  A Banach space operator $T\in B({\cal X})$ is polaroid if points
$\lambda\in\iso\sigma\sigma(T)$ are poles of the resolvent of $T$. Let
$\sigma_a(T)$, $\sigma_w(T)$, $\sigma_{aw}(T)$, $\sigma_{SF_+}(T)$ and
$\sigma_{SF_-}(T)$ denote, respectively, the approximate point, the Weyl, the
Weyl essential approximate, the upper semi--Fredholm and lower semi--Fredholm
spectrum of $T$. For $A$, $B$ and $C\in B({\cal X})$, let $M_C$ denote the
operator matrix $(A & C 0 & B)$. If $A$ is polaroid on
$\pi_0(M_C)=\{\lambda\in\iso\sigma(M_C) 0<\dim(M_C-\lambda)^{-1}(0)<\infty\}$,
$M_0$ satisfies Weyl's theorem, and $A$ and $B$ satisfy either of the
hypotheses (i) $A$ has SVEP at points
$\lambda\in\sigma_w(M_0)\setminus\sigma_{SF_+}(A)$ and $B$ has SVEP at points
$\mu\in\sigma_w(M_0)\setminus\sigma_{SF_-}(B)$, or, (ii) both $A$ and $A^*$
have SVEP at points $\lambda\in\sigma_w(M_0)\setminus\sigma_{SF_+}(A)$, or,
(iii) $A^*$ has SVEP at points
$\lambda\in\sigma_w(M_0)\setminus\sigma_{SF_+}(A)$ and $B^*$ has SVEP at points
$\mu\in\sigma_w(M_0)\setminus\sigma_{SF_-}(B)$, then
$\sigma(M_C)\setminus\sigma_w(M_C)=\pi_0(M_C)$. Here the hypothesis that
$\lambda\in\pi_0(M_C)$ are poles of the resolvent of $A$ can not be replaced by
the hypothesis $\lambda\in\pi_0(A)$ are poles of the resolvent of $A$.
  For an operator $T\in B(\X)$, let
$\pi_0^a(T)=\{\lambda:\lambda\in\iso\sigma_a(T),
0<\dim(T-\lambda)^{-1}(0)<\infty\}$. We prove that if $A^*$ and $B^*$ have
SVEP, $A$ is polaroid on $\pi_0^a(\M)$ and $B$ is polaroid on $\pi_0^a(B)$,
then $\sigma_a(\M)\setminus\sigma_{aw}(\M)=\pi_0^a(\M)$.


  We prove a number of new results on the large-scale geometry of the
$L^p$-metrics on the group of area-preserving diffeomorphisms of each
orientable surface. Our proofs use in a key way the Fulton-MacPherson type
compactification of the configuration space of $n$ points on the surface due to
Axelrod-Singer and Kontsevich. This allows us to apply the Schwarz-Milnor lemma
to configuration spaces, a natural approach which we carry out successfully for
the first time. As sample results, we prove that all right-angled Artin groups
admit quasi-isometric embeddings into the group of area-preserving
diffeomorphisms endowed with the $L^p$-metric, and that all Gambaudo-Ghys
quasi-morphisms on this metric group coming from the braid group on $n$ strands
are Lipschitz. This was conjectured to hold, yet proven only for low values of
$n$ and the genus $g$ of the surface.


  Identifiability of statistical models is a key notion in unsupervised
representation learning. Recent work of nonlinear independent component
analysis (ICA) employs auxiliary data and has established identifiable
conditions. This paper proposes a statistical model of two latent vectors with
single auxiliary data generalizing nonlinear ICA, and establishes various
identifiability conditions. Unlike previous work, the two latent vectors in the
proposed model can have arbitrary dimensions, and this property enables us to
reveal an insightful dimensionality relation among two latent vectors and
auxiliary data in identifiability conditions. Furthermore, surprisingly, we
prove that the indeterminacies of the proposed model has the same as
\emph{linear} ICA under certain conditions: The elements in the latent vector
can be recovered up to their permutation and scales. Next, we apply the
identifiability theory to a statistical model for graph data. As a result, one
of the identifiability conditions includes an appealing implication:
Identifiability of the statistical model could depend on the maximum value of
link weights in graph data. Then, we propose a practical method for
identifiable graph embedding. Finally, we numerically demonstrate that the
proposed method well-recovers the latent vectors and model identifiability
clearly depends on the maximum value of link weights, which supports the
implication of our theoretical results


  We develop the spectral representation of propagator for $n$ mixing fermion
fields in the case of $\mathsf{P}$-parity violation. The approach based on the
eigenvalue problem for inverse matrix propagator makes possible to build the
system of orthogonal projectors and to represent the matrix propagator as a sum
of poles with positive and negative energies. The procedure of multiplicative
renormalization in terms of spectral representation is investigated and the
renormalization matrices are obtained in a closed form without the use of
perturbation theory. Since in theory with $\mathsf{P}$-parity violation the
standard spin projectors do not commute with the dressed propagator, they
should be modified. The developed approach allows us to build the modified
(dressed) spin projectors for a single fermion and for a system of fermions.


  We develop the theory of reflective subfibrations on an $\infty$-topos
$\mathcal{E}$. A reflective subfibration $L_\bullet$ on $\mathcal{E}$ is a
pullback-compatible assignment of a reflective subcategory
$\mathcal{D}_X\subseteq \mathcal{E}{/X}$, for every $X \in \mathcal{E}$.
Reflective subfibrations abound in homotopy theory, albeit often disguised,
e.g., as stable factorization systems. We prove that $L$-local maps (i.e.,
those maps that belong to some $\mathcal{D}_X$) admit a classifying map, and we
introduce the class of $L$-separated maps, that is, those maps with $L$-local
diagonal. $L$-separated maps are the local class of maps for a reflective
subfibration $L'_\bullet$ on $\mathcal{E}$. We prove this fact in the
compantion paper "$L'$-localization in an $\infty$-topos". In this paper, we
investigate some interactions between $L_\bullet$ and $L'_\bullet$ and explain
when the two reflective subfibrations coincide.


  This paper presents analytic results on the anatomy of nested sampling, from
which a technique is developed to estimate the run-time of the algorithm that
works for any nested sampling implementation. We test these methods on both toy
models and true cosmological nested sampling runs. The method gives an
order-of-magnitude prediction of the end point at all times, forecasting the
true endpoint within standard error around the halfway point.


  Hydroxyapatite (HAp) [Ca10(PO4)6(OH)2] nanorods were synthesized using a
surfactant templating method, with cetyltrimethylammonium bromide (CTAB)
micelles acting as template for HAp growth. The effects of the sintering
temperature on the morphological and crystallographic characteristics and on
chemical composition of the "as-prepared" structures are discussed. The
experimental results show that low heat-treatment temperatures are preferred in
order to obtain high quality nanorods, with diameters ranging between 20 nm and
50 nm. High heat-treatment temperatures enhance the thermal decomposition of
HAp into other calcium phosphate compounds, and the sintering of particles into
micrometer ball-like structures. The stability of aqueous suspensions of HAp
nanorods is also discussed.


  We present preliminary results for $B_K$ calculated using improved staggered
fermions with a mixed action (HYP-smeared staggered valence quarks and AsqTad
staggered sea quarks). We investigate the effect of non-degenerate quarks on
$B_K$ and attempt to estimate the ${\cal O}(a^2)$ effect due to non-Goldstone
pions in loops. We fit the data to continuum partially quenched chiral
perturbation theory. We find that the quality of fit for $B_K$ improves if we
include non-degenerate quark mass combinations. We also observe, however, that
the fitting curve deviates from the data points in the light quark mass region.
This may indicate the need to include taste-breaking in pion loops.


  In this paper, for each finite group $G$, we construct explicitly a
non-compact complete finite-volume arithmetic hyperbolic $4$-manifold $M$ such
that $\mathrm{Isom}\,M \cong G$, or $\mathrm{Isom}^{+}\,M \cong G$. In order to
do so, we use essentially the geometry of Coxeter polytopes in the hyperbolic
$4$-space, on one hand, and the combinatorics of simplicial complexes, on the
other.


  The article discusses the gradient discretisation method (GDM) for
distributed optimal control problems governed by diffusion equation with pure
Neumann boundary condition. Using the GDM framework enables to develop an
analysis that directly applies to a wide range of numerical schemes, from
conforming and non-conforming finite elements, to mixed finite elements, to
finite volumes and mimetic finite differences methods. Optimal order error
estimates for state, adjoint and control variables for low order schemes are
derived under standard regularity assumptions. A novel projection relation
between the optimal control and the adjoint variable allows the proof of a
super-convergence result for post-processed control. Numerical experiments
performed using a modified active set strategy algorithm for conforming,
nonconforming and mimetic finite difference methods confirm the theoretical
rates of convergence.


  We report a theoretical study of light diffraction by a spherical magnetic
particle with a vortex magnetization distribution. It is shown that the
intensity of the diffracted light involves a non-reciprocal contribution. This
contribution depends on the vorticity of particle magnetization. It appears due
to the excitation of an electric quadrupole, magnetic dipole and the addition
to the electric dipole moment in the particle, that depend on the particle
magnetization vorticity. The estimation of the non-reciprocal contrbution for a
cobalt particle and two linear polarizations of the incident light fits the
data of recent experimental studies in the lattice of triangle magnetic
particles by an order of magnitude.


  This work explores the relationship between optimal control theory and
adiabatic passage techniques in quantum systems. The study is based on a
geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin
Maximum Principle. In a three-level quantum system, we show that the Stimulated
Raman Adiabatic Passage technique can be associated to a peculiar Hamiltonian
singularity. One deduces that the adiabatic pulse is solution of the optimal
control problem only for a specific cost functional. This analysis is extended
to the case of a four-level quantum system.


  We monitor the time evolution of the temperature of phononic collective modes
in a one-dimensional quasicondensate submitted to losses. At long times the
ratio between the temperature and the energy scale $mc^2$, where $m$ is the
atomic mass and $c$ the sound velocity takes, within a precision of 20\%, an
asymptotic value. This asymptotic value is observed while $mc^2$ decreases in
time by a factor as large as 2.5. Moreover this ratio is shown to be
independent on the loss rate and on the strength of interactions. These results
confirm theoretical predictions and the measured stationary ratio is in
quantitative agreement with the theoretical calculations.


  In supersymmetric theories, the top quark can decay into its scalar partner
plus a neutralino, with an appreciable rate. We calculate the $O(\alpha_s)$ QCD
corrections to this decay mode in the minimal supersymmetric extension of the
Standard Model. These corrections can be either positive or negative and
increase logarithmically with the gluino mass. For gluino masses below 1 TeV,
they are at most of the order of ten percent and therefore, well under control.


  We present a careful and thorough microscopic derivation of the Kondo
Hamiltonian for single-molecule magnets (SMMs) transistors. When the molecule
is strongly coupled to metallic leads, we show that by applying a transverse
magnetic field it is possible to topologically induce or quench the Kondo
effect in the conductance of a SMM with either an integer or a half-integer
spin S>1/2. This topological Kondo effect is due to the Berry phase
interference between multiple quantum tunneling paths of the spin. We calculate
the renormalized Berry phase oscillations of the two Kondo peaks as a function
of the transverse magnetic field by means of the poor man's scaling. In
particular, we show that the Kondo exchange interaction between itinerant
electrons in the leads and the SMM pseudo spin 1/2 depends crucially on the SMM
spin selection rules for the addition and subtraction of an electron and can
range from antiferromagnetic to ferromagnetic. We illustrate our findings with
the SMM Ni4, which we propose as a possible candidate for the experimental
observation of the conductance oscillations.


  We prove a two-sided transference theorem between $L^{p}$ spherical
multipliers on the compact symmetric space $U/K$ and $L^{p}$ multipliers on the
vector space $i\mathfrak{p},$ where the Lie algebra of $U$ has Cartan
decomposition $\mathfrak{k\oplus }i\mathfrak{p}$. This generalizes the classic
theorem transference theorem of deLeeuw relating multipliers on $%
L^{p}(\mathbb{T)}$ and $L^{p}(\mathbb{R)}$.


  This paper is concerned with a class of stochastic differential equations
with Markovian switching. The Malliavin calculus is used to study the
smoothness of the density of the solution under a H\"{o}rmander type condition.
Furthermore, we obtain a Bismut type formula which is used to establish the
strong Feller property.


  In 1969 Leighton developed a quasi-1D mathematical model of the solar dynamo,
building upon the phenomenological scenario of Babcock(1961). Here we present a
modification and extension of Leighton's model. Using the axisymmetric
component of the magnetic field, we consider the radial field component at the
solar surface and the radially integrated toroidal magnetic flux in the
convection zone, both as functions of latitude. No assumptions are made with
regard to the radial location of the toroidal flux. The model includes the
effects of turbulent diffusion at the surface and in the convection zone,
poleward meridional flow at the surface and an equatorward return flow
affecting the toroidal flux, latitudinal differential rotation and the
near-surface layer of radial rotational shear, downward convective pumping of
magnetic flux in the shear layer, and flux emergence in the form of tilted
bipolar magnetic regions. While the parameters relevant for the transport of
the surface field are taken from observations, the model condenses the unknown
properties of magnetic field and flow in the convection zone into a few free
parameters (turbulent diffusivity, effective return flow, amplitude of the
source term, and a parameter describing the effective radial shear). Comparison
with the results of two-dimensional flux transport dynamo codes shows that the
model captures the essential features of these simulations. We carry out a
parameter study over the four-dimensional parameter space and identify the
parameter ranges that provide solar-like solutions. Dipole parity is always
preferred and solutions with periods around 22 years and a correct phase
difference between flux emergence in low latitudes and the strength of the
polar fields are found for a return flow speed around 2~m/s, turbulent
diffusivity <80~km^2/s, and dynamo excitation not too far above the threshold
(linear growth rate <0.1/yr).


  Perturbation theory of vacuum spherically-symmetric spacetimes is a crucial
tool to understand the dynamics of black hole perturbations. Spherical symmetry
allows for an expansion of the perturbations in scalar, vector, and tensor
harmonics. The resulting perturbative equations are decoupled for modes with
different parity and different harmonic numbers. Moreover, for each harmonic
and parity, the equations for the perturbations can be decoupled in terms of
(gauge-invariant) master functions that satisfy 1+1 wave equations. By working
in a completely general perturbative gauge, in this paper we study what is the
most general master function that is linear in the metric perturbations and
their first-order derivatives and satisfies a wave equation with a potential.
The outcome of the study is that for each parity we have two branches of
solutions with similar features. One of the branches includes the known
results: In the odd-parity case, the most general master function is an
arbitrary linear combination of the Regge-Wheeler and the
Cunningham-Price-Moncrief master functions whereas in the even-parity case it
is an arbitrary linear combination of the Zerilli master function and another
master function that is new to our knowledge. The other branch is very
different since it includes an infinite collection of potentials which in turn
lead to an independent collection master of functions which depend on the
potential. The allowed potentials satisfy a non-linear ordinary differential
equation. Finally, all the allowed master functions are gauge invariant and can
be written in a fully covariant form.


  We prove that, for an undirected graph with $n$ vertices and $m$ edges, each
labeled with a linear function of a parameter $\lambda$, the number of
different minimum spanning trees obtained as the parameter varies can be
$\Omega(m\log n)$.


  Contrastive self-supervised learning has emerged as a promising approach to
unsupervised visual representation learning. In general, these methods learn
global (image-level) representations that are invariant to different views
(i.e., compositions of data augmentation) of the same image. However, many
visual understanding tasks require dense (pixel-level) representations. In this
paper, we propose View-Agnostic Dense Representation (VADeR) for unsupervised
learning of dense representations. VADeR learns pixelwise representations by
forcing local features to remain constant over different viewing conditions.
Specifically, this is achieved through pixel-level contrastive learning:
matching features (that is, features that describes the same location of the
scene on different views) should be close in an embedding space, while
non-matching features should be apart. VADeR provides a natural representation
for dense prediction tasks and transfers well to downstream tasks. Our method
outperforms ImageNet supervised pretraining (and strong unsupervised baselines)
in multiple dense prediction tasks.


  Starting from an ancient observation of Tits concerning the interpretation of
symmetric groups as Chevalley groups over a (non-existing) field having only
one element, we describe combinatorial geometry over this field, as well as
Linear Algebra. We arrive at an "absolute mantra" which is one of the basic
principles of the present book.


  In the industries that involved either chemistry or biology, such as
pharmaceutical industries, chemical industries or food industry, the analytical
methods are the necessary eyes and hear of all the material produced or used.
If the quality of an analytical method is doubtful, then the whole set of
decision that will be based on those measures is questionable. For those
reasons, being able to assess the quality of an analytical method is far more
than a statistical challenge; it's a matter of ethic and good business
practices. Many regulatory documents have been releases, primarily ICH and FDA
documents in the pharmaceutical industry (FDA, 1995, 1997, 2001) to address
that issue.


  By benefiting from perceptual losses, recent studies have improved
significantly the performance of the super-resolution task, where a
high-resolution image is resolved from its low-resolution counterpart. Although
such objective functions generate near-photorealistic results, their capability
is limited, since they estimate the reconstruction error for an entire image in
the same way, without considering any semantic information. In this paper, we
propose a novel method to benefit from perceptual loss in a more objective way.
We optimize a deep network-based decoder with a targeted objective function
that penalizes images at different semantic levels using the corresponding
terms. In particular, the proposed method leverages our proposed OBB (Object,
Background and Boundary) labels, generated from segmentation labels, to
estimate a suitable perceptual loss for boundaries, while considering texture
similarity for backgrounds. We show that our proposed approach results in more
realistic textures and sharper edges, and outperforms other state-of-the-art
algorithms in terms of both qualitative results on standard benchmarks and
results of extensive user studies.


  We give a method to estimate Seshadri constants on toric varieties at any
point. By using the estimations and toric degenerations, we can obtain some new
computations or estimations of Seshadri constants on non-toric varieties. In
particular, we investigate Seshadri constants on hypersurfaces in projective
spaces and Fano 3-folds with Picard number one in detail.


  The rotational and torsional dynamics of the prototypical floppy
$\text{indole}(\text{H}_2\text{O})$ molecular cluster was theoretically and
computationally analyzed. The time-dependent Schr\"odinger equation was solved
for a reduced-dimensionality description of the cluster, taking into account
overall rotations and the internal rotation of the water moiety. Based on our
results, it became clear that coupling between the internal and the overall
rotations are small, and that for typical field strengths in alignment and
mixed-field orientation experiments the rigid rotor approximation can be
employed to describe the investigated dynamics. Furthermore, the parameter
space over which this is valid and its boundaries where the coupling of the
internal and overall rotation can no longer be neglected were explored.


  The effect of the magnetic field on the critical behavior of Sr0:9La0:1CuO2
is explored in terms of reversible magnetization data. As the correlation
length transverse to the magnetic field Hi,applied along the i-axis, cannot
grow beyond the limiting magnetic length LHi, related to the average distance
between vortex lines, one expects a magnetic field induced finite size effect.
Invoking the scaling theory of critical phenomena we provide clear evidence for
this effect. It implies that in type II superconductors there is a 3D to 1D
crossover line Hpi(T). Consequently, below Tc and above Hpi(T) uperconductivity
is confined to cylinders with diameter LHi(1D). Accordingly, there is no
continuous phase transition in the (H,T)-plane along the Hc2-lines as predicted
by the mean-field treatment.


  The existence of an SU(3) X SU(2)_L X SU(2)_R X U(1) gauge symmetry with g_L
= g_R at the TeV energy scale is shown to be consistent with supersymmetric
SO(10) grand unification at around 1O^{16} GeV if certain new particles are
assumed. The additional imposition of a discrete Z_2 symmetry leads to a
generalized definition of R parity as well as highly suppressed Majorana
neutrino masses. Another model based on SO(10) X SO(10) is also discussed.


  The study of fundamental optics effects has been stimulated through the
increasing ability to structure light in all its degrees of freedom (DOFs) in
sophisticated but simple experimental settings. However, with such an increase
in experimental capabilities, it has also become important to study theoretical
descriptions for a more intuitive understanding of the underlying concepts.
Here, we introduce a visual representation of light that is structured in its
transverse space, frequency, and polarization in the form of a higher-order
Poincar\'e sphere and discuss interesting links to its fundamental counterpart.
We further leverage this connection to discuss and experimentally generate
light possessing all possible polarization states across its spatio-spectral
shape, which we term spatio-spectral Poincar\'e beams. By invoking all DOFs of
light in the powerful description of higher-order Poincar\'e spheres, our work
can pave the way for a deeper understanding and beneficial application of
structured light as a powerful tool in optics.


  The purpose of this note is to present two elementary, but useful, facts
concerning actions on uniformly convex spaces. We demonstrate how each of them
can be used in an alternative proof of the triviality of the first
$L_p$-cohomology of higher rank simple Lie groups, proved in [BFGM].


  We simulate a theory with $N_f=2$ heavy quarks of mass $M$. At energies much
smaller than $M$ the heavy quarks decouple and the theory can be described by
an effective theory which is a pure gauge theory to leading order in $1/M$. We
present results for the mass dependence of ratios such as $t_0(M)/t_0(0)$. We
compute these ratios from simulations and compare them to the perturbative
prediction. The latter relies on a factorisation formula for the ratios which
is valid to leading order in $1/M$.


  Consider a weighted Coxeter system $(W,S,\mathscr{L})$. Via its associated
Iwahori-Hecke algebra, we may determine the partition of $W$ into
Kazhdan-Lusztig cells. In this paper, we use the theory of Vogan classes
introduced by Bonnaf\'e--Geck to obtain a combinatorial description of the left
cells of type $B_n$ when the ratio of the weights of the first to second
generator is $n-1$. We further give information on the left cells when this
ratio lies in the interval $(n-2,n-1)$.


  We give a systematic method for discretizing Hamiltonian partial differential
equations (PDEs) with constant symplectic structure, while preserving their
energy exactly. The same method, applied to PDEs with constant dissipative
structure, also preserves the correct monotonic decrease of energy. The method
is illustrated by many examples. In the Hamiltonian case these include: the
sine-Gordon, Korteweg-de Vries, nonlinear Schrodinger, (linear) time-dependent
Schrodinger, and Maxwell equations. In the dissipative case the examples are:
the Allen-Cahn, Cahn-Hilliard, Ginzburg-Landau, and heat equations.


  We investigate the impact on basic quantum transport properties of
disorder-induced exceptional points (EPs) that emerge in a disorder-averaged
Green's function description of two-dimensional (2D) Dirac semimetals with
spin- or orbital-dependent potential scattering. Remarkably, we find that EPs
may promote the nearly vanishing conductance of a finite sample at the Dirac
point to a sizable value that increases with disorder strength. This striking
behavior exhibits a strong directional anisotropy that is closely related to
the Fermi arcs connecting the EPs. We corroborate our results by numerically
exact simulations, thus revealing the fingerprints of characteristic
non-Hermitian spectral features also on the localization properties of the
considered systems. Finally, several candidates for the experimental
verification of our theoretical analysis are discussed, including disordered
electronic square-net materials and cold atoms in spin-dependent optical
lattices.


  We explore the connection between $K3$ categories and 0-cycles on holomorphic
symplectic varieties. In this paper, we focus on Kuznetsov's noncommutative
$K3$ category associated to a nonsingular cubic 4-fold.
  By introducing a filtration on the $\mathrm{CH}_1$-group of a cubic 4-fold
$Y$, we conjecture a sheaf/cycle correspondence for the associated $K3$
category $\mathcal{A}_Y$. This is a noncommutative analog of O'Grady's
conjecture concerning derived categories of $K3$ surfaces. We study instances
of our conjecture involving rational curves in cubic 4-folds, and verify the
conjecture for sheaves supported on low degree rational curves.
  Our method provides systematic constructions of (a) the Beauville-Voisin
filtration on the $\mathrm{CH}_0$-group and (b) algebraically coisotropic
subvarieties of a holomorphic symplectic variety which is a moduli sace of
stable objects in $\mathcal{A}_Y$.


  All-dielectric nanophotonics opens a venue for a variety of novel phenomena
and scattering regimes driven by unique optical effects in semiconductor and
dielectric nanoresonators. Their peculiar optical signatures enabled by
simultaneous electric and magnetic responses in the visible range pave a way
for a plenty of new applications in nano-optics, biology, sensing, etc. In this
work, we investigate fabrication-friendly truncated cone resonators and achieve
several important scattering regimes due to the inherent property of cones -
broken symmetry along the main axis without involving complex geometries or
structured beams. We show this symmetry breaking to deliver various kinds of
Kerker effects (Generalized and Transverse Kerker effects), non-scattering
hybrid anapole regime (simultaneous anapole conditions for all the multipoles
in a particle leading to the nearly full scattering suppression) and, vice
versa, superscattering regime. Being governed by the same straightforward
geometrical paradigm, discussed effects could greatly simplify the
manufacturing process of photonic devices with different functionalities.
Moreover, the additional degrees of freedom driven by the conicity open new
horizons to tailor light-matter interactions at the nanoscale.


  random_tree() is a linear time and space C++ implementation able to create
trees of up to a billion nodes for genetic programming and genetic improvement
experiments. A 3.60GHz CPU can generate more than 18 million random nodes for
GP program trees per second.


  We study stability criteria for discrete time switching systems. We
investigate the structure of sets of LMIs that are a sufficient condition for
stability (i.e., such that any switching system which satisfies these LMIs is
stable). We provide an exact characterization of these sets. As a corollary, we
show that it is PSPACE-complete to recognize whether a particular set of LMIs
implies the stability of a switching system.


  We analytically study heat conduction in a chain with interparticle
interaction V(x)=lambda[1-cos(x)] and harmonic on-site potential. We start with
each site of the system connected to a Langevin heat bath, and investigate the
case of small coupling for the interior sites in order to understand the
behavior of the system with thermal reservoirs at the boundaries only. We
study, in a perturbative analysis, the heat current in the steady state of the
one-dimensional system with weak interparticle potential. We obtain an
expression for the thermal conductivity, compare the low and high temperature
regimes, and show that, as we turn off the couplings with the interior heat
baths, there is a "phase transition:'' the Fourier's law holds only at high
temperatures.


  We propose a universal background subtraction framework based on the
Arithmetic Distribution Neural Network (ADNN) for learning the distributions of
temporal pixels. In our ADNN model, the arithmetic distribution operations are
utilized to introduce the arithmetic distribution layers, including the product
distribution layer and the sum distribution layer. Furthermore, in order to
improve the accuracy of the proposed approach, an improved Bayesian refinement
model based on neighboring information, with a GPU implementation, is
incorporated. In the forward pass and backpropagation of the proposed
arithmetic distribution layers, histograms are considered as probability
density functions rather than matrices. Thus, the proposed approach is able to
utilize the probability information of the histogram and achieve promising
results with a very simple architecture compared to traditional convolutional
neural networks. Evaluations using standard benchmarks demonstrate the
superiority of the proposed approach compared to state-of-the-art traditional
and deep learning methods. To the best of our knowledge, this is the first
method to propose network layers based on arithmetic distribution operations
for learning distributions during background subtraction.


  Modelling a large collection of functional time series arises in a broad
spectral of real applications. Under such a scenario, not only the number of
functional variables can be diverging with, or even larger than the number of
temporally dependent functional observations, but each function itself is an
infinite-dimensional object, posing a challenging task. In this paper, we
propose a three-step procedure to estimate high-dimensional functional time
series models. To provide theoretical guarantees for the three-step procedure,
we focus on multivariate stationary processes and propose a novel functional
stability measure based on their spectral properties. Such stability measure
facilitates the development of some useful concentration bounds on sample
(auto)covariance functions, which serve as a fundamental tool for further
convergence analysis in high-dimensional settings. As functional principal
component analysis (FPCA) is one of the key dimension reduction techniques in
the first step, we also investigate the non-asymptotic properties of the
relevant estimated terms under a FPCA framework. To illustrate with an
important application, we consider vector functional autoregressive models and
develop a regularization approach to estimate autoregressive coefficient
functions under the sparsity constraint. Using our derived non-asymptotic
results, we investigate convergence properties of the regularized estimate
under high-dimensional scaling. Finally, the finite-sample performance of the
proposed method is examined through both simulations and a public financial
dataset.


  The standard energy conditions of classical general relativity are (mostly)
linear in the stress-energy tensor, and have clear physical interpretations in
terms of geodesic focussing, but suffer the significant drawback that they are
often violated by semi-classical quantum effects. In contrast, it is possible
to develop non-standard energy conditions that are intrinsically non-linear in
the stress-energy tensor, and which exhibit much better well-controlled
behaviour when semi-classical quantum effects are introduced, at the cost of a
less direct applicability to geodesic focussing. In this article we will first
review the standard energy conditions and their various limitations. (Including
the connection to the Hawking--Ellis type I, II, III, and IV classification of
stress-energy tensors). We shall then turn to the averaged, nonlinear, and
semi-classical energy conditions, and see how much can be done once
semi-classical quantum effects are included.


  Towards integrating renewable electricity generation sources into the grid,
an important facilitator is the energy flexibility provided by buildings'
thermal inertia. Most of the existing research follows a single-step price- or
incentive-based scheme for unlocking the flexibility potential of buildings. In
contrast, this paper proposes a novel two-step design approach for better
harnessing buildings' energy flexibility. In a first step, a robust
optimization model is formulated for assessing the energy flexibility of
buildings in the presence of uncertain predictions of external conditions, such
as ambient temperature, solar irradiation, etc. In a second step, energy
flexibility is activated in response to a feasible demand response (DR) request
from grid operators without violating indoor temperature constraints, even in
the presence of uncertain external conditions. The proposed approach is tested
on a high-fidelity Modelica simulator to evaluate its effectiveness. Simulation
results show that, compared with price-based demand-side management, the
proposed approach achieves greater energy reduction during peak hours.


  This article studies the vortical nature and structure of phase-space holes
-- nonlinear B.G.K. trapping modes found in the phase-space collision-free
plasmas. A fluid-like outlook of the particles' phase-space is explored, which
makes it convenient to analytically identify electron and ion holes as vortices
-- similar to that of ordinary two-dimensional fluids. A fluid velocity is
defined for the phase-space of the electrons and ions, continuity and momentum
equations describing the flow of the phase-space fluid representing the
particle system are then developed. Pressure formation and associated diffusion
in phase-space of such systems is introduced and a vorticity field of the
phase-space is then defined. Using these equations, electron holes and ion
holes are analytically identified as vortices in the phase-space of the plasma.
A relation between Schamel's trapping parameter ($\beta$), hole speed ($M$),
hole phase-space depth ($-\Gamma$) and hole potential amplitude ($\chi_0$) is
derived. The approach introduces a new technique to study the phase-space holes
of collision-less plasmas, allowing fluid-vortex-like treatment to these
kinetic structures. Phase-space distribution functions for electron hole
regions can then be analytically derived from this model, reproducing the
schamel-df equations and thus acting as a precursor to the pseudo-potential
approach, avoiding the need to assume a solution to the phase-space density.


  Adapting standard methods from geometric measure theory, we provide an
example of a polynomial-valued measure $\mu$ on tame sets in $\mathbb{R}^d$
which satisfies many desirable properties. Among these is strict monotonicity:
the measure of a proper subset is strictly less than the measure of the whole
set. Using techniques from non-standard analysis, we display that the domain of
$\mu$ can be extended to all subsets of $\mathbb{R}^d$ (up to equivalence
modulo infinitesimals). The resulting extension is a numerosity function that
encodes the $i$-dimensional Hausdorff measure for all $i\in \mathbb{N}$, as
well as the $i$-th intrinsic volume functions.


  We give a brief account of supersymmetric Born-Infeld theories with extended
supersymmetry, including those with partially broken supersymmetry. Some latest
developments in this area are presented. One of them is N=3 supersymmetric
Born-Infeld theory which admits a natural off-shell formulation in N=3 harmonic
superspace.


  Digital quantum simulation is the process of simulating the dynamics of a
physical system by a programmable quantum computer. The universality of quantum
computers makes it possible to simulate any quantum system, whether fermionic
or bosonic. In this work, we discuss the application of digital quantum
simulations to simulate a ubiquitous bosonic system, a beam splitter. To
perform the boson-to-qubit mapping, we used the gray code, whose superiority
over other encoding schemes has been shown recently. We validated our quantum
circuit that mimics the action of a beam splitter by simulating the
Hong-Ou-Mandel interference experiment. We simulated the experiment in both
quantum simulators and actual quantum backends and were able to observe the HOM
interference.


  Translating natural language to SQL queries for table-based question
answering is a challenging problem and has received significant attention from
the research community. In this work, we extend a pointer-generator and
investigate the order-matters problem in semantic parsing for SQL. Even though
our model is a straightforward extension of a general-purpose
pointer-generator, it outperforms early works for WikiSQL and remains
competitive to concurrently introduced, more complex models. Moreover, we
provide a deeper investigation of the potential order-matters problem that
could arise due to having multiple correct decoding paths, and investigate the
use of REINFORCE as well as a dynamic oracle in this context.


  Since the Maxwell theory of electromagnetic phenomena is a gauge theory, it
is quite important to evaluate the zero-point energy of the quantized
electromagnetic field by a careful assignment of boundary conditions on the
potential and on the ghost fields. Recent work by the authors has shown that,
for a perfectly conducting spherical shell, it is precisely the contribution of
longitudinal and normal modes of the potential which enables one to reproduce
the result first due to Boyer. This is obtained provided that one works with
the Lorenz gauge-averaging functional, and with the help of the Feynman choice
for a dimensionless gauge parameter. For arbitrary values of the gauge
parameter, however, covariant and non-covariant gauges lead to an entangled
system of three eigenvalue equations. Such a problem is crucial both for the
foundations and for the applications of quantum field theory.


  The one-term distributive homology was introduced by J.H.Przytycki as an
atomic replacement of rack and quandle homology, which was first introduced and
developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and
M.Saito. This homology was initially suspected to be torsion-free, but we show
in this paper that the one-term homology of a finite spindle can have torsion.
We carefully analyze spindles of block decomposition of type (n,1) and
introduce various techniques to compute their homology precisely. In addition,
we show that any finite group can appear as the torsion subgroup of the first
homology of some finite spindle. Finally, we show that if a shelf satisfies a
certain, rather general, condition then the one-term homology is trivial.


  We present polar Kerr effect measurements of the filled skutterudite
superconductor PrOs$_4$Sb$_{12}$. Simultaneous AC susceptibility measurements
allow us to observe the superconducting transition under the influence of
heating from the optical beam. A nonzero Kerr angle $\theta_K$ develops below
the superconducting transition, saturating at $\sim 300$ nrad at low
temperatures. This result is repeated across several measurements of multiple
samples. By extrapolating the measured $\theta_K(T)$ to zero optical power, we
are able to show that the Kerr angle onset temperature in one set of
measurements is consistent with the transition to the B phase at $T_{C2}$. We
discuss the possible explanations for this result and its impact on the
understanding of multi-phase and inhomogeneous superconductivity in
PrOs$_4$Sb$_{12}$.


  The bosonic su(n) Hubbard model was recently introduced. The model was shown
to be integrable in one dimension by exhibiting the infinite set of conserved
quantities. I derive the R-matrix and use it to show that the conserved charges
commute among themselves. This new matrix is a non-additive solution of the
Yang-Baxter equation. Some properties of this matrix are derived.


  This paper proposes an efficient contractor for the TDoA (Time Differential
of Arrival) equation. The contractor is based on a minimal inclusion test which
is built using the Karush-Kuhn-Tucker (KKT) conditions. An application related
to the localization of sound sources using a TDoA technique is proposed.


  Given a bicovariant differential calculus $(\mathcal{E}, d)$ such that the
braiding map is diagonalisable in a certain sense, the bimodule of two-tensors
admits a direct sum decomposition into symmetric and anti-symmetric tensors.
This is used to prove the existence of a bicovariant torsionless connection on
$\mathcal{E}$. Following Heckenberger and Schm{\"u}dgen, we study invariant
metrics and the compatibility of covariant connections with such metrics. A
sufficient condition for the existence and uniqueness of bicovariant
Levi-Civita connections is derived. This condition is shown to hold for cocycle
deformations of classical Lie groups.


  The mobile data traffic has been exponentially growing during the last
decades, which has been enabled by the densification of the network
infrastructure in terms of increased cell density (i.e., ultra-dense network
(UDN)) and/or increased number of active antennas per access point (AP) (i.e.,
massive multiple-input multiple-output (mMIMO)). However, neither UDN nor mMIMO
will meet the increasing data rate demands of the sixth generation (6G)
wireless communications due to the inter-cell interference and large
quality-of-service variations, respectively. Cell-free (CF) mMIMO, which
combines the best aspects of UDN and mMIMO, is viewed as a key solution to this
issue. In such systems, each user equipment (UE) is served by a preferred set
of surrounding APs cooperatively. In this paper, we provide a survey of the
state-of-the-art literature on CF mMIMO. As a starting point, the significance
and the basic properties of CF mMIMO are highlighted. We then present the
canonical framework, where the essential details (i.e., transmission procedure
and mathematical system model) are discussed. Next, we provide a deep look at
the resource allocation and signal processing problems related to CF mMIMO and
survey the up-to-date schemes and algorithms. After that, we discuss the
practical issues when implementing CF mMIMO. Potential future directions are
then pointed out. Finally, we conclude this paper with a summary of the key
lessons learned in this field. This paper aims to provide a starting point for
anyone who wants to conduct research on CF mMIMO for future wireless networks.


  This paper aims at studying the difference between Ritz-Galerkin (R-G) method
and deep neural network (DNN) method in solving partial differential equations
(PDEs) to better understand deep learning. To this end, we consider solving a
particular Poisson problem, where the information of the right-hand side of the
equation f is only available at n sample points, that is, f is known at finite
sample points. Through both theoretical and numerical studies, we show that
solution of the R-G method converges to a piecewise linear function for the one
dimensional (1D) problem or functions of lower regularity for high dimensional
problems. With the same setting, DNNs however learn a relative smooth solution
regardless of the dimension, this is, DNNs implicitly bias towards functions
with more low-frequency components among all functions that can fit the
equation at available data points. This bias is explained by the recent study
of frequency principle (Xu et al., (2019) [17] and Zhang et al., (2019) [11,
19]). In addition to the similarity between the traditional numerical methods
and DNNs in the approximation perspective, our work shows that the implicit
bias in the learning process, which is different from traditional numerical
methods, could help better understand the characteristics of DNNs.


  Context. The spectrum of the hydrogen atom was explained by Bohr more than
one century ago. We revisit here some of the aspects of the underlying quantum
structure, with a modern formalism, focusing on the limit of the Balmer series.
  Aims. We investigate the behaviour of the absorption coefficient of the
isolated hydrogen atom in the neighbourhood of the Balmer limit.
  Methods. We analytically computed the total cross-section arising from
bound-bound and bound-free transitions in the isolated hydrogen atom at the
Balmer limit, and established a simplified semi-analytical model for the
surroundings of that limit. We worked within the framework of the formalism of
Landi Degl'Innocenti & Landolfi (2004, Astrophys. Space Sci. Lib., 307), which
permits an almost straight-forward generalization of our results to other atoms
and molecules, and which is perfectly suitable for including polarization
phenomena in the problem.
  Results. We analytically show that there is no discontinuity at the Balmer
limit, even though the concept of a "Balmer jump" is still meaningful.
Furthermore, we give a possible definition of the location of the Balmer jump,
and we check that this location is dependent on the broadening mechanisms. At
the Balmer limit, we compute the cross-section in a fully analytical way.
  Conclusions. The Balmer jump is produced by a rapid drop of the total Balmer
cross-section, yet this variation is smooth and continuous when both
bound-bound and bound-free processes are taken into account, and its shape and
location is dependent on the broadening mechanisms.


  We start by presenting a theory of finite sets using the approach which is
essentially that taken by Whitehead and Russell in Principia Mathematica}, and
which does not involve the natural numbers (or any other infinite set). This
theory is then applied to prove results about structures which, like the
natural numbers, satisfy the principle of mathematical induction, but do not
necessarily satisfy the remaining Peano axioms.


  Application conditions for rules and constraints for graphs are well-known in
the theory of graph transformation and have been extended already to M-adhesive
transformation systems. According to the literature we distinguish between two
kinds of satisfaction for constraints, called general and initial satisfaction
of constraints, where initial satisfaction is defined for constraints over an
initial object of the base category. Unfortunately, the standard definition of
general satisfaction is not compatible with negation in contrast to initial
satisfaction.
  Based on the well-known restriction of objects along type morphisms, we study
in this paper restriction and amalgamation of application conditions and
constraints together with their solutions. In our main result, we show
compatibility of initial satisfaction for positive constraints with restriction
and amalgamation, while general satisfaction fails in general.
  Our main result is based on the compatibility of composition via pushouts
with restriction, which is ensured by the horizontal van Kampen property in
addition to the vertical one that is generally satisfied in M-adhesive
categories.


  This paper investigates the robustness and optimality of the multi-kernel
correntropy (MKC) on linear regression. We first derive an upper error bound
for a scalar regression problem in the presence of arbitrarily large outliers
and reveal that the kernel bandwidth should be neither too small nor too big in
the sense of the lowest upper error bound. Meanwhile, we find that the proposed
MKC is related to a specific heavy-tail distribution, and the level of the
heavy tail is controlled by the kernel bandwidth solely. Interestingly, this
distribution becomes the Gaussian distribution when the bandwidth is set to be
infinite, which allows one to tackle both Gaussian and non-Gaussian problems.
We propose an expectation-maximization (EM) algorithm to estimate the parameter
vectors and explore the kernel bandwidths alternatively. The results show that
our algorithm is equivalent to the traditional linear regression under Gaussian
noise and outperforms the conventional method under heavy-tailed noise. Both
numerical simulations and experiments on a magnetometer calibration application
verify the effectiveness of the proposed method.


  The global attractor conjecture says that toric dynamical systems (i.e., a
class of polynomial dynamical systems on the positive orthant) have a globally
attracting point within each positive linear invariant subspace -- or,
equivalently, complex balanced mass-action systems have a globally attracting
point within each positive stoichiometric compatibility class. A proof of this
conjecture implies that a large class of nonlinear dynamical systems on the
positive orthant have very simple and stable dynamics. The conjecture
originates from the 1972 breakthrough work by Fritz Horn and Roy Jackson, and
was formulated in its current form by Horn in 1974. We introduce toric
differential inclusions, and we show that each positive solution of a toric
differential inclusion is contained in an invariant region that prevents it
from approaching the origin. We use this result to prove the global attractor
conjecture. In particular, it follows that all detailed balanced mass action
systems and all deficiency zero weakly reversible networks have the global
attractor property.


  We study the classical dynamics of a non-abelian Higgs theory coupled to
gravity in an isotropic and homogeneous Universe. For non-minimal coupling,
this theory leads to a model of cosmic inflation that is very attractive due to
its simplicity and consistency with the latest experimental data. We show that
this theory can also explain the current accelerated expansion of the Universe,
provided that all the gravitational and bosonic degrees of freedom, together
with their symmetries, are correctly taken in account.


  Parameterized quantum circuits have been extensively used as the basis for
machine learning models in regression, classification, and generative tasks.
For supervised learning, their expressivity has been thoroughly investigated
and several universality properties have been proven. However, in the case of
quantum generative modelling, much less is known, especially when the task is
to model distributions over continuous variables. In this work, we elucidate
expectation value sampling-based models. Such models output the expectation
values of a set of fixed observables from a quantum circuit into which
classical random data has been uploaded. We prove the universality of such
variational quantum algorithms for the generation of multivariate
distributions. We explore various architectures which allow universality and
prove tight bounds connecting the minimal required qubit number, and the
minimal required number of measurements needed. Our results may help guide the
design of future quantum circuits in generative modelling tasks.


  We study the problem of estimating the average causal effect of treating
every member of a population, as opposed to none, using an experiment that
treats only some. This is the policy-relevant estimand when deciding whether to
scale up an intervention based on the results of an RCT, for example, but
differs from the usual average treatment effect in the presence of spillovers.
We consider both estimation and experimental design given a bound (parametrized
by $\eta > 0$) on the rate at which spillovers decay with the ``distance''
between units, defined in a generalized way to encompass spatial and
quasi-spatial settings, e.g. where the economically relevant concept of
distance is a gravity equation. Over all estimators linear in the outcomes and
all cluster-randomized designs the optimal geometric rate of convergence is
$n^{-\frac{1}{2+\frac{1}{\eta}}}$, and this rate can be achieved using a
generalized ``Scaling Clusters'' design that we provide. We then introduce the
additional assumption, implicit in the OLS estimators used in recent applied
studies, that potential outcomes are linear in population treatment
assignments. These estimators are inconsistent for our estimand, but a refined
OLS estimator is consistent and rate optimal, and performs better than IPW
estimators when clusters must be small. Its finite-sample performance can be
improved by incorporating prior information about the structure of spillovers.
As a robust alternative to the linear approach we also provide a method to
select estimator-design pairs that minimize a notion of worst-case risk when
the data generating process is unknown. Finally, we provide asymptotically
valid inference methods.


  We find all hyper-K\"ahler 4-manifolds admitting conformal K\"ahler
structures with respect to either orientation, and we show that these
structures can be expressed as a combination of twistor elementary states (and
possibly a self-dual dyon) in locally flat spaces. The complex structures of
different flat pieces are not compatible however, reflecting that the global
geometry is not a linear superposition. For either orientation the space must
be Gibbons-Hawking (thus excluding the Atiyah-Hitchin metric), and, if the
orientations are opposite, it must also be toric and have an irreducible
Killing tensor. We also show that the only hyper-K\"ahler 4-metric with a
non-constant Killing-Yano tensor is the half-flat Taub-NUT instanton.


  We say that the signs of association measures among three variables {X, Y, Z}
are transitive if a positive association measure between the variable X and the
intermediate variable Y and further a positive association measure between Y
and the endpoint variable Z imply a positive association measure between X and
Z. We introduce four association measures with different stringencies, and
discuss conditions for the transitivity of the signs of these association
measures. When the variables follow exponential family distributions, the
conditions become simpler and more interpretable. Applying our results to two
data sets from an observational study and a randomized experiment, we
demonstrate that the results can help us to draw conclusions about the signs of
the association measures between X and Z based only on two separate studies
about {X, Y} and {Y, Z}.


  We propose a protocol for creating a fully entangled GHZ-type state of
neutral atoms in spatially separated optical atomic clocks. In our scheme,
local operations make use of the strong dipole-dipole interaction between
Rydberg excitations, which give rise to fast and reliable quantum operations
involving all atoms in the ensemble. The necessary entanglement between distant
ensembles is mediated by single-photon quantum channels and collectively
enhanced light-matter couplings. These techniques can be used to create the
recently proposed quantum clock network based on neutral atom optical clocks.
We specifically analyze a possible realization of this scheme using neutral Yb
ensembles.


  In recent years, there has been a growing interest in using machine learning
to overcome the high cost of numerical simulation, with some learned models
achieving impressive speed-ups over classical solvers whilst maintaining
accuracy. However, these methods are usually tested at low-resolution settings,
and it remains to be seen whether they can scale to the costly high-resolution
simulations that we ultimately want to tackle.
  In this work, we propose two complementary approaches to improve the
framework from MeshGraphNets, which demonstrated accurate predictions in a
broad range of physical systems. MeshGraphNets relies on a message passing
graph neural network to propagate information, and this structure becomes a
limiting factor for high-resolution simulations, as equally distant points in
space become further apart in graph space. First, we demonstrate that it is
possible to learn accurate surrogate dynamics of a high-resolution system on a
much coarser mesh, both removing the message passing bottleneck and improving
performance; and second, we introduce a hierarchical approach (MultiScale
MeshGraphNets) which passes messages on two different resolutions (fine and
coarse), significantly improving the accuracy of MeshGraphNets while requiring
less computational resources.


  We generalize the Lee-Suzuki iteration method for summing the folded diagram
series to the case where the unperturbed model-space energies are
non-degenerate. A condition is derived for the convergence of the iteration
scheme and this depends on the choice of the model space projection operators.
Two choices are examined, in the first the projection operators are defined in
terms of the unperturbed states and in the second they are defined in terms of
the eigenfunctions obtained at each stage of the iteration. As is illustrated
by calculations with a simple model, the second procedure gives the better
convergence and, by suitable choice of the starting energies, allows the
reproduction of any subset of the exact eigenvalues.


  The ability to make decisions based on data, with its inherent uncertainties
and variability, is a complex and vital skill in the modern world. The need for
such quantitative critical thinking occurs in many different contexts, and
while it is an important goal of education, that goal is seldom being achieved.
We argue that the key element for developing this ability is repeated practice
in making decisions based on data, with feedback on those decisions. We
demonstrate a structure for providing suitable practice that can be applied in
any instructional setting that involves the acquisition of data and relating
that data to scientific models. This study reports the results of applying that
structure in an introductory physics lab course. Students in an experimental
condition were repeatedly instructed to make and act on quantitative
comparisons between datasets, and between data and models, an approach that is
common to all science disciplines. These instructions were slowly faded across
the course. After the instructions had been removed, students in the
experimental condition were 12 times more likely to spontaneously propose or
make changes to improve their experimental methods than a control group, who
performed traditional experimental activities. They were also four times more
likely to identify and explain a limitation of a physical model using their
data. Students in the experimental condition also showed much more
sophisticated reasoning about their data. These differences between the groups
were seen to persist into a subsequent course taken the following year.


  In this paper, we compute the {\Sigma}^n(G) and {\Omega}^n(G) invariants when
1 \rightarrow H \rightarrow G \rightarrow K \rightarrow 1 is a short exact
sequence of finitely generated groups with K finite. We also give sufficient
conditions for G to have the R_{\infty} property in terms of {\Omega}^n(H) and
{\Omega}^n(K) when either K is finite or the sequence splits. As an
application, we construct a group F \rtimes? Z_2 where F is the R. Thompson's
group F and show that F \rtimes Z_2 has the R_{\infty} property while F is not
characteristic.


  Recently, it was proposed that a small true vacuum universe can inflate
spontaneously, in principle. Furthermore, there should be matter creation in
vacuum inflation due to quantum fluctuations, and the matter created will
influence the inflation simultaneously. In this paper, scalar and tensor
perturbations in this model are analyzed and confronted with recent
observations. These perturbations are derived and expressed with Hubble
flow-functions. By comparing our calculations with experimental results, we can
determine all the parameters in this model. Finally, with the determined
parameters, we compute the evolution of the matter density and show that the
matter produced in inflation roughly fits the observations at present.


  Unlike robots, humans learn, adapt and perceive their bodies by interacting
with the world. Discovering how the brain represents the body and generates
actions is of major importance for robotics and artificial intelligence. Here
we discuss how neuroscience findings open up opportunities to improve current
estimation and control algorithms in robotics. In particular, how active
inference, a mathematical formulation of how the brain resists a natural
tendency to disorder, provides a unified recipe to potentially solve some of
the major challenges in robotics, such as adaptation, robustness, flexibility,
generalization and safe interaction. This paper summarizes some experiments and
lessons learned from developing such a computational model on real embodied
platforms, i.e., humanoid and industrial robots. Finally, we showcase the
limitations and challenges that we are still facing to give robots human-like
perception


  Some simple arguments are introduced for a possible explanation of the
behavior of the lateral shower age of proton-initiated showers. The
corresponding analytical treatment based on the proposed argument is then
illustrated. Using the Monte Carlo simulation (MC) code CORSIKA, we have
validated how the different characteristics associated with the lateral shower
age predicted in the present analytical parametrization, can be understood. The
lateral shower age of a proton-initiated shower and its correlations with the
lateral shower ages of electron- and neutral pion-initiated showers supports
the idea that the result of superposition of several electromagnetic
sub-showers initiated by neutral pions might produce the lateral density
distribution of electrons of a proton initiated shower. It is also noticed with
the simulated data that the stated feature still persists even in the local
shower age representation.


  This work investigates the asymptotic behaviour of the gradient approximation
method called the generalized simplex gradient (GSG). This method has an error
bound that at first glance seems to tend to infinity as the number of sample
points increases, but with some careful construction, we show that this is not
the case. For functions in finite dimensions, we present two new error bounds
ad infinitum depending on the position of the reference point. The error bounds
are not a function of the number of sample points and thus remain finite.


  In this paper we extend the work of Smith and Papamichail (1999) and present
fast approximate Bayesian algorithms for learning in complex scenarios where at
any time frame, the relationships between explanatory state space variables can
be described by a Bayesian network that evolve dynamically over time and the
observations taken are not necessarily Gaussian. It uses recent developments in
approximate Bayesian forecasting methods in combination with more familiar
Gaussian propagation algorithms on junction trees. The procedure for learning
state parameters from data is given explicitly for common sampling
distributions and the methodology is illustrated through a real application.
The efficiency of the dynamic approximation is explored by using the Hellinger
divergence measure and theoretical bounds for the efficacy of such a procedure
are discussed.


  Elucidating the demographic and phylogeographic histories of species provides
insight into the processes responsible for generating biological diversity, and
genomic datasets are now permitting the estimation of histories and demographic
parameters with unprecedented accuracy. We used a genomic single nucleotide
polymorphism (SNP) dataset generated using a RAD-Seq method to investigate the
historical demography and phylogeography of a widespread lowland Neotropical
bird (Xenops minutus). As expected, we found that prominent landscape features
that act as dispersal barriers, such as Amazonian rivers and the Andes
Mountains, are associated with the deepest phylogeographic breaks, and also
that isolation by distance is limited in areas between these barriers. In
addition, we inferred positive population growth for most populations and
detected evidence of historical gene flow between populations that are now
physically isolated. Even with genomic estimates of historical demographic
parameters, we found the prominent diversification hypotheses to be untestable.
We conclude that investigations into the multifarious processes shaping species
histories, aided by genomic datasets, will provide greater resolution of
diversification in the Neotropics, but that future efforts should focus on
understanding the processes shaping the histories of lineages rather than
trying to reconcile these histories with landscape and climatic events in Earth
history.


  The J-PET scanner, which allows for single bed imaging of the whole human
body, is currently under development at the Jagiellonian University. The dis-
cussed detector offers improvement of the Time of Flight (TOF) resolution due
to the use of fast plastic scintillators and dedicated electronics allowing for
sam- pling in the voltage domain of signals with durations of few nanoseconds.
In this paper we show that recovery of the whole signal, based on only a few
samples, is possible. In order to do that, we incorporate the training signals
into the Tikhonov regularization framework and we perform the Principal
Component Analysis decomposition, which is well known for its compaction
properties. The method yields a simple closed form analytical solution that
does not require iter- ative processing. Moreover, from the Bayes theory the
properties of regularized solution, especially its covariance matrix, may be
easily derived. This is the key to introduce and prove the formula for
calculations of the signal recovery error. In this paper we show that an
average recovery error is approximately inversely proportional to the number of
acquired samples.


  We offer a method of correlations mapping on the full celestial sphere that
allows to check the quality of reconstructed maps, their non-Gaussianity and
conduct experiments in various frequency ranges. The method was evaluated on
the WMAP data, both on the reconstructed maps and foreground components, and on
the NRAO VLA Sky Survey (NVSS) data. We detected a significant shift in the
correlation data of the dust component, which can be preconditioned by a more
complex dust model than the one currently in use for component separation.
While studying the NVSS correlation data, we demonstrated that the statistics
of the coinciding spots in the microwave background and in the NVSS survey
corresponds to the one expected in the $\Lambda$CDM model. This can testify for
a chance coincidence of the spots in the NVSS and WMAP data in the CMB Cold
Spot region. Our method is software-implemented in the GLESP package.


  Other nongravitational heating processes are needed to resolve the
disagreement between the absence of cool gas components in the centers of
galaxy clusters revealed recently by Chandra and XMM observations and the
expectations of conventional radiative cooling models. Here we propose that the
interaction between dark matter particles and ordinary baryonic matter may act
as an alternative for the reheating of intracluster medium (ICM) in the inner
regions of clusters, in which kinetic energy of dark matter is transported to
ICM to balance the radiative cooling. Using the Chandra and XMM data of typical
clusters, we set a useful constraint on the dark matter-baryon cross-section:
$\sigma_{xp}/m_x \sim 1 \times 10^{-25}$ cm$^2$GeV$^{-1}$, where $m_x$ is the
mass of dark matter particles.


  We present a method for fitting monotone curves using cubic B-splines, which
is equivalent to putting a monotonicity constraint on the coefficients. We
explore different ways of enforcing this constraint and analyze their
theoretical and empirical properties. We propose two algorithms for solving the
spline fitting problem: one that uses standard optimization techniques and one
that trains a Multi-Layer Perceptrons (MLP) generator to approximate the
solutions under various settings and perturbations. The generator approach can
speed up the fitting process when we need to solve the problem repeatedly, such
as when constructing confidence bands using bootstrap. We evaluate our method
against several existing methods, some of which do not use the monotonicity
constraint, on some monotone curves with varying noise levels. We demonstrate
that our method outperforms the other methods, especially in high-noise
scenarios. We also apply our method to analyze the polarization-hole phenomenon
during star formation in astrophysics. The source code is accessible at
\texttt{\url{https://github.com/szcf-weiya/MonotoneSplines.jl}}.


  We present a new multilevel minimization framework for the training of deep
residual networks (ResNets), which has the potential to significantly reduce
training time and effort. Our framework is based on the dynamical system's
viewpoint, which formulates a ResNet as the discretization of an initial value
problem. The training process is then formulated as a time-dependent optimal
control problem, which we discretize using different time-discretization
parameters, eventually generating multilevel-hierarchy of auxiliary networks
with different resolutions. The training of the original ResNet is then
enhanced by training the auxiliary networks with reduced resolutions. By
design, our framework is conveniently independent of the choice of the training
strategy chosen on each level of the multilevel hierarchy. By means of
numerical examples, we analyze the convergence behavior of the proposed method
and demonstrate its robustness. For our examples we employ a multilevel
gradient-based methods. Comparisons with standard single level methods show a
speedup of more than factor three while achieving the same validation accuracy.


  We have obtained 18 new high-resolution spectropolarimetric observations of
the B2Vp star sigma Ori E with both the Narval and ESPaDOnS
spectropolarimeters. The aim of these observations is to test, with modern
data, the assumptions of the Rigidly Rotating Magnetosphere (RRM) model of
Townsend & Owocki (2005), applied to the specific case of sigma Ori E by
Townsend et al. (2005). This model includes a substantially offset dipole
magnetic field configuration, and approximately reproduces previous
observational variations in longitudinal field strength, photometric
brightness, and Halpha emission. We analyze new spectroscopy, including H I, He
I, C II, Si III and Fe III lines, confirming the diversity of variability in
photospheric lines, as well as the double S-wave variation of circumstellar
hydrogen. Using the multiline analysis method of Least-Squares Deconvolution
(LSD), new, more precise longitudinal magnetic field measurements reveal a
substantial variance between the shapes of the observed and RRM model
time-varying field. The phase resolved Stokes V profiles of He I 5876 A and
6678 A lines are fit poorly by synthetic profiles computed from the magnetic
topology assumed by Townsend et al. (2005). These results challenge the offset
dipole field configuration assumed in the application of the RRM model to sigma
Ori E, and indicate that future models of its magnetic field should also
include complex, higher-order components.


  The superintegrability of two-dimensional Hamiltonians with a position
dependent mass (pdm) is studied (the kinetic term contains a factor $m$ that
depends of the radial coordinate). First, the properties of Killing vectors are
studied and the associated Noether momenta are obtained. Then the existence of
several families of superintegrable Hamiltonians is proved and the quadratic
integrals of motion are explicitly obtained. These families include, as
particular cases, some systems previously obtained making use of different
approaches. We also relate the superintegrability of some of these pdm systems
with the existence of complex functions endowed with interesting Poisson
bracket properties. Finally the relation of these pdm Hamiltonians with the
Euclidean Kepler problem and with the Euclidean harmonic oscillator is
analyzed.


  Over the past three decades, considerable effort has been devoted to studying
the rich and diverse phenomenologies of heterotic strings exhibiting spacetime
supersymmetry. Unfortunately, during this same period, there has been
relatively little work studying the phenomenologies associated with their
non-supersymmetric counterparts. The primary reason for this relative lack of
attention is the fact that strings without spacetime supersymmetry are
generally unstable, exhibiting large one-loop dilaton tadpoles. In this paper,
we demonstrate that this hurdle can be overcome in a class of tachyon-free
four-dimensional string models realized through coordinate-dependent
compactifications. Moreover, as we shall see, it is possible to construct
models in this class whose low-lying states resemble the Standard Model (or
even potential unified extensions thereof) --- all without any light
superpartners, and indeed without supersymmetry at any energy scale. The
existence of such models thus opens the door to general studies of
non-supersymmetric string phenomenology, and in this paper we proceed to
discuss a variety of theoretical and phenomenological issues associated with
such non-supersymmetric strings. On the theoretical side, we discuss the
finiteness properties of such strings, the general characteristics of their
mass spectra, the magnitude and behavior of their one-loop cosmological
constants, and their interpolation properties. By contrast, on the
phenomenological side, the properties we discuss are more model-specific and
include their construction techniques, their natural energy scales, their
particle and charge assignments, and the magnitudes of their associated Yukawa
couplings and scalar masses.


  The chaotic spike train of a homoclinic dynamical system is self-synchronized
by re-inserting a small fraction of the delayed output. Due to the sensitive
nature of the homoclinic chaos to external perturbations, stabilization of very
long periodic orbits is possible. On these orbits, the dynamics appears chaotic
over a finite time, but then it repeats with a recurrence time that is slightly
longer than the delay time. The effect, called delayed self-synchronization
(DSS), displays analogies with neurodynamic events which occur in the build-up
of long term memories.


  We present a new approach based on real time domain Feynman path integrals
(RTPI) for electronic structure calculations and quantum dynamics, which
includes correlations between particles exactly but within the numerical
accuracy. We demonstrate that incoherent propagation by keeping the wave
function real is a novel method for finding and simulation of the ground state,
similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools
lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong
correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and
compare against DMC. This system provides an excellent test case due to exact
solutions for some confinements and because in 1D the Coulomb singularity is
stronger than in two or three dimensional space. The use of Monte Carlo grid is
shown to be efficient for which we determine useful numerical parameters.
Furthermore, we discuss another novel approach achieved by combining the
strengths of iRTPI and DMC. We also show usefulness of the perturbation theory
for analytical approximates in case of strong confinements.


  We consider the following perturbed Hamiltonian $\mathcal{H}= -\partial_x^2 +
V(x)$ on the real line. The potential $V(x)$ is a real - valued function of
short range type. We study the equivalence of classical homogeneous Sobolev
type spaces $\dot{H}^s_p$, $p \in (1,\infty)$ and the corresponding perturbed
homogeneous Sobolev spaces associated with the perturbed Hamiltonian. It is
shown that the assumption zero is not a resonance guarantees that the perturbed
and unperturbed homogeneous Sobolev norms of order $s = \gamma - 1 \in [0,1/p)$
are equivalent. As a corollary, the corresponding wave operators leave
classical homogeneous Sobolev spaces of order $s \in [0,1/p)$ invariant.


  The proton-proton ($pp$) collisions at the Large Hadron Collider (LHC), CERN,
Switzerland has brought up new challenges and opportunities in understanding
the experimental findings in contrast to the conventional lower energy $pp$
collisions. Usually $pp$ collisions are used as the baseline measurement at the
GeV and TeV energies in order to understand a possible high density QCD medium
formation in heavy-ion collisions. However, the TeV $pp$ collisions have
created a new domain of research, where scientists have started observing
heavy-ion-like features (signatures) in high-multiplicity $pp$ collisions. This
warrants a relook into TeV $pp$ collisions, if at all QGP-droplets are produced
in such collisions. In this presentation, I discuss some of the new findings
and concepts emerging out in $pp$ collisions at the LHC energies along with
some of the new emergent phenomena in particle production.


  The measurement outcomes of two incompatible observables on a particle can be
precisely predicted when it is maximally entangled with a quantum memory, as
quantified recently [Nature Phys. 6, 659 (2010)]. We explore the behavior of
the uncertainty relation under the influence of local unital and nonunital
noisy channels. While the unital noises only increase the amount of
uncertainty, the amplitude-damping nonunital noises may amazingly reduce the
amount of uncertainty in the long-time limit. This counterintuitive phenomenon
could be justified by different competitive mechanisms between quantum
correlations and the minimal missing information after local measurement.


  Existing face forgery detection models try to discriminate fake images by
detecting only spatial artifacts (e.g., generative artifacts, blending) or
mainly temporal artifacts (e.g., flickering, discontinuity). They may
experience significant performance degradation when facing out-domain
artifacts. In this paper, we propose to capture both spatial and temporal
artifacts in one model for face forgery detection. A simple idea is to leverage
a spatiotemporal model (3D ConvNet). However, we find that it may easily rely
on one type of artifact and ignore the other. To address this issue, we present
a novel training strategy called AltFreezing for more general face forgery
detection. The AltFreezing aims to encourage the model to detect both spatial
and temporal artifacts. It divides the weights of a spatiotemporal network into
two groups: spatial-related and temporal-related. Then the two groups of
weights are alternately frozen during the training process so that the model
can learn spatial and temporal features to distinguish real or fake videos.
Furthermore, we introduce various video-level data augmentation methods to
improve the generalization capability of the forgery detection model. Extensive
experiments show that our framework outperforms existing methods in terms of
generalization to unseen manipulations and datasets. Code is available at
https: //github.com/ZhendongWang6/AltFreezing.


  Two-dimensional (2D) Pb nanoisland has established an ideal platform for
studying the quantum size effects on growth mechanism, electronic structures as
well as high-temperature superconductivity. Here, we investigate the growth and
quantum well electronic states of the 2D Pb nanoisland on Nb-doped SrTiO3(001)
by scanning tunneling microscopy and spectroscopy. In contrast to Pb/Si(111),
Pb/Cu(111) and Pb/Ag(111), there is no wetting layer of Pb formed on Nb-doped
SrTiO3(001) surface, resulting in isolated Pb nanoislands with an apparent
height of 4 atomic layers as the building blocks for the island growth.
According to the thickness-dependent quantum well states resolved in both
occupied and unoccupied energy regions, the constant group velocity vg =
1.804+-0.106 m/s and Fermi wavevector kF = 1.575 {\AA}-1, have been extracted
from a linear fit of the Pb(111) band dipersion along the {\Gamma}-L direction.
In addition, the energy-dependent scattering phase shift {\phi}(E) obtained by
means of phase accumulation model shows a metallic-like scattering interface
analogous to Pb/Ag(111). These spatially decoupled 2D Pb nanoislands thus
realize an opportunity to explore the intrinic quantum confinement phenomena in
nanoscale superconductors on the doped titanium-oxide-type substrate.


  We present a thorough theoretical study of ordering phenomena in nitride
ternary alloys GaInN, AlInN, and AlGaN. Using the Monte Carlo approach and
energetics based on the Keating model we analyze the influence of various
factors on ordering in bulk crystals and epitaxial layers. We characterize the
degree of both short range order (SRO) and long ranger order (LRO) for
different compositions, temperatures and for substrates associated with
different epitaxial strain. For the description of the SRO the Warren-Cowley
parameters related to the first four coordination shells are used. The LRO is
detected by means of the introduced sim-LRO parameter, based on the
Bragg-Williams approach. The description of the observed long-range ordering
patterns and conditions for their occurrence follows.


  Solar coronal loops show significant plasma motions during their formation
and eruption stages. Dynamic cool coronal structures, on the other hand, are
often observed to propagate along coronal loops. In this paper, we report on
the discovery of two types of dynamic cool coronal structures, and characterize
their fundamental properties. Using the EUV 304 angstrom images from the
Extreme UltraViolet Imager (EUVI) telescope on the Solar TErrestrial RElation
Observatory (STEREO) and the Ca II filtergrams from the Solar Optical Telescope
(SOT) instrument on HINODE, we study the evolution of an EUV arch and the
kinematics of cool coronal structures. The EUV 304 angstrom observations show
that a missile-like plasmoid moves along an arch-shaped trajectory, with an
average velocity of 31 km/s. About three hours later, a plasma arch forms along
the trajectory, subsequently the top part of the arch fades away and
disappears, meanwhile the plasma belonging to the two legs of the arch flows
downward to the arch feet. During the arch formation and disappearance, SOT Ca
II images explore dynamic cool coronal structures beneath the arch. By tracking
these structures, we classify them into two types. Type I is threadlike in
shape and flows downward with a greater average velocity of 72 km/s, finally it
combines a loop fibril at chromospheric altitude. Type II is
shape-transformable and sometimes rolling as it flows downward with a smaller
velocity of 37 km/s, then disappears insularly in the chromosphere. It is
suggested that the two types of structures are possibly controlled by different
magnetic configurations.


  We discuss the idea that the model-independent (MI) axion of string theory is
the source of quintessential dark energy. The scenario is completed with a
composite QCD axion from hidden sector squark condensation that could serve as
dark matter candidate. The mechanism relies on the fact that the hidden sector
anomaly contribution to the composite axion is much smaller than the QCD
anomaly term. This intuitively surprising scenario is based on the fact that
below the hidden sector scale $\Lambda_h$ there are many light hidden sector
quarks. Simply, by counting engineering dimensions the hidden sector instanton
potential can be made negligible compared to the QCD anomaly term.


  Existing state-of-the-art techniques in exemplar-based image-to-image
translation hold several critical concerns. Existing methods related to
exemplar-based image-to-image translation are impossible to translate on an
image tuple input (source, target) that is not aligned. Additionally, we can
confirm that the existing method exhibits limited generalization ability to
unseen images. In order to overcome this limitation, we propose Multiple GAN
Inversion for Exemplar-based Image-to-Image Translation. Our novel Multiple GAN
Inversion avoids human intervention by using a self-deciding algorithm to
choose the number of layers using Fr\'echet Inception Distance(FID), which
selects more plausible image reconstruction results among multiple hypotheses
without any training or supervision. Experimental results have in fact, shown
the advantage of the proposed method compared to existing state-of-the-art
exemplar-based image-to-image translation methods.


  During the current mental health crisis, the importance of identifying
potential indicators of mental issues from social media content has surged.
Overlooking the multifaceted nature of mental and social well-being can have
detrimental effects on one's mental state. In traditional therapy sessions,
professionals manually pinpoint the origins and outcomes of underlying mental
challenges, a process both detailed and time-intensive. We introduce an
approach to this intricate mental health analysis by framing the identification
of wellness dimensions in Reddit content as a wellness concept extraction and
categorization challenge. We've curated a unique dataset named WELLXPLAIN,
comprising 3,092 entries and totaling 72,813 words. Drawing from Halbert L.
Dunn's well-regarded wellness theory, our team formulated an annotation
framework along with guidelines. This dataset also includes human-marked
textual segments, offering clear reasoning for decisions made in the wellness
concept categorization process. Our aim in publishing this dataset and
analyzing initial benchmarks is to spearhead the creation of advanced language
models tailored for healthcare-focused concept extraction and categorization.


  Motion of massive test particles in the nonvacuum spherically symmetric
radiating Vaidya spacetime is investigated, allowing for physical interaction
of the particles with the radiation field in terms of which the source
energy-momentum tensor is interpreted. This "Poynting-Robertson-like effect" is
modeled by the usual effective term describing a Thomson-type radiation drag
force. The equations of motion are studied for simple types of motion including
free motion (without interaction), purely radial and purely azimuthal
(circular) motion, and for the particular case of "static" equilibrium;
appropriate solutions are given where possible. The results---mainly those on
the possible existence of equilibrium positions---are compared with their
counterparts obtained previously for a test spherically symmetric radiation
field in a vacuum Schwarzschild background.


  The basic thermodynamic quantities for a non-interacting scalar field in a
periodic potential composed of either a one-dimensional chain of Dirac
$\delta$-$\delta^\prime$ functions or a specific potential with extended
compact support are calculated. First, we consider the representation in terms
of real frequencies (or one-particle energies). Then we turn the axis of
frequency integration towards the imaginary axis by a finite angle, which
allows for easy numerical evaluation, and finally turn completely to the
imaginary frequencies and derive the corresponding Matsubara representation,
which this way appears also for systems with band structure. In the limit case
$T \to 0$ we confirm earlier results on the vacuum energy. We calculate for the
mentioned examples the free energy and the entropy and generalize earlier
results on negative entropy.


  We prove weak convergence of order one for a class of exponential based
integrators for SDEs with non-globally Lipschtiz drift. Our analysis covers
tamed versions of Geometric Brownian Motion (GBM) based methods as well as the
standard exponential schemes. The numerical performance of both the GBM and
exponential tamed methods through four different multi-level Monte Carlo
techniques are compared. We observe that for linear noise the standard
exponential tamed method requires severe restrictions on the stepsize unlike
the GBM tamed method.


  In this paper, we propose a quantum version of the differential cryptanalysis
which offers a quadratic speedup over the existing classical one and show the
quantum circuit implementing it. The quantum differential cryptanalysis is
based on the quantum minimum/maximum-finding algorithm, where the values to be
compared and filtered are obtained by calling the quantum counting algorithm.
Any cipher which is vulnerable to the classical differential cryptanalysis
based on counting procedures can be cracked more quickly under this quantum
differential attack.


  The thermodynamic properties of the hot plasma in galaxy clusters retains
information on the processes leading to the formation and evolution of the gas
in their deep, dark matter potential wells. These processes are dictated not
only by gravity but also by gas physics, e.g. AGN feedback and turbulence. In
this work, we study the thermodynamic properties, e.g. density, temperature,
pressure, and entropy, of the most massive and the most distant ($z > 1.2$)
SPT-selected clusters, and compare them with those of the nearby clusters
($z<0.1$) to constrain their evolution as a function of time and radius. We
find that thermodynamic properties in the outskirts of high redshift clusters
are remarkably similar to the low redshift clusters, and their evolution
follows the prediction of the self-similar model. Their intrinsic scatter is
larger, indicating that the physical properties that lead to the formation and
virialization of cluster outskirts show evolving variance. On the other hand,
thermodynamic properties in the cluster cores deviates significantly from
self-similarity indicating that the processes that regulate the core are
already in place in these very high redshift clusters. This result is supported
by the unevolving physical scatter of all thermodynamic quantities in cluster
cores.


  We use numerical simulations to model the effect of seeing and extinction
modulations on weak lensing surveys. We find that systematic fluctuations in
the shear amplitude and source depth can give rise to changes in the $E$-mode
signal and to varying amplitudes of large scale $B$-modes. Exquisite control of
such systematics will be required as we approach the era of precision cosmology
with weak lensing.


  This paper shows that how to approximate general fuzzy number by using
convolution method.


  A spatially-selective and internal-state-selective triggering pulse is an
important component to realize the unitary dynamical state-locking process
which may be used to realize the reversible and unitary halting protocol and
construct the unstructured quantum search process based on the tensor-product
Hilbert-space symmetric structure and the unitary quantum dynamics. In this
paper it is shown how a spatially-selective and internal-state-selective
triggering pulse is constructed generally in the quantum system of a single
atom. Rigorous theoretical calculation and error estimation, which are based on
the Trotter-Suzuki decomposition method and the multiple-Gaussian-wave-packet
expansion method, are carried out for the time evolution process of a single
atom in the double-well potential field and in the presence of the
spatially-selective and internal-state-selective triggering pulse. It proves
that the spatially-selective and internal-state-selective triggering pulse is
feasible, that is, the possible errors generated by the triggering pulse are
shown to be controllable. This rigorous theoretical calculation also shows that
the spatially-selective and internal-state-selective triggering pulse may be
different from its corresponding ideal internal-state-selective triggering
pulse that is not spatially selective, but the difference between their final
states of the time evolution process is controllable. These computational
results are achieved with the help of the Gaussian wave-packet motional states
and the space-dependent quadratic Hamiltonians of a single atom. The methods
and techniques developed in the paper are useful for studying the
quantum-computing speedup mechanism of the unitary quantum dynamics in the
quantum system of a single atom.


  Networks and temporal point processes serve as fundamental building blocks
for modeling complex dynamic relational data in various domains. We propose the
latent space Hawkes (LSH) model, a novel generative model for continuous-time
networks of relational events, using a latent space representation for nodes.
We model relational events between nodes using mutually exciting Hawkes
processes with baseline intensities dependent upon the distances between the
nodes in the latent space and sender and receiver specific effects. We
demonstrate that our proposed LSH model can replicate many features observed in
real temporal networks including reciprocity and transitivity, while also
achieving superior prediction accuracy and providing more interpretable fits
than existing models.


  Single frame data contains finite information which limits the performance of
the existing vision-based multi-camera 3D object detection paradigms. For
fundamentally pushing the performance boundary in this area, a novel paradigm
dubbed BEVDet4D is proposed to lift the scalable BEVDet paradigm from the
spatial-only 3D space to the spatial-temporal 4D space. We upgrade the naive
BEVDet framework with a few modifications just for fusing the feature from the
previous frame with the corresponding one in the current frame. In this way,
with negligible additional computing budget, we enable BEVDet4D to access the
temporal cues by querying and comparing the two candidate features. Beyond
this, we simplify the task of velocity prediction by removing the factors of
ego-motion and time in the learning target. As a result, BEVDet4D with robust
generalization performance reduces the velocity error by up to -62.9%. This
makes the vision-based methods, for the first time, become comparable with
those relied on LiDAR or radar in this aspect. On challenge benchmark nuScenes,
we report a new record of 54.5% NDS with the high-performance configuration
dubbed BEVDet4D-Base, which surpasses the previous leading method BEVDet-Base
by +7.3% NDS. The source code is publicly available for further research at
https://github.com/HuangJunJie2017/BEVDet .


  We present MLTCP, a technique to augment today's congestion control
algorithms to accelerate DNN training jobs in shared GPU clusters. MLTCP
enables the communication phases of jobs that compete for network bandwidth to
interleave with each other, thereby utilizing the network efficiently. At the
heart of MLTCP lies a very simple principle based on a key conceptual insight:
DNN training flows should scale their congestion window size based on the
number of bytes sent at each training iteration. We show that integrating this
principle into today's congestion control protocols is straightforward: by
adding 30-60 lines of code to Reno, CUBIC, or DCQCN, MLTCP stabilizes flows of
different jobs into an interleaved state within a few training iterations,
regardless of the number of competing flows or the start time of each flow. Our
experiments with popular DNN training jobs demonstrate that enabling MLTCP
accelerates the average and 99th percentile training iteration time by up to 2x
and 4x, respectively.


  Reinforcement learning with human feedback (RLHF) has become the dominant
method to align large models to user preferences. Unlike fine-tuning, for which
there are many studies regarding training data memorization, it is not clear
how memorization is affected by or introduced in the RLHF alignment process.
Understanding this relationship is important as real user data may be collected
and used to align large models; if user data is memorized during RLHF and later
regurgitated, this could raise privacy concerns. In this work, we analyze how
training data memorization can surface and propagate through each phase of
RLHF. We focus our study on code completion models, as code completion is one
of the most popular use cases for large language models. We find that RLHF
significantly decreases the chance that data used for reward modeling and
reinforcement learning is memorized, in comparison to aligning via directly
fine-tuning on this data, but that examples already memorized during the
fine-tuning stage of RLHF, will, in the majority of cases, remain memorized
after RLHF.


  We give a new bijective interpretation of the Cauchy identity for Schur
operators which is a commutation relation between two formal power series with
operator coefficients. We introduce a plactic algebra associated with the
Kashiwara's extremal weight crystals over the Kac-Moody algebra of type
$A_{+\infty}$, and construct a Knuth type correspondence preserving the plactic
relations. This bijection yields the Cauchy identity for Schur operators as a
homomorphic image of its associated identity for plactic characters of extremal
weight crystals, and also recovers the Sagan and Stanley's correspondence for
skew tableaux as its restriction.