  We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time
nonlinear observer state estimation problem. Integrated within a single-step
exact observer linearization framework, the proposed PINN approach aims at
learning a nonlinear state transformation map by solving a system of
inhomogeneous functional equations. The performance of the proposed PINN
approach is assessed via two illustrative case studies for which the observer
linearizing transformation map can be derived analytically. We also perform an
uncertainty quantification analysis for the proposed PINN scheme and we compare
it with conventional power-series numerical implementations, which rely on the
computation of a power series solution.


  For the first time, the estimates of the non-centered Weyl-group invariant
heat kernel for curved Riemannian spaces and for Opdam-Cherednik Laplacians are
studied systematically.
  We prove sharp estimates for the root system $A_1$ with arbitrary
multiplicity $k>0$. Sharp estimates of Opdam-Cherednik's radial heat kernel are
conjectured for any root system.


  A numerical and analytic treatment is presented here of the evolution of
initial data of the kind that was conjectured by Hertog, Horowitz and Maeda to
lead to a violation of cosmic censorship. That initial data is essentially a
thick domain wall connecting two regions of anti de Sitter space. The evolution
results in no violation of cosmic censorship, but rather the formation of a
small black hole.


  Nonextreme black hole in a cavity can achieve the extreme state with a zero
surface gravity at a finite temperature on a boundary, the proper distance
between the boundary and the horizon being finite. The classical geometry in
this state is found explicitly for four-dimensional spherically-symmetrical and
2+1 rotating holes. In the first case the limiting geometry depends only on one
scale factor and the whole Euclidean manifold is described by the
Bertotti-Robinson spacetime. The general structure of a metric in the limit
under consideration is also found with quantum corrections taken into account.
Its angular part represents two-sphere of a constant radius. In all cases the
Lorentzian counterparts of the metrics are free from singularities.


  We present a detailed theoretical analysis of micro-motion in a time-averaged
orbiting potential trap. Our treatment is based on the Gross-Pitaevskii
equation, with the full time dependent behaviour of the trap systematically
approximated to reduce the trapping potential to its dominant terms. We show
that within some well specified approximations, the dynamic trap has
solitary-wave solutions, and we identify a moving frame of reference which
provides the most natural description of the system. In that frame eigenstates
of the time-averaged orbiting potential trap can be found, all of which must be
solitary-wave solutions with identical, circular centre of mass motion in the
lab frame. The validity regime for our treatment is carefully defined, and is
shown to be satisfied by existing experimental systems.


  The purpose of this paper is to study some new concrete approximation
processes for continuous vector-valued mappings defined on the infinite
dimensional cube or on a subset of a real Hilbert space. In both cases these
operators are modelled on classical Bernstein polynomials and represent a
possible extension to an infinite dimensional setting.
  The same idea is generalized to obtain from a given approximation process for
function defined on a real interval a new approximation process for
vector-valued mappings defined on subsets of a real Hilbert space.


  Starting with Lagrangians, which turn out to be degenerate, the Hamiltonian
operators for integrable systems can be constructed using Dirac's theory of
constraints. We illustrate this by giving a systematic discussion of the first
Hamiltonian structure of KdV. The first symplectic 2-form obtained from Dirac's
theory is the time component of the covariant Witten-Zuckerman symplectic
2-form current. We derive the flux of the first symplectic 2-form. Then we turn
to a new Lagrangian for KdV recently obtained by Pavlov and present the
corresponding new covariant symplectic structure for KdV. This shows that the
inverse of Magri's second Hamiltonian operator is also a Hamiltonian operator
for KdV.


  We study a specific correction to the Bethe logarithm induced by potentials
which are proportional to a Dirac-delta function in coordinate space ("local
potentials"). Corrections of this type occur naturally in the calculation of
various self-energy corrections to the energy of bound states. Examples include
logarithmic higher-order binding corrections to the two-loop self-energy,
vacuum-polarization induced corrections to the self-energy and radiative
corrections induced by the finite size of the nucleus. We obtain results for
excited S and P states and find that the dependence of the corrections on the
principal quantum number is remarkable. For the ground state, we find a small
modification as compared to previously reported results. Our results are based
on mathematical techniques for the treatment of quantum electrodynamic bound
states discussed previously in [J. Phys. A 35 (2002) 1927, hep-ph/0111084].


  Tensor network states provide an efficient class of states that faithfully
capture strongly correlated quantum models and systems in classical statistical
mechanics. While tensor networks can now be seen as becoming standard tools in
the description of such complex many-body systems, close to optimal variational
principles based on such states are less obvious to come by. In this work, we
generalize a recently proposed variational uniform matrix product state
algorithm for capturing one-dimensional quantum lattices in the thermodynamic
limit, to the study of regular two-dimensional tensor networks with a
non-trivial unit cell. A key property of the algorithm is a computational
effort that scales linearly rather than exponentially in the size of the unit
cell. We demonstrate the performance of our approach on the computation of the
classical partition functions of the antiferromagnetic Ising model and
interacting dimers on the square lattice, as well as of a quantum doped
resonating valence bond state.


  The fear of social stigma leads many individuals worldwide to hesitate in
disclosing their sexual orientation. Since concealing identity is costly, it is
crucial to understand the extent of anti-LGB sentiments and reactions to coming
out. This paper uses an innovative data source from a popular online game
together with a natural experiment to overcome existing data and endogeneity
issues. We exploit exogenous variation in the identity of a character to
identify the effects of coming out on players' revealed preferences for that
character across diverse regions globally. Our findings reveal a substantial
and persistent negative impact of coming out.


  We show that Trevisan's extractor and its variants \cite{T99,RRV99} are
secure against bounded quantum storage adversaries. One instantiation gives the
first such extractor to achieve an output length $\Theta(K-b)$, where $K$ is
the source's entropy and $b$ the adversary's storage, together with a
poly-logarithmic seed length. Another instantiation achieves a logarithmic key
length, with a slightly smaller output length $\Theta((K-b)/K^\gamma)$ for any
$\gamma>0$. In contrast, the previous best construction \cite{TS09} could only
extract $(K/b)^{1/15}$ bits. Some of our constructions have the additional
advantage that every bit of the output is a function of only a polylogarithmic
number of bits from the source, which is crucial for some cryptographic
applications.
  Our argument is based on bounds for a generalization of quantum random access
codes, which we call \emph{quantum functional access codes}. This is crucial as
it lets us avoid the local list-decoding algorithm central to the approach in
\cite{TS09}, which was the source of the multiplicative overhead.


  We consider the electromagnetic response of a topological Weyl semimetal
(TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the
surface Brillouin zone. We compute the frequency-dependent complex
conductivities $\sigma_{\alpha\beta}(\omega)$ and also take into account the
modification of Maxwell equations by the topological $\theta$-term to obtain
the Kerr and Faraday rotations in a variety of geometries. For TWS films
thinner than the wavelength, the Kerr and Faraday rotations, determined by the
separation between Weyl nodes, are significantly larger than in topological
insulators. In thicker films, the Kerr and Faraday angles can be enhanced by
choice of film thickness and substrate refractive index. We show that, for
radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday
rotation but the electric field develops a longitudinal component inside the
TWS, and there is magnetic linear dichroism. Our results have implications for
probing the TWS phase in various experimental systems.


  A brief description of the library of the Standard Model and anomalous
WWgamma coupling contribution to the matrix element for e+e- -> \nu \bar{\nu}
n\gamma process is given. It can be used with any Monte Carlo program for e+e-
-> f \bar f n\gamma processes. A working example of the application for the
KORALZ version 4.04 is also provided.


  Current approaches of knowledge editing struggle to effectively propagate
updates to interconnected facts. In this work, we delve into the barriers that
hinder the appropriate propagation of updated knowledge within these models for
accurate reasoning. To support our analysis, we introduce a novel
reasoning-based benchmark -- ReCoE (Reasoning-based Counterfactual Editing
dataset) -- which covers six common reasoning schemes in real world. We conduct
a thorough analysis of existing knowledge editing techniques, including input
augmentation, finetuning, and locate-and-edit. We found that all model editing
methods show notably low performance on this dataset, especially in certain
reasoning schemes. Our analysis over the chain-of-thought generation of edited
models further uncover key reasons behind the inadequacy of existing knowledge
editing methods from a reasoning standpoint, involving aspects on fact-wise
editing, fact recall ability, and coherence in generation. We will make our
benchmark publicly available.


  We study the interaction between a topological insulator nanoparticle and a
quantum dot subject to an applied electric field. The electromagnetic response
of the topological insulator is derived from axion electrodynamics in the
quasistatic approximation. Localized modes are quantized in terms of dipolar
bosonic modes, which couples dipolarly to the quantum dot. Hence, we treat the
hybrid as a two-level system interacting with a single bosonic mode, where the
coupling strength encodes the information concerning the nontrivial topology of
the nanoparticle. The interaction of the hybrid with the environment is
implemented through the coupling with a continuum reservoir of radiative output
modes and a reservoir of phonon modes. In particular, we use the method of
Zubarev's Green functions to derive an expression for the optical absorption
spectrum of the system. We apply our results to a realistic system which
consists of a topological insulator nanoparticle made of TlBiSe$_{2}$
interacting with a cadmium selenide quantum dot, both immersed in a polymer
layer such as poly(methyl methacrylate). The optical absorption spectrum
exhibits Fano resonances with a line shape that strongly depends on the
polarization of the electric field as well as on the topological
magnetoelectric polarizability $\theta$. Our results and methods can also be
applied to nontopological magnetoelectric materials such as Cr$_{2}$O$_{3}$.


  We present the discovery of a distant methane dwarf, the first from the
Institute for Astronomy (IfA) Deep Survey. The object ("IfA 0230-Z1") was
identified from deep optical I and z'-band imaging, being conducted as an
IfA-wide collaboration using the prime-focus imager Suprime-Cam on the Subaru
8.2-m Telescope. IfA 0230-Z1 is extremely red in the Iz'J (0.8--1.2 micron)
bands but relatively blue in J-H; such colors are uniquely characteristic of T
dwarfs. A near-IR spectrum taken with the Keck Telescope shows strong H2O
absorption and a continuum break indicative of CH4, confirming the object has a
very cool atmosphere. Comparison with nearby T dwarfs gives a spectral type of
T3-T4 and a distance of ~45 pc. Simple estimates based on previous T dwarf
discoveries suggest that the IfA survey will find a comparable number of T
dwarfs as the 2MASS survey, albeit at a much larger average distance. We also
discuss the survey's ability to probe the galactic scale height of ultracool (L
and T) dwarfs.


  We construct elliptic extensions of the alpha-parameter rook model introduced
by Goldman and Haglund and of the rook model for matchings of Haglund and
Remmel. In particular, we extend the product formulas of these models to the
elliptic setting. By specializing the parameter alpha in our elliptic extension
of the alpha-parameter model and the shape of the Ferrers board in different
ways, we obtain elliptic analogues of the Stirling numbers of the first kind
and of the Abel polynomials, and obtain an a,q-analogue of the matching
numbers. We further generalize the rook theory model for matchings by
introducing l-lazy graphs which correspond to l-shifted boards, where l is a
finite vector of positive integers. The corresponding elliptic product formula
generalizes Haglund and Remmel's product formula for matchings already in the
non-elliptic basic case.


  We review recent works on the modelling of Generalised Parton Distributions
within the Dyson-Schwinger formalism. We highlight how covariant computations,
using the impulse approximation, allows one to fulfil most of the theoretical
constraints of the GPDs. Specific attention is brought to chiral properties and
especially the so-called soft pion theorem, and its link with the Axial-Vector
Ward-Takahashi identity. The limitation of the impulse approximation are also
explained. Beyond impulse approximation computations are reviewed in the
forward case. Finally, we stress the advantages of the overlap of lightcone
wave functions, and possible ways to construct covariant GPD models within this
framework, in a two-body approximation.


  An integrable eight state supersymmtric $U$ model is proposed, which is a
fermion model with correlated single-particle and pair hoppings as well as
uncorrelated triple-particle hopping. It has an $gl(3|1)$ supersymmetry and
contains one symmetry-preserving free parameter. The model is solved and the
Bethe ansatz equations are obtained.


  We consider regular and singular perturbations of the Dirichlet and Neumann
boundary value problems for the Helmholtz equation in $n$-dimensional
cylinders. Existence of eigenvalues and their asymptotics are studied.


  With the increasing adoption of the Proof of Stake (PoS) blockchain, it is
timely to study the economy created by such blockchain. In this chapter, we
will survey recent progress on the trading and wealth evolution in a
cryptocurrency where the new coins are issued according to the PoS protocol. We
first consider the wealth evolution in the PoS protocol assuming no trading,
and focus on the problem of decentralisation. Next we consider each miner's
trading incentive and strategy through the lens of optimal control, where the
miner needs to trade off PoS mining and trading. Finally, we study the
collective behavior of the miners in a PoS trading environment by a mean field
model. We use both stochastic and analytic tools in our study. A list of open
problems are also presented.


  The pulsar profile is characterised by two distinct emission components, the
core and the cone. The standard model of a pulsar radio emission beam
originating from dipolar magnetic fields, places the core at the centre
surrounded by concentric layers of inner and outer conal components. The core
emission is expected to have steeper spectra compared to the cones. We present
a detailed analysis of the relative differences in spectra between the core and
conal emission from a large sample of 53 pulsars over a wide frequency range
between 100 MHz and 10 GHz. The core was seen to be much steeper than the cones
particularly between 100 MHz and 1 GHz with a relative difference between the
spectral index $\Delta\alpha_{core/cone}\sim$ -1.0. In addition we also found
the spectra of the outer conal components to be steeper than the inner cone
with relative difference in the spectral index $\Delta\alpha_{in/out}\sim$
+0.5. The flattening of the spectra from the magnetic axis towards the edge of
the open field line region with increasing curvature of the field lines is a
natural outcome of the coherent curvature radiation from charged soliton
bunches, and explains the difference in spectra between the core and the cones.
In addition due to the relativistic beaming effect, the radiation is only
visible when it is directed towards the observer over a narrow angle
$\theta\leq 1/\gamma$, where $\gamma$ is the Lorentz factor of the outflowing
plasma clouds. This restricts the emission particularly from outer cones, that
are associated with field lines with larger curvature thereby making the
spectra steeper than the inner cones.


  With the utilization of Transformer architecture, large Vision and Language
(V&L) models have shown promising performance in even zero-shot settings.
Several studies, however, indicate a lack of robustness of the models when
dealing with complex linguistics and visual attributes. In this work, we
introduce a novel V&L benchmark - ColorFoil, by creating color-related foils to
assess the models' perception ability to detect colors like red, white, green,
etc. We evaluate seven state-of-the-art V&L models including CLIP, ViLT,
GroupViT, and BridgeTower, etc. in a zero-shot setting and present intriguing
findings from the V&L models. The experimental evaluation indicates that ViLT
and BridgeTower demonstrate much better color perception capabilities compared
to CLIP and its variants and GroupViT. Moreover, CLIP-based models and GroupViT
struggle to distinguish colors that are visually distinct to humans with normal
color perception ability.


  1. Animal movement patterns contribute to our understanding of variation in
breeding success and survival of individuals, and the implications for
population dynamics. 2. Over time, sensor technology for measuring movement
patterns has improved. Although older technologies may be rendered obsolete,
the existing data are still valuable, especially if new and old data can be
compared to test whether a behaviour has changed over time. 3. We used
simulated data to assess the ability to quantify and correctly identify
patterns of seabird flight lengths under observational regimes used in
successive generations of tracking technology. 4. Care must be taken when
comparing data collected at differing time-scales, even when using inference
procedures that incorporate the observational process, as model selection and
parameter estimation may be biased. In practice, comparisons may only be valid
when degrading all data to match the lowest resolution in a set. 5. Changes in
tracking technology that lead to aggregation of measurements at different
temporal scales make comparisons challenging. We therefore urge ecologists to
use synthetic data to assess whether accurate parameter estimation is possible
for models comparing disparate data sets before conducting analyses such as
responses to environmental changes or the assessment of management actions.


  We study the proton and the Roper resonance together with the meson cloud
model, by constructing a Hamiltonian matrix and solving the eigenvalue
equation. The proton sea quark flavour asymmetry and some properties of the
Roper resonance are thus reproduced in one scheme.


  Deep neural networks have been shown to be highly miscalibrated. often they
tend to be overconfident in their predictions. It poses a significant challenge
for safety-critical systems to utilise deep neural networks (DNNs), reliably.
Many recently proposed approaches to mitigate this have demonstrated
substantial progress in improving DNN calibration. However, they hardly touch
upon refinement, which historically has been an essential aspect of
calibration. Refinement indicates separability of a network's correct and
incorrect predictions. This paper presents a theoretically and empirically
supported exposition reviewing refinement of a calibrated model. Firstly, we
show the breakdown of expected calibration error (ECE), into predicted
confidence and refinement under the assumption of over-confident predictions.
Secondly, linking with this result, we highlight that regularization based
calibration only focuses on naively reducing a model's confidence. This
logically has a severe downside to a model's refinement as correct and
incorrect predictions become tightly coupled. Lastly, connecting refinement
with ECE also provides support to existing refinement based approaches which
improve calibration but do not explain the reasoning behind it. We support our
claims through rigorous empirical evaluations of many state of the art
calibration approaches on widely used datasets and neural networks. We find
that many calibration approaches with the likes of label smoothing, mixup etc.
lower the usefulness of a DNN by degrading its refinement. Even under natural
data shift, this calibration-refinement trade-off holds for the majority of
calibration methods.


  In this note, we show that there is a one-to-one correspondence between the
set of biclosed sets in an irreducible root system of type $A_n$ and the set of
quasitrivial semigroup structures on a set with $n+1$ elements.


  Within the macroscopic Landau-de Gennes approach, we examine the Gaussian
normal mode fluctuations of semi-infinite nematic liquid crystals in a regime
of critical wetting. It is argued that surface free-energy potentials that
strongly suppress the long-range nematic order favor the appearance of bound
biaxial nematic-director fluctuation modes, located in the domain occupied by
the thermodynamic phase wetting the wall. Instead, substrates enhancing the
orientational order promote the existence of uniaxial nematic-director local
excitations. Close to the phase coexistence temperature both types of local
exciations are strongly softened as compared to their bulk counterparts and
acquire characteristic cusplike low-energy spectra. These spectrum
peculiarities are directly connected to the critical behavior of the mean-field
interface position and can provide a valuable insight on the nature of surface
interactions and critical wetting phenomena in nematic liquid crystals.
Possible changes in the local director mode properties resulting from the
critical interface position fluctuations and order electricity effects are also
discussed.


  We prove a Cauchy-type integral representation for classes of functions
holomorphic in four priviledged tuboid domains of the complexified one-sheeted
two-dimensional hyperboloid. From a physical viewpoint, this hyperboloid can be
used for describing both the two-dimensional de Sitter and anti-de Sitter
universes. For two of these tuboids, called ``the Lorentz tuboids'' and
relevant for de Sitter Quantum Field Theory, the boundary values onto the real
hyperboloid of functions holomorphic in these domains admit continuous
Fourier-Helgason-type transforms. For the other two tuboids, called the
``chiral tuboids'' and relevant for anti-de Sitter Quantum Field Theory, the
boundary values on the reals of functions holomorphic in these domains admit
discrete Fourier-Helgason-type transforms. In both cases, the inversion
formulae for these transformations are derived by using the previous Cauchy
representation for the respective classes of functions. The decomposition of
functions on the real hyperboloid into sums of boundary values of holomorphic
functions from the previous four tuboids gives a complete and explicit
treatment of the Gelfand-Gindikin program for the one-sheeted hyperboloid.


  Unbiased CLTR requires click propensities to compensate for the difference
between user clicks and true relevance of search results via IPS. Current
propensity estimation methods assume that user click behavior follows the PBM
and estimate click propensities based on this assumption. However, in reality,
user clicks often follow the CM, where users scan search results from top to
bottom and where each next click depends on the previous one. In this cascade
scenario, PBM-based estimates of propensities are not accurate, which, in turn,
hurts CLTR performance. In this paper, we propose a propensity estimation
method for the cascade scenario, called CM-IPS. We show that CM-IPS keeps CLTR
performance close to the full-information performance in case the user clicks
follow the CM, while PBM-based CLTR has a significant gap towards the
full-information. The opposite is true if the user clicks follow PBM instead of
the CM. Finally, we suggest a way to select between CM- and PBM-based
propensity estimation methods based on historical user clicks.


  An auto-B\"acklund transformation for the quad equation $\mathrm{Q1}_1$ is
considered as a discrete equation, called $\mathrm{H2}^a$, which is a so called
torqued version of $\mathrm{H2}$. The equations $\mathrm{H2}^a$ and
$\mathrm{Q1}_1$ compose a consistent cube, from which a auto-B\"acklund
transformation and a Lax pair for $\mathrm{H2}^a$ are obtained. More generally
it is shown that auto-B\"acklund transformations admit auto-B\"acklund
transformations. Using the auto-B\"acklund transformation for $\mathrm{H2}^a$
we derive a seed solution and a one-soliton solution. From this solution it is
seen that $\mathrm{H2}^a$ is a semi-autonomous lattice equation, as the spacing
parameter $q$ depends on $m$ but it disappears from the plain wave factor.


  {\em Quantum Fourier analysis} is a new subject that combines an algebraic
Fourier transform (pictorial in the case of subfactor theory) with analytic
estimates. This provides interesting tools to investigate phenomena such as
quantum symmetry. We establish bounds on the quantum Fourier transform $\FS$,
as a map between suitably defined $L^{p}$ spaces, leading to a new uncertainty
principle for relative entropy. We cite several applications of the quantum
Fourier analysis in subfactor theory, in category theory, and in quantum
information. We suggest a new topological inequality, and we outline several
open problems.


  Susceptibilities of conserved quantities, such as baryon number, strangeness
and electric charge are sensitive to the onset of quantum chromodynamics (QCD)
phase transition and are expected to provide information on the matter produced
in heavy-ion collision experiments. A comprehensive study of the second-order
diagonal susceptibilities and cross correlations has been made within a thermal
model approach of the hadron resonance gas (HRG) model as well as with a
hadronic transport model, UrQMD. We perform a detailed analysis of the effect
of detector acceptances and choice of particle species in the experimental
measurements of the susceptibilities for heavy-ion collisions corresponding to
\sNN = 4 GeV to 200 GeV. The transverse momentum cutoff dependence of suitably
normalised susceptibilities are proposed as useful observables to probe the
properties of the medium at freezeout.


  Active context-free games are two-player games on strings over finite
alphabets with one player trying to rewrite the input string to match a target
specification. These games have been investigated in the context of exchanging
Active XML (AXML) data. While it was known that the rewriting problem is
undecidable in general, it is shown here that it is EXPSPACE-complete to decide
for a given context-free game, whether all safely rewritable strings can be
safely rewritten in a left-to-right manner, a problem that was previously
considered by Abiteboul et al. Furthermore, it is shown that the corresponding
problem for games with finite replacement languages is EXPTIME-complete.


  We consider matrices with entries in a local ring, Mat(m,n;R). Fix an action
of group G on Mat(m,n;R), and a subset of allowed deformations, \Sigma in
Mat(m,n;R). The standard question (along the lines of Singularity Theory) is
the finite-(\Sigma,G)-determinacy of matrices.
  In our previous work this determinacy question was reduced to the study of
the tangent spaces to \Sigma and to the orbit, T_{(\Sigma,A)}, T_{(GA,A)}, and
their quotient: the tangent module to the miniversal deformation. In
particular, the order of determinacy is controlled by the annihilator of this
tangent module.
  Then we have studied this tangent module for the group action GL(m,R)\times
GL(n,R) on Mat(m,n;R) and for various natural subgroups of it. These are
R-linear group actions.
  In the current work we study this tangent module for group actions that
involve the automorphisms of the ring, or, geometrically, group-actions that
involve the local coordinate changes. (These actions are not R-linear.) We
obtain various bounds on the support of this module. This gives ready-to-use
criteria of determinacy for matrices, (embedded) modules and (skew-)symmetric
forms.


  The preponderance of white dwarfs in the Milky Way were formed from the
remnants of stars of the same or somewhat higher mass as the Sun, i.e., from
G-stars. We know that life can exist around G-stars. Any technologically
advanced civilization residing within the habitable zone of a G-star will face
grave peril when its star transitions from the main sequence and successively
enters sub-giant, red giant, planetary nebula, and white dwarf stages. In fact,
if the civilization takes no action it will face certain extinction. The two
alternatives to passive extinction are (a) migrate away from the parent star in
order to colonize another star system, or (b) find a viable solution within
one's own solar system. It is argued in this paper that migration of an entire
biological population or even a small part of a population is virtually
impossible, but in any event, far more difficult than remaining in one's home
solar system where the problem of continued survival can best be solved. This
leads to the conclusion that sub-giants, red giants, planetary nebula, and
white dwarfs are the best possible candidate targets for SETI observations.
Search strategies are suggested.


  In this paper we investigate using the methodology of algebraic logic, deep
algebraic results to prove three new omitting types theorems for finite
variable fragments of first order logic. As a sample, we show that it T is an
L_n theory and |T|=lambda, lambda a regular cardinal, if T admits elimination
of quantifiers, then T omits < 2^{\lambda} many non isolated {\it maximal}
types. This is basically a result of Shelah's restricted to L_n. that is not
completely representable. We also show, using a rainbow construction for
cylindric algebras, that the omitting types theorem fails for L_n even if we
consider clique guarded semantics. This is done by constructing a an atomic
\A\in \PEA_n with countably many atoms (which are coloured graphs) who Sc
(Pinter's) reduct is not in S_c\Nr_n\Sc_{n+3}, but $A$ is elementary equivalent
to a countable completely representable (polyadic equality) algebra. Various
connections between the notions of strong representability and complete
representability are given in terms of neat embeddings. Several examples, using
rainbow constructions and Monk-like algebras are also given to show that our
results are best possible. As a sample we show that, assuming the existence of
certain finite relation algebras, that for any k\in \omega, there exists \A\in
{\sf RPEA}_n\cap \Nr_n\PEA_{n+k} such that Rd_{\sf Sc}\Cm\At\A\notin
S\Nr_n\Sc_{n+k+1}. This implies that for any finite n\geq 3, for any k\geq 0,
there is an L_n theory and a type \Gamma such that Gamma is realized in every
n+k+1 relativized smooth model, but cannot be isolated by a witness using n+k
variables.


  Regardless of whether or not all fast radio bursts (FRBs) repeat, those that
do form a population with a distribution of rates. This work considers a
power-law model of this population, with rate distribution $\Phi_r \sim
R^{\gamma_r}$ between $R_{\rm min}$ and $R_{\rm max}$. The zDM code is used to
model the probability of detecting this population as either apparently
once-off or repeat events as a function of redshift, $z$, and dispersion
measure, DM. I demonstrate that in the nearby Universe, repeating sources can
contribute significantly to the total burst rate. This causes an apparent
deficit in the total number of observed sources (once-off and repeaters)
relative to the distant Universe that will cause a bias in FRB population
models. Thus instruments with long exposure times should explicitly take
repetition into account when fitting the FRB population.
  I then fit data from The Canadian Hydrogen Intensity Mapping Experiment
(CHIME). The relative number of repeat and apparently once-off FRBs, and their
DM, declination, and burst rate distributions, can be well-explained by
50--100\% of CHIME single FRBs being due to repeaters, with $R_{\rm max} >
0.75$ day$^{-1}$ above $10^{39}$ erg, and ${\gamma_r} = -2.2_{-0.8}^{+0.6}$.
This result is surprisingly consistent with follow-up studies of FRBs detected
by the Australian Square Kilometre Array Pathfinder (ASKAP). Thus the evidence
suggests that CHIME and ASKAP view the same repeating FRB population, which is
responsible not just for repeating FRBs, but the majority of apparently
once-off bursts.
  For greater quantitative accuracy, non-Poissonian arrival times, second-order
effects in the CHIME response, and a simultaneous fit to the total FRB
population parameters, should be treated in more detail in future studies.


  A new Cr-based quasi-one-dimensional superconductor Na2Cr3As3 was synthesized
by an ion-exchange method in sodium naphthalenide solution. The crystals are
thread-like and the structure was analyzed by X-ray diffraction with a
noncentrosymmetric hexagonal space group P-6m2 (No. 187), in which the
(Cr3As3)2- linear chains are separated by Na+ ions, and the refined lattice
parameters are a = 9.239(2) {\AA} and c = 4.209(6) {\AA}. The measurements for
electrical resistivity, magnetic susceptibility, and heat capacity reveal a
superconducting transition with unconventional characteristic at the Tc of 8.6
K, which exceeds that of all previously reported Cr-based superconductors.


  Using first-principles calculations based on a variational density functional
perturbation theory, we investigate the lattice dynamics of solid solutions of
barium and strontium titanates. Averaging the information available for the
related pure compounds yields results equivalent to those obtained within the
virtual crystal approximation, providing frequencies which are a good
approximation to those computed for a (111) ordered supercell. Using the same
averaging technique we report the evolution of the ferroelectric and
antiferrodistortive instabilities with composition.


  General rogue waves in (1+1)-dimensional three-wave resonant interaction
systems are derived by the bilinear method. These solutions are divided into
three families, which correspond to a simple root, two simple roots and a
double root of a certain quartic equation arising from the dimension reduction
respectively. It is shown that while the first family of solutions associated
with a simple root exist for all signs of the nonlinear coefficients in the
three-wave interaction equations, the other two families of solutions
associated with two simple roots and a double root can only exist in the
so-called soliton-exchange case, where the nonlinear coefficients have certain
signs. Many of these rogue wave solutions, such as those associated with two
simple roots, and higher-order solutions associated with a simple root, are new
solutions which have not been reported before. Technically, our bilinear
derivation of rogue waves for the double-root case is achieved by a
generalization to the previous dimension reduction procedure in the bilinear
method, and this generalized procedure allows us to treat roots of arbitrary
multiplicities. Dynamics of the derived rogue waves is also examined, and new
rogue-wave patterns are presented. Connection between these bilinear rogue
waves and those derived earlier by Darboux transformation is also explained.


  In this note we collect, systemise and generalise the existing results for
relations between general Horndeski theories and beyond Horndeski theories via
disformal transformations of metric. We derive additional disformal
transformation rules relating Lagrangian functions of beyond Horndeski theory
and corresponding Horndeski theory and demonstrate that some of them become
singular at some moments(s) once one constructs a non-singular cosmological
solution in beyond Horndeski theory that is free from ghost, gradient
instabilities and strong gravity regime during the entire evolution of the
system. The key issue here is that such solutions are banned in Horndeski
theory due to existing no-go theorem. The proof of singular behaviour of
disformal relations in this case resolves the apparent contradiction between
the fact that Horndeski and beyond Horndeski theories appear related by field
redefinition but describe different physics in the context of non-singular
cosmologies.


  We exhibit a numerical method to compute three-point branched covers of the
complex projective line. We develop algorithms for working explicitly with
Fuchsian triangle groups and their finite index subgroups, and we use these
algorithms to compute power series expansions of modular forms on these groups.


  We present the current controlled motion of dynamic soliton embedded in spin
wave background in ferromagnetic nanowire. With the stronger breather character
we get the novel magnetic rogue wave and clarify its formation mechanism. The
generation of magnetic rogue wave is mainly arose from the accumulation of
energy and magnons toward to its central part. We also observe that the
spin-polarized current can control the exchange rate of magnons between
envelope soliton and background, and the critical current condition is obtained
analytically. Even more interesting is that the spin-transfer torque plays the
completely opposite role for the cases of below and above the critical value.


  We consider the vectorial approach to the binary Darboux transformations for
the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We
obtain explicit formulae for the Darboux transformed potentials in terms of
Grammian type determinants. We also study the $n$-th Gel'fand-Dickey hierarchy
introducing spectral operators and obtaining similar results. We reduce the
above mentioned results to the Kadomtsev-Petviashvili I and II real forms,
obtaining corresponding vectorial Darboux transformations. In particular for
the Kadomtsev-Petviashvili I hierarchy we get the line soliton, the lump
solution and the Johnson-Thompson lump, and the corresponding determinant
formulae for the non-linear superposition of several of them. For
Kadomtsev-Petviashvili II apart from the line solitons we get singular rational
solutions with its singularity set describing the motion of strings in the
plane. We also consider the I and II real forms for the Gel'fand-Dickey
hierarchies obtaining the vectorial Darboux transformation in both cases.


  A new approach on cryptanalysis is proposed where the goal is to explore the
fundamental limits of a specific class of attacks against a particular
cryptosystem. As a first step, the approach is applied on ABSG, which is an
LFSR-based stream cipher where irregular decimation techniques are utilized.
Consequently, under some mild assumptions, which are common in cryptanalysis,
the tight lower bounds on the algorithmic complexity of successful Query-Based
Key-Recovery attacks are derived for two different setups of practical
interest. The proofs rely on the concept of ``typicality'' of information
theory.


  We derive some combinatorial consequences from the positivity of
Donaldson-Thomas invariants for symmetric quivers conjectured by Kontsevich and
Soibelman and proved recently by Efimov. These results are used to prove the
Kac conjecture for quivers having at least one loop at every vertex.


  Chiral structures have reported radiation of circular polarized
electromagnetic waves (CPs) in a specific direction. Here we report a class of
torus knot radiators that is not only chiral but also three-dimensional (3-D)
rotational symmetric along X, Y and Z axes. Because of this exotic chirality
and symmetry, the knot radiator presented is able to demonstrate
omnidirectional circular polarized radiation, which has never been reported in
any known structures.


  According to the theory of relativity and causality, a special type of
correlation beyond quantum mechanics is possible in principle under the name of
{\it non-local box}. The concept has been introduced from the principle of
non-locality which satisfies relativistic causality. In this paper, we show
that a correlation leading to the non-local box is possible to be derived
consistently if we release the one of major axioms in quantum mechanics, {\it
Born's rule}. This allows us to obtain a theory which in one end of the
spectrum agrees with the classical probability and in the other end, agrees
with the theory of non-local causality. At the same time, we argue that the
correlation lies in a space with special mathematical constraints such that a
physical realization of the correlation through a probability measure is not
possible in one direction of its limit and is possible in the other limit.


  Convolutional neural networks (CNNs) are the state-of-the-art technique for
identifying strong gravitational lenses. Although they are highly successful in
recovering genuine lens systems with a high true-positive rate, the unbalanced
nature of the data set (lens systems are rare), still leads to a high false
positive rate. For these techniques to be successful in upcoming surveys (e.g.
with Euclid) most emphasis should be set on reducing false positives, rather
than on reducing false negatives. In this paper, we introduce densely connected
neural networks (DenseNets) as the CNN architecture in a new pipeline-ensemble
model containing an ensemble of classification CNNs and regression CNNs to
classify and rank-order lenses, respectively. We show that DenseNets achieve
comparable true positive rates but considerably lower false positive rates
(when compared to residual networks; ResNets). Thus, we recommend DenseNets for
future missions involving large data sets, such as Euclid, where low false
positive rates play a key role in the automated follow-up and analysis of large
numbers of strong gravitational lens candidates when human vetting is no longer
feasible


  As NLP models become larger, executing a trained model requires significant
computational resources incurring monetary and environmental costs. To better
respect a given inference budget, we propose a modification to contextual
representation fine-tuning which, during inference, allows for an early (and
fast) "exit" from neural network calculations for simple instances, and late
(and accurate) exit for hard instances. To achieve this, we add classifiers to
different layers of BERT and use their calibrated confidence scores to make
early exit decisions. We test our proposed modification on five different
datasets in two tasks: three text classification datasets and two natural
language inference benchmarks. Our method presents a favorable speed/accuracy
tradeoff in almost all cases, producing models which are up to five times
faster than the state of the art, while preserving their accuracy. Our method
also requires almost no additional training resources (in either time or
parameters) compared to the baseline BERT model. Finally, our method alleviates
the need for costly retraining of multiple models at different levels of
efficiency; we allow users to control the inference speed/accuracy tradeoff
using a single trained model, by setting a single variable at inference time.
We publicly release our code.


  Thin films of perovskite Ruthenates of the general formula ARuO3 (A = Ca and
Sr) are versatile electrical conductors for viable oxide electronics. They are
also scientifically intriguing, as they exhibit non-trivial electromagnetic
ground states depending on the A-site element. Among them, realization of the
cubic perovskite (3C) BaRuO3 thin film has been a challenge so far, because the
3C phase is metastable with the largest formation energy among the various
polymorph phases of BaRuO3. In this study, we successfully prepared 3C BaRuO3
thin films employing epitaxial stabilization. The 3C BaRuO3 thin films show
itinerant ferromagnetism with a transition temperature of ~48 K and a non-Fermi
liquid phase. The epitaxial stabilization of the 3C BaRuO3 further enabled us
to make a standard comparison of perovskite Ruthenates thin films, thereby
establishing the importance of the Ru-O orbital hybridization in understanding
the itinerant magnetic system.


  For a panel model considered by Abadie et al. (2010), the counterfactual
outcomes constructed by Abadie et al., Hsiao et al. (2012), and Doudchenko and
Imbens (2017) may all be confounded by uncontrolled heterogenous trends. Based
on exact-matching on the trend predictors, I propose new methods of estimating
the model-specific treatment effects, which are free from heterogenous trends.
When applied to Abadie et al.'s (2010) model and data, the new estimators
suggest considerably smaller effects of California's tobacco control program.


  Precision tests of first-row unitarity of the Cabibbo-Kobayashi-Maskawa
matrix currently display two intriguing tensions, both at the $3\sigma$ level.
First, combining determinations of $V_{ud}$ from superallowed $\beta$ decays
with $V_{us}$ from kaon decays suggests a deficit in the unitarity relation. At
the same time, a tension of similar significance has emerged between $K_{\ell
2}$ and $K_{\ell 3}$ decays. In this Letter, we point out that a measurement of
the $K_{\mu3}/K_{\mu 2}$ branching fraction at the level of $0.2\%$ would have
considerable impact on clarifying the experimental situation in the kaon
sector, especially in view of tensions in the global fit to kaon data as well
as the fact that the $K_{\mu2}$ channel is currently dominated by a single
experiment. Such a measurement, as possible for example at NA62, would further
provide important constraints on physics beyond the Standard Model, most
notably on the role of right-handed vector currents.


  Motion control algorithms in the presence of pedestrians are critical for the
development of safe and reliable Autonomous Vehicles (AVs). Traditional motion
control algorithms rely on manually designed decision-making policies which
neglect the mutual interactions between AVs and pedestrians. On the other hand,
recent advances in Deep Reinforcement Learning allow for the automatic learning
of policies without manual designs. To tackle the problem of decision-making in
the presence of pedestrians, the authors introduce a framework based on Social
Value Orientation and Deep Reinforcement Learning (DRL) that is capable of
generating decision-making policies with different driving styles. The policy
is trained using state-of-the-art DRL algorithms in a simulated environment. A
novel computationally-efficient pedestrian model that is suitable for DRL
training is also introduced. We perform experiments to validate our framework
and we conduct a comparative analysis of the policies obtained with two
different model-free Deep Reinforcement Learning Algorithms. Simulations
results show how the developed model exhibits natural driving behaviours, such
as short-stopping, to facilitate the pedestrian's crossing.


  Let $R$ be a commutative ring with $1 \neq 0$. A proper ideal $I$ of $R$ is a
{\it square-difference factor absorbing ideal} (sdf-absorbing ideal) of $R$ if
whenever $a^2 - b^2 \in I$ for $0 \neq a, b \in R$, then $a + b \in I$ or $a -
b \in I$. In this paper, we introduce and investigate sdf-absorbing ideals.


  We investigate the Schatten-von Neumann properties of pseudo-differential
operators using the method proposed by A. Boulkhemair in \cite{Boulkhemair 2}.
The symbols are elements of the ideals $S_{w}^{p}$ of the Sj\"ostrand algebra
$S_{w}$.


  We study the problem of determining the emergent behaviors that are possible
given a functionally heterogeneous swarm of robots with limited capabilities.
Prior work has considered behavior search for homogeneous swarms and proposed
the use of novelty search over either a hand-specified or learned behavior
space followed by clustering to return a taxonomy of emergent behaviors to the
user. In this paper, we seek to better understand the role of novelty search
and the efficacy of using clustering to discover novel emergent behaviors.
Through a large set of experiments and ablations, we analyze the effect of
representations, evolutionary search, and various clustering methods in the
search for novel behaviors in a heterogeneous swarm. Our results indicate that
prior methods fail to discover many interesting behaviors and that an iterative
human-in-the-loop discovery process discovers more behaviors than random
search, swarm chemistry, and automated behavior discovery. The combined
discoveries of our experiments uncover 23 emergent behaviors, 18 of which are
novel discoveries. To the best of our knowledge, these are the first known
emergent behaviors for heterogeneous swarms of computation-free agents. Videos,
code, and appendix are available at the project website:
https://sites.google.com/view/heterogeneous-bd-methods


  In this paper we study the asymptotic behavior of the number of summands in
tensor products of finite dimensional representations of affine (semi)group
(super)schemes and related objects.


  Millisecond pulsars with white dwarf companions have typical eccentricities
$e\sim 10^{-6}-10^{-3}$. The eccentricities of helium white dwarfs are
explained well by applying the fluctuation-dissipation theorem to convective
eddies in their red giant progenitors. We extend this theory to more massive
carbon-oxygen (CO) white dwarfs with asymptotic giant branch (AGB) progenitors.
Due to the radiation pressure in AGB stars, the dominant factor in determining
the remnant white dwarf's eccentricity is the critical residual hydrogen
envelope mass $m_{\rm env}$ required to inflate the star to giant proportions.
Using a suite of MESA stellar evolution simulations with $\Delta m_{\rm
c}=10^{-3}\,{\rm M}_\odot$ core-mass intervals, we resolved the AGB thermal
pulses and found that the critical $m_{\rm env}\propto m_{\rm c}^{-6}$. This
steep dependence causes the $e(m_{\rm c})$ relation to turn over, such that
$e\sim 3\times 10^{-3}$ almost independently of the remnant CO white dwarf's
mass $m_{\rm c}$. Nearly all of the measured eccentricities lie below this
robust theoretical limit, indicating that the eccentricity is damped during the
common-envelope inspiral that follows the unstable Roche-lobe overflow of the
AGB star. Specifically, we focused on white dwarfs with median masses $m_{\rm
c}>0.6\,{\rm M}_\odot$. These massive white dwarfs begin their inspiral with
practically identical orbital periods and eccentricities, eliminating any
dependence on the initial conditions. For this sub-sample, we find an empirical
relation $e\propto P^{3/2}$ between the final period and eccentricity that is
much tighter than previous studies - motivating theoretical work on the
eccentricity evolution during the common envelope phase.


  The problem of cooperative fusion in the presence of Byzantine sensors is
considered. An information theoretic formulation is used to characterize the
Shannon capacity of sensor fusion. It is shown that when less than half of the
sensors are Byzantine, the effect of Byzantine attack can be entirely
mitigated, and the fusion capacity is identical to that when all sensors are
honest. But when at least half of the sensors are Byzantine, they can
completely defeat the sensor fusion so that no information can be transmitted
reliably. A capacity achieving transmit-then-verify strategy is proposed for
the case that less than half of the sensors are Byzantine, and its error
probability and coding rate is analyzed by using a Markov decision process
modeling of the transmission protocol.


  The recent results from Daya Bay and RENO reactor neutrino experiments have
firmly established that the smallest reactor mixing angle $\theta_{13}$ is
non-vanishing at the $5 \sigma$ level, with a relatively large value, i.e.,
$\theta_{13}\approx 9^{\circ}$. Using the fact that the neutrino mixing matrix
can be represented as $V_{\rm PMNS}=U_l^{\dagger} U_{\nu} P_\nu$, where $U_l$
and $U_\nu$ result from the diagonalization of the charged lepton and neutrino
mass matrices and $P_\nu$ is a diagonal matrix containing the Majorana phases
and assuming the tri-bimaximal form for $U_\nu$, we investigate the possibility
of accounting for the large reactor mixing angle due to the corrections of the
charged lepton mixing matrix. The form of $U_{l}$ is assumed to be that of CKM
mixing matrix of the quark sector. We find that with this modification it is
possible to accommodate the large observed reactor mixing angle $\theta_{13}$.
We also study the implications of such corrections on the other
phenomenological observables.


  A lot of information concerning solutions of linear differential equations
can be computed directly from the equation. It is therefore natural to consider
these equations as a data-structure, from which mathematical properties can be
computed. A variety of algorithms has thus been designed in recent years that
do not aim at "solving", but at computing with this representation. Many of
these results are surveyed here.


  Hybrid precoding is a cost-efficient technique for millimeter wave (mmWave)
massive multiple-input multiple-output (MIMO) communications. This paper
proposes a deep learning approach by using a distributed neural network for
hybrid analog-and-digital precoding design with limited feedback. The proposed
distributed neural precoding network, called DNet, is committed to achieving
two objectives. First, the DNet realizes channel state information (CSI)
compression with a distributed architecture of neural networks, which enables
practical deployment on multiple users. Specifically, this neural network is
composed of multiple independent sub-networks with the same structure and
parameters, which reduces both the number of training parameters and network
complexity. Secondly, DNet learns the calculation of hybrid precoding from
reconstructed CSI from limited feedback. Different from existing black-box
neural network design, the DNet is specifically designed according to the data
form of the matrix calculation of hybrid precoding. Simulation results show
that the proposed DNet significantly improves the performance up to nearly 50%
compared to traditional limited feedback precoding methods under the tests with
various CSI compression ratios.


  In this article we use the philosophy in [OS22] to construct the quantum
difference equation of affine type $A$ quiver varieties in terms of the quantum
toroidal algebra $U_{q,t}(\hat{\hat{\mathfrak{sl}}}_{r})$. In the construction,
and we define the set of wall for each quiver varieties by the action of the
universal $R$-matrix, which is shown to be almost equivalent to that of the
$K$-theoretic stable envelope on each interval in $H^2(X,\mathbb{Q})$. We also
give the examples of the instanton moduli space $M(n,r)$ and the equivariant
Hilbert scheme $\text{Hilb}_{n}([\mathbb{C}^2/\mathbb{Z}_{r}])$ to show the
explicit form of the quantum difference operator.


  Reconstructing accurate 3D surface models of sinus anatomy directly from an
endoscopic video is a promising avenue for cross-sectional and longitudinal
analysis to better understand the relationship between sinus anatomy and
surgical outcomes. We present a patient-specific, learning-based method for 3D
reconstruction of sinus surface anatomy directly and only from endoscopic
videos. We demonstrate the effectiveness and accuracy of our method on in and
ex vivo data where we compare to sparse reconstructions from Structure from
Motion, dense reconstruction from COLMAP, and ground truth anatomy from CT. Our
textured reconstructions are watertight and enable measurement of clinically
relevant parameters in good agreement with CT. The source code is available at
https://github.com/lppllppl920/DenseReconstruction-Pytorch.


  Given a family of binary-input memoryless output-symmetric (BMS) channels
having a fixed capacity, we derive the BMS channel having the highest (resp.
lowest) capacity among all channels that are degraded (resp. upgraded) with
respect to the whole family. We give an explicit characterization of this
channel as well as an explicit formula for the capacity of this channel.


  I review a particular class of physical applications of Logarithmic Conformal
Field Theory in strings propagating in changing (not necessarily conformal)
backgrounds, namely D-brane recoil in flat or time-dependent cosmological
backgrounds. The role of recoil logarithmic vertex operators as non-conformal
deformations, requiring in some cases Liouville dressing, is pointed out. It is
also argued that, although in the case of non-supersymmetric recoil
deformations the representation of target time as a Liouville zero mode may
lead to non-linear quantum mechanics for stringy defects, such non-linearities
disappear (or, at least, are strongly suppressed) after world-sheet
supersymmetrization. A possible link is therefore suggested between
(world-sheet) supersymmetry and linearity of quantum mechanics in this
framework.


  Monte Carlo simulations on the SK model have been done to investigate aging
processes after a rapid quench from $T=\infty$ to the spin-glass phase. The
time range of simulations is taken care of so that the system does not surmount
free-energy barriers between the pure states which are considered to diverge in
the thermodynamic limit. We simulate time evolutions of extensive energy of the
system, Parisi's overlap distribution function, auto-correlation and
clones-correlation functions, distribution functions of the two correlations,
and magnetization induced by the field applied after a certain waiting time.
The data simulated exhibit a rich variety of aging phenomena. Most of them can
be interpreted in a unified way, though qualitatively, by the scenario of
``growth of quasi-equilibrium domains'' which we will introduce in this work.
More surprisingly, they suggest strongly that a basin of attraction of one
dominant pure state spans almost an entire phase space of the system with a
common time-reversal symmetry.


  Motivated by diquark exchange, we construct a class of extensions of the
standard model. These models can generate large CP conserving and CP violating
contributions to the doubly Cabbibo suppressed decays D^0\to K^+\pi^- without
affecting D^0-\overline{D^0} mixing, contrary to what is usually believed in
the literature. We find an interesting specific realization of these models,
which has the LR chiral structure and can induce novel density \times density
operators. It is new for non-leptonic kaon decays, and particularly, may
provide a possible solution to the \Delta I=1/2 rule and direct CP violation,
without inducing large flavour changing neutral currents.


  Pulse compression can enhance both the performance in range resolution and
sensitivity for weather radar. However, it will introduce the issue of high
sidelobes if not delicately implemented. Motivated by this fact, we focus on
the pulse compression design for weather radar in this paper. Specifically, we
jointly design both the subpulse codes and extended mismatch filter based on
the alternating direction method of multipliers (ADMM). This joint design will
yield a pulse compression with low sidelobes, which equivalently implies a high
signal-to-interference-plus-noise ratio (SINR) and a low estimation error on
meteorological reflectivity. The experiment results demonstrate the efficacy of
the proposed pulse compression strategy since its achieved meteorological
reflectivity estimations are highly similar to the ground truth.


  Generating synchronized and natural lip movement with speech is one of the
most important tasks in creating realistic virtual characters. In this paper,
we present a combined deep neural network of one-dimensional convolutions and
LSTM to generate vertex displacement of a 3D template face model from
variable-length speech input. The motion of the lower part of the face, which
is represented by the vertex movement of 3D lip shapes, is consistent with the
input speech. In order to enhance the robustness of the network to different
sound signals, we adapt a trained speech recognition model to extract speech
feature, and a velocity loss term is adopted to reduce the jitter of generated
facial animation. We recorded a series of videos of a Chinese adult speaking
Mandarin and created a new speech-animation dataset to compensate the lack of
such public data. Qualitative and quantitative evaluations indicate that our
model is able to generate smooth and natural lip movements synchronized with
speech.


  The phase diagram of the two-dimensional t-J model is determined accurately
at low electron density by a combination of analytic and numerical techniques.
The ground state exhibits three phases in the limit of zero electron density:
an unpaired state at small J/t, a gas of s-wave pairs for 2 < J/t < 3.4367, and
a phase separated state at larger interaction strengths. Bound states of larger
clusters are never realized, and the instabilities present at small densities
are discussed.


  Ad-hoc social networks (ASNETs) represent a special type of traditional
ad-hoc network in which a user's social properties (such as the social
connections and communications metadata as well as application data) are
leveraged for offering enhanced services in a distributed infrastructureless
environments. However, the wireless medium, due to limited bandwidth, can
easily suffer from the problem of congestion when social metadata and
application data are exchanged among nodes---a problem that is compounded by
the fact that some nodes may act selfishly and not share its resources. While a
number of congestion control schemes have been proposed for the traditional
ad-hoc networks, there has been limited focus on incorporating social awareness
into congestion control schemes. We revisit the existing traditional ad-hoc
congestion control and data distribution protocols and motivate the need for
embedding social awareness into these protocols to improve performance. We
report that although some work is available in opportunistic network that uses
socially-aware techniques to control the congestion issue, this area is largely
unexplored and warrants more research attention. In this regards, we highlight
the current research progress and identify multiple future directions of
research.


  We have synthesized two new interstitial compounds (RPd3)8Mn (R = La and Ce).
The Mn ions present in "dilute" concentration of just 3 molar percent form a
sublattice with an unusually large Mn-Mn near neighbor distance of ~ 85 nm.
While the existence of (RPd3)8M (where M is a p-block element) is already
documented in the literature, the present work reports for the first time the
formation of this phase with M being a 3d element. In (LaPd3)8Mn, the Mn
sub-lattice orders antiferromagnetically as inferred from the peaks in
low-field magnetization at 48 K and 23 K. The latter peak progressively shifts
towards lower temperatures in increasing magnetic field and disappears below
1.8 K in a field of ~ 8 kOe. On the other hand in (CePd3)8Mn the Mn sublattice
undergoes a ferromagnetic transition around 35 K. The Ce ions form a dense
Kondo-lattice and are in a paramagnetic state at least down to 1.5 K. A
strongly correlated electronic ground state arising from Kondo effect is
inferred from the large extrapolated value of C/T = 275 mJ/Ce-mol K^2 at T = 0
K. In contrast, the interstitial alloys RPd3Mnx (x = 0.03 and 0.06), also
synthesized for the first time, have a spin glass ground state due to the
random distribution of the Mn ions over the available "1b" sites in the parent
RPd3 crystal lattice.


  In this review we present a comprehensive discussion of peculiar velocity
field measured recently on very large scales with a novel method using X-ray
galaxy clusters as tracers. The measurement is based on the kinematic component
of the Sunyaev-Zeldovich (KSZ) effect produced by Compton scattering of cosmic
microwave background (CMB) photons off the hot intracluster gas, and uses a
large catalog of X-ray selected clusters and all-sky CMB maps obtained with the
WMAP satellite. The method probes the dipole of the CMB temperature field
evaluated at the cluster positions and within the apertures in which the CMB
monopole contribution vanishes, thereby isolating the signal remaining from the
KSZ effect produced by coherently moving clusters. The detection of a highly
significant dipole out to the depth of at least ~ 800 Mpc casts doubt on the
notion that gravitational instability from the observed mass distribution is
the sole -- or even dominant -- cause of the detected motions. Rather it
appears that the flow may extend across the entire observable Universe.
Possible implications include the possibility to constrain the primeval
preinflationary structure of space-time and its landscape, and/or the need for
modifications of presently known physics (e.g. arising from a
higher-dimensional structure of gravity). We review these possibilities in
light of the measurements described here and specifically discuss the prospects
of future measurements and the issues they should resolve. We address the
consistency of these large-scale velocity measurements with those obtained on
smaller scales by studies using galaxies as tracers, and resolve the
discrepancies with two recent claims based on modified CMB analysis schemes.


  In this paper we introduce the space-fractional Poisson process whose state
probabilities $p_k^\alpha(t)$, $t>0$, $\alpha \in (0,1]$, are governed by the
equations $(\mathrm d/\mathrm dt)p_k(t) = -\lambda^\alpha (1-B)p_k^\alpha(t)$,
where $(1-B)^\alpha$ is the fractional difference operator found in the study
of time series analysis. We explicitly obtain the distributions
$p_k^\alpha(t)$, the probability generating functions $G_\alpha(u,t)$, which
are also expressed as distributions of the minimum of i.i.d.\ uniform random
variables. The comparison with the time-fractional Poisson process is
investigated and finally, we arrive at the more general space-time fractional
Poisson process of which we give the explicit distribution.


  Fast and precise robot motion is needed in certain applications such as
electronic manufacturing, additive manufacturing and assembly. Most industrial
robot motion controllers allow externally commanded motion profile, but the
trajectory tracking performance is affected by the robot dynamics and joint
servo controllers which users have no direct access and little information. The
performance is further compromised by time delays in transmitting the external
command as a setpoint to the inner control loop. This paper presents an
approach of combining neural networks and iterative learning control to improve
the trajectory tracking performance for a multi-axis articulated industrial
robot. For a given desired trajectory, the external command is iteratively
refined using a high fidelity dynamical simulator to compensate for the robot
inner loop dynamics. These desired trajectories and the corresponding refined
input trajectories are then used to train multi-layer neural networks to
emulate the dynamical inverse of the nonlinear inner loop dynamics. We show
that with a sufficiently rich training set, the trained neural networks can
generalize well to trajectories beyond the training set. In applying the
trained neural networks to the physical robot, the tracking performance still
improves but not as much as in the simulator. We show that transfer learning
can effectively bridge the gap between simulation and the physical robot. In
the end, we test the trained neural networks on other robot models in
simulation and demonstrate the possibility of a general purpose network.
Development and evaluation of this methodology is based on the ABB IRB6640-180
industrial robot and ABB RobotStudio software packages.


  We consider numerically the growth of neutrino asymmetry in active-sterile
neutrino oscillations in the early universe. It is shown that the final sign of
the asymmetry can be highly sensitive to small variations of the oscillation
parameters. We find regions which are completely or partially chaotic, but also
regions where the sign remains very robust. The consequences for atmospheric
neutrino oscillations and primordial nucleosynthesis are then discussed. In the
completely chaotic region the predicted He(4)-abundance has an inherent
arbitrariness \Delta Y \simeq 0.01.


  The electron beam propagation in a plasma medium is susceptible to several
instabilities. In the relativistic regime typically the weibel instability
leading to the current separation dominates. The linear instability analysis is
carried out for a system wherein the transverse extent of the beam is infinite.
Even in simulations, infinite transverse extent of the beam has been chosen. In
real situations, however, beam width will always be finite. keeping this in
view the role of finite beam width on the evolution of the beam plasma system
has been studied here using Particle - in - Cell simulations. It is observed
that the current separation between the forward and return shielding current
for a beam with finite beam occurs at the scale length of the beam width
itself. Consequently the magnetic field structures that form have maximum power
at the scale length of the beam width. This behaviour is distinct from what
happens with a beam with having an infinite extent represented by simulations
in a periodic box, where the initial scale length at which the magnetic field
appears is that of the electron skin depth.


  In vector lattices, the concept of a projection band is a basic tool. We deal
with projection bands in the more general setting of an Archimedean pre-Riesz
space $X$. We relate them to projection bands in a vector lattice cover $Y$ of
$X$. If $X$ is pervasive, then a projection band in $X$ extends to a projection
band in $Y$, whereas the restriction of a projection band $B$ in $Y$ is not a
projection band in $X$, in general. We give conditions under which the
restriction of $B$ is a projection band in $X$. We introduce atoms and discrete
elements in $X$ and show that every atom is discrete. The converse implication
is true, provided $X$ is pervasive. In this setting, we link atoms in $X$ to
atoms in $Y$. If $X$ contains an atom $a>0$, we show that the principal band
generated by $a$ is a projection band. Using atoms in a finite dimensional
Archimedean pre-Riesz space $X$, we establish that $X$ is pervasive if and only
if it is a vector lattice.


  We theoretically study spin and charge currents through finite-size
two-dimensional $s$-wave superconductor/uniform ferromagnet/s-wave
superconductor (SFS) junctions with intrinsic spin-orbit interactions (ISOIs)
using a quasiclassical approach. Considering experimentally realistic
parameters, we demonstrate that the combination of spontaneously broken
time-reversal symmetry and lack of inversion symmetry can result in
spontaneously accumulated spin currents at the edges of finite-size
two-dimensional magnetic SF hybrids. Due to the spontaneous edge spin
accumulation, the corners of the F wire host the maximum spin current density.
We further reveal that this type edge phenomena are robust and independent of
either the actual type of ISOIs or exchange field orientation. Moreover, we
study spin current-phase relations in these diffusive spin-orbit coupled SFS
junctions. Our results unveil net spin currents, not accompanied by charge
supercurrent, that spontaneously accumulate at the sample edges through a
modulating superconducting phase difference. Finally, we discuss possible
experimental implementations to observe these edge phenomena.


  In this talk, we propose a GUT scenario in which doublet-triplet splitting is
naturally realized in SO(10) unification using the Dimopoulos-Wilczek mechanism
and the realistic mass matrices of quarks and leptons are obtained in a simple
way. For the neutrino sector, bi-maximal neutrino mixing angles are realized.
Moreover, the generic interaction is allowed, namely, all the terms which are
allowed by the symmetry are included in the scenario. Therefore, once we fix
the integer number charges of the anomalous U(1)_A symmetry, which plays an
essential role in the scenario, all the scales, GUT breaking scale, mass scales
of superheavy particles, are determined. The scenario can be extended into E_6
unification, in which a condition for suppression of flavor changing neutral
current (FCNC) is automatically satisfied.


  Recently wide application in engineering-economic problems was received with
problems of vector optimization. Development of methods of the decision of
these problems it is executed in works A. Messac and others. Complexity of the
offered methods consists in construction of an aggregate objective function. In
the given work an algorithm of the solution of a vector optimization problem is
suggested carry out by use analytical representation of Pareto cone.


  Quantitative assessment of left ventricle (LV) function from cine MRI has
significant diagnostic and prognostic value for cardiovascular disease
patients. The temporal movement of LV provides essential information on the
contracting/relaxing pattern of heart, which is keenly evaluated by clinical
experts in clinical practice. Inspired by the expert way of viewing Cine MRI,
we propose a new CNN module that is able to incorporate the temporal
information into LV segmentation from cine MRI. In the proposed CNN, the
optical flow (OF) between neighboring frames is integrated and aggregated at
feature level, such that temporal coherence in cardiac motion can be taken into
account during segmentation. The proposed module is integrated into the U-net
architecture without need of additional training. Furthermore, dilated
convolution is introduced to improve the spatial accuracy of segmentation.
Trained and tested on the Cardiac Atlas database, the proposed network resulted
in a Dice index of 95% and an average perpendicular distance of 0.9 pixels for
the middle LV contour, significantly outperforming the original U-net that
processes each frame individually. Notably, the proposed method improved the
temporal coherence of LV segmentation results, especially at the LV apex and
base where the cardiac motion is difficult to follow.


  We investigate the relationship between the star formation rate (SFR) and
dense molecular gas mass in the nuclei of galaxies. To do this, we utilize the
observed 850 micron luminosity as a proxy for the infrared luminosity and SFR,
and correlate this with the observed CO (J=3-2) luminosity. We find tentative
evidence that the LIR-CO (J=3-2) index is similar to the Kennicutt-Schmidt (KS)
index (N ~ 1.5) in the central ~1.7 kpc of galaxies, and flattens to a roughly
linear index when including emission from the entire galaxy. This result may
imply that the volumetric Schmidt relation is the underlying driver behind the
observed SFR-dense gas correlations, and provides tentative confirmation for
recent numerical models. While the data exclude the possibility of a constant
LIR-CO (J=3-2) index for both galaxy nuclei and global measurements at the ~80%
confidence level, the considerable error bars cannot preclude alternative
interpretations.


  In this paper we establish a sharp non-uniqueness result for stochastic
$d$-dimensional ($d\geq2$) incompressible Navier-Stokes equations. First, for
every divergence free initial condition in $L^2$ we show existence of infinite
many global in time probabilistically strong and analytically weak solutions in
the class $L^\alpha\big(\Omega,L^p_tL^\infty\big)$ for any $1\leq
p<2,\alpha\geq1$. Second, we prove the above result is sharp in the sense that
pathwise uniqueness holds in the class of $L^p_tL^q$ for some
$p\in[2,\infty],q\in(2,\infty]$ such that $\frac2{p}+\frac{d}{q}\leq1$, which
is a stochastic version of Ladyzhenskaya-Prodi-Serrin criteria. Moreover, for
stochastic $d$-dimensional incompressible Euler equation, existence of
infinitely many global in time probabilistically strong and analytically weak
solutions is obtained. Compared to the stopping time argument used in
\cite{HZZ19, HZZ21a}, we developed a new stochastic version of the convex
integration. More precisely, we introduce expectation during convex integration
scheme and construct directly solutions on the whole time interval
$[0,\infty)$.


  Hybrid polymer-plasmonic nanostructures might combine high enhancement of
localized fields from metal nanoparticles with light confinement and long-range
transport in subwavelength dielectric structures. Here we report on the complex
behavior of fluorophores coupling to Au nanoparticles within polymer nanowires,
which features localized metal-enhanced fluorescence (MEF) with unique
characteristics compared to conventional structures. The intensification effect
when the particle is placed in the organic filaments is remarkably higher with
respect to thin films of comparable thickness, thus highlighting a specific,
nanowire-related enhancement of MEF effects. A dependence on the confinement
volume in the dielectric nanowire is also evidenced, with MEF significantly
increasing upon reducing the wire diameter. These findings are rationalized by
finite element simulations, predicting a position-dependent enhancement of the
quantum yield of fluorophores embedded in the fibers. Calculation of the
ensemble-averaged fluorescence enhancement unveils the possibility of strongly
enhancing the overall emission intensity for structures with size twice the
diameter of the embedded metal particles. These new, hybrid fluorescent systems
with localized enhanced emission, as well as the general Nanowire-Intensified
MEF effect associated to them, are highly relevant for developing nanoscale
light-emitting devices with high efficiency and inter-coupled through nanofiber
networks, highly sensitive optical sensors, and novel laser architectures.


  Recently, Extropy was introduced by Lad, Sanfilippo and Agr\`o as a
complement dual of Shannon Entropy. In this paper, we propose dynamic versions
of Extropy for doubly truncated random variables as measures of uncertainty
called Interval Extropy and Weighted Interval Extropy. Some characterizations
of random variables related to these new measures are given. Several examples
are shown. These measures are evaluated under the effect of linear
transformations and, finally, some bounds for them are presented.


  This study proposes a Network to recognize displacement of a RC frame
structure from a video by a monocular camera. The proposed Network consists of
two modules which is FlowNet2 and POFRN-Net. FlowNet2 is used to generate dense
optical flow as well as POFRN-Net is to extract pose parameter H. FlowNet2
convert two video frames into dense optical flow. POFRN-Net is inputted dense
optical flow from FlowNet2 to output the pose parameter H. The displacement of
any points of structure can be calculated from parameter H. The Fast Fourier
Transform (FFT) is applied to obtain frequency domain signal from corresponding
displacement signal. Furthermore, the comparison of the truth displacement on
the First floor of the First video is shown in this study. Finally, the
predicted displacements on four floors of RC frame structure of given three
videos are exhibited in the last of this study.


  We study additive properties of the set $S$ of bijections (or permutations)
$\{1,\dots,n\}\to G$, thought of as a subset of $G^n$, where $G$ is an
arbitrary abelian group of order $n$. Our main result is an asymptotic for the
number of solutions to $\pi_1 + \pi_2 + \pi_3 = f$ with $\pi_1,\pi_2,\pi_3\in
S$, where $f:\{1,\dots,n\}\to G$ is an arbitary function satisfying
$\sum_{i=1}^n f(i) = \sum G$. This extends recent work of Manners, Mrazovi\'c,
and the author. Using the same method we also prove a less interesting
asymptotic for solutions to $\pi_1 + \pi_2 + \pi_3 + \pi_4 = f$, and we also
show that the distribution $\pi_1+\pi_2$ is close to flat in $L^2$.
  As in the previous paper, our method is based on Fourier analysis, and we
prove our results by carefully carving up $\widehat{G}^n$ and bounding various
character sums. This is most complicated when $G$ has even order, say when $G =
\mathbf{F}_2^d$.
  At the end of the paper we explain two applications, one coming from the
Latin squares literature (counting transversals in Latin hypercubes) and one
from cryptography (PRP-to-PRF conversion).


  We discuss the reaction $\pi^- e^- \to \pi^- e^- \pi^{0}$ with the purpose of
obtaining information on the $\gamma \pi \to \pi\pi$ anomalous amplitude ${\cal
F}_{3\pi}$. We compare a full calculation at ${\cal O}(p^6)$ in chiral
perturbation theory and various phenomenological predictions with the existing
data of Amendolia {\em et al}. By integrating our theory results using Monte
Carlo techniques we obtain $\sigma= 2.05 $ nb at ${\cal O}(p^6)$ and $\sigma=
2.17 $ nb after including the dominant electromagnetic correction. Both results
are in good agreement with the experimental cross section of $\sigma= (2.11 \pm
0.47)$ nb. On the basis of the ChPT results one would extract from the the
experimental cross section as amplitudes ${\cal F}_{3\pi}^{(0)\rm extr} = (9.9
\pm 1.1)$ GeV$^{-3}$ and ${\cal F}_{3\pi}^{(0)\rm extr} = (9.6 \pm 1.1)$
GeV$^{-3}$, respectively, which have to be compared with the low-energy theorem
${\cal F}_{3\pi}=e/(4\pi^2 F_\pi^3)=9.72 {GeV}^{-3}$. We emphasize the need for
new data to allow for a comparison of experimental and theoretical
distributions and to obtain ${\cal F}_{3\pi}$ with smaller uncertainty.


  Thermal infrared (TIR) tracking is pivotal in computer vision tasks due to
its all-weather imaging capability. Traditional tracking methods predominantly
rely on hand-crafted features, and while deep learning has introduced
correlation filtering techniques, these are often constrained by rudimentary
correlation operations. Furthermore, transformer-based approaches tend to
overlook temporal and coordinate information, which is critical for TIR
tracking that lacks texture and color information. In this paper, to address
these issues, we apply natural language modeling to TIR tracking and propose a
coordinate-aware thermal infrared tracking model called NLMTrack, which
enhances the utilization of coordinate and temporal information. NLMTrack
applies an encoder that unifies feature extraction and feature fusion, which
simplifies the TIR tracking pipeline. To address the challenge of low detail
and low contrast in TIR images, on the one hand, we design a multi-level
progressive fusion module that enhances the semantic representation and
incorporates multi-scale features. On the other hand, the decoder combines the
TIR features and the coordinate sequence features using a causal transformer to
generate the target sequence step by step. Moreover, we explore an adaptive
loss aimed at elevating tracking accuracy and a simple template update strategy
to accommodate the target's appearance variations. Experiments show that
NLMTrack achieves state-of-the-art performance on multiple benchmarks. The Code
is publicly available at \url{https://github.com/ELOESZHANG/NLMTrack}.


  Two-dimensional Projected Entangled Pair States (PEPS) provide a unique
framework giving access to detailed entanglement features of correlated (spin
or electronic) systems. For a bi-partitioned quantum system, it has been argued
that the Entanglement Spectrum (ES) is in a one-to-one correspondence with the
physical edge spectrum on the cut and that the structure of the corresponding
Entanglement Hamiltonian (EH) reflects closely bulk properties (finite
correlation length, criticality, topological order, etc...). However,
entanglement properties of systems with spontaneously broken continuous
symmetry are still not fully understood. The spin-1/2 square lattice Heisenberg
antiferromagnet provides a simple example showing spontaneous breaking of SU(2)
symmetry down to U(1). The ground state can be viewed as a "quantum N\'eel
state" where the classical (N\'eel) staggered magnetization is reduced by
quantum fluctuations. Here I consider the (critical) Resonating Valence Bond
state doped with spinons to describe such a state, that enables to use the
associated PEPS representation (with virtual bond dimension $D=3$) to compute
the EH and the ES for a partition of an (infinite) cylinder. In particular, I
find that the EH is (almost exactly) a chain of a dilute mixture of heavy
($\downarrow$ spins) and light ($\uparrow$ spins) hardcore bosons, where light
particles are subject to long-range hoppings. The corresponding ES shows
drastic differences with the typical ES obtained previously for ground states
with restored SU(2)-symmetry (on finite systems).


  The origin of the extragalactic gamma-ray background (EGRB) is still an open
question, even after nearly forty years of its discovery. The emission could
originate from either truly diffuse processes or from unresolved point sources.
Although the majority of the 271 point sources detected by EGRET (Energetic
Gamma Ray Experiment Telescope) are unidentified, of the identified sources,
blazars are the dominant candidates. Therefore, unresolved blazars may be
considered the main contributor to the EGRB, and many studies have been carried
out to understand their distribution, evolution and contribution to the EGRB.
Considering that gamma-ray emission comes mostly from jets of blazars and that
the jet emission decreases rapidly with increasing jet to line-of-sight angle,
it is not surprising that EGRET was not able to detect many large inclination
angle active galactic nuclei (AGNs). Though Fermi could only detect a few large
inclination angle AGNs in the first three months' survey, it is expected to
detect many such sources in the near future. Since non-blazar AGNs are expected
to have higher density as compared to blazars, these could also contribute
significantly to the EGRB. In this paper we discuss contributions from
unresolved discrete sources including normal galaxies, starburst galaxies,
blazars and off-axis AGNs to the EGRB.


  The structure and strain of ultrathin CoO films grown on a Pt(001) substrate
and on a ferromagnetic PtFe pseudomorphic layer on Pt(001) have been determined
with insitu and real time surface x-ray diffraction. The films grow epitaxially
on both surfaces with an in-plane hexagonal pattern that yields a pseudo-cubic
CoO(111) surface. A refined x-ray diffraction analysis reveals a slight
monoclinic distortion at RT induced by the anisotropic stress at the interface.
The tetragonal contribution to the distortion results in a ratio c/a > 1,
opposite to that found in the low temperature bulk CoO phase. This distortion
leads to a stable Co2+ spin configuration within the plane of the film.


  Branch prediction is an architectural feature that speeds up the execution of
branch instruction on pipeline processors and reduces the cost of branching.
Recent advancements of Deep Learning (DL) in the post Moore's Law era is
accelerating areas of automated chip design, low-power computer architectures,
and much more. Traditional computer architecture design and algorithms could
benefit from dynamic predictors based on deep learning algorithms which learns
from experience by optimizing its parameters on large number of data. In this
survey paper, we focus on traditional branch prediction algorithms, analyzes
its limitations, and presents a literature survey of how deep learning
techniques can be applied to create dynamic branch predictors capable of
predicting conditional branch instructions. Prior surveys in this field focus
on dynamic branch prediction techniques based on neural network perceptrons. We
plan to improve the survey based on latest research in DL and advanced Machine
Learning (ML) based branch predictors.


  Recent works have revealed an essential paradigm in designing loss functions
that differentiate individual losses vs. aggregate losses. The individual loss
measures the quality of the model on a sample, while the aggregate loss
combines individual losses/scores over each training sample. Both have a common
procedure that aggregates a set of individual values to a single numerical
value. The ranking order reflects the most fundamental relation among
individual values in designing losses. In addition, decomposability, in which a
loss can be decomposed into an ensemble of individual terms, becomes a
significant property of organizing losses/scores. This survey provides a
systematic and comprehensive review of rank-based decomposable losses in
machine learning. Specifically, we provide a new taxonomy of loss functions
that follows the perspectives of aggregate loss and individual loss. We
identify the aggregator to form such losses, which are examples of set
functions. We organize the rank-based decomposable losses into eight
categories. Following these categories, we review the literature on rank-based
aggregate losses and rank-based individual losses. We describe general formulas
for these losses and connect them with existing research topics. We also
suggest future research directions spanning unexplored, remaining, and emerging
issues in rank-based decomposable losses.


  During the past decade, smart mobility and intelligent vehicles have
attracted increasing attention, because they promise to create a highly
efficient and safe transportation system in the future. Meanwhile, digital
twin, as an emerging technology, will play an important role in automated
driving and intelligent transportation systems. This technology is applied in
this paper to design a platform for smart mobility, providing large-scale route
planning services. Utilizing sensing technologies and cloud/edge computing, we
build a digital twin system model that reflects the static and dynamic objects
from the real world in real time. With the smart mobility platform, we realize
traffic monitoring and route planning through cooperative environment
perception to help automated vehicles circumvent jams. A proof-of-concept test
with a real vehicle in real traffic is conducted to validate the functions and
the delay performance of the proposed platform.


  Excited state properties play a pivotal role in various chemical and physical
phenomena, such as charge separation and light emission. However, the primary
focus of most existing quantum algorithms has been the ground state, as seen in
quantum phase estimation and the variational quantum eigensolver (VQE).
Although VQE-type methods have been extended to explore excited states, these
methods grapple with optimization challenges. In contrast, the quantum Krylov
subspace (QKS) method has been introduced to address both ground and excited
states, positioning itself as a cost-effective alternative to quantum phase
estimation. Our research presents an economic QKS algorithm, which we term the
quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative
expansion of the Krylov subspace and the incorporation of a pre-conditioner
within the Davidson framework. By using the residues of eigenstates to expand
the Krylov subspace, we manage to formulate a compact subspace that aligns
closely with the exact solutions. This iterative subspace expansion paves the
way for a more rapid convergence in comparison to other QKS techniques, such as
the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson
algorithm to delve into the excited state properties of various systems,
spanning from the Heisenberg spin model to real molecules. Compared to the
existing QKS methods, the QDavidson algorithm not only converges swiftly but
also demands a significantly shallower circuit. This efficiency establishes the
QDavidson method as a pragmatic tool for elucidating both ground and excited
state properties on quantum computing platforms.


  A physical metric is introduced as one that directly gives experimental data
without further coordinate transformation. It will be shown that the geodesic
equation for the Schwartzschild metric does not give the correct expression for
the Shapiro time delay experiment. In the physical metric the speed of light on
the surface of the earth is exactly the same as that in vacuum to first order
in gravity, and this should eliminate the inconsistency of the speed of the
neutrino exceeding that of light, if enough care is exerted in the discussion.


  Embedded Si and Ge nanocrystals (NCs) in wide band-gap matrices are studied
theoretically using an atomistic pseudopotential approach. From small clusters
to large NCs containing on the order of several thousand atoms are considered.
Effective band-gap values as a function of NC diameter reproduce very well the
available experimental and theoretical data. It is observed that the highest
occupied molecular orbital for both Si and Ge NCs and the lowest unoccupied
molecular orbital for Si NCs display oscillations with respect to size among
the different irreducible representations of the $C_{3v}$ point group to which
these spherical NCs belong. Based on this electronic structure, first the
interband absorption is thoroughly studied which shows the importance of
surface polarization effects that significantly reduce the absorption when
included. This reduction is found to increase with decreasing NC size or with
increasing permittivity mismatch between the NC core and the host matrix.
Reasonable agreement is observed with the experimental absorption spectra where
available. The deformation of spherical NCs into prolate or oblate ellipsoids
are seen to introduce no pronounced effects for the absorption spectra. Next,
intraconduction and intravalence band absorption coefficients are obtained in
the wavelength range from far-infrared to visible region. These results can be
valuable for the infrared photodetection prospects of these NC arrays. Finally,
excited-state absorption at three different optical pump wavelengths, 532 nm,
355 nm and 266 nm are studied for 3- and 4 nm-diameter NCs. This reveals strong
absorption windows in the case of holes and a broad spectrum in the case of
electrons which can especially be relevant for the discussions on achieving
gain in these structures.


  In the framework of Relativistic MOND theory (TeVeS), we show that a late
time background $\Lambda$CDM cosmology can be attained by choosing a specific
$F(\mu)$ that also meets the requirement for the existence of Newtonian and
MOND limits. We investigate the dynamics of the scalar field $\phi$ under our
chosen $F(\mu)$ and show that the "slow roll" regime of $\phi$ corresponds to a
dynamical attractor, where the whole system reduces to $\Lambda$CDM cosmology.


  We propose a new type of waveguide optical amplifier. The device consists of
collinearly propagating pump and amplified Stokes beams with periodic imaging
of the Stokes beam due to the Talbot effect. The application of this device as
an Image preamplifier for Mid Wave Infrared (MWIR) remote sensing is discussed
and its performance is described. Silicon is the preferred material for this
application in MWIR due to its excellent transmission properties, high thermal
conductivity, high damage threshold and the mature fabrication technology. In
these devices, the Raman amplification process also includes four-wave-mixing
between various spatial modes of pump and Stokes signals. This phenomenon is
unique to nonlinear interactions in multimode waveguides and places a limit on
the maximum achievable gain, beyond which the image begins to distort. Another
source of image distortion is the preferential amplification of Stokes modes
that have the highest overlap with the pump. These effects introduce a tradeoff
between the gain and image quality. We show that a possible solution to this
trade-off is to restrict the pump into a single higher order waveguide mode.


  The authors survey recent results in special functions of classical analysis
and geometric function theory, in particular the circular and hyperbolic
functions, the gamma function, the elliptic integrals, the Gaussian
hypergeometric function, power series, and mean values.


  Photon-pair generation must satisfy both the energy conservation and
phase-matching conditions with a specific pump wavelength and dispersion of
nonlinear optical medium, but finding a photon-pair, which has a desired
specific wavelength, generation medium is challenging. Here, we present a
method to create photon pairs that functions efficiently even the pump
wavelength is much larger than the zero GVD wavelength of medium. In this
study, we employ short SMF-28 fibers having ~1310 nm zero GVD wavelength and
C-band pump (1552.52 nm) to generate C-band photon pairs. The measured pair
generation rate and coincidence-to-accidental ratios are comparable to those
from a long dispersion-shifted fiber. Polarization-entangled states are
prepared, and an S value of 2.659 +- 0.094 is achieved from Bell inequality
measurements. Our results indicate that the use of a short SFWM medium yields
adequate photon-pair generation rates regardless of its dispersion properties
in almost any material at any pump wavelength.