  We develop two new estimators for a general class of stationary GARCH models
with possibly heavy tailed asymmetrically distributed errors, covering
processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH,
VGARCH and Quadratic GARCH. The first estimator arises from negligibly trimming
QML criterion equations according to error extremes. The second imbeds
negligibly transformed errors into QML score equations for a Method of Moments
estimator. In this case, we exploit a sub-class of redescending transforms that
includes tail-trimming and functions popular in the robust estimation
literature, and we re-center the transformed errors to minimize small sample
bias. The negligible transforms allow both identification of the true parameter
and asymptotic normality. We present a consistent estimator of the covariance
matrix that permits classic inference without knowledge of the rate of
convergence. A simulation study shows both of our estimators trump existing
ones for sharpness and approximate normality including QML, Log-LAD, and two
types of non-Gaussian QML (Laplace and Power-Law). Finally, we apply the
tail-trimmed QML estimator to financial data.


  We compute the cobordism ring $MU^*(BG)\otimes \mathbb{F}_p$ when $G$ is a
Chevalley group. In the particular case of the general linear group, we prove
that it agrees with the Chow ring (as defined by Totaro).


  We are given a stack of pancakes of different sizes and the only allowed
operation is to take several pancakes from top and flip them. The unburnt
version requires the pancakes to be sorted by their sizes at the end, while in
the burnt version they additionally need to be oriented burnt-side down. We
present an algorithm with the average number of flips, needed to sort a stack
of n burnt pancakes, equal to 7n/4+O(1) and a randomized algorithm for the
unburnt version with at most 17n/12+O(1) flips on average.
  In addition, we show that in the burnt version, the average number of flips
of any algorithm is at least n+\Omega(n/log n) and conjecture that some
algorithm can reach n+\Theta(n/log n).
  We also slightly increase the lower bound on g(n), the minimum number of
flips needed to sort the worst stack of n burnt pancakes. This bound, together
with the upper bound found by Heydari and Sudborough in 1997, gives the exact
number of flips to sort the previously conjectured worst stack -I_n for n=3 mod
4 and n>=15. Finally we present exact values of f(n) up to n=19 and of g(n) up
to n=17 and disprove a conjecture of Cohen and Blum by showing that the burnt
stack -I_{15} is not the worst one for n=15.


  Quantum logic gates can perform calculations much more efficiently than their
classical counterparts. However, the level of control needed to obtain a
reliable quantum operation is correspondingly higher. In order to evaluate the
performance of experimental quantum gates, it is therefore necessary to
identify the essential features that indicate quantum coherent operation. In
this paper, we show that an efficient characterization of an experimental
device can be obtained by investigating the classical logic operations on a
pair of complementary basis sets. It is then possible to obtain reliable
predictions about the quantum coherent operations of the gate such as
entanglement generation and Bell state discrimination even without performing
these operations directly.


  Representation theory and the theory of symmetric functions have played a
central role in Random Matrix Theory in the computation of quantities such as
joint moments of traces and joint moments of characteristic polynomials of
matrices drawn from the Circular Unitary Ensemble and other Circular Ensembles
related to the classical compact groups. The reason is that they enable the
derivation of exact formulae, which then provide a route to calculating the
large-matrix asymptotics of these quantities. We develop a parallel theory for
the Gaussian Unitary Ensemble of random matrices, and other related unitary
invariant matrix ensembles. This allows us to write down exact formulae in
these cases for the joint moments of the traces and the joint moments of the
characteristic polynomials in terms of appropriately defined symmetric
functions. As an example of an application, for the joint moments of the traces
we derive explicit asymptotic formulae for the rate of convergence of the
moments of polynomial functions of GUE matrices to those of a standard normal
distribution when the matrix size tends to infinity.


  We present a one-dimensional nonlocal hopping model with exclusion on a ring.
The model is related to the Raise and Peel growth model. A nonnegative
parameter $u$ controls the ratio of the local backwards and nonlocal forwards
hopping rates. The phase diagram and consequently the values of the current,
depend on $u$ and the density of particles. In the special case of half-filling
and $u = 1$ the system is conformal invariant and an exact value of the current
for any size $L$ of the system is conjectured and checked for large lattice
sizes in Monte Carlo simulations. For $u > 1$ the current has a non-analytic
dependence on the density when the latter approaches the half-filling value.


  Black holes supported by self-interacting conformal scalar fields can be
considered as renormalizably dressed since the conformal potential is nothing
but the top power-counting renormalizable self-interaction in the relevant
dimension. On the other hand, potentials defined by powers which are lower than
the conformal one are also phenomenologically relevant since they are in fact
super-renormalizable. In this work we provide a new map that allows to build
black holes dressed with all the (super-)renormalizable contributions starting
from known conformal seeds. We explicitly construct several new examples of
these solutions in dimensions $D=3$ and $D=4$, including not only stationary
configurations but also time-dependent ones.


  Deep neural networks (DNNs) have achieved significant success in numerous
applications. The remarkable performance of DNNs is largely attributed to the
availability of massive, high-quality training datasets. However, processing
such massive training data requires huge computational and storage resources.
Dataset distillation is a promising solution to this problem, offering the
capability to compress a large dataset into a smaller distilled dataset. The
model trained on the distilled dataset can achieve comparable performance to
the model trained on the whole dataset.
  While dataset distillation has been demonstrated in image data, none have
explored dataset distillation for audio data. In this work, for the first time,
we propose a Dataset Distillation Framework for Audio Data (DDFAD).
Specifically, we first propose the Fused Differential MFCC (FD-MFCC) as
extracted features for audio data. After that, the FD-MFCC is distilled through
the matching training trajectory distillation method. Finally, we propose an
audio signal reconstruction algorithm based on the Griffin-Lim Algorithm to
reconstruct the audio signal from the distilled FD-MFCC. Extensive experiments
demonstrate the effectiveness of DDFAD on various audio datasets. In addition,
we show that DDFAD has promising application prospects in many applications,
such as continual learning and neural architecture search.


  We consider the minimum mass planet, as a function of radius, that is capable
of opening a gap in an $\alpha$-accretion disk. We estimate that a half Jupiter
mass planet can open a gap in a disk with accretion rate $\dot M \la 10^{-8}
M_\odot$/yr for viscosity parameter $\alpha =0.01$, and Solar mass and
luminosity. The minimum mass is approximately proportional to $\dot M^{0.48}
\alpha^{0.8} M_*^{0.42} L_*^{-0.08}$. This estimate can be used to rule out the
presence of massive planets in gapless accretion disks. We identify two radii
at which an inwardly migrating planet may become able to open a gap and so slow
its migration; the radius at which the heating from viscous dissipation is
similar to that from stellar radiation in a flared disk, and the radius at
which the disk has optical depth order 1 in a self-shadowed disk. If a gap
opening planet cuts off disk accretion allowing the formation of a central hole
or clearing in the disk then we would estimate that the clearing radius would
approximately be proportional to the stellar mass.


  We revisit the interaction of a first-quantized atomic system (consisting of
two charged quantum particles) with the quantum electromagnetic field, pointing
out the subtleties related to the gauge nature of electromagnetism and the
effect of multipole approximations. We connect the full minimal-coupling model
with the typical effective models used in quantum optics and relativistic
quantum information such as the Unruh-DeWitt (UDW) model and the dipole
coupling approximation. We point out in what regimes different degrees of
approximation are reasonable and in what cases effective models need to be
refined to capture the features of the light-matter interaction. This is
particularly important when considering the center of mass (COM) of the atom as
a quantum system that can be delocalized over multiple trajectories. For
example, we show that the simplest UDW approximation with a quantum COM fails
to capture crucial R\"ontgen terms coupling COM and internal atomic degrees of
freedom with each other and the field. Finally we show how effective dipole
interaction models can be covariantly prescribed for relativistically moving
atoms.


  We study properties of relative types of plurisubharmonic functions with
respect to maximal plurisubharmonic weights. It is shown that they give a
general form for upper semicontinuous, tropically additive functionals on
plurisubharmonic singularities. We consider some extremal problems whose
solutions are Green-like functions that give best possible bounds on a
plurisubharmonic function, given the values of its types relative to some of
(or all) the weights. An analyticity theorem is proved for the upperlevel sets
for the types with respect to exponentially H\"older continuous weights, which
leads to a result on propagation of plurisubharmonic singularities.


  The anomalous dimension of the heavy-light quark current in HQET is
calculated up to four loops. The N$^3$LL perturbative correction to $f_B/f_D$
is obtained.


  We demonstrate that long-range interaction in a system can lead to a very
strong interaction between long-wavelength quasiparticles and make them heavily
damped. In particular, we discuss magnon spectrum using 1/S expansion in 3D
Heisenberg ferromagnet (FM) with arbitrary small dipolar forces at T<<T_C. We
obtain that a fraction of long-wavelength magnons with energies e_k<T has
anomalously large damping G_k (ratio G_k/e_k reaches 0.3 for certain k). This
effect is observed both in quantum and classical FMs. Remarkably, this result
contradicts expectation of the quasiparticle concept according which a weakly
excited state of a many-body system can be represented as a collection of
weakly interacting elementary excitations. Particular materials are pointed out
which are suitable for corresponding experiments.


  Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely
generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly
reductive group scheme over $\Bbbk$ equipped with a representation
$\rho:\underline{G}_{R}\rightarrow
\underline{\textrm{Aut}}_{\textrm{Mod}(R)}(M)$. For the graded $T$-algebra $A$,
defined as $ A := \left( S_{T}^{\bullet} (M^{\vee} \otimes_{R}N )\right)^{G}, $
we determine the conditions under which the graded $T$-algebra $A$ is finitely
generated, finitely presented, or flat. Furthermore, we establish the
conditions under which a closed embedding of $\textrm{Proj} \ A$ into a
projective space exists. Since we do not impose any Noetherian hypotheses, our
results generalize those in the literature, providing new powerful tools
regarding moduli problems.


  The entropy production rate for an open quantum system with a classically
chaotic limit has been previously argued to be independent of $\hbar$ and $D$,
the parameter denoting coupling to the environment, and to be equal to the sum
of generalized Lyapunov exponents, with these results applying in the
near-classical regime. We present results for a specific system going well
beyond earlier work, considering how these dynamics are altered for the Duffing
problem by changing $\hbar,D$ and show that the entropy dynamics have a
transition from classical to quantum behavior that scales, at least for a
finite time, as a function of $\hbar^2/D$.


  Electrical Impedance Imaging would suffer a serious obstruction if for two
different conductivities the potential and current measured at the boundary
were the same. The Calder\'on's problem is to decide whether the conductivity
is indeed uniquely determined by the data at the boundary. In $\mathbb{R}^d$,
for $d=5,6$, we show that uniqueness holds when the conductivity is in
$W^{1+\frac{d-5}{2p}+, p}(\Omega)$, for $d\le p <\infty$. This improves on
recent results of Haberman, and of Ham, Kwon and Lee. The main novelty of the
proof is an extension of Tao's bilinear Theorem.


  One of the most important objectives of solar physics is the physical
understanding of the solar atmosphere, the structure of which is also described
in terms of the density (N) and temperature (T) distributions of the
atmospheric matter. Several multi-frequency analyses show that the
characteristics of these distributions are still debated, especially for the
outer coronal emission.
  We aim to constrain the T and N distributions of the solar atmosphere through
observations in the centimetric radio domain. We employ single-dish
observations from two of the INAF radio telescopes at the K-band frequencies
(18 - 26 GHz). We investigate the origin of the significant brightness
temperature ($T_B$) level that we detected up to the upper corona ($\sim 800$
Mm of altitude with respect to the photospheric solar surface).
  To probe the physical origin of the atmospheric emission and to constrain
instrumental biases, we reproduced the solar signal by convolving specific 2D
antenna beam models. The analysis of the solar atmosphere is performed by
adopting a physical model that assumes the thermal bremsstrahlung as the
emission mechanism, with specific T and N distributions. The modelled $T_B$
profiles are compared with those observed by averaging solar maps obtained
during the minimum of solar activity (2018 - 2020).
  The T and N distributions are compatible (within $25\%$ of uncertainty) with
the model up to $\sim 60$ Mm and $\sim 100$ Mm of altitude, respectively. The
analysis of the role of the antenna beam pattern on our solar maps proves the
physical nature of the atmospheric emission in our images up to the coronal
tails seen in our $T_B$ profiles. The challenging analysis of the coronal radio
emission at higher altitudes, together with the data from satellite instruments
will require further multi-frequency measurements.


  We consider a bipartite mixed state of the form, $\rho =\sum_{\alpha, \beta
=1}^{l}a_{\alpha \beta} | \psi_{\alpha}> < \psi_ \beta}| $, where $|
\psi_{\alpha}>$ are normalized bipartite state vectors, and matrix $(a_{\alpha
\beta})$ is positive semidefinite. We provide a necessary and sufficient
condition for the state $\rho $ taking the form of maximally correlated states
by a local unitary transformation. More precisely, we give a criterion for
simultaneous Schmidt decomposability of $| \psi_{\alpha}>$ for $\alpha
=1,2,..., l$. Using this criterion, we can judge completely whether or not the
state $\rho $ is equivalent to the maximally correlated state, in which the
distillable entanglement is given by a simple formula. For generalized Bell
states, this criterion is written as a simple algebraic relation between
indices of the states. We also discuss the local distinguishability of the
generalized Bell states that are simultaneously Schmidt decomposable.


  The generation of high-order harmonics in diatomic molecules is investigated
within the framework of the strong-field approximation. We show that the
conventional saddle-point approximation is not suitable for large internuclear
distances. An adapted saddle-point method that takes into account the molecular
structure is presented. We analyze the predictions for the harmonic-generation
spectra in both the velocity and the length gauge. At large internuclear
separations, we compare the resulting cutoffs with the predictions of the
simple-man's model. Good agreement is obtained only by using the adapted
saddle-point method combined with the velocity gauge.


  The distribution of thermally excited vortex loops near a superfluid phase
transition is calculated from a renormalized theory. The number density of
loops with a given perimeter is found to change from exponential decay with
increasing perimeter to algebraic decay as T_c is approached, in agreement with
recent simulations of both cosmic strings and high-T_c superconductors.
Predictions of the value of the exponent of the algebraic decay at T_c and of
critical behavior in the vortex density are confirmed by the simulations,
giving strong support to the vortex-folding model proposed by Shenoy.


  We report a decaying kink oscillation of a flux rope during a confined
eruptive flare, observed off the solar limb by SDO/AIA, that lacked a
detectable white-light coronal mass ejection. The erupting flux rope underwent
kinking, rotation, and apparent leg-leg interaction during the event. The
oscillations were observed simultaneously in multiple AIA channels at 304, 171,
and 193 {\AA}, indicating that multithermal plasma was entrained in the rope.
After reaching the overlying loops in the active region, the flux rope
exhibited large-amplitude, decaying kink oscillations with an apparent initial
amplitude of 30 Mm, period of about 16 min, and decay time of about 17 min. We
interpret these oscillations as a fundamental standing kink mode of the flux
rope. The oscillation polarization has a clear vertical component, while the
departure of the detected waveform from a sinusoidal signal suggests that the
oscillation could be circularly or elliptically polarized. The estimated kink
speed is 1080 km/s, corresponding to an Alfv\'en speed of about 760 km/s. This
speed, together with the estimated electron density in the rope from our DEM
analysis, $n_e \approx$(1.5--2.0)$\times 10^9$cm$^{-3}$, yields a magnetic
field strength of about 15 G. To the best of our knowledge, decaying kink
oscillations of a flux rope with non-horizontal polarization during a confined
eruptive flare have not been reported before. These oscillations provide unique
opportunities for indirect measurements of the magnetic-field strength in
low-coronal flux ropes during failed eruptions.


  This paper proposes a new method for estimating the joint probability mass
function of a pair of discrete random variables. This estimator is used to
construct joint Shannon R\'enyi-Tsallis entropies, and the mutual information
estimates of a pair of discrete random variables. Almost sure consistency and
central limit Theorems are established. Our theorical results are validated by
simulations.


  In this paper, we study some optimization problems in uniformly convex and
uniformly smooth Bochner spaces. We consider four cases of the underlying
subsets: closed and convex subsets, closed and convex cones, closed subspaces
and closed balls. In each case, we study the existence problems and the inverse
image properties. We think that the results and the analytic methods in this
paper could be applied to the theories of stochastic optimization, stochastic
variational inequality and stochastic fixed point.


  When a binary liquid is confined by a strongly repulsive wall, the local
density is depleted near the wall and an interface similar to that between the
liquid and its vapor is formed. This analogy suggests that the composition of
the binary liquid near this interface should exhibit spatial modulation similar
to that near a liquid-vapor interface even if the interactions of the wall with
the two components of the liquid are the same. The Guggenheim adsorption
relation quantifies the concentrations of two components of a binary mixture
near a liquid-vapor interface and qualitatively states that the majority
(minority) component enriches the interface for negative (positive) mixing
energy if the surface tensions of the two components are not very different.
From molecular dynamics simulations of binary mixtures with different
compositions and interactions, we find that the Guggenheim relation is
qualitatively satisfied at wall-induced interfaces for systems with negative
mixing energy at all state points considered. For systems with positive mixing
energy, this relation is found to be qualitatively valid at low densities,
while it is violated at state points with high density where correlations in
the liquid are strong. This observation is validated by a calculation of the
density profiles of the two components of the mixture using density functional
theory with the Ramakrishnan-Yussouff free-energy functional. Possible reasons
for the violation of the Guggenheim relation are discussed.


  We consider bootstrap percolation on the binomial random graph $G(n,p)$ with
infection threshold $r\in \mathbb{N}$, an infection process which starts from a
set of initially infected vertices and in each step every vertex with at least
$r$ infected neighbours becomes infected. We improve the results of Janson, \L
uczak, Turova, and Valier (2012) by strengthening the probability bounds on the
number of infected vertices at the end of the process, using simple arguments
based on martingales and giant components.


  We present a novel data set made up of omnidirectional video of multiple
objects whose centroid positions are annotated automatically. Omnidirectional
vision is an active field of research focused on the use of spherical imagery
in video analysis and scene understanding, involving tasks such as object
detection, tracking and recognition. Our goal is to provide a large and
consistently annotated video data set that can be used to train and evaluate
new algorithms for these tasks. Here we describe the experimental setup and
software environment used to capture and map the 3D ground truth positions of
multiple objects into the image. Furthermore, we estimate the expected
systematic error on the mapped positions. In addition to final data products,
we release publicly the software tools and raw data necessary to re-calibrate
the camera and/or redo this mapping. The software also provides a simple
framework for comparing the results of standard image annotation tools or
visual tracking systems against our mapped ground truth annotations.


  In this work we investigate the X-ray edge singularity problem realized in
noninteracting quantum dots. We analytically calculate the exponent of the
singularity in the absorption spectrum near the threshold and extend known
analytical results to the whole parameter regime of local level detunings.
Additionally, we highlight the connections to work distributions and to the
Loschmidt echo.


  A subgroup $H$ of a topological abelian group $X$ is said to be characterized
by a sequence $\mathbf v =(v_n)$ of characters of $X$ if $H=\{x\in X:v_n(x)\to
0\ \text{in}\ \mathbb T\}$. We study the basic properties of characterized
subgroups in the general setting, extending results known in the compact case.
For a better description, we isolate various types of characterized subgroups.
Moreover, we introduce the relevant class of autochacaracterized groups
(namely, the groups that are characterized subgroups of themselves by means of
a sequence of non-null characters); in the case of locally compact abelian
groups, these are proved to be exactly the non-compact ones. As a by-product of
our results, we find a complete description of the characterized subgroups of
discrete abelian groups.


  Whenever two irreversible processes occur simultaneously, time-reversal
symmetry of microscopic dynamics gives rise, on a macroscopic level, to
Onsager's reciprocal relations, which impose constraints on the number of
independent components of any transport coefficient tensor. Here, we show that
in the antiferromagnetic YbMnBi$_2$, which displays a strong
temperature-dependent anisotropy, the Onsager's reciprocal relations are
strictly satisfied for anomalous electric ($\sigma^A_{ij}$) and anomalous
thermoelectric ($\alpha^A_{ij}$) conductivity tensors. In contradiction with
what was recently reported by Pan $et~al.$ [Nat.Mater. 21, 203 (2022)], we find
that $\sigma^A_{ij} (H)= \sigma^A_{ji} (-H)$, and $\alpha^A_{ij} (H)=
\alpha^A_{ji} (-H)$. This equality holds in the whole temperature window
irrespective of the relative weights of the intrinsic or extrinsic mechanisms.
The $\alpha^A_{ij}/\sigma^A_{ij}$ ratio is close to $k_B/e$ at room
temperature, but peaks to an unprecedented magnitude of 2.9 $k_B/e$ at $\sim$
150 K, which may involve nondegenerate carriers of small Fermi surface pockets.


  We present results based on full-mission Planck observations of temperature
and polarization anisotropies of the CMB. These data are consistent with the
six-parameter inflationary LCDM cosmology. From the Planck temperature and
lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9)
km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar
spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured
parameters and 95% limits on other parameters.) Combined with Planck
temperature and lensing data, Planck LFI polarization measurements lead to a
reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with
other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective
number of relativistic degrees of freedom and the sum of neutrino masses is
constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005.
For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent
with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck
(BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We
find no evidence for isocurvature perturbations or cosmic defects. The equation
of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big
bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent
agreement with observations. We investigate annihilating dark matter and
deviations from standard recombination, finding no evidence for new physics.
The Planck results for base LCDM are in agreement with BAO data and with the
JLA SNe sample. However the amplitude of the fluctuations is found to be higher
than inferred from rich cluster counts and weak gravitational lensing. Apart
from these tensions, the base LCDM cosmology provides an excellent description
of the Planck CMB observations and many other astrophysical data sets.


  Compared with two-dimensional imaging, three-dimensional imaging is much more
advantageous to catch the characteristic information of the target for remote
sensing. We report a range-resolving ghost imaging ladar system together with
the experimental demonstration of three-dimensional remote sensing with a large
field of view. The experiments show that, by measuring the correlation function
of intensity fluctuations between two light fields, a three-dimensional map at
about 1.0 km range with 25 cm resolution in lateral direction and 60 cm
resolution in axial direction has been achieved by time-resolved measurements
of the reflection signals.


  We present general formulae to compute Wilson line correlators with the Color
Glass Condensate described by the McLerran-Venugopalan model. We explicitly
construct a complete and non-orthogonal set of color-singlet bases and write
matrix elements down, so that the exponential of the matrix leads to the Wilson
line correlators. We further develop a systematic perturbative expansion of
dipole Wilson line correlators in terms of $1/N_c$ where $N_c$ is the color
number. As a phenomenological application we calculate the flow harmonics
$v_n\{m\}$ in the dipole model and discuss the $N_c$ scaling.


  We propose a convex and fast signal reconstruction method for block sparsity
under arbitrary linear transform with unknown block structure. The proposed
method is a generalization of the similar existing method and can reconstruct
signals with block sparsity under non-invertible transforms, unlike the
existing method. Our work broadens the scope of block sparse regularization,
enabling more versatile and powerful applications across various signal
processing domains. We derive an iterative algorithm for solving proposed
method and provide conditions for its convergence to the optimal solution.
Numerical experiments demonstrate the effectiveness of the proposed method.


  The rise of AI has brought remarkable advancements in education, with AI
models demonstrating their ability to analyse and provide instructive solutions
to complex problems. This study compared and analysed the responses of four
Generative AI-powered chatbots (GenAIbots) - ChatGPT-3.5, ChatGPT-4, Bing Chat,
and Bard - within the constructivist theoretical framework. Using a single-case
study methodology, interaction logs between the GenAIbots and a simulated
student in Physics learning scenarios were analysed. The GenAIbots were
presented with conceptually dense Physics problems to promote deep
understanding. The qualitative analysis focused on tutor traits such as
subject-matter knowledge, empathy, assessment emphasis, facilitation skills,
and comprehension of the learning process. Findings showed that all GenAIbots
functioned as agents-to-think-with, fostering critical thinking,
problem-solving, and subject-matter knowledge. ChatGPT-4 stood out for
demonstrating empathy and a deep understanding of the learning process.
However, inconsistencies and shortcomings were observed, highlighting the need
for human intervention in AI-assisted learning. In conclusion, while GenAIbots
have limitations, their potential as agents-to-think-with in Physics education
offers promising prospects for revolutionising instruction.


  We calculate the stationary current through two double quantum dots which are
interacting via a common phonon environment. Numerical and analytical solutions
of a master equation in the stationary limit show that the current can be
increased as well as decreased due to a dissipation mediated interaction. This
effect is closely related to collective, spontaneous emission of phonons (Dicke
super- and subradiance effect), and the generation of a `cross-coherence' with
entanglement of charges in singlet or triplet states between the dots.
Furthermore, we discuss an inelastic `current switch' mechanism by which one
double dot controls the current of the other.


  A mechanism for creating amino acid enantiomerism that always selects the
same global chirality is identified, and subsequent chemical replication and
galactic mixing that would populate the galaxy with the predominant species is
described. This involves: (1) the spin of the 14N in the amino acids, or in
precursor molecules from which amino acids might be formed, coupling to the
chirality of the molecules; 2) the neutrinos emitted from the supernova,
together with magnetic field from the nascent neutron star or black hole formed
from the supernova selectively destroying one orientation of the 14N, and thus
selecting the chirality associated with the other 14N orientation; (3) chemical
evolution, by which the molecules replicate and evolve to more complex forms of
a single chirality on a relatively short timescale; and (4) galactic mixing on
a longer timescale mixing the selected molecules throughout the galaxy.


  Aging population ratios are rising significantly. Meanwhile, smart home based
health monitoring services are evolving rapidly to become a viable alternative
to traditional healthcare solutions. Such services can augment qualitative
analyses done by gerontologists with quantitative data. Hence, the recognition
of Activities of Daily Living (ADL) has become an active domain of research in
recent times. For a system to perform human activity recognition in a
real-world environment, multiple requirements exist, such as scalability,
robustness, ability to deal with uncertainty (e.g., missing sensor data), to
operate with multi-occupants and to take into account their privacy and
security. This paper attempts to address the requirements of scalability and
robustness, by describing a reasoning mechanism based on modular spatial and/or
temporal context models as a network of ontologies. The reasoning mechanism has
been implemented in a smart home system referred to as Arianna+. The paper
presents and discusses a use case, and experiments are performed on a simulated
dataset, to showcase Arianna+'s modularity feature, internal working, and
computational performance. Results indicate scalability and robustness for
human activity recognition processes.


  Knowing the structure of an offline social network facilitates a variety of
analyses, including studying the rate at which infectious diseases may spread
and identifying a subset of actors to immunize in order to reduce, as much as
possible, the rate of spread. Offline social network topologies are typically
estimated by surveying actors and asking them to list their neighbours. While
identifying close friends and family (i.e., strong ties) can typically be done
reliably, listing all of one's acquaintances (i.e., weak ties) is subject to
error due to respondent fatigue. This issue is commonly circumvented through
the use of so-called "fixed choice" surveys where respondents are asked to name
a fixed, small number of their weak ties (e.g., two or ten). Of course, the
resulting crude observed network will omit many ties, and using this crude
network to infer properties of the network, such as its degree distribution or
clustering coefficient, will lead to biased estimates. This paper develops
estimators, based on the method of moments, for a number of network
characteristics including those related to the first and second moments of the
degree distribution as well as the network size, using fixed-choice survey
data. Experiments with simulated data illustrate that the proposed estimators
perform well across a variety of network topologies and measurement scenarios,
and the resulting estimates are significantly more accurate than those obtained
directly using the crude observed network, which are commonly used in the
literature. We also describe a variation of the Jackknife procedure that can be
used to obtain an estimate of the estimator variance.


  An impulsive feedback-adaptive control is developed in order to drive
trajectories of a dynamical system towards an invariant manifold with fixed and
spaced impulsive controls. The approach requires the explicit knowledge of the
set of equations defining the invariant manifold and is based on the concept of
stability exponents of invariant manifolds.


  This paper presents VAEneu, an innovative autoregressive method for multistep
ahead univariate probabilistic time series forecasting. We employ the
conditional VAE framework and optimize the lower bound of the predictive
distribution likelihood function by adopting the Continuous Ranked Probability
Score (CRPS), a strictly proper scoring rule, as the loss function. This novel
pipeline results in forecasting sharp and well-calibrated predictive
distribution. Through a comprehensive empirical study, VAEneu is rigorously
benchmarked against 12 baseline models across 12 datasets. The results
unequivocally demonstrate VAEneu's remarkable forecasting performance. VAEneu
provides a valuable tool for quantifying future uncertainties, and our
extensive empirical study lays the foundation for future comparative studies
for univariate multistep ahead probabilistic forecasting.


  After confirmation of the presence of a nonthermal hard X-ray excess with
respect to the thermal emission in the Coma cluster from two independent
observations, obtained using the Phoswich Detection System onboard BeppoSAX, we
present in this Letter also for Abell 2256 the results of two observations
performed with a time interval of about 2.5 yr. In both spectra a nonthermal
excess is present at a confidence level of ~3.3sigma and ~3.7sigma,
respectively. The combined spectrum obtained by adding up the two spectra
allows to measure an excess at the level of ~4.8sigma in the 20-80 keV energy
range. The nonthermal X-ray flux is in agreement with the published value of
the first observation (Fusco-Femiano et al. 2000) and with that measured by a
Rossi X-Ray Timing Explorer observation (Rephaeli & Gruber 2003).


  Sensitive information is intrinsically tied to interactions in healthcare,
and its protection is of paramount importance for achieving high-quality
patient outcomes. Research in healthcare privacy and security is predominantly
focused on understanding the factors that increase the susceptibility of users
to privacy and security breaches. To understand further, we systematically
review 26 research papers in this domain to explore the existing user studies
in healthcare privacy and security. Following the review, we conducted a
card-sorting exercise, allowing us to identify 12 themes integral to this
subject such as "Data Sharing," "Risk Awareness," and "Privacy." Further to the
identification of these themes, we performed an in-depth analysis of the 26
research papers report on the insights into the discourse within the research
community about healthcare privacy and security, particularly from the user
perspective.


  We study the problem of stabilization for a class of evolution systems with
fractional-damping. After writing the equations as an augmented system we prove
in this article first that the problem is well posed. Second, using the
LaSalle's invariance principle we show that the energy of the system is
Strongly stable. Then, based on a resolvent approach we show a luck of uniform
stabilization. Next, using multiplier techniques combined with the frequency
domain method, we shall give a polynomially stabilization result under some
consideration on the stabilization of an auxiliary dissipating system. Finally,
we give some applications to the wave equation.


  Detection and direct power conversion of high energy and high intensity
ionizing radiation could be a key element in next generation nuclear reactor
safety systems and space-born devices. For example, the Fukushima catastrophe
in 2011 could have been largely prevented if 1\% of the reactor's remnant
radiation ($\gamma$-rays of the nuclear fission) were directly converted within
the reactor to electricity to power the water cooling circuit. It is reported
here that the hybrid halide perovskite methylammonium lead triiodide could
perfectly play the role of a converter. Single crystals were irradiated by a
typical shut-down $\gamma$-spectrum of a nuclear reactor with 7.61E14 Bq
activity exhibit a high-efficiency of $\gamma$-ray to free charge carrier
conversion with radiation hardening. The power density of 0.3 mW/kg of
methylammonium lead triiodide at 50 Sv/h means a four times higher efficiency
than that for silicon-based cells. The material was stable to the limits of the
experiment without changing its performance up to 100 Sv/h dose rate and 57 Sv
H*(10) ambient total $\gamma$-dose. Moreover, the {\gamma}-shielding
performance of methylammonium lead triiodide was found to be superior to both
ordinary and barite concrete.


  In this paper, the 2-category $\mathfrak{Rep}_{{\bf
2Mat}_{\mathbb{C}}}(\mathbb{G})$ of (weak) representations of an arbitrary
(weak) 2-group $\mathbb{G}$ on (some version of) Kapranov and Voevodsky's
2-category of (complex) 2-vector spaces is studied. In particular, the set of
equivalence classes of representations is computed in terms of the invariants
$\pi_0(\mathbb{G})$, $\pi_1(\mathbb{G})$ and $[\alpha]\in
H^3(\pi_0(\mathbb{G}),\pi_1(\mathbb{G}))$ classifying $\mathbb{G}$. Also the
categories of morphisms (up to equivalence) and the composition functors are
determined explicitly. As a consequence, we obtain the the {\it monoidal}
category of linear representations (more generally, the category of
$[z]$-projective representations, for any given cohomology class $[z]\in
H^2(\pi_0(\mathbb{G}),\mathbb{C}^*)) of the first homotopy group
$\pi_0(\mathbb{G})$ as well as its category of representations on finite sets
both live in $\mathfrak{Rep}_{{\bf 2Mat}_{\mathbb{C}}}(\mathbb{G})$, the first
as the monoidal category of endomorphisms of the trivial representation (more
generally, as the category of morphisms between suitable 1-dimensional
representations) and the second as a subcategory of the homotopy category of
$\mathfrak{Rep}_{{\bf 2Mat}_{\mathbb{C}}}(\mathbb{G})$.


  Following an approach developed by Gieseker, Kn\"orrer and Trubowitz for
discretized Schr\"odinger operators, we study the spectral theory of Harper
operators in dimension two and one, as a discretized model of magnetic
Laplacians, from the point of view of algebraic geometry. We describe the
geometry of an associated family of Bloch varieties and compute their density
of states. Finally, we also compute some spectral functions based on the
density of states.
  We discuss the difference between the cases with rational or irrational
parameters: for the two dimensional Harper operator, the compactification of
the Bloch variety is an ordinary variety in the rational case and an
ind-pro-variety in the irrational case. This gives rise, at the
algebro-geometric level of Bloch varieties, to a phenomenon similar to the
Hofstadter butterfly in the spectral theory. In dimension two, the density of
states can be expressed in terms of period integrals over Fermi curves, where
the resulting elliptic integrals are independent of the parameters.
  In dimension one, for the almost Mathieu operator, with a similar argument we
find the usual dependence of the spectral density on the parameter, which gives
rise to the well known Hofstadter butterfly picture.


  We study the dynamics of an electron wave packet in a strong constant crossed
electromagnetic field with account for radiative corrections due to interaction
of the electron with the vacuum fluctuations. We evaluate a wave packet
composed of the solutions to the Dyson-Schwinger equation, which describes
electron propagation without emission of real photons. Spacetime dependence of
the wave packet is obtained analytically for a short time interval, the more
restricted from above the wider is the packet in momentum space. The radiative
corrections alter the electron wavefunction, resulting in particular in a
damping of the wave packet. The expectation value of the Dirac spin operator
also gets modified.


  Linear index coding can be formulated as an interference alignment problem,
in which precoding vectors of the minimum possible length are to be assigned to
the messages in such a way that the precoding vector of a demand (at some
receiver) is independent of the space of the interference (non
side-information) precoding vectors. An index code has rate $\frac{1}{l}$ if
the assigned vectors are of length $l$. In this paper, we introduce the notion
of strictly rate $\frac{1}{L}$ message subsets which must necessarily be
allocated precoding vectors from a strictly $L$-dimensional space ($L=1,2,3$)
in any rate $\frac{1}{3}$ code. We develop a general necessary condition for
rate $\frac{1}{3}$ feasibility using intersections of strictly rate
$\frac{1}{L}$ message subsets. We apply the necessary condition to show that
the presence of certain interference configurations makes the index coding
problem rate $\frac{1}{3}$ infeasible. We also obtain a class of index coding
problems, containing certain interference configurations, which are rate
$\frac{1}{3}$ feasible based on the idea of \textit{contractions} of an index
coding problem. Our necessary conditions for rate $\frac{1}{3}$ feasibility and
the class of rate $\frac{1}{3}$ feasible problems obtained subsume all such
known results for rate $\frac{1}{3}$ index coding.


  Common wisdom has it that small distinctions in the probabilities
(parameters) quantifying a belief network do not matter much for the results of
probabilistic queries. Yet, one can develop realistic scenarios under which
small variations in network parameters can lead to significant changes in
computed queries. A pending theoretical question is then to analytically
characterize parameter changes that do or do not matter. In this paper, we
study the sensitivity of probabilistic queries to changes in network parameters
and prove some tight bounds on the impact that such parameters can have on
queries. Our analytic results pinpoint some interesting situations under which
parameter changes do or do not matter. These results are important for
knowledge engineers as they help them identify influential network parameters.
They also help explain some of the previous experimental results and
observations with regards to network robustness against parameter changes.


  Highly anisotropic "nematically ordered" aerogel induces global uniaxial
anisotropy in superfluid 3He. The anisotropy lowers symmetry of 3He in aerogel
from spherical to axial. As a result instead of one transition temperature in
the state, characterized by the orbital moment l=1 there are two, corresponding
to projections l_z=o and l_z=\pm 1. The splitting of transition has a
pronounced effect on the phase diagram of superfluid 3He and on a structures of
appearing phases. Possible phase diagrams, obtained phenomenologically on a
basis of Landau expansion of thermodynamic potential in a vicinity of the
transition temperature are presented here. The order parameters, corresponding
to each phase and their temperature dependencies are found.


  For n>2, we prove the mod 2 cohomology of the finite Chevalley group
Spin_n(F_q) is isomorphic to that of the classifying space of the loop group of
the spin group Spin(n).


  The characteristic variety plays an important role in the analysis of the
solution space of partial differential equations and exterior differential
systems. This article studies the linear span of this variety, measuring its
dimension via an integrable extension of the original system. In the PDE case
with locally constant characteristic variety, this extension yields a recursive
version of Guillemin normal form, inducing a sequence of foliations on integral
manifolds.


  Deep learning has thrived by training on large-scale datasets. However, in
robotics applications sample efficiency is critical. We propose a novel
adaptive masked proxies method that constructs the final segmentation layer
weights from few labelled samples. It utilizes multi-resolution average pooling
on base embeddings masked with the label to act as a positive proxy for the new
class, while fusing it with the previously learned class signatures. Our method
is evaluated on PASCAL-$5^i$ dataset and outperforms the state-of-the-art in
the few-shot semantic segmentation. Unlike previous methods, our approach does
not require a second branch to estimate parameters or prototypes, which enables
it to be used with 2-stream motion and appearance based segmentation networks.
We further propose a novel setup for evaluating continual learning of object
segmentation which we name incremental PASCAL (iPASCAL) where our method
outperforms the baseline method. Our code is publicly available at
https://github.com/MSiam/AdaptiveMaskedProxies.


  We present the first application to real data from the BOSS DR12 dataset of
the Extractor procedure to determine the acoustic scale imprinted on Baryonic
Acoustic Oscillations (BAO). We show that, being largely insensitive to the
broadband shape of the Power Spectrum, this procedure requires a lower number
of nuisance parameters than those used by the BOSS collaboration, For
non-reconstructed data our analysis improves the accuracy on the acoustic scale
by about 20 %, while for reconstructed ones we get essentially the same level
of accuracy as the BOSS analysis.


  We prove that if a totally disconnected locally compact group admits a
topologically free boundary, then the reduced crossed product of continuous
functions on its Furstenberg boundary by the group is simple. We also prove a
partial converse of this result.


  An exploratory numerical study of the influence of heavy fermion doublets on
the mass of the Higgs boson is performed in the decoupling limit of a chiral
$\rm SU(2)_L \otimes SU(2)_R$ symmetric Yukawa model with mirror fermions. The
behaviour of fermion and boson masses is investigated at infinite bare quartic
coupling on $4^3 \cdot 8$, $6^3 \cdot 12$ and $8^3 \cdot 16$ lattices. A first
estimate of the upper bound on the renormalized quartic coupling as a function
of the renormalized Yukawa-coupling is given.


  We calculate the counting statistics of electron transfer through an open
quantum dot with charging interaction. A dot that is connected to leads by two
single-channel quantum point contacts in an in-plane magnetic field is
described by a Luttinger liquid with impurity at the Toulouse point. We find
that the fluctuations of the current through this conductor exhibit distinctive
interaction effects. Fluctuations saturate at high voltages, while the mean
current increases linearly with the bias voltage. All cumulants higher than the
second one reach at large bias a temperature independent limit.


  Let $\Lambda$ be a connected closed region with smooth boundary contained in
the $d$-dimensional continuous torus $\bb T^d$. In the discrete torus $N^{-1}
\bb T^d_N$, we consider a nearest neighbor symmetric exclusion process where
occupancies of neighboring sites are exchanged at rates depending on $\Lambda$
in the following way: if both sites are in $\Lambda$ or $\Lambda^\complement$,
the exchange rate is one; If one site is in $\Lambda$ and the other one is in
$\Lambda^\complement$ and the direction of the bond connecting the sites is
$e_j$, then the exchange rate is defined as $N^{-1}$ times the absolute value
of the inner product between $e_j$ and the normal exterior vector to
$\p\Lambda$. We show that this exclusion type process has a non-trivial
hydrodynamical behavior under diffusive scaling and, in the continuum limit,
particles are not blocked or reflected by $\partial\Lambda$. Thus the model
represents a system of particles under hard core interaction in the presence of
a permeable membrane which slows down the passage of particles between two
complementar regions.


  Today dropshipping wins the Internet promptly and transformed to one of the
basic tools of marketing in e-commerce. Marketing features, mechanisms and
value dropshipping in the conditions of network economy of the XXI century
reveal in article. The author carries out the comparative analysis of
institutional development dropshipping in the USA, China and Russia.


  In this study, we propose an encoder-decoder structured system with fully
convolutional networks to implement voice activity detection (VAD) directly on
the time-domain waveform. The proposed system processes the input waveform to
identify its segments to be either speech or non-speech. This novel
waveform-based VAD algorithm, with a short-hand notation "WVAD", has two main
particularities. First, as compared to most conventional VAD systems that use
spectral features, raw-waveforms employed in WVAD contain more comprehensive
information and thus are supposed to facilitate more accurate speech/non-speech
predictions. Second, based on the multi-branched architecture, WVAD can be
extended by using an ensemble of encoders, referred to as WEVAD, that
incorporate multiple attribute information in utterances, and thus can yield
better VAD performance for specified acoustic conditions. We evaluated the
presented WVAD and WEVAD for the VAD task in two datasets: First, the
experiments conducted on AURORA2 reveal that WVAD outperforms many
state-of-the-art VAD algorithms. Next, the TMHINT task confirms that through
combining multiple attributes in utterances, WEVAD behaves even better than
WVAD.


  We report on the detection of the alignment between galaxies and large-scale
structure at z~0.6 based on the CMASS galaxy sample from the Baryon Oscillation
Spectroscopy Survey data release 9. We use two statistics to quantify the
alignment signal: 1) the alignment two-point correlation function which probes
the dependence of galaxy clustering at a given separation in redshift space on
the projected angle (theta_p) between the orientation of galaxies and the line
connecting to other galaxies, and 2) the cos(2theta)-statistic which estimates
the average of cos(2theta_p) for all correlated pairs at given separation. We
find significant alignment signal out to about 70 Mpc/h in both statistics.
Applications of the same statistics to dark matter halos of mass above 10^12
M_sun/h in a large cosmological simulation show similar scale-dependent
alignment signals to the observation, but with higher amplitudes at all scales
probed. We show that this discrepancy may be partially explained by a
misalignment angle between central galaxies and their host halos, though
detailed modeling is needed in order to better understand the link between the
orientations of galaxies and host halos. In addition, we find systematic trends
of the alignment statistics with the stellar mass of the CMASS galaxies, in the
sense that more massive galaxies are more strongly aligned with the large-scale
structure.


  The local nonglobal minimizer of trust-region subproblem, if it exists, is
shown to have the second smallest objective function value among all KKT
points. This new property is extended to $p$-regularized subproblem. As a
corollary, we show for the first time that finding the local nonglobal
minimizer of Nesterov-Polyak subproblem corresponds to a generalized eigenvalue
problem.


  The first-passage-time distribution of a leaky integrate-and-fire neuron
driven by a characteristically coloured noise is approximated by matching a
transient and a steady-state solution of the membrane voltage distribution.
These approximations follow from a simple manipulation, made possible by the
specific `eigen' colouring of the noise, which allows to express the membrane
potential as a Gaussian diffusion process on top of a deterministic exponential
movement. Following, the presented method is extended to the case of an
arbitrarily coloured noise driving by factoring out the `eigen' noise and
replacing the residue with an equivalent Gaussian process. It is shown that the
obtained expressions agree well with numerical simulations for different values
of the neuron parameters and noise colouring.


  We examine the properties of the host galaxies of 22,623 narrow-line AGN with
0.02<z<0.3 selected from a complete sample of 122,808 galaxies from the Sloan
Digital Sky Survey. We focus on the luminosity of the [OIII]$\lambda$5007
emission line as a tracer of the strength of activity in the nucleus. We study
how AGN host properties compare to those of normal galaxies and how they depend
on L[OIII]. We find that AGN of all luminosities reside almost exclusively in
massive galaxies and have distributions of sizes, stellar surface mass
densities and concentrations that are similar to those of ordinary early-type
galaxies in our sample. The host galaxies of low-luminosity AGN have stellar
populations similar to normal early-types. The hosts of high- luminosity AGN
have much younger mean stellar ages. The young stars are not preferentially
located near the nucleus of the galaxy, but are spread out over scales of at
least several kiloparsecs. A significant fraction of high- luminosity AGN have
strong H$\delta$ absorption-line equivalent widths, indicating that they
experienced a burst of star formation in the recent past. We have also examined
the stellar populations of the host galaxies of a sample of broad-line AGN. We
conclude that there is no significant difference in stellar content between
type 2 Seyfert hosts and QSOs with the same [OIII] luminosity and redshift.
This establishes that a young stellar population is a general property of AGN
with high [OIII] luminosities.


  Evidence from a large sample of quasar absorption-line spectra in damped
Lyman-alpha systems has suggested a possible time variation of the fine
structure constant alpha. The most statistically significant portion of this
sample involves the comparison of Mg and Fe wavelength shifts using the
many-multiplet (MM) method. However, the sensitivity of this method to the
abundance of heavy isotopes, especially Mg, is enough to imitate an apparent
variation in alpha in the redshift range 0.5 < z < 1.8. We implement recent
yields of intermediate mass (IM) stars into a chemical evolution model and show
that the ensuing isotope distribution of Mg can account for the observed
variation in alpha provided the early IMF was particularly rich in intermediate
mass stars (or the heavy Mg isotope yields from AGB stars are even higher than
in present-day models). As such, these observations of quasar absorption
spectra can be used to probe the nucleosynthetic history of low-metallicity
damped Lyman-alpha systems in the redshift range 0.5 < z < 1.8. This analysis,
in conjunction with other abundance measurements of low-metallicity systems,
reinforces the mounting evidence that star formation at low metallicities may
have been strongly influenced by a population of IM stars. Such IM stars have a
significant influence on other abundances, particularly nitrogen. We constrain
our models with independent measurements of N, Si, and Fe in damped Lyman-alpha
systems as well as C/O in low-metallicity stars. In this way, we obtain
consistent model parameters for this chemical-evolution interpretation of the
MM method results.


  In these two related parts we present a set of methods, analytical and
numerical, which can illuminate the behaviour of quantum system, especially in
the complex systems. The key points demonstrating advantages of this approach
are: (i) effects of localization of possible quantum states, more proper than
"gaussian-like states"; (ii) effects of non-perturbative multiscales which
cannot be calculated by means of perturbation approaches; (iii) effects of
formation of complex quantum patterns from localized modes or classification
and possible control of the full zoo of quantum states, including (meta) stable
localized patterns (waveletons). We'll consider calculations of Wigner
functions as the solution of Wigner-Moyal-von Neumann equation(s) corresponding
to polynomial Hamiltonians. Modeling demonstrates the appearance of (meta)
stable patterns generated by high-localized (coherent) structures or
entangled/chaotic behaviour. We can control the type of behaviour on the level
of reduced algebraical variational system. At the end we presented the
qualitative definition of the Quantum Objects in comparison with their
Classical Counterparts, which natural domain of definition is the category of
multiscale/multiresolution decompositions according to the action of
internal/hidden symmetry of the proper realization of scales of functional
spaces. It gives rational natural explanation of such pure quantum effects as
``self-interaction''(self-interference) and instantaneous quantum interaction.


  We present a robust and scalable preconditioner for the solution of
large-scale linear systems that arise from the discretization of elliptic PDEs
amenable to rank compression. The preconditioner is based on hierarchical
low-rank approximations and the cyclic reduction method. The setup and
application phases of the preconditioner achieve log-linear complexity in
memory footprint and number of operations, and numerical experiments exhibit
good weak and strong scalability at large processor counts in a distributed
memory environment. Numerical experiments with linear systems that feature
symmetry and nonsymmetry, definiteness and indefiniteness, constant and
variable coefficients demonstrate the preconditioner applicability and
robustness. Furthermore, it is possible to control the number of iterations via
the accuracy threshold of the hierarchical matrix approximations and their
arithmetic operations, and the tuning of the admissibility condition parameter.
Together, these parameters allow for optimization of the memory requirements
and performance of the preconditioner.


  Tracking a target in cluttered and dynamic environments is challenging but
forms a core component in applications like aerial cinematography. The
obstacles in the environment not only pose collision risk but can also occlude
the target from the field-of-view of the robot. Moreover, the target future
trajectory may be unknown and only its current state can be estimated. In this
paper, we propose a learned probabilistic neural policy for safe,
occlusion-free target tracking.
  The core novelty of our work stems from the structure of our policy network
that combines generative modeling based on Conditional Variational Autoencoder
(CVAE) with differentiable optimization layers. The role of the CVAE is to
provide a base trajectory distribution which is then projected onto a learned
feasible set through the optimization layer. Furthermore, both the weights of
the CVAE network and the parameters of the differentiable optimization can be
learned in an end-to-end fashion through demonstration trajectories.
  We improve the state-of-the-art (SOTA) in the following respects. We show
that our learned policy outperforms existing SOTA in terms of
occlusion/collision avoidance capabilities and computation time. Second, we
present an extensive ablation showing how different components of our learning
pipeline contribute to the overall tracking task. We also demonstrate the
real-time performance of our approach on resource-constrained hardware such as
NVIDIA Jetson TX2. Finally, our learned policy can also be viewed as a reactive
planner for navigation in highly cluttered environments.


  As computing hardware becomes more specialized, designing environmentally
sustainable computing systems requires accounting for both hardware and
software parameters. Our goal is to design low carbon computing systems while
maintaining a competitive level of performance and operational efficiency.
Despite previous carbon modeling efforts for computing systems, there is a
distinct lack of holistic design strategies to simultaneously optimize for
carbon, performance, power and energy. In this work, we take a data-driven
approach to characterize the carbon impact (quantified in units of CO2e) of
various artificial intelligence (AI) and extended reality (XR) production-level
hardware and application use-cases. We propose a holistic design exploration
framework to optimize and design for carbon-efficient computing systems and
hardware. Our frameworks identifies significant opportunities for carbon
efficiency improvements in application-specific and general purpose hardware
design and optimization. Using our framework, we demonstrate 10$\times$ carbon
efficiency improvement for specialized AI and XR accelerators (quantified by a
key metric, tCDP: the product of total CO2e and total application execution
time), up to 21% total life cycle carbon savings for existing general-purpose
hardware and applications due to hardware over-provisioning, and up to
7.86$\times$ carbon efficiency improvement using advanced 3D integration
techniques for resource-constrained XR systems.


  We have analyzed the far-UV spectrum of two Galactic O4 stars, the O4If+
supergiant HD190429A and the O4V((f)) dwarf HD96715, using archival FUSE and
IUE data. We have conducted a quantitative analysis based on the two NLTE model
atmosphere and wind codes, TLUSTY and CMFGEN. We have derived the stellar and
wind parameters and the surface composition of the two stars. The surface of
HD190429A has a composition typical of an evolved O supergiant (N-rich, C and
O-poor), while HD96715 exhibits surface N enhancement similar to the enrichment
found in SMC O dwarfs and attributed to rotationally-induced mixing. We find
that homogeneous wind models could not match the observed profile of O V1371
and require very low phosphorus abundance to fit the P V1118-1128 resonance
lines. However, we are able to match the O V and P V lines using clumped wind
models. We find that N IV1718 is also sensitive to wind clumping. For both
stars, we have calculated clumped wind models that match well all these lines
from different species and that remain consistent with Halpha data. These fits
therefore provide a coherent and thus much stronger evidence of wind clumping
in O stars than earlier claims. We find that the wind of these two stars is
highly clumped, as expressed by very small volume filling factors, namely
f=0.04 for HD190429A and f=0.02 for HD96715. In agreement with our analysis of
SMC stars, clumping starts deep in the wind, just above the sonic point. The
most crucial consequence of our analysis is that the mass loss rates of O stars
need to be revised downward significantly, by a factor of 3 and more.
Accounting for wind clumping is essential when determining the wind properties
of O stars. Our study therefore calls for a fundamental revision in our
understanding of mass loss and of O-type star winds. (abridged)


  We study theoretically the critical current in semiconductor nanowire
Josephson junction with strong spin-orbit interaction. The critical current
oscillates by an external magnetic field. We reveal that the oscillation of
critical current depends on the orientation of magnetic field in the presence
of spin-orbit interaction. We perform a numerical simulation for the nanowire
by using a tight-binding model. The Andreev levels are calculated as a function
of phase difference $\varphi$ between two superconductors. The DC Josephson
current is evaluated from the Andreev levels in the case of short junctions.
The spin-orbit interaction induces the effective magnetic field. When the
external field is parallel with the effective one, the critical current
oscillates accompanying the $0$-$\pi$ like transition. The period of
oscillation is longer as the angle between the external and effective fields is
larger.


  The connection between the axion and right-handed neutrinos is explored in
the framework of the minimal SUSY SO(10) model. The former is related to the
Peccei-Quinn (PQ) solution to the strong CP problem and the latter is to the
light Majorana neutrinos through the see-saw mechanism. In this model, a
relative phase between $({\bf 10,1,3}) (\equiv {\bf \bar{\Delta}}_R) \subset
{\bf \bar{126}}$ and $({\bf \bar{10},1,3}) (\equiv {\bf \Delta}_R) \subset {\bf
126}$ multiplets of ${\rm SU}(4) \times {\rm SU}(2)_L \times {\rm SU}(2)_R
\subset {\rm SO}(10)$ becomes a physical degree of freedom identified with the
axion. Then, the PQ symmetry breaking scale ($\Lambda_{\rm PQ}$) and the $B-L$
symmetry breaking scale ($\Lambda_{\rm B-L}$) coincide through the VEV of ${\bf
\bar{\Delta}}_R$. The scalar partner of the lightest right-handed neutrino is
regarded as the inflaton, which gives a consistent density fluctuation for the
CMB.


  We present a number of low-resource approaches to the tasks of the Zero
Resource Speech Challenge 2021. We build on the unsupervised representations of
speech proposed by the organizers as a baseline, derived from CPC and clustered
with the k-means algorithm. We demonstrate that simple methods of refining
those representations can narrow the gap, or even improve upon the solutions
which use a high computational budget. The results lead to the conclusion that
the CPC-derived representations are still too noisy for training language
models, but stable enough for simpler forms of pattern matching and retrieval.


  Energetic positrons have been observed in the interstellar medium, and
high-energy positrons with relativistic energies up to approximately 1 TeV have
been detected in Galactic cosmic rays. We conducted a study on the acceleration
of particles, specifically positrons, in a nonrelativistic quasiparallel
collisionless shock induced by a plasma consisting of protons, electrons, and
positrons. The positron-to-proton number density ratio in the plasma is 0.1. We
focused on a representative shock with a sonic Mach number of 17.1 and an
Alfv\'{e}nic Mach number of 16.8 in the rest frame of the shock. To investigate
the acceleration mechanisms of particles including positrons in the shock, we
utilized one-dimensional particle-in-cell (PIC) simulations. It was found that
all three species of particles in the shock can be accelerated and exhibit
power law spectra. At the shock front, a significant portion of incoming
upstream particles are reflected and undergo significant energy increase, and
these reflected particles can be efficiently injected into the process of
diffusive shock acceleration (DSA). Moveover, the reflected positrons can be
further accelerated by an electric field parallel to the magnetic field when
they move along the magnetic field upstream of the shock. As a result,
positrons can be preferentially accelerated to be injected in the DSA process
compared to electrons.


  We provide a theoretical analysis of recently measured fusion cross sections
which show a surprising enhancement at low $E_\mathrm{c.m.}$ energies for the
system $^{132}$Sn+$^{40}$Ca as compared to the more neutron-rich system
$^{132}$Sn+$^{48}$Ca. Dynamic microscopic calculations are carried out on a
three-dimensional lattice with a time-dependent density-constrained density
functional theory. There are no adjustable parameters, the only input is the
Skyrme effective NN interaction. Heavy-ion potentials $V(R)$,
coordinate-dependent mass parameters $M(R)$, and total fusion cross sections
$\sigma(E_\mathrm{c.m.})$ are calculated for both systems. We are able to
explain the measured fusion enhancement in terms of the {\it narrower width} of
the ion-ion potential for $^{132}$Sn+$^{40}$Ca, while the barrier heights and
positions are approximately the same in both systems.


  Cloud providers sell their idle capacity on markets through an auction-like
mechanism to increase their return on investment. The instances sold in this
way are called spot instances. In spite that spot instances are usually 90%
cheaper than on-demand instances, they can be terminated by provider when their
bidding prices are lower than market prices. Thus, they are largely used to
provision fault-tolerant applications only. In this paper, we explore how to
utilize spot instances to provision web applications, which are usually
considered availability-critical. The idea is to take advantage of differences
in price among various types of spot instances to reach both high availability
and significant cost saving. We first propose a fault-tolerant model for web
applications provisioned by spot instances. Based on that, we devise novel
auto-scaling polices for hourly billed cloud markets. We implemented the
proposed model and policies both on a simulation testbed for repeatable
validation and Amazon EC2. The experiments on the simulation testbed and the
real platform against the benchmarks show that the proposed approach can
greatly reduce resource cost and still achieve satisfactory Quality of Service
(QoS) in terms of response time and availability.


  The completely positive rank is an analogue of topological covering
dimension, defined for nuclear C*-algebras via completely positive
approximations. These may be thought of as simplicial approximations of the
algebra, which leads to the concept of piecewise homogeneous maps and a notion
of noncommutative simplicial complexes.
  We introduce a technical variation of the completely positive rank and show
that the two theories coincide in many important cases. Furthermore we analyze
some of their properties; in particular we show that both theories behave
nicely with respect to ideals and that they coincide with covering dimension of
the spectrum for certain continuous trace C*-algebras.


  We study multi-parameter sensing of 2D and 3D vector fields within the
Bayesian framework for $SU(2)$ quantum interferometry. We establish a method to
determine the optimal quantum sensor, which establishes the fundamental limit
on the precision of simultaneously estimating multiple parameters with an
$N$-atom sensor. Keeping current experimental platforms in mind, we present
sensors that have limited entanglement capabilities, and yet, significantly
outperform sensors that operate without entanglement and approach the optimal
quantum sensor in terms of performance. Furthermore, we show how these sensors
can be implemented on current programmable quantum sensors with variational
quantum circuits by minimizing a metrological cost function. The resulting
circuits prepare tailored entangled states and perform measurements in an
appropriate entangled basis to realize the best possible quantum sensor given
the native entangling resources available on a given sensor platform. Notable
examples include a 2D and 3D quantum ``compass'' and a 2D sensor that provides
a scalable improvement over unentangled sensors. Our results on optimal and
variational multi-parameter quantum metrology are useful for advancing
precision measurements in fundamental science and ensuring the stability of
quantum computers, which can be achieved through the incorporation of optimal
quantum sensors in a quantum feedback loop.


  Zooplankton images, like many other real world data types, have intrinsic
properties that make the design of effective classification systems difficult.
For instance, the number of classes encountered in practical settings is
potentially very large, and classes can be ambiguous or overlap. In addition,
the choice of taxonomy often differs between researchers and between
institutions. Although high accuracy has been achieved in benchmarks using
standard classifier architectures, biases caused by an inflexible
classification scheme can have profound effects when the output is used in
ecosystem assessments and monitoring.
  Here, we propose using a deep convolutional network to construct a vector
embedding of zooplankton images. The system maps (embeds) each image into a
high-dimensional Euclidean space so that distances between vectors reflect
semantic relationships between images. We show that the embedding can be used
to derive classifications with comparable accuracy to a specific classifier,
but that it simultaneously reveals important structures in the data.
Furthermore, we apply the embedding to new classes previously unseen by the
system, and evaluate its classification performance in such cases.
  Traditional neural network classifiers perform well when the classes are
clearly defined a priori and have sufficiently large labeled data sets
available. For practical cases in ecology as well as in many other fields this
is not the case, and we argue that the vector embedding method presented here
is a more appropriate approach.


  We present a unique application of OxRAM devices in CMOS Image Sensors (CIS)
for dynamic range (DR) improvement. We propose a modified 3T-APS (Active Pixel
Sensor) circuit that incorporates OxRAM in 1T-1R configuration. DR improvement
is achieved by resistive compression of the pixel output signal through
autonomous programming of OxRAM device resistance during exposure. We show that
by carefully preconditioning the OxRAM resistance, pixel DR can be enhanced.
Detailed impact of OxRAM SET-to-RESET and RESET-to-SET transitions on pixel DR
is discussed. For experimental validation with specific OxRAM preprogrammed
states, a 4 Kb 10 nm thick HfOx (1T-1R) matrix was fabricated and
characterized. Best case, relative pixel DR improvement of ~ 50 dB was obtained
for our design.


  We generalize the work of M. Harris and R. Taylor on the local Langlands
correspondence for the linear group over $\mathbb{Q}_p$. We prove some cases of
the Kottwitz conjectures for the supercuspidal part of the compactly supported
$\ell$-adic cohomology of Rapoport-Zink rigid-analytic spaces. This means that
we decompose this part in terms of local Langlands correspondences.
  In particular, we prove the first case of a non-abelian reciprocity law
constructed geometrically and associated to groups other than inner forms of
the linear group. More precisely, we do this for the unramified unitary group
in three variables over $\mathbb{Q}_p$.


  An initial-boundary value in a strip with homogeneous Dirichlet boundary
conditions for two-dimensional Zakharov-Kuznetsov-Burgers equation is
considered. Results on global well-posedness and long-time decay of solutions
in Sobolev spaces are established.


  We consider non-homogeneous media with properties which can be characterized
by rapidly oscillated coefficients. For such coefficients we define a notion of
two-scale extension, present several ways to construct two-scale extensions,
discuss their properties and relation to homogenization


  The qualitative reliability of the dynamical mean field theory (DMFT) is
investigated for systems in which either the actual carrier density or the
effective carrier density is low, by comparing the exact perturbative and
dynamical mean field expressions of electron scattering rates and optical
conductivities. We study two interacting systems: tight binding models in which
the chemical potential is near a band edge and Dirac systems in which the
chemical potential is near the Dirac point. In both systems it is found that
DMFT underestimates the low frequency, near-Fermi surface single particle
scattering rate by a factor proportional to the particle density. The
quasiparticle effective mass is qualitatively incorrect for the low density
tight binding model but not necessarily for Dirac systems. The dissipative part
of the optical conductivity is more subtle: in the exact calculation vertex
corrections, typically neglected in DMFT calculations, suppress the low
frequency optical absorption, compensating for some of the DMFT underestimate
of the scattering rate. The role of vertex corrections in calculating the
conductivity for Dirac systems is clarified and a systematic discussion is
given of the approach to the Galilean/Lorentz invariant low density limit.
Relevance to recent calculations related to Weyl metals is discussed.


  We present for the first time Very-Long-Baseline Interferometry images of the
radio galaxy Cygnus A at the frequency of $86$ $\rm GHz$. Thanks to the high
spatial resolution of only ${\sim}200$ Schwarzschild radii ($R_{\bf S}$), such
observations provide an extremely detailed view of the nuclear regions in this
archetypal object and allow us to derive important constraints for theoretical
models describing the launching of relativistic jets. A pixel-based analysis of
the jet outflow, which still appears two-sided on the scales probed, was
performed. By fitting Gaussian functions to the transverse intensity profiles,
we could determine the jet width in the nuclear region. The base of the jets
appears wide. The minimum measured transverse width of ${\sim} (227\pm98)$
$R_{\bf S}$ is significantly larger than the radius of the Innermost Stable
Circular Orbit, suggesting that the outer accretion disk is contributing to the
jet launching. The existence of a faster and Doppler de-boosted inner section,
powered either from the rotation of the inner regions of the accretion disk or
by the spinning black hole, is suggested by the kinematic properties and by the
observed limb brightening of the flow.


  Consider a broken geodesics $\alpha([0,l])$ on a compact Riemannian manifold
$(M,g)$ with boundary of dimension $n\geq 3$. The broken geodesics are unions
of two geodesics with the property that they have a common end point. Assume
that for every broken geodesic $\alpha([0,l])$ starting at and ending to the
boundary $\partial M$ we know the starting point and direction
$(\alpha(0),\alpha'(0))$, the end point and direction $(\alpha(l),\alpha'(l))$,
and the length $l$. We show that this data determines uniquely, up to an
isometry, the manifold $(M,g)$. This result has applications in inverse
problems on very heterogeneous media for situations where there are many
scattering points in the medium, and arises in several applications including
geophysics and medical imaging. As an example we consider the inverse problem
for the radiative transfer equation (or the linear transport equation) with a
non-constant wave speed. Assuming that the scattering kernel is everywhere
positive, we show that the boundary measurements determine the wave speed
inside the domain up to an isometry.


  A numerical method using discontinuous polynomial approximations is
formulated for solving a phase-field model of two immiscible fluids with a
soluble surfactant. The scheme recovers the Langmuir adsorption isotherms at
equilibrium. Simulations of spinodal decomposition, flow through a cylinder and
flow through a sequence of pore throats show the dynamics of the flow with and
without surfactant. Finally the numerical method is used to simulate fluid
flows in the pore space of Berea sandstone obtained by micro-CT imaging.


  We analyze a variational time discretization of geodesic calculus on finite-
and certain classes of infinite-dimensional Riemannian manifolds. We
investigate the fundamental properties of discrete geodesics, the associated
discrete logarithm, discrete exponential maps, and discrete parallel transport,
and we prove convergence to their continuous counterparts. The presented
analysis is based on the direct methods in the calculus of variation, on
$\Gamma$-convergence, and on weighted finite element error estimation. The
convergence results of the discrete geodesic calculus are experimentally
confirmed for a basic model on a two-dimensional Riemannian manifold.
  This provides a theoretical basis for applications in computer vision: In
particular, discrete geodesics offer an effective tool for shape morphing and
the computation of a distance between shapes, the discrete logarithm allows a
linear representation of strongly nonlinear shape variability, the discrete
exponential map provides a robust tool for shape extrapolation, and the
discrete parallel transport can be used to transfer geometric details from one
shape to another. The basic operations are exemplarily illustrated for two
different shape spaces, the space of viscous volumetric objects and the space
of discrete viscous shells.


  Braid theory is used to calcualte the topological entropy of data from the
belousov-Zhabotinskii reaction, the results agree well with one-dimensional
theory to the order of approximation considered.


  We introduce specific solutions to the linear harmonic oscillator, named
bubbles. They form resonant families of invariant tori of the linear dynamics,
with arbitrarily large Sobolev norms. We use these modulated bubbles of energy
to construct a class of potentials which are real, smooth, time dependent and
uniformly decaying to zero with respect to time, such that the corresponding
perturbed quantum harmonic oscillator admits solutions which exhibit a
logarithmic growth of Sobolev norms. The resonance mechanism is explicit in
space variables and produces highly oscillatory solutions. We then give several
recipes to construct similar examples using more specific tools based on the
continuous resonant (CR) equation in dimension two.


  In this work, we propose a new source for gravitational wave (GW) radiation
associated with the quantum chromodynamics (QCD) phase transition in the inner
cores of neutron stars. The mechanism is based on the bubble dynamics during
the first-order phase transition from nuclear matter to quark matter. We
identify the characteristic frequency to be of order $\omega_c\sim 10^6~{\rm
rad/s}$ for this kind of sources and the strain magnitude ($h\sim 10^{-24}$ for
a neutron star at a distance of $0.1~{\rm Mpc}$) reachable by future GW
detectors. The GW spectra are shown to be useful to check the transition nature
at high baryon chemical potential as well as to constrain the radius and
density of the inner cores, which are still indistinct up to now.


  The radiation from extreme Reissner-Nordstr\"{o}m black holes is computed by
explicitly considering the collapse of a spherical charged shell. No neutral
scalar radiation is found but there is emission of charged particles, provided
the charge to mass ratio be different from one. The absence of thermal effects
is in accord with the predictions of the euclidean theory but since the body
emits charged particles the entropy issue is not the same as for eternal
extreme black holes.


  Let $L_{D_{\ell}}(-\ell +{3/2},0)$ (resp. $L_{B_{\ell}}(-\ell +{3/2},0)$) be
the simple vertex operator algebra associated to affine Lie algebra of type
$D_{\ell}^{(1)}$ (resp. $B_{\ell}^{(1)}$) with the lowest admissible
half-integer level $-\ell + {3/2}$. We show that $L_{D_{\ell}}(-\ell +{3/2},0)$
is a vertex subalgebra of $L_{B_{\ell}}(-\ell +{3/2},0)$ with the same
conformal vector. For $\ell =4$, $L_{D_{4}}(-{5/2},0)$ is a vertex subalgebra
of three copies of $L_{B_{4}}(-{5/2},0)$ contained in $L_{F_{4}}(-{5/2},0)$,
and all five of these vertex operator algebras have the same conformal vector.


  Recent studies seem to suggest that the stellar initial mass function (IMF)
in early-type galaxies might be different from a classical Kroupa or Chabrier
IMF, i.e. contain a larger fraction of the total mass in low-mass stars. From a
theoretical point of view, supersonic turbulence has been the subject of
interest in many analytical theories proposing a strong correlation with the
characteristic mass of the core mass function (CMF) in star forming regions,
and as a consequence with the stellar IMF. Performing two suites of smoothed
particles hydrodynamics (SPH) simulations with different mass resolutions, we
aim at testing the effects of variations in the turbulent properties of a
dense, star forming molecular cloud on the shape of the system mass function in
different density regimes. While analytical theories predict a shift of the
peak of the CMF towards lower masses with increasing velocity dispersion of the
cloud, we observe in the low-density regime the opposite trend, with high Mach
numbers giving rise to a top-heavy mass distribution. For the high-density
regime we do not find any trend correlating the Mach number with the
characteristic mass of the resulting IMF, implying that the dynamics of
protostellar accretion discs and fragmentation on small scales is not strongly
affected by turbulence driven at the scale of the cloud. Furthermore, we
suggest that a significant fraction of dense cores are disrupted by turbulence
before stars can be formed in their interior through gravitational collapse.
Although this particular study has limitations in its numerical resolution, we
suggest that our results, along with those from other studies, cast doubt on
the turbulent fragmentation models on the IMF that simply map the CMF to the
IMF.


  The Event Horizon Telescope is a global very-long baseline interferometer
capable of probing potential deviations from the Kerr metric, which is believed
to provide the unique description of astrophysical black holes. Here we report
an updated constraint on the quadrupolar deviation of Sagittarius A* within the
context of a radiatively inefficient accretion flow model in a quasi-Kerr
background. We also simulate near-future constraints obtainable by the
forthcoming eight-station array and show that in this model already a one-day
observation can measure the spin magnitude to within $0.005$, the inclination
to within $0.09^\circ$, the position angle to within $0.04^\circ$, and the
quadrupolar deviation to within $0.005$ at $3\sigma$ confidence. Thus, we are
entering an era of high-precision strong gravity measurements.


  We construct a new class of quantum vertex algebras associated with the
normalized Yang $R$-matrix. They are obtained as Yangian deformations of
certain $\mathcal{S}$-commutative quantum vertex algebras and their
$\mathcal{S}$-locality takes the form of a single $RTT$-relation. We establish
some preliminary results on their representation theory and then further
investigate their braiding map. In particular, we show that its fixed points
are closely related with Bethe subalgebras in the Yangian quantization of the
Poisson algebra $\mathcal{O}(\mathfrak{gl}_N((z^{-1})))$, which were recently
introduced by Krylov and Rybnikov. Finally, we extend this construction of
commutative families to the case of trigonometric $R$-matrix of type $A$.


  We derive explicit integrability conditions for stochastic integrals taken
over time and space driven by a random measure. Our main tool is a canonical
decomposition of a random measure which extends the results from the purely
temporal case. We show that the characteristics of this decomposition can be
chosen as predictable strict random measures, and we compute the
characteristics of the stochastic integral process. We apply our conditions to
a variety of examples, in particular to ambit processes, which represent a rich
model class.


  In part 1 we identified a new coupling between death spikes and birth dips
that occurs following catastrophic events such as influenza pandemics and
earthquakes. Here we seek to characterize some of the key features. We
introduce a transfer function defined as the amplitude of the birth trough (the
output) divided by the amplitude of the death spike (the input). This has two
features: it is always smaller than one so is an attenuation factor and as a
function of the amplitude of the death spike, it may be characterized by a
power law with exponent close to unity. Since many countries do not publish
monthly data, merely annual data, we attempt to extend the analysis to cover
such data and how to identify the death-birth coupling. Finally we compare the
response to unexpected death spikes and regular seasonal death peaks, such as
winter death peaks which occur annually in many countries.


  We show that for any semilinear partial differential equation of order m, the
infinitesimals of the independent variables depend only on the independent
variables and, if m>1 and the equation is also linear in its derivatives of
order m-1 of the dependent variable, then the infinitesimal of the dependent
variable is at most linear on the dependent variable. Many examples of
important partial differential equations in Analysis, Geometry and Mathematical
- Physics are given in order to enlighten the main result.


  The usual modelling of the syllogisms of the Organon by a calculus of classes
does not include relations. Aristotle may however have envisioned them in the
first two books as the category of relatives, where he allowed them to compose
with themselves. Composition is the main operation in combinatory logic, which
therefore offers itself for a new kind of modelling. The resulting calculus
includes also composition of predicates by logical connectives.


  The coherent interaction of light with matter imprints the phase information
of the light field on the wavefunction of the photon-dressed electronic state.
Driving electric field, together with a stable phase that is associated with
the optical probe pulses, enables the role of the dressed state in the optical
response to be investigated. We observed optical absorption strengths modulated
on a sub-cycle timescale in a GaAs quantum well in the presence of a
multi-cycle terahertz driving pulse using a near-infrared probe pulse. The
measurements were in good agreement with the analytical formula that accounts
for the optical susceptibilities caused by the dressed state of excitons, which
indicates that the output probe intensity was coherently reshaped by the
excitonic sideband emissions.


  The Rogers-Szeg\"o polynomials are natural q-analogues of Newton binomials.
In general they have no closed expression. We consider some exceptional cases
which are products of a factor with a closed formula and another one with nice
values for q=1 and q=-1. These are related to normalized Rogers-Szeg\"o
polynomials which have nice expansions and Hankel determinants. The Exposition
of the paper is elementary and almost self-contained.


  The Gaia spacecraft has just released a large set of parallaxes, including 41
novae for which the fractional error is <30%. I have used these to evaluate the
accuracy and bias of the many prior methods for getting nova-distances. The
best of the prior methods is the geometrical parallaxes from HST for just four
novae, although the real error bars are 3X larger than stated. The canonical
method for prior nova-distances has been the expansion parallaxes from the nova
shells, but this method is found to have real 1-sigma uncertainty of 0.95 mag
in the distance modulus, and the prior quoted error bars are on average 3.6X
worse than advertised. The many variations on the
maximum-magnitude-rate-of-decline (MMRD) relation are all found to be poor, too
poor to be useable, and even to be non-applicable for 5-out-of-7 samples of
nova, so the MMRD should no longer be used. The prior method of using various
measures of the extinction from the interstellar medium have been notoriously
bad, but now a new version by Ozdonmez and coworkers has improved this to an
unbiased method with 1-sigma uncertainty of 1.14 mag in the distance modulus.
For the future, I recommend in order (1) using the Gaia parallax, (2) using the
catalog of Ozdonmez, (3) using M_max = -7.0 +- 1.4 mag as an empirical method
of poor accuracy, and (4) if none of these methods is available, then to not
use the nova for purposes where a distance is needed.


  Efficient and robust algorithms for decentralized estimation in networks are
essential to many distributed systems. Whereas distributed estimation of sample
mean statistics has been the subject of a good deal of attention, computation
of $U$-statistics, relying on more expensive averaging over pairs of
observations, is a less investigated area. Yet, such data functionals are
essential to describe global properties of a statistical population, with
important examples including Area Under the Curve, empirical variance, Gini
mean difference and within-cluster point scatter. This paper proposes new
synchronous and asynchronous randomized gossip algorithms which simultaneously
propagate data across the network and maintain local estimates of the
$U$-statistic of interest. We establish convergence rate bounds of $O(1/t)$ and
$O(\log t / t)$ for the synchronous and asynchronous cases respectively, where
$t$ is the number of iterations, with explicit data and network dependent
terms. Beyond favorable comparisons in terms of rate analysis, numerical
experiments provide empirical evidence the proposed algorithms surpasses the
previously introduced approach.


  We design a Quasi-Polynomial time deterministic approximation algorithm for
computing the integral of a multi-dimensional separable function, supported by
some underlying hyper-graph structure, appropriately defined. Equivalently, our
integral is the partition function of a graphical model with continuous
potentials. While randomized algorithms for high-dimensional integration are
widely known, deterministic counterparts generally do not exist. We use the
correlation decay method applied to the Riemann sum of the function to produce
our algorithm. For our method to work, we require that the domain is bounded
and the hyper-edge potentials are positive and bounded on the domain. We
further assume that upper and lower bounds on the potentials separated by a
multiplicative factor of $1 + O(1/\Delta^2)$, where $\Delta$ is the maximum
degree of the graph. When $\Delta = 3$, our method works provided the upper and
lower bounds are separated by a factor of at most $1.0479$. To the best of our
knowledge, our algorithm is the first deterministic algorithm for
high-dimensional integration of a continuous function, apart from the case of
trivial product form distributions.


  We discuss non-conformal gauge theories from type IIB D3-branes embedded in
orbifolded space-times. Such theories can be obtained by allowing some
non-vanishing logarithmic twisted tadpoles. In certain cases with N=0,1
supersymmetry correlation functions in the planar limit are the same as in the
parent N=2 supersymmetric theories. In particular, the effective action in such
theories perturbatively is not renormalized beyond one loop in the planar
limit. In the N=2 as well as such N=0,1 theories quantum corrections in the
D3-brane gauge theories are encoded in the corresponding classical higher
dimensional field theories whose actions contain the twisted fields with
non-vanishing tadpoles. We argue that this duality can be extended to the
non-perturbative level in the N=2 theories. We give some evidence that this
might also be the case for N=0,1 theories as well.


  The conventional picture for the origin of the polarization of a supernova is
based on a model of Thomson or resonance scattering of photons traveling
through an aspherical supernova atmosphere. Positive detection of intrinsic
polarization in SN 1987A is then interpretated as evidence of an asymmetrical
supernova atmosphere. We show here a different view based on the scattering of
the supernova light by a dusty circumstellar material (CSM), or the ``light
echo'' effect. At a given epoch after the explosion, the observed photons
consist of both those propagating directly from the supernova and those
scattered by dust particles in the CSM. Polarized light can be produced if the
distribution of the dust particles is aspherical. The model can reproduce both
the time evolution of the observed broad band polarization of SN 1987A and
major features of the polarization spectra. It is also successful in providing
a natural model for the early infrared light curve, in particular the observed
30 day delay of the IR maximum compared to the maximum of the bolometric light
curve.


  Which part of medicine, if any, can and should be entrusted to AI, now or at
some moment in the future? That both medicine and AI will continue to change
goes without saying.


  The categoricity spectrum of a class of structures is the collection of
cardinals in which the class has a single model up to isomorphism. Assuming
that cardinal exponentiation is injective (a weakening of the generalized
continuum hypothesis, GCH), we give a complete list of the possible
categoricity spectrums of an abstract elementary class with amalgamation and
arbitrarily large models. Specifically, the categoricity spectrum is either
empty, an end segment starting below the Hanf number, or a closed interval
consisting of finite successors of the L\"owenheim-Skolem-Tarski number (there
are examples of each type). We also prove (assuming a strengthening of the GCH)
that the categoricity spectrum of an abstract elementary class with no maximal
models is either bounded or contains an end segment. This answers several
longstanding questions around Shelah's categoricity conjecture.