  In recent years, powered by the learned discriminative representation via
graph neural network (GNN) models, deep graph matching methods have made great
progresses in the task of matching semantic features. However, these methods
usually rely on heuristically generated graph patterns, which may introduce
unreliable relationships to hurt the matching performance. In this paper, we
propose a joint \emph{graph learning and matching} network, named GLAM, to
explore reliable graph structures for boosting graph matching. GLAM adopts a
pure attention-based framework for both graph learning and graph matching.
Specifically, it employs two types of attention mechanisms, self-attention and
cross-attention for the task. The self-attention discovers the relationships
between features and to further update feature representations over the learnt
structures; and the cross-attention computes cross-graph correlations between
the two feature sets to be matched for feature reconstruction. Moreover, the
final matching solution is directly derived from the output of the
cross-attention layer, without employing a specific matching decision module.
The proposed method is evaluated on three popular visual matching benchmarks
(Pascal VOC, Willow Object and SPair-71k), and it outperforms previous
state-of-the-art graph matching methods by significant margins on all
benchmarks. Furthermore, the graph patterns learnt by our model are validated
to be able to remarkably enhance previous deep graph matching methods by
replacing their handcrafted graph structures with the learnt ones.


  In-context learning (ICL) enables large language models (LLMs) to adapt to
new tasks by conditioning on demonstrations of question-answer pairs and it has
been shown to have comparable performance to costly model retraining and
fine-tuning. Recently, ICL has been extended to allow tabular data to be used
as demonstration examples by serializing individual records into natural
language formats. However, it has been shown that LLMs can leak information
contained in prompts, and since tabular data often contain sensitive
information, understanding how to protect the underlying tabular data used in
ICL is a critical area of research. This work serves as an initial
investigation into how to use differential privacy (DP) -- the long-established
gold standard for data privacy and anonymization -- to protect tabular data
used in ICL. Specifically, we investigate the application of DP mechanisms for
private tabular ICL via data privatization prior to serialization and
prompting. We formulate two private ICL frameworks with provable privacy
guarantees in both the local (LDP-TabICL) and global (GDP-TabICL) DP scenarios
via injecting noise into individual records or group statistics, respectively.
We evaluate our DP-based frameworks on eight real-world tabular datasets and
across multiple ICL and DP settings. Our evaluations show that DP-based ICL can
protect the privacy of the underlying tabular data while achieving comparable
performance to non-LLM baselines, especially under high privacy regimes.


  Within Bohm`s interpretation of quantum mechanics particles follow classical
trajectories that are determined by the full solution of the time dependent
Schroedinger equation. If this interpretation is consistent it must be possible
to determine the probability distribution at time t from the probability
distribution at time t=0 by using these trajectories. In this paper it is shown
that this is the case indeed.


  I describe some examples in support of the conjecture that the horizon area
of a near equilibrium black hole is an adiabatic invariant. These include a
Schwarzschild black hole perturbed by quasistatic scalar fields (which may be
minimally or nonminimally coupled to curvature), a Kerr black under the
influence of scalar radiation at the superradiance treshold, and a
Reissner--Nordstr\"om black hole absorbing a charge marginally. These clarify
somewhat the conditions under which the conjecture would be true. The desired
``adiabatic theorem'' provides an important motivation for a scheme for black
hole quantization.


  This paper highlights a practical research of the possibility of forming
quantum circuits for training neural networks. The demonstrated quantum
circuits were based on the principles of Grover's Search Algorithm. The
perceptron was chosen as the architecture for the example neural network. The
multilayer perceptron is a popular neural network architecture due to its
scalability and applicability for solving a wide range of problems.


  In this work, we investigate the dynamics of stochastic gradient descent
(SGD) when training a single-neuron autoencoder with linear or ReLU activation
on orthogonal data. We show that for this non-convex problem, randomly
initialized SGD with a constant step size successfully finds a global minimum
for any batch size choice. However, the particular global minimum found depends
upon the batch size. In the full-batch setting, we show that the solution is
dense (i.e., not sparse) and is highly aligned with its initialized direction,
showing that relatively little feature learning occurs. On the other hand, for
any batch size strictly smaller than the number of samples, SGD finds a global
minimum which is sparse and nearly orthogonal to its initialization, showing
that the randomness of stochastic gradients induces a qualitatively different
type of "feature selection" in this setting. Moreover, if we measure the
sharpness of the minimum by the trace of the Hessian, the minima found with
full batch gradient descent are flatter than those found with strictly smaller
batch sizes, in contrast to previous works which suggest that large batches
lead to sharper minima. To prove convergence of SGD with a constant step size,
we introduce a powerful tool from the theory of non-homogeneous random walks
which may be of independent interest.


  We derive a formula which relates the QCD potentials in momentum space and in
position space in terms of the beta-function of the renormalization-group
equation for the potential. This formula is used to study the theoretical
uncertainties in the potential and in particular in its application to the
determination of the pole mass m_b when we use perturbative expansions. We
demonstrate the existence of these uncertainties for the Richardson potential
explicitly and then discuss the limited theoretical accuracy in the
perturbative QCD potential. We conclude that a theoretical uncertainty of m_b
much below 100 MeV would not be achievable within perturbative QCD.


  Cyanogen (NCCN) is the simplest member of the series of dicyanopolyynes. It
has been hypothesized that this family of molecules can be important
constituents of interstellar and circumstellar media, although the lack of a
permanent electric dipole moment prevents its detection through
radioastronomical techniques. Here we present the first solid evidence of the
presence of cyanogen in interstellar clouds through the detection of its
protonated form toward the cold dark clouds TMC-1 and L483. Protonated cyanogen
(NCCNH+) has been identified through the J=5-4 and J=10-9 rotational
transitions using the 40m radiotelescope of Yebes and the IRAM 30m telescope.
We derive beam averaged column densities for NCCNH+ of (8.6+/-4.4)e10 cm-2 in
TMC-1 and (3.9+/-1.8)e10 cm-2 in L483, which translate to fairly low fractional
abundances relative to H2, in the range (1-10)e-12. The chemistry of protonated
molecules in dark clouds is discussed, and it is found that, in general terms,
the abundance ratio between the protonated and non protonated forms of a
molecule increases with increasing proton affinity. Our chemical model predicts
an abundance ratio NCCNH+/NCCN of 1e-4, which implies that the abundance of
cyanogen in dark clouds could be as high as (1-10)e-8 relative to H2, i.e.,
comparable to that of other abundant nitriles such as HCN, HNC, and HC3N.


  Value iteration is a commonly used and empirically competitive method in
solving many Markov decision process problems. However, it is known that value
iteration has only pseudo-polynomial complexity in general. We establish a
somewhat surprising polynomial bound for value iteration on deterministic
Markov decision (DMDP) problems. We show that the basic value iteration
procedure converges to the highest average reward cycle on a DMDP problem in
heta(n^2) iterations, or heta(mn^2) total time, where n denotes the number of
states, and m the number of edges. We give two extensions of value iteration
that solve the DMDP in heta(mn) time. We explore the analysis of policy
iteration algorithms and report on an empirical study of value iteration
showing that its convergence is much faster on random sparse graphs.


  We propose a criterion to characterize interacting theories in a suitable
Wightman framework of relativistic quantum field theories which incorporates a
"singularity hypothesis", which has been conjectured for a long time, is
supported by renormalization group theory, but has never been formulated
mathematically. The (nonperturbative) wave function renormalization $Z$
occurring in these theories is shown not to be necessarily equal to zero,
except if the equal time commutation relations (ETCR) are assumed. Since the
ETCR are not justified in general (because the interacting fields cannot in
general be restricted to sharp times, as is known from model studies), the
condition $Z=0$ is not of general validity in interacting theories. We
conjecture that it characterizes either unstable (composite) particles or the
charge-carrying particles, which become infraparticles in the presence of
massless particles. In the case of QED, such "dressed" electrons are not
expected to be confined, but in QCD we propose a quark confinement criterion,
which follows naturally from lines suggested by the works of Casher, Kogut and
Susskind and Lowenstein and Swieca.


  We analyze the influence of finite ion size effects in the response of a
salt-free concentrated suspension of spherical particles to an oscillating
electric field. Salt-free suspensions are just composed of charged colloidal
particles and the added counterions released by the particles to the solution,
that counterbalance their surface charge. In the frequency domain, we study the
dynamic electrophoretic mobility of the particles and the dielectric response
of the suspension. We find that the Maxwell-Wagner-O'Konski process associated
with the counterions condensation layer, is enhanced for moderate to high
particle charges, yielding an increment of the mobility for such frequencies.
We also find that the increment of the mobility grows with ion size and
particle charge. All these facts show the importance of including ion size
effects in any extension attempting to improve standard electrokinetic models.


  Intrinsic random functions (IRF) provide a versatile approach when the
assumption of second-order stationarity is not met. Here, we develop the IRF
theory on the circle with its universal kriging application. Unlike IRF in
Euclidean spaces, where differential operations are used to achieve
stationarity, our result shows that low-frequency truncation of the Fourier
series representation of the IRF is required for such processes on the circle.
All of these features and developments are presented through the theory of
reproducing kernel Hilbert space. In addition, the connection between kriging
and splines is also established, demonstrating their equivalence on the circle.


  New generations of power systems, containing high shares of renewable energy
resources, require improved data-driven tools which can swiftly adapt to
changes in system operation. Many of these tools, such as ones using machine
learning, rely on high-quality training datasets to construct probabilistic
models. Such models should be able to accurately represent the system when
operating at its limits (i.e., operating with a high degree of ``active
constraints"). However, generating training datasets that accurately represent
the many possible combinations of these active constraints is a particularly
challenging task, especially within the realm of nonlinear AC Optimal Power
Flow (OPF), since most active constraints cannot be enforced explicitly. Using
bilevel optimization, this paper introduces a data collection routine that
sequentially solves for OPF solutions which are ``optimally far" from
previously acquired voltage, power, and load profile data points. The routine,
termed RAMBO, samples critical data close to a system's boundaries much more
effectively than a random sampling benchmark. Simulated test results are
collected on the 30-, 57-, and 118-bus PGLib test cases.


  New evidence is presented that Richard Price gave Thomas Bayes's famous essay
a very different title from the commonly reported one. It is argued that this
implies Price almost surely and Bayes not improbably embarked upon this work
seeking a defensive tool to combat David Hume on an issue in theology.


  We provide analytical $O(\alpha_s)$ results for the three polarized decay
structure functions $H_{++},\,H_{00}$ and $H_{--}$ that describe the decay of a
polarized $W$ boson into massive quark--antiquark pairs. As an application we
consider the decay $t\to b+W^+$ involving the helicity fractions $\rho_{mm}$ of
the $W^+$ boson followed by the polarized decay $\hbox{$W^+(\uparrow)$}\to
q_1\bar{q}_2$ described by the polarized decay structure functions $H_{mm}$. We
thereby determine the $O(\alpha_s)$ polar angle decay distribution of the
cascade decay process $t\to b+W^+(\to q_1\bar{q}_2)$. As a second example we
analyze quark mass and off-shell effects in the cascade decays $H\to
W^{-}+W^{\ast +}(\to q_1\bar{q}_2)$ and $H\to Z+Z^{\ast}(\to q\bar{q})$. For
the decays $H\to W^{-}+W^{\ast +}(\to c\bar b)$ and $H\to Z+Z^{\ast}(\to
b\bar{b})$ we find substantial deviations from the mass-zero approximation in
particular in the vicinity of the threshold region.


  We provide the first comprehensive study of hyperons in neutron star mergers
and quantify their specific impact. We discuss the thermal behavior of
hyperonic equations of state~(EoSs) as a distinguishing feature from purely
nucleonic models in the remnants of binary mergers using a large set of
numerical simulations. Finite temperature enhances the production of hyperons,
which leads to a reduced pressure as highly degenerate nucleons are
depopulated. This results in a characteristic increase of the dominant
postmerger gravitational-wave frequency by up to $\sim150$~Hz compared to
purely nucleonic EoS models. By our comparative approach we can directly link
this effect to the occurrence of hyperons. Although this feature is generally
weak, it is in principle measurable if the EoS and stellar parameters of cold
neutron stars are sufficiently well determined. Considering that the
mass-radius relations of purely nucleonic and hyperonic EoSs may be
indistinguishable and the overall challenge to infer the presence of hyperons
in neutron stars, these findings are important as a new route to answer the
outstanding question about hyperonic degrees of freedom in high-density matter.


  We present two methods to algorithmically compute both least and greatest
solutions of polynomial equation systems over absorptive semirings (with
certain completeness and continuity assumptions), such as the tropical
semiring. Both methods require a polynomial number of semiring operations,
including semiring addition, multiplication and an infinitary power operation.
Our main result is a closed-form solution for least and greatest fixed points
based on the fixed-point iteration. The proof builds on the notion of (possibly
infinite) derivation trees; a careful analysis of the shape of these trees
allows us to collapse the fixed-point iteration to a linear number of steps.
The second method is an iterative symbolic computation in the semiring of
generalized absorptive polynomials, largely based on results on Kleene
algebras.


  This paper presents a detailed study of excess line broadening in EUV
emission lines during the impulsive phase of a C-class solar flare. In this
work, which utilizes data from the EUV Imaging Spectrometer (EIS) onboard
Hinode, the broadened line profiles were observed to be co-spatial with the two
HXR footpoints as observed by RHESSI. By plotting the derived nonthermal
velocity for each pixel within the Fe XV and Fe XVI rasters against its
corresponding Doppler velocity a strong correlation (|r| > 0.59) was found
between the two parameters for one of the footpoints. This suggested that the
excess broadening at these temperatures is due to a superposition of flows
(turbulence), presumably as a result of chromospheric evaporation due to
nonthermal electrons. Also presented are diagnostics of electron densities
using five pairs of density-sensitive line ratios. Density maps derived using
the Mg XII and Si X line pairs showed no appreciable increase in electron
density at the footpoints, while the Fe XII, Fe XIII, and Fe XIV line pairs
revealed densities approaching 10^(11.5) cm^(-3). Using this information, the
nonthermal velocities derived from the widths of the two Fe XIV lines were
plotted against their corresponding density values derived from their ratio.
This showed that pixels with large nonthermal velocities were associated with
pixels of moderately higher densities. This suggests that nonthermal broadening
at these temperatures may have been due to enhanced densities at the
footpoints, although estimates of the amount of opacity broadening and pressure
broadening appeared to be negligible.


  Chudnovsky, Scott, Seymour and Spirkl recently proved a conjecture by Kalai
and Meshulam stating that the reduced Euler characteristic of the independence
complex of a graph without induced cycles of length divisible by three is in
{-1,0,1}. Gauthier had earlier proved that assuming no cycles of those lengths,
induced or not. Kalai and Meshulam also stated a stronger topological
conjecture, that the total betti numbers are in {0,1}. Towards that we prove an
even stronger statement in the same setting as Gauthier: The independence
complexes are either contractible or homotopy equivalent to spheres. We
conjecture that it also holds in the general setting.


  We provide a simple new randomized contraction approach to the global minimum
cut problem for simple undirected graphs. The contractions exploit 2-out edge
sampling from each vertex rather than the standard uniform edge sampling. We
demonstrate the power of our new approach by obtaining better algorithms for
sequential, distributed, and parallel models of computation. Our end results
include the following randomized algorithms for computing edge connectivity
with high probability:
  -- Two sequential algorithms with complexities $O(m \log n)$ and $O(m+n
\log^3 n)$. These improve on a long line of developments including a celebrated
$O(m \log^3 n)$ algorithm of Karger [STOC'96] and the state of the art $O(m
\log^2 n (\log\log n)^2)$ algorithm of Henzinger et al. [SODA'17]. Moreover,
our $O(m+n \log^3 n)$ algorithm is optimal whenever $m = \Omega(n \log^3 n)$.
Within our new time bounds, whp, we can also construct the cactus
representation of all minimal cuts.
  -- An $\~O(n^{0.8} D^{0.2} + n^{0.9})$ round distributed algorithm, where D
denotes the graph diameter. This improves substantially on a recent
breakthrough of Daga et al. [STOC'19], which achieved a round complexity of
$\~O(n^{1-1/353}D^{1/353} + n^{1-1/706})$, hence providing the first sublinear
distributed algorithm for exactly computing the edge connectivity.
  -- The first $O(1)$ round algorithm for the massively parallel computation
setting with linear memory per machine.


  As the next generation of wireless system targets at providing a wider range
of services with divergent QoS requirements, new applications will be enabled
by the fifth generation (5G) network. Among the emerging applications,
vehicle-to-everything (V2X) communication is an important use case targeted by
5G to enable an improved traffic safety and traffic efficiency. Since the V2X
communication requires a low end-to-end (E2E) latency and an ultra-high
reliability, the legacy cellular networks can not meet the service requirement.
In this work, we inspect on the system performance of applying the LTE-Uu and
PC5 interfaces to enable the V2X communication. With the LTE-Uu interface, one
V2X data packet is transmitted through the cellular network infrastructure,
while the PC5 interface facilitates the direct V2X communication without
involving the network infrastructure in user-plane. In addition, due to the
high reliability requirement, the application of a single V2X transmission
technology can not meet the targets in some scenarios. Therefore, we also
propose a multi-radio access technologies (multi-RATs) scheme where the data
packet travels through both the LTE-Uu and PC5 interfaces to obtain a diversity
gain. Last but not least, in order to derive the system performance, a system
level simulator is implemented in this work. The numerical results provide us
insights on how the different technologies will perform in different scenarios
and also validate the proposed multi-RATs scheme.


  We present a theory of the Josephson effect in a twofold-tilted Josephson
junction made by d-wave anisotropic layered superconductors. We find the
appearance of an intrinsic electrical resistance that arises from the
misalignment of the superconductive planes (the CuO_2 planes in YBCO) in the
two electrodes. This intrinsic contribution to the tunnel barrier has several
non-trivial consequences. The result is relevant for understanding the electric
transport properties of [100] tilt and [100] tilt-tilt Josephson junctions
based on d-wave superconductors.


  Principal component analysis (PCA) is one of the most popular dimension
reduction methods. The usual PCA is known to be sensitive to the presence of
outliers, and thus many robust PCA methods have been developed. Among them, the
Tyler's M-estimator is shown to be the most robust scatter estimator under the
elliptical distribution. However, when the underlying distribution is
contaminated and deviates from ellipticity, Tyler's M-estimator might not work
well. In this article, we apply the semiparametric theory to propose a robust
semiparametric PCA. The merits of our proposal are twofold. First, it is robust
to heavy-tailed elliptical distributions as well as robust to non-elliptical
outliers. Second, it pairs well with a data-driven tuning procedure, which is
based on active ratio and can adapt to different degrees of data outlyingness.
Theoretical properties are derived, including the influence functions for
various statistical functionals and asymptotic normality. Simulation studies
and a data analysis demonstrate the superiority of our method.


  In succession to the first paper (arXiv 1406.6204v5), the impurity-atom
concentrations when the Fermi levels are either at the valence band maximum
(VBM) or the conduction band minimum (CBM) were identified for diamond, cubic
boron nitride (cBN), and hexagonal boron nitride (hBN) using the
Korringa-Kohn-Rostoker (KKR) scheme using the local density approximation
(LDA). In the present paper, the generalized gradient approximation (GGA) was
used instead of the LDA for exchange-correlation. The impurity atoms were B and
N for diamond, Be, Si, and C for cBN, and Be for hBN; these impurity atoms were
known in the first paper to form degenerate states by increased impurity-atom
concentrations. The impurity-atom concentrations when the Fermi level was
located either at the VBM or the CBM were as follows: (i) the B concentration
was 0.27 at.% in B-doped diamond, (ii) the N concentration was 0.25 at.% in
N-doped diamond, (iii) the concentration of Be substituting B was 0.88 at.% in
cBN, (iv) the concentration of Si substituting B was 0.06 at.% in cBN, (v) the
concentration of C substituting B was 0.07 at.% in cBN, (vi) the concentration
of C substituting N was 0.88 at.% in cBN, and (vii) the concentration of Be
substituting B was 1.80 at.% in hBN. The values of (iv) and (v) were
significantly smaller than the corresponding values in paper I, but it was
attributed to the input parameters used in the present paper, hence it was
concluded that the computed concentrations were not sensitive to the GGA used.


  In this note, we provide some categorical perspectives on the relativization
construction arising from quantum measurement theory in the presence of
symmetries and occupying a central place in the operational approach to quantum
reference frames. This construction provides, for any quantum system, a quantum
channel from the system's algebra to the invariant algebra on the composite
system also encompassing the chosen reference, contingent upon a choice of the
pointer observable. These maps are understood as relativizing observables on
systems upon the specification of a quantum reference frame. We begin by
extending the construction to systems modelled on subspaces of algebras of
operators to then define a functor taking a pair consisting of a reference
frame and a system and assigning to them a subspace of relative operators
defined in terms of an image of the corresponding relativization map. When a
single frame and equivariant channels are considered, the relativization maps
can be understood as a natural transformation. Upon fixing a system, the
functor provides a novel kind of frame transformation that we call external.
Results achieved provide a deeper structural understanding of the framework of
interest and point towards its categorification and potential application to
local systems of algebraic quantum field theories.


  Asymptotic freedom of gluons in QCD is obtained in the leading terms of their
renormalized Hamiltonian in the Fock space, instead of considering virtual
Green's functions or scattering amplitudes. Namely, we calculate the
three-gluon interaction term in the front-form Hamiltonian for effective gluons
in the Minkowski space-time using the renormalization group procedure for
effective particles (RGPEP), with a new generator. The resulting three-gluon
vertex is a function of the scale parameter, $s$, that has an interpretation of
the size of effective gluons. The corresponding Hamiltonian running coupling
constant, $g_\lambda$, depending on the associated momentum scale $\lambda =
1/s$, is calculated in the series expansion in powers of $g_0 = g_{\lambda_0}$
up to the terms of third order, assuming some small value for $g_0$ at some
large $\lambda_0$. The result exhibits the same finite sensitivity to small-$x$
regularization as the one obtained in an earlier RGPEP calculation, but the new
calculation is simpler than the earlier one because of a simpler generator.
This result establishes a degree of universality for pure-gauge QCD in the
RGPEP.


  We predict the existence of a topological superradiant state in a
two-component degenerate Fermi gas in a cavity. The superradiant light
generation in the transversely driven cavity mode induces a cavity-assisted
spin-orbit coupling in the system and opens a bulk gap at half-filling. This
mechanism can simultaneously drive a topological phase transition in the
system, yielding a topological superradiant phase. We map out the steady-state
phase diagram of the system in the presence of an effective Zeeman field, and
identify a critical quadracritical point beyond which the topological and the
conventional superraidiant phase boundaries separate. We also propose to detect
the topological phase transitions based on the unique signatures in the
momentum-space density distribution.


  Context: The conventional approach to direct imaging has been the use of a
single aperture coronagraph with wavefront correction via extreme adaptive
optics. Such systems are limited to observing beyond an inner working (IWA) of
a few $\mathit\lambda/D$. Nulling interferometry with two or more apertures
will enable detections of companions at separations at and beyond the formal
diffraction limit.
  Aims: This paper evaluates the astrophysical potential of a kernel-nuller as
the prime high-contrast imaging mode of the Very Large Telescope Interferometer
(VLTI).
  Methods: By taking into account baseline projection effects which are induced
by Earth rotation, we introduce some diversity in the response of the nuller as
a function of time. This response is depicted by transmission maps. We also
determine whether we can extract the astrometric parameters of a companion from
the kernel outputs, which are the primary intended observable quantities of the
kernel-nuller. This then leads us to comment on the characteristics of a
possible observing program for the discovery of exoplanets.
  Results: We present transmission maps for both the raw nuller outputs and
their subsequent kernel outputs. To further examine the properties of the
kernel-nuller, we introduce maps of the absolute value of the kernel output. We
also identify 38 targets for the direct detection of exoplanets with a
kernel-nuller at the focus of the VLTI.
  Conclusions: With continued upgrades of the VLTI infrastructure that will
reduce fringe tracking residuals, a kernel-nuller would enable the detection of
young giant exoplanets at separations < 10 AU, where radial velocity and
transit methods are more sensitive.


  Blockchain-based cryptocurrencies have demonstrated how to securely implement
traditionally centralized systems, such as currencies, in a decentralized
fashion. However, there have been few measurement studies on the level of
decentralization they achieve in practice. We present a measurement study on
various decentralization metrics of two of the leading cryptocurrencies with
the largest market capitalization and user base, Bitcoin and Ethereum. We
investigate the extent of decentralization by measuring the network resources
of nodes and the interconnection among them, the protocol requirements
affecting the operation of nodes, and the robustness of the two systems against
attacks. In particular, we adapted existing internet measurement techniques and
used the Falcon Relay Network as a novel measurement tool to obtain our data.
We discovered that neither Bitcoin nor Ethereum has strictly better properties
than the other. We also provide concrete suggestions for improving both
systems.


  We study the spin dependence of accretion onto rotating Kerr black holes
using analytic techniques. In its linear regime, angular momentum transport in
MHD turbulent accretion flow involves the generation of radial magnetic field
connecting plasma in a differentially rotating flow. We take a first principles
approach, highlighting the constraint that limits the generation and
amplification of radial magnetic fields, stemming from the transfer of energy
from mechanical to magnetic form. Because the energy transferred in magnetic
form is ultimately constrained by gravitational potential energy or Killing
energy, the spin-dependence of the latter allows us to derive spin-dependent
constraints on the success of the accreting plasma to expel its angular
momentum and accrete. We find an inverse relationship between this ability and
black hole spin. If this radial magnetic field generation forms the basis for
angular momentum transfer in accretion flows, accretion rates involving Kerr
black holes are expected to be lower as the black hole spin increases in the
prograde sense.


  We construct updated solar models with different sets of solar abundances,
including the most recent determinations by Asplund et al. (2009). The latter
work predicts a larger ($\sim 10%$) solar metallicity compared to previous
measurements by the same authors but significantly lower ($\sim 25%$) than the
recommended value from a decade ago by Grevesse & Sauval (1998). We compare the
results of our models with determinations of the solar structure inferred
through helioseismology measurements. The model that uses the most recent solar
abundance determinations predicts the base of the solar convective envelope to
be located at $R_{\rm CZ}= 0.724{\rm R_\odot}$ and a surface helium mass
fraction of $Y_{\rm surf}=0.231$. These results are in conflict with
helioseismology data ($R_{\rm CZ}= 0.713\pm0.001{\rm R_\odot}$ and $Y_{\rm
surf}=0.2485\pm0.0035$) at 5$-\sigma$ and 11$-\sigma$ levels respectively.
Using the new solar abundances, we calculate the magnitude by which radiative
opacities should be modified in order to restore agreement with
helioseismology. We find that a maximum change of $\sim 15%$ at the base of the
convective zone is required with a smooth decrease towards the core, where the
change needed is $\sim 5%$. The required change at the base of the convective
envelope is about half the value estimated previously. We also present the
solar neutrino fluxes predicted by the new models. The most important changes
brought about by the new solar abundances are the increase by $\sim 10%$ in the
predicted $^{13}$N and $^{15}$O fluxes that arise mostly due to the increase in
the C and N abundances in the newly determined solar composition.


  We present some results of long term studies of pulsating stars conducted in
the course of the OGLE and Araucaria projects. In particular very scarce
eclipsing binaries containing pulsating stars are discussed. Such systems
provide a unique opportunity to improve calibration of the cosmic distance
scale and to better calibrate stellar evolutionary models.


  A T-net of order $m$ is a graph with $m$ nodes and $2m$ directed edges, where
every node has indegree and outdegree equal to $2$. (A well known example of
T-nets are de Bruijn graphs.) Given a T-net $N$ of order $m$, there is the so
called "doubling" process that creates a T-net $N^*$ from $N$ with $2m$ nodes
and $4m$ edges. Let $|X|$ denote the number of Eulerian cycles in a graph $X$.
It is known that $| N^*|=2^{m-1}|N|$. In this paper we present a new proof of
this identity. Moreover we prove that $|N|\leq 2^{m-1}$. Let $\Theta(X)$ denote
the set of all Eulerian cycles in a graph $X$ and $S(n)$ the set of all binary
sequences of length $n$. Exploiting the new proof we construct a bijection
$\Theta(N)\times S(m-1)\rightarrow \Theta(N^*)$, which allows us to solve one
of Stanley's open questions: we find a bijection between de Bruijn sequences of
order $n$ and $S(2^{n-1})$.


  Spin-polarized electron emission from the first superlattice photocathodes
developed with strain compensation is investigated. An opposite strain in the
quantum well and barrier layers is complished using an InAlGaAs/GaAsP
superlattice structure. The measured values of maximum polarization and quantum
yield for the structure with a 0.18 um-thick working layer are close to the
best results reported for any strained superlattice photocathode structure,
demonstrating the high potential of strain compensation for future photocathode
applications. An analysis of the photoemission spectra is used to estimate the
parameters responsible for the polarization losses.


  We propose a general algebraic analytic scheme for the spectral transform of
solutions of nonlinear evolution equations. This allows us to give the general
integrable evolution corresponding to an arbitrary time and space dependence of
the spectral transform (in general nonlinear and with non-analytic dispersion
relations). The main theorem is that the compatibility conditions gives always
a true nonlinear evolution because it can always be written as an identity
between polynomials in the spectral variable $k$. This general result is then
used to obtain first a method to generate a new class of solutions to the
nonlinear Schroedinger equation, and second to construct the spectral transform
theory for solving initial-boundary value problems for resonant wave-coupling
processes (like self-induced transparency in two-level media, or stimulated
Brillouin scattering of plasma waves or else stimulated Raman scattering in
nonlinear optics etc...).


  The idea of single exomoon detection due to the radio emissions caused by its
interaction with the host exoplanet is extended to multiple-exomoon systems.
The characteristic radio emissions are made possible in part by plasma from the
exomoons own ionosphere (Noyola et. al. 2014). In this work, it is demonstrated
that neighboring exomoons and the exoplanetary magnetosphere could also provide
enough plasma to generate a detectable signal. In particular, the
plasma-torus-sharing phenomenon is found to be particularly well suited to
facilitate the radio detection of plasma-deficient exomoons. The efficiency of
this process is evaluated, and the predicted power and frequency of the
resulting radio signals are presented.


  A new type of redescending M-estimators is constructed, based on data
augmentation with an unspecified outlier model. Necessary and sufficient
conditions for the convergence of the resulting estimators to the Hubertype
skipped mean are derived. By introducing a temperature parameter the concept of
deterministic annealing can be applied, making the estimator insensitive to the
starting point of the iteration. The properties of the annealing M-estimator as
a function of the temperature are explored. Finally, two applications are
presented. The first one is the robust estimation of interaction vertices in
experimental particle physics, including outlier detection. The second one is
the estimation of the tail index of a distribution from a sample using robust
regression diagnostics.


  The recommender systems have long been investigated in the literature.
Recently, users' implicit feedback like `click' or `browse' are considered to
be able to enhance the recommendation performance. Therefore, a number of
attempts have been made to resolve this issue. Among them, the variational
autoencoders (VAE) approach already achieves a superior performance. However,
the distributions of the encoded latent variables overlap a lot which may
restrict its recommendation ability. To cope with this challenge, this paper
tries to extend the Wasserstein autoencoders (WAE) for collaborative filtering.
Particularly, the loss function of the adapted WAE is re-designed by
introducing two additional loss terms: (1) the mutual information loss between
the distribution of latent variables and the assumed ground truth distribution,
and (2) the L1 regularization loss introduced to restrict the encoded latent
variables to be sparse. Two different cost functions are designed for measuring
the distance between the implicit feedback data and its re-generated version of
data. Experiments are valuated on three widely adopted data sets, i.e., ML-20M,
Netflix and LASTFM. Both the baseline and the state-of-the-art approaches are
chosen for the performance comparison which are Mult-DAE, Mult-VAE, CDAE and
Slim. The performance of the proposed approach outperforms the compared methods
with respect to evaluation criteria Recall@1, Recall@5 and NDCG@10, and this
demonstrates the efficacy of the proposed approach.


  The effectiveness of a model is heavily reliant on the quality of the fusion
representation of multiple modalities in multimodal sentiment analysis.
Moreover, each modality is extracted from raw input and integrated with the
rest to construct a multimodal representation. Although previous methods have
proposed multimodal representations and achieved promising results, most of
them focus on forming positive and negative pairs, neglecting the variation in
sentiment scores within the same class. Additionally, they fail to capture the
significance of unimodal representations in the fusion vector. To address these
limitations, we introduce a framework called Supervised Angular-based
Contrastive Learning for Multimodal Sentiment Analysis. This framework aims to
enhance discrimination and generalizability of the multimodal representation
and overcome biases in the fusion vector's modality. Our experimental results,
along with visualizations on two widely used datasets, demonstrate the
effectiveness of our approach.


  With the ever-increasing demand for high-speed wireless data transmission,
beamforming techniques have been proven to be crucial in improving the data
rate and the signal-to-noise ratio (SNR) at the receiver. However, they require
feedback mechanisms that need an overhead of information and increase the
system complexity, potentially challenging the efficiency and capacity of
modern wireless networks. This paper investigates novel index-based feedback
mechanisms that aim at reducing the beamforming feedback overhead in Wi-Fi
links. The proposed methods mitigate the overhead by generating a set of
candidate beamforming vectors using an unsupervised learning-based framework.
The amount of feedback information required is thus reduced by using the index
of the candidate as feedback instead of transmitting the entire beamforming
matrix. We explore several methods that consider different representations of
the data in the candidate set. In particular, we propose five different ways to
generate and represent the candidate sets that consider the covariance matrices
of the channel, serialize the feedback matrix, and account for the effective
distance, among others. Additionally, we also discuss the implications of using
partial information in the compressed beamforming feedback on the link
performance and compare it with the newly proposed index-based methods.
Extensive IEEE 802.11 standard-compliant simulation results show that the
proposed methods effectively minimize the feedback overhead, enhancing the
throughput while maintaining an adequate link performance.


  Federated Learning (FL) enables collaborative model training among
participants while guaranteeing the privacy of raw data. Mainstream FL
methodologies overlook the dynamic nature of real-world data, particularly its
tendency to grow in volume and diversify in classes over time. This oversight
results in FL methods suffering from catastrophic forgetting, where the trained
models inadvertently discard previously learned information upon assimilating
new data. In response to this challenge, we propose a novel Federated
Class-Incremental Learning (FCIL) method, named \underline{Fed}erated
\underline{C}lass-Incremental \underline{L}earning with New-Class
\underline{A}ugmented \underline{S}elf-Di\underline{S}tillation (FedCLASS). The
core of FedCLASS is to enrich the class scores of historical models with new
class scores predicted by current models and utilize the combined knowledge for
self-distillation, enabling a more sufficient and precise knowledge transfer
from historical models to current models. Theoretical analyses demonstrate that
FedCLASS stands on reliable foundations, considering scores of old classes
predicted by historical models as conditional probabilities in the absence of
new classes, and the scores of new classes predicted by current models as the
conditional probabilities of class scores derived from historical models.
Empirical experiments demonstrate the superiority of FedCLASS over four
baseline algorithms in reducing average forgetting rate and boosting global
accuracy.


  Ignition delay times of cyclopentene-oxygen-argon mixtures were measured
behind reflected shock waves. Mixtures contained 0.5 or 1 % of hydrocarbons for
equivalence ratios ranging from 0.5 to 1.5. Reflected shock waves conditions
were: temperatures from 1300 to 1700 K and pressures from 7 to 9 atm. When
comparing to previous results obtained under similar conditions, it can be
observed that the reactivity of cyclopentene is much lower than that of
cyclohexene, but very close to that of cyclopentane. A kinetic mechanism
recently proposed for the combustion of cyclopentene in a flame has been used
to model these results and a satisfactory agreement has been obtained. The main
reaction pathways have been derived from flow rate, simulated temporal profiles
of products and sensitivity analyses.


  The Hubble constant ($H_0$), which represents the expansion rate of the
Universe, is one of the most important cosmological parameters. The recent
measurements of $H_0$ using the distance ladder methods such as Type Ia
Supernovae (SNe Ia) are significantly greater than the CMB measurements by
Planck. The difference points to a crisis in the standard model of cosmology
termed as Hubble tension.
  In this work we compare different cosmological models, determine the Hubble
constant and comment on the Hubble tension using the data from differential
ages of galaxies. The data we use is free from the systematic effects as the
absolute age estimation of the galaxies is not needed. We have used the
Bayesian approach along with the commonly used maximum likelihood method to
estimate $H_0$ and have calculated the AIC scores to compare the different
cosmological models.The non-flat cosmological model provides a higher value for
matter density as well as the Hubble constant compared to the flat $\Lambda$CDM
model. The AIC score is smaller for the flat $\Lambda$CDM cosmology compared to
the non-flat model indicating the flat model a better choice. The best-fit
value of $H_0$ for both these models are $68.7\pm3.1$ km/s/Mpc and $72.2\pm4$
km/s/Mpc, respectively. Our results are consistent with the CCHP measurements.
However, flat model result does not agree with the SH0ES result, while the
non-flat result is inconsistent with the Planck value.


  While finite type Artin groups and right-angled Artin groups are
well-understood, little is known about more general Artin groups. In this paper
we use the action of an infinite type Artin group $A_\Gamma$ on a CAT(0) cube
complex to prove that $A_\Gamma$ has trivial center providing the graph
$\Gamma$ is not the star of a single vertex, and is acylindrically hyperbolic
providing $\Gamma$ is not a join.


  We show that one-dimensional binary mixtures of bosons or of a boson and a
spin-polarized fermion are Luttinger liquids with the following instabilities:
i) For different particle densities, strong attraction between the mixture
components leads to collapse, while strong repulsion leads to demixing, ii) For
a low-density mixture of two gases of impenetrable bosons (or a spin-polarized
fermion and an impenetrable boson) of equal densities, the system develops a
gap and exhibits enhanced pairing fluctuations when there is attraction between
the components. In the boson-fermion mixture, the pairing fluctuations occur at
finite momentum. Our conclusions apply to mixtures both on the continuum and on
optical lattices away from integer or fractional commensurability.


  The aim of the present work is to specify the spatio-temporal characteristics
of flare activity observed by the Reuven Ramaty High Energy Solar Spectroscopic
Imager (RHESSI) and Geostationary Operational Environmental Satellite (GOES)
satellites in connection with the behaviour of the longitudinal domain of
enhanced sunspot activity known as active longitude (AL). By using our method
developed for this purpose, we identified the AL in every Carrington Rotation
provided by the Debrecen Photoheliographic Data (DPD). The spatial probability
of flare occurrence has been estimated depending on the longitudinal distance
from AL in the northern and southern hemispheres separately. We have found that
more than the 60\% of the RHESSI and GOES flares is located within $\pm
36^{\circ}$ from the active longitude. Hence, the most flare-productive active
regions tend to be located in or close to the active longitudinal belt. This
observed feature may allow predicting the geo-effective position of the domain
of enhanced flaring probability. Furthermore, we studied the temporal
properties of flare occurrence near the active longitude and several
significant fluctuations were found. More precisely, the results of the method
are the following fluctuations: $0.8$ years, $1.3$ years and $1.8$ years. These
temporal and spatial properties of the solar flare occurrence within the active
longitudinal belts could provide us enhanced solar flare forecasting
opportunity.


  We extend our study of the field-theoretic description of matrix-vector
models and the associated many-body problems of one dimensional particles with
spin. We construct their Yangian-su(R) invariant Hamiltonian. It describes an
interacting theory of a c=1 collective boson and a k=1 su(R) current algebra.
When $R \geq 3$ cubic-current terms arise. Their coupling is determined by the
requirement of the Yangian symmetry. The Hamiltonian can be consistently
reduced to finite-dimensional subspaces of states, enabling an explicit
computation of the spectrum which we illustrate in the simplest case.


  The quest for Kitaev spin liquids in particular three dimensional solids is
long sought goal in condensed matter physics, as these states may give rise to
exotic new types of quasi-particle excitations carrying fractional quantum
numbers namely Majorana Fermionic excitations. Here we report the experimental
signature of this characteristic feature of the Kitaev spin liquid via Raman
measurements. Sm2ZnIrO6 is a strongly spin orbit coupled Mott insulator, where
Jeff = 1/2 controls the physics, which provide striking evidence for this
characteristic feature of the Kitaev spin liquid. As the temperature is
lowered, we find that the spin excitations form a continuum in contrast to the
conventional sharp modes expected in ordered antiferromagnets. Our observation
of a broad magnetic continuum and anomalous renormalization of the phonon
self-energy parameters evidence the existence of Majorana fermions from spin
fractionalization in double perovskites structure as theoretically conjectured
in a Kitaev-Heisenberg geometrically frustrated double perovskite systems.


  We study the evolution of close binary systems formed by a normal (solar
composition), intermediate mass donor star together with a neutron star. We
consider models including irradiation feedback and evaporation. These
non-standard ingredients deeply modify the mass transfer stages of these
binaries. While models that neglect irradiation feedback undergo continuous,
long standing mass transfer episodes, models including these effect suffer a
number cycles of mass transfer and detachment. During mass transfer the systems
should reveal themselves as low-mass X-ray binaries (LMXBs), whereas when
detached they behave as a binary radio pulsars. We show that at these stages
irradiated models are in a Roche lobe overflow (RLOF) state or in a quasi-RLOF
state. Quasi-RLOF stars have a radius slightly smaller than its Roche lobe.
Remarkably, these conditions are attained for orbital period and donor mass
values in the range corresponding to a family of binary radio pulsars known as
"redbacks". Thus, redback companions should be quasi-RLOF stars. We show that
the characteristics of the redback system PSR J1723-2837 are accounted for by
these models.
  In each mass transfer cycle these systems should switch from LMXB to binary
radio pulsar states with a timescale of \sim million years. However, there is
recent and fast growing evidence of systems switching on far shorter, human
timescales. This should be related to instabilities in the accretion disc
surrounding the neutron star and/or radio ejection, still to be included in the
model having the quasi-RLOF state as a general condition.


  We report extensive resistivity, Hall, and magnetoresistance measurements on
thin films of the electron-doped cuprate \PCCO~(PCCO), as a function of doping,
temperature and magnetic field. The doping dependence of the resistivity and
Hall number at low temperatures are characteristic of a system near a quantum
phase transition or a Fermi Surface Reconstruction (FSR) point. The spin
magnetoresistance drops to zero near the critical point. The data presented in
this paper were compiled during the 2004-2007 period but were never published
in this comprehensive form. Because of the recent interest in very similar
results now being found in the normal state of hole-doped cuprates, we believe
the results of our older, mostly unpublished, work will be of interest to the
present community of cuprate researchers. In particular, Fig.11 shows the large
change in Hall number at the FSR point in \PCCO, similar to that found recently
in YBCO and LSCO (See ref[1] and [2]). Also, Fig.6 illustrates how the
resistivity upturn is affected by the FSR. The cause of the resistivity upturn
has been attributed to the loss of carriers at doping below the FSR in the
hole-doped cuprates (see Ref. 3), however, this scenario does not explain the
data for PCCO. The upturn in n-doped cuprates is more-likely due to a
combination of carrier decrease and a change in the scattering rate below the
FSR (see also Ref. 4). The change in spin scattering below the FSR is
illustrated by Fig.18 in this paper. Chen et al. [5] have developed a model
based on spin scattering that is able to explain qualitatively the resistivity
upturn in all the cuprates.


  Quantum emitters coupled to optical resonators are quintessential systems for
exploring fundamental phenomena in cavity quantum electrodynamics (cQED) and
are commonly used in quantum devices acting as qubits, memories and
transducers. Many previous experimental cQED studies have focused on regimes in
which a small number of identical emitters interact with a weak external drive,
such that the system can be described with simple, effective models. However,
the dynamics of a disordered, many-body quantum system subject to a strong
drive have not been fully explored, despite its importance and potential in
quantum applications. Here we study how a large, inhomogeneously broadened
ensemble of solid-state emitters coupled with high cooperativity to a
nanophotonic resonator behaves under strong excitation. We discover a sharp,
collectively induced transparency (CIT) in the cavity reflection spectrum,
resulting from quantum interference and collective response induced by the
interplay between driven inhomogeneous emitters and cavity photons.
Furthermore, coherent excitation within the CIT window leads to highly
nonlinear optical emission, spanning from fast superradiance to slow
subradiance. These phenomena in the many-body cQED regime enable new mechanisms
for achieving slow light and frequency referencing, pave a way towards
solid-state superradiant lasers and inform the development of ensemble-based
quantum interconnects.


  We show, in detail, that the only non-trivial black hole (BH) solutions for a
neutral as well as a charged spherically symmetric space-times, using the class
${\textit F(R)}={\textit R}\pm{\textit F_1 (R)} $, must-have metric potentials
in the form $h(r)=\frac{1}{2}-\frac{2M}{r}$ and
$h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}$. These BHs have a non-trivial
form of Ricci scalar, i.e., $R=\frac{1}{r^2}$ and the form of ${\textit F_1
(R)}=\mp\frac{\sqrt{\textit R}} {3M} $. We repeat the same procedure for
(Anti-)de Sitter, (A)dS, space-time and got the metric potentials of neutral as
well as charged in the form $h(r)=\frac{1}{2}-\frac{2M}{r}-\frac{2\Lambda r^2}
{3} $ and $h(r)=\frac{1}{2}-\frac{2M}{r}+\frac{q^2}{r^2}-\frac{2\Lambda r^2}
{3} $, respectively. The Ricci scalar of the (A)dS space-times has the form
${\textit R}=\frac{1+8r^2\Lambda}{r^2}$ and the form of ${\textit
F_1(R)}=\mp\frac{\textit 2\sqrt{R-8\Lambda}}{3M}$. We calculate the
thermodynamical quantities, Hawking temperature, entropy, quasi-local energy,
and Gibbs-free energy for all the derived BHs, that behaves asymptotically as
flat and (A)dS, and show that they give acceptable physical thermodynamical
quantities consistent with the literature. Finally, we prove the validity of
the first law of thermodynamics for those BHs.


  We combine observations from ALMA, ATCA, MUSE, andHerschel to study
gas-to-dust ratios in 15 Fornax cluster galaxies detected in the FIR/sub-mm by
Herschel and observed by ALMA as part of the ALMA Fornax Cluster Survey
(AlFoCS). The sample spans a stellar mass range of 8.3 $\leq$ log (M$_*$ /
M$_\odot$) $\leq$ 11.16, and a variety of morphological types. We use gas-phase
metallicities derived from MUSE observations (from the Fornax3D survey) to
study these ratios as a function of metallicity, and to study dust-to-metal
ratios, in a sub-sample of nine galaxies. We find that gas-to-dust ratios in
Fornax galaxies are systematically lower than those in field galaxies at fixed
stellar mass/metallicity. This implies that a relatively large fraction of the
metals in these Fornax systems is locked up in dust, which is possibly due to
altered chemical evolution as a result of the dense environment. The low ratios
are not only driven by HI deficiencies, but H$_2$-to-dust ratios are also
significantly decreased. This is different in the Virgo cluster, where low
gas-to-dust ratios inside the virial radius are driven by low HI-to-dust
ratios, while H$_2$-to-dust ratios are increased. Resolved observations of
NGC1436 show a radial increase in H$_2$-to-dust ratio, and show that low ratios
are present throughout the disc. We propose various explanations for the low
H$_2$-to-dust ratios in the Fornax cluster, including the more efficient
stripping of H$_2$ compared to dust, more efficient enrichment of dust in the
star formation process, and altered ISM physics in the cluster environment.


  According to a theorem of Treves, the conserved functionals of the KdV
equation vanish on each formal Laurent series 1/x^2 + u0 + u2 x^2 + u3 x^3 +
>... . We propose a new, very simple geometrical proof for this statement.


  We revisit the scaling properties of growing spheres randomly seeded in d=2,3
and 4 dimensions using a mean-field approach. We model the insertion
probability without assuming a priori a functional form for the radius
distribution. The functional form of the insertion probability shows an
unprecedented agreement with numerical simulations in d=2, 3 and 4 dimensions.
We infer from the insertion probability the scaling behavior of the Random
Apollonian Packing and its fractal dimensions. The validity of our model is
assessed with sets of 256 simulations each containing 20 million spheres in 2,
3 and 4 dimensions.


  The deep supervised and reinforcement learning paradigms (among others) have
the potential to endow interactive multimodal social robots with the ability of
acquiring skills autonomously. But it is still not very clear yet how they can
be best deployed in real world applications. As a step in this direction, we
propose a deep learning-based approach for efficiently training a humanoid
robot to play multimodal games---and use the game of `Noughts & Crosses' with
two variants as a case study. Its minimum requirements for learning to perceive
and interact are based on a few hundred example images, a few example
multimodal dialogues and physical demonstrations of robot manipulation, and
automatic simulations. In addition, we propose novel algorithms for robust
visual game tracking and for competitive policy learning with high winning
rates, which substantially outperform DQN-based baselines. While an automatic
evaluation shows evidence that the proposed approach can be easily extended to
new games with competitive robot behaviours, a human evaluation with 130 humans
playing with the Pepper robot confirms that highly accurate visual perception
is required for successful game play.


  The degenerate third Painlev\'{e} equation, $u^{\prime \prime} =
\frac{(u^{\prime})^{2}}{u} - \frac{u^{\prime}}{\tau} + \frac{1}{\tau}(-8
\epsilon u^{2} + 2ab) + \frac{b^{2}}{u}$, where $\epsilon,b \in \mathbb{R}$,
and $a \in \mathbb{C}$, and the associated tau-function are studied via the
Isomonodromy Deformation Method. Connection formulae for asymptotics of the
general as $\tau \to \pm 0$ and $\pm i0$ solution and general regular as $\tau
\to \pm \infty$ and $\pm i \infty$ solution are obtained.


  Modeling artificial scanning electron microscope (SEM) and scanning ion
microscope images has recently become important. This is because of the need to
provide repeatable images with a priori determined parameters. Modeled
artificial images are highly useful in the evaluation of new imaging and
metrological techniques, like image-sharpness calculation, or drift-corrected
image composition (DCIC). Originally, the NIST-developed artificial image
generator was designed only to produce the SEM images of gold-on-carbon
resolution sample for image-sharpness evaluation. Since then, the new improved
version of the software was written in C++ programming language and is in the
Public Domain. The current version of the software can generate arbitrary
samples, any drift function, and many other features. This work describes
scanning in charged-particle microscopes, which is applied both in the
artificial image generator and the DCIC technique. As an example, the
performance of the DCIC technique is demonstrated.


  We are concerned with the instability of a generic compressible two-fluid
model in the whole space $\mathbb{R}^3$, where the capillary pressure
$f(\alpha^-\rho^-)=P^+-P^-\neq 0$ is taken into account. For the case that the
capillary pressure is a strictly decreasing function near the equilibrium,
namely, $f'(1)<0$, Evje-Wang-Wen established global stability of the constant
equilibrium state for the three-dimensional Cauchy problem under some smallness
assumptions. Recently, Wu-Yao-Zhang proved global stability of the constant
equilibrium state for the case $P^+=P^-$ (corresponding to $f'(1)=0$). In this
work, we investigate the instability of the constant equilibrium state for the
case that the capillary pressure is a strictly increasing function near the
equilibrium, namely, $f'(1)>0$. First, by employing Hodge decomposition
technique and making detailed analysis of the Green's function for the
corresponding linearized system, we construct solutions of the linearized
problem that grow exponentially in time in the Sobolev space $H^k$, thus
leading to a global instability result for the linearized problem. Moreover,
with the help of the global linear instability result and a local existence
theorem of classical solutions to the original nonlinear system, we can then
show the instability of the nonlinear problem in the sense of Hadamard by
making a delicate analysis on the properties of the semigroup. Therefore, our
result shows that for the case $f'(1)>0$, the constant equilibrium state of the
two-fluid model is linearly globally unstable and nonlinearly locally unstable
in the sense of Hadamard, which is in contrast to the cases $f'(1)<0$ and
$P^+=P^-$ (corresponding to $f'(1)=0$) where the constant equilibrium state of
the two--fluid model is nonlinearly globally stable.


  A new wave energy device features a submerged ballasted air bag connected at
the top to a rigid float. Under wave action, the bag expands and contracts,
creating a reciprocating air flow through a turbine between the bag and another
volume housed within the float. Laboratory measurements are generally in good
agreement with numerical predictions. Both show that the trajectory of possible
combinations of pressure and elevation at which the device is in static
equilibrium takes the shape of an S. This means that statically the device can
have three different draughts, and correspondingly three different bag shapes,
for the same pressure. The behaviour in waves depends on where the mean
pressure-elevation condition is on the static trajectory. The captured power is
highest for a mean condition on the middle section.


  Recent interest in New Early Dark Energy (NEDE), a cosmological model with a
vacuum energy component decaying in a triggered phase transition around
recombination, has been sparked by its impact on the Hubble tension. Previous
constraints on the model parameters were derived in a Bayesian framework with
Markov-chain Monte Carlo (MCMC) methods. In this work, we instead perform a
frequentist analysis using the profile likelihood in order to assess the impact
of prior volume effects on the constraints. We constrain the maximal fraction
of NEDE $f_\mathrm{NEDE}$, finding $f_\mathrm{NEDE}=0.076^{+0.040}_{-0.035}$ at
$68 \%$ CL with our baseline dataset and similar constraints using either data
from SPT-3G, ACT or full-shape large-scale structure, showing a preference over
$\Lambda$CDM even in the absence of a SH0ES prior on $H_0$. While this is
stronger evidence for NEDE than obtained with the corresponding Bayesian
analysis, our constraints broadly match those obtained by fixing the NEDE
trigger mass. Including the SH0ES prior on $H_0$, we obtain
$f_\mathrm{NEDE}=0.136^{+0.024}_{-0.026}$ at $68 \%$ CL. Furthermore, we
compare NEDE with the Early Dark Energy (EDE) model, finding similar
constraints on the maximal energy density fractions and $H_0$ in the two
models. At $68 \%$ CL in the NEDE model, we find $H_0 = 69.56^{+1.16}_{-1.29}
\text{ km s}^{-1}\text{ Mpc}^{-1}$ with our baseline and $H_0 =
71.62^{+0.78}_{-0.76} \text{ km s}^{-1}\text{ Mpc}^{-1}$ when including the
SH0ES measurement of $H_0$, thus corroborating previous conclusions that the
NEDE model provides a considerable alleviation of the $H_0$ tension.


  We show that $3$-uniform hypergraphs with the property that all vertices have
a quasirandom link graph with density bigger than $1/3$ contain a clique on
five vertices. This result is asymptotically best possible.


  In a recent comment (arXiv:1906.05742) on the preprint (arXiv:1807.08572)
entitled "Coexistence of Diamagnetism and Vanishingly Small Electrical
Resistance at Ambient Temperature and Pressure in Nanostructures", it is
pointed out that the reduction of the four-probe resistance ($R_{4P}$) to zero
value is accompanied by a rise in the two probe resistance ($R_{2P}$) in the
same temperature range. This curious correlation between $R_{4P}$ and $R_{2P}$
is said to be pointing towards a non-superconducting "conductance percolation"
transition (rather than "percolating superconducting transition" as proposed in
the revised version of arxiv:1807.08572). The explanation offered in preprint
arXiv:1906.05742 is quite reasonable, but the author leaves open the question
of giant diamagnetism. In this short comment I suggest a plausible cause of the
giant diamagnetism found in nanostructures. It could be due to gapped
electronic energy spectrum of nanoparticles which is due to quantum confinement
effects, and that suppresses the electronic scattering mechanism leading to a
very high value of Langevin diamagnetism.


  We investigate the discrimination between photon polarizations when measured
by moving detectors. Both unambiguous and minimum-error discriminations are
considered, and we analyze the the optimal successful (correct) probability as
a function of the apparatus' velocity. The Holevo bound for polarization
discrimination is also discussed and explicit calculation shows that the Holevo
bound and the optimal successful (correct) probability for unambiguous
(minimum-error) discrimination simultaneously increase or decrease.


  Lecture notes from the Jerusalem Winter School on Theoretical Physics
"Correlated Electron Systems", Dec. 1991 -- Jan. 1992. Contains a review of
recent and not so recent results in the theory of correlated fermions in one
dimension.


  This paper studies optimal control and stabilization problems for
continuous-time mean-field systems with input delay, which are the fundamental
development of control and stabilization problems for mean-field systems. There
are two main contributions: 1) To the best of our knowledge, the present paper
is first to establish the necessary and sufficient solvability condition for
this kind of optimal control problem with delay, and to derive an optimal
controller through overcoming the obstacle that separation principle no longer
holds for multiplicative-noise systems; 2) For the stabilization problem, under
the assumption of exact observability, we strictly prove thatthe system is
stabilizable if and only if the algebraic Riccati equation has a unique
positive definite solution.


  Bayesian nonparametric mixtures and random partition models are powerful
tools for probabilistic clustering. However, standard independent mixture
models can be restrictive in some applications such as inference on cell
lineage due to the biological relations of the clusters. The increasing
availability of large genomic data requires new statistical tools to perform
model-based clustering and infer the relationship between homogeneous subgroups
of units. Motivated by single-cell RNA applications we develop a novel
dependent mixture model to jointly perform cluster analysis and align the
clusters on a graph. Our flexible graph-aligned random partition model (GARP)
exploits Gibbs-type priors as building blocks, allowing us to derive analytical
results on the graph-aligned random partition's probability mass function
(pmf). We derive a generalization of the Chinese restaurant process from the
pmf and a related efficient and neat MCMC algorithm to perform Bayesian
inference. We perform posterior inference on real single-cell RNA data from
mice stem cells. We further investigate the performance of our model in
capturing the underlying clustering structure as well as the underlying graph
by means of simulation studies.


  We investigate the integrals of motion of general conformal mechanical
systems with and without confining harmonic potential as well as of the related
angular subsystems, by employing the SL(2,R) algebra and its representations.
In particular, via the tensor product of two representations we construct new
integrals of motion from old ones. Furthermore, the temporally periodic
observables (including the integrals) of the angular subsystem are explicitly
related to those of the full system in a confining harmonic potential. The
techniques are illustrated for the rational Calogero models and their angular
subsystems, where they generalize known methods for obtaining conserved charges
beyond the Liouville ones.


  Drones are increasingly used in fields like industry, medicine, research,
disaster relief, defense, and security. Technical challenges, such as
navigation in GPS-denied environments, hinder further adoption. Research in
visual odometry is advancing, potentially solving GPS-free navigation issues.
Traditional visual odometry methods use geometry-based pipelines which, while
popular, often suffer from error accumulation and high computational demands.
Recent studies utilizing deep neural networks (DNNs) have shown improved
performance, addressing these drawbacks. Deep visual odometry typically employs
convolutional neural networks (CNNs) and sequence modeling networks like
recurrent neural networks (RNNs) to interpret scenes and deduce visual odometry
from video sequences. This paper presents a novel real-time monocular visual
odometry model for drones, using a deep neural architecture with a
self-attention module. It estimates the ego-motion of a camera on a drone,
using consecutive video frames. An inference utility processes the live video
feed, employing deep learning to estimate the drone's trajectory. The
architecture combines a CNN for image feature extraction and a long short-term
memory (LSTM) network with a multi-head attention module for video sequence
modeling. Tested on two visual odometry datasets, this model converged 48%
faster than a previous RNN model and showed a 22% reduction in mean
translational drift and a 12% improvement in mean translational absolute
trajectory error, demonstrating enhanced robustness to noise.


  Electron properties of graphene are described in terms of Dirac fermions.
Here we thoroughly outline the elastic scattering theory for the
two-dimensional massive Dirac fermions in the presence of an axially symmetric
potential. While the massless limit is relevant for pristine graphene, keeping
finite mass allows for generalizations onto situations with broken symmetry
between the two sublattices, and provides a link to the scattering theory of
electrons in a parabolic band. We demonstrate that the Dirac theory requires
short-distance regularization for potentials which are more singular than 1/r.
The formalism is then applied to scattering off a smooth short-ranged
potential. Next we consider the Coulomb potential scattering, where the Dirac
theory is consistent for a point scatterer only for the effective impurity
strength below 1/2. From the scattering phase shifts we obtain the exact
Coulomb transport cross-section in terms of the impurity strength. The results
are relevant for transport in graphene in the presence of impurities that do
not induce scattering between the Dirac points in the Brillouin zone.


  This paper reviews the structure of standard quantum mechanics, introducing
the basics of the von Neumann-Dirac axiomatic formulation as well as the
well-known Copenhagen interpretation. We review also the major conceptual
difficulties arising from this theory, first and foremost, the well-known
measurement problem. The main aim of this essay is to show the possibility to
solve the conundrums affecting quantum mechanics via the methodology provided
by the primitive ontology approach. Using Bohmian mechanics as an example, the
paper argues for a realist attitude towards quantum theory. In the second
place, it discusses the Quinean criterion for ontology and its limits when it
comes to quantum physics, arguing that the primitive ontology programme should
be considered as an improvement on Quine's method in determining the
ontological commitments of a theory.


  We use the S-matrix formalism of bound-state QED to study the photon-atom
scattering. We find that the internal lines in Feynman diagrams which
describing the propagation of off-shell bound electrons provide the off-shell
amplitudes of photons' propagation in atoms phenomenally. Our work set up the
connection between the property of Feynman propagators in bound-state QED and
the superluminal but casual propagating behavior of light in atomic media. We
also studied the relation between the bound-state QED and the widely used
light-atom interacting model in quantum optics, and give the experimental
condition where only the bound-state QED is valid.


  The density of accessible levels in the ($^3$He,$\alpha \gamma$) reaction has
been extracted for the $^{162}$Dy, $^{166}$Er and $^{172}$Yb nuclei. The
nuclear temperature is measured as a function of excitation energy in the
region of 0 -- 6 MeV. The temperature curves reveal structures indicating new
degrees of freedom. The heat capacity of the nuclear system is discussed within
the framework of a canonical ensemble.


  This paper is concerned with the limiting spectral behaviors of large
dimensional Kendall's rank correlation matrices generated by samples with
independent and continuous components. We do not require the components to be
identically distributed, and do not need any moment conditions, which is very
different from the assumptions imposed in the literature of random matrix
theory. The statistical setting in this paper covers a wide range of highly
skewed and heavy-tailed distributions. We establish the central limit theorem
(CLT) for the linear spectral statistics of the Kendall's rank correlation
matrices under the Marchenko-Pastur asymptotic regime, in which the dimension
diverges to infinity proportionally with the sample size. We further propose
three nonparametric procedures for high dimensional independent test and their
limiting null distributions are derived by implementing this CLT. Our numerical
comparisons demonstrate the robustness and superiority of our proposed test
statistics under various mixed and heavy-tailed cases.


  We discuss medium modifications of the unitarized pion-pion interaction in
the nuclear medium. We incorporate both the effects of chiral symmetry
restoration and the influence of collective nuclear pionic modes, originating
from the p-wave coupling of the pion to delta-hole configurations. We show how
the resulting strong enhancement of the sigma-meson spectral function is
related to large fluctuations of the condensate associated with the partial
restoration of chiral symmetry.


  Turbulent scaling phenomena are studied in an ultracold Bose gas away from
thermal equilibrium. Fixed points of the dynamical evolution are characterized
in terms of universal scaling exponents of correlation functions. The scaling
behavior is determined analytically in the framework of quantum field theory,
using a nonperturbative approximation of the two-particle irreducible effective
action. While perturbative Kolmogorov scaling is recovered at higher energies,
scaling solutions with anomalously large exponents arise in the infrared regime
of the turbulence spectrum. The extraordinary enhancement in the momentum
dependence of long-range correlations could be experimentally accessible in
dilute ultracold atomic gases. Such experiments have the potential to provide
insight into dynamical phenomena directly relevant also in other present-day
focus areas like heavy-ion collisions and early-universe cosmology.


  The paper is joined with arXiv:0911.5428 and improved.
  We prove that Landau-Ginzburg models for all 17 smooth Fano threefolds with
Picard rank 1 can be represented as Laurent polynomials in 3 variables
exhibiting them case by case. We check that these Landau-Ginzburg models can be
compactified to open Calabi-Yau varieties. In the spirit of L. Katzarkov's
program we prove that numbers of irreducible components of the central fibers
of compactifications of these pencils are dimensions of intermediate Jacobians
of Fano varieties plus 1. In particular these numbers do not depend on
compactifications. We state most of known methods of finding Landau-Ginzburg
models in terms of Laurent polynomials. We discuss Laurent polynomial
representation of Landau-Ginzburg models of Fano varieties and state some
problems related to it.


  The Virasoro conjecture is a conjectured sequence of relations among the
descendent Gromov-Witten invariants of a smooth projective variety in all
genera; the only varieties for which it is known to hold are a point
(Kontsevich) and Calabi-Yau threefolds (S. Katz). We review the statement of
the conjecture and its proof in genus 0, following Eguchi, Hori and Xiong.
  This version incorporates many changes and improvements compared with the
first, and a small number of misprints from the second. It will appear in the
AMS volume "Hirzebruch 70", edited by P. Pragacz et al.


  Experiments of in vitro formation of blood vessels show that cells randomly
spread on a gel matrix autonomously organize to form a connected vascular
network. We propose a simple model which reproduces many features of the
biological system. We show that both the model and the real system exhibit a
fractal behavior at small scales, due to the process of migration and dynamical
aggregation, followed at large scale by a random percolation behavior due to
the coalescence of aggregates. The results are in good agreement with the
analysis performed on the experimental data.


  In this clarifying note we discuss the late decay of an Affleck-Dine
condensate by providing a no-go theorem that attributes to conserved global
charges which are identified by the net particle number in fields which are
included in the flat direction(s). For a rotating condensate, this implies
that: (1) the net baryon/lepton number density stored in the condensate is
always conserved, and (2) the total particle number density in the condensate
cannot decrease. This reiterates that, irrespective of possible
non-perturbative particle production due to $D$-terms in a multiple flat
direction case, the prime decay mode of an Affleck-Dine condensate will be
perturbative as originally envisaged. As a result, cosmological consequences of
flat directions such as delayed thermalization as a novel solution to the
gravitino overproduction problem will remain virtually intact.


  We study the nonlinear $\sigma$-model in an external magnetic field applied
on curved surfaces with rotational symmetry. The Euler-Lagrange equations
derived from the Hamiltonian yield the double sine-Gordon equation (DSG)
provided the magnetic field is tuned with the curvature of the surface. A
$2\pi$ skyrmion appears like a solution for this model and surface deformations
are predicted at the sector where the spins point in the opposite direction to
the magnetic field. We also study some specific examples by applying the model
on three rotationally symmetric surfaces: the cylinder, the catenoid and the
hyperboloid. The coupling between a magnetic field and the curvature of the
substract is an interesting result and we believe that this issue may be
relevant to be applied in condensed matter systems, e.g., superconductors,
nematic liquid crystals, graphene and topological insulators.


  In this paper, we present a concurrent implementation of a powerful
topological thinning operator. This operator is able to act directly over
grayscale images without modifying their topology. We introduce an adapted
parallelization methodology which combines split, distribute and merge (SDM)
strategy and mixed parallelism techniques (data and thread parallelism). The
introduced strategy allows efficient parallelization of a large class of
topological operators including, mainly, {\lambda}-leveling, skeletonization
and crest restoring algorithms. To achieve a good speedup, we cared about
coordination of threads. Distributed work during thinning process is done by a
variable number of threads. Tests on 2D grayscale image (512*512), using shared
memory parallel machine (SMPM) with 8 CPU cores (2x Xeon E5405 running at
frequency of 2 GHz), showed an enhancement of 6.2 with a maximum achieved
cadency of 125 images/s using 8 threads.


  This paper studies the concept of instantaneous arbitrage in continuous time
and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage
is equivalent to the existence of a trading strategy which satisfies the CAPM
beta pricing relation in place of the market. Thus the difference between the
arbitrage argument and the CAPM argument in Black and Scholes (1973) is this:
the arbitrage argument assumes that there exists some portfolio satisfying the
capm equation, whereas the CAPM argument assumes, in addition, that this
portfolio is the market portfolio.


  Ultrafast manipulation of magnetic states is one of the necessities in modern
data storage technology. Quantum antiferromagnets are promising candidates in
this respect. The orientation of the order parameter, the sublattice
magnetization, can be used to encode "0" and "1" of a bit. Then, the switching
of magnetization and the full control of its reorientation are crucial for
writing data. We show that the magnetization can be switched efficiently by an
external short THz pulses with relatively low amplitude. The coupling to the
spin degrees can be direct via the magnetic field or indirect via the electric
field inducing spin-polarized charge currents. Our description is based on
time-dependent Schwinger boson mean-field theory which includes the intrinsic
dephasing mechanisms beyond a macrospin description. The findings help to
introduce the use of antiferromagnets in data storage technology.


  Many-site Bose-Hubbard lattices display complex semiclassical dynamics, with
both chaotic and regular features. We have characterised chaos in the
semiclassical dynamics of short Bose-Hubbard chains using both stroboscopic
phase space projections and finite-time Lyapunov exponents. We found that chaos
was present for intermediate collisional nonlinearity in the open trimer and
quatramer systems, with soft chaos and Kolmogoroff-Arnold-Moser islands
evident. We have found that the finite-time Lyapunov exponents are consistent
with stroboscopic maps for the prediction of chaos in these small systems. This
gives us confidence that the finite-time Lyapunov exponents will be a useful
tool for the characterisation of chaos in larger systems, where meaningful
phase-space projections are not possible and the dimensionality of the problem
can make the standard methods intractable.


  Recently there have been several proposals on exciton-polariton topological
insulators, most requiring strong external magnetic fields induced by bulky
superconducting coils. We propose an alternate design for a polariton
topological insulator, where excitons are in a proximity of an additional layer
of a ferromagnetic material with a predefined magnetic moment located between
the pillars of the cavity. Our design supports a variety of topological phases
and transitions between Chern numbers $\pm 2$ and $\pm 1$ by varying either the
magnetic moment of the ferromagnetic material or the spin-orbit coupling
between different spin projections, thus enabling compact polariton devices
harnessing switchable topological edge modes.


  A simple formula for the scattering of wave packets from a square well at
long times is derived. The expression shows that the phenomenon of wave packet
diffraction in space and time exists in three dimensions also. An experiment
for the verification of the phenomenon is described and simulated numerically.


  We investigate the topological properties of $N_f = 2+1$ QCD with physical
quark masses, both at zero and finite temperature. We adopt stout improved
staggered fermions and explore a range of lattice spacings $a \sim 0.05 - 0.12$
fm. At zero temperature we estimate both finite size and finite cut-off
effects, comparing our continuum extrapolated results for the topological
susceptibility $\chi$ with predictions from chiral perturbation theory. At
finite temperature, we explore a region going from $T_c$ up to around $4\,
T_c$, where we provide continuum extrapolated results for the topological
susceptibility and for the fourth moment of the topological charge
distribution. While the latter converges to the dilute instanton gas prediction
the former differs strongly both in the size and in the temperature dependence.
This results in a shift of the axion dark matter window of almost one order of
magnitude with respect to the instanton computation.


  Regression methods for interval-valued data have been increasingly studied in
recent years. As most of the existing works focus on linear models, it is
important to note that many problems in practice are nonlinear in nature and
therefore development of nonlinear regression tools for interval-valued data is
crucial. In this paper, we propose a tree-based regression method for
interval-valued data, which is well applicable to both linear and nonlinear
problems. Unlike linear regression models that usually require additional
constraints to ensure positivity of the predicted interval length, the proposed
method estimates the regression function in a nonparametric way, so the
predicted length is naturally positive without any constraints. A simulation
study is conducted that compares our method to popular existing regression
models for interval-valued data under both linear and nonlinear settings.
Furthermore, a real data example is presented where we apply our method to
analyze price range data of the Dow Jones Industrial Average index and its
component stocks.


  The SABRE (Sodium iodide with Active Background REjection) experiment aims to
detect an annual rate modulation from dark matter interactions in ultra-high
purity NaI(Tl) crystals in order to provide a model independent test of the
signal observed by DAMA/LIBRA. It is made up of two separate detectors; SABRE
South located at the Stawell Underground Physics Laboratory (SUPL), in regional
Victoria, Australia, and SABRE North at the Laboratori Nazionali del Gran Sasso
(LNGS). SABRE South is designed to disentangle seasonal or site-related effects
from the dark matter-like modulated signal by using an active veto and muon
detection system. Ultra-high purity NaI(Tl) crystals are immersed in a linear
alkyl benzene (LAB) based liquid scintillator veto, further surrounded by
passive steel and polyethylene shielding and a plastic scintillator muon veto.
Significant work has been undertaken to understand and mitigate the background
processes, that take into account radiation from the detector materials, from
both intrinsic and cosmogenic activated processes, and to understand the
performance of both the crystal and veto systems. SUPL is a newly built
facility located 1024 m underground (about 2900 m water equivalent) within the
Stawell Gold Mine and its construction has been completed in mid-2022. The
laboratory will house rare event physics searches, including the upcoming SABRE
dark matter experiment, as well as measurement facilities to support low
background physics experiments and applications such as radiobiology and
quantum computing. The SABRE South commissioning is expected to occur in 2023.
This paper describes the setup and projections for the experiment, and the
description of the underground laboratory.


  Multiplicative analogues of the shuffle elements of the braid group rings are
introduced; in local representations they give rise to certain graded
associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the
(anti)-symmetrizers have simple expressions in terms of the multiplicative
shuffles. The (anti)-symmetrizers can be expressed in terms of the highest
multiplicative 1-shuffles (for the Hecke and BMW algebras) and in terms of the
highest additive 1-shuffles (for the Hecke algebras). The spectra and
multiplicities of eigenvalues of the operators of the multiplication by the
multiplicative and additive 1-shuffles are examined.


  We review studies of vibrational energy transfer in a molecular junction
geometry, consisting of a molecule bridging two heat reservoirs, solids or
large chemical compounds. This setup is of interest for applications in
molecular electronics, thermoelectrics, and nanophononics, and for addressing
basic questions in the theory of classical and quantum transport. Calculations
show that system size, disorder, structure, dimensionality, internal
anharmonicities, contact interaction, and quantum coherent effects, are factors
that interplay to determine the predominant mechanism (ballistic/diffusive),
effectiveness (poor/good) and functionality (linear/nonlinear) of thermal
conduction at the nanoscale. We review recent experiments and relevant
calculations of quantum heat transfer in molecular junctions. We recount the
Landauer approach, appropriate for the study of elastic (harmonic) phononic
transport, and outline techniques which incorporate molecular anharmonicities.
Theoretical methods are described along with examples illustrating the
challenge of reaching control over vibrational heat conduction in molecules.


  Deep-learning-based video processing has yielded transformative results in
recent years. However, the video analytics pipeline is energy-intensive due to
high data rates and reliance on complex inference algorithms, which limits its
adoption in energy-constrained applications. Motivated by the observation of
high and variable spatial redundancy and temporal dynamics in video data
streams, we design and evaluate an adaptive-resolution optimization framework
to minimize the energy use of multi-task video analytics pipelines. Instead of
heuristically tuning the input data resolution of individual tasks, our
framework utilizes deep reinforcement learning to dynamically govern the input
resolution and computation of the entire video analytics pipeline. By
monitoring the impact of varying resolution on the quality of high-dimensional
video analytics features, hence the accuracy of video analytics results, the
proposed end-to-end optimization framework learns the best non-myopic policy
for dynamically controlling the resolution of input video streams to globally
optimize energy efficiency. Governed by reinforcement learning, optical flow is
incorporated into the framework to minimize unnecessary spatio-temporal
redundancy that leads to re-computation, while preserving accuracy. The
proposed framework is applied to video instance segmentation which is one of
the most challenging computer vision tasks, and achieves better energy
efficiency than all baseline methods of similar accuracy on the YouTube-VIS
dataset.


  We perform the a posteriori error analysis of residual type of a transmission
problem with sign changing coefficients. According to [6] if the contrast is
large enough, the continuous problem can be transformed into a coercive one. We
further show that a similar property holds for the discrete problem for any
regular meshes, extending the framework from [6]. The reliability and
efficiency of the proposed estimator is confirmed by some numerical tests.


  We discuss a recent analysis of $t\bar{t}$ threshold effects and its
implications for the determination of electroweak parameters. We show that the
new formulation, when applied to the $\rho$ parameter for $m_t\approx158$~GeV,
gives a result of similar magnitude to those previously obtained. In fact, it
is quite close to our ``resonance'' calculation. We also present a simple
estimate of the size of the threshold effects based on an elementary Bohr-atom
model of $t\bar{t}$ resonances.


  We investigate a progenitor mass distribution of core-collapse supernova
remnants (CCSNRs) in our Galaxy and the Large and Small Magellanic Clouds, for
the first time. We count the number of CCSNRs in three mass ranges divided by
the zero-age main-sequence mass, $M_{\rm ZAMS}$; A: $M_{\rm ZAMS} < 15\ {\rm
M}_\odot$, B: $15\ {\rm M}_\odot < M_{\rm ZAMS} < 22.5\ {\rm M}_\odot$, C:
$M_{\rm ZAMS} > 22.5\ {\rm M}_\odot$. Simple compilation of progenitor masses
in the literature yields a progenitor mass distribution of $f_{\rm A}: f_{\rm
B}: f_{\rm C} =0.24:0.28:0.48$, where $f$ is the number fraction of the
progenitors. The distribution is inconsistent with any standard initial mass
functions. We notice, however, that previous mass estimates are subject to
large systematic uncertainties because most of the relative abundances (X/Si)
are not really good probe for the progenitor masses. Instead, we propose to
rely only on the Fe/Si ratio which is sensitive to the CO core mass ($M_{\rm
COcore}$) and $M_{\rm ZAMS}$. Comparing Fe/Si ratios in SNRs in the literature
with the newest theoretical model, we estimate 33 $M_{\rm COcore}$ and $M_{\rm
ZAMS}$, leading to a revised progenitor mass distribution of $f_{\rm A}: f_{\rm
B}: f_{\rm C} = 0.47: 0.32 : 0.21$. This is consistent with the standard
Salpeter initial mass function. However, the relation between $M_{\rm COcore}$
and $M_{\rm ZAMS}$ could be affected by binary evolution, which is not taken
into account in this study and should be considered in the future work to
derive a better progenitor mass distribution estimate.


  A mixed group of manned and unmanned aerial vehicles is considered as a
distributed system. A lattice of tasks which may be fulfilled by the system
matches to it. An external multiplication operation is defined at the lattice,
which defines correspondingly linear logic operations. Linear implication and
tensor product are used to choose a system reconfiguration variant, i.e., to
determine a new task executor choice. The task lattice structure (i.e., the
system purpose) and the operation definitions largely define the choice. Thus,
the choice is mainly the system purpose consequence. Such a method of the
behavior variant choice facilitates the decision making by the pilot
controlling the group. The suggested approach is illustrated using an example
of a mixed group control at forest fire compression.


  We tackle the problem of online reward maximisation over a large finite set
of actions described by their contexts. We focus on the case when the number of
actions is too big to sample all of them even once. However we assume that we
have access to the similarities between actions' contexts and that the expected
reward is an arbitrary linear function of the contexts' images in the related
reproducing kernel Hilbert space (RKHS). We propose KernelUCB, a kernelised UCB
algorithm, and give a cumulative regret bound through a frequentist analysis.
For contextual bandits, the related algorithm GP-UCB turns out to be a special
case of our algorithm, and our finite-time analysis improves the regret bound
of GP-UCB for the agnostic case, both in the terms of the kernel-dependent
quantity and the RKHS norm of the reward function. Moreover, for the linear
kernel, our regret bound matches the lower bound for contextual linear bandits.


  We calculate the mass and width of the sigma meson in nuclear medium by
considering that it couples to two virtual pions and to a pair of
nucleon-antinucleon states and to particle-hole states. The mass is calculated
by using the spectral function in the Walecka model, finding that it is about
380MeV. In addition, we obtain the value of 340MeV for the width of its
spectral function. We find that there is a reduction in the mass value compared
with that in vacuum. This result is consistent with those reported by other
authors who have used different models predicting a decreasing of the mass as a
function of the density.


  From the generalized fluctuation-dissipation theorem, it is known that a body
at rest made of nonreciprocal material may experience a torque, even in vacuum,
if it is not in thermal equilibrium with its environment. However, it does not
experience self-propulsion in such circumstances, except in higher order.
Nevertheless, such a body may experience both a normal torque and a lateral
force when adjacent to an ordinary surface with transverse translational
symmetry. We explore how these phenomena arise, discuss what terminal
velocities might be achieved, and point out some of the limitations of applying
our results to observations, including the Lorenz-Lorentz correction, and the
cooling due to radiation. In spite of these limitations, the effects discussed
would seem to be observable.


  Given Poincare spaces M and X, we study the possibility of compressing
embeddings of M x I in X x I down to embeddings of M in X. This results in a
new approach to embedding in the metastable range both in the smooth and
Poincare duality categories.


  Suppose that the edges of a complete graph are assigned weights independently
at random and we ask for the weight of the minimal-weight spanning tree, or
perfect matching, or Hamiltonian cycle. For these and several other common
optimisation problems, we establish asymptotically tight bounds when the
weights are independent copies of a symmetric random variable (satisfying a
mild condition on tail probabilities), in particular when the weights are
Gaussian.