  Let G be a reductive affine group scheme defined over a semilocal ring k.
Assume that either G is semisimple or k is normal and noetherian. We show that
G has a finite k-subgroup S such that the natural map H^1(R, S) --> H^1(R, G)
is surjective for every semilocal ring R containing k. In other words,
G-torsors over Spec(R) admit reduction of structure to S. We also show that the
natural map H^1(X, S) --> H^1(X, G) is surjective in several other contexts,
under suitable assumptions on the base ring k, the scheme X/k and the group
scheme G/k. These results have already been used to study loop algebras as well
as essential dimension of connected algebraic groups in prime characteristic.
Additional applications are presented at the end of this paper.


  We report on measurements of forces acting between two conducting surfaces in
a spherical-plane configuration in the 35 nm-1 micrometer separation range. The
measurements are obtained by performing electrostatic calibrations followed by
a residual analysis after subtracting the electrostatic-dependent component. We
find in all runs optimal fitting of the calibrations for exponents smaller than
the one predicted by electrostatics for an ideal sphere-plane geometry. We also
find that the external bias potential necessary to minimize the electrostatic
contribution depends on the sphere-plane distance. In spite of these anomalies,
by implementing a parametrixation-dependent subtraction of the electrostatic
contribution we have found evidence for short-distance attractive forces of
magnitude comparable to the expected Casimir-Lifshitz force. We finally discuss
the relevance of our findings in the more general context of Casimir-Lifshitz
force measurements, with particular regard to the critical issues of the
electrical and geometrical characterization of the involved surfaces.


  We show that axially symmetric solutions on $\mathbb{S}^4$ to a constant
$Q$-curvature type equation (it may also be called fourth order mean field
equation) must be constant, provided that the parameter $\alpha$ in front of
the Paneitz operator belongs to $[\frac{473 + \sqrt{209329}}{1800}\approx0.517,
1)$. This is in contrast to the case $\alpha=1$, where a family of solutions
exist, known as standard bubbles. The phenomenon resembles the Gaussian
curvature equation on $ \mathbb{S}^2$. As a consequence, we prove an improved
Beckner's inequality on $\mathbb{S}^4$ for axially symmetric functions with
their centers of mass at the origin. Furthermore, we show uniqueness of axially
symmetric solutions when $\alpha=\frac15$ by exploiting Pohozaev-type
identities, and prove existence of a non-constant axially symmetric solution
for $\alpha \in (\frac15, \frac12)$ via a bifurcation method.


  In this paper we develop a new approach to the design of direct numerical
methods for multidimensional problems of the calculus of variations. The
approach is based on a transformation of the problem with the use of a new
class of Sobolev-like spaces that is studied in the article. This
transformation allows one to analytically compute the direction of steepest
descent of the main functional of the calculus of variations with respect to a
certain inner product, and, in turn, to construct new direct numerical methods
for multidimensional problems of the calculus of variations. In the end of the
paper we point out how the approach developed in the article can be extended to
the case of problems with more general boundary conditions, problems for
functionals depending on higher order derivatives, and problems with
isoperimetric and/or pointwise constraints.


  Unconventional fermions, such as three-fold, four-fold, six-fold, and
eight-fold fermions have attracted intense attention in recent years. However,
the concrete materials hosting unconventional fermions are still in urgent
scarcity. In this work, based first-principle calculations and symmetry
analysis, we reveal rich unconventional fermions in existing compound Re2C3 (Re
= Y, La, Ce, Pr, Nd, Sm, Tb, Dy, Ho, Er, Tm, Yb, Lu). We show that these
compounds host quadratic dispersive three-fold (TP), linear dispersive
four-fold (FP) and six-fold points (SP) near the Fermi level in their electric
band structures when spin-orbital coupling (SOC) is not included. Notably, the
FP is charge-2 Dirac-like point. More importantly, among compound Re2C3, the
compound Yb2C3 has very clean band structure, and its unconventional fermions
are closed to the Fermi level. We also find that a uniaxial strain can
transform the unconventional fermions into other types fermions, depending on
the directions of strain. When SOC is considered, a SP transform to an
eightfold degenerate point and a fourfold degenerate point. Overall, our work
provides a family of realistic materials to study the unconventional fermions.


  We discuss a classical nonlinear oscillator, which is proved to be a
superintegrable system for which the bounded motions are quasiperiodic
oscillations and the unbounded (scattering) motions are represented by
hyperbolic functions. This oscillator can be seen as a position-dependent mass
system and we show a natural quantization prescription admitting a
factorization with shape invariance for the $n=1$ case, and then the energy
spectrum is found. Other isochronous systems which can also be considered as a
generalization of the harmonic oscillator and admit a nonstandard Lagrangian
description are also discussed.


  This paper is devoted to the study of solutions with critical regularity for
the two-dimensional Muskat equation. We prove that the Cauchy problem is
well-posed on the endpoint Sobolev space of $L^2$ functions with three-half
derivative in $L^2$. This result is optimal with respect to the scaling of the
equation. One well-known difficulty is that one cannot define a flow map such
that the lifespan is bounded from below on bounded subsets of this critical
Sobolev space. To overcome this, we estimate the solutions for a norm which
depends on the initial data themselves, using the weighted fractional
Laplacians introduced in our previous works. Our proof is the first in which a
null-type structure is identified for the Muskat equation, allowing to
compensate for the degeneracy of the parabolic behavior for large slopes.


  We study coresets for clustering with capacity and fairness constraints. Our
main result is a near-linear time algorithm to construct
$\tilde{O}(k^2\varepsilon^{-2z-2})$-sized $\varepsilon$-coresets for
capacitated $(k,z)$-clustering which improves a recent
$\tilde{O}(k^3\varepsilon^{-3z-2})$ bound by [BCAJ+22, HJLW23]. As a corollary,
we also save a factor of $k \varepsilon^{-z}$ on the coreset size for fair
$(k,z)$-clustering compared to them.
  We fundamentally improve the hierarchical uniform sampling framework of
[BCAJ+22] by adaptively selecting sample size on each ring instance,
proportional to its clustering cost to an optimal solution. Our analysis relies
on a key geometric observation that reduces the number of total ``effective
centers" from [BCAJ+22]'s $\tilde{O}(k^2\varepsilon^{-z})$ to merely $O(k\log
\varepsilon^{-1})$ by being able to ``ignore'' all center points that are too
far or too close to the ring center.


  The first observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
superconducting state and a subsequent detection of the spin-dependent
effective masses of quasiparticles in the CeCoIn_5 heavy fermion system are
combined into a single theoretical framework. The appearance of the spin-split
masses extends essentially the regime of temperatures and applied magnetic
fields, in which FFLO is observable and thus is claimed to be very important
for the FFLO detectability. We also stress that the quasiparticles composing
Cooper pair become distinguishable in the nonzero field. The analysis is
performed within the Kondo-lattice limit of the finite-U Anderson-lattice model
containing both the mass renormalization and real-space pairing within a single
scheme.


  This article is devoted to the study of smooth desingularization, which are
customary employed in the definition of De Rham Intersection Cohomology with
differential forms. In this paper we work with the category of Thom-Mather
simple spaces. We construct a functor which sends each Thom-Mather simple space
into a smooth manifold called its primary unfolding. Hence we prove that the
primary unfoldings are unique up Thom-Mather isomorphisms.


  In a two-dimensional (2D) turbulent fluid containing point-like vortices,
Lars Onsager predicted that adding energy to the fluid can lead to the
formation of persistent clusters of like-signed vortices, i.e., Onsager vortex
(OV) clusters. In the evolution of 2D superfluid turbulence in a uniform
disk-shaped Bose-Einstein condensate (BEC), it was discovered that a pair of OV
clusters with opposite signs can form without any energy input. This striking
spontaneous order was explained as due to a vortex evaporative-heating
mechanism, i.e., annihilations of vortex-antivortex pairs which remove the
lowest-energy vortices and thereby boost the mean energy per vortex. However,
in our search for exotic OV states in a boundaryless 2D spherical BEC, we found
that OV clusters never form despite the annihilations of vortex pairs. Our
analysis reveals that contrary to the general belief, vortex-pair annihilation
emits intense sound waves, which damp the motion of all vortices and hence
suppress the formation of OV clusters. We also present unequivocal evidences
showing that the true mechanism underlying the observed spontaneous OV state is
the escaping of vortices from the BEC boundary. Uncovering this mechanism paves
the way for a comprehensive understanding of emergent vortex orders in 2D
manifolds of superfluids driven far from equilibrium.


  To which degree are shape indices of individual cells of a tessellation
characteristic for the stochastic process that generates them? Within the
context of stochastic geometry and the physics of disordered materials, this
corresponds to the question of relationships between different stochastic
models. In the context of image analysis of synthetic and biological materials,
this question is central to the problem of inferring information about
formation processes from spatial measurements of resulting random structures.
We address this question by a theory-based simulation study of shape indices
derived from Minkowski tensors for a variety of tessellation models. We focus
on the relationship between two indices: an isoperimetric ratio of the
empirical averages of cell volume and area and the cell elongation quantified
by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for
these quantities, as well as for distributions thereof and for correlations of
cell shape and volume, are presented for Voronoi mosaics of the Poisson point
process, determinantal and permanental point processes, and Gibbs hard-core and
random sequential absorption processes as well as for Laguerre tessellations of
polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data
are complemented by mechanically stable crystalline sphere and disordered
ellipsoid packings and area-minimising foam models. We find that shape indices
of individual cells are not sufficient to unambiguously identify the generating
process even amongst this limited set of processes. However, we identify
significant differences of the shape indices between many of these tessellation
models. Given a realization of a tessellation, these shape indices can narrow
the choice of possible generating processes, providing a powerful tool which
can be further strengthened by density-resolved volume-shape correlations.


  Biomedical sciences are increasingly recognising the relevance of gene
co-expression-networks for analysing complex-systems, phenotypes or diseases.
When the goal is investigating complex-phenotypes under varying conditions, it
comes naturally to employ comparative network methods. While approaches for
comparing two networks exist, this is not the case for multiple networks. Here
we present a method for the systematic comparison of an unlimited number of
networks: Co-expression Differential Network Analysis (CoDiNA) for detecting
links and nodes that are common, specific or different to the networks.
Applying CoDiNA to a neurogenesis study identified genes for neuron
differentiation. Experimentally overexpressing one candidate resulted in
significant disturbance in the underlying neurogenesis' gene regulatory
network. We compared data from adults and children with active tuberculosis to
test for signatures of HIV. We also identified common and distinct network
features for particular cancer types with CoDiNA. These studies show that
CoDiNA successfully detects genes associated with the diseases.


  The OGD is seen as a political and socio-economic phenomenon that promises to
promote civic engagement and stimulate public sector innovations in various
areas of public life. To bring the expected benefits, data must be reused and
transformed into value-added products or services. This, in turn, sets another
precondition for data that are expected to not only be available and comply
with open data principles, but also be of value, i.e., of interest for reuse by
the end-user. This refers to the notion of 'high-value dataset' (HVD),
recognized by the European Data Portal as a key trend in the OGD area in 2022.
While there is a progress in this direction, e.g., the Open Data Directive,
incl. identifying 6 key categories, a list of HVDs and arrangements for their
publication and re-use, they can be seen as 'core' / 'base' datasets aimed at
increasing interoperability of public sector data with a high priority,
contributing to the development of a more mature OGD initiative. Depending on
the specifics of a region and country - geographical location, social,
environmental, economic issues, cultural characteristics, (under)developed
sectors and market specificities, more datasets can be recognized as of high
value for a particular country. However, there is no standardized approach to
assist chief data officers in this. In this paper, we present a systematic
review of existing literature on the HVD determination, which is expected to
form an initial knowledge base for this process, incl. used approaches and
indicators to determine them, data, stakeholders.


  We introduce and study "quasidualizing" modules. An artinian R-module T is
quasidualizing if the homothety map \hat R\rightarrow Hom(T,T) is an
isomorphism and Ext_R^i(T,T)=0 for each integer i>0. Quasidualizing modules are
associated to semidualizing modules via Matlis duality. We investigate the
associations via Matlis duality between subclasses of the Auslander class and
Bass class and subclasses of derived T-reflexive modules.


  Associated to a differential character is an integral cohomology class,
referred to as the characteristic class, and a closed differential form,
referred to as the curvature. The characteristic class and curvature are equal
in de Rham cohomology, and this is encoded in a commutative square. In the
Hopkins--Singer model, where differential characters are equivalence classes of
differential cocycles, there is a natural notion of trivializing a differential
cocycle. In this paper, we extend the notion of characteristic class,
curvature, and de Rham class to trivializations of differential cocycles. These
structures fit into a commutative square, and this square is a torsor for the
commutative square associated to characters with degree one less. Under the
correspondence between degree 2 differential cocycles and principal circle
bundles with connection, we recover familiar structures associated to global
sections.


  We describe criteria for implementation of quantum computation in qudits. A
qudit is a d-dimensional system whose Hilbert space is spanned by states |0>,
|1>,... |d-1>. An important earlier work of Mathukrishnan and Stroud [1]
describes how to exactly simulate an arbitrary unitary on multiple qudits using
a 2d-1 parameter family of single qudit and two qudit gates. Their technique is
based on the spectral decomposition of unitaries. Here we generalize this
argument to show that exact universality follows given a discrete set of single
qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to
the QR-matrix decomposition of numerical linear algebra. We consider a generic
physical system in which the single qudit Hamiltonians are a small collection
of H_{jk}^x=\hbar\Omega (|k><j|+|j><k|) and H_{jk}^y =\hbar\Omega
(i|k><j|-i|j><k|). A coupling graph results taking nodes 0,... d-1 and edges
j<->k iff H_{jk}^{x,y} are allowed Hamiltonians. One qudit exact universality
follows iff this graph is connected, and complete universality results if the
two-qudit Hamiltonian H=-\hbar\Omega |d-1,d-1><d-1,d-1| is also allowed. We
discuss implementation in the eight dimensional ground electronic states of
^{87}Rb and construct an optimal gate sequence using Raman laser pulses.


  The 16O nucleus was investigated through the 15N(p,{\alpha})12C reaction at
excitation energies from Ex = 12 231 to 15 700 keV using proton beams from a 5
MeV Van de Graaff accelerator at beam energies of Ep = 331 to 3800 keV. Alpha
decay from resonant states in 16O was strongly observed for ten known excited
states in this region. The candidate 4-alpha cluster state at Ex = 15.1 MeV was
investigated particularly intensely in order to understand its particle decay
channels.


  Modeling via fractional partial differential equations or a L\'evy process
has been an active area of research and has many applications. However, the
lack of efficient numerical computation methods for general nonlocal operators
impedes people from adopting such modeling tools. We proposed an efficient
solver for the convection-diffusion equation whose operator is the
infinitesimal generator of a L\'evy process based on $\mathcal{H}$-matrix
technique. The proposed Crank Nicolson scheme is unconditionally stable and has
a theoretical $\mathcal{O}(h^2+\Delta t^2)$ convergence rate. The
$\mathcal{H}$-matrix technique has theoretical $\mathcal{O}(N)$ space and
computational complexity compared to $\mathcal{O}(N^2)$ and $\mathcal{O}(N^3)$
respectively for the direct method. Numerical experiments demonstrate the
efficiency of the new algorithm.


  In the paper we study two types of relations: a one is between the elliptic
genus of Calabi-Yau manifolds and Jacobi modular forms, another one is between
the second quantized elliptic genus, Siegel modular forms and Lorentzian
Kac-Moody Lie algebras. We also determine the structure of the graded ring of
the weak Jacobi forms with integral Fourier coefficients. It gives us a number
of applications to the theory of elliptic genus and of the second quantized
elliptic genus.


  The recent experimental determination of the parity violating asymmetry
$A_{\rm pv}$ in ${}^{48}$Ca and ${}^{208}$Pb at Jefferson Lab is important for
our understanding on how neutrons and protons arrange themselves inside the
atomic nucleus. To better understand the impact of these measurements, we
present a rigorous theoretical investigation of $A_{\rm pv}$ in ${}^{48}$Ca and
${}^{208}$Pb and assess the associated uncertainties. We complement our study
by inspecting the static electric dipole polarizability in these nuclei. The
analysis is carried out within nuclear energy density functional theory with
quantified input. We conclude that the simultaneous accurate description of
$A_{\rm pv}$ in ${}^{48}$Ca and ${}^{208}$Pb cannot be achieved by our models
that accommodate a pool of global nuclear properties, such as masses and charge
radii, throughout the nuclear chart, and describe -- within one standard
deviation -- the experimental dipole polarizabilities $\alpha_{\rm D}$ in these
nuclei.


  We propose a first-order fast algorithm for the weighted max-min fair (MMF)
multi-group multicast beamforming problem in large-scale systems. Utilizing the
optimal multicast beamforming structure obtained recently, we convert the
nonconvex MMF problem into a min-max weight minimization problem and show that
it is a weakly convex problem. We propose using the projected subgradient
algorithm (PSA) to solve the problem directly, instead of the conventional
method that requires iteratively solving its inverse problem. We show that PSA
for our problem has closed-form updates and thus is computationally cheap.
Furthermore, PSA converges to a near-stationary point of our problem within
finite time. Simulation results show that our PSA-based algorithm offers
near-optimal performance with considerably lower computational complexity than
existing methods for large-scale systems.


  We study bound states generated by a unique potential minimum in the
situation where the system is strongly confined to a bounded region containing
the minimum (by imposing Dirichlet boundary conditions). In this case the
eigenvalues of the confined system differ from those of the unconfined system
by an exponentially small quantity in the semiclassical limit. An asymptotic
expansion for this shift is established. The formulas are evaluated explicitly
for the harmonic oscillator and an application to the Coulomb potential at a
fixed angular momentum is given.


  While the rapid adaptation of mobile devices changes our daily life more
conveniently, the threat derived from malware is also increased. There are lots
of research to detect malware to protect mobile devices, but most of them adopt
only signature-based malware detection method that can be easily bypassed by
polymorphic and metamorphic malware. To detect malware and its variants, it is
essential to adopt behavior-based detection for efficient malware
classification. This paper presents a system that classifies malware by using
common behavioral characteristics along with malware families. We measure the
similarity between malware families with carefully chosen features commonly
appeared in the same family. With the proposed similarity measure, we can
classify malware by malware's attack behavior pattern and tactical
characteristics. Also, we apply a community detection algorithm to increase the
modularity within each malware family network aggregation. To maintain high
classification accuracy, we propose a process to derive the optimal weights of
the selected features in the proposed similarity measure. During this process,
we find out which features are significant for representing the similarity
between malware samples. Finally, we provide an intuitive graph visualization
of malware samples which is helpful to understand the distribution and likeness
of the malware networks. In the experiment, the proposed system achieved 97%
accuracy for malware classification and 95% accuracy for prediction by K-fold
cross-validation using the real malware dataset.


  Inferring the structure and dynamics of network models is critical to
understanding the functionality and control of complex systems, such as
metabolic and regulatory biological networks. The increasing quality and
quantity of experimental data enable statistical approaches based on
information theory for model selection and goodness-of-fit metrics. We propose
an alternative method to infer networked nonlinear dynamical systems by using
sparsity-promoting $\ell_1$ optimization to select a subset of nonlinear
interactions representing dynamics on a fully connected network. Our method
generalizes the sparse identification of nonlinear dynamics (SINDy) algorithm
to dynamical systems with rational function nonlinearities, such as biological
networks. We show that dynamical systems with rational nonlinearities may be
cast in an implicit form, where the equations may be identified in the
null-space of a library of mixed nonlinearities including the state and
derivative terms; this approach applies more generally to implicit dynamical
systems beyond those containing rational nonlinearities. This method,
implicit-SINDy, succeeds in inferring three canonical biological models:
Michaelis-Menten enzyme kinetics, the regulatory network for competence in
bacteria, and the metabolic network for yeast glycolysis.


  Most existing machine learning classifiers are highly vulnerable to
adversarial examples. An adversarial example is a sample of input data which
has been modified very slightly in a way that is intended to cause a machine
learning classifier to misclassify it. In many cases, these modifications can
be so subtle that a human observer does not even notice the modification at
all, yet the classifier still makes a mistake. Adversarial examples pose
security concerns because they could be used to perform an attack on machine
learning systems, even if the adversary has no access to the underlying model.
Up to now, all previous work have assumed a threat model in which the adversary
can feed data directly into the machine learning classifier. This is not always
the case for systems operating in the physical world, for example those which
are using signals from cameras and other sensors as an input. This paper shows
that even in such physical world scenarios, machine learning systems are
vulnerable to adversarial examples. We demonstrate this by feeding adversarial
images obtained from cell-phone camera to an ImageNet Inception classifier and
measuring the classification accuracy of the system. We find that a large
fraction of adversarial examples are classified incorrectly even when perceived
through the camera.


  Jamming and percolation of square objects of size $k \times k$ ($k^2$-mers)
isotropically deposited on simple cubic lattices have been studied by numerical
simulations complemented with finite-size scaling theory. The $k^2$-mers were
irreversibly deposited into the lattice. Jamming coverage $\theta_{j,k}$ was
determined for a wide range of $k$ ($2 \leq k \leq 200$). $\theta_{j,k}$
exhibits a decreasing behavior with increasing $k$, being
$\theta_{j,k\rightarrow\infty}=0.4285(6)$ the limit value for large $k^2$-mer
sizes. On the other hand, the obtained results shows that percolation
threshold, $\theta_{c,k}$, has a strong dependence on $k$. It is a decreasing
function in the range $2 \leq k \leq 18$ with a minimum around $k=18$ and, for
$k \geq 18$, it increases smoothly towards a saturation value. Finally, a
complete analysis of critical exponents and universality has been done, showing
that the percolation phase transition involved in the system has the same
universality class as the 3D random percolation, regardless of the size $k$
considered.


  We explore the structure and kinematics of a dispersed filament of galaxies
residing between the Local Void and the Virgo cluster. For such purpose, we
consider a sample of 361 galaxies with radial velocities $V_{LG} < 2000$ km/s
inside the sky area of RA = [13.0 ... 18.0]$^h$ and Dec. = [$-$5 ...
$+$10]$^\circ$. At present, 161 of them have individual distance estimates. The
galaxy distribution on peculiar velocities along the strip exhibits the known
Virgo-centric infall at RA < 14$^h$ and some signs of outflow from the Local
Void at RA > 17$^h$. Majority of the Bootes strip galaxies (56%) belong to 13
groups and 11 pairs, with the most prominent group around NGC5846. The Bootes
strip groups reside within [17$-$27]Mpc, being all farther from us than the
Virgo cluster. The Bootes filament contains the total stellar mass of
$2.7\times10^{12} M_\odot$ and the total virial mass of $9.07\times10^{13}
M_\odot$, having the average density of dark matter to be $\Omega_m = 0.09$,
i.e. a factor three lower than the global cosmic average.


  We measure whether there are numerous pairs of twin primes (hereafter
referred to as twin prime pairs) according to the prime number inferred by
sieve of Eratosthenes. In this study, we reveal at least three additional twin
prime pairs increased as n is increased by 1, while setting (6n+5)**2 as the
range for estimating twin prime pairs. As a result, we prove the Twin Prime
Conjecture proposed by de Polignac in 1849. That is, there are numerous twin
prime pairs, indicating that there are numerous prime number p for each natural
number k by making p + 2k as prime number for the case of k = 1.


  In this study, the inverse problem of the scattering theory on the half line
for a piecewise continuous Sturm-Liouville equation with boundary condition
depending quadratic on the spectral parameter is considered. The scattering
data of the problem is defined, some properties of the scattering data are
investigated. The main equation is derived and uniqueness algorithm to the
potential with given scattering data is studied.


  The aim of this paper is to generalize the $m-$Segre invariant for vector
bundles to coherent systems. Let $X$ be a non-singular irreducible complex
projective curve of genus $g$ over $\mathbb{C}$ and $(E,V)$ be a coherent
system on $X$ of type $(n,d,k)$. For any pair of integers $m, t$, $0 < m < n$,
$0 \leq t \leq k$ we define the $(m,t)-$Segre invariant, denoted by
$S^\alpha_{m,t}$ and show that $S^\alpha_{m,t}$ induces a semicontinuous
function on the families of coherent systems. Thus, $S^\alpha_{m,t}$ gives a
stratification of the moduli space $G(\alpha;n,d,k)$ of $\alpha-$stable
coherent systems of type $(n,d,k)$ on $X$ into locally closed subvarieties
$G(\alpha;n,d,k;m,t;s)$ according to the value $s$ of $S^\alpha_{m,t}$. We
study the stratification, determine conditions under which the different strata
are non-empty and compute their dimension.


  We examine how the Sunyaev-Zel'dovich (SZ) effect of clusters can probe
$\Omega_{o}$. Using self-consistent models of X-ray clusters in the context of
hierarchical models of structure formation, we show that both the mean Compton
{\it y} parameter and the number of clusters observed via the SZ effect
strongly depend on $\Omega_{o}$. These quantities are higher in open
cosmological models due to the earlier epoch of structure formation.
Specifically, we compare two models which are able to reproduce the present
abundance of X-ray clusters, one for $\Omega_{o}=0.2$ and the other $\Omega =
1$. For $\Omega_{o}=0.2$, ${\ymean}$ exceeds the current FIRAS limit of
$1.5\times10^{-5}$. Also, the SZ redshift source distribution considerably
differs in the two cosmological models. Thus, these results show that both an
improvement in our knowledge of CMB spectral distortions and the realization of
millimeter surveys to look for SZ sources over a large area of the sky should
produce interesting constraints on $\Omega_{o}$ and on the evolution of the
baryonic fractionof virialized structures.


  We investigate the quantum nucleation of pairs of charged circular cosmic
strings in de Sitter space. By including self-gravity we obtain the classical
potential energy barrier and compute the quantum mechanical tunneling
probability in the semiclassical approximation. We also discuss the classical
evolution of charged circular strings after their nucleation.


  Recent Josephson tunneling experiments on twisted flakes of high-$T_c$
cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ revealed a non-reciprocal
behavior of the critical interlayer Josephson current - i.e., a Josephson diode
effect. Motivated by these findings we study theoretically the emergence of the
Josephson diode effect in twisted interfaces between nodal superconductors, and
highlight a strong dependence on the twist angle $\theta$ and damping of the
junction. In all cases, the theory predicts diode efficiency that vanishes
exactly at $\theta = 45^\circ$ and has a strong peak at a twist angle close to
$\theta = 45^\circ$, consistent with experimental observations. Near
$45^\circ$, the junction breaks time-reversal symmetry ${\cal T}$
spontaneously. We find that for underdamped junctions showing hysteretic
behavior, this results in a \emph{dynamical} Josephson diode effect in a part
of the ${\cal T}$-broken phase. The direction of the diode is trainable in this
case by sweeping the external current bias. This effect provides a sensitive
probe of spontaneous ${\cal T}$-breaking. We then show that explicit ${\cal
T}$-breaking perturbations with the symmetry of a magnetic field perpendicular
to the junction plane lead to a {\em thermodynamic} diode effect that survives
even in the overdamped limit. We discuss an experimental protocol to probe the
double-well structure in the Josephson free energy that underlies the tendency
towards spontaneous ${\cal T}$-breaking even if ${\cal T}$ is broken
explicitly. Finally, we show that in-plane magnetic fields can control the
diode effect in the short junction limit, and predict the signatures of
explicit ${\cal T}$-breaking in Shapiro steps.


  Tampering of metering infrastructure of an electrical distribution system can
significantly cause customers' billing discrepancy. The large-scale deployment
of smart meters may potentially be tampered by malware by propagating their
agents to other IP-based meters. Such a possibility is to pivot through the
physical perimeters of a smart meter. While this framework may help utilities
to accurately energy consumption information on the regular basis, it is
challenging to identify malicious meters when there is a large number of users
that are exploited to vulnerability and kWh information being altered. This
paper presents a reconfiguration switching scheme based on graph theory
incorporating the concept of distributed generators to accelerate the anomaly
localization process within an electrical distribution network. First, a data
form transformation from a visualized grid topology to a graph with vertices
and edges is presented. A conversion from the graph representation to machine
recognized matrix representation is then performed. The connection of the grid
topology is illustrated as an adjacency or incidence matrix for the following
analysis. A switching procedure to change elements in the topological matrix is
used to detect and localize the tampered node or cluster. The procedure has to
meet the electrical and the temporary closed-loop operational constraints. The
customer-level anomaly detection is then performed in accordance with
probability derived from smart meter anomalies.


  We develop a complete analytical description of the time evolution of
squeezed states of a charged particle under the Fock-Darwin Hamiltonian and a
time-dependent electric field. This result generalises a relation obtained by
Infeld and Pleba\'nski for states of the one-dimensional harmonic oscillator.
We relate the evolution of a state-vector subjected to squeezing to that of
state which is not subjected to squeezing and for which the time-evolution
under the simple harmonic oscillator dynamics is known (e.g. an eigenstate of
the Hamiltonian). A corresponding relation is also established for the Wigner
functions of the states, in view of their utility in the analysis of cold-ion
experiments. In an appendix, we compute the response functions of the FD
Hamiltonian to an external electric field, using the same techniques as in the
main text.


  The astrophysical origins of the binary black hole systems seen with
gravitational waves are still not well understood. However, features in the
distribution of black-hole masses, spins, redshifts, and eccentricities provide
clues into how these systems form. Much has been learned by investigating these
distributions one parameter at a time. However, we can extract additional
information by studying the covariance between pairs of parameters. Previous
work has shown preliminary support for an anti-correlation between mass ratio
$q \equiv m_2/m_1$ and effective inspiral spin $\chi_\mathrm{eff}$ in the
binary black hole population. In this study, we test for the existence of this
anti-correlation using updated data from the third gravitational wave transient
catalogue (GWTC-3) and improve our copula-based framework to employ a more
robust model for black-hole spins. We find evidence for an anti-correlation in
$(q, \chi_\mathrm{eff})$ with 99.7% credibility. This may imply high
common-envelope efficiencies, stages of super-Eddington accretion, or a
tendency for binary black hole systems to undergo mass-ratio reversal during
isolated evolution. Covariance in $(q,\chi_\mathrm{eff})$ may also be used to
investigate the physics of tidal spin-up as well as the properties of
binary-black-hole-forming active galactic nuclei.


  Arrival/Travel times for public transit exhibit variability on account of
factors like seasonality, dwell times at bus stops, traffic signals, travel
demand fluctuation etc. The developing world in particular is plagued by
additional factors like lack of lane discipline, excess vehicles, diverse modes
of transport and so on. This renders the bus arrival time prediction (BATP) to
be a challenging problem especially in the developing world. A novel
data-driven model based on recurrent neural networks (RNNs) is proposed for
BATP (in real-time) in the current work. The model intelligently incorporates
both spatial and temporal correlations in a unique (non-linear) fashion
distinct from existing approaches. In particular, we propose a Gated Recurrent
Unit (GRU) based Encoder-Decoder(ED) OR Seq2Seq RNN model (originally
introduced for language translation) for BATP. The geometry of the dynamic real
time BATP problem enables a nice fit with the Encoder-Decoder based RNN
structure. We feed relevant additional synchronized inputs (from previous
trips) at each step of the decoder (a feature classically unexplored in machine
translation applications). Further motivated from accurately modelling
congestion influences on travel time prediction, we additionally propose to use
a bidirectional layer at the decoder (something unexplored in other time-series
based ED application contexts). The effectiveness of the proposed algorithms is
demonstrated on real field data collected from challenging traffic conditions.
Our experiments indicate that the proposed method outperforms diverse existing
state-of-art data-driven approaches proposed for the same problem.


  Tropical algebraic geometry is the geometry of the tropical semiring (R, min,
+). The theory of total positivity is a natural generalization of the study of
matrices with all minors positive. In this paper we introduce the totally
positive part of the tropicalization of an arbitrary affine variety, an object
which has the structure of a polyhedral fan. We then investigate the case of
the Grassmannian, denoting the resulting fan \Trop^+ Gr_{k,n}. We show that
\Trop^+ Gr_{2,n} is the Stanley-Pitman fan, which is combinatorially the fan
dual to the (type A_{n-3}) associahedron, and that \Trop^+ Gr_{3,6} and \Trop^+
Gr_{3,7} are closely related to the fans dual to the types D_4 and E_6
associahedra. These results are reminiscent of the results of Fomin and
Zelevinsky, and Scott, who showed that the Grassmannian has a natural cluster
algebra structure which is of types A_{n-3}, D_4, and E_6 for Gr_{2,n},
Gr_{3,6}, and Gr_{3,7}. We suggest a general conjecture about the positive part
of the tropicalization of a cluster algebra.


  In this paper we study symmetric Leibniz and related algebras, namely
symmetric dialgebras and symmetric Perm-algebras. We also calculate their
Koszul duals, if not known. This will give us Lie-admissible algebras and new
types of algebras, which we call commutative and associative admissible
algebras. Finally we prove that all operads describing the considered algebras
are Koszul.


  Non-Equilibrium Social Science (NESS) emphasizes dynamical phenomena, for
instance the way political movements emerge or competing organizations
interact. This paper argues that predictive analysis is an essential element of
NESS, occupying a central role in its scientific inquiry and representing a key
activity of practitioners in domains such as economics, public policy, and
national security. We begin by clarifying the distinction between models which
are useful for prediction and the much more common explanatory models studied
in the social sciences. We then investigate a challenging real-world predictive
analysis case study, and find evidence that the poor performance of standard
prediction methods does not indicate an absence of human predictability but
instead reflects (1.) incorrect assumptions concerning the predictive utility
of explanatory models, (2.) misunderstanding regarding which features of social
dynamics actually possess predictive power, and (3.) practical difficulties
exploiting predictive representations.


  The target space of the non-linear $\sigma$-model is a Riemannian manifold.
Although it can be any Riemannian metric, there are certain physically
interesting geometries which are worth to study. Here, we numerically evolve
the time-symmetric foliations of a family of spherically symmetric
asymptotically flat wormholes under the $1$-loop renormalization group flow of
the non-linear $\sigma$-model, the Ricci flow, and under the $2$-loop
approximation, RG-2 flow. We rely over some theorems adapted from the compact
case for studying the evolution of different wormhole types, specially those
with high curvature zones. Some metrics expand and others contract at the
beginning of the flow, however, all metrics pinch-off at a certain time. This
is related with the fact that the flow does not converge to a fixed point when
its starting geometry is the spatial sections of a Morris-Thorne wormhole, and
therefore the corresponding non-linear $\sigma$-model is
non-integrable/renormalizable. We present a numerical study of the evolution of
wormhole singularities in three dimensions extending the theoretical
estimations. Finally, we compute the evolution of the Hamilton's entropy and
the Brown-York energy.


  The present work is an extension of a previous study of the nucleon-nucleon
interaction based on the chromo-dielectric soliton model. The former approach
was static, leading to an adiabatic potential. Here we perform a dynamical
study in the framework of the Generator Coordinate Method. In practice, we
derive an approximate Hill-Wheeler differential equation and obtain a local
nucleon-nucleon potential as a function of a mean generator coordinate. This
coordinate is related to an effective separation distance between the two
nucleons by a Fujiwara transformation. This latter relationship is especially
useful in studying the quark substructure of light nuclei. We investigate the
explicit contribution of the one-gluon exchange part of the six-quark
Hamiltonian to the nucleon-nucleon potential, and we find that the dynamics are
responsible for a significant part of the short-range N-N repulsion.


  Edge modes in topological insulators are known to be robust against defects.
We investigate if this also holds true when the defect is not static, but
varies in time. We study the influence of defects with time-dependent coupling
on the robustness of the transport along the edge in a Floquet system of
helically curved waveguides. Waveguide arrays are fabricated via direct laser
writing in a negative tone photoresist. We find that single dynamic defects do
not destroy the chiral edge current, even when the temporal modulation is
strong. Quantitative numerical simulation of the intensity in the bulk and edge
waveguides confirms our observation.


  Suppose that the critical locus $\Sigma$ of a complex analytic function $f$
on affine space is, itself, a space with an isolated singular point at the
origin $\0$, and that the Milnor number of $f$ restricted to normal slices of
$\Sigma-\{\0\}$ is constant. Then, the general theory of perverse sheaves puts
severe restrictions on the cohomology of the Milnor fiber of $f$ at $\0$, and
even more surprising restrictions on the cohomology of the Milnor fiber of
generic hyperplane slices.


  In the past two decades, geometric phases have provided a powerful new way of
looking at quantum mechanical systems, manifesting themselves in subtle but
observable ways. Here, we use them to define a versatile function
("distribution of electron charge centres" or DECC) which can be easily
evaluated and interpreted, providing information about electronic structure in
real space. Its utility is illustrated by application to a large variety of
insulators, metals and molecules, treated here within the framework of density
functional theory. The DECC is shown to provide a precise and compact
description of bonding. Unshared-electron (ionic) and shared-electron
(covalent, metallic) bonds are shown to present clearly distinct signatures:
the former are uni-centred while the latter are $n$-centred (n > 1). Moreover,
the charge contained in the DECC peaks gives either the ionic charge or the
number of shared electrons, which is an even integer for covalent bonds. One
obtains revealing insight into the microscopic chemical origins of macroscopic
phenomena such as ferroelectricity in PbTi0$_3$ and the anomalous mechanical
behaviour of bulk Al relative to that of Cu.


  A tutorial review is given of some developments and applications of
stochastic processes from the point of view of the practicioner physicist. The
index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient
Stochastic Dynamics 4.- Noise in Dynamical Systems 5.- Noise Effects in
Spatially Extended Systems 6.- Fluctuations, Phase Transitions and
Noise-Induced Transitions.


  We compare observations of HI from the Very Large Array (VLA) and the Arecibo
Observatory and observations of HCO$^+$ from the Atacama Large
Millimeter/submillimeter Array (ALMA) and the Northern Extended Millimeter
Array (NOEMA) in the diffuse ($A_V\lesssim1$) interstellar medium (ISM) to
predictions from a photodissociation region (PDR) chemical model and
multi-phase ISM simulations. Using a coarse grid of PDR models, we estimate the
density, FUV radiation field, and cosmic ray ionization rate (CRIR) for each
structure identified in HCO$^+$ and HI absorption. These structures fall into
two categories. Structures with $T_s<40~\mathrm{K}$, mostly with
$N(\mathrm{HCO^+})\lesssim10^{12}~\mathrm{cm^{-2}}$, are consistent with modest
density, FUV radiation field, and CRIR models, typical of the diffuse molecular
ISM. Structures with spin temperature $T_s>40~\mathrm{K}$, mostly with
$N(\mathrm{HCO^+})\gtrsim10^{12}~\mathrm{cm^{-2}}$, are consistent with high
density, FUV radiation field, and CRIR models, characteristic of environments
close to massive star formation. The latter are also found in directions with a
significant fraction of thermally unstable HI. In at least one case, we rule
out the PDR model parameters, suggesting that alternative mechanisms (e.g.,
non-equilibrium processes like turbulent dissipation and/or shocks) are
required to explain the observed HCO$^+$ in this direction. Similarly, while
our observations and simulations of the turbulent, multi-phase ISM agree that
HCO$^+$ formation occurs along sightlines with
$N(\mathrm{HI})\gtrsim10^{21}~\mathrm{cm^{-2}}$, the simulated data fail to
explain HCO$^+$ column densities
$\gtrsim\rm{few}\times10^{12}~\mathrm{cm^{-2}}$. Since a majority of our
sightlines with HCO$^+$ had such high column densities, this likely indicates
that non-equilibrium chemistry is important for these lines of sight.


  We study the phase space structure of exact quantum Wightman functions in
spatially homogeneous, temporally varying systems. In addition to the usual
mass shells, the Wightman functions display additional coherence shells around
zero frequency $k_0=0$, which carry the information of the local quantum
coherence of particle-antiparticle pairs. We find also other structures, which
encode non-local correlations in time, and discuss their role and decoherence.
We give a simple derivation of the cQPA formalism, a set of quantum transport
equations, that can be used to study interacting systems including the local
quantum coherence. We compute quantum currents created by a temporal change in
a particle's mass, comparing the exact Wightman function approach, the cQPA and
the semiclassical methods. We find that the semiclassical approximation, which
is fully encompassed by the cQPA, works surprisingly well even for very sharp
temporal features. This is encouraging for the application of semiclassical
methods in electroweak baryogenesis with strong phase transitions.


  We use both FEM (finite element method) and FDTD (finite difference time
domain method) to simulate the field distribution in Maxwell's fish eye lens
with one or more passive drains around the image point. We use the same
Maxwell's fish eye lens structure as the one used in recent microwave
experiment [arXiv:1007.2530]: Maxwell's fish eye lens bounded by PEC (perfect
electric conductor) is inserted between two parallel PEC plates (as a waveguide
structure). Our simulation results indicate that if one uses an active coaxial
cable as the object and set an array of passive drains around the image region,
what one obtains is not an image of the object but only multiple spots
resembling the array of passive drains. The resolution of Maxwell's fish eye is
finite even with such passive drains at the image locations. We also found that
the subwavelength spot around the passive drain is due to the local field
enhancement of the metal tip of the drain rather than the fish eye medium or
the ability of the drain in extracting waves.


  The Reed-Muller (RM) code encoding $n$-variate degree-$d$ polynomials over
${\mathbb F}_q$ for $d < q$, with its evaluation on ${\mathbb F}_q^n$, has
relative distance $1-d/q$ and can be list decoded from a $1-O(\sqrt{d/q})$
fraction of errors. In this work, for $d \ll q$, we give a length-efficient
puncturing of such codes which (almost) retains the distance and list
decodability properties of the Reed-Muller code, but has much better rate.
Specificially, when $q =\Omega( d^2/\epsilon^2)$, we given an explicit rate
$\Omega\left(\frac{\epsilon}{d!}\right)$ puncturing of Reed-Muller codes which
have relative distance at least $(1-\epsilon)$ and efficient list decoding up
to $(1-\sqrt{\epsilon})$ error fraction. This almost matches the performance of
random puncturings which work with the weaker field size requirement $q=
\Omega( d/\epsilon^2)$. We can also improve the field size requirement to the
optimal (up to constant factors) $q =\Omega( d/\epsilon)$, at the expense of a
worse list decoding radius of $1-\epsilon^{1/3}$ and rate
$\Omega\left(\frac{\epsilon^2}{d!}\right)$.
  The first of the above trade-offs is obtained by substituting for the
variables functions with carefully chosen pole orders from an algebraic
function field; this leads to a puncturing for which the RM code is a subcode
of a certain algebraic-geometric code (which is known to be efficiently list
decodable). The second trade-off is obtained by concatenating this construction
with a Reed-Solomon based multiplication friendly pair, and using the list
recovery property of algebraic-geometric codes.


  Synaptic, dendritic and single-cell kinetics generate significant time delays
that shape the dynamics of large networks of spiking neurons. Previous work has
shown that such effective delays can be taken into account with a rate model
through the addition of an explicit, fixed delay [Roxin et al. PRL 238103
(2005)]. Here we extend this work to account for arbitrary symmetric patterns
of synaptic connectivity and generic nonlinear transfer functions.
Specifically, we conduct a weakly nonlinear analysis of the dynamical states
arising via primary instabilities of the asynchronous state. In this way we
determine analytically how the nature and stability of these states depend on
the choice of transfer function and connectivity. We arrive at two general
observations of physiological relevance that could not be explained in previous
works. These are: 1 - Fast oscillations are always supercritical for realistic
transfer functions. 2 - Traveling waves are preferred over standing waves given
plausible patterns of local connectivity. We finally demonstrate that these
results show a good agreement with those obtained performing numerical
simulations of a network of Hodgkin-Huxley neurons.


  We report on generic relations between fractional flow and pressure in steady
two-phase flow in porous media. The main result is a differential equation for
fractional flow as a function of phase saturation. We infer this result from
two underlying observations of steady flow simulations in two and three
dimensions using biperiodic boundary conditions. The resulting equation is
solved generally, and the result is tested against simulations and experimental
relative permeability results found in the literature.


  Despite the remarkable success of deep learning, an optimal convolution
operation on point clouds remains elusive owing to their irregular data
structure. Existing methods mainly focus on designing an effective continuous
kernel function that can handle an arbitrary point in continuous space. Various
approaches exhibiting high performance have been proposed, but we observe that
the standard pointwise feature is represented by 1D channels and can become
more informative when its representation involves additional spatial feature
dimensions. In this paper, we present Multidimensional Kernel Convolution
(MKConv), a novel convolution operator that learns to transform the point
feature representation from a vector to a multidimensional matrix. Unlike
standard point convolution, MKConv proceeds via two steps. (i) It first
activates the spatial dimensions of local feature representation by exploiting
multidimensional kernel weights. These spatially expanded features can
represent their embedded information through spatial correlation as well as
channel correlation in feature space, carrying more detailed local structure
information. (ii) Then, discrete convolutions are applied to the
multidimensional features which can be regarded as a grid-structured matrix. In
this way, we can utilize the discrete convolutions for point cloud data without
voxelization that suffers from information loss. Furthermore, we propose a
spatial attention module, Multidimensional Local Attention (MLA), to provide
comprehensive structure awareness within the local point set by reweighting the
spatial feature dimensions. We demonstrate that MKConv has excellent
applicability to point cloud processing tasks including object classification,
object part segmentation, and scene semantic segmentation with superior
results.


  The Calogero model is a one-dimensional quantum integrable system with
inverse-square long-range interactions confined in an external harmonic well.
It shares the same algebraic structure with the Sutherland model, which is also
a one-dimensional quantum integrable system with inverse-sine-square
interactions. Inspired by the Rodrigues formula for the Jack polynomials, which
form the orthogonal basis of the Sutherland model, recently found by Lapointe
and Vinet, we construct the Rodrigues formula for the Hi-Jack (hidden-Jack)
polynomials that form the orthogonal basis of the Calogero model.


  The mechanisms of the magnetization switching of magnetic multilayers driven
by a current are studied by including exchange interaction between local
moments and spin accumulation of conduction electrons. It is found that this
exchange interaction leads to two additional terms in the
Landau-Lifshitz-Gilbert equation: an effective field and a spin torque. Both
terms are proportional to the transverse spin accumulation and have comparable
magnitudes.


  Given an undirected graph and two disjoint vertex pairs $s_1,t_1$ and
$s_2,t_2$, the Shortest two disjoint paths problem (S2DP) asks for the minimum
total length of two vertex disjoint paths connecting $s_1$ with $t_1$, and
$s_2$ with $t_2$, respectively.
  We show that for cubic planar graphs there are NC algorithms, uniform
circuits of polynomial size and polylogarithmic depth, that compute the S2DP
and moreover also output the number of such minimum length path pairs.
  Previously, to the best of our knowledge, no deterministic polynomial time
algorithm was known for S2DP in cubic planar graphs with arbitrary placement of
the terminals. In contrast, the randomized polynomial time algorithm by
Bj\"orklund and Husfeldt, ICALP 2014, for general graphs is much slower, is
serial in nature, and cannot count the solutions.
  Our results are built on an approach by Hirai and Namba, Algorithmica 2017,
for a generalisation of S2DP, and fast algorithms for counting perfect
matchings in planar graphs.


  Until a couple of years ago, the only known examples of Lie groups admitting
left-invariant metrics with negative Ricci curvature were either solvable or
semisimple. We use a general construction from a previous article of the second
named author to produce a great amount of examples with compact Levy factor.
Given a compact semisimple real Lie algebra $\mathfrak u$ and a real
representation $\pi$ satisfying some technical properties, the construction
returns a metric Lie algebra $\mathfrak l(\mathfrak u,\pi)$ with negative Ricci
operator. In this paper, when $\mathfrak u$ is assumed to be simple, we prove
that $\mathfrak l(\mathfrak u,\pi)$ admits a metric having negative Ricci
curvature for all but finitely many finite-dimensional irreducible
representations of $\mathfrak u\otimes_{\mathbb R} \mathbb C$, regarded as a
real representation of $\mathfrak u$. We also prove in the last section a more
general result where the nilradical is not abelian, as it is in every
$\mathfrak l(\mathfrak u,\pi)$.


  This paper has been withdrawn by the author(s). Please refer to
quant-ph/0311171.


  The problem of the least prime number in an arithmetic progression is one of
the most important topics in Number Theory. In [11], we are the first to study
the relations between this problem and Goldbach's conjecture. In this paper, we
further consider its applications to Goldbach's conjecture and refine the
result in [11]. Moreover, we also try to generalize the problem of the least
prime number in an arithmetic progression and give an analogy of Goldbach's
conjecture.


  We revisit a singlet Majoron model in which neutrino masses arise from the
spontaneous violation of lepton number. If the Majoron obtains a mass of order
MeV, it can play the role of dark matter. We discuss constraints on the
couplings of the massive Majoron with masses of order MeV to neutrinos from
supernova data. In the dense supernova core, Majoron-emitting neutrino
annihilations are allowed and can change the signal of a supernova. Based on
the observation of SN1987A, we exclude a large range of couplings from the
luminosity and the deleptonization arguments, taking the effect of the
background medium into account. If the Majoron mass does not exceed the Q-value
of the experiment, the neutrino-Majoron couplings allow for neutrinoless double
beta decay with Majoron emission. We derive constraints on the couplings for a
Majoron mass of order MeV based on the phase space suppression and the
diminishing signal-to-background ratio due to the Majoron mass. The combination
of constraints from astrophysics and laboratory experiments excludes a large
range of neutrino-Majoron couplings in the mass range of intererest for Majoron
dark matter.


  Fully supervised segmentation methods require a large training cohort of
already segmented images, providing information at the pixel level of each
image. We present a method to automatically segment and model pathologies in
medical images, trained solely on data labelled on the image level as either
healthy or containing a visual defect. We base our method on CycleGAN, an
image-to-image translation technique, to translate images between the domains
of healthy and pathological images. We extend the core idea with two key
contributions. Implementing the generators as residual generators allows us to
explicitly model the segmentation of the pathology. Realizing the translation
from the healthy to the pathological domain using a variational autoencoder
allows us to specify one representation of the pathology, as this
transformation is otherwise not unique. Our model hence not only allows us to
create pixelwise semantic segmentations, it is also able to create inpaintings
for the segmentations to render the pathological image healthy. Furthermore, we
can draw new unseen pathology samples from this model based on the distribution
in the data. We show quantitatively, that our method is able to segment
pathologies with a surprising accuracy being only slightly inferior to a
state-of-the-art fully supervised method, although the latter has per-pixel
rather than per-image training information. Moreover, we show qualitative
results of both the segmentations and inpaintings. Our findings motivate
further research into weakly-supervised segmentation using image level
annotations, allowing for faster and cheaper acquisition of training data
without a large sacrifice in segmentation accuracy.


  Van der Waals heterostructures obtained by artificially stacking
two-dimensional crystals represent the frontier of material engineering,
demonstrating properties superior to those of the starting materials. Fine
control of the interlayer twist angle has opened new possibilities for
tailoring the optoelectronic properties of these heterostructures. Twisted
bilayer graphene with a strong interlayer coupling is a prototype of twisted
heterostructure inheriting the intriguing electronic properties of graphene.
Understanding the effects of the twist angle on its out-of-equilibrium optical
properties is crucial for devising optoelectronic applications. With this aim,
we here combine excitation-resolved hot photoluminescence with femtosecond
transient absorption microscopy. The hot charge carrier distribution induced by
photo-excitation results in peaked absorption bleaching and photo-induced
absorption bands, both with pronounced twist angle dependence. Theoretical
simulations of the electronic band structure and of the joint density of states
enable to assign these bands to the blocking of interband transitions at the
van Hove singularities and to photo-activated intersubband transitions. The
tens of picoseconds relaxation dynamics of the observed bands is attributed to
the angle-dependence of electron and phonon heat capacities of twisted bilayer
graphene.


  We propose a new representation of the fourth Painlev\'e equation in which
the $A^{(1)}_2$-symmetries become clearly visible. By means of this
representation, we clarify the internal relation between the fourth Painlev\'e
equation and the modified KP hierarchy. We obtain in particular a complete
description of the rational solutions of the fourth Painlev\'e equation in
terms of Schur functions. This implies that the so-called Okamoto polynomials,
which arise from the $\tau$-functions for rational solutions, are in fact
expressible by the 3-reduced Schur functions.


  An argument is given to associate integrable nonintegrable transition of
discrete maps with the transition of Lawvere's fixed point theorem to its own
contrapositive. We show that the classical description of nonlinear maps is
neither complete nor totally predictable.


  The present study deals with the analysis and classification of interest rate
curves. Interest rate curves (IRC) are the basic financial curves in many
different fields of economics and finance. They are extremely important tools
in banking and financial risk management problems. Interest rates depend on
time and maturity which defines term structure of the interest rate curves. IRC
are composed of interest rates at different maturities (usually fixed number)
which move coherently in time. In the present study machine learning
algorithms, namely Self-Organising maps - SOM (Kohonen maps), are used to find
clusters and to classify Swiss franc (CHF) interest rate curves.


  We consider evolutionary games in which the agent selected for update
compares their payoff to q neighbours, rather than a single neighbour as in
standard evolutionary game theory. Through studying fixed point stability and
fixation times for 2x2 games with all-to-all interactions, we find that the
flow changes significantly as a function of q. Further, we investigate the
effects of changing the underlying topology from an all-to-all interacting
system to an uncorrelated graph via the pair approximation. We also develop the
framework for studying games with more than two strategies, such as the
rock-paper-scissors game where we show that changing q leads to the emergence
of new types of flow.


  This paper is devoted to Nash equilibrium for games in capacities. Such games
with payoff expressed by Choquet integral were considered by Kozhan and
Zarichnyi (Nash equilibria for games in capacities, Econ. Theory {\bf 35}
(2008) 321--331) and existence of Nash equilibrium was proved. We also consider
games in capacities but with expected payoff expressed by Sugeno integral. We
prove existence of Nash equilibrium using categorical methods and abstract
convexity theory.


  We present a flexible Monte Carlo implementation of the perturbative
framework of High Energy Jets, describing multi-jet events at hadron colliders.
The description includes a resummation which ensures leading logarithmic
accuracy for large invariant mass between jets, and is matched to tree-level
accuracy for multiplicities up to 4 jets. The resummation includes all-order
hard corrections, which become important for increasing centre-of-mass energy
of the hadronic collision.
  We discuss observables relevant for confronting the perturbative framework
with 7 TeV data from the LHC, and the impact of the perturbative corrections on
several dijet and trijet observables which are relevant in the search for new
physics.


  This introductory chapter briefly outlines the main theme of this volume,
namely, to review the new opportunities and risks of digital healthcare from
various disciplinary perspectives. These perspectives include law, public
policy, organisational studies, and applied ethics. Based on this
interdisciplinary approach, we hope that effective strategies may arise to
ensure that benefits of this on-going revolution are deployed in a responsible
and sustainable manner. The second part of the chapter comprises a brief review
of the four parts and fourteen substantive chapters that comprise this volume.


  A Monte Carlo (MC) simulation method based on the Gillespie algorithm is
developed for the polymerization of branched polyetherimides from two back-bone
monomers [4,4'-bisphenol A dianhydride (BPADA) and m-phenylenediamine (MPD)], a
chain terminator [phthalic anhydride (PA)], and a branching agent
[tris[4-(4-aminophenoxy)phenyl] ethane (TAPE)]. This polymerization involves 4
reactions that all can be reduced to a condensation reaction between an amine
group and a carboxylic anhydride group. By comparing the MC simulation results
to the predictions of the Flory-Stockmayer theory on the molecular weight
distribution, we show that the rates of the 4 reactions in the MC simulations
should be set based on the concentrations of the functional groups on the
monomers involved in each reaction. Using the MC simulations, we show that the
Flory-Stockmayer theory predicts the molecular weight distribution well for
systems below the gel point that is set by the functionality of the branching
agent but starts to fail for systems around or above the gel point. However,
for all the systems the MC simulations can be used to reliably predict the
molecular weight distribution. Even for a macroscopic system, a converging
distribution can be quickly obtained through the MC simulations on a system of
only a few hundred to a few thousand monomers but with the same molar ratios of
monomers as in the macroscopic system.


  While reinforcement learning has shown experimental success in a number of
applications, it is known to be sensitive to noise and perturbations in the
parameters of the system, leading to high variance in the total reward amongst
different episodes in slightly different environments. To introduce robustness,
as well as sample efficiency, risk-sensitive reinforcement learning methods are
being thoroughly studied. In this work, we provide a definition of robust
reinforcement learning policies and formulate a risk-sensitive reinforcement
learning problem to approximate them, by solving an optimization problem with
respect to a modified objective based on exponential criteria. In particular,
we study a model-free risk-sensitive variation of the widely-used Monte Carlo
Policy Gradient algorithm and introduce a novel risk-sensitive online
Actor-Critic algorithm based on solving a multiplicative Bellman equation using
stochastic approximation updates. Analytical results suggest that the use of
exponential criteria generalizes commonly used ad-hoc regularization
approaches, improves sample efficiency, and introduces robustness with respect
to perturbations in the model parameters and the environment. The
implementation, performance, and robustness properties of the proposed methods
are evaluated in simulated experiments.


  Relaying over power line communication (PLC) channels can considerably
enhance the performance and reliability of PLC systems. This paper is dedicated
to study and analyze the energy efficiency of multi-hop cooperative relaying
PLC systems. Incremental decode-and-forward (IDF) relying is exploited to
reduce the transmit power consumption. The PLC channel is assumed to experience
log-normal fading with impulsive noise. The performances of single-hop and
conventional DF relaying systems are also analyzed in terms of outage
probability and energy efficiency for which analytical expressions are derived.
Results show that using more relays can improve the outage probability
performance; however, this is achieved at the expense of increased power
consumption due to the increased static power of the relays, especially when
the total source-to-destination distance is relatively small. Results also
demonstrate that the IDF PLC system has better energy efficiency performance
compared to the other schemes.


  Adequate modelling of the multiphase interstellar medium requires optically
thin radiative cooling, comprising an inherent thermal instability. The size of
the occurring condensation and evaporation interfaces is determined by the
so-called Field-length, which gives the dimension at which the instability is
significantly damped by thermal conduction. Our aim is to study the relevance
of conduction scale effects in the numerical modelling of a bistable medium and
check the applicability of conventional and alternative adaptive mesh
techniques. The low physical value of the thermal conduction within the ISM
defines a multiscale problem, hence promoting the use of adaptive meshes. We
here introduce a new refinement strategy that applies the Field condition by
Koyama & Inutsuka as a refinement criterion. The described method is very
similar to the Jeans criterion for gravitational instability by Truelove and
efficiently allows to trace the unstable gas situated at the thermal
interfaces. We present test computations that demonstrate the greater accuracy
of the newly proposed refinement criterion in comparison to refinement based on
the local density gradient. Apart from its usefulness as a refinement trigger,
we do not find evidence in favour of the Field criterion as a prerequisite for
numerical stability.


  Harmonic model predictive control (HMPC) is a recent model predictive control
(MPC) formulation for tracking piece-wise constant references that includes a
parameterized artificial harmonic reference as a decision variable, resulting
in an increased performance and domain of attraction with respect to other MPC
formulations. This article presents an extension of the HMPC formulation to
track periodic harmonic references and discusses its use to track arbitrary
references. The proposed formulation inherits the benefits of its predecessor,
namely its good performance and large domain of attraction when using small
prediction horizons, and that the complexity of its optimization problem does
not depend on the period of the periodic reference. We show closed-loop results
discussing its performance and comparing it to other MPC formulations.


  The broadening of one-dimensional Gaussian wave packets is presented in all
textbooks on quantum mechanics. It is used to elucidate Heisenberg's
uncertainty relation. The behaviour on a lattice is drastically different if
the amplitude and/or phase of the wave packet varies on the scale of the
lattice constant. Important examples are very narrow wave packets ot wave
packets with an average velocity comparable to the maximum velocity on the
lattice. Analytical and numerical results for the time dependence of wave
packets on a one-dimensional lattice are presented.


  Herein, we propose a spatio-temporal extension of RBFNN for nonlinear system
identification problem. The proposed algorithm employs the concept of
time-space orthogonality and separately models the dynamics and nonlinear
complexities of the system. The proposed RBF architecture is explored for the
estimation of a highly nonlinear system and results are compared with the
standard architecture for both the conventional and fractional gradient
decent-based learning rules. The spatio-temporal RBF is shown to perform better
than the standard and fractional RBFNNs by achieving fast convergence and
significantly reduced estimation error.


  In recent years, we have seen a colossal effort in pre-training multilingual
text encoders using large-scale corpora in many languages to facilitate
cross-lingual transfer learning. However, due to typological differences across
languages, the cross-lingual transfer is challenging. Nevertheless, language
syntax, e.g., syntactic dependencies, can bridge the typological gap. Previous
works have shown that pre-trained multilingual encoders, such as mBERT
\cite{devlin-etal-2019-bert}, capture language syntax, helping cross-lingual
transfer. This work shows that explicitly providing language syntax and
training mBERT using an auxiliary objective to encode the universal dependency
tree structure helps cross-lingual transfer. We perform rigorous experiments on
four NLP tasks, including text classification, question answering, named entity
recognition, and task-oriented semantic parsing. The experiment results show
that syntax-augmented mBERT improves cross-lingual transfer on popular
benchmarks, such as PAWS-X and MLQA, by 1.4 and 1.6 points on average across
all languages. In the \emph{generalized} transfer setting, the performance
boosted significantly, with 3.9 and 3.1 points on average in PAWS-X and MLQA.


  The most promising approaches for efficient detection in multiple-input
multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The
conventional (and optimum) norm that is used to conduct the tree traversal step
in SD is the l-2 norm. It was, however, recently observed that using the
l-infinity norm instead reduces the hardware complexity of SD considerably at
only a marginal performance loss. These savings result from a reduction in the
length of the critical path in the circuit and the silicon area required for
metric computation, but are also, as observed previously through simulation
results, a consequence of a reduction in the computational (i.e., algorithmic)
complexity. The aim of this paper is an analytical performance and
computational complexity analysis of l-infinity norm SD. For i.i.d. Rayleigh
fading MIMO channels, we show that l-infinity norm SD achieves full diversity
order with an asymptotic SNR gap, compared to l-2 norm SD, that increases at
most linearly in the number of receive antennas. Moreover, we provide a
closed-form expression for the computational complexity of l-infinity norm SD
based on which we establish that its complexity scales exponentially in the
system size. Finally, we characterize the tree pruning behavior of l-infinity
norm SD and show that it behaves fundamentally different from that of l-2 norm
SD.


  We find an exact solution of BPS wall in five-dimensional supergravity using
a gravitational deformation of the massive Eguchi-Hanson nonlinear sigma model.
The warp factor decreases for both infinities of the extra dimension. Our
solution requires no fine-tuning between boundary and bulk cosmological
constants, in contrast to the Randall-Sundrum model. Wall solutions are also
obtained with warp factors which are flat or increasing in one side by varying
a deformation parameter.


  We consider the long time behavior of heterogeneously interacting diffusive
particle systems and their large population limit. The interaction is of mean
field type with weights characterized by an underlying graphon. The limit is
given by a graphon particle system consisting of independent but heterogeneous
nonlinear diffusions whose probability distributions are fully coupled. Under
suitable assumptions, including a certain convexity condition, we show the
exponential ergodicity for both systems, establish the uniform-in-time law of
large numbers for marginal distributions as the number of particles increases,
and introduce the uniform-in-time Euler approximation. The precise rate of
convergence of the Euler approximation is provided.


  Simulated dark matter haloes are fitted by self-similar, universal density
profiles, where the scaled parameters depend only on a scaled (truncation)
radius which, in turn, is supposed to be independent on the mass and the
formation redshift. A criterion for the choice of the best fitting density
profile is proposed, with regard to a set of high-resolution simulations, where
some averaging procedure on scaled density profiles has been performed, in
connection with a number of fitting density profiles. An application is made to
a pair of sets each made of a dozen of high-resolution simulations, which are
available in literature, in connection with two currently used fitting density
profiles, where the dependence of the scaled radius on the mass and the
formation redshift, may be neglected to a first extent. Some features of the
early evolution of dark matter haloes represented by fitting density profiles,
are discussed in the limit of the spherical top-hat model.


  Recent results related to the chemical equilibration of hadrons in the final
state of p-p and heavy ion collisions are reviewed.


  Traditional language models, adept at next-token prediction in text
sequences, often struggle with transduction tasks between distinct symbolic
systems, particularly when parallel data is scarce. Addressing this issue, we
introduce \textit{symbolic autoencoding} ($\Sigma$AE), a self-supervised
framework that harnesses the power of abundant unparallel data alongside
limited parallel data. $\Sigma$AE connects two generative models via a discrete
bottleneck layer and is optimized end-to-end by minimizing reconstruction loss
(simultaneously with supervised loss for the parallel data), such that the
sequence generated by the discrete bottleneck can be read out as the transduced
input sequence. We also develop gradient-based methods allowing for efficient
self-supervised sequence learning despite the discreteness of the bottleneck.
Our results demonstrate that $\Sigma$AE significantly enhances performance on
transduction tasks, even with minimal parallel data, offering a promising
solution for weakly supervised learning scenarios.


  We develop randomized modifications of Markov chains and apply these
modifications to the routing chains of customers in Jacksonian stochastic
networks. The aim of our investigations is to find new rerouting schemes for
non standard Jackson networks which hitherto resist computing explicitly the
stationary distribution.
  The non standard properties we can handle by suitable algorithms encompass
several modifications of Jackson networks known in the literature, especially
breakdown and repair of nodes with access modification for customers to down
nodes, finite buffers with control of buffer overflow. The rerouting schemes
available in the literature for these situations are special cases of our
rerouting schemes, which can deal also with partial degrading of service
capacities and even with speed up of service.
  In any case we require our algorithms to react on such general changes in the
network with the aim to maintain the utilization of the nodes. To hold this
invariant under change of service speeds (intensities) our algorithms not only
adapt the routing probabilities but decrease automatically the overall arrival
rate to the network if necessary.
  Our main application is for stochastic networks in a random environment. The
impact of the environment on the network is by changing service speeds (by
upgrading and/or degrading, breakdown, repair) and we implement the
randomization algorithms to react to the changes of the environment. On the
other side, customers departing from the network may enforce the environment to
jump immediately. So our environment is not Markov for its own.
  The main result is to compute explicitly the joint stationary distribution of
the queue lengths vector and the environment which is of product form:
Environment and queue lengths vector, and the queue lengths over the network
are decomposable.


  We show that in positive characteristic special loci of deformation spaces of
rank one $\ell$-adic local systems are quasilinear. From this we deduce the
Hard Lefschetz theorem for rank one $\ell$-adic local systems and a generic
vanishing theorem. Last version: a few typos corrected


  Let $\sigma,t\in{\mathbb{R}}$, $s=\sigma+\mathrm{{i}}t$, $\Gamma (s)$ be the
Gamma function, $\zeta(s)$ be the Riemann zeta function and $\xi(s):=s(s-1)\pi
^{-s/2}\Gamma(s/2)\zeta(s)$ be the complete Riemann zeta function. We show that
$\Xi_{\sigma}(t):=\xi (\sigma-\mathrm{{i}}t)/\xi(\sigma)$ is a characteristic
function for any $\sigma\in{\mathbb{R}}$ by giving the probability density
function. Next we prove that the Riemann hypothesis is true if and only if each
$\Xi_{\sigma}(t)$ is a pretended-infinitely divisible characteristic function,
which is defined in this paper, for each $1/2<\sigma<1$. Moreover, we show that
$\Xi_{\sigma}(t)$ is a pretended-infinitely divisible characteristic function
when $\sigma=1$. Finally we prove that the characteristic function
$\Xi_{\sigma}(t)$ is not infinitely divisible but quasi-infinitely divisible
for any $\sigma>1$.


  Self-assembly is one of the most promising strategies for making functional
materials at the nanoscale, yet new design principles for making self-limiting
architectures, rather than spatially unlimited periodic lattice structures, are
needed. To address this challenge, we explore the trade-offs between
addressable assembly and self-closing assembly of a specific class of
self-limiting structures: cylindrical tubules. We make triangular subunits
using DNA origami that have specific, valence-limited interactions and designed
binding angles, and study their assembly into tubules that have a self-limited
width that is much larger than the size of an individual subunit. In the
simplest case, the tubules are assembled from a single component by
geometrically programming the dihedral angles between neighboring subunits. We
show that the tubules can reach many micrometers in length and that their
average width can be prescribed through the dihedral angles. We find that there
is a distribution in the width and the chirality of the tubules, which we
rationalize by developing a model that considers the finite bending rigidity of
the assembled structure as well as the mechanism of self-closure. Finally, we
demonstrate that the distributions of tubules can be further sculpted by
increasing the number of subunit species, thereby increasing the assembly
complexity, and demonstrate that using two subunit species successfully reduces
the number of available end states by half. These results help to shed light on
the roles of assembly complexity and geometry in self-limited assembly and
could be extended to other self-limiting architectures, such as shells,
toroids, or triply-periodic frameworks.


  Reconstruction of the Fermi surface of high-temperature superconducting
cuprates in the pseudogap state is analyzed within nearly exactly solvable
model of the pseudogap state, induced by short-range order fluctuations of
antiferromagnetic (AFM, spin density wave (SDW), or similar charge density wave
(CDW)) order parameter, competing with superconductivity. We explicitly
demonstrate the evolution from "Fermi arcs" (on the "large" Fermi surface)
observed in ARPES experiments at relatively high temperatures (when both the
amplitude and phase of density waves fluctuate randomly) towards formation of
typical "small" electron and hole "pockets", which are apparently observed in
de Haas - van Alfen and Hall resistance oscillation experiments at low
temperatures (when only the phase of density waves fluctuate, and correlation
length of the short-range order is large enough). A qualitative criterion for
quantum oscillations in high magnetic fields to be observable in the pseudogap
state is formulated in terms of cyclotron frequency, correlation length of
fluctuations and Fermi velocity.


  In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized
to represent the random model responses, which are computationally expensive
and usually obtained by deterministic numerical modeling approaches including
finite element and finite-difference time-domain methods. Recently, efforts
have been made on improving the prediction performance of the PCE-based model
and building efficiency by only selecting the influential basis polynomials
(e.g., via the approach of least angle regression). This paper proposes an
approach, named as resampled PCE (rPCE), to further optimize the selection by
making use of the knowledge that the true model is fixed despite the
statistical uncertainty inherent to sampling in the training. By simulating
data variation via resampling ($k$-fold division utilized here) and collecting
the selected polynomials with respect to all resamples, polynomials are ranked
mainly according to the selection frequency. The resampling scheme (the value
of $k$ here) matters much and various configurations are considered and
compared. The proposed resampled PCE is implemented with two popular selection
techniques, namely least angle regression and orthogonal matching pursuit, and
a combination thereof. The performance of the proposed algorithm is
demonstrated on two analytical examples, a benchmark problem in structural
mechanics, as well as a realistic case study in computational dosimetry.


  Error concealment is of great importance for block-based video systems, such
as DVB or video streaming services. In this paper, we propose a novel scalable
spatial error concealment algorithm that aims at obtaining high quality
reconstructions with reduced computational burden. The proposed technique
exploits the excellent reconstructing abilities of the kernel-based minimum
mean square error K-MMSE estimator. We propose to decompose this approach into
a set of hierarchically stacked layers. The first layer performs the basic
reconstruction that the subsequent layers can eventually refine. In addition,
we design a layer management mechanism, based on profiles, that dynamically
adapts the use of higher layers to the visual complexity of the area being
reconstructed. The proposed technique outperforms other state-of-the-art
algorithms and produces high quality reconstructions, equivalent to K-MMSE,
while requiring around one tenth of its computational time.


  We show that coupled two level systems like qubits studied in quantum
information can be used as a thermodynamic machine. At least three qubits or
spins are necessary and arranged in a chain. The system is interfaced between
two split baths and the working spin in the middle is externally driven. The
machine performs Carnot-type cycles and is able to work as heat pump or engine
depending on the temperature difference of the baths $\Delta T$ and the energy
differences in the spin system $\Delta E$. It can be shown that the efficiency
is a function of $\Delta T$ and $\Delta E$.


  We study the mass of the lightest Higgs boson in an effective Kaluza-Klein
theory with two sources of supersymmetry breaking. When stop mass matrices are
non-diagonal with respect to Kaluza-Klein modes and each element is not small
in unit of the inverse compactification radius, a very small eigenvalue can be
accommodated in the diagonalized basis. We show that in the model with the two
sources, the Higgs boson mass can receive suitable corrections for various
compactification radii.


  In this paper, we propose a self-training approach for automatic speech
recognition (ASR) for low-resource settings. While self-training approaches
have been extensively developed and evaluated for high-resource languages such
as English, their applications to low-resource languages like Punjabi have been
limited, despite the language being spoken by millions globally. The scarcity
of annotated data has hindered the development of accurate ASR systems,
especially for low-resource languages (e.g., Punjabi and M\=aori languages). To
address this issue, we propose an effective self-training approach that
generates highly accurate pseudo-labels for unlabeled low-resource speech. Our
experimental analysis demonstrates that our approach significantly improves
word error rate, achieving a relative improvement of 14.94% compared to a
baseline model across four real speech datasets. Further, our proposed approach
reports the best results on the Common Voice Punjabi dataset.


  We establish a closing property for thin trapped homoclinic classes. Taking
advantage of this property, we proved that if the homoclinic class $H(p)$
admits a dominated splitting $T_{H(p)}M=E\oplus_{<}F$, where $E$ is thin
trapped (see Definition \ref{Def:TP}) and all periodic points homoclinically
related to $p$ are uniformly $F$-expanding at the period (see Definition
\ref{Def:expanding}), then $F$ is expanded (see Definition \ref{Def:TP}).


  Let $B=\{ B_{t}\} _{t\ge 0}$ be a one-dimensional standard Brownian motion.
As an application of a recent result of ours on exponential functionals of
Brownian motion, we show in this paper that, for every fixed $t>0$, the process
given by \begin{align*}
  B_{s}-B_{t}-\Bigl|
  B_{t}+\max _{0\le u\le s}B_{u}-\max _{s\le u\le t}B_{u}
  \Bigr|
  +\Bigl|
  \max _{0\le u\le s}B_{u}-\max _{s\le u\le t}B_{u}
  \Bigr| ,\quad 0\le s\le t, \end{align*} is a Brownian motion. The path
transformation that describes the above process is proven to be an involution,
commute with time reversal, and preserve Pitman's transformation. A connection
with Pitman's $2M-X$ theorem is also discussed.


  The question of which non-interacting Green's function "best" describes an
interacting many-body electronic system is both of fundamental interest as well
as of practical importance in describing electronic properties of materials in
a realistic manner. Here, we study this question within the framework of
Baym-Kadanoff theory, an approach where one locates the stationary point of a
total energy functional of the one-particle Green's function in order to find
the total ground-state energy as well as all one-particle properties such as
the density matrix, chemical potential, or the quasiparticle energy spectrum
and quasiparticle wave functions. For the case of the Klein functional, our
basic finding is that minimizing the length of the gradient of the total energy
functional over non-interacting Green's functions yields a set of
self-consistent equations for quasiparticles that is identical to those of the
Quasiparticle Self-Consistent GW (QSGW) [1] approach, thereby providing an a
priori justification for such an approach to electronic structure calculations.
In fact, this result is general, applies to any self-energy operator, and is
not restricted to any particular approximation, e.g. the GW approximation for
the self-energy. The approach also shows that, when working in the basis of
quasiparticle states, solving the diagonal part of the self-consistent Dyson
equation is of primary importance while the off-diagonals are of secondary
importance, a common observation in the electronic structure literature of
self-energy calculations. Finally, numerical tests and analytical arguments
show that when the Dyson equation produces multiple quasiparticle solutions
corresponding to a single non-interacting state, minimizing the length of the
gradient translates into choosing the solution with largest quasiparticle
weight.


  We introduce an analogue of Bridgeland's stability conditions for polarised
varieties. Much as Bridgeland stability is modelled on slope stability of
coherent sheaves, our notion of Z-stability is modelled on the notion of
K-stability of polarised varieties. We then introduce an analytic counterpart
to stability, through the notion of a Z-critical K\"ahler metric, modelled on
the constant scalar curvature K\"ahler condition. Our main result shows that a
polarised variety which is analytically K-semistable and asymptotically
Z-stable admits Z-critical K\"ahler metrics in the large volume regime. We also
prove a local converse, and explain how these results can be viewed in terms of
local wall crossing. A special case of our framework gives a manifold analogue
of the deformed Hermitian Yang-Mills equation.


  Numerical simulations based on the Lambda-CDM model of cosmology predict a
large number of as yet unobserved Galactic dark matter satellites. We report
the results of a Large Area Telescope (LAT) search for these satellites via the
gamma-ray emission expected from the annihilation of weakly interacting massive
particle (WIMP) dark matter. Some dark matter satellites are expected to have
hard gamma-ray spectra, finite angular extents, and a lack of counterparts at
other wavelengths. We sought to identify LAT sources with these
characteristics, focusing on gamma-ray spectra consistent with WIMP
annihilation through the $b \bar b$ channel. We found no viable dark matter
satellite candidates using one year of data, and we present a framework for
interpreting this result in the context of numerical simulations to constrain
the velocity-averaged annihilation cross section for a conventional 100 GeV
WIMP annihilating through the $b \bar b$ channel.


  In this article, the JAGS software program is systematically introduced to
fit common Bayesian cognitive diagnosis models (CDMs), including the
deterministic inputs, noisy "and" gate (DINA) model, the deterministic inputs,
noisy "or" gate (DINO) model, the linear logistic model, the reduced
reparameterized unified model (rRUM), and the log-linear CDM (LCDM). The
unstructured latent structural model and the higher-order latent structural
model are both introduced. We also show how to extend those models to consider
the polytomous attributes, the testlet effect, and the longitudinal diagnosis.
Finally, an empirical example is presented as a tutorial to illustrate how to
use the JAGS codes in R.


  We compute the last missing piece of the two-loop ${\cal O}(\alpha \alpha_s)$
corrections to $\gamma t \bar{t}$ vertex at the $t \bar{t}$ threshold due to
the exchange of a $W$ boson and a gluon. This contribution constitutes a
building block of the top quark threshold production cross section at electron
positron colliders.


  In a recent paper, Robert Griffiths [Phys. Rev. A 107, 062219 (2023)]
analyzed a protocol for transmission of information between two parties
introduced by Salih et al. [Phys. Rev. Lett. 110, 170502 (2013)]. There is a
considerable controversy about the counterfactuality of this protocol, and
Griffiths suggested to resolve it by introducing a new measure of channel
usage, which he called "Cost". I argue that this measure is not appropriate
because the original interaction-free measurement protocol which triggered the
definition of the concept of counterfactuality is not counterfactual according
to this measure.


  In this paper, we discuss spherically symmetric wormhole solutions in
$f(R,T)$ modified theory of gravity by introducing well-known non-commutative
geometry in terms of Gaussian and Lorentizian distributions of string theory.
For some analytic discussion, we consider an interesting model of $f(R,T)$
gravity defined by $f(R,T)=f_{1}(R)+\lambda T$. By taking two different choices
for the function $f_{1}(R)$, that is, $f_{1}(R)=R$ and $f_{1}(R)=R+\alpha
R^{2}+\gamma R^{n}$, we discuss the possible existence of wormhole solutions.
In the presence of non-commutative Gaussian and Lorentizian distributions, we
get exact and numerical solutions for both these models. By taking appropriate
values of the free parameters, we discuss different properties of these
wormhole models analytically and graphically. Further, using equilibrium
condition, it is found that these solutions are stable. Also, we discuss the
phenomenon of gravitational lensing for the exact wormhole model and it is
found that the deflection angle diverges at wormhole throat.


  We carry out a search for strong-lens systems containing high-redshift lens
galaxies with the goal of extending strong-lensing-assisted galaxy evolutionary
studies to earlier cosmic time. Two strong-lens classifiers are constructed
from a deep residual network and trained with datasets of different
lens-redshift and brightness distributions. We classify a sample of 5,356,628
pre-selected objects from the Wide-layer fields in the second public data
release of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) by applying
the two classifiers to their HSC $gri$-filter cutouts. Cutting off at
thresholds that correspond to a false positive rate of $10^{-3}$ on our test
set, the two classifiers identify 5,468 and 6,119 strong-lens candidates.
Visually inspecting the cutouts of those candidates results in 735 grade-A or B
strong-lens candidates in total, of which 277 candidates are discovered for the
first time. This is the single largest set of galaxy-scale strong-lens
candidates discovered with HSC data to date, and nearly half of it (331/735)
contains lens galaxies with photometric redshifts above 0.6. Our discoveries
will serve as a valuable target list for ongoing and scheduled spectroscopic
surveys such as the Dark Energy Spectroscopic Instrument, the Subaru Prime
Focus Spectrograph project, and the Maunakea Spectroscopic Explorer.