable gyrotron and a Fabry-P\'{e}rot cavity. This system opens a
new era of millimeter-wave spectroscopy, and enables us to directly determine
both the hyperfine interval and the decay width of {\it p-}Ps.


  We show that parton confinement in the final state generates large $1/Q^2$
(higher twist) corrections to Bjorken scaling. For treatment of these
non-perturbative effects, we derive a new expansion in powers of $1/Q^2$ for
the structure function that is free of infra-red singularities and which
reduces corrections to the leading term. The leading term represents scattering
from an off-mass-shell parton, which keeps the same virtual mass in the final
state. This term appears as a function of a new variable $\bar x(x,Q^2)$, which
coincides with the Bjorken variable x for $Q^2\to\infty$. Analysis of the data
shows excellent scaling at large x, where power corrections are dominant. The
approach accommodates also the QCD logarithmic corrections and the behavior of
the structure functions is well reproduced within a wide kinematical range.
Since the new scaling variable $\bar x(x,Q^2)$ incorporates the higher twist
effects, it allows us to extract the ratio $F_2^n(x)/F_2^p(x)$ for $x\to 1$
from the available data at moderate Q^2.


  We investigate radiative processes of inertial two-level atoms in an
entangled state interacting with a quantum electromagnetic field. Our intention
is to clarify and to analyze the contributions of vacuum fluctuations and
radiation reaction to the decay rate of the entangled state. The possible
relevance of the findings in the present work is discussed.


  We prove that a free group F_2 admits a faithful discrete representation into
Diff_{+}(I). We also prove that F_2 admits a faithful discrete representation
into Homeo_{+}(I). Some properties of these representations have been studied.
In the last section we raise several questions.


  We have developed a linearly-polarized Ytterbium-doped fiber ring laser with
single longitudinal-mode output at 1064nm for LISA and other space
applications. Single longitudinal-mode selection was achieved by using a fiber
Bragg grating (FBG) and a fiber Fabry-Perot (FFP). The FFP also serves as a
frequency-reference within our ring laser. Our laser exhibits comparable low
frequency and intensity noise to Non-Planar Ring Oscillator (NPRO). By using a
fiber-coupled phase modulator as a frequency actuator, the laser frequency can
be electro-optically tuned at a rate of 100kHz. It appears that our fiber ring
laser is promising for space applications where robustness of fiber optics is
desirable.


  The most recent pointwise Large Language Model (LLM) rankers have achieved
remarkable ranking results. However, these rankers are hindered by two major
drawbacks: (1) they fail to follow a standardized comparison guidance during
the ranking process, and (2) they struggle with comprehensive considerations
when dealing with complicated passages. To address these shortcomings, we
propose to build a ranker that generates ranking scores based on a set of
criteria from various perspectives. These criteria are intended to direct each
perspective in providing a distinct yet synergistic evaluation. Our research,
which examines eight datasets from the BEIR benchmark demonstrates that
incorporating this multi-perspective criteria ensemble approach markedly
enhanced the performance of pointwise LLM rankers.


  We show that Bonnesen's isoperimetic defect has a systolic analog for
Loewner's torus inequality. The isosystolic defect is expressed in terms of the
probabilistic variance of the conformal factor of the metric g with respect to
the flat metric of unit area in the conformal class of g.


  We present experimentally and numerically accessible quantities that can be
used to differentiate among various families of random entangled states. To
this end, we analyze the entanglement properties of bipartite reduced states of
a tripartite pure state. We introduce a ratio of simple polynomials of
low-order moments of the partially transposed reduced density matrix and show
that this ratio takes well-defined values in the thermodynamic limit for
various families of entangled states. This allows to sharply distinguish
entanglement phases, in a way that can be understood from a quantum information
perspective based on the spectrum of the partially transposed density matrix.
We analyze in particular the entanglement phase diagram of Haar random states,
states resulting form the evolution of chaotic Hamiltonians, stabilizer states,
which are outputs of Clifford circuits, Matrix Product States, and fermionic
Gaussian states. We show that for Haar random states the resulting phase
diagram resembles the one obtained via the negativity and that for all the
cases mentioned above a very distinctive behaviour is observed. Our results can
be used to experimentally test necessary conditions for different types of
mixed-state randomness, in quantum states formed in quantum computers and
programmable quantum simulators.


  This work studies the robust design of downlink precoding for cloud radio
access network (C-RAN) in the presence of asynchronism among remote radio heads
(RRHs). Specifically, a C-RAN downlink system is considered in which non-ideal
fronthaul links connecting two RRHs to a Baseband Unit (BBU) may cause a time
offset, as well as a phase offset, between the transmissions of the two RRHs.
The offsets are a priori not known to the BBU. With the aim of counteracting
the unknown time offset, a robust precoding scheme is considered that is based
on the idea of correlating the signal transmitted by one RRH with a number of
delayed versions of the signal transmitted by the other RRH. For this
transmission strategy, the problem of maximizing the worst-case minimum rate is
tackled while satisfying per-RRH transmit power constraints. Numerical results
are reported that verify the advantages of the proposed robust scheme as
compared to conventional non-robust design criteria as well as non-cooperative
transmission.


  A general theoretical framework is developed for interpreting
spectropolarimetric observations of optically thin emission line scattering
from small dust particles. Spatially integrated and spatially resolved line
profiles of both scattered intensity and polarization are calculated
analytically from a variety of simple kinematic models. These calculations will
provide a foundation for further studies of emission line scattering from dust
and electrons in such diverse astrophysical environments as Herbig-Haro
objects, symbiotic stars, starburst galaxies and active galactic nuclei.


  Deep Learning (DL) has shown remarkable results in solving inverse problems
in various domains. In particular, the Tikhonet approach is very powerful to
deconvolve optical astronomical images (Sureau et al. 2020). Yet, this approach
only uses the $\ell_2$ loss, which does not guarantee the preservation of
physical information (e.g. flux and shape) of the object reconstructed in the
image. In Nammour et al. (2021), a new loss function was proposed in the
framework of sparse deconvolution, which better preserves the shape of galaxies
and reduces the pixel error. In this paper, we extend Tikhonet to take into
account this shape constraint, and apply our new DL method, called ShapeNet, to
optical and radio-interferometry simulated data set. The originality of the
paper relies on i) the shape constraint we use in the neural network framework,
ii) the application of deep learning to radio-interferometry image
deconvolution for the first time, and iii) the generation of a simulated radio
data set that we make available for the community. A range of examples
illustrates the results.


  The first part of these notes is devoted to an introduction to algebraic
$D$-modules. Several basic notions are introduced. In the second part,
$D$-modules with group action are treated. Several important examples in this
situation are discussed in details. Particularly, the Harish-Chandra systems
for group characters and the Gelfand generalized hypergeometric systems are our
main topics.


  Non-intrusive load monitoring (NILM) is essential for understanding
customer's power consumption patterns and may find wide applications like
carbon emission reduction and energy conservation. The training of NILM models
requires massive load data containing different types of appliances. However,
inadequate load data and the risk of power consumer privacy breaches may be
encountered by local data owners during the NILM model training. To prevent
such potential risks, a novel NILM method named Fed-NILM which is based on
Federated Learning (FL) is proposed in this paper. In Fed-NILM, local model
parameters instead of local load data are shared among multiple data owners.
The global model is obtained by weighted averaging the parameters. Experiments
based on two measured load datasets are conducted to explore the generalization
ability of Fed-NILM. Besides, a comparison of Fed-NILM with locally-trained
NILMs and the centrally-trained NILM is conducted. The experimental results
show that Fed-NILM has superior performance in scalability and convergence.
Fed-NILM outperforms locally-trained NILMs operated by local data owners and
approximates the centrally-trained NILM which is trained on the entire load
dataset without privacy protection. The proposed Fed-NILM significantly
improves the co-modeling capabilities of local data owners while protecting
power consumers' privacy.


  The gravitational field of a galaxy can act as a lens and deflect the light
emitted by a more distant object such as a quasar. Strong gravitational lensing
causes multiple images of the same quasar to appear in the sky. Since the light
in each gravitationally lensed image traverses a different path length from the
quasar to the Earth, fluctuations in the source brightness are observed in the
several images at different times. The time delay between these fluctuations
can be used to constrain cosmological parameters and can be inferred from the
time series of brightness data or light curves of each image. To estimate the
time delay, we construct a model based on a state-space representation for
irregularly observed time series generated by a latent continuous-time
Ornstein-Uhlenbeck process. We account for microlensing, an additional source
of independent long-term extrinsic variability, via a polynomial regression.
Our Bayesian strategy adopts a Metropolis-Hastings within Gibbs sampler. We
improve the sampler by using an ancillarity-sufficiency interweaving strategy
and adaptive Markov chain Monte Carlo. We introduce a profile likelihood of the
time delay as an approximation of its marginal posterior distribution. The
Bayesian and profile likelihood approaches complement each other, producing
almost identical results; the Bayesian method is more principled but the
profile likelihood is simpler to implement. We demonstrate our estimation
strategy using simulated data of doubly- and quadruply-lensed quasars, and
observed data from quasars Q0957+561 and J1029+2623.


  In this work, we introduce long range version of the extended Hubbard model.
The system is defined on a non-uniform lattice. We show that the system is
integrable. The ground state, the ground state energies, the energy spectrum
are also found for the system. Another long range version of the extended
Hubbard model is also introduced on a uniform lattice, and this system is
proven to be integrable.


  Theoretical studies recently predicted the condensation of spin-orbit
excitons at momentum $q$=$\pi$ in $t_{2g}^4$ spin-orbit coupled three-orbital
Hubbard models at electronic density $n=4$. In parallel, experiments involving
iridates with non-integer valence states for the Ir ions are starting to
attract considerable attention. In this publication, using the density matrix
renormalization group technique we present evidence for the existence of a
novel excitonic condensate at $n=3.5$ in a one-dimensional Hubbard model with a
degenerate $t_{2g}$ sector, when in the presence of spin-orbit coupling. At
intermediate Hubbard $U$ and spin-orbit $\lambda$ couplings, we found an
excitonic condensate at the unexpected momentum $q$=$\pi/2$ involving
$j_{\textrm{eff}}=3/2,m=\pm1/2$ and $j_{\textrm{eff}}=1/2,m=\pm1/2$ bands in
the triplet channel, coexisting with an also unexpected block magnetic order.
We also present the entire $\lambda$ vs $U$ phase diagram, at a fixed and
robust Hund coupling. Interestingly, this new `block excitonic phase' is
present even at large values of $\lambda$, unlike the $n=4$ excitonic phase
discussed before. Our computational study helps to understand and predict the
possible magnetic phases of materials with $d^{3.5}$ valence and robust
spin-orbit coupling.


  High-speed measurement confronts the extreme speed limit when the signal
becomes comparable to the noise level. In the context of broadband mid-infrared
spectroscopy, state-of-the-art ultrafast Fourier-transform infrared
spectrometers, in particular dual-comb spectrometers, have improved the
measurement rate up to a few Mspectra/s, which is limited by the
signal-to-noise ratio. Time-stretch infrared spectroscopy, an emerging
ultrafast frequency-swept mid-infrared spectroscopy technique, has shown a
record-high rate of 80 Mspectra/s with an intrinsically higher signal-to-noise
ratio than Fourier-transform spectroscopy by more than the square-root of the
number of spectral elements. However, it can measure no more than ~30 spectral
elements with a low resolution of several cm-1. Here, we significantly increase
the measurable number of spectral elements to more than 1,000 by incorporating
a nonlinear upconversion process. The one-to-one mapping of a broadband
spectrum from the mid-infrared to the near-infrared telecommunication region
enables low-loss time-stretching with a single-mode optical fiber and low-noise
signal detection with a high-bandwidth photoreceiver. We demonstrate
high-resolution mid-infrared spectroscopy of gas-phase methane molecules with a
high resolution of 0.017 cm-1. This unprecedentedly high-speed vibrational
spectroscopy technique would satisfy various unmet needs in experimental
molecular science, e.g., measuring ultrafast dynamics of irreversible
phenomena, statistically analyzing a large amount of heterogeneous spectral
data, or taking broadband hyperspectral images at a high frame rate.


  We present arguments pointing to a behavior of the string free energy in the
presence of a black hole horizon similar to the Atick-Witten dependence on
temperature beyond the Hagedorn transition. We give some evidence based on
orbifold techniques applied to Rindler space and further support is found
within a Hamiltonian approach. However, we argue that the interpretation in
terms of a reduction of degrees of freedom is confronted by serious problems.
Finally, we point out the problems concerning heuristic red-shift arguments and
the local interpretation of thermodynamical quantities.


  We report the fabrication and the characterization of carbon fibre tips for
their use in combined scanning tunnelling and force microscopy based on
piezoelectric quartz tuning fork force sensors. We find that the use of carbon
fibre tips results in a minimum impact on the dynamics of quartz tuning fork
force sensors yielding a high quality factor and consequently a high force
gradient sensitivity. This high force sensitivity in combination with high
electrical conductivity and oxidation resistance of carbon fibre tips make them
very convenient for combined and simultaneous scanning tunnelling microscopy
and atomic force microscopy measurements. Interestingly, these tips are quite
robust against occasionally occurring tip crashes. An electrochemical
fabrication procedure to etch the tips is presented that produces a sub-100 nm
apex radius in a reproducible way which can yield high resolution images.


  IIt is shown that a weak measurement of a quantum system produces a new state
of the quantum system which depends on the prior state, as well as the
(uncontrollable) measured position of the pointer variable of the weak
measurement apparatus. The result imposes a constraint on hidden-variable
theories which assign a different state to a quantum system than standard
quantum mechanics. The constraint means that a crypto-nonlocal hidden-variable
theory can be ruled out in a more direct way than previously.


  We consider holomorphic functions on the unit disc whose images are contained
in a strip of the complex plane. Under an additional condition, such functions
are constants. We also consider appropriate operator valued versions.
Applications are found to the theory of semigroups.


  The aim of this paper is to study a class of positive solutions of the fast
diffusion equation with specific persistent singular behavior. First, we
construct new types of solutions with anisotropic singularities. Depending on
parameters, either these solutions solve the original equation in the
distributional sense, or they are not locally integrable in space-time. We show
that the latter also holds for solutions with snaking singularities, whose
existence has been proved recently by M. Fila, J.R. King, J. Takahashi, and E.
Yanagida. Moreover, we establish that in the distributional sense, isotropic
solutions whose existence was proved by M. Fila, J. Takahashi, and E. Yanagida
in 2019, actually solve the corresponding problem with a moving Dirac source
term. Last, we discuss the existence of solutions with anisotropic
singularities in a critical case.


  We consider the partial theta function $\theta (q,z):=\sum
_{j=0}^{\infty}q^{j(j+1)/2}z^j$, where $(q,z)\in \mathbb{C}^2$, $|q|<1$. We
show that for any $0<\delta _0<\delta <1$, there exists $n_0\in \mathbb{N}$
such that for any $q$ with $\delta _0\leq |q|\leq \delta$ and for any $n\geq
n_0$ the function $\theta$ has exactly $n$ zeros with modulus $<|q|^{-n-1/2}$
counted with multiplicity.


  We show that many bounded rationality patterns of choice can be alternatively
represented as testable models of limited consideration, and we elicit the
features of the associated unobserved consideration sets from the observed
choice. Moreover, we characterize some testable choice procedures in which the
DM considers as few alternatives as possible. These properties, compatible with
the empirical evidence, allow the experimenter to uniquely infer the DM's
unobserved consideration sets from irrational features of the observed
behavior.