  Taking advantage of a novel multiprobe setup we have measured, on a unique
sample, the ac-magnetic susceptibility, the resistivity, the ac-specific heat
and the thermopower of the superconductor heavy fermion CeCu$_{2}$Si$_{2}$
under pressure up to 5.1 GPa. At the superconducting transition temperature
$T_c$, the Meissner signal corresponds to that expected for the sample volume
and coincides with the specific heat jump and the resistive transition
completion temperatures. Differing from previous observations, here the
susceptibility measurements did not reveal any anomaly in the vicinity of the
resistive transition onset.


  The remarkable success of Vision Transformers in Artificial Neural Networks
(ANNs) has led to a growing interest in incorporating the self-attention
mechanism and transformer-based architecture into Spiking Neural Networks
(SNNs). While existing methods propose spiking self-attention mechanisms that
are compatible with SNNs, they lack reasonable scaling methods, and the overall
architectures proposed by these methods suffer from a bottleneck in effectively
extracting local features. To address these challenges, we propose a novel
spiking self-attention mechanism named Dual Spike Self-Attention (DSSA) with a
reasonable scaling method. Based on DSSA, we propose a novel spiking Vision
Transformer architecture called SpikingResformer, which combines the
ResNet-based multi-stage architecture with our proposed DSSA to improve both
performance and energy efficiency while reducing parameters. Experimental
results show that SpikingResformer achieves higher accuracy with fewer
parameters and lower energy consumption than other spiking Vision Transformer
counterparts. Notably, our SpikingResformer-L achieves 79.40% top-1 accuracy on
ImageNet with 4 time-steps, which is the state-of-the-art result in the SNN
field.


  In this paper we present a mathematical model and a numerical workflow for
the simulation of a thermal single-phase flow with reactive transport in porous
media, in the presence of fractures. The latter are thin regions which might
behave as high or low permeability channels depending on their physical
parameters, and are thus of paramount importance in underground flow problems.
Chemical reactions may alter the local properties of the porous media as well
as the fracture walls, changing the flow path and possibly occluding some
portions of the fractures or zones in the porous media. To solve numerically
the coupled problem we propose a temporal splitting scheme so that the
equations describing each physical process are solved sequentially. Numerical
tests shows the accuracy of the proposed model and the ability to capture
complex phenomena, where one or multiple fractures are present.


  A rigorous foundation for the contact homology of Legendrian submanifolds in
a contact manifold of the form $P\times \R$ where $P$ is an exact symplectic
manifold is established. The class of such contact manifolds include 1-jet
spaces of smooth manifolds. As an application, contact homology is used to
provide (smooth) isotopy invariants of submanifolds of $\R^n$ and, more
generally, invariants of self transverse immersions into $\R^n$ up to
restricted regular homotopies. When $n=3$, this application is the first step
in extending and providing a contact geometric underpinning for the new knot
invariants of Ng


  We prove that any integer power of $2$ can be realized as the Tamagawa number
of a torus attached to a CM algebra considered by Guo Sheu Yu and Liang Yang
Yu. Such a result is obtained by Liang Yang Yu under assuming "a generalized
Landau conjecture". The main contribution of this paper is to remove the above
assumption.


  We reconsider top condensate models from the perspective that not only two
quark composite fields can form but also four quark ones. We obtain a model
which contains a Higgs doublet and a Higgs triplet, where one of the neutral
components of the Higgs triplet identifies with the Higgs boson found at the
LHC. We discuss some of the phenomenological consequences.


  Exploratory data analysis (EDA) is a vital procedure for data science
projects. In this work, we introduce a stable equilibrium point (SEP) - based
framework for improving the efficiency and solution quality of EDA. By
exploiting the SEPs to be the representative points, our approach aims to
generate high-quality clustering and data visualization for large-scale data
sets. A very unique property of the proposed method is that the SEPs will
directly encode the clustering properties of data sets. Compared with prior
state-of-the-art clustering and data visualization methods, the proposed
methods allow substantially improving computing efficiency and solution quality
for large-scale data analysis tasks.


  In this paper we consider a hierarchical pose graph optimization (HPGO) for
Simultaneous Localization and Mapping (SLAM). We propose a fast incremental
procedure for building hierarchy levels in pose graphs. We study the properties
of this procedure and show that our solution delivers high execution speed,
high reduction rate and good flexibility. We propose a way to do partial
hierarchical optimization and compare it to other optimization modes. We show
that given a comparatively large amount of poses, partial HPGO gives a 10x
speed up comparing to the original optimization, not sacrificing the quality.


  The many-body localised (MBL) to thermal crossover observed in exact
diagonalisation studies remains poorly understood as the accessible system
sizes are too small to be in an asymptotic scaling regime. We develop a model
of the crossover in short 1D chains in which the MBL phase is destabilised by
the formation of many-body resonances. The model reproduces several properties
of the numerically observed crossover, including an apparent correlation length
exponent $\nu=1$, exponential growth of the Thouless time with disorder
strength, linear drift of the critical disorder strength with system size,
scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged
spectral functions, and sub-thermal entanglement entropy of small subsystems.
In the crossover, resonances induced by a local perturbation are rare at
numerically accessible system sizes $L$ which are smaller than a
\emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$, resonances
typically overlap, and this model does not describe the asymptotic transition.
The model further reproduces controversial numerical observations which Refs.
[\v{S}untajs et al, 2019] and [Sels & Polkovnikov, 2020] claimed to be
inconsistent with MBL. We thus argue that the numerics to date is consistent
with a MBL phase in the thermodynamic limit.


  The evaluation of the path-integral representation for stochastic processes
in the weak-noise limit shows that these systems are governed by a set of
equations which are those of a classical dynamics. We show that, even when the
noise is colored, these may be put into a Hamiltonian form which leads to
better insights and improved numerical treatments. We concentrate on solving
Hamilton's equations over an infinite time interval, in order to determine the
leading order contribution to the mean escape time for a bistable potential.
The paths may be oscillatory and inherently unstable, in which case one must
use a multiple shooting numerical technique over a truncated time period in
order to calculate the infinite time optimal paths to a given accuracy. We look
at two systems in some detail: the underdamped Langevin equation driven by
external exponentially correlated noise and the overdamped Langevin equation
driven by external quasi-monochromatic noise. We deduce that caustics, focusing
and bifurcation of the optimal path are general features of all but the
simplest stochastic processes.


  We study the scattering properties of a Bose-Einstein condensate held in a
finite depth well when the incoming particles are identical to the ones in the
condensate. We calculate phase shifts and corresponding transmission and
reflection coefficients, and we show that the transmission times can be
negative, i.e., the atomic wavepacket seemingly leaves the condensate before it
arrives.


  Spectral state transitions in neutron star LMXB systems have been widely
observed yet not well understood. Here we report an abrupt spectral change in
4U 1608-52, a typical atoll source, during its decay phase of the 2004
outburst. The source is found to undergo sudden changes in its spectral
hardness and other properties. The transition occurred when its luminosity is
between (3.3-5.3) E36 ergs/s, assuming a distance of 3.6 kpc. Interpreting this
event in terms of the propeller effect, we infer the neutron star surface
magnetic field as (1.4-1.8) E8 Gauss. We also briefly discuss similarities and
differences between the spectral states of neutron star and black hole binary
systems.


  We study the standing periodic waves in the semi-discrete integrable system
modelled by the Ablowitz-Ladik equation. We have related the stability spectrum
to the Lax spectrum by separating the variables and by finding the
characteristic polynomial for the standing periodic waves. We have also
obtained rogue waves on the background of the modulationally unstable standing
periodic waves by using the end points of spectral bands and the corresponding
eigenfunctions. The magnification factors for the rogue waves have been
computed analytically and compared with their continuous counterparts. The main
novelty of this work is that we explore a non-standard linear Lax system, which
is different from the standard Lax representation of the Ablowitz-Ladik
equation.


  As the 5G communication networks are being widely deployed worldwide, both
industry and academia have started to move beyond 5G and explore 6G
communications. It is generally believed that 6G will be established on
ubiquitous Artificial Intelligence (AI) to achieve data-driven Machine Learning
(ML) solutions in heterogeneous and massive-scale networks. However,
traditional ML techniques require centralized data collection and processing by
a central server, which is becoming a bottleneck of large-scale implementation
in daily life due to significantly increasing privacy concerns. Federated
learning, as an emerging distributed AI approach with privacy preservation
nature, is particularly attractive for various wireless applications,
especially being treated as one of the vital solutions to achieve ubiquitous AI
in 6G. In this article, we first introduce the integration of 6G and federated
learning and provide potential federated learning applications for 6G. We then
describe key technical challenges, the corresponding federated learning
methods, and open problems for future research on federated learning in the
context of 6G communications.


  The superconductor-insulator transition in ultrathin films of amorphous Bi
was tuned by changing the film thickness, with and without an applied magnetic
field. The first experimentally obtained phase diagram is mapped as a function
of thickness and magnetic field in the T=0 limit. A finite size scaling
analysis has been carried out to determine the critical exponent product vz,
which was found to be 1.2 for the zero field transition, and 1.4 for the finite
field transition. Both results are different from the exponents found for the
magnetic field tuned transition in the same system, 0.7.


  In this study, we present a simple stochastic order-book model for investors'
swarm behaviors seen in the continuous double auction mechanism, which is
employed by major global exchanges. Our study shows a characteristic called
"fat tail" is seen in the data obtained from our model that incorporates the
investors' swarm behaviors. Our model captures two swarm behaviors: one is
investors' behavior to follow a trend in the historical price movement, and
another is investors' behavior to send orders that contradict a trend in the
historical price movement. In order to capture the features of influence by the
swarm behaviors, from price data derived from our simulations using these
models, we analyzed the price movement range, that is, how much the price is
moved when it is continuously moved in a single direction. Depending on the
type of swarm behavior, we saw a difference in the cumulative frequency
distribution of this price movement range. In particular, for the model of
investors who followed a trend in the historical price movement, we saw the
power law in the tail of the cumulative frequency distribution of this price
movement range. In addition, we analyzed the shape of the tail of the
cumulative frequency distribution. The result demonstrated that one of the
reasons the trend following of price occurs is that orders temporarily swarm on
the order book in accordance with past price trends.


  Many analyses of microwave background experiments neglect the correlation of
noise in different frequency or polarization channels. We show that these
correlations, should they be present, can lead to severe misinterpretation of
an experiment. In particular, correlated noise arising from either electronics
or atmosphere may mimic a cosmic signal. We quantify how the likelihood
function for a given experiment varies with noise correlation, using both
simple analytic models and actual data. For a typical microwave background
anisotropy experiment, noise correlations at the level of 1\% of the overall
noise can seriously {\it reduce} the significance of a given detection.


  In this paper we introduce and study $n$-point Virasoro algebras,
$\tilde{\W_a}$, which are natural generalizations of the classical Virasoro
algebra and have as quotients multipoint genus zero Krichever-Novikov type
algebras. We determine necessary and sufficient conditions for the latter two
such Lie algebras to be isomorphic. Moreover we determine their automorphisms,
their derivation algebras, their universal central extensions, and some other
properties. The list of automorphism groups that occur is $C_n$, $D_n$, $A_4$,
$S_4$ and $A_5$. We also construct a large class of modules which we call
modules of densities, and determine necessary and sufficient conditions for
them to be irreducible.


  We present the first results of high-spectral resolution (0.023 km/s)
N$_2$H$^+$ observations of dense gas dynamics at core scales (~0.01 pc) using
the recently commissioned Argus instrument on the Green Bank Telescope (GBT).
While the fitted linear velocity gradients across the cores measured in our
targets nicely agree with the well-known power-law correlation between the
specific angular momentum and core size, it is unclear if the observed
gradients represent core-scale rotation. In addition, our Argus data reveal
detailed and intriguing gas structures in position-velocity (PV) space for all
5 targets studied in this project, which could suggest that the velocity
gradients previously observed in many dense cores actually originate from
large-scale turbulence or convergent flow compression instead of rigid-body
rotation. We also note that there are targets in this study with their
star-forming disks nearly perpendicular to the local velocity gradients, which,
assuming the velocity gradient represents the direction of rotation, is
opposite to what is described by the classical theory of star formation. This
provides important insight on the transport of angular momentum within
star-forming cores, which is a critical topic on studying protostellar disk
formation.


  As carriers slowly move through a disordered energy landscape in organic
semiconductors, tiny spatial variations in spin dynamics relieve spin blocking
at transport bottlenecks or in the electron-hole recombination process that
produces light. Large room-temperature magnetic-field effects (MFE) ensue in
the conductivity and luminescence. Sources of variable spin dynamics generate
much larger MFE if their spatial structure is correlated on the nanoscale with
the energetic sites governing conductivity or luminescence such as in
co-evaporated organic blends within which the electron resides on one molecule
and the hole on the other (an exciplex). Here we show that exciplex
recombination in blends exhibiting thermally-activated delayed fluorescence
(TADF) produces MFE in excess of 60% at room temperature. In addition, effects
greater than 4000% can be achieved by tuning the device's current-voltage
response curve by device conditioning. These immense MFEs are both the largest
reported values for their device type at room temperature. Our theory traces
this MFE and its unusual temperature dependence to changes in spin mixing
between triplet exciplexes and light-emitting singlet exciplexes. In contrast,
spin mixing of excitons is energetically suppressed, and thus spin mixing
produces comparatively weaker MFE in materials emitting light from excitons by
affecting the precursor pairs. Demonstration of immense MFE in common organic
blends provides a flexible and inexpensive pathway towards magnetic
functionality and field sensitivity in current organic devices without
patterning the constituent materials on the nanoscale. Magnetic fields increase
the power efficiency of unconditioned devices by 30% at room temperature, also
showing that magnetic fields may increase the efficiency of the TADF process.


  Context. Chromospheric fibrils are thin and elongated structures that connect
nearby photospheric magnetic field concentrations of opposite polarities. Aims.
We assess the possibilities and drawbacks related to the use of current
instrumentation and inversion techniques to infer the thermodynamic structure
of chromospheric fibrils. Methods. We employed spectroscopic observations
obtained in the Ca ii 854.2 nm line with the CRISP instrument at the Swedish
1-m Solar Telescope and in coordination with observations in the ultraviolet Mg
ii h & k lines taken with the IRIS satellite. We studied the temperature
sensitivity of these chromospheric lines to properly invert their spectral
profiles with the Stockholm inversion Code and determine the temperature,
line-of-sight velocity, and microturbulent velocity of manually traced
chromospheric fibrils present in the field of view. Results. Fibril-like
structures show a very particular dependence of their temperature as a function
of the position along their length. Their temperatures at the detected
footpoints are, on average, 300 K higher than the temperature at the midpoint.
The temperature variation appears to be almost symmetrical in shape, with
partially traced fibrils showing a similar trend for the temperature variation.
Additionally, the response of the Ca ii 854.2 nm line core to variations of the
temperature for the inverted models of the atmosphere in fibril areas seems to
be insufficient to properly resolve the aforementioned temperature structure.
Only the addition of more temperature sensitive lines such as the Mg ii h & k
lines would make it possible to properly infer the thermodynamic properties of
chromospheric fibrils. Comparisons between the results obtained here and in
previous studies focused on bright Ca ii K fibrils yield great similarities
between these structures in terms of their temperature.


  We present the first results from our on-going Australia Telescope Compact
Array survey of CO(1-0) in ALMA-identified submillimetre galaxies in the
Extended Chandra Deep Field South. Strong detections of CO(1-0) emission from
two submillimetre galaxies, ALESS 122.1 (z = 2.0232) and ALESS 67.1 (z =
2.1230), were obtained. We estimate gas masses of M_gas ~ 1.3 \times 10^{11}
M_odot and M_gas ~ 1.0 \times 10^{11} M_\odot for ALESS 122.1 and ALESS 67.1,
respectively, adopting alpha_CO = 1.0. Dynamical mass estimates from the
kinematics of the CO(1-0) line yields M_dyn (sin i)^2 = 2.1 +- 1.1 \times
10^{11} M_odot and (3.2 +- 0.9) \times 10^{11} M_\odot for ALESS 122.1 and
ALESS 67.1, respectively. This is consistent with the total baryonic mass
estimates of these two systems. We examine star formation efficiency using the
L_FIR versus L'_CO(1-0) relation for samples of local ULIRGs and LIRGs, and
more distant star-forming galaxies, with CO(1-0) detections. We find some
evidence of a shallower slope for ULIRGs and SMGs compared to less luminous
systems, but a larger sample is required for definite conclusions. We determine
gas-to-dust ratios of 170 +- 30 and 140 +- 30 for ALESS 122.1 and ALESS 67.1,
respectively, showing ALESS 122.1 has an unusually large gas reservoir. By
combining the 38.1 GHz continuum detection of ALESS 122.1 with 1.4 and 5.5 GHz
data, we estimate that the free-free contribution to radio emission at 38.1 GHz
is 34 +- 17 microJy, yielding a star formation rate (1400 +- 700 M_\odot
yr^{-1}) consistent with that from the infrared luminosity.


  We consider the extended half-filled Hubbard model on the honeycomb lattice
for second nearest neighbors interactions. Using a functional integral
approach, we find that collective fluctuations suppress topological states and
instead favor charge ordering, in agreement with previous numerical studies.
However, we show that the critical point is not of the putative semimetal-Mott
insulator variety. Due to the frustrated nature of the interactions, the ground
state is described by a novel hidden {\it metallic} charge order with {\it
semi-Dirac} excitations. We conjecture that this transition is not in the
Gross-Neveu universality class.


  We propose a new method to constrain elastic scattering between dark matter
(DM) and standard model particles in the early Universe. Direct or indirect
thermal coupling of non-relativistic DM with photons leads to a heat sink for
the latter. This results in spectral distortions of the cosmic microwave
background (CMB), the amplitude of which can be as large as a few times the
DM-to-photon number ratio. We compute CMB spectral distortions due to
DM-proton, DM-electron and DM-photon scattering for generic energy-dependent
cross sections and DM mass m_DM >~ 1 keV. Using FIRAS measurements we set
constraints on the cross sections for m_DM <~ 0.1 MeV. In particular, for
energy-independent scattering we obtain sigma[DM-proton] <~ 10^(-24) cm^2
(keV/m_DM)^(1/2), sigma[DM-electron] <~ 10^(-27) cm^2 (keV/m_DM)^(1/2) and
sigma[DM-photon] <~ 10^(-39) cm^2 (m_DM/keV). An experiment with the
characteristics of PIXIE would extend the regime of sensitivity up to masses
m_DM ~ 1 GeV.


  A novel distributed algorithm is proposed for finite-time converging to a
feasible consensus solution satisfying global optimality to a certain accuracy
of the distributed robust convex optimization problem (DRCO) subject to bounded
uncertainty under a uniformly strongly connected network. Firstly, a
distributed lower bounding procedure is developed, which is based on an outer
iterative approximation of the DRCO through the discretization of the compact
uncertainty set into a finite number of points. Secondly, a distributed upper
bounding procedure is proposed, which is based on iteratively approximating the
DRCO by restricting the constraints right-hand side with a proper positive
parameter and enforcing the compact uncertainty set at finitely many points.
The lower and upper bounds of the global optimal objective for the DRCO are
obtained from these two procedures. Thirdly, two distributed termination
methods are proposed to make all agents stop updating simultaneously by
exploring whether the gap between the upper and the lower bounds reaches a
certain accuracy. Fourthly, it is proved that all the agents finite-time
converge to a feasible consensus solution that satisfies global optimality
within a certain accuracy. Finally, a numerical case study is included to
illustrate the effectiveness of the distributed algorithm.


  We discuss the strength of the trilinear Higgs boson coupling in technicolor
(or composite) models in a model independent way. The coupling is determined as
a function of a very general ansatz for the technicolor self-energy, and turns
out to be equal or smaller than the one of the standard model Higgs boson
depending on the dynamics of the theory. With this trilinear coupling we
estimate the cross section for Higgs boson pair production at the LHC. This
measurement is quite improbable in the case of a heavy standard model Higgs
boson, but it will be even worse when this boson is dynamically generated.


  The flow of a liquid crystal around a particle does not only depend on its
shape and the viscosity coefficients but also on the direction of the
molecules. We studied the resulting drag force on a sphere moving in a nematic
liquid crystal (MBBA) in a low Reynold's number approach for a fixed director
field (low Ericksen number regime) using the computational artificial
compressibility method. Taking the necessary disclination loop around the
sphere into account, the value of the drag force anisotropy
(F_\perp/F_\parallel=1.50) for an exactly computed field is in good agreement
with experiments (~1.5) done by conductivity diffusion measurements. We also
present data for weak anchoring of the molecules on the particle surface and of
trial fields, which show to be sufficiently good for most applications.
Furthermore, the behaviour of the friction close to the transition point
nematic <-> isotropic and for a rod-like and a disc-like liquid crystal will be
given.


  "Quasi-harmonic" (QH) theory should not be considered a low-order theory of
anharmonic effects in crystals, but should be recognized as an important effect
separate from "true" anharmonicity. The original and widely used meaning of QH
theory is to put T=0 volume-dependent harmonic phonon energies omega_Q(V) into
the non-interacting phonon free energy. This paper uses that meaning, but
extends it to include the use of T=0 V-dependent single-particle electron
energies epsilon_K(V). It is demonstrated that the "bare" quasiparticle (QP)
energies omega_Q(V) and epsilon_K(V) correctly give the first-order term in the
V-dependence of the Helmholtz free energy F(V,T). Therefore, they give the
leading order result for thermal expansion alpha(T) and for the
temperature-dependence of the bulk modulus B(T)-B_0. However, neglected
interactions which shift and broaden omega_Q with T, also shift the free
energy. In metals, the low T electron-phonon mass enhancement of states near
the Fermi level causes a shift in free energy that is similar in size to the
electronic QH term. Before T reaches the Debye temperature, the mass
renormalization essentially disappears, and remaining electron-phonon shifts of
free energy contribute only higher-order terms to thermal expansion. Similarly,
anharmonic phonon-phonon interactions shift the free energy, but contribute to
thermal expansion only in higher order. Explicit next order formulas are given
for thermal expansion, which relate "true" anharmonic and similar free energy
corrections to quasiparticle self-energy shifts. The text below, except for
Sec. IX, was already published in Modern Physics Letters B, Vol. 34, No. 2
(2020) 2050025. Since then an important error was discovered. The error is
corrected in Sec. IX, and will be published as an erratum in Modern Physics
Letters B.


  The regularized trace formula of first order for the Sturm-Liouville equation
with spectral parameter in the boundary conditions is obtained.


  (Abridged) We have investigated the reliability of the widely used I-band Tip
of the RGB relative distances for a sample of Local Group galaxies with complex
Star Formation Histories (SFR) and Age Metallicity Relationships (AMR) namely
the LMC, SMC and LGS3. The use of the K-band is also discussed. By employing
theoretical stellar population synthesis techniques, we find that using actual
determinations of SFR and AMR of the LMC and SMC, their RGB is populated by
stars much younger (by 9 Gyr) than the Galactic globular cluster counterparts,
on which the I-band (and K-band) TRGB absolute magnitude is calibrated. This
age difference induces a bias in both the photometric metallicity estimates
based on the comparison of RGB colours with globular cluster ones, and the TRGB
distances. The extent of the distance bias is strongly dependent on the
specific TRGB technique applied, and on the assumed I-band BC scale adopted;
the correction to apply to the SMC-LMC distance modulus ranges from 0 up to
+0.10 mag. LGS3 is an example of galaxy populated mainly by old stars, so that
photometric metallicity and distance estimates using globular cluster
calibrations are reliable. However, the relative distance moduli between
Magellanic Clouds and LGS3 are affected by the population effects discussed for
the LMC and SMC. The corrections to apply to the K-band TRGB distances are
larger than the I-band case. Our results clearly show that the presence of a
well developed RGB in the CMD of a stellar system with a complex SFR does not
guarantee that it is populated by globular cluster-like red giants, and
therefore the TRGB method for distance determination has to be applied with
caution.


  Quantum key distribution (QKD) promises information-theoretically secure
communication, and is already on the verge of commercialization. Thus far,
different QKD protocols have been proposed theoretically and implemented
experimentally [1, 2]. The next step will be to implement high-dimensional
protocols in order to improve noise resistance and increase the data rate
[3-7]. Hitherto, no experimental verification of high-dimensional QKD in the
single-photon regime has been conducted outside of the laboratory. Here, we
report the realization of such a single-photon QKD system in a turbulent
free-space link of 0.3 km over the city of Ottawa, taking advantage of both the
spin and orbital angular momentum photonic degrees of freedom. This combination
of optical angular momenta allows us to create a 4-dimensional state [8];
wherein, using a high-dimensional BB84 protocol [3, 4], a quantum bit error
rate of 11\% was attained with a corresponding secret key rate of 0.65 bits per
sifted photon. While an error rate of 5\% with a secret key rate of 0.43 bits
per sifted photon is achieved for the case of 2-dimensional structured photons.
Even through moderate turbulence without active wavefront correction, it is
possible to securely transmit information carried by structured photons,
opening the way for intra-city high-dimensional quantum communications under
realistic conditions.


  The relation between two approaches to the su(2)-algebraic many-fermion model
is discussed: (1) the BCS-Bogoliubov approach in terms of the use of the
quasiparticles representing all the degrees of freedom except those related to
the Cooper-pairs and (2) the conventional algebraic approach in terms of the
use of the minimum weight states, from which the Cooper-pairs are excluded. In
order to arrive at the goal, the idea of the quasiparticles is brought up in
the conservation of the fermion number. Under the c-number replacement for the
three su(2)-generators, the quasiparticles suggested in this paper are reduced
to those in the BCS-Bogoliubov approach. It is also shown that the two
approaches are equivalent through the c-number replacement. Further, a certain
modification of the BCS-Bogoliubov approach is discussed.


  We extend Norton-Borcherds-Koike's replication formulae to super-replicable
ones by working with the congruence groups $\Gamma_1(N)$ and find the product
identities which characterize super-replicable functions. These will provide a
clue for constructing certain new infinite dimensional Lie superalgebras whose
denominator identities coincide with the above product identities. Therefore it
could be one way to find a connection between modular functions and infinite
dimensional Lie algebras.


  Recently, an aziridinium lead iodide perovskite was proposed as a possible
solar cell absorber material. We investigated the stability of this material
using a density-functional theory with an emphasis on the ring strain
associated with the three-membered aziridinium cation. It is shown that the
aziridinium ring is prone to opening within the PbI$_3$ environment. When
exposed to moisture, aziridinium lead iodide can readily react with water. The
resultant product will not likely be a stoichiometric lead halide perovskite
structure.


  We study the electron transport in a magnetically doped three dimensional
topological insulator (TI) by taking the effects of impurity-impurity exchange
interactions into account. The interactions between magnetic impurities give
rise to the formation of {\it magnetic clusters} with temperature dependent
mean sizes, randomly distributed on the surface of the TI. Instead of dealing
with single magnetic impurities, we consider surface Dirac electrons to be
scattered off magnetic clusters, and define the scattering potential in terms
of clusters mean sizes. Within the semiclassical Boltzmann approach, employing
a generalized relaxation time approximation, we obtain the surface conductivity
of the TI by solving four sets of recursive relations and demonstrate that, the
system is highly anisotropic and the surface conductivities possess
non-monotonic behaviors, they strongly depends on the direction, the mean size
and the number of magnetic clusters. We demonstrate that the dependence of the
anisotropic magnetoresistance (AMR) to the spin direction of the magnetic
clusters is inconsistent with the angular dependence of the TI doped with
non-interacting magnetic impurities. Our results are consistent with the recent
experiment on the AMR of the Cr-doped $\rm {(Bi, Sb)}_2{\rm Te}_3$ TI.


  The connection between self-assembly and computation suggests that a shape
can be considered the output of a self-assembly ``program,'' a set of tiles
that fit together to create a shape. It seems plausible that the size of the
smallest self-assembly program that builds a shape and the shape's
descriptional (Kolmogorov) complexity should be related. We show that when
using a notion of a shape that is independent of scale, this is indeed so: in
the Tile Assembly Model, the minimal number of distinct tile types necessary to
self-assemble a shape, at some scale, can be bounded both above and below in
terms of the shape's Kolmogorov complexity. As part of the proof of the main
result, we sketch a general method for converting a program outputting a shape
as a list of locations into a set of tile types that self-assembles into a
scaled up version of that shape. Our result implies, somewhat
counter-intuitively, that self-assembly of a scaled-up version of a shape often
requires fewer tile types. Furthermore, the independence of scale in
self-assembly theory appears to play the same crucial role as the independence
of running time in the theory of computability. This leads to an elegant
formulation of languages of shapes generated by self-assembly. Considering
functions from integers to shapes, we show that the running-time complexity,
with respect to Turing machines, is polynomially equivalent to the scale
complexity of the same function implemented via self-assembly by a finite set
of tile types. Our results also hold for shapes defined by Wang tiling -- where
there is no sense of a self-assembly process -- except that here time
complexity must be measured with respect to non-deterministic Turing machines.


  In this paper, we explore the possibility of deriving a quantum wavefunction
for continuous-time recurrent neural network (CTRNN). We did this by first
starting with a two-dimensional dynamical system that describes the classical
dynamics of a continuous-time recurrent neural network, and then deriving a
Hamiltonian. After this, we quantized this Hamiltonian on a Hilbert space
$\mathbb{H} = L^2(\mathbb{R})$ using Weyl quantization. We then solved the
Schrodinger equation which gave us the wavefunction in terms of Kummer's
confluent hypergeometric function corresponding to the neural network
structure. Upon applying spatial boundary conditions at infinity, we were able
to derive conditions/restrictions on the weights and hyperparameters of the
neural network, which could potentially give insights on the the nature of
finding optimal weights of said neural networks.


  High-relative-degree control barrier functions (hi-rel-deg CBFs) play a
prominent role in automotive safety and in robotics. In this paper we launch a
generalization of this concept for PDE control, treating a specific,
physically-relevant model of thermal dynamics where the boundary of the PDE
moves due to a liquid-solid phase change -- the so-called Stefan model. The
familiar QP design is employed to ensure safety but with CBFs that are
infinite-dimensional (including one control barrier "functional") and with safe
sets that are infinite-dimensional as well. Since, in the presence of actuator
dynamics, at the boundary of the Stefan system, this system's main CBF is of
relative degree two, an additional CBF is constructed, by backstepping design,
which ensures the positivity of all the CBFs without any additional
restrictions on the initial conditions. It is shown that the "safety filter"
designed in the paper guarantees safety in the presence of an arbitrary
operator input. This is similar to an automotive system in which a safety
feedback law overrides -- but only when necessary -- the possibly unsafe
steering, acceleration, or braking by a vigorous but inexperienced driver.
Simulations have been performed for a process in metal additive manufacturing,
which show that the operator's heat-and-cool commands to the Stefan model are
being obeyed but without the liquid ever freezing.


  Field-effect phototransistors were fabricated based on individual carbon
nanotubes (CNTs) sensitized by CH$_3$NH$_3$PbI$_3$ nanowires (MAPbI$_3$NW).
These devices represent light responsivities of R=7.7x10$^5$ A/W at
low-lighting conditions in the nWmm$^{-2}$ range, unprecedented among CNT-based
photo detectors. At high incident power (~1 mWmm$^{-2}$), light soaking results
in a negative photocurrent, the device turns insulating. We interpret the
phenomenon as a result of efficient electron-hole separation and charge
transfer of holes from the perovskite to the carbon nanotube, which improves
conductance by increasing the number of carriers, but leaves electrons behind.
At high illumination intensity the random electrostatic potential of these
quench the mobility in the nanotube. The single CNT device geometry allows the
local study of the MAPbI$_3$NW/CNT interface for metallic and semiconducting
CNTs separately. Infrared and Raman spectroscopy studies of
CNT-CH$_3$NH$_3$PbI$_3$ composites revealed that photo-doping takes place at
the interface.


  Let $\phi(z)=(\phi_1(z), ...,\phi_n(z))$ be a holomorphic self-map of $U^n$
and $\psi(z)$ a holomorphic function on $U^n,$ where $U^n$ is the unit polydisk
of ${\Bbb C}^n.$ Let $p\geq 0,$ $q\geq 0$, this paper gives some necessary and
sufficient conditions for the weighted composition operator $W_{\psi,\phi}$
induced by $\psi$ and $\phi$ to be bounded and compact between $p$-Bloch space
${\cal B}^p(U^n)$ and $q$-Bloch space ${\cal B}^q(U^n).$


  Vehicle service providers can display commercial ads in their vehicles based
on passengers' origins and destinations to create a new revenue stream. In this
work, we study a vehicle service provider who can generate different ad
revenues when displaying ads on different arcs (i.e., origin-destination
pairs). The provider needs to ensure the vehicle flow balance at each location,
which makes it challenging to analyze the provider's vehicle assignment and
pricing decisions for different arcs. For example, the provider's price for its
service on an arc depends on the ad revenues on other arcs as well as on the
arc in question. To tackle the problem, we show that the traffic network
corresponds to an electrical network. When the effective resistance between two
locations is small, there are many paths between the two locations and the
provider can easily route vehicles between them. We characterize the dependence
of an arc's optimal price on any other arc's ad revenue using the effective
resistances between these two arcs' origins and destinations. Furthermore, we
study the provider's optimal selection of advertisers when it can only display
ads for a limited number of advertisers. If each advertiser has one target arc
for advertising, the provider should display ads for the advertiser whose
target arc has a small effective resistance. We investigate the performance of
our advertiser selection strategy based on a real-world dataset.


  The existence of a new perturbation mode [`self-gravito-acoustic mode'
(SGAM)] in cold self-gravitating degenerate quantum plasmas (SGDQPs) is
theoretically predicted. This new SGAM is developed in the perturbed SGDQPs, in
which the compression is mainly provided by the self-gravitational pressure of
the heavy particle species, and the rarefaction is mainly provided by the
degenerate pressure of the light particle species. The SGAM is a new
perturbation mode since it completely disappears if the degenerate pressure of
the light particle species is neglected. The prediction of this new SGAM is
applied in a white dwarf SGDQP.


  We study the possibility that partonic matter produced at early stage of
ultrarelativistic heavy-ion collisions is out of chemical equilibrium. It is
assumed that initially this matter is mostly composed of gluons, but quarks and
antiquarks are produced at later times. The dynamical evolution of partonic
system is described by the Bjorken-like ideal hydrodynamics with a time
dependent quark fugacity. The results of this model are compared with those
obtained by assuming the complete chemical equilibrium of partons already at
the initial stage. It is shown that in a chemically non-equilibrium scenario
the entropy gradually increases, and about 25% of the total final entropy is
generated during the hydrodynamic evolution of deconfined matter. We argue that
the (anti)quark suppression included in this approach may be responsible for
reduced (anti)baryon to meson ratios observed in heavy-ion collisions at LHC
energies.


  In this paper, we present a novel approach to fitting mixture models based on
estimating first the posterior distribution of the auxiliary variables that
assign each observation to a group in the mixture. The posterior distributions
of the remainder of the parameters in the mixture is obtained by averaging over
their conditional posterior marginals on the auxiliary variables using Bayesian
model averaging.
  A new algorithm based on Gibbs sampling is used to approximate the posterior
distribution of the auxiliary variables without sampling any other parameter in
the model. In particular, the modes of the full conditionals of the parameters
of the densities in the mixture are computed and these are plugged-in to the
full conditional of the auxiliary variables to draw samples. This
approximation, that we have called 'modal' Gibbs sampling, reduces the
computational burden in the Gibbs sampling algorithm and still provides very
good estimates of the posterior distribution of the auxiliary variables.
Conditional models on the auxiliary variables are fitted using the Integrated
Nested Laplace Approximation (INLA) to obtain the conditional posterior
distributions, including modes, of the distributional parameters in the
mixtures.
  This approach is general enough to consider mixture models with discrete or
continuous outcomes from a wide range of distributions and latent models as
conditional model fitting is done with INLA. This presents several other
advantages, such as fast fitting of the conditional models, not being
restricted to the use of conjugate priors on the model parameters and being
less prone to label switching. Within this framework, computing the marginal
likelihood of the mixture model when the number of groups in the mixture is
known is easy and it can be used to tackle selection of the number of
components.


  We propose an optimization-based method for reconstructing a time-domain
signal from a low-dimensional spectral representation such as a
mel-spectrogram. Phase reconstruction has been studied to reconstruct a
time-domain signal from the full-band short-time Fourier transform (STFT)
magnitude. The Griffin-Lim algorithm (GLA) has been widely used because it
relies only on the redundancy of STFT and is applicable to various audio
signals. In this paper, we jointly reconstruct the full-band magnitude and
phase by considering the bi-level relationships among the time-domain signal,
its STFT coefficients, and its mel-spectrogram. The proposed method is
formulated as a rigorous optimization problem and estimates the full-band
magnitude based on the criterion used in GLA. Our experiments demonstrate the
effectiveness of the proposed method on speech, music, and environmental
signals.


  Water is a unique compound with many anomalies and properties not fully
understood. Designing an experiment in the laboratory to study such anomalies,
we set up a series of experiments where a tube was placed inside a sealed
container with thermocouples attached to the outer surface of the tube and in
the air adjacent to the tube. Alternately, deionized water and other compounds
were added to the tube and cooled to freezing. Several of the thermocouples
suspended in the air and adjacent to the tube showed thermal oscillations as
the overall temperature of the container was decreasing. The temperature of the
thermocouples increased and decreased in a sinusoidal way during part of the
cool down to freezing. Thermal oscillations as large as 3 degrees Celsius were
recorded with typical frequencies of about 5 oscillations per minute.


  We surveyed a 50 sq arcmin region in the Virgo cluster core to search for
intergalactic planetary nebulae, and found 11 candidates in the surveyed area.
The measured fluxes of these unresolved sources are consistent with these
objects being planetary nebulae from an intracluster population of stars. We
compute the cumulative luminosity function of these 11 planetary nebula
candidates. If we assume that they belong to the Virgo cluster, their
cumulative luminosity function is in good agreement with planetary nebula
luminosity function simulations. This comparison allows us to estimate the
surface mass density of the intracluster stellar population at the surveyed
field in the cluster core.


  Fermi J1544-0649 is a transient GeV source first detected during its GeV
flares in 2017. Multi-wavelength observations during the flaring time
demonstrate variability and spectral energy distribution(SED) that are typical
of a blazar. Other than the flare time, Fermi J1544-0649 is quiet in the GeV
band and looks rather like a quiet galaxy (2MASX J15441967-0649156) for a
decade. Together with the broad absorption lines feature we further explore the
"misaligned blazar scenario". We analyzed the Very Long Baseline Array (VLBA)
and East Asian VLBI Network (EAVN) data from 2018 to 2020 and discovered the
four jet components from Fermi J1544-0649. We found a viewing angle around
3.7{\deg} to 7.4{\deg}. The lower limit of the viewing angle indicates a blazar
with an extremely low duty cycle of the gamma-ray emission, the upper limit of
it supports the "misaligned blazar scenario". Follow-up multi-wavelength
observations after 2018 show Fermi J1544-0649 remains quiet in GeV, X-ray, and
optical bands. Multi-messenger search of neutrinos is also performed, and an
excess of 3.1 {\sigma} significance is found for this source.


  We consider heat semigroups of the form $\exp(t(\Delta -
\lambda\mathbf{1}_{\Omega_0}))$ on bounded domains. Using variants of Moser
iteration, we show sub-exponential decay in the ``large coupling limit", i.e.
as $\lambda\nearrow\infty$, in compact subdomains of the ``obstacle",
$\Omega_0$.


  In this rather computational paper, we determine certain representation
numbers of ideals in real quadratic number fields explicitly in order to obtain
a representation of the associated Dirichlet series in terms of Dirichlet
L-functions and a generalized divisor sum. A direct and important consequence
is that the Dirichlet series has a meromorphic continuation to the whole
complex plane and a simple pole at $s=2$ whose residue can be made explicit in
terms of the Dirichlet L-functions and the generalized divisor sum.


  In this thesis, we draw inspiration from both classical system identification
and modern machine learning in order to solve estimation problems for
real-world, physical systems. The main approach to estimation and learning
adopted is optimization based. Concepts such as regularization will be utilized
for encoding of prior knowledge and basis-function expansions will be used to
add nonlinear modeling power while keeping data requirements practical. The
thesis covers a wide range of applications, many inspired by applications
within robotics, but also extending outside this already wide field. Usage of
the proposed methods and algorithms are in many cases illustrated in the
real-world applications that motivated the research. Topics covered include
dynamics modeling and estimation, model-based reinforcement learning, spectral
estimation, friction modeling and state estimation and calibration in robotic
machining. In the work on modeling and identification of dynamics, we develop
regularization strategies that allow us to incorporate prior domain knowledge
into flexible, overparameterized models. We make use of classical control
theory to gain insight into training and regularization while using flexible
tools from modern deep learning. A particular focus of the work is to allow use
of modern methods in scenarios where gathering data is associated with a high
cost. In the robotics-inspired parts of the thesis, we develop methods that are
practically motivated and ensure that they are implementable also outside the
research setting. We demonstrate this by performing experiments in realistic
settings and providing open-source implementations of all proposed methods and
algorithms.


  In the present work certain features of the Penner model, such its
enumerative meaning and its relation to the Chern-Simons theory on the
3-sphere, are reviewed. Also, some features related to geometric transitions at
the level of the observables are discussed. In this setup, the non commutative
five dimensional U(1) Nekrasov partition function is interpreted as a limiting
case of a mean value of the Ooguri-Vafa operator for a Chern-Simons model,
which is dual to the A-model on a toric Calabi-Yau with $h_{1,1}=1$ and
$h_{2,1}=2$. We work out a B-model interpretation of this identification
explicitly by considering this model on the corresponding mirror geometries.


  It is argued that highly degenerate ground states arising from spontaneous
symmetry breaking with a type-B Goldstone mode are scale-invariant, with a
salient feature that the entanglement entropy $S(n)$ scales logarithmically
with the block size $n$ in the thermodynamic limit. As it turns out, the
prefactor is half the number of type-B Goldstone modes $N_B$. This is achieved
by performing an exact singular value decomposition of the degenerate ground
states, thus unveiling their self-similarities - the essence of a fractal.
Combining with a field-theoretic prediction [O. A. Castro-Alvaredo and B.
Doyon, Phys. Rev. Lett. \textbf{108}, 120401 (2012)], we are led to the
identification of the fractal dimension $d_f$ with the number of type-B
Goldstone modes $N_B$ for quantum many-body systems undergoing spontaneous
symmetry breaking.


  The asymptotic tails of the probability distributions of thermodynamic
quantities convey important information about the physics of nanoscopic systems
driven out of equilibrium. We apply a recently proposed method to analytically
determine the asymptotics of work distributions in Langevin systems to an
one-dimensional model of single-molecule force spectroscopy. The results are in
excellent agreement with numerical simulations, even in the centre of the
distributions. We compare our findings with a recent proposal for an universal
form of the asymptotics of work distributions in single-molecule experiments.


  The present study proposes a highly accurate lattice Boltzmann direct
coupling cell-vertex algorithm, well suited for industrial purposes, making it
highly valuable for aeroacoustic applications. It is indeed known that the
convection of vortical structures across a grid refinement interface, where
cell size is abruptly doubled, is likely to generate spurious noise that may
corrupt the solution over the whole computational domain. This issue becomes
critical in the case of aeroacoustic simulations, where accurate pressure
estimations are of paramount importance. Consequently, any interfering noise
that may pollute the acoustic predictions must be reduced.
  The proposed grid refinement algorithm differs from conventionally used ones,
in which an overlapping mesh layer is considered. Instead, it provides a direct
connection allowing a tighter link between fine and coarse grids, especially
with the use of a coherent equilibrium function shared by both grids. Moreover,
the direct coupling makes the algorithm more local and prevents the duplication
of points, which might be detrimental for massive parallelization. This work
follows our first study (Astoul~\textit{et al. 2020}) on the deleterious effect
of non-hydrodynamic modes crossing mesh transitions, which can be addressed
using an appropriate collision model. The Hybrid Recursive Regularized model is
then used for this study. The grid coupling algorithm is assessed and compared
to a widely-used cell-vertex algorithm on an acoustic pulse test case, a
convected vortex and a turbulent circular cylinder wake flow at high Reynolds
number.


  Generative adversarial networks (GANs) are an expressive class of neural
generative models with tremendous success in modeling high-dimensional
continuous measures. In this paper, we present a scalable method for unbalanced
optimal transport (OT) based on the generative-adversarial framework. We
formulate unbalanced OT as a problem of simultaneously learning a transport map
and a scaling factor that push a source measure to a target measure in a
cost-optimal manner. In addition, we propose an algorithm for solving this
problem based on stochastic alternating gradient updates, similar in practice
to GANs. We also provide theoretical justification for this formulation,
showing that it is closely related to an existing static formulation by Liero
et al. (2018), and perform numerical experiments demonstrating how this
methodology can be applied to population modeling.


  Powder metallurgy with hot isostatic pressing (PM-HIP) is an advanced
manufacturing process that is envisioned to replace forging for heavy nuclear
components, including the reactor pressure vessel (RPV). But PM-HIP products
must at least demonstrate comparable irradiation tolerance than forgings in
order to be qualified for nuclear applications. The objective of this study is
to directly compare PM-HIP to forged SA508 Grade 3 Class 1 low-alloy RPV steel
at two neutron irradiation conditions: ~0.5-1.0 displacements per atom (dpa) at
~270C and ~370C. PM-HIP SA508 experiences greater irradiation hardening and
embrittlement (total elongation) than forged SA508. However, uniform elongation
and approximate toughness are comparable across all irradiated materials,
suggesting irradiated PM-HIP SA508 exhibits superior ductility at maximum
load-bearing capacity. The irradiation hardening mechanism is linked to
composition rather than fabrication method. Since PM-HIP SA508 has higher Mn
and Ni concentration, it is more susceptible to irradiation-induced nucleation
of Mn-Ni-Si-P (MNSP) nanoprecipitates and dislocation loops, which both
contribute to hardening. Conversely, the forged material nucleates fewer MNSPs,
causing dislocation loops to control irradiation hardening. These results show
promise for the irradiation performance of PM-HIP SA508 and can motivate future
nuclear code qualification of PM-HIP fabrication for RPVs.


  The eigenvalue problem for 3x3 octonionic Hermitian matrices contains some
surprises, which we have reported elsewhere. In particular, the eigenvalues
need not be real, there are 6 rather than 3 real eigenvalues, and the
corresponding eigenvectors are not orthogonal in the usual sense. The
nonassociativity of the octonions makes computations tricky, and all of these
results were first obtained via brute force (but exact) Mathematica
computations. Some of them, such as the computation of real eigenvalues, have
subsequently been implemented more elegantly; others have not. We describe here
the use of Mathematica in analyzing this problem, and in particular its use in
proving a generalized orthogonality property for which no other proof is known.


  Zn0.96Mn0.04O samples were synthesized by solid state reaction technique to
explore their magnetic behavior. Structural, morphological and magnetic
properties of the samples have been found to be modified by 50 MeV Li+3 ion
beam irradiation. The samples exhibit impurity phase and upon irradiation it
disappears. Rietveld refinement analysis indicates that substitutional
incorporation of Mn in the host lattice increases with irradiation. Grain size
decreases with irradiation. Field dependent magnetization (M-H) measurement
explicitly indicates ferromagnetic (FM) nature. It has been established from
temperature dependent magnetization (M-T) measurement (500 Oe) and ac
susceptibility (\chi-T) measurement that ferromagnetism in the system seems to
be mainly intrinsic; though superparamagnetic Mn nanoparticles also has a minor
role. The analysis of M-T data at comparatively high field (5000-Oe) provides
an estimation of antiferromagnetic (AFM) exchange, which acts as a reducing
agent for observed magnetic moment. The value of saturation magnetization has
been increased upon irradiation and is highly correlated with dissolution of
impurity phase. Actually structural property has been modified with ion
irradiation and this modification may cause some definite positive change in
magnetic property.


  We consider the generation of magnetic field by the flow of a fluid for which
the electrical conductivity is nonuniform. A new amplification mechanism is
found which leads to dynamo action for flows much simpler than those considered
so far. In particular, the fluctuations of the electrical conductivity provide
a way to bypass anti-dynamo theorems. For astrophysical objects, we show
through three-dimensional global numerical simulations that the
temperature-driven fluctuations of the electrical conductivity can amplify an
otherwise decaying large scale equatorial dipolar field. This effect could play
a role for the generation of the unusually tilted magnetic field of the iced
giants Neptune and Uranus.


  Let G be a connected reductive group defined over a finite field F_q. We give
a parametrization of the irreducible representations of G(F_q) in terms of
(twisted) categorical centres of various monoidal categories associated to G.
(Results of this type were known earlier for unipotent representations.
Analogous results for the parametrization of character sheaves on G were also
known earlier.)


  In a first study of thermoelastic waves, such as on the textbook of Landau
and Lifshitz, one might at first glance understand that when the given period
is very short, waves are isentropic because heat conduction does not set in,
while if the given period is very long waves are isothermal because there is
enough time for thermalization to be thoroughly accomplished. When one pursues
the study of these waves further, by the mathematical inspection of the
complete thermoelastic wave equation he finds that if the period is very short,
much shorter than a characteristic time of the material, the wave is
isothermal, while if it is very long, much longer than the characteristic time,
the wave is isentropic. One also learns that this fact is supported by
experiments: at low frequencies the elastic waves are isentropic, while they
are isothermal when the frequencies are so high that can be attained in few
cases. The authors show that there is no contradiction between the first glance
understanding and the mathematical treatment of the elastic wave equation: for
thermal effects very long periods are so short and very short periods are so
long.


  A cooperative Sense and Avoid (SAA) algorithm for safe navigation of
small-sized UAVs within an airspace is proposed in this paper. The proposed
method relies upon cooperation between the UAV and the surrounding
transponder-equipped aviation obstacles. To do so, the aviation obstacles share
their altitude and identification code with the UAV by using a Mode S operation
of the Secondary Surveillance Radar (SSR) after interrogation. The proposed SAA
algorithm benefits from the estimate of the aviation obstacle's elevation angle
for ranging. This results in more accurate ranging compared to the round-trip
time-based ranging, which is currently used in existing SAA systems. We also
propose a low-complexity and accurate radial velocity estimator for the Mode S
operation of the SSR which is employed in the proposed SAA system. Furthermore,
by considering the Pulse-Position Modulation (PPM) of the transponder reply as
a waveform of pulse radar with random pulse repetition intervals, the maximum
unambiguous radial velocity is obtained. The proposed SAA is equipped with an
intruder identification method that determines the risk level ofthe surrounding
transponder-equipped aviation obstacles. Given the estimated parameters, the
intruder identification method classifies the aviation obstacles into high-,
medium-, and low-risk intruders. The output of the classifier enables the UAV
to plan its path or maneuver for safe navigation accordingly. The root mean
square error (RMSE) of the proposed estimators are analytically derived, and
the effectiveness of our SAA solution is confirmed through simulation
experiments.


  We study the energy landscape of a model of a single particle on a random
potential, that is, we investigate the topology of level sets of smooth random
fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where
$X_{N}$ is a Gaussian process with isotropic increments. We derive asymptotic
formulas for the mean number of critical points with critical values in an open
set as the dimension $N$ goes to infinity. In a companion paper, we provide the
same analysis for the number of critical points with a given index.


  \v{C}ech cohomology $H^n(X)$ of a separable metrizable space $X$ is defined
in terms of cohomology of its nerves (or ANR neighborhoods) $P_\beta$ whereas
Steenrod-Sitnikov homology $H_n(X)$ is defined in terms of homology of compact
subsets $K_\alpha\subset X$.
  We show that one can also go vice versa: in a sense, $H^n(X)$ can be
reconstructed from $H^n(K_\alpha)$, and if $X$ is finite dimensional, $H_n(X)$
can be reconstructed from $H_n(P_\beta)$.
  The reconstruction is via a Bousfield-Kan/Araki-Yoshimura type spectral
sequence, except that the derived limits have to be "corrected" so as to take
into account a natural topology on the indexing set. The corrected derived
limits coincide with the usual ones when the topology is discrete, and in
general are applied not to an inverse system but to a "partially ordered
sheaf".
  The "correction" of the derived limit functors in turn involves constructing
a "correct" (metrizable) topology on the order complex $|P|$ of a partially
ordered metrizable space $P$ (such as the hyperspace $K(X)$ of nonempty compact
subsets of $X$ with the Hausdorff metric). It turns out that three natural
approaches (by using the space of measurable functions, the space of
probability measures, or the usual embedding $K(X)\to C(X;\mathbb R)$) all lead
to the same topology on $|P|$.


  We propose a systematic theoretical framework for the topological amplitudes
of the heavy meson decays and their $SU(N)$ decomposition. In the framework,
the topological amplitudes are expressed in invariant tensors and classified
into tree- and penguin-operator-induced diagrams according to which four-quark
operators, tree or penguin, being inserted into their effective weak vertexes.
By decomposing the four-quark operators into irreducible representations of
$SU(N)$ group, one can derive the $SU(N)$ irreducible amplitudes from the
tensor form of the topology. Taking the $D\to PP$ decay ($P$ denoting a
pseudoscalar meson) with $SU(3)_F$ symmetry as an example, we show our
framework in detail. The fact that some topologies are not independent in the
$SU(3)_F$ limit is explained by group theory. It is found that there are only
nine independent topologies in all tree- and penguin-operator-induced diagrams
contributing to the $D\to PP$ decays in the Standard Model. If a large
quark-loop diagram is assumed, the large $\Delta A_{CP}$ and the very different
$D^0\to K^+K^-$ and $D^0\to \pi^+\pi^-$ branching fractions can be explained
with a normal $U$-spin breaking. Moreover, our framework provides a simple and
systematic way to analyze the $SU(N)$ breaking effects. As examples, the linear
$SU(3)_F$ breaking and the high order $U$-spin breaking in charm decays are
re-investigated in our framework, which are consistent with literature. We
propose the concepts of splitting and degeneracy of topologies, and use them to
describe the charm-less bottom decay. We find $SU(3)_F$ analysis for the
charm-less $B$ decays is different from the $D$ decays because the charm-quark
loop is beyond the $SU(3)$ symmetry and should be investigated in the symmetry
breaking chain of $SU(4)\to SU(3)$.


  A highly reflective sail provides a way to propel a spacecraft out of the
solar system using solar radiation pressure. The closer the spacecraft is to
the Sun when it starts its outward journey, the larger the radiation pressure
and so the larger the final velocity. For a spacecraft starting on the Earth's
orbit, closer proximity can be achieved via a retrograde impulse from a rocket
engine. The sail is then deployed at the closest approach to the Sun. Employing
the so-called Oberth effect, a second, prograde, impulse at closest approach
will raise the final velocity further. Here I investigate how a fixed total
impulse ({\Delta}v) can best be distributed in this procedure to maximize the
sail's velocity at infinity. Once {\Delta}v exceeds a threshold that depends on
the lightness number of the sail (a measure of its sun-induced acceleration),
the best strategy is to use all of the {\Delta}v in the retrograde impulse to
dive as close as possible to the Sun. Below the threshold the best strategy is
to use all of the {\Delta}v in the prograde impulse and thus not to dive at
all. Although larger velocities can be achieved with multi-stage impulsive
transfers, this study shows some interesting and perhaps counter-intuitive
consequences of combining impulses with solar sails.


  The Navier-Stokes equation driven by heat conduction is studied. As a
prototype we consider Rayleigh-B\'enard convection, in the Boussinesq
approximation. Under a large aspect ratio assumption, which is the case in
Rayleigh-B\'enard experiments with Prandtl number close to one, we prove the
existence of a global strong solution to the 3D Navier-Stokes equation coupled
with a heat equation, and the existence of a maximal B-attractor. A rigorous
two-scale limit is obtained by homogenization theory. The mean velocity field
is obtained by averaging the two-scale limit over the unit torus in the local
variable.


  Strain engineering is a powerful and widely used strategy for boosting the
performance of electronic and optoelectronic devices. Here, we demonstrate an
approach to tune the photoelectric properties of Platinum sulfide (PtS$_2$) by
using a ferroelectric substrate PMN-PT as the strain generator. It is found
that both the drain current and responsivity of the PtS$_2$ photodetector is
directly coupled to the electrostriction of PMN-PT, showing a high strain-tuned
ratio $10^{3}$, high responsivity up to $6.3\times 10^{3}$ A/W and detectivity
of $9.3\times 10^{12}$ Jones. Additionally, a high photogain $\approx 5\times
10^{5}$ is obtained at a gate voltage Vg = 15 V. Our results provide an
effective method for manipulating electrical properties and optimizing
performance of two dimensional layered (2D) materials based optoelectronic
devices.


  When a quantum wire is weakly confined, a conductance plateau appears at
e^2/h with decreasing carrier density in zero magnetic field accompanied by a
gradual suppression of the 2e^2/h plateau. Applying an in-plane magnetic field
B|| does not alter the value of this quantization; however, the e^2/h plateau
weakens with increasing B|| up to 9 T, and then strengthens on further
increasing B||, which also restores the 2e^2/h plateau. Our results are
consistent with spin-incoherent transport in a one-dimensional wire.


  This paper presents a new abstract method for proving lower bounds in
computational complexity. Based on the notion of topological and measurable
entropy for dynamical systems, it is shown to generalise three previous lower
bounds results from the literature in algebraic complexity. We use it to prove
that $\mathtt{maxflow}$, a $\mathrm{Ptime}$ complete problem, is not computable
in polylogarithmic time on parallel random access machines (prams) working with
real numbers. This improves on a result of Mulmuley since the class of machines
considered extends the class "prams without bit operations". We further improve
on this result by showing that euclidean division cannot be computable in
polylogarithmic time using division on the reals, pinpointing that euclidean
division provides a significant boost in expressive power.
  On top of showing this new separation result, we show our method captures
previous lower bounds results from the literature: Steele and Yao's lower
bounds for algebraic decision trees, Ben-Or's lower bounds for algebraic
computation trees, Cucker's proof that $\mathrm{NC}$ is not equal to
$\mathrm{Ptime}$ in the real case, and Mulmuley's lower bounds for prams
without bit operations.


  The structure of categorical at zero semigroups is studied from the point of
view their likeness to categories.


  The Herschel Space Observatory's recent detections of water vapor in the
cold, dense cloud L1544 allow a direct comparison between observations and
chemical models for oxygen species in conditions just before star formation. We
explain a chemical model for gas phase water, simplified for the limited number
of reactions or processes that are active in extreme cold ($<$ 15 K). In this
model, water is removed from the gas phase by freezing onto grains and by
photodissociation. Water is formed as ice on the surface of dust grains from O
and OH and released into the gas phase by photodesorption. The reactions are
fast enough with respect to the slow dynamical evolution of L1544 that the gas
phase water is in equilibrium for the local conditions thoughout the cloud. We
explain the paradoxical radiative transfer of the H$_2$O ($1_{10}-1_{01}$)
line. Despite discouragingly high optical depth caused by the large Einstein A
coefficient, the subcritical excitation in the cold, rarefied H$_2$ causes the
line brightness to scale linearly with column density. Thus the water line can
provide information on the chemical and dynamical processes in the darkest
region in the center of a cold, dense cloud. The inverse P-Cygni profile of the
observed water line generally indicates a contracting cloud. This profile is
reproduced with a dynamical model of slow contraction from unstable
quasi-static hydrodynamic equilibrium (an unstable Bonnor-Ebert sphere).


  A few grid-computing tools are available for public use. However, such
systems are usually quite complex and require several man-months to set up. In
case the user wishes to set-up an ad-hoc grid in a small span of time, such
tools cannot be used. Moreover, the complex services they provide, like,
reliable file transfer, extra layers of security etc., act as an overhead to
performance in case the network is small and reliable.
  In this paper we describe the structure of our grid-computing framework,
which can be implemented and used, easily on a moderate sized network.


  Traditionally, the formation of amorphous shear bands (SBs) in crystalline
materials has been undesirable, because SBs can nucleate voids and act as
precursors to fracture. They also form as a final stage of accumulated damage.
Only recently SBs were found to form in undefected crystals, where they serve
as the primary driver of plasticity without nucleating voids. Here, we have
discovered trends in materials properties that determine when amorphous shear
bands will form and whether they will drive plasticity or lead to fracture. We
have identified the materials systems that exhibit SB deformation, and by
varying the composition, we were able to switch from ductile to brittle
behavior. Our findings are based on a combination of experimental
characterization and atomistic simulations, and they provide a potential
strategy for increasing toughness of nominally brittle materials.


  We generalize Voisin's theorem on deformations of pairs of a symplectic
manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing
subvarieties. Partial results are obtained for arbitrary Lagrangian
subvarieties. We apply our results to the study of singular fibers of
Lagrangian fibrations.


  The diverse massive stellar population in the young massive cluster
Westerlund 1 (Wd~1) provides an ideal laboratory to observe and constrain
mass-loss processes throughout the transitional phase of massive star
evolution. A set of high sensitivity radio observations of Wd~1 leads to the
detection of 18 cluster members, a sample dominated by cool hypergiants, but
with detections among hotter OB supergiants and WR stars. Here the diverse
radio properties of the detected sample are briefly described. The mass-loss
rates of the detected objects are surprisingly similar across the whole
transitional phase of massive star evolution, at ~10^-5 solar masses per year.
Such as rate is insufficient to strip away the H-rich mantle in a massive star
lifetime, unless the stars go through a period of enhanced mass-loss. The radio
luminous star W9 provides an example of such an object, with evidence for two
eras of mass-loss with rates of ~10^-4 solar masses per year.


  We say a finite word $x$ is a palindromic periodicity if there exist two
palindromes $p$ and $s$ such that $|x| \geq |ps|$ and $x$ is a prefix of the
word $(ps)^\omega = pspsps\cdots$. In this paper we examine the palindromic
periodicities occurring in some classical infinite words, such as Sturmian
words, episturmian words, the Thue-Morse word, the period-doubling word, the
Rudin-Shapiro word, the paperfolding word, and the Tribonacci word, and prove a
number of results about them.


  Recent work in the literature had evaluated the energy-momentum tensor of a
Casimir apparatus in a weak gravitational field, for an electromagnetic field
subject to perfect conductor boundary conditions on parallel plates. The
Casimir apparatus was then predicted to experience a tiny push in the upwards
direction, and the regularized energy-momentum tensor was found to have a trace
anomaly. The latter, unexpected property made it compelling to assess what
happens in a simpler case. For this purpose, the present paper studies a free,
real massless scalar field subject to homogeneous Dirichlet conditions on the
parallel plates. Working to first order in the constant gravity acceleration,
the resulting regularized and renormalized energy-momentum tensor is found to
be covariantly conserved, while the trace anomaly vanishes if the massless
scalar field is conformally coupled to gravity. Conformal coupling also ensures
a finite Casimir energy and finite values of the pressure upon parallel plates.


  This study is focused on the qualitative and quantitative characterization of
chaotic systems with the use of symbolic description. We consider two famous
systems: Lorenz and R\"ossler models with their iconic attractors, and
demonstrate that with adequately chosen symbolic partition three measures of
complexity, such as the Shannon source entropy, the Lempel-Ziv complexity and
the Markov transition matrix, work remarkably well for characterizing the
degree of chaoticity, and precise detecting stability windows in the parameter
space. The second message of this study is to showcase the utility of symbolic
dynamics with the introduction of a fidelity test for reservoir computing for
simulating the properties of the chaos in both models' replicas. The results of
these measures are validated by the comparison approach based on
one-dimensional return maps and the complexity measures.


  We aim to identify QSO2 candidates in the redshift desert using optical and
infrared photometry. At this intermediate redshift range, most of the prominent
optical emission lines in QSO2 sources (e.g. CIV1549; [OIII]4959,5008) fall
either outside the wavelength range of the SDSS optical spectra or in
particularly noisy wavelength ranges, making QSO2 identification challenging.
Therefore, we adopted a semi-supervised machine learning approach to select
candidates in the SDSS galaxy sample. Recent applications of machine learning
in astronomy focus on problems involving large data sets, with small data sets
often being overlooked. We developed a few-shot learning approach for the
identification and classification of rare-object classes using limited training
data (200 sources). The new AMELIA pipeline uses a transfer-learning based
approach with decision trees, distance-based, and deep learning methods to
build a classifier capable of identifying rare objects on the basis of an
observational training data set. We validated the performance of AMELIA by
addressing the problem of identifying QSO2s at 1 $\leq$ z $\leq$ 2 using SDSS
and WISE photometry, obtaining an F1-score above 0.8 in a supervised approach.
We then used AMELIA to select new QSO2 candidates in the redshift desert and
examined the nature of the candidates using SDSS spectra, when available. In
particular, we identified a sub-population of [NeV]3426 emitters at z $\sim$
1.1, which are highly likely to contain obscured AGNs. We used X-ray and radio
cross-matching to validate our classification and investigated the performance
of photometric criteria from the literature showing that our candidates have an
inherent dusty nature. Finally, we derived physical properties for our QSO2
sample using photoionisation models and verified the AGN classification using
an SED fitting.


  In this paper we present Kvik: an implementation of a task-based "middleware"
for shared memory parallel programming in the Rust language built on top of the
Rayon library. We devise a system allowing several task-splitting schedulers to
be finely tuned by the end users. Among these, we propose an implementation of
an adaptive scheduler reducing tasks creations (splits) to bare minimum by
linking tasks splitting to steal requests. Another important scheduler that
allows turning computations into sequences of parallel operations is described.
This operator proves itself particularly useful for interruptible computations.
We exhibit different code examples well suited for different types of
schedulers. We conclude our work with a set of benchmarks making heavy use of
composability. In particular we present a parallel stable sort implementation
with up to 1.5x more speedup when compared to the state-of-the-art parallel
sorting implementation.


We illustrate the concept of mathematical proof.


  In these notes we present an introductory review on various topics about low
energy pion physics (some kaon physics is discussed as well). Among these, we
include the uses of analyticity and unitarity to describe partial wave
amplitudes (for which we give accurate and economical parametrizations) and
form factors; (forward) dispersion relations; and the use of the
Froissart--Gribov representation to evaluate accurately the low energy
parameters (scattering lengths and effective ranges) for higher ($l\geq1$)
waves. Finally, we describe some pion physics in QCD and then pass on to study
the nonlinear sigma model, and the chiral perturbation theory approach to low
energy pion interactions.\hb \indent Most of the results presented here are
well known, but we also give a set of state of the art, precise determinations
of some scattering lengths as well as an independent calculation of three of
the parameters $\bar{l}_2$, $\bar{l}_4$, $\bar{l}_6$
  (to one loop), and one $\bar{f}_2$, to two loops, that appear in chiral
perturbation theory. The S waves are discussed and compared with chiral
perturbation theory expectations, and the same is done for larger $l$
scattering lengths and effective range parameters. Also new is the evaluation
of some electromagnetic corrections.


  Let $\mathfrak{g}$ be a real finite-dimensional Lie algebra containing
pointed generating invariant closed convex cones. We determine those
derivations $D$ of $\mathfrak{g}$ which induce a 3-grading of the form
$\mathfrak{g} = \mathfrak{g}_{-1} \oplus \mathfrak{g}_0 \oplus \mathfrak{g}_1$
on $\mathfrak{g}$ such that the $(\pm 1)$-eigenspaces $\mathfrak{g}_{\pm 1}$ of
$D$ are generated by the intersections with generating cones of the form $W =
\mathcal{O}_f^*$, where $\mathcal{O}_f$ is the coadjoint orbit of a linear
functional $f \in \mathfrak{z}(\mathfrak{g})^*$ and $\mathcal{O}_f^*$ is the
dual cone of $\mathcal{O}_f$. In particular, we show that, if $\mathfrak{g}$ is
solvable, no such derivation except the trivial one exists.
  This continues our classification of Lie algebras generated by Lie wedges of
endomorphism semigroups of standard subspaces. The classification is motivated
by the relation of nets of standard subspaces to Haag-Kastler nets of von
Neumann algebras in Algebraic Quantum Field Theory.


  Viscoelastic materials have the properties both of elasticity and viscosity.
In a previous work we investigate glass relaxation in the framework of
viscoelasticity. Here we consider the Burgers model, a first but meaningful
step in the general analysis, showing a reachability theorem thanks the
analysis of the gap between eigenvalues and the representation of the solution
in Fourier series.


  We provide N=1 Super Yang-Mills theory in the Wess-Zumino gauge with mass
terms for the supersymmetric partners of the gauge fields and of the matter
fields, together with a supersymmetric mass term for the fermionic matter
fields. All mass terms are chosen in such a way to induce soft supersymmetry
breakings at most, while preserving gauge invariance to all orders of
perturbation theory. The breakings are controlled through an extended
Slavnov-Taylor identity. The renormalization analysis, both in the ultraviolet
and in the infrared region, is performed.


  The discovery that most of the energy density in the universe is stored in
the form of dark energy has profound consequences for our future. In particular
our current limited understanding of quantum theory of gravity indicates that
some time in the future our universe will undergo a phase transition that will
destroy us and everything else around us instantaneously. However the laws of
gravity also suggest a way out -- some of our descendants could survive this
catastrophe by riding gravity away from the danger. In this essay I describe
the tale of this escape from doomsday.


  We consider the problem of comparing the volumes of two star bodies in an
even-dimensional euclidean space $\mathbb R^{2n} = \mathbb C^n$ by comparing
their cross sectional areas along complex lines (special 2-dimensional real
planes) through the origin. Under mild symmetry conditions on one of the bodies
a Busemann-Petty type theorem holds. Quaternionic and Octonionic analogs also
hold. The argument relies on integration in polar coordinates coupled with
Jensen's inequality. Along the way we provide a criterion that detects which
centered bodies are {\it circular}. i.e., stabilized by multiplication by
complex numbers of unit modulus. Our goal is to present a Busemann-Petty type
result with a minimum of required background and, in addition, to suggest
characterizations of classes of star bodies by means of integral geometric
inequalities.


  Non-linear hierarchical models are commonly used in many disciplines.
However, inference in the presence of non-nested effects and on large datasets
is challenging and computationally burdensome. This paper provides two
contributions to scalable and accurate inference. First, I derive a new
mean-field variational algorithm for estimating binomial logistic hierarchical
models with an arbitrary number of non-nested random effects. Second, I propose
"marginally augmented variational Bayes" (MAVB) that further improves the
initial approximation through a step of Bayesian post-processing. I prove that
MAVB provides a guaranteed improvement in the approximation quality at low
computational cost and induces dependencies that were assumed away by the
initial factorization assumptions.
  I apply these techniques to a study of voter behavior using a
high-dimensional application of the popular approach of multilevel regression
and post-stratification (MRP). Existing estimation took hours whereas the
algorithms proposed run in minutes. The posterior means are well-recovered even
under strong factorization assumptions. Applying MAVB further improves the
approximation by partially correcting the under-estimated variance. The
proposed methodology is implemented in an open source software package.


  We study N=1 dualities in four dimensional supersymmetric gauge theories as
the worldvolume theory of D4 branes with one compact direction in type IIA
string theory. We generalize the previous work for SO(N_{c1}) x Sp(N_{c2}) with
the superpotential W=Tr X^4 to the case of W= Tr X^4(k+1) in terms of brane
configuration. We conjecture that the new dualities for the product gauge
groups of SO(N_{c1}) x Sp(N_{c2}) x SO(N_{c3}), SO(N_{c1}) x Sp(N_{c2}) x
SO(N_{c3}) x Sp(N_{c4}) and higher multiple product gauge groups can be
obtained by reversing the ordering of NS5 branes and D6 branes while preserving
the linking numbers. We also describe the above dualities in terms of wrapping
D6 branes around 3 cycles of Calabi-Yau threefolds in type IIA string theory.
The theory with adjoint matter can be regarded as taking multiple copies of NS5
brane in the configuration of brane or geometric approaches.


  We confirm a conjecture of Friedland and Milnor: if two polynomial
automorphisms f and g in Aut(C^2) with dynamical degree >1 are conjugate by
some holomorphic diffeomorphism \phi of C^2, then \phi is a polynomial
automorphism; thus, f and g are conjugate inside Aut(C^2). We also discuss a
number of variations on this result.


  We study theoretically and experimentally the response of a microwave
superconducting stripline resonator, integrated with a microbridge, to a
monochromatic injected signal. We find that there is a certain range of driving
parameters, in which a novel nonlinear phenomenon immerges, and self-sustained
modulation of the reflected power off the resonator is generated by the
resonator. A theoretical model which attributes the self modulation to a
thermal instability yields a good agreement with the experimental results.


  Humans are masters at quickly learning many complex tasks, relying on an
approximate understanding of the dynamics of their environments. In much the
same way, we would like our learning agents to quickly adapt to new tasks. In
this paper, we explore how model-based Reinforcement Learning (RL) can
facilitate transfer to new tasks. We develop an algorithm that learns an
action-conditional, predictive model of expected future observations, rewards
and values from which a policy can be derived by following the gradient of the
estimated value along imagined trajectories. We show how robust policy
optimization can be achieved in robot manipulation tasks even with approximate
models that are learned directly from vision and proprioception. We evaluate
the efficacy of our approach in a transfer learning scenario, re-using
previously learned models on tasks with different reward structures and visual
distractors, and show a significant improvement in learning speed compared to
strong off-policy baselines. Videos with results can be found at
https://sites.google.com/view/ivg-corl19


  We consider viscous two-dimensional steady flows of incompressible fluids
past doubly periodic arrays of solid obstacles. In a class of such flows, the
autocorrelations for the Lagrangian observables decay in accordance with the
power law, and the Fourier spectrum is neither discrete nor absolutely
continuous. We demonstrate that spreading of the droplet of tracers in such
flows is anomalously fast. Since the flow is equivalent to the integrable
Hamiltonian system with 1 degree of freedom, this provides an example of
integrable dynamics with long-range correlations, fractal power spectrum, and
anomalous transport properties.


  In this paper we are interested in symmetries of alternating knots, more
precisely in those related to achirality. We call the following statement
Tait's Conjecture on alternating -achiral knots: Let K be an alternating
-achiral knot. Then there exists a minimal projection {\Pi} of K in S^2 \subset
S^3 and an involution {\phi}:S^3\toS^3 such that: 1) {\phi} reverses the
orientation of $S^3$; 2) {\phi}(S^2) = S^2; 3) {\phi} ({\Pi}) = {\Pi}; 4)
{\phi} has two fixed points on {\Pi} and hence reverses the orientation of K.
The purpose of this paper is to prove this statement.


  Existing visual question answering methods often suffer from cross-modal
spurious correlations and oversimplified event-level reasoning processes that
fail to capture event temporality, causality, and dynamics spanning over the
video. In this work, to address the task of event-level visual question
answering, we propose a framework for cross-modal causal relational reasoning.
In particular, a set of causal intervention operations is introduced to
discover the underlying causal structures across visual and linguistic
modalities. Our framework, named Cross-Modal Causal RelatIonal Reasoning
(CMCIR), involves three modules: i) Causality-aware Visual-Linguistic Reasoning
(CVLR) module for collaboratively disentangling the visual and linguistic
spurious correlations via front-door and back-door causal interventions; ii)
Spatial-Temporal Transformer (STT) module for capturing the fine-grained
interactions between visual and linguistic semantics; iii) Visual-Linguistic
Feature Fusion (VLFF) module for learning the global semantic-aware
visual-linguistic representations adaptively. Extensive experiments on four
event-level datasets demonstrate the superiority of our CMCIR in discovering
visual-linguistic causal structures and achieving robust event-level visual
question answering. The datasets, code, and models are available at
https://github.com/HCPLab-SYSU/CMCIR.


  It is often claimed that overdensities of (or even individual bright)
submillimetre-selected galaxies (SMGs) trace the assembly of the most-massive
dark matter structures in the Universe. We test this claim by performing a
counts-in-cells analysis of mock SMG catalogues derived from the Bolshoi
cosmological simulation to investigate how well SMG associations trace the
underlying dark matter structure. We find that SMGs exhibit a relatively
complex bias: some regions of high SMG overdensity are underdense in terms of
dark matter mass, and some regions of high dark matter overdensity contain no
SMGs. Because of their rarity, Poisson noise causes scatter in the SMG
overdensity at fixed dark matter overdensity. Consequently, rich associations
of less-luminous, more-abundant galaxies (i.e. Lyman-break galaxy analogues)
trace the highest dark matter overdensities much better than SMGs. Even on
average, SMG associations are relatively poor tracers of the most significant
dark matter overdensities because of 'downsizing': at z < ~2.5, the
most-massive galaxies that reside in the highest dark matter overdensities have
already had their star formation quenched and are thus no longer SMGs. At a
given redshift, of the 10 per cent most-massive overdensities, only ~25 per
cent contain at least one SMG, and less than a few per cent contain more than
one SMG.


  Massive multiple-input multiple-output (mMIMO) regime reaps the benefits of
spatial diversity and multiplexing gains, subject to precise channel state
information (CSI) acquisition. In the current communication architecture, the
downlink CSI is estimated by the user equipment (UE) via dedicated pilots and
then fed back to the gNodeB (gNB). The feedback information is compressed with
the goal of reducing over-the-air overhead. This compression increases the
inaccuracy of acquired CSI, thus degrading the overall spectral efficiency.
This paper proposes a computationally inexpensive machine learning (ML)-based
CSI feedback algorithm, which exploits twin channel predictors. The proposed
approach can work for both time-division duplex (TDD) and frequency-division
duplex (FDD) systems, and it allows to reduce feedback overhead and improves
the acquired CSI accuracy. To observe real benefits, we demonstrate the
performance of the proposed approach using the empirical data recorded at the
Nokia campus in Stuttgart, Germany. Numerical results show the effectiveness of
the proposed approach in terms of reducing overhead, minimizing quantization
errors, increasing spectral efficiency, cosine similarity, and precoding gain
compared to the traditional CSI feedback mechanism.


  We suppose that a L\'evy process is observed at discrete time points.
Starting from an asymptotically minimax family of estimators for the continuous
part of the L\'evy Khinchine characteristics, i.e., the covariance, we derive a
data-driven parameter choice for the frequency of estimating the covariance. We
investigate a Lepski\u{i}-type stopping rule for the adaptive procedure.
Consequently, we use a balancing principle for the best possible data-driven
parameter. The adaptive estimator achieves almost the optimal rate. Numerical
experiments with the proposed selection rule are also presented.


  LIME is a popular approach for explaining a black-box prediction through an
interpretable model that is trained on instances in the vicinity of the
predicted instance. To generate these instances, LIME randomly selects a subset
of the non-zero features of the predicted instance. After that, the perturbed
instances are fed into the black-box model to obtain labels for these, which
are then used for training the interpretable model. In this study, we present a
systematic evaluation of the interpretable models that are output by LIME on
the two use-cases that were considered in the original paper introducing the
approach; text classification and object detection. The investigation shows
that the perturbation and labeling phases result in both data and label shift.
In addition, we study the correlation between the shift and the fidelity of the
interpretable model and show that in certain cases the shift negatively
correlates with the fidelity. Based on these findings, it is argued that there
is a need for a new sampling approach that mitigates the shift in the LIME's
framework.


  A quantum system weakly interacting with a fast environment usually undergoes
a relaxation with complex frequencies whose imaginary parts are damping rates
quadratic in the coupling to the environment, in accord with Fermi's ``Golden
Rule''. We show for various models (spin damped by harmonic-oscillator or
random-matrix baths, quantum diffusion, quantum Brownian motion) that upon
increasing the coupling up to a critical value still small enough to allow for
weak-coupling Markovian master equations, a new relaxation regime can occur. In
that regime, complex frequencies lose their real parts such that the process
becomes overdamped. Our results call into question the standard belief that
overdamping is exclusively a strong coupling feature.


  The randomized Kaczmarz (RK) method is an iterative method for approximating
the least-squares solution of large linear systems of equations. The standard
RK method uses sequential updates, making parallel computation difficult. Here,
we study a parallel version of RK where a weighted average of independent
updates is used. We analyze the convergence of RK with averaging and
demonstrate its performance empirically. We show that as the number of threads
increases, the rate of convergence improves and the convergence horizon for
inconsistent systems decreases.


  Several $X$ and $Z_{cs}$ exotic hadrons were claimed in the LHCb's amplitude
analysis on $B^+\to J/\psi \phi K^+$. The data shows that all the peaks and
also dips in the spectra are located at thresholds of seemingly relevant
meson-meson channels. While the LHCb analysis fitted the peaks with
Breit-Wigner resonances, threshold kinematical cusps might be the cause of such
structures. We thus analyze the LHCb data considering the threshold cusps. Our
model is simultaneously fitted to $J/\psi \phi$, $J/\psi K^+$, and $K^+\phi$
invariant mass distributions. The threshold cusps fit well all the $X$,
$Z_{cs}$, and dip structures. Our analysis indicates that spin-parity of the
$X(4274)$ and $X(4500)$ structures are $0^-$ and $1^-$, respectively. This is
different from the LHCb's spin-parity assignments ($1^+$ and $0^+$). The number
of fitting parameters can be significantly reduced by considering the relevant
threshold cusps. Our analysis shows that $D_s^{(*)}\bar{D}^{*}$ scattering
lengths are consistent with zero. This disfavors an explanation of
$Z_{cs}(4000)$ and $Z_{cs}(4220)$ as $D_s^{(*)}\bar{D}^{*}$ molecules, which is
consistent with lattice QCD via the SU(3) relation.


  Exponential tightness of a family of Skorohod integrals is studied in this
paper. We first provide a counterexample to illustrate that in general the
exponential tightness with speed $\epsilon$ similar to It\^o integral does not
hold, even for any speed $\epsilon^\alpha$ with $\alpha > 0$. Then, some
characterizations of this subject are given. Application is also provided to
illustrate the proposed results.


  Subword tokenization is the de facto standard for tokenization in neural
language models and machine translation systems. Three advantages are
frequently cited in favor of subwords: shorter encoding of frequent tokens,
compositionality of subwords, and ability to deal with unknown words. As their
relative importance is not entirely clear yet, we propose a tokenization
approach that enables us to separate frequency (the first advantage) from
compositionality. The approach uses Huffman coding to tokenize words, by order
of frequency, using a fixed amount of symbols. Experiments with CS-DE, EN-FR
and EN-DE NMT show that frequency alone accounts for 90%-95% of the scores
reached by BPE, hence compositionality has less importance than previously
thought.