  We present a high resolution (R ~ 43000) abundance analysis of a total of
nine stars in three of the five globular clusters associated with the nearby
Fornax dwarf spheroidal galaxy. These three clusters (1, 2 and 3) trace the
oldest, most metal-poor stellar populations in Fornax. We determine abundances
of O, Mg, Ca, Ti, Cr, Mn, Fe, Ni, Zn, Y, Ba, La, Nd and Eu in most of these
stars, and for some stars also Mn and La. We demonstrate that classical
indirect methods (isochrone fitting and integrated spectra) of metallicity
determination lead to values of [Fe/H] which are 0.3 to 0.5 dex too high, and
that this is primarily due to the underlying reference calibration typically
used by these studies. We show that Cluster 1, with [Fe /H] = -2.5, now holds
the record for the lowest metallicity globular cluster. We also measure an
over-abundance of Eu in Cluster 3 stars that has only been previously detected
in a subgroup of stars in M15. We find that the Fornax globular cluster
properties are a global match to what is found in their Galactic counterparts;
including deep mixing abundance patterns in two stars. We conclude that at the
epoch of formation of globular clusters both the Milky Way and the Fornax dwarf
spheroidal galaxy shared the same initial conditions, presumably pre-enriched
by the same processes, with identical nucleosynthesis patterns.


  After having investigated the real conic sections and their isoptic curves in
the hyperbolic plane $\bH^2$ we consider the problem of the isoptic curves of
generalized conic sections in the extended hyperbolic plane.
  This topic is widely investigated in the Euclidean plane $\BE^2$ (see for
example \cite{Lo}), but in the hyperbolic and elliptic planes there are few
results (see \cite{CsSz1}, \cite{CsSz2} and \cite{CsSz3}). In this paper we
recall the former results on isoptic curves in the hyperbolic plane geometry,
and define the notion of the generalised hyperbolic angle between proper and
non-proper straight lines, summarize the notions of generalized hyperbolic
conic sections classified by K.~Fladt in \cite{KF1} and \cite{KF2} and gy
E.~Moln\'ar in \cite{M81}. Furthermore, we determine and visualize the
generalized isoptic curves to all hyperbolic conic sections.
  We use for the computations the classical models which are based on the
projective interpretation of the hyperbolic geometry and in this manner the
isoptic curves can be visualized on the Euclidean screen of computer.


  We present cortical surface parcellation using spherical deep convolutional
neural networks. Traditional multi-atlas cortical surface parcellation requires
inter-subject surface registration using geometric features with high
processing time on a single subject (2-3 hours). Moreover, even optimal surface
registration does not necessarily produce optimal cortical parcellation as
parcel boundaries are not fully matched to the geometric features. In this
context, a choice of training features is important for accurate cortical
parcellation. To utilize the networks efficiently, we propose cortical
parcellation-specific input data from an irregular and complicated structure of
cortical surfaces. To this end, we align ground-truth cortical parcel
boundaries and use their resulting deformation fields to generate new pairs of
deformed geometric features and parcellation maps. To extend the capability of
the networks, we then smoothly morph cortical geometric features and
parcellation maps using the intermediate deformation fields. We validate our
method on 427 adult brains for 49 labels. The experimental results show that
our method out-performs traditional multi-atlas and naive spherical U-Net
approaches, while achieving full cortical parcellation in less than a minute.


  We propose a dissipative method for the preparation of many-body steady
entangled states in spin and fermionic chains. The scheme is accomplished by
means of an engineered set of Lindbladians acting over the eigenmodes of the
system, whose spectrum is assumed to be resolvable. We apply this idea to
prepare a particular entangled state of a spin chain described by the XY model,
emphasizing its generality and experimental feasibility. Our results show that
our proposal is capable of achieving high fidelities and purities for a given
target state even when dephasing and thermal dissipative processes are taken
into account. Moreover, the method exhibits a remarkable robustness against
fluctuations in the model parameters.


  We present Monte Carlo simulations of the dynamical evolution of the Oort
cloud over the age of the Solar System, using an initial sample of one million
test comets without any cloning. Our model includes perturbations due to the
Galactic tide (radial and vertical) and passing stars. We present the first
detailed analysis of the injection mechanism into observable orbits by
comparing the complete model with separate models for tidal and stellar
perturbations alone. We find that a fundamental role for injecting comets from
the region outside the loss cone (perihelion distance q > 15 AU) into
observable orbits (q < 5 AU) is played by stellar perturbations. These act in
synergy with the tide such that the total injection rate is significantly
larger than the sum of the two separate rates. This synergy is as important
during comet showers as during quiescent periods and concerns comets with both
small and large semi-major axes. We propose different dynamical mechanisms to
explain the synergies in the inner and outer parts of the Oort Cloud. We find
that the filling of the observable part of the loss cone under normal
conditions in the present-day Solar System rises from <1 % for a < 20 000 AU to
about 100 % for a >= 100 000 AU.


  Motivated by concerns about diversity in social networks, we consider the
following pattern formation problems in rings. Assume $n$ mobile agents are
located at the nodes of an $n$-node ring network. Each agent is assigned a
colour from the set $\{c_1, c_2, \ldots, c_q \}$. The ring is divided into $k$
contiguous {\em blocks} or neighbourhoods of length $p$. The agents are
required to rearrange themselves in a distributed manner to satisfy given
diversity requirements: in each block $j$ and for each colour $c_i$, there must
be exactly $n_i(j) >0$ agents of colour $c_i$ in block $j$. Agents are assumed
to be able to see agents in adjacent blocks, and move to any position in
adjacent blocks in one time step. When the number of colours $q=2$, we give an
algorithm that terminates in time $N_1/n^*_1 + k + 4$ where $N_1$ is the total
number of agents of colour $c_1$ and $n^*_1$ is the minimum number of agents of
colour $c_1$ required in any block. When the diversity requirements are the
same in every block, our algorithm requires $3k+4$ steps, and is asymptotically
optimal. Our algorithm generalizes for an arbitrary number of colours, and
terminates in $O(nk)$ steps. We also show how to extend it to achieve arbitrary
specific final patterns, provided there is at least one agent of every colour
in every pattern.


  The aim of various technical applications (for example fusion research) is to
control a plasma by magnetic fields in a desired fashion. In our model the
plasma is described by the Vlasov-Poisson system that is equipped with an
external magnetic field. We will prove that this model satisfies some basic
properties that are necessary for calculus of variations. After that, we will
analyze an optimal control problem with a tracking type cost functional with
respect to the following topics: Necessary conditions of first order for local
optimality, derivation of an optimality system, sufficient conditions of second
order for local optimality, uniqueness of the optimal control under certain
conditions.


  In this work we use Monte Carlo simulations to study the phase behavior of
spherical caps confined between two parallel hard walls separated by a distance
H. The particle model consists of a hard sphere of diameter \sigma cut off by a
plane at a height \chi, and it is loosely based on mushroom cap-shaped
particles whose phase behavior was recently studied experimentally [E. K. Riley
and C. M. Liddell, Langmuir, 26, 11648 (2010)]. The geometry of the particles
is characterized by the reduced height \chi^* = \chi/\sigma, such that the
model extrapolates between hard spheres for \chi^* \leftarrow 1 and infinitely
thin hard platelets for \chi^* \letfarrow 0. Three different particle shapes
are investigated: (a) three-quarter height spherical caps (\chi^* = 3/4), (b)
one-half height spherical caps or hemispheres (\chi^* = 1/2), and (c)
one-quarter height spherical caps (\chi^* = 1/4). These three models are used
to rationalize the effect of particle shape, obtained by cutting off spheres at
different heights, on the entropy-driven self-assembly of the particles under
strong confinements; i.e., for 1 < H/\chi < 2.5. As H is varied, a sequence of
crystal structures are observed, including some having similar symmetry as that
of the structures observed in confined hard spheres on account of the remaining
spherical surface in the particles, but with additional features on account of
the particle shapes having intrinsic anisotropy and orientational degrees of
freedom. The \chi^* = 3/4 system is found to exhibit a phase diagram that is
most similar to the one obtained experimentally for the confined mushroom
cap-shaped colloidal particles under. A qualitative global phase diagram is
constructed that helps reveal the interrelations among different phases for all
the particle shapes and confinements studied.


  Bayesian curve fitting plays an important role in inverse problems, and is
often addressed using the Reversible Jump Markov Chain Monte Carlo (RJMCMC)
algorithm. However, this algorithm can be computationally inefficient without
appropriately tuned proposals. As a remedy, we present an adaptive RJMCMC
algorithm for the curve fitting problems by extending the Adaptive Metropolis
sampler from a fixed-dimensional to a trans-dimensional case. In this presented
algorithm, both the size and orientation of the proposal function can be
automatically adjusted in the sampling process. Specifically, the curve fitting
setting allows for the approximation of the posterior covariance of the a
priori unknown function on a representative grid of points. This approximation
facilitates the definition of efficient proposals. In addition, we introduce an
auxiliary-tempered version of this algorithm via non-reversible parallel
tempering. To evaluate the algorithms, we conduct numerical tests involving a
series of controlled experiments. The results demonstrate that the adaptive
algorithms exhibit significantly higher efficiency compared to the conventional
ones. Even in cases where the posterior distribution is highly complex, leading
to ineffective convergence in the auxiliary-tempered conventional RJMCMC, the
proposed auxiliary-tempered adaptive RJMCMC performs satisfactorily.
Furthermore, we present a realistic inverse example to test the algorithms. The
successful application of the adaptive algorithm distinguishes it again from
the conventional one that fails to converge effectively even after millions of
iterations.


  By means of the Bessel operator a polynomial sequence is constructed to which
several properties are given. Among them, its explicit expression, the
connection with the Euler numbers, its integral representation via the
Kontorovich-Lebedev transform. Despite its non-orthogonality, it is possible to
associate to the canonical element of its dual sequence a positive-definite
measure as long as certain stronger constraints are imposed.


  The paper is devoted to the description a measurable time-interval (``proper
time'') in the Hamiltonian version of general relativity with the Dirac-ADM
metric. To separate the dynamical parameter of evolution from the space metric
we use the Lichnerowicz conformally invariant variables. In terms of these
variables GR is equivalent to the conformally invariant
Penrose-Chernicov-Tagirov theory of a scalar field the role of which is played
by the scale factor multiplied on the Planck constant. Identification of this
scalar field with the modulus of the Higgs field in the standard model of
electroweak and strong interactions allows us to formulate an example of
conformally invariant unified theory where the vacuum averaging of the scalar
field is determined by cosmological integrals of motion of the Universe
evolution.


  The future gravitational wave (GW) observations of compact binaries and their
possible electromagnetic counterparts may be used to probe the nature of the
extra dimension. It is widely accepted that gravitons and photons are the only
two completely confirmed objects that can travel along null geodesics in our
four-dimensional space-time. However, if there exist extra dimensions and only
GWs can propagate freely in the bulk, the causal propagations of GWs and
electromagnetic waves (EMWs) are in general different. In this paper, we study
null geodesics of GWs and EMWs in a five-dimensional anti-de Sitter space-time
in the presence of the curvature of the universe. We show that for general
cases the horizon radius of GW is longer than EMW within equal time. Taking the
GW150914 event detected by the Advanced Laser Interferometer Gravitational-Wave
Observatory and the X-ray event detected by the Fermi Gamma-ray Burst Monitor
as an example, we study how the curvature $k$ and the constant curvature radius
$l$ affect the horizon radii of GW and EMW in the de Sitter and Einstein-de
Sitter models of the universe. This provides an alternative method for probing
extra dimension through future GW observations of compact binaries and their
electromagnetic counterparts.


  Flaky tests have gained attention from the research community in recent years
and with good reason. These tests lead to wasted time and resources, and they
reduce the reliability of the test suites and build systems they affect.
However, most of the existing work on flaky tests focus exclusively on
traditional unit tests. This work ignores UI tests that have larger input
spaces and more diverse running conditions than traditional unit tests. In
addition, UI tests tend to be more complex and resource-heavy, making them
unsuited for detection techniques involving rerunning test suites multiple
times.
  In this paper, we perform a study on flaky UI tests. We analyze 235 flaky UI
test samples found in 62 projects from both web and Android environments. We
identify the common underlying root causes of flakiness in the UI tests, the
strategies used to manifest the flaky behavior, and the fixing strategies used
to remedy flaky UI tests. The findings made in this work can provide a
foundation for the development of detection and prevention techniques for
flakiness arising in UI tests.


  We present a novel approach for high-order accurate numerical differentiation
on unstructured meshes of quadrilateral elements. To differentiate a given
function, an auxiliary function with greater smoothness properties is defined
which when differentiated provides the derivatives of the original function.
The method generalises traditional finite difference methods to meshes of
arbitrary topology in any number of dimensions for any order of derivative and
accuracy. We demonstrate the accuracy of the numerical scheme using dual
quadrilateral meshes and a refinement method based on subdivision surfaces. The
scheme is applied to the solution of a range of partial differential equations,
including both linear and nonlinear, second and fourth order equations, and a
time-dependent first order equation.


  Single-photon atom gradiometry is a powerful experimental technique that can
be employed to search for the oscillation of atomic transition energies induced
by ultralight scalar dark matter (ULDM). In the sub-Hz regime the background is
expected to be dominated by gravity gradient noise (GGN), which arises as a
result of mass fluctuations around the experiment. In this work we model the
GGN as surface Rayleigh waves, and we construct a likelihood-based analysis
that consistently folds GGN into the sensitivity estimates of vertical atom
gradiometers in the frequency window between 1 mHz and 1 Hz. We show that in
certain geological settings GGN can be significantly mitigated when operating a
multigradiometer configuration, which consists of three or more atom
interferometers in the same baseline. Multigradiometer experiments, such as
future versions of AION and MAGIS-100, have the potential to probe regions of
scalar ULDM parameter space in the sub-Hz regime that have not been excluded by
existing experiments.


  Fitness functions map large combinatorial spaces of biological sequences to
properties of interest. Inferring these multimodal functions from experimental
data is a central task in modern protein engineering. Global epistasis models
are an effective and physically-grounded class of models for estimating fitness
functions from observed data. These models assume that a sparse latent function
is transformed by a monotonic nonlinearity to emit measurable fitness. Here we
demonstrate that minimizing contrastive loss functions, such as the
Bradley-Terry loss, is a simple and flexible technique for extracting the
sparse latent function implied by global epistasis. We argue by way of a
fitness-epistasis uncertainty principle that the nonlinearities in global
epistasis models can produce observed fitness functions that do not admit
sparse representations, and thus may be inefficient to learn from observations
when using a Mean Squared Error (MSE) loss (a common practice). We show that
contrastive losses are able to accurately estimate a ranking function from
limited data even in regimes where MSE is ineffective. We validate the
practical utility of this insight by showing contrastive loss functions result
in consistently improved performance on benchmark tasks.


  The Swift-Hohenberg equation describes an instability which forms
finite-wavenumber patterns near onset. We study this equation posed with a
spatial inhomogeneity; a jump-type parameter that renders the zero solution
stable for $x<0$ and unstable for $x>0$. Using normal forms and spatial
dynamics, we prove the existence of a family of steady-state solutions that
represent a transition in space from a homogeneous state to a striped pattern
state. The wavenumbers of these stripes are contained in a narrow band whose
width grows linearly with the size of the jump. This represents a severe
restriction from the usual constant-parameter case, where the allowed band
grows with the square root of the parameter. We corroborate our predictions
using numerical continuation and illustrate implications on stability of
growing patterns in direct simulations.


  One principal approach for illuminating a black-box neural network is feature
attribution, i.e. identifying the importance of input features for the
network's prediction. The predictive information of features is recently
proposed as a proxy for the measure of their importance. So far, the predictive
information is only identified for latent features by placing an information
bottleneck within the network. We propose a method to identify features with
predictive information in the input domain. The method results in fine-grained
identification of input features' information and is agnostic to network
architecture. The core idea of our method is leveraging a bottleneck on the
input that only lets input features associated with predictive latent features
pass through. We compare our method with several feature attribution methods
using mainstream feature attribution evaluation experiments. The code is
publicly available.


  Scientific CMOS image sensors are a modern alternative for a typical CCD
detectors, as they offer both low read-out noise, large sensitive area, and
high frame rates. All these makes them promising devices for a modern
wide-field sky surveys. However, the peculiarities of CMOS technology have to
be properly taken into account when analyzing the data. In order to
characterize these, we performed an extensive laboratory testing of Andor
Marana sCMOS camera. Here we report its results, especially on the temporal
stability and linearity, and compare it to the previous versions of Andor sCMOS
cameras. We also present the results of an on-sky testing of this sensor
connected to a wide-field lens, and discuss its applications for an
astronomical sky surveys.


  Cuspidal robots can travel from one inverse kinematic solution to another
without meeting a singularity. The name cuspidal was coined based on the
existence of a cusp point in the workspace of 3R serial robots. The existence
of a cusp point was proved to be a necessary and sufficient condition for
orthogonal robots to be cuspidal, but it was not possible to extend this
condition to non-orthogonal robots. The goal of this paper is to prove that
this condition stands for any generic 3R robot. This result would give the
designer more flexibility. In the presented work, the geometrical
interpretation of the inverse kinematics of 3R robots is revisited and
important observations on the nonsingular change of posture are noted. The
paper presents a theorem regarding the existence of reduced aspects in any
generic 3R serial robot. Based on these observations and on this theorem, we
prove that the existence of a cusp point is a necessary and sufficient
condition for any 3R generic robot to be cuspidal.


  We study the edge-mode excitations of a fractional quantum Hall droplet by
expressing the edge state wavefunctions as linear combinations of Jack
polynomials with a negative parameter. We show that the exact diagonalization
within subspace of Jack polynomials can be used to generate the chiral
edge-mode excitation spectrum in the Laughlin phase and the Moore-Read phase
with realistic Coulomb interaction. The truncation technique for the edge
excitations simplifies the procedure to extract reliably the edge-mode
velocities, which avoids the otherwise complicated analysis of the full
spectrum that contains both edge and bulk excitations. Generalization to the
Read-Rezayi state is also discussed.


  A novel concept for coherent beam combining is presented based on a simple
setup with microlens arrays. These standard components are used in a
proof-of-principle experiment for both coherent beam splitting and combination
of 5 x 5 beams. Here a combination efficiency above 90% is achieved. We call
this novel concept mixed aperture.


  The product m_k of the first k primes (2..p_k) has neighbours m_k +/- 1 with
all prime divisors beyond p_k, implying there are infinitely many primes
[Euclid]. All primes between p_k and m_k are in the group G_1 of units in
semigroup Z_{m_k}(.) of mutiplication mod m_k. Due to the squarefree modulus
Z_{m_k} is a disjoint union of 2^k groups, with as many idempotents - one per
divisor of m_k, which form a Boolean lattice BL. The generators of Z_{m_k} and
the additive properties of its lattice are studied. It is shown that each
complementary pair in BL adds to 1 mod m_k and each even idempotent e in BL has
successor e+1 in G_1. It follows that G_1+G_1 \equiv E, the set of even
residues in Z_{m_k}, so each even residue is the sum of two roots of unity,
proving "Goldbach for Residues" mod m_k ("GR"). . . . Induction on k by
extending residues mod m_k with "carry" a < p_{k+1} of weight m_k, yields a
prime sieve for integers. Failure of Goldbach's Conjecture ("GC") for some 2n
contradicts GR(k) for some k. By Bertrand's Postulate (on prime i<p<2i for each
i>1) successive 2n are in overlapping intervals, while the smallest composite
unit in G_1 mod m_k is p_{k+1}^2, yielding "GC": Each 2n > 4 is the sum of two
odd primes.


  We consider an electron which is electromagnetically dressed in such a way
that it is both gauge invariant and that it has the associated electric and
magnetic fields expected of a moving charge. We study the propagator of this
dressed electron and, for small velocities, show explicitly at one loop that at
the natural (on-shell) renormalisation point, $p_0=m$, ${\bold p}= m{\bold v}$,
one can renormalise the propagator multiplicatively. Furthermore the
renormalisation constants are infra-red finite. This shows that the dressing we
use corresponds to a slowly moving, physical asymptotic field.


  We report a combined experimental and theoretical study of KCuF3, which
offers - because of this material's relatively simple lattice structure and
valence configuration (d9, i.e., one hole in the d-shell) - a particularly
clear view of the essential role of the orbital degree of freedom in governing
the dynamical coupling between the spin and lattice degrees of freedom. We
present Raman and x-ray scattering evidence that the phase behaviour of KCuF3
is dominated above the Neel temperature (T_N = 40 K) by coupled orbital/lattice
fluctuations that are likely associated with rotations of the CuF6 octahedra,
and we show that these orbital fluctuations are interrupted by a static
structural distortion that occurs just above T_N. A detailed model of the
orbital and magnetic phases of KCuF3 reveals that these orbital fluctuations -
and the related frustration of in-plane spin-order-are associated with the
presence of nearly degenerate low-energy spin-orbital states that are highly
susceptible to thermal fluctuations over a wide range of temperatures. A
striking implication of these results is that the ground state of KCuF3 at
ambient pressure lies near a quantum critical point associated with an
orbital/spin liquid phase that is obscured by emergent Neel ordering of the
spins; this exotic liquid phase might be accessible via pressure studies.


  This work presents a novel methodology for analysis and control of nonlinear
fluid systems using neural networks. The approach is demonstrated on four
different study cases being the Lorenz system, a modified version of the
Kuramoto-Sivashinsky equation, a streamwise-periodic 2D channel flow, and a
confined cylinder flow. Neural networks are trained as models to capture the
complex system dynamics and estimate equilibrium points through a Newton
method, enabled by backpropagation. These neural network surrogate models
(NNSMs) are leveraged to train a second neural network, which is designed to
act as a stabilizing closed-loop controller. The training process employs a
recurrent approach, whereby the NNSM and the neural network controller (NNC)
are chained in closed loop along a finite time horizon. By cycling through
phases of combined random open-loop actuation and closed-loop control, an
iterative training process is introduced to overcome the lack of data near
equilibrium points. This approach improves the accuracy of the models in the
most critical region for achieving stabilization. Through the use of L1
regularization within loss functions, the NNSMs can also guide optimal sensor
placement, reducing the number of sensors from an initial candidate set. The
datasets produced during the iterative training process are also leveraged for
conducting a linear stability analysis through a modified dynamic mode
decomposition approach. The results demonstrate the effectiveness of
computationally inexpensive neural networks in modeling, controlling, and
enabling stability analysis of nonlinear systems, providing insights into the
system behaviour and offering potential for stabilization of complex fluid
systems.


  Exotic singular objects, known as exceptional points, are ubiquitous in
non-Hermitian physics. They might be spectral singularities in energy bands
that produce anomalous effects and defectiveness. The quantum entanglement of a
generic non-Hermitian model with two different types of spectral exceptional
points (SEPs) is systematically investigated in this paper. We discovered a
relationship between non-unitary conformal field theories and the
$k$-linear-type SEPs, which is typically associated with
$\mathcal{PT}$-symmetry or pesdo-Hermicity spontaneous breaking. The underlying
association between $k$-square-root-type SEPs, which arise concurrently with
real (imaginary) gap closing in the complex spectrum, mimicking
first-order-phase-transition criticalities, and complex conformal field
theories (cCFTs) is addressed through the calculation of complex central
charges. From the entanglement spectrum, zero-energy exceptional modes are
found to be distinct from normal zero modes or topological boundary modes.
Finally, we include a brief discussion of analogous non-Hermitian quantum spin
models and endeavor to establish an intuitive understanding of exceptional
points through the spin picture in various scenarios.


  After a few decades of development, computational argumentation has become
one of the active realms in AI. This paper considers extension-based concrete
and abstract semantics of argumentation. For concrete ones, based on Grossi and
Modgil's recent work, this paper considers some issues on graded
extension-based semantics of abstract argumentation framework (AAF, for short).
First, an alternative fundamental lemma is given, which generalizes the
corresponding result due to Grossi and Modgil by relaxing the constraint on
parameters. This lemma provides a new sufficient condition for preserving
conflict-freeness and brings a Galois adjunction between admissible sets and
complete extensions, which is of vital importance in constructing some special
extensions in terms of iterations of the defense function. Applying such a
lemma, some flaws in Grossi and Modgil's work are corrected, and the structural
property and universal definability of various extension-based semantics are
given. Second, an operator so-called reduced meet modulo an ultrafilter is
presented, which is a simple but powerful tool in exploring infinite AAFs. The
neutrality function and the defense function, which play central roles in
Dung's abstract argumentation theory, are shown to be distributive over reduced
meets modulo any ultrafilter. A variety of fundamental semantics of AAFs,
including conflict-free, admissible, complete and stable semantics, etc, are
shown to be closed under this operator. Based on this fact, a number of
applications of such operators are considered. In particular, we provide a
simple and uniform method to prove the universal definability of a family of
range related semantics. Since all graded concrete semantics considered in this
paper are generalizations of corresponding non-graded ones, all results about
them obtained in this paper also hold in the traditional situation.


  This paper presents results on structures in P based on tools developed from
subjects of elementary number theory. Key findings are: The arithmetical
sequence H = (+-3*2; 1) is in Z the smallest superset of P \ {3, 2}. H is a
semigroup. A revised definition of P. Unique Gestalt of p in Z. The prime
number lattice packing H exp n. The geometrical locus in HxH of the family of
solutions of: - the set of prime twins, - the set of PRACHAR prime twins, - in
H exp 2, H exp 3 family of solutions of the GOLDBACH conjunction. Partition of
H in p exp 2-intervals. Prime numbers in p exp 2-intervals. Infinity of the set
of prime twins. Verification of the GOLDBACH conjunction.


  Recent researches on designs for computer experiments with both qualitative
and quantitative factors have advocated the use of marginally coupled designs.
This paper proposes a general method of constructing such designs for which the
designs for qualitative factors are multi-level orthogonal arrays and the
designs for quantitative factors are Latin hypercubes with desirable
space-filling properties. Two cases are introduced for which we can obtain the
guaranteed low-dimensional space-filling property for quantitative factors.
Theoretical results on the proposed constructions are derived. For practical
use, some constructed designs for three-level qualitative factors are
tabulated.


  Double Chooz is unique among modern reactor-based neutrino experiments
studying $\bar \nu_e$ disappearance in that data can be collected with all
reactors off. In this paper, we present data from 7.53 days of reactor-off
running. Applying the same selection criteria as used in the Double Chooz
reactor-on oscillation analysis, a measured background rate of 1.0$\pm$0.4
events/day is obtained. The background model for accidentals, cosmogenic
$\beta$-$n$-emitting isotopes, fast neutrons from cosmic muons, and
stopped-$\mu$ decays used in the oscillation analysis is demonstrated to be
correct within the uncertainties. Kinematic distributions of the events, which
are dominantly cosmic-ray-produced correlated-background events, are provided.
The background rates are scaled to the shielding depths of two other
reactor-based oscillation experiments, Daya Bay and RENO.


  When $A$ in the Kauffman bracket skein relation is a primitive $2N$th root of
unity, where $N\geq 3$ is odd, the Kauffman bracket skein algebra $K_N(F)$ of a
finite type surface $F$ is a ring extension of the $SL_2\mathbb{C}$-characters
$\chi(F)$ of the fundamental group of $F$. We localize by inverting the nonzero
characters to get an algebra $S^{-1}K_N(F)$ over the function field of the
character variety. We prove that if $F$ is noncompact, the algebra
$S^{-1}K_N(F)$ is a symmetric Frobenius algebra. Along the way we prove $K(F)$
is finitely generated, $K_N(F)$ is a finite rank module over $\chi(F)$, and the
simple closed curves that make up any simple diagram on $F$ generate a finite
field extension of $S^{-1}\chi(F)$ inside $S^{-1}K_N(F)$.


  A spatial distributional regression model is presented to predict the forest
structural diversity in terms of the distributions of the stem diameter at
breast height (DBH) in the protection forests in Ebensee, Austria. In total
36,338 sample trees were measured via a handheld mobile personal laser scanning
system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne
laser scanning (ALS) data was used to derive regression covariates from the
normalized digital vegetation height model (DVHM) and the digital terrain model
(DTM). Candidate models were constructed that differed in their linear
predictors of the two gamma distribution parameters. Non-linear smoothing
splines outperformed linear parametric slope coefficients, and the best
implementation of spatial structured effects was achieved by a Gaussian process
smooth. Model fitting and posterior parameter inference was achieved by using
full Bayesian methodology and MCMC sampling algorithms implemented in the
R-package BAMLSS. Spatial predictions of stem count proportions per DBH classes
revealed that regeneration of smaller trees was lacking in certain areas of the
protection forest landscape.


  We study the nonlinear Helmholtz equation $(\Delta - \lambda^2)u = \pm
|u|^{p-1}u$ on $\mathbb{R}^n$, $\lambda > 0$, $p \in \mathbb{N}$ odd, and more
generally $(\Delta_g + V - \lambda^2)u = N[u]$, where $\Delta_g$ is the
(positive) Laplace-Beltrami operator on an asymptotically Euclidean or conic
manifold, $V$ is a short range potential, and $N[u]$ is a more general
polynomial nonlinearity. Under the conditions $(p-1)(n-1) > 4$ and $k >
(n-1)/2$, for every $f \in H^k(S^{n-1}_\omega)$ of sufficiently small norm, we
show there is a nonlinear Helmholtz eigenfunction taking the form
\begin{equation*} u(r, \omega) = r^{-(n-1)/2} \Big( e^{-i\lambda r} f(\omega) +
e^{+i\lambda r} b(\omega) + O(r^{-\epsilon}) \Big), \qquad \text{as } r \to
\infty, \end{equation*} for some $b \in H^k(S_\omega^{n-1})$ and $\epsilon >
0$. That is, the scattering matrix $f \mapsto b$ preserves Sobolev regularity,
which is an improvement over the authors' previous work with Zhang, that proved
a similar result with a loss of four derivatives.


  We present simultaneous, multi-colour optical light curves of the companion
star to the black-widow pulsar PSR J2051-0827, obtained approximately 10 years
apart using ULTRACAM and HiPERCAM, respectively. The ULTRACAM light curves
confirm the previously reported asymmetry in which the leading hemisphere of
the companion star appears to be brighter than the trailing hemisphere. The
HiPERCAM light curves, however, do not show this asymmetry, demonstrating that
whatever mechanism is responsible for it varies on timescales of a decade or
less. We fit the symmetrical HiPERCAM light curves with a direct-heating model
to derive the system parameters, finding an orbital inclination of
$55.9^{+4.8}_{-4.1}$ degrees, in good agreement with radio-eclipse constraints.
We find that approximately half of the pulsar's spin-down energy is converted
to optical luminosity, resulting in temperatures ranging from approximately
$5150^{+190}_{-190}$ K on the day side to $2750^{+130}_{-150}$ K on the night
side of the companion star. The companion star is close to filling its Roche
lobe ($f_{\rm RL} =0.88^{+0.02}_{-0.02}$) and has a mass of
$0.039^{+0.010}_{-0.011}$ M$_{\odot}$, giving a mean density of
$20.24^{+0.59}_{-0.44}$ g cm$^{-3}$ and an apsidal motion constant in the range
$0.0036 < k_2 < 0.0047$. The companion mass and mean density values are
consistent with those of brown dwarfs, but the apsidal motion constant implies
a significantly more centrally-condensed internal structure than is typical for
such objects.


  This is an expanded version of the lectures given at the Trieste Summer
School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter
Physicists.


  In this paper we determine all the bijective linear maps on the space of
bounded observables which preserve a fixed moment or the variance. Nonlinear
versions of the corresponding results are also presented.


  We analyze the classical phase space of the hydrogen atom in crossed magnetic
and circularly polarized microwave fields in the high frequency regime, using
the Chirikov resonance overlap criterion and the renormalization map. These
methods are used to compute thresholds to large scale chaos and to ionization.
The effect of the magnetic field is a strong stabilization of a set of
invariant tori which bound the trajectories and prevent stochastic ionization.
In order to ionize, larger amplitudes of the microwave field are necessary in
the presence of a magnetic field.


  The model consists of a signal process $X$ which is a general Brownian
diffusion process and an observation process $Y$, also a diffusion process,
which is supposed to be correlated to the signal process. We suppose that the
process $Y$ is observed from time 0 to $s>0$ at discrete times and aim to
estimate, conditionally on these observations, the probability that the
non-observed process $X$ crosses a fixed barrier after a given time $t>s$. We
formulate this problem as a usual nonlinear filtering problem and use optimal
quantization and Monte Carlo simulations techniques to estimate the involved
quantities.


  We propose a novel cluster-based reduced-order modelling (CROM) strategy of
unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's
group (Burkardt et al. 2006) and and transition matrix models introduced in
fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a
potential alternative to POD models and generalises the Ulam-Galerkin method
classically used in dynamical systems to determine a finite-rank approximation
of the Perron-Frobenius operator. The proposed strategy processes a
time-resolved sequence of flow snapshots in two steps. First, the snapshot data
are clustered into a small number of representative states, called centroids,
in the state space. These centroids partition the state space in complementary
non-overlapping regions (centroidal Voronoi cells). Departing from the standard
algorithm, the probabilities of the clusters are determined, and the states are
sorted by analysis of the transition matrix. Secondly, the transitions between
the states are dynamically modelled using a Markov process. Physical mechanisms
are then distilled by a refined analysis of the Markov process, e.g. using
finite-time Lyapunov exponent and entropic methods. This CROM framework is
applied to the Lorenz attractor (as illustrative example), to velocity fields
of the spatially evolving incompressible mixing layer and the three-dimensional
turbulent wake of a bluff body. For these examples, CROM is shown to identify
non-trivial quasi-attractors and transition processes in an unsupervised
manner. CROM has numerous potential applications for the systematic
identification of physical mechanisms of complex dynamics, for comparison of
flow evolution models, for the identification of precursors to desirable and
undesirable events, and for flow control applications exploiting nonlinear
actuation dynamics.


  Accretion disk coronae are believed to account for X-ray emission in Active
Galactic Nuclei (AGNs). In this paper the observed emission is assumed to be
due to a population of relativistic, non-thermal electrons (e.g. produced in a
flare) injected at the top of an accretion disk magnetic loop. While electrons
stream along magnetic field lines their energy distribution evolves in time
essentially because of inverse Compton and synchrotron losses. The
corresponding time dependent emission due, in the X-ray energy range, to the
inverse Compton mechanism, has been computed. Since the typical decay time of a
flare is shorter than the integration time for data acquisition in the X-ray
domain, the resulting spectrum is derived as the temporal mean of the real,
time-dependent, emission, as originated by a series of consecutive and
identical flares. The model outcome is compared to both the broad band BeppoSAX
X-ray data of the bright Seyfert 1 NGC 5548, and to a few general X-ray
spectral properties of Seyfert 1s as a class. The good agreement between model
and observations suggests that the presently proposed non-thermal,
non-stationary model could be a plausible explanation of AGN X-ray emission, as
an alternative to thermal coronae models.


  It is has been assumed for over half a century that the earliest animals were
obligate aerobes with relatively high oxygen requirements. However, the
conserved biochemistry and widespread phylogenetic distribution of anaerobic
energy metabolism in animals suggests a deep ancestral possession of the genes
and enzymes necessary for a facultative anaerobic lifestyle. Additionally,
non-bilaterian bodyplans are not expected to require particularly high
environmental oxygen levels. This is consistent with experimental evidence
demonstrating the low-oxygen tolerance of the sponge Halichondria panicea.
While it is conceivable that low-oxygen-adapted animals evolved only sometime
during the past 541 million years, perhaps in response to oceanic anoxic
events, they most reasonably date back to the first animals themselves, as the
last common ancestor of animals likely emerged in a relatively low-oxygen
world, possessed the genetic means for anaerobiosis, and exhibited a bodyplan
conducive to aerobic growth under oxygen levels less than 4% of modern
atmospheric saturation.


  Given two sets of objects, metric similarity join finds all similar pairs of
objects according to a particular distance function in metric space. There is
an increasing demand to provide a scalable similarity join framework which can
support efficient query and analytical services in the era of Big Data. The
existing distributed metric similarity join algorithms adopt random sampling
techniques to produce pivots and utilize holistic partitioning methods based on
the generated pivots to partition data, which results in data skew problem
since both the generated pivots and the partition strategies have no quality
guarantees.
  To address the limitation, we propose SP-Join, an end-to-end framework to
support distributed similarity join in metric space based on the MapReduce
paradigm, which (i) employs an estimation-based stratified sampling method to
produce pivots with quality guarantees for any sample size, and (ii) devises an
effective cost model as the guideline to split the whole datasets into
partition in map and reduce phases according to the sampled pivots. Although
obtaining an optimal set of partitions is proven to be NP-Hard, SP-Join adopts
efficient partitioning strategies based on such a cost model to achieve an even
partition with explainable quality. We implement our framework upon Apache
Spark platform and conduct extensive experiments on four real-world datasets.
The results show that our method significantly outperforms state-of-the-art
methods.


  Many web-search queries serve as the beginning of an exploration of an
unknown space of information, rather than looking for a specific web page. To
answer such queries effec- tively, the search engine should attempt to organize
the space of relevant information in a way that facilitates exploration. We
describe the Aspector system that computes aspects for a given query. Each
aspect is a set of search queries that together represent a distinct
information need relevant to the original search query. To serve as an
effective means to explore the space, Aspector computes aspects that are
orthogonal to each other and to have high combined coverage. Aspector combines
two sources of information to compute aspects. We discover candidate aspects by
analyzing query logs, and cluster them to eliminate redundancies. We then use a
mass-collaboration knowledge base (e.g., Wikipedia) to compute candidate
aspects for queries that occur less frequently and to group together aspects
that are likely to be "semantically" related. We present a user study that
indicates that the aspects we compute are rated favorably against three
competing alternatives -related searches proposed by Google, cluster labels
assigned by the Clusty search engine, and navigational searches proposed by
Bing.


  We study the role of drift effect in the temporal changes of the anisotropy
of galactic cosmic rays (GCRs) and the influence of the sector structure of the
heliospheric magnetic field on it. We analyze the GCRs anisotropy in the Solar
Cycle 24 and solar minimum 23_24 with negative polarity for the period of
2007-2009 and near minimum 24_25 with positive polarity in 2017-2018 using data
of global network of Neutron Monitors. We use the harmonic analyses method to
calculate the radial and tangential components of the anisotropy of GCRs for
different sectors (plus corresponds to the positive and minus to the negative
directions) of the heliospheric magnetic field. We compare the analysis of GCRs
anisotropy using different evaluations of the mean GCRs rigidity related to
Neutron Monitor observations. Then the radial and tangential components are
used for characterizing the GCRs modulation in the heliosphere. We show that in
the solar minimum 23_24 in 2007-2009 when negative, the drift effect is not
visibly evident in the changes of the radial component, i.e. the drift effect
is found to produce 4 % change in the radial component of the GCRs anisotropy
for 2007-2009. Hence the diffusion dominated model of GCRs transport is more
acceptable in 2007-2009. In turn, near the solar minimum 24_25 in 2017-2018
when positive, the drift effect is evidently visible and produce 40% change in
the radial component of the GCRs anisotropy for 2017-2018. So in the period of
2017-2018 diffusion model with noticeably manifested drift is acceptable. The
results of this work are in good agreement with the drift theory of GCRs
modulation, according to which during negative (positive) polarity cycles, a
drift stream of GCRs is directed toward (away from) the Sun, thus giving rise
to a 22-year cycle variation of the radial GCRs anisotropy.


  We present a comprehensive analysis of the Johnson (like) noise based
classical key-distribution scheme presented by Kish [1]. We suggest two passive
attack strategies that enable an adversary to gain complete knowledge of the
exchanged key. The first approach exploits the transient response of the
voltage difference on the transmission line after the resistors are switched
and the second one exploits the finite impedance of the wire connecting the two
parties.


  We investigate biases induced by the conversion between the observed image
shape to shear distortion in current weak lensing analysis methods. Such
overall calibration biases cannot be detected by the standard tests such as E/B
decomposition or calibration with stars. We find that the non-Gaussianity of
point spread function has a significant effect and can lead to up to 15 per
cent error on the linear amplitude of fluctuations sigma_8 depending on the
method of analysis. This could explain some of the discrepancies seen in recent
amplitude determinations from weak lensing. Using an elliptical Laguerre
expansion method we develop a re-Gaussianization method which reduces the error
to calibration error of order 1 per cent even for poorly resolved galaxies. We
also discuss a new type of shear selection bias which results in up to roughly
8 percent underestimation of the signal. It is expected to scale with redshift,
inducing errors in the growth factor extraction if not properly corrected for.
Understanding and correcting for such effects is crucial if weak lensing is to
become a high precision probe of cosmology.


  The Alpha Magnetic Spectrometer (AMS) experiment to be installed on the
International Space Station (ISS) will be equipped with a proximity focusing
Ring Imaging Cherenkov (RICH) detector for measuring the electric charge and
velocity of the charged cosmic particles. A RICH prototype consisting of 96
photomultiplier units, including a piece of the conical reflector, was built
and its performance evaluated with ion beam data. Preliminary results of the
in-beam tests performed with ion fragments resulting from collisions of a 158
GeV/c/nuc primary beam of Indium ions (CERN SPS) on a Pb target are reported.
The collected data included tests to the final front-end electronics and to
different aerogel radiators. Cherenkov rings for a large range of charged
nuclei and with reflected photons were observed. The data analysis confirms the
design goals. Charge separation up to Fe and velocity resolution of the order
of 0.1% for singly charged particles are obtained.


  The dependence of the multiplicity on the number of collisions and the
transverse momentum distribution for central and peripheral Au-Au collisions
are studied in the model of percolation of strings relative to the experimental
conditions at RHIC. The comparison with the first RHIC data shows a good
agreement.


  In this paper, we propose TensorFHE, an FHE acceleration solution based on
GPGPU for real applications on encrypted data. TensorFHE utilizes Tensor Core
Units (TCUs) to boost the computation of Number Theoretic Transform (NTT),
which is the part of FHE with highest time-cost. Moreover, TensorFHE focuses on
performing as many FHE operations as possible in a certain time period rather
than reducing the latency of one operation. Based on such an idea, TensorFHE
introduces operation-level batching to fully utilize the data parallelism in
GPGPU. We experimentally prove that it is possible to achieve comparable
performance with GPGPU as with state-of-the-art ASIC accelerators. TensorFHE
performs 913 KOPS and 88 KOPS for NTT and HMULT (key FHE kernels) within NVIDIA
A100 GPGPU, which is 2.61x faster than state-of-the-art FHE implementation on
GPGPU; Moreover, TensorFHE provides comparable performance to the ASIC FHE
accelerators, which makes it even 2.9x faster than the F1+ with a specific
workload. Such a pure software acceleration based on commercial hardware with
high performance can open up usage of state-of-the-art FHE algorithms for a
broad set of applications in real systems.


  This paper introduces a new method for estimating the penetration of the end
effector and the parameters of a soft body using a collaborative robotic arm.
This is possible using the dimensionality reduction method that simplifies the
Hunt-Crossley model. The parameters can be found without a force sensor thanks
to the information of the robotic arm controller. To achieve an online
estimation, an extended Kalman filter is employed, which embeds the contact
dynamic model. The algorithm is tested with various types of silicone,
including samples with hard intrusions to simulate cancerous cells within a
soft tissue. The results indicate that this technique can accurately determine
the parameters and estimate the penetration of the end effector into the soft
body. These promising preliminary results demonstrate the potential for robots
to serve as an effective tool for early-stage cancer diagnostics.


  The effective diffusivity $D_e$ of tracer particles diffusing in periodically
corrugated axisymmetric two and three dimensional channels is studied. The
majority of previous studies of this class of problems are based on
perturbative analyses about narrow channels, where the problem can be reduced
to an effectively one dimensional one. Here we show how to analyze this class
of problems using a much more general approach which even includes the limit of
infinitely wide channels. Using the narrow and wide channel asymptotics, we
provide a Pad{\'e} approximant scheme that is able to describe the dispersion
properties of a wide class of channels. Furthermore, we systematically identify
all the exact asymptotic scaling regimes of $D_e$ and the accompanying physical
mechanisms that control dispersion, clarifying the distinction between smooth
channels and compartmentalized ones, and identifying the regimes in which $D_e$
can be linked to first passage problems.


  We investigate novel protocols for entanglement purification of qubit Bell
pairs. Employing genetic algorithms for the design of the purification circuit,
we obtain shorter circuits achieving higher success rates and better final
fidelities than what is currently available in the literature. We provide a
software tool for analytical and numerical study of the generated purification
circuits, under customizable error models. These new purification protocols
pave the way to practical implementations of modular quantum computers and
quantum repeaters. Our approach is particularly attentive to the effects of
finite resources and imperfect local operations - phenomena neglected in the
usual asymptotic approach to the problem. The choice of the building blocks
permitted in the construction of the circuits is based on a thorough
enumeration of the local Clifford operations that act as permutations on the
basis of Bell states.


  The intensity of debate between the realists and antirealists shows no sign
of abating. Here a new hypothesis is proposed to resolve the issue. The
requirement of consistency and continuity are built-in in the methodology of
this hypothesis. This new hypothesis supports realism.


  Context. LS I +61 303 is a member of the select group of gamma-ray binaries:
galactic binary systems that contain a massive star and a compact object, show
a changing milliarcsecond morphology and a similar broad spectral energy
distribution (SED) that peaks at MeV-TeV energies and is modulated by the
orbital motion. The nature of the compact object is unclear in LS I +61 303, LS
5039 and HESS J0632+057, whereas PSR B1259-63 harbours a 47.74 ms radio pulsar.
Aims. A scenario in which a young pulsar wind interacts with the stellar wind
has been proposed to explain the very high energy (VHE, E > 100 GeV) gamma-ray
emission detected from LS I +61 303, although no pulses have been reported from
this system at any wavelength. We aim to find evidence of the pulsar nature of
the compact object. Methods. We performed phased array observations with the
Giant Metrewave Radio Telescope (GMRT) at 1280 MHz centred at phase 0.54.
Simultaneous data from the multi-bit phased array (PA) back-end with a sampling
time of tsamp = 128 microsec and from the polarimeter (PMT) back-end with tsamp
= 256 microsec where taken. Results. No pulses have been found in the data set,
with a minimum detectable mean flux density of \sim 0.38 mJy at 8-sigma level
for the pulsed emission from a putative pulsar with period P >2 ms and duty
cycle D = 10% in the direction of LS I +61 303. Conclusions. The detection of
posible radio pulsations will require deep and sensitive observations at
frequencies \sim0.5-5 GHz and orbital phases 0.6-0.7. However, it may be
unfeasible to detect pulses if the putative pulsar is not beamed at the Earth
or if there is a strong absorption within the binary system.


  A geometric reformulation of the martingale problem associated with a set of
diffusion processes is proposed. This formulation, based on second order
geometry and Ito integration on manifolds, allows us to give a natural and
effective definition of Lie symmetries for diffusion processes.


  We study the layered $J_1$-$J_2$ classical Heisenberg model on the square
lattice using a self-consistent bond theory. We derive the phase diagram for
fixed $J_1$ as a function of temperature $T$, $J_2$ and interplane coupling
$J_z$. Broad regions of (anti)ferromagnetic and stripe order are found, and are
separated by a first-order transition near $J_2\approx 0.5$ (in units of
$|J_1|$). Within the stripe phase the magnetic and vestigial nematic
transitions occur simultaneously in first-order fashion for strong $J_z$. For
weaker $J_z$ there is in addition, for $J_2^*<J_2 < J_2^{**}$, an intermediate
regime of split transitions implying a finite temperature region with nematic
order but no long-range stripe magnetic order. In this split regime, the order
of the transitions depends sensitively on the deviation from $J_2^*$ and
$J_2^{**}$, with split second-order transitions predominating for $J_2^* \ll
J_2 \ll J_2^{**}$. We find that the value of $J_2^*$ depends weakly on the
interplane coupling and is just slightly larger than $0.5$ for $|J_z| \lesssim
0.01$. In contrast the value of $J_2^{**}$ increases quickly from $J_2^*$ at
$|J_z| \lesssim 0.01$ as the interplane coupling is further reduced. In
addition, the magnetic correlation length is shown to directly depend on the
nematic order parameter and thus exhibits a sharp increase (or jump) upon
entering the nematic phase. Our results are broadly consistent with predictions
based on itinerant electron models of the iron-based superconductors in the
normal-state, and thus help substantiate a classical spin framework for
providing a phenomenological description of their magnetic properties.


  We prove local refined versions of Hardy's and Rellich's inequalities as well
as of uncertainty principles for sums of squares of vector fields on bounded
sets of smooth manifolds under certain assumptions on the vector fields. We
also give some explicit examples, in particular, for sums of squares of vector
fields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.


  Melting of boron subphosphide (B12P2) to 26 GPa has been studied by in situ
synchrotron X-ray powder diffraction in a laser-heated diamond anvil cell, and
by quenching and electrical resistance measurements in a toroid-type
high-pressure apparatus. B12P2 melts congruently, and the melting curve has a
positive slope of 23(6) K/GPa. No solid-state phase transition was observed up
to the melting in the whole pressure range under study.


  A family of harmonic superspaces associated with four-dimensional spacetime
is described. Some applications to supersymmetric field theories, including
supergravity, are given.


  We prove an estimate for spherical functions $\varphi_\lambda(a)$ on
$\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral
parameter $\lambda$ when the group parameter $a$ is restricted to a compact
subset of the abelian subgroup $\mathrm{A}$. In the case of
$\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C.
Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain
regular. As in their work, we estimate the oscillatory integral that appears in
the integral formula for spherical functions by the method of stationary phase.
However, the major difference is that we investigate the stability of the
singularities arising from the linearized phase function by classifying their
local normal forms when the parameters $\lambda$ and $a$ vary.


  We analyse a family of brane-world black holes which solve the effective
four-dimensional Einstein equations for a wide range of parameters related to
the unknown bulk/brane physics. We first constrain the parameters using known
experimental bounds and, for the allowed cases, perform a numerical analysis of
their time evolution, which includes accretion through the Earth. The study is
aimed at predicting the typical behavior one can expect if such black holes
were produced at the LHC. Most notably, we find that, under no circumstances,
would the black holes reach the (hazardous) regime of Bondi accretion.
Nonetheless, the possibility remains that black holes live long enough to
escape from the accelerator (and even from the Earth's gravitational field) and
result in missing energy from the detectors.


  In this article, we define the l-adic homology for a morphism of schemes
satisfying certain finiteness conditions. This homology has these functors
similar to the Chow groups: proper push-forward, flat pull-back, base change,
cap-product, etc. In particular on singular varieties, this kind of l-adic
homology behaves much better that the classical l-adic cohomology. As an
application, we give an much easier approach to construct the cycle maps for
arbitrary algebraic schemes over fields of finite cohomology dimension. And we
prove these cycle maps kill the algebraic equivalences and commute with the
Chern action of locally free sheaves.


  We consider two categorifications of the cohomology of a topological space X
by taking coefficients in the category of differential graded categories. We
consider both derived global sections of a constant presheaf and singular
cohomology and find the resulting dg-categories are quasi-equivalent and
moreover quasi-equivalent to representations in perfect complexes of chains on
the loop space of X.


  The pure $R^2$ gravity is equivalent to Einstein gravity with cosmological
constant and a massless scalar field and it further possesses the so-called
restricted Weyl symmetry which is a symmetry larger than scale symmetry. To
incorporate matter, we consider a restricted Weyl invariant action composed of
pure $R^2$ gravity, SU(2) Yang-Mills fields and a non-minimally coupled
massless Higgs field (a triplet of scalars). When the restricted Weyl symmetry
is spontaneously broken, it is equivalent to an Einstein-Yang-Mills-Higgs
(EYMH) action with a cosmological constant and a massive Higgs non-minimally
coupled to gravity i.e. via a term $\tilde{\xi} R |\Phi|^2$. When the
restricted Weyl symmetry is not spontaneously broken, linearization about
Minkowski space-time does not yield gravitons in the original $R^2$ gravity and
hence it does not gravitate. However, we show that in the broken gauge sector
of our theory, where the Higgs field acquires a non-zero vacuum expectation
value, Minkowski space-time is a viable gravitating background solution. We
then obtain numerically gravitating magnetic monopole solutions for non-zero
coupling constant $\tilde{\xi}=1/6$ in three different backgrounds: Minkowski,
anti-de Sitter (AdS) and de Sitter (dS), all of which are realized in our
restricted Weyl invariant theory.


  The observational properties of the six known Anomalous X-ray Pulsars are
described in the context of the main theoretical models for this enigmatic
class of objects.


  Since 1996 a monitoring campaign of the Galactic Bulge region has been
performed by the BeppoSAX Wide Field Cameras in the 2-28 keV band. This allowed
accurate and unbiased studies of classes of objects. In particular the type-I
X-ray bursters, whose distribution is concentrated in the monitored sky region,
have been investigated. High luminosity radius-expansion bursts have been
observed from nine sources, allowing to estimate important physical parameters
such as distance, photospheric radius, averaged luminosity and accretion rate.
An overview of these results is presented.


  We investigate the dynamics of heavy impurities embedded in an ultra-cold
Fermi gas by using a Generalized Langevin equation. The latter -- derived by
means of influence functional theory -- describes the stochastic classical
dynamics of the impurities and the quantum nature of the fermionic bath
manifests in the emergent interaction between the impurities and in the
viscosity tensor. By focusing on the two-impurity case, we predict the
existence of bound states, in different conditions of coupling and temperature,
and whose life-time can be analytically estimated. Our predictions should be
testable using cold-gases platforms within current technology.


  The concept of $p$-adic quincunx Haar MRA was introduced and studied
in~\cite{KS10}. In contrast to the real setting, infinitely many different
wavelet bases are generated by a $p$-adic MRA. We give an explicit description
for all wavelet functions corresponding to the quincunx Haar MRA. Each one
generates an orthogonal basis, one of them was presented in~\cite{KS10}. A
connection between quincunx Haar bases and two-dimensional separable Haar MRA
is also found.


  We construct left invariant quaternionic contact (qc) structures on Lie
groups with zero and non-zero torsion and with non-vanishing quaternionic
contact conformal curvature tensor, thus showing the existence of non-flat
quaternionic contact manifolds. We prove that the product of the real line with
a seven dimensional manifold, equipped with a certain qc structure, has a
quaternionic Kaehler metric as well as a metric with holonomy contained in
Spin(7). As a consequence we determine explicit quaternionic Kaehler metrics
and Spin(7)-holonomy metrics which seem to be new. Moreover, we give explicit
non-compact eight dimensional almost quaternion hermitian manifolds with either
a closed fundamental four form or fundamental two forms defining a differential
ideal that are not quaternionic Kaehler.


  We study autonomous Tonelli Lagrangians on closed surfaces. We aim to clarify
the relationship between the Aubry set and the Mather set, when the latter
consists of periodic orbits which are not fixed points. Our main result says
that in that case the Aubry set and the Mather set almost always coincide.


  Machines are designed to communicate widely and efficiently. Humans, less so.
We evolved social structures that function best as small subgroups interacting
within larger populations. Technology changes this dynamic, by allowing all
individuals to be connected at the speed of light. A dense, tightly connected
population can behave like a single agent. In animals, this happens in
constrained areas where stampedes can easily form. Machines do not need these
kinds of conditions. The very techniques used to design best-of-breed solutions
may increase the risk of dangerous mass behaviors among homogeneous machines.
In this paper we argue that ecologically-based design principles such as the
presence of diversity are a broadly effective strategy to defend against
unintended consequences at scale.


  We construct a Chern-Simons type gauged N=8 supergravity in three spacetime
dimensions with gauge group SO(4) x T_\infty over the infinite dimensional
coset space SO(8,\infty)/(SO(8) x SO(\infty)), where T_\infty is an infinite
dimensional translation subgroup of SO(8,\infty). This theory describes the
effective interactions of the (infinitely many) supermultiplets contained in
the two spin-1 Kaluza-Klein towers arising in the compactification of N=(2,0)
supergravity in six dimensions on AdS_3 x S^3 with the massless supergravity
multiplet. After the elimination of the gauge fields associated with T_\infty,
one is left with a Yang Mills type gauged supergravity with gauge group SO(4),
and in the vacuum the symmetry is broken to the (super-)isometry group of AdS_3
x S^3, with infinitely many fields acquiring masses by a variant of the
Brout-Englert-Higgs effect.


  This article proposes a novel system concept named universal wireless power
transfer, in which power can be wirelessly transferred between different
entities (e.g. vehicles, robots, homes, grid facilities, consumer electronic
devices, etc.) equipped with proper energy transmitters and receivers, whether
stationary or in motion. This concept generalizes individually existing
wireless power transfer systems, where a specific wireless power transfer
technology is used, and where the wireless energy transmitter or receiver is
fixed. As a result, energy mobility, flexibility, and convenience are
significantly improved by the proposed universal wireless power transfer
concept in this study. Moreover, factors relevant to system energy efficiency
are analyzed according to each utilized wireless power transfer technology.
Necessary market mechanisms for such a concept to be successfully deployed are
also introduced, along with an analysis of the benefits engendered in terms of
improving energy systems, the environment, human comfort, and convenience.
Finally, a discussion of the proposed concept, policy implications and
recommendations for future research directions which will underpin universal
wireless power transfer systems are presented.


  Large language models (LLMs) have achieved impressive performance on various
natural language generation tasks. Nonetheless, they suffer from generating
negative and harmful contents that are biased against certain demographic
groups (e.g., female), raising severe fairness concerns. As remedies, prior
works intervened the generation by removing attitude or demographic
information, inevitably degrading the generation quality and resulting in
notable \textit{fairness-fluency} trade-offs. However, it is still
under-explored to what extent the fluency \textit{has to} be affected in order
to achieve a desired level of fairness. In this work, we conduct the first
formal study from an information-theoretic perspective. We show that previous
approaches are excessive for debiasing and propose LIDAO, a general framework
to debias a (L)LM at a better fluency provably. We further robustify LIDAO in
adversarial scenarios, where a carefully-crafted prompt may stimulate LLMs
exhibiting instruction-following abilities to generate texts with fairness
issue appears only when the prompt is also taken into account. Experiments on
three LMs ranging from 0.7B to 7B parameters demonstrate the superiority of our
method.


  In a complete metric space that is equipped with a doubling measure and
supports a Poincar\'e inequality, we prove a new Cartan-type property for the
fine topology in the case $p=1$. Then we use this property to prove the
existence of $1$-finely open \emph{strict subsets} and \emph{strict
quasicoverings} of $1$-finely open sets. As an application, we study fine
Newton-Sobolev spaces in the case $p=1$, that is, Newton-Sobolev spaces defined
on $1$-finely open sets.


  We study analytically the dynamics of a $d$-dimensional Klein-Gordon lattice
with periodic boundary conditions, for $d \leq 3$. We consider initial data
supported on one low-frequency Fourier mode. We show that, in the continuous
approximation, the resonant normal form of the system is given by a
small-dispersion nonlinear Schr\"odinger (NLS) equation. By exploiting a result
about the growth of Sobolev norms for solutions of small-dispersion NLS, we are
able to describe an energy cascade phenomenon for the Klein-Gordon lattice,
where part of the energy is transferred to modes associated to higher
frequencies. Such phenomenon holds within the time-scale for which we can
ensure the validity of the continuous approximation.


  A total of 126 isotopes with Z $\le$ 10 have been identified to date. The
discovery of these isotopes which includes the observation of unbound nuclei,
is discussed. For each isotope a brief summary of the first refereed
publication, including the production and identification method, is presented.


  A previously introduced multi-boson technique for the simulation of QCD with
dynamical quarks is described and some results of first test runs on a
$6^3\times12$ lattice with Wilson quarks and gauge group SU(2) are reported.


  We report imaging photometry of the radio-jet black hole candidate source GRS
1915+105 in the infrared K band. The observations reveal rapid infrared flare
events on timescales of less than an hour. These events are strikingly similar
to those regularly observed in radio monitoring at 15 GHz. Furthermore, when
dereddened, the infrared events have comparable amplitudes to the radio
oscillations, and observations at 15 GHz made approx. 8 hr after our infrared
observations reveal that the source was indeed displaying radio oscillations at
this time. We suggest that we have observed infrared synchrotron emission from
this source. We estimate the equipartition magnetic field and power required to
accelerate the particles for the repeated radio events, and find both to be
orders of magnitude greater than those estimated for any other X-ray binary.


  We review possible mechanisms for energy transfer based on 'rare' or
'non-perturbative' effects, in physical systems that present a many-body
localized phenomenology. The main focus is on classical systems, with or
without quenched disorder. For non-quantum systems, the breakdown of
localization is usually not regarded as an issue, and we thus aim at
identifying the fastest channels for transport. Next, we contemplate the
possibility of applying the same mechanisms in quantum systems, including
disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized
systems with mobility edges at energies below the edge, and strongly disordered
lattice systems in $d>1$. For quantum mechanical systems, the relevance of
these considerations for transport is currently a matter of debate.


  In recent years, a crisis in the standard cosmology has been caused by
inconsistencies in the measurements of some key cosmological parameters, Hubble
constant $H_0$ and cosmic curvature parameter $\Omega_K$ for example. It is
necessary to remeasure them with the cosmological model-independent methods. In
this paper, based on the distance sum rule, we present such a way to constrain
$H_0$ and $\Omega_K$ simultaneously in the late universe from strong
gravitational lensing time delay (SGLTD) data and gravitational wave (GW)
standard siren data simulated from the future observation of the Einstein
Telescope (ET). Based on the currently 6 observed SGLTD data, we find that the
constraint precision of $H_0$ from the combined 100 GW events can be comparable
with the measurement from SH0ES collaboration. As the number of GW events
increases to 700, the constraint precision of $H_0$ will exceed that of the
\textit{Planck} 2018 results. Considering 1000 GW events as the conservative
estimation of ET in ten-year observation, we obtain $H_0=73.69\pm 0.36
\mathrm{~km~s^{-1}~Mpc^{-1}}$ with a 0.5\% uncertainty and
$\Omega_K=0.076^{+0.068}_{-0.087}$. In addition, we simulate 55 SGL systems
with 6.6\% uncertainty for the measurement of time-delay distance. By combining
with 1000 GWs, we infer that $H_0=73.65\pm0.35 \mathrm{~km~s^{-1}~Mpc^{-1}}$
and $\Omega_K=0.008\pm0.048$. Our results suggest that this approach can play
an important role in exploring cosmological tensions.


  We study, by means of mirror symmetry, the quantum geometry of the
K\"ahler-class parameters of a number of Calabi-Yau manifolds that have
$b_{11}=2$. Our main interest lies in the structure of the moduli space and in
the loci corresponding to singular models. This structure is considerably
richer when there are two parameters than in the various one-parameter models
that have been studied hitherto. We describe the intrinsic structure of the
point in the (compactification of the) moduli space that corresponds to the
large complex structure or classical limit. The instanton expansions are of
interest owing to the fact that some of the instantons belong to families with
continuous parameters. We compute the Yukawa couplings and their expansions in
terms of instantons of genus zero. By making use of recent results of
Bershadsky et al. we compute also the instanton numbers for instantons of genus
one. For particular values of the parameters the models become birational to
certain models with one parameter. The compactification divisor of the moduli
space thus contains copies of the moduli spaces of one parameter models. Our
discussion proceeds via the particular models $\P_4^{(1,1,2,2,2)}[8]$ and
$\P_4^{(1,1,2,2,6)}[12]$. Another example, $\P_4^{(1,1,1,6,9)}[18]$, that is
somewhat different is the subject of a companion paper.


  A thermodynamical description for the quasi-static collapse of radiating,
self-gravitating spherical shells of matter in anti-de Sitter space-time is
obtained. It is shown that the specific heat at constant area and other
thermodynamical quantities may diverge before a black hole has eventually
formed. This suggests the possibility of a phase transition occurring along the
collapse process. The differences with respect to the asymptotically flat case
are also highlighted.


  We analyze the performance of a generalized Kitaev's phase estimation
algorithm where N phase gates, acting on $M$ qubits prepared in a product
state, may be distributed in an arbitrary way. Unlike the standard algorithm,
where the mean square error scales as 1/N, the optimal generalizations offer
the Heisenberg $1/N^2$ error scaling and we show that they are in fact very
close to the fundamental Bayesian estimation bound. We also demonstrate that
the optimality of the algorithm breaks down when losses are taken into account,
in which case the performance is inferior to the optimal entanglement-based
estimation strategies. Finally, we show that when an alternative resource
quantification is adopted, which describes the phase estimation in Shor's
algorithm more accurately, the standard Kitaev's procedure is indeed optimal
and there is no need to consider its generalized version.


  It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys.
Rev. Lett. {\bf 77}, 1032 (1996)] that quantum interference between two
molecular transitions can lead to a suppression or enhancement of spontaneous
emission. This is manifested in the fluorescent intensity as a function of the
detuning of the driving field from the two-photon resonance condition. Here we
present a theory which explains the observed variation of the number of peaks
with the mutual polarization of the molecular transition dipole moments. Using
master equation techniques we calculate analytically as well as numerically the
steady-state fluorescence, and find that the number of peaks depends on the
excitation process. If the molecule is driven to the upper levels by a
two-photon process, the fluorescent intensity consists of two peaks regardless
of the mutual polarization of the transition dipole moments. If the excitation
process is composed of both a two-step one-photon process and a one-step,
two-photon process, then there are two peaks on transitions with parallel
dipole moments and three peaks on transitions with antiparallel dipole moments.
This latter case is in excellent agreement with the experiment.


  We announce new existence and $\varepsilon$-regularity results for minimisers
of the relaxation of strongly quasiconvex integrals that on smooth maps
$u\colon\Omega\subset\mathbb{R}^{n}\to\mathbb{R}^{N}$ are defined by $$u\mapsto
\int_{\Omega}F(\nabla^{k}u)dx.$$ The results cover the case of integrands $F$
with $(1,q)$-growth in the full range of exponents $1<q<\frac{n}{n-1}$ for
which a measure representation of the relaxed functional is possible and the
minimizers belong to the space $BV^k$ of maps whose $k$-th order derivatives
are measures.


  We consider distributed and dynamic caching of coded content at small base
stations (SBSs) in an area served by a macro base station (MBS). Specifically,
content is encoded using a maximum distance separable code and cached according
to a time-to-live (TTL) cache eviction policy, which allows coded packets to be
removed from the caches at periodic times. Mobile users requesting a particular
content download coded packets from SBSs within communication range. If
additional packets are required to decode the file, these are downloaded from
the MBS. We formulate an optimization problem that is efficiently solved
numerically, providing TTL caching policies minimizing the overall network
load. We demonstrate that distributed coded caching using TTL caching policies
can offer significant reductions in terms of network load when request arrivals
are bursty. We show how the distributed coded caching problem utilizing TTL
caching policies can be analyzed as a specific single cache, convex
optimization problem. Our problem encompasses static caching and the single
cache as special cases. We prove that, interestingly, static caching is optimal
under a Poisson request process, and that for a single cache the optimization
problem has a surprisingly simple solution.


  We show that the Kahler-Ricci flow on an algebraic manifold of positive
Kodaira dimension and semi-ample canonical line bundle converges to a unique
canonical metric on its canonical model. It is also shown that there exists a
canonical measure of analytic Zariski decomposition on an algebraic manifold of
positive Kodaira dimension. Such a canonical measure is unique and invariant
under birational transformations under the assumption of the finite generation
of canonical rings.


  High-intensity high-energy neutrino beams could be produced by exploiting a
very intense future muon source, and allowing the muons to decay in a storage
ring containing a long straight section. Taking the parameters of muon source
designs that are currently under study, the characteristics of the neutrino
beams that could be produced are discussed and some examples of their physics
potential given. It is shown that the neutrino and antineutrino beam
intensities may be sufficient to produce hundreds of charged current
interactions per year in a detector on the far side of the Earth.


  Solar eruptions occurring at different places within a relatively short time
interval are considered to be sympathetic. However, it is difficult to
determine whether there exists a cause and effect between them. Here we study a
failed and a successful filament eruption following an X1.8-class flare on 2014
December 20, in which slipping-like magnetic reconnections serve as a key
causal link among the eruptions. Reconnection signatures and effects are: at
both sides of the filament experiencing the failed eruption, serpentine ribbons
extend along chromospheric network to move away from the filament, while a hot
loop apparently grows above it; at the filament undergoing the successful
eruption, overlying cold loops contract, while coronal dimming appears at both
sides even before the filament eruption. These effects are understood by
reconnections continually transforming magnetic fluxes overlying one filament
to the other, which adjusts how the magnetic field decays with increasing
height above the filaments in opposite trends, therefore either strengthening
or weakening the magnetic confinement of each filament.


  The aim of in-trawl catch monitoring for use in fishing operations is to
detect, track and classify fish targets in real-time from video footage.
Information gathered could be used to release unwanted bycatch in real-time.
However, traditional multi-object tracking (MOT) methods have limitations, as
they are developed for tracking vehicles or pedestrians with linear motions and
diverse appearances, which are different from the scenarios such as livestock
monitoring. Therefore, we propose a novel MOT method, built upon an existing
observation-centric tracking algorithm, by adopting a new iterative association
step to significantly boost the performance of tracking targets with a uniform
appearance. The iterative association module is designed as an extendable
component that can be merged into most existing tracking methods. Our method
offers improved performance in tracking targets with uniform appearance and
outperforms state-of-the-art techniques on our underwater fish datasets as well
as the MOT17 dataset, without increasing latency nor sacrificing accuracy as
measured by HOTA, MOTA, and IDF1 performance metrics.


  These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at
the thematic school on "Quantum topology and geometry". The goal of these
lectures is to (a) explain some incarnations, in the last ten years, of the
idea of topological recursion: in two dimensional quantum field theories, in
cohomological field theories, in the computation of Weil-Petersson volumes of
the moduli space of curves; (b) relate them more specifically to Eynard-Orantin
topological recursion (revisited from Kontsevich-Soibelman point of view based
on quantum Airy structures).


  How much does the curvature perturbation change after it leaves the horizon,
and when should one evaluate the power spectrum? To answer these questions we
study single field inflation models numerically, and compare the evolution of
different curvature perturbations from horizon crossing to the end of
inflation. In particular we calculate the number of efolds it takes for the
curvature perturbation at a given wavenumber to settle down to within a given
fraction of their value at the end of inflation. We find that e.g. in chaotic
inflation, the amplitude of the comoving and the curvature perturbation on
uniform density hypersurfaces differ by up to 180 % at horizon crossing
assuming the same amplitude at the end of inflation, and that it takes
approximately 3 efolds for the curvature perturbation to be within 1 % of its
value at the end of inflation.


  The inhomogeneous distribution of matter in the non-linear regime of
galaxies, clusters of galaxies and voids is described by an exact, spherically
symmetric inhomogeneous solution of Einstein's gravitational field equations,
corresponding to an under-dense void. The solution becomes the homogeneous and
isotropic Einstein-de Sitter solution for a red shift $z > 10-20$, which
describes the matter dominated CMB data with small inhomogeneities
$\delta\rho/\rho\sim 10^{-5}$. A spatial volume averaging of physical
quantities is introduced and the averaged time evolution expansion parameter
$\theta$ in the Raychoudhuri equation can give rise in the late-time universe
to a volume averaged deceleration parameter $<q>$ that is negative for a
positive matter density. This allows for a region of accelerated expansion
which does not require a negative pressure dark energy or a cosmological
constant. A negative deceleration parameter can be derived by this volume
averaging procedure from the Lema\^{i}tre-Tolman-Bondi open void solution,
which describes the late-time non-linear regime associated with galaxies and
under-dense voids and solves the ``coincidence'' problem.


  I present a deep reinforcement learning (RL) solution to the mathematical
problem known as the Newsvendor model, which seeks to optimize profit given a
probabilistic demand distribution. To reflect a more realistic and complex
situation, the demand distribution can change for different days of the week,
thus changing the optimum behavior. I used a Twin-Delayed Deep Deterministic
Policy Gradient agent (written as completely original code) with both an actor
and critic network to solve this problem. The agent was able to learn optimal
behavior consistent with the analytical solution of the problem, and could
identify separate probability distributions for different days of the week and
behave accordingly.


  We study several effects that influence the strength of the proton cyclotron
and atomic features in the thermal spectra of magnetic neutron stars. We show
that it is possible for vacuum polarization to strongly suppress the spectral
lines when the magnetic field B\ga 10^14 G. For weaker fields (B\la 7\times
10^13 G), the surface spectrum is unaffected by vacuum polarization; thus the
proton cyclotron absorption line can have a large equivalent width. Using an
approximate calculation of the synthetic spectra, we show that variation of
magnetic fields over the neutron star surface leads to broadening of the line.
The recently detected absorption features from the isolated neutron stars RX
J1308.6+2127, RX J1605.3+3249, and RX J0720.4-3125 can plausibly be explained
by the proton cyclotron resonance, with possible blending due to atomic
transitions, in the atmosphere of the star.


  SL_2-tilings were introduced by Assem, Reutenauer, and Smith in connection
with frieses and their applications to cluster algebras.
  An SL_2-tiling is a bi-infinite matrix of positive integers such that each
adjacent 2 x 2-submatrix has determinant 1.
  We construct a large class of new SL_2-tilings which contains the previously
known ones. More precisely, we show that there is a bijection between our class
of SL_2-tilings and certain combinatorial objects, namely triangulations of the
strip.


  We introduce a crisp metric $d_M$ as the common limit of two different nets
$(\Delta_{M,\lambda})$ and $(\delta_{M,\lambda})$ of crisp metrics induced by a
fuzzy metric $M$ and prove that the existence of each of these limits is
equivalent to that of the other and it is characterized by another condition on
the original fuzzy metric $M$. We also derive some of the properties of these
approximate metrics $\Delta_\lambda$ and $\delta_\lambda$. On the other hand,
for a given a crisp metric $d$, establish that the fuzzy metric representing
$M_d$ with values in $\{0,1\}$ and $d$ are compatible with the same topology.
Further, we prove that if a crisp metric $d$ induces a fuzzy metric $M_d$, then
all the approximate crisp metrics $\Delta_{M,\lambda}$ and $\delta_{M,\lambda}$
induced by this fuzzy metric are equal to the original metric $d$.


  In systems composed of water and hydrocarbons Van der Waals-interactions are
dominated by the non-retarded, classical (Keesom) part of the
Lifshitz-interaction; the interaction is screened by salt and extends over
mesoscopic distances of the order of the size of the (micellar) constituents of
complex fluids. We show that these interactions are included intrinsically in a
recently introduced local Monte Carlo algorithm for simulating electrostatic
interactions between charges in the presence of non-homogeneous dielectric
media.


  We discuss solar system constraints on f(G) gravity models, where f is a
function of the Gauss-Bonnet term G. We focus on cosmologically viable f(G)
models that can be responsible for late-time cosmic acceleration. These models
generally give rise to corrections of the form epsilon*(r/rs)^p to the vacuum
Schwarzschild solution, where epsilon = H^2 rs^2 << 1, rs is the Schwarzschild
radius of Sun, and H is the Hubble parameter today. We generally estimate the
strength of modifications to General Relativity in order to confront models
with a number of experiments such as the deflection of light and the perihelion
shift. We show that cosmologically viable f(G) models can be consistent with
solar system constraints for a wide range of model parameters.


  Fluorescent nanodiamonds have been used to a large extent in various
biological systems due to their robust nature, inert properties and the
relative ease of modifying their surface for attachment to different functional
groups. Within a given batch, however, each nanodiamond is indistinguishable
from its neighbors and so far one could only rely on fluorescence statistics
for some global information about the ensemble. Here, we propose and measure
the possibility of adding another layer of unique information, relying on the
coupling between the strain in the nanodiamond and the spin degree-of-freedom
in the nitrogen-vacancy center in diamond. We show that the large variance in
axial and transverse strain can be encoded to an individual radio-frequency
identity for a cluster of nanodiamonds. When using single nanodiamonds, this
unique fingerprint can then be potentially tracked in real-time in, e.g.,
cells, as their size is compatible with metabolism intake. From a completely
different aspect, in clusters of nanodiamonds, this can already now serve as a
platform for anti-counterfeiting measures.


  Agol proved that hyperbolic cubulated groups are virtually special. The aim
of these notes is to make the proof accessible to a wider audience; we retain
the underlying ideas and constructions of Agol, but substantially change or add
to many parts of the argument to give a more transparent and detailed account.


  Two types of room temperature detectors of terahertz laser radiation have
been developed which allow in an all-electric manner to determine the plane of
polarization of linearly polarized radiation and the Stokes parameters of
elliptically polarized radiation, respectively. The operation of the detectors
is based on photogalvanic effects in semiconductor quantum well structures of
low symmetry. The photogalvanic effects have nanoseconds time constants at room
temperature making a high time resolution of the polarization detectors
possible.


  We view the reconstruction of CAD models in the boundary representation
(B-Rep) as the detection of geometric primitives of different orders, i.e.
vertices, edges and surface patches, and the correspondence of primitives,
which are holistically modeled as a chain complex, and show that by modeling
such comprehensive structures more complete and regularized reconstructions can
be achieved. We solve the complex generation problem in two steps. First, we
propose a novel neural framework that consists of a sparse CNN encoder for
input point cloud processing and a tri-path transformer decoder for generating
geometric primitives and their mutual relationships with estimated
probabilities. Second, given the probabilistic structure predicted by the
neural network, we recover a definite B-Rep chain complex by solving a global
optimization maximizing the likelihood under structural validness constraints
and applying geometric refinements. Extensive tests on large scale CAD datasets
demonstrate that the modeling of B-Rep chain complex structure enables more
accurate detection for learning and more constrained reconstruction for
optimization, leading to structurally more faithful and complete CAD B-Rep
models than previous results.


  A quantum Langevin model, similar to models used recently for optomechanics,
was used to predict intermodulation phonon sidebands (IPS). Ab initio
calculations of anharmonic phonons in rocksalt NaBr showed these spectral
features as "many-body effects". Modern inelastic neutron scattering
measurements on a crystal of NaBr at 300K revealed diffuse intensity at high
phonon energy from a predicted upper IPS. The transverse optical (TO) part of
the new features originates from phonon intermodulation between the transverse
acoustic (TA) and TO phonons. The longitudinal optical (LO) spectral features
originate from three-phonon coupling between the TA modes and the TO lattice
modes. The partner lower IPS proves to be an "intrinsic localized mode".
Interactions with the thermal bath broaden and redistribute the spectral weight
of the IPS pair. These sidebands are a probe of anharmonicity and quantum
noise, which originate from interactions between the phonons in NaBr.


  Electrical impedance tomography (EIT) uses current-voltage measurements on
the surface of an imaging subject to detect conductivity changes or anomalies.
EIT is a promising new technique with great potential in medical imaging and
non-destructive testing. However, in many applications, EIT suffers from
inconsistent reliability due to its enormous sensitivity to modeling and
measurement errors.
  In this work we show that rigorous resolution guarantees are possible within
a realistic EIT measurement setting including systematic and random errors. We
derive a constructive criterion to decide whether a desired resolution can be
achieved in a given measurement setup. Our result covers the detection of
anomalies of a known minimal contrast using noisy measurements on a number of
electrodes attached to a subject with imprecisely known background
conductivity.


  Reinforcement Learning (RL) is used extensively in Autonomous Systems (AS) as
it enables learning at runtime without the need for a model of the environment
or predefined actions. However, most applications of RL in AS, such as those
based on Q-learning, can only optimize one objective, making it necessary in
multi-objective systems to combine multiple objectives in a single objective
function with predefined weights. A number of Multi-Objective Reinforcement
Learning (MORL) techniques exist but they have mostly been applied in RL
benchmarks rather than real-world AS systems. In this work, we use a MORL
technique called Deep W-Learning (DWN) and apply it to the Emergent Web Servers
exemplar, a self-adaptive server, to find the optimal configuration for runtime
performance optimization. We compare DWN to two single-objective optimization
implementations: {\epsilon}-greedy algorithm and Deep Q-Networks. Our initial
evaluation shows that DWN optimizes multiple objectives simultaneously with
similar results than DQN and {\epsilon}-greedy approaches, having a better
performance for some metrics, and avoids issues associated with combining
multiple objectives into a single utility function.


  Non-adaptive geostatistical designs (NAGD) offer standard ways of collecting
and analysing geostatistical data in which sampling locations are fixed in
advance of any data collection. In contrast, adaptive geostatistical designs
(AGD) allow collection of exposure and outcome data over time to depend on
information obtained from previous information to optimise data collection
towards the analysis objective. AGDs are becoming more important in spatial
mapping, particularly in poor resource settings where uniformly precise mapping
may be unrealistically costly and priority is often to identify critical areas
where interventions can have the most health impact. Two constructions are:
$singleton$ and $batch$ adaptive sampling. In singleton sampling, locations
$x_i$ are chosen sequentially and at each stage, $x_{k+1}$ depends on data
obtained at locations $x_1,\ldots , x_k$. In batch sampling, locations are
chosen in batches of size $b > 1$, allowing new batch, $\{x_{(k+1)},\ldots
,x_{(k+b)}\}$, to depend on data obtained at locations $x_1,\ldots, x_{kb}$. In
most settings, batch sampling is more realistic than singleton sampling. We
propose specific batch AGDs and assess their efficiency relative to their
singleton adaptive and non-adaptive counterparts by using simulations. We show
how we apply these findings to inform an AGD of a rolling Malaria Indicator
Survey, part of a large-scale, five-year malaria transmission reduction project
in Malawi.