  This article presents new methodology for sample-based Bayesian inference
when data are partitioned and communication between the parts is expensive, as
arises by necessity in the context of "big data" or by choice in order to take
advantage of computational parallelism. The method, which we call the Laplace
enriched multiple importance estimator, uses new multiple importance sampling
techniques to approximate posterior expectations using samples drawn
independently from the local posterior distributions (those conditioned on
isolated parts of the data). We construct Laplace approximations from which
additional samples can be drawn relatively quickly and improve the methods in
high-dimensional estimation. The methods are "embarrassingly parallel", make no
restriction on the sampling algorithm (including MCMC) to use or choice of
prior distribution, and do not rely on any assumptions about the posterior such
as normality. The performance of the methods is demonstrated and compared
against some alternatives in experiments with simulated data.


  We report the results of video observations of tiny (diameter less than 100
m) near-Earth objects (NEOs) with Tomo-e Gozen on the Kiso 105 cm Schmidt
telescope. A rotational period of a tiny asteroid reflects its dynamical
history and physical properties since smaller objects are sensitive to the YORP
effect. We carried out video observations of 60 tiny NEOs at 2 fps from 2018 to
2021 and successfully derived the rotational periods and axial ratios of 32
NEOs including 13 fast rotators with rotational periods less than 60 s. The
fastest rotator found during our survey is 2020 HS7 with a rotational period of
2.99 s. We statistically confirmed that there is a certain number of tiny fast
rotators in the NEO population, which have been missed with any previous
surveys. We have discovered that the distribution of the tiny NEOs in a
diameter and rotational period (D-P) diagram is truncated around a period of 10
s. The truncation with a flat-top shape is not explained well either by a
realistic tensile strength of NEOs or suppression of YORP by meteoroid impacts.
We propose that the dependence of the tangential YORP effect on the rotational
period potentially explains the observed pattern in the D-P diagram.


  The problem of velocity selection of reaction-diffusion fronts has been
widely investigated. While the mean field limit results are well known
theoretically, there is a lack of analytic progress in those cases in which
fluctuations are to be taken into account. Here, we construct an analytic
theory connecting the first principles of the reaction-diffusion process to an
effective equation of motion via field-theoretic arguments, and we arrive at
the results already confirmed by numerical simulations.


  The flooding games, which are called Flood-It, Mad Virus, or HoneyBee, are a
kind of coloring games and they have been becoming popular online. In these
games, each player colors one specified cell in his/her turn, and all connected
neighbor cells of the same color are also colored by the color. This flooding
or coloring spreads on the same color cells. It is natural to consider these
new coloring games on more general boards, or general graphs. Recently,
computational complexities of the variants of the flooding games on several
graph classes have been studied. In this paper, we investigate the flooding
games on some graph classes characterized by interval representations. Our
results state that the number of colors is a key parameter to determine the
computational complexity of the flooding games. When the number of colors is a
fixed constant, these games can be solved in polynomial time on an interval
graph. On the other hand, if the number of colors is not bounded, the flooding
game is NP-complete on a proper interval graph. We also state similar results
for split graphs.


  This paper focuses on the problem of modeling the correspondence pattern for
ordinary people. Suppose that letters arrive at a rate $\lambda$ and are
answered at a rate $\mu$. Furthermore, we assume that, for a constant $T$, a
letter is disregarded when its waiting time exceeds $T$, and the remains are
answered in {\it last in first out} order. Let $W_n$ be the waiting time of the
$n$-th {\it answered} letter. It is proved that $W_n$ converges weekly to
$W_T$, a non-negative random variable which possesses a density with {\it
power-law} tail when $\lambda=\mu$ and with exponential tail otherwise. Note
that this may provide a reasonable explanation to the phenomenons reported by
Oliveira and Barab\'asi in \cite{OB}.


  We have studied a three-unit-cell-thick YBa2Cu3O7-x (YBCO) superconducting
film grown on a slightly vicinal SrTiO3 substrate that was polished from the
(001) plane by a small miscut angle (less than 0.5 degrees). This produced, on
its surface, a linear array of single-unit-cell-height steps with a period
larger than 40 nm. A characteristic fault, with a displacement corresponding to
one-third of the c-axis length of YBCO, is generated in the film on each
substrate step, as observed by atomic force microscopy. Transport measurements
with current flows parallel and perpendicular to the fault show that the fault
serves as a superconducting weak link, as well as a unique one-dimensional
flux-pinning center in an applied magnetic field. In addition, a characteristic
fine structure is found in the flux-flow resistivity as a function of magnetic
field, the origin of which may be ascribed to a matching effect between the
periodically aligned faults and the flux lattice.


  We shall use symmetry breaking as a tool to attack the problem of identifying
the topology of chaotic scatteruing with more then two degrees of freedom.
specifically we discuss the structure of the homoclinic/heteroclinic tangle and
the connection between the chaotic invariant set, the scattering functions and
the singularities in the cross section for a class of scattering systems with
one open and two closed degrees of freedom.


  We give a simple construction of the log-convex minorant of a sequence
$\{M_\alpha\}_{\alpha\in\mathbb{N}_0^d}$ and consequently extend to the
$d$-dimensional case the well-known formula that relates a log-convex sequence
$\{M_p\}_{p\in\mathbb{N}_0}$ to its associated function $\omega_M$, that is
$M_p=\sup_{t>0}t^p\exp(-\omega_M(t))$. We show that in the more dimensional
anisotropic case the classical log-convex condition $M_\alpha^2\leq
M_{\alpha-e_j}M_{\alpha+e_j}$ is not sufficient: convexity as a function of
more variables is needed (not only coordinate-wise). We finally obtain some
applications to the inclusion of spaces of rapidly decreasing
ultradifferentiable functions in the matrix weighted setting.


  In this study different types of intuitionistic fuzzy continuities (IFCs) and
intuitionistic fuzzy boundedness (IFBs) in intuitionistic fuzzy pseudo normed
linear spaces are studied. Relations (intra and inter) on intuitionistic fuzzy
continuities and intuitionistic fuzzy boundedness are investigated.


  Out-of-equilibrium investigation of strongly correlated materials deciphers
the hidden equilibrium properties. Herein, we have investigated the
out-of-equilibrium magnetic properties of polycrystalline Dy2Ti2O7 and Ho2Ti2O7
spin ices. The experimental results show the emergence of magnetic
field-induced anomalous hysteresis observed only in temperature/magnetic
field-dependent ac susceptibility measurements. The observed memory effect
(anomalous thermomagnetic hysteresis) strongly depends on the driving thermal
and non-thermal variables. Contrary, in the absence of the magnetic field,
dipolar interaction induced Ising paramagnetic to spin ice crossover develops a
liquid-gas transition type hysteresis below 4 K. Unlike field-induced
hysteresis, it shows weak dependency on thermal and non-thermal variables. Due
to the non-colinear spin structure, the applied dc bias magnetic field produces
quench disorder sites in the cooperative Ising spin matrix and suppresses the
spin-phonon coupling. These quench disorders create dynamic spin correlations
governed by quantum fluctuations, having slow spin relaxation and quick decay
times, which additionally contribute to ac susceptibility. The initial
conditions and measurement protocol decide the magnitude and sign of this
dynamical term contributing to ac susceptibility. It has been suggested that
such kind of out-of-equilibrium properties emerge by the cumulative effect of
geometric frustration, disorder, quantum fluctuations, and the cooperative
nature of spin dynamics of these materials.


  We introduce the mean inverse integrator (MII), a novel approach to increase
the accuracy when training neural networks to approximate vector fields of
dynamical systems from noisy data. This method can be used to average multiple
trajectories obtained by numerical integrators such as Runge-Kutta methods. We
show that the class of mono-implicit Runge-Kutta methods (MIRK) has particular
advantages when used in connection with MII. When training vector field
approximations, explicit expressions for the loss functions are obtained when
inserting the training data in the MIRK formulae, unlocking symmetric and
high-order integrators that would otherwise be implicit for initial value
problems. The combined approach of applying MIRK within MII yields a
significantly lower error compared to the plain use of the numerical integrator
without averaging the trajectories. This is demonstrated with experiments using
data from several (chaotic) Hamiltonian systems. Additionally, we perform a
sensitivity analysis of the loss functions under normally distributed
perturbations, supporting the favorable performance of MII.


  We report the detection of a long-duration optical flare in the recenltly
discovered, X-ray selected, chromospherically binary 2RE J0743+224. The high
resolution echelle spectroscopic observations taken in 12-21th January 1998
exhibit a dramatic increase in the chromospheric emissions (H_alpha and CaII
IRT lines) that we interpret as a flare based on: the temporal evolution of the
event, the broad component observed in the H_alpha line profile, the detection
of the HeI D_3 in emission and a filled-in HeI 6678 A. During these obsevations
we detect a LiI 6708 A line enhancement which is clearly related with the
temporal evolution of the flare. The maximum LiI enhancement occurs just after
the maximum chromospheric emission observed in the flare. A significant
increase of the 6Li/7Li isotopic ratio is also detected. From all this we
suggest that this LiI enhancement is produced by spallation reactions during
the flare. This is the first time that such LiI enhancement associate with a
stellar flare is reported, and probably the long-duration of this flare is a
key factor for this detection. A large fraction of the stellar surface seems to
be covered by starspots during the event, as we deduce for the analysis of the
TiO 7055 A band. Thus taking into account that LiI line is very temperature
sensitive, we can not discard that the LiI variations are related the presence
of starspots. However, the correlation with the temporal evolution of the
flare, lack of detection of changes in the other photospheric absorption lines,
and the large changes observed in the core of the LiI, as predict the models,
argue in favour of the hypothesis that the LiI is produced during the flare.


  We construct toric manifolds of complex dimension $\geq 4$, whose orbit
spaces by the action of the compact torus are not homeomorphic to simple
polytopes (as manifolds with corners). These provide the first known examples
of toric manifolds which are not quasitoric manifolds.


  Self-accelerating solutions in massive gravity provide explicit, calculable
examples that exhibit the general interplay between superluminality, the
well-posedness of the Cauchy problem, and strong coupling. For three particular
classes of vacuum solutions, one of which is new to this work, we construct the
conformal diagram for the characteristic surfaces on which isotropic
stress-energy perturbations propagate. With one exception, all solutions
necessarily possess spacelike characteristics, indicating perturbative
superluminality. Foliating the spacetime with these surfaces gives a
pathological frame where kinetic terms of the perturbations vanish, confusing
the Hamiltonian counting of degrees of freedom. This frame dependence
distinguishes the vanishing of kinetic terms from strong coupling of
perturbations or an ill-posed Cauchy problem. We give examples where spacelike
characteristics do and do not originate from a point where perturbation theory
breaks down and where spacelike surfaces do or do not intersect all
characteristics in the past light cone of a given observer. The global
structure of spacetime also reveals issues that are unique to theories with two
metrics: in all three classes of solutions, the Minkowski fiducial space fails
to cover the entire de Sitter spacetime allowing worldlines of observers to end
in finite proper time at determinant singularities. Characteristics run tangent
to these surfaces requiring {\it ad hoc} rules to establish continuity across
singularities.


  We study the thermopower and some related transport quantities due to the
orbital Kondo effect in a single quantum dot system with a finite value of
Coulomb repulsion by means of the noncrossing approximation applied to the
multiorbital impurity Anderson model. It is elucidated how the asymmetry of the
renormalized tunneling resonance due to the two-orbital Kondo effect causes
characteristic behavior of the thermopower at finite temperatures under
gate-voltage and magnetic-field control, which is compared with that of the
ordinary spin Kondo effect.


  We develop the perturbative QCD formalism including Sudakov effects for
semi-leptonic $B$ meson decays. We evaluate the differential decay rate of
$B\to \pi l \nu$, and find that the perturbative calculation is reliable for
the energy fraction of the pion above 0.3. Combining predictions from the soft
pion theorems, we extract the value of the matrix element $|V_{ub}|$ which is
roughly $2.7\times 10^{-3}$.


  Ultrafast electron delocalization induced by a fs laser pulse is a well-known
process and is the initial step for important applications such as
fragmentation of molecules or laser ablation in solids. It is well understood
that an intense fs laser pulse can remove several electrons from an atom within
its pulse duration. [1] However, the speed of electron localization out of an
electron gas, the capture of an electron by ion, is unknown. Here, we
demonstrate that electronic localization out of the conduction band can occur
within only a few hundred femtoseconds. This ultrafast electron localization
into 4f states has been directly quantified by transient x-ray absorption
spectroscopy following photo-excitation of a Eu based correlated metal with a
fs laser pulse. Our x-ray experiments show that the driving force for this
process is either an ultrafast reduction of the energy of the 4f states, a
change of their bandwidth or an increase of the hybridization between the 4f
and the 3d states. The observed ultrafast electron localization process raises
further basic questions for our understanding of electron correlations and
their coupling to the lattice.


  We investigate the cascade decay mechanism for ultrafast intersystem crossing
mediated by the spin-orbit coupling in transition-metal complexes. A
quantum-mechanical description of the cascading process that occurs after
photoexcitation is presented. The conditions for ultrafast cascading are given,
which relate the energy difference between the levels in the cascading process
to the electron-phonon self energy. These limitations aid in the determination
of the cascade path. For $Fe^{2+}$ spin-crossover complexes, this leads to the
conclusion that the ultrafast decay primarily occurs in the manifold of
antibonding metal-to-ligand charge-transfer states. We also give an
interpretation why some intermediate states are bypassed.


  In material research, structural characterization often requires multiple
complementary techniques to obtain a holistic morphological view of the
synthesized material. Depending on the availability of and accessibility of the
different characterization techniques (e.g., scattering, microscopy,
spectroscopy), each research facility or academic research lab may have access
to high-throughput capability in one technique but face limitations (sample
preparation, resolution, access time) with other techniques(s). Furthermore,
one type of structural characterization data may be easier to interpret than
another (e.g., microscopy images are easier to interpret than small angle
scattering profiles). Thus, it is useful to have machine learning models that
can be trained on paired structural characterization data from multiple
techniques so that the model can generate one set of characterization data from
the other. In this paper we demonstrate one such machine learning workflow,
PairVAE, that works with data from Small Angle X-Ray Scattering (SAXS) that
presents information about bulk morphology and images from Scanning Electron
Microscopy (SEM) that presents two-dimensional local structural information of
the sample. Using paired SAXS and SEM data of novel block copolymer assembled
morphologies [open access data from Doerk G.S., et al. Science Advances. 2023
Jan 13;9(2): eadd3687], we train our PairVAE. After successful training, we
demonstrate that the PairVAE can generate SEM images of the block copolymer
morphology when it takes as input that sample's corresponding SAXS 2D pattern,
and vice versa. This method can be extended to other soft materials
morphologies as well and serves as a valuable tool for easy interpretation of
2D SAXS patterns as well as creating a database for other downstream
calculations of structure-property relationships.


  In this note, we shall overview some results related to ultraparacompactness
and ultranormality in the general topological and point-free contexts. This
note contains some standard results and counterexamples along with some results
which are not that well known and even of my new results.


  A simple relativistic treatment of Michelson-Morley type of experiments shows
the remarkable internal consistency of 1932 Miller's cosmic solution v_{earth}
\sim 208 km/s deduced from the experimental fringe shifts observed with his
apparatus. The same analysis of present-day experiments is in good agreement
with the existing data.


  The standard approach to incorporate linguistic information to neural machine
translation systems consists in maintaining separate vocabularies for each of
the annotated features to be incorporated (e.g. POS tags, dependency relation
label), embed them, and then aggregate them with each subword in the word they
belong to. This approach, however, cannot easily accommodate annotation schemes
that are not dense for every word.
  We propose a method suited for such a case, showing large improvements in
out-of-domain data, and comparable quality for the in-domain data. Experiments
are performed in morphologically-rich languages like Basque and German, for the
case of low-resource scenarios.


  We review up-to-date results on high-pt particles and jets in heavy ion
collisions by three major LHC experiments, ALICE, ATLAS, and CMS. Results of
analyses of 2010 and 2011 Pb+Pb data at $\sqrt{s_{NN}} = 2.76$ TeV are
discussed. We concentrate mainly on results by fully reconstructed jets and
discuss similarities and important differences in measurements among
experiments. We point to the importance of understanding the results in a view
of difference between quark-initiated and gluon-initiated jets


  Graphene monolayers can be used for atomically thin three-dimensional
shell-shaped superscatterer designs. Due to the excitation of the first-order
resonance of transverse magnetic (TM) graphene plasmons, the scattering cross
section of the bare subwavelength dielectric particle is enhanced significantly
by five orders of magnitude. The superscattering phenomenon can be intuitively
understood and interpreted with Bohr model. Besides, based on the analysis of
Bohr model, it is shown that contrary to the TM case, superscattering is hard
to occur by exciting the resonance of transverse electric (TE) graphene
plasmons due to their poor field confinements.


  We demonstrate that a Peierls dimerization can occur in ferromagnetic spin
chains activated by thermal fluctuations. The dimer order parameter and
entanglement measures are studied as functions of the modulation of the
magnetic exchange interaction and temperature, using a spin-wave theory and the
density-matrix renormalization group. We discuss the case where a periodic
modulation is caused by spin-phonon coupling and the case where electronic
states effectively induce such a modulation. The importance of the latter for a
number of transition metal oxides is highlighted.


  We describe how to calculate standard errors for A/B tests that include
clustered data, ratio metrics, and/or covariate adjustment. We may do this for
power analysis/sample size calculations prior to running an experiment using
historical data, or after an experiment for hypothesis testing and confidence
intervals. The different applications have a common framework, using the sample
variance of certain residuals. The framework is compatible with modular
software, can be plugged into standard tools, doesn't require computing
covariance matrices, and is numerically stable. Using this approach we estimate
that covariate adjustment gives a median 66% variance reduction for a key
metric, reducing experiment run time by 66%.


  This work explores Lyapunov characterizations of the input-output-to-state
stability (IOSS) property for nonlinear systems. The notion of IOSS is a
natural generalization of the standard zero-detectability property used in the
linear case. The main contribution of this work is to establish a complete
equivalence between the input-output-to-state stability property and the
existence of a certain type of smooth Lyapunov function. As corollaries, one
shows the existence of ``norm-estimators'', and obtains characterizations of
nonlinear detectability in terms of relative stability and of finite-energy
estimates.


  The computation of (i) $\varepsilon$-kernels, (ii) approximate diameter, and
(iii) approximate bichromatic closest pair are fundamental problems in
geometric approximation. In this paper, we describe new algorithms that offer
significant improvements to their running times. In each case the input is a
set of $n$ points in $R^d$ for a constant dimension $d \geq 3$ and an
approximation parameter $\varepsilon > 0$. We reduce the respective running
times (i) from $O((n + 1/\varepsilon^{d-2})\log(1/\varepsilon))$ to $O(n
\log(1/\varepsilon) + 1/\varepsilon^{(d-1)/2+\alpha})$, (ii) from $O((n +
1/\varepsilon^{d-2})\log(1/\varepsilon))$ to $O(n \log(1/\varepsilon) +
1/\varepsilon^{(d-1)/2+\alpha})$, and (iii) from $O(n / \varepsilon^{d/3})$ to
$O(n / \varepsilon^{d/4+\alpha}),$ for an arbitrarily small constant $\alpha >
0$. Result (i) is nearly optimal since the size of the output
$\varepsilon$-kernel is $\Theta(1/\varepsilon^{(d-1)/2})$ in the worst case.
  These results are all based on an efficient decomposition of a convex body
using a hierarchy of Macbeath regions, and contrast to previous solutions that
decompose space using quadtrees and grids. By further application of these
techniques, we also show that it is possible to obtain near-optimal
preprocessing time for the most efficient data structures to approximately
answer queries for (iv) nearest-neighbor searching, (v) directional width, and
(vi) polytope membership.


  Applying heavy-baryon chiral perturbation theory to ordinary muon capture
(OMC) on a proton, we calculate the capture rate and neutron helicity asymmetry
up to next-to-next-to-leading order. For the singlet hyperfine state, we obtain
the capture rate Gamma_0 = 695 sec^{-1} while, for the triplet hyperfine state,
we obtain the capture rate Gamma_1 = 11.9 sec^{-1} and the neutron asymmetry
alpha_1 = 0.93. If the existing formalism is used to relate these atomic
capture rates to Gamma_{liq}, the OMC rate in liquid hydrogen, then Gamma_{liq}
corresponding to our improved values of Gamma_0 and Gamma_1 is found to be
significantly larger than the experimental value, primarily due to the updated
larger value of g_A. We argue that this apparent difficulity may be correlated
to the specious anomaly recently reported for mu^- + p to n + nu_mu + gamma,
and we suggest a possibility to remove these two "problems" simply and
simultaneously by reexamining the molecular physics input that underlies the
conventional analysis of Gamma_{liq}.


  Infrastructure as code (IaC) scripts are used to automate the maintenance and
configuration of software development and deployment infrastructure. IaC
scripts can be complex in nature, containing hundreds of lines of code, leading
to defects that can be difficult to debug, and lead to wide-scale system
discrepancies such as service outages at scale. Use of IaC scripts is getting
increasingly popular, yet the nature of defects that occur in these scripts
have not been systematically categorized. A systematic categorization of
defects can inform practitioners about process improvement opportunities to
mitigate defects in IaC scripts. The goal of this paper is to help software
practitioners improve their development process of infrastructure as code (IaC)
scripts by categorizing the defect categories in IaC scripts based upon a
qualitative analysis of commit messages and issue report descriptions. We mine
open source version control systems collected from four organizations namely,
Mirantis, Mozilla, Openstack, and Wikimedia Commons to conduct our research
study. We use 1021, 3074, 7808, and 972 commits that map to 165, 580, 1383, and
296 IaC scripts, respectively, collected from Mirantis, Mozilla, Openstack, and
Wikimedia Commons. With 89 raters we apply the defect type attribute of the
orthogonal defect classification (ODC) methodology to categorize the defects.
We also review prior literature that have used ODC to categorize defects, and
compare the defect category distribution of IaC scripts with 26 non-IaC
software systems. Respectively, for Mirantis, Mozilla, Openstack, and Wikimedia
Commons, we observe (i) 49.3%, 36.5%, 57.6%, and 62.7% of the IaC defects to
contain syntax and configuration-related defects; (ii) syntax and
configuration-related defects are more prevalent amongst IaC scripts compared
to that of previously-studied non-IaC software.


  Here we present an analysis of the paper "Universelle Bedeutung des
Wirkungsquantums" (The universal meaning of the quantum of action), published
by Jun Ishiwara in German in the "Proceedings of Tokyo Mathematico-Physical
Society 8 (1915) 106-116". In his work, Ishiwara, established in the Sendai
University, Japan, proposed - simultaneously with Arnold Sommerfeld, William
Wilson and Niels Bohr in Europe - the phase-space-integral quantization, a rule
that would be incorporated into the old-quantum-theory formalism. The
discussions and analysis render this paper fully accessible to undergraduate
students of physics with elementary knowledge of quantum mechanics.


  With the advent of modern AI architectures, a shift has happened towards
end-to-end architectures. This pivot has led to neural architectures being
trained without domain-specific biases/knowledge, optimized according to the
task. We in this paper, learn audio embeddings via diverse feature
representations, in this case, domain-specific. For the case of audio
classification over hundreds of categories of sound, we learn robust separate
embeddings for diverse audio properties such as pitch, timbre, and neural
representation, along with also learning it via an end-to-end architecture. We
observe handcrafted embeddings, e.g., pitch and timbre-based, although on their
own, are not able to beat a fully end-to-end representation, yet adding these
together with end-to-end embedding helps us, significantly improve performance.
This work would pave the way to bring some domain expertise with end-to-end
models to learn robust, diverse representations, surpassing the performance of
just training end-to-end models.


  In this paper we prove that geodesic mappings of (pseudo-) Riemannian
manifolds preserve the class of differentiability \hbox{$(C^r, r\geq1)$}. Also,
if the Einstein space $V_n$ admits a non trivial geodesic mapping onto a
\hbox{(pseudo-)} Riemannian manifold $\bar V_n\in C^1$, then $\bar V_n$ is an
Einstein space.
  If a four-dimensional Einstein space with non constant curvature globally
admits a geodesic mapping onto a (pseudo-) Riemannian manifold $\bar V_4\in
C^1$, then the mapping is affine and, moreover, if the scalar curvature is non
vanishing, then the mapping is homothetic, i.e. $\bar g={\rm const}\cdot g$.


  In this paper we show how to attain the capacity of discrete symmetric
channels with polynomial time decoding complexity by considering iterated
$(U|U+V)$ constructions with Reed-Solomon code or algebraic geometry code
components. These codes are decoded with a recursive computation of the {\em a
posteriori} probabilities of the code symbols together with the Koetter-Vardy
soft decoder used for decoding the code components in polynomial time. We show
that when the number of levels of the iterated $(U|U+V)$ construction tends to
infinity, we attain the capacity of any discrete symmetric channel in this way.
This result follows from the polarization theorem together with a simple lemma
explaining how the Koetter-Vardy decoder behaves for Reed-Solomon codes of rate
close to $1$. However, even if this way of attaining the capacity of a
symmetric channel is essentially the Ar{\i}kan polarization theorem, there are
some differences with standard polar codes.
  Indeed, with this strategy we can operate succesfully close to channel
capacity even with a small number of levels of the iterated $(U|U+V)$
construction and the probability of error decays quasi-exponentially with the
codelength in such a case (i.e. exponentially if we forget about the
logarithmic terms in the exponent). We can even improve on this result by
considering the algebraic geometry codes constructed in \cite{TVZ82}. In such a
case, the probability of error decays exponentially in the codelength for any
rate below the capacity of the channel. Moreover, when comparing this strategy
to Reed-Solomon codes (or more generally algebraic geometry codes) decoded with
the Koetter-Vardy decoding algorithm, it does not only improve the noise level
that the code can tolerate, it also results in a significant complexity gain.


  This paper presents a rank rigidity result for negatively curved spaces. Let
$M$ be a compact manifold with negative sectional curvature and suppose that
along every geodesic in $M$ there is a parallel vector field making curvature
$-a^2$ with the geodesic direction. We prove that $M$ has constant curvature
equal to $-a^2$ if $M$ is odd dimensional, or if $M$ is even dimensional and
has sectional curvature pinched as follows: $-\Lambda^2 < K < -\lambda^2$ where
$\lambda/\Lambda > .93$. When $a$ is extremal, i.e. $-a^2$ is the curvature
minimum or maximum for the manifold, this result is analogous to rank rigidity
results in various other curvature settings where higher rank implies that the
space is locally symmetric. In particular, this result is the first positive
result for lower rank (i.e. when $-a^2$ is minimal), and in the upper rank case
gives a shorter proof of the hyperbolic rank rigidity theorem of
Hamenst\"{a}dt, subject to the pinching condition in even dimension. We also
present a rigidity result using only an assumption on maximal Lyapunov
exponents in direct analogy with work done by Connell. Our proof of the main
theorem uses the ergodic theory of the frame flow developed by Brin and others
- in particular the transitivity group associated to this flow.


  Due to the difficulty in generating the effective descriptors which are
robust to occlusion and viewpoint changes, place recognition for 3D point cloud
remains an open issue. Unlike most of the existing methods that focus on
extracting local, global, and statistical features of raw point clouds, our
method aims at the semantic level that can be superior in terms of robustness
to environmental changes. Inspired by the perspective of humans, who recognize
scenes through identifying semantic objects and capturing their relations, this
paper presents a novel semantic graph based approach for place recognition.
First, we propose a novel semantic graph representation for the point cloud
scenes by reserving the semantic and topological information of the raw point
cloud. Thus, place recognition is modeled as a graph matching problem. Then we
design a fast and effective graph similarity network to compute the similarity.
Exhaustive evaluations on the KITTI dataset show that our approach is robust to
the occlusion as well as viewpoint changes and outperforms the state-of-the-art
methods with a large margin. Our code is available at:
\url{https://github.com/kxhit/SG_PR}.


  It is shown that the molecular model for the X{3872) state contradicts the
new experimental data as well as the old ones. It is suggested to study the
\chi_{c1} and \chi_{b1} states in the e+e-\to\chi_{c1}/\chi_{b1} reactions.


  Near-field radiative heat transfer (NFRHT) between dissimilar materials
supporting surface polaritons in the infrared is of critical importance for
applications such as photonic thermal rectification and near-field
thermophotovoltaics. Here, we measure NFRHT between millimetersize surfaces
made of 6H-SiC and doped Si, respectively supporting surface phonon-polaritons
(SPhPs) and surface plasmon-polaritons (SPPs) in the infrared, separated by a
150-nm-thick vacuum gap spacing maintained via SiO2 nanopillars. For purpose of
comparison, measurements are also performed between two doped Si surfaces. The
measured radiative flux is in good agreement with theoretical predictions based
on fluctuational electrodynamics. A flux enhancement beyond the blackbody limit
of ~ 8.2 is obtained for the SiC-Si sample, which is smaller than the
enhancement for the Si-Si sample (~ 12.5) owing to the spectral mismatch of the
SiC and Si light lines, and SPhP and SPP resonances. However, due to lower
losses in SiC than Si and weaker SPhP-SPP coupling than SPP coupling, the
near-field enhancement for the SiC-Si sample exhibits a more pronounced
monochromatic behavior with a resonant flux that is ~ 5 times larger than the
resonant flux for the Si-Si sample. This work demonstrates that it is possible
to modulate NFRHT via surface polariton coupling, and will accelerate the
development of energy conversion and thermal management devices capitalizing on
the near-field effects of thermal radiation between dissimilar materials.


  In the era of Web of Things and Services, Context-aware Web Services (CASs)
are emerging as an important technology for building innovative context-aware
applications. CASs enable the information integration from both the physical
and virtual world, which affects human living. However, it is challenging to
build CASs, due to the lack of context provisioning management approach and
limited generic approach for formalizing the development process. We therefore
propose ContextServ, a platform that uses a model-driven approach to support
the full life cycle of CASs development, hence offering significant design and
management flexibility. ContextServ implements a proposed UML-based modelling
language ContextUML to support multiple modelling languages. It also supports
dynamic adaptation of WS-BPEL based context-aware composite services by weaving
context-aware rules into the process. Extensive experimental evaluations on
ContextServ and its components showcase that ContextServ can support effective
development and efficient execution of context-aware Web services.


  We analyze the model of a self-interacting $\phi^4_{\star}$ scalar field
theory in Snyder-de Sitter space. After analytically computing the one-loop
beta functions {in the small noncommutativity and curvature limit}, we solve
numerically the corresponding system of differential equations, showing that in
this limit the model possesses at least one regime in which the theory is
asymptotically free. Moreover, in a given region of the parameter space we also
observe a peculiar running of the parameter associated to the curvature, which
changes its sign and therefore can be interpreted as a transition from an IR
de-Sitter space to and UV anti-de Sitter one.


  Quasi error-free 10 Gbit/s data transmission is demonstrated over a novel
type of 50 micron core diameter photonic crystal fiber with as much as 100 m
length. Combined with 850$ nm VCSEL sources, this fiber is an attractive
alternative to graded-index multi-mode fibers for datacom applications. A
comparison to numerical simulations suggests that the high bit-rate may be
partly explained by inter-modal diffusion.


  We analyze the problem of learning a single user's preferences in an active
learning setting, sequentially and adaptively querying the user over a finite
time horizon. Learning is conducted via choice-based queries, where the user
selects her preferred option among a small subset of offered alternatives.
These queries have been shown to be a robust and efficient way to learn an
individual's preferences. We take a parametric approach and model the user's
preferences through a linear classifier, using a Bayesian prior to encode our
current knowledge of this classifier. The rate at which we learn depends on the
alternatives offered at every time epoch. Under certain noise assumptions, we
show that the Bayes-optimal policy for maximally reducing entropy of the
posterior distribution of this linear classifier is a greedy policy, and that
this policy achieves a linear lower bound when alternatives can be constructed
from the continuum. Further, we analyze a different metric called
misclassification error, proving that the performance of the optimal policy
that minimizes misclassification error is bounded below by a linear function of
differential entropy. Lastly, we numerically compare the greedy entropy
reduction policy with a knowledge gradient policy under a number of scenarios,
examining their performance under both differential entropy and
misclassification error.


  In the medical domain, the continuous stream of scientific research contains
contradictory results supported by arguments and counter-arguments. As medical
expertise occurs at different levels, part of the human agents have
difficulties to face the huge amount of studies, but also to understand the
reasons and pieces of evidences claimed by the proponents and the opponents of
the debated topic. To better understand the supporting arguments for new
findings related to current state of the art in the medical domain we need
tools able to identify arguments in scientific papers. Our work here aims to
fill the above technological gap.
  Quite aware of the difficulty of this task, we embark to this road by relying
on the well-known interleaving of domain knowledge with natural language
processing. To formalise the existing medical knowledge, we rely on ontologies.
To structure the argumentation model we use also the expressivity and reasoning
capabilities of Description Logics. To perform argumentation mining we
formalise various linguistic patterns in a rule-based language. We tested our
solution against a corpus of scientific papers related to breast cancer. The
run experiments show a F-measure between 0.71 and 0.86 for identifying
conclusions of an argument and between 0.65 and 0.86 for identifying premises
of an argument.


  A key feature of inductive logic programming (ILP) is its ability to learn
first-order programs, which are intrinsically more expressive than
propositional programs. In this paper, we introduce techniques to learn
higher-order programs. Specifically, we extend meta-interpretive learning (MIL)
to support learning higher-order programs by allowing for \emph{higher-order
definitions} to be used as background knowledge. Our theoretical results show
that learning higher-order programs, rather than first-order programs, can
reduce the textual complexity required to express programs which in turn
reduces the size of the hypothesis space and sample complexity. We implement
our idea in two new MIL systems: the Prolog system \namea{} and the ASP system
\nameb{}. Both systems support learning higher-order programs and higher-order
predicate invention, such as inventing functions for \tw{map/3} and conditions
for \tw{filter/3}. We conduct experiments on four domains (robot strategies,
chess playing, list transformations, and string decryption) that compare
learning first-order and higher-order programs. Our experimental results
support our theoretical claims and show that, compared to learning first-order
programs, learning higher-order programs can significantly improve predictive
accuracies and reduce learning times.


  In federated learning (FL), multiple clients collaborate to train machine
learning models together while keeping their data decentralized. Through
utilizing more training data, FL suffers from the potential negative transfer
problem: the global FL model may even perform worse than the models trained
with local data only. In this paper, we propose FedCollab, a novel FL framework
that alleviates negative transfer by clustering clients into non-overlapping
coalitions based on their distribution distances and data quantities. As a
result, each client only collaborates with the clients having similar data
distributions, and tends to collaborate with more clients when it has less
data. We evaluate our framework with a variety of datasets, models, and types
of non-IIDness. Our results demonstrate that FedCollab effectively mitigates
negative transfer across a wide range of FL algorithms and consistently
outperforms other clustered FL algorithms.


  The discussion on causality in human history dates back to ancient Greece,
yet to this day, there is still no consensus. Fundamentally, this stems from
the nature of human cognition, as understanding causality requires abstract
tools to transcend the limitations of human cognition. In recent decades, the
rapid development of mathematical and computational tools has provided new
theoretical and technical means for exploring causality, creating more avenues
for investigation.
  Based on this, this paper introduces a new definition of causality using
category theory, proposed by Samuel Eilenberg and Saunders Mac Lane in 1945 to
avoid the self-referential contradictions in set theory, notably the Russell
paradox. Within this framework, the feasibility of indicator synthesis in
causal inference is demonstrated. Due to the limitations in the development of
category theory-related technical tools, this paper adopts the widely-used
probabilistic causal graph tool proposed by Judea Pearl in 1995 to study the
application of causal inference in personal credit risk management. The
specific work includes: research on the construction method of causal inference
index system, definition of causality and feasibility proof of indicator
synthesis causal inference within this framework, application methods of causal
graph model and intervention alternative criteria in personal credit risk
management, and so on.


  Using the symmetry properties of the three-anyon spectrum, we obtain exactly
the multiplicities of states with given energy and angular momentum. The
results are shown to be in agreement with the proper quantum mechanical and
semiclassical considerations, and the unexplained points are indicated.


  We investigate ground-state properties of a $t_{\rm 2g}$-orbital Hubbard
model on a zigzag chain relevant for CaV$_{2}$O$_{4}$, by exploiting numerical
techniques such as Lanczos diagonalization and density-matrix renormalization
group. Assuming a V$^{3+}$ ion, a local spin $S$=$1$ state is formed by two
electrons in the $t_{\rm 2g}$ orbitals. That is, the system is a Haldane system
with active $t_{\rm 2g}$-orbital degrees of freedom. We observe orbital-state
transitions, yielding a distinct spin system under the orbital-ordered
background. We also discuss the orbital structure induced by open edges,
originating in the spatial anisotropy of the $t_{\rm 2g}$ orbitals.


  With the aid of utilising tensor products, we give a simplified proof to the
fundamental theorem of Benedetto and Fickus about the existence and
characterisation of finite, normalised tight frames. We also establish
unit-norm tensor resolutions for symmetric, positive semi-definite matrices.


  Topological materials are derived from the interplay between symmetry and
topology. Advances in topological band theories have led to the prediction that
the antiperovskite oxide Sr$_3$SnO is a topological crystalline insulator, a
new electronic phase of matter where the conductivity in its (001)
crystallographic planes is protected by crystallographic point group
symmetries. Realization of this material, however, is challenging. Guided by
thermodynamic calculations we design and implement a deposition approach to
achieve the adsorption-controlled growth of epitaxial Sr$_3$SnO single-crystal
films by molecular-beam epitaxy (MBE). In-situ transport and angle-resolved
photoemission spectroscopy measurements reveal the metallic and non-trivial
topological nature of the as-grown samples. Compared with conventional MBE, the
synthesis route used results in superior sample quality and is readily adapted
to other topological systems with antiperovskite structures. The successful
realization of thin films of topological crystalline insulators opens
opportunities to manipulate topological states by tuning symmetries via
epitaxial strain and heterostructuring.


  This is an English (annotated) translation of the German paper by Max Planck
(1943) about "The history of the discovery of the physical quantum of action"


  We develop a numerical solver for the integral-differential equations, which
describes the radiative transfer of photon distribution in the frequency space
with resonant scattering of Lyalpha photons by hydrogen gas in the early
universe. The time-dependent solutions of this equation is crucial to the
estimation of the effect of the Wouthuysen-Field (WF) coupling in relation to
the 21 cm emission and absorption at the epoch of reionization. The resonant
scattering leads to the photon distribution in the frequency space to be
piecewise smooth containing sharp changes. The weighted essentially
nonoscillatory (WENO) scheme is suitable to handle this problem, as this
algorithm has been found to be highly stable and robust for solving Boltzmann
equation. We test this numerical solver against analytic solutions of the
evolution of the photon distribution in rest background, analytic solution in
expanding background without resonant scattering and formation of local
Boltzmann distribution around the resonant frequency with the temperature same
as that of atom for recoil. We find that evolution of photon distribution
undergoes three phases; profile is similar to the initial one, a flat plateau
(without recoil) or local Boltzmann distribution (with recoil) forms around the
resonant frequency, and finally the distribution around the resonant frequency
is saturated when the photons from the source is balanced by the redshift of
the expansion. This result indicates that the onset of the W-F coupling should
not be determined by the third phase, but by the time scale of the second
phase. We found that the time scale of the W-F coupling is equal to about a few
hundreds of the mean free flight time of photons with resonant frequency, and
is independent of the Sobolev parameter if this parameter is much less than 1.


  Dissociation of quarkonium in quark-gluon plasma (QGP) is a long standing
topic in relativistic heavy-ion collisions because it has been believed to
signal one of the fundamental natures of the QGP -- Debye screening due to the
liberation of color degrees of freedom. Among recent new theoretical
developments is the application of open quantum system framework to quarkonium
in the QGP. Open system approach enables us to describe how dynamical as well
as static properties of QGP influences the time evolution of quarkonium in a
coherent way.
  Currently, there are several master equations for quarkonium corresponding to
various scale assumptions, each derived in different theoretical frameworks. In
this review, all of the existing master equations are systematically rederived
as Lindblad equations in a unified framework. Also, as one of the most relevant
descriptions in relativistic heavy-ion collisions, quantum Brownian motion of
heavy quark pair in the QGP is studied in detail. The quantum Brownian motion
is parametrized by a few fundamental quantities of QGP such as real and
imaginary parts of heavy quark potential (complex potential), heavy quark
momentum diffusion constant, and thermal dipole self-energy constant, which
constitute in-medium self-energy of a static quarkonium. This indicates that
the yields of quarkonia such as $J/\psi$ and $\Upsilon$ in the relativistic
heavy-ion collisions have the potential to determine these fundamental
quantities.


  The near-threshold photo-productions of heavy quarkonia are important ways to
test the QCD-inspired models and to constrain the gluon distribution of nucleon
in the large x region. Investigating the various models, we choose a
photon-gluon fusion model and a pomeron exchange model for J/$\Psi$
photo-production near threshold, emphasising on the explanation of the recent
experimental measurement by GlueX at JLab. We find that these two models are
not only valid in a wide range of the center-of-mass energy of $\gamma$ and
proton, but also can be generalized to describe the $\Upsilon$(1S)
photo-production. Using these two models, we predict the electro-production
cross-sections of $\Upsilon$(1S) at EicC to be 48 fb to 85 fb at the
center-of-mass energy of 16.75 GeV.


  The goal of this paper is to establish a global well-posedness for a broad
class of strictly hyperbolic Cauchy problems with coefficients in
$C^2((0,T];C^\infty(\mathbb{R}^n))$ growing polynomially in $x$ and singular in
$t$. The problems we study are of strictly hyperbolic type with respect to a
generic weight and a metric on the phase space. The singular behavior is
captured by the blow-up of the first and second $t$-derivatives of the
coefficients which allows the coefficients to be either logarithmic-type or
oscillatory-type near $t=0$. To arrive at an energy estimate, we perform a
conjugation by a pseudodifferential operator of the form
$e^{\nu(t)\Theta(x,D_x)},$ where $\Theta(x,D_x)$ explains the quantity of the
loss by linking it to the metric on the phase space and the singular behavior
while $\nu(t)$ gives a scale for the loss. We call the conjugating operator as
{\itshape{loss operator}} and depending on its order we report that the
solution experiences zero, arbitrarily small, finite or infinite loss in
relation to the initial datum. We also provide a counterexample and derive the
anisotropic cone conditions in our setting.


  In this paper we use the notion of stability for free boundary surfaces with
constant higher order mean curvature to obtain rigidity results for
$H_2$-surfaces with free boundary of a geodesic ball of a simply connected
$3$-dimensional space form or a slab of $\mathbb{R}^3$.


  We study formation and evolution of solitons within a model with two real
scalar fields with the potential having a saddle point. The set of these
configurations can be split into disjoint equivalence classes. We give a simple
expression for the winding number of an arbitrary closed loop in the field
space and discuss the evolution scenarios that change the winding number. These
non-trivial field configurations lead to formation of the domain walls in the
three-dimensional physical space.


  We report the Meissner effect studies on an FeSe thin film grown on Nb doped
SrTiO3 substrate by molecular beam epitaxy. Two-coil mutual inductance
measurement clearly demonstrates the onset of diamagnetic screening at 65 K,
which is consistent with the gap opening temperature determined by previous
angle resolved photoemission spectroscopy results. The applied magnetic field
causes a broadening of the superconducting transition near the onset
temperature, which is the typical behavior for quasi-two-dimensional
superconductors. Our results provide direct evidence that FeSe thin film grown
on Nb doped SrTiO3 substrate has an onset TC ~ 65 K, which is the highest among
all iron based superconductors discovered so far.


  Dynamic homogenization aims at describing the macroscopic characteristics of
wave propagation in microstructured systems. Using a simple method, we derive
frequency-dependent homogenized parameters that reproduce the exact dispersion
relations of infinitely periodic flexural systems. Our scheme evades the need
to calculate field variables at each point, yet capable of recovering them, if
wanted. Through reflected energy analysis in scattering problems, we quantify
the applicability of the homogenized approximation. We show that at low
frequencies, our model replicates the transmission characteristics of
semi-infinite and finite periodic media. We quantify the decline in the
approximation as frequency increases, having certain characteristics sensitive
to microscale details. We observe that the homogenized model captures the
dynamic response of locally resonant media more accurately and across a wider
range of frequencies than the dynamic response of media without local
resonance.


  Slave-particle method is a powerful tool to tackle the correlation effect in
quantum many-body physics. Although it has been successfully used to comprehend
various intriguing problems, such as Mott metal-insulator transition and Kondo
effect, there is still no convincing theory so far on the availability and
limitation of this method. The abuse of slave-particle method may lead to wrong
physics. As the simplest slave-particle method, $\mathbb{Z}_2$ slave spin,
which is widely applied to many strongly correlated problems, is highly
accessible and researchable. In this work, we will uncover the nature of
$\mathbb{Z}_2$ slave-spin method by studying a two-site Hubbard model. After
exploring some properties of this toy model, we make a comparative analysis of
the results obtained by three methods: (i) slave-spin method on mean-field
level, (ii) slave-spin method with gauge constraint and (iii) the exact
solution as a benchmark. We find that, protected by particle-hole symmetry, the
slave-spin mean-field method can recover the static properties of ground state
exactly at half filling. Furthermore, in the parameter space where both $U$ and
$T$ are small enough, slave-spin mean-field method is also reliable in
calculating dynamic and thermal dynamic properties. However, when $U$ or $T$ is
considerably large, the mean-field approximation gives ill-defined behavior,
which results from the unphysical states in enlarged Hilbert space. These
findings lead to our conclusion that the accuracy of slave particle can be
guaranteed if we can exclude all unphysical states by enforcing gauge
constraints.Our work demonstrates the promising prospect of slave-particle
method in studying complex strongly correlated models with specific symmetry or
in certain parameter space.


  The near-side ridge observed in A+A collisions at RHIC has been described as
arising from the radial flow of Glasma flux tubes formed at very early times in
the collisions. We investigate the viability of this scenario by performing a
non-perturbative numerical computation of double inclusive gluon production in
the Glasma. Our results support the conjecture that the range of transverse
color screening of correlations determining the size of the flux tubes is a
semi-hard scale, albeit with non-trivial structure. We discuss our results in
the context of ridge correlations in the RHIC heavy ion experiments.


  In the burgeoning field of artificial intelligence (AI), understanding the
capabilities and limitations of programming-oriented models is crucial. This
paper presents a novel evaluation of the programming proficiency of Generative
Pretrained Transformer (GPT) models, specifically GPT-3.5 and GPT-4, against
coding problems of varying difficulty levels drawn from Codewars. The
experiments reveal a distinct boundary at the 3kyu level, beyond which these
GPT models struggle to provide solutions. These findings led to the proposal of
a measure for coding problem complexity that incorporates both problem
difficulty and the time required for solution. The research emphasizes the need
for validation and creative thinking capabilities in AI models to better
emulate human problem-solving techniques. Future work aims to refine this
proposed complexity measure, enhance AI models with these suggested
capabilities, and develop an objective measure for programming problem
difficulty. The results of this research offer invaluable insights for
improving AI programming capabilities and advancing the frontier of AI
problem-solving abilities.


  The Multi-adaptive optics Imaging CamerA for Deep Observations (MICADO) will
image a field of view of nearly 1 arcminute at the diffraction limit of the
Extremely Large Telescope (ELT), making use of the adaptive optics correction
provided by single-conjugate adaptive optics (SCAO) and multi-conjugate
adaptive optics (MCAO). Its simple and robust design will yield an
unprecedented combination of sensitivity and resolution across the field. This
article outlines the characteristics of the observing modes offered and
illustrates each of them with an astrophysical application. Potential users can
explore their own ideas using the data simulator ScopeSim.


  The ITER Ion Cyclotron Resonance Heating (ICRH) system is designed to couple
to the plasma 20 MW of RF power from two antennas in the 40-55 MHz frequency
range during long pulses of up to 3600 s and under various plasma conditions
with Edge Localized Modes. Radio-Frequency (RF) contacts are integrated within
the ITER ICRH launcher in order to ensure the RF current continuity and ease
the mechanical assembly by allowing the free thermal expansion of the Removable
Vacuum Transmission Line coaxial conductors during RF operations or during
250{\textdegree}C baking phases. A material study has been carried out to
determine which materials and associated coatings are relevant for RF contacts
application in ITER. In parallel, RF tests have been performed with a new
prototype of Multi-Contact (r) LA-CUT/0,25/0 contacts made of silver-coated
CuCrZr louvers. During these tests on a RF vacuum resonator, currents between
1.2 kA and 1.3 kA peak have been reached a few tens of times in steady-state
conditions without any visible damage on the louvers. A final 62MHz pulse
ending in a 300s flat top at 1.9kA resulted in severe damage to the contact. In
addition, a test bed which performs sliding test cycles has been built in order
to reproduce the wear of the contact prototype after 30 000 sliding cycles on a
3 mm stroke at 175{\textdegree}C under vacuum. The silver coating of the
louvers is removed after approximately a hundred cycles whilst, to the
contrary, damage to the CuCrZr louvers is relatively low.


  In condensed-matter systems, electrons are subjected to two different
interactions under certain conditions. Even if both interactions are weak, it
is difficult to perform perturbative calculations due to the complexity caused
by the interplay of two interactions. When one or two interactions are strong,
ordinary perturbation theory may become invalid. Here we consider undoped
graphene as an example and provide a non-perturbative quantum-field-theoretic
analysis of the interplay of electron-phonon interaction and Coulomb
interaction. We treat these two interactions on an equal footing and derive the
exact Dyson-Schwinger integral equation of the full Dirac-fermion propagator.
This equation depends on several complicated correlation functions and thus is
difficult to handle. Fortunately, we find that these correlation functions obey
a number of exact identities, which allows us to prove that the Dyson-Schwinger
equation of the full fermion propagator is self-closed. After solving this
self-closed equation, we obtain the renormalized velocity of Dirac fermions and
show that its energy (momentum) dependence is dominantly determined by the
electron-phonon (Coulomb) interaction. In particular, the renormalized velocity
exhibits a logarithmic momentum dependence and a non-monotonic energy
dependence.


  The description of number of dual (quasy)-exactly solvable models with its
hidden symmetry algebra has been given at different levels of analysis within
the framework of generalized Kustaanheimo-Stiefel (KS)-transformations. It's
shown that N-dimensionall singular oscillator and (n+1)-dimensional generalized
MICZ-Kepler system are dual to each other and the duality transformation is the
generalized version of the KS transformation. The solvability of the
Schrodinger equation of these problems by the variables separation method is
given in a double, spherical and parabolic coordinates. The quadratic Hahn
algebra QH(3) as a hidden symmetry remains unchanged with different
decomposition of the original real space ${\rm I \!R}^{N}$ into components in
the framework of addition rule for SU(1,1) algebra. Also the hidden symmetry
algebra as Higgs/Hahn algebras is clearly shown by the commutant approach in
the sense of Howe duality. A dimensional reduction is carried out to a singular
oscillator of two dimensions where every variable is the n-dimensional
hyper-radius r. The dual connection with (N=2n)-dimensional singular oscillator
and the (n+1) general MICZ-Kepler system in the class of quasi-exact (QE)
problems also are considered. The certain generalization both of harmonic
oscillator model by anisotropic and nonlinear inharmonic terms and its dual
analog is shown and analyzed in the framework of generalized KS
transformations. The exact analytical solutions of the Schrodinger equation for
abovementioned problems for QE class are discused and given for four series of
dual quasi-exact solvable models. In particular, a comparison with similar
results in lower dimensions and its generalization are given.


  We propose using nonlinear Mach-Zehnder interferometer (NMZI) to efficiently
prepare photonic quantum states from a classical input. We first analytically
investigate the simple NMZI that can filtrate single photon state from weak
coherent state by preferrentially blocking two-photon component. As a
generalization, we show that the cascaded NMZI can deterministically extract
arbitrary quantum state from a strong coherent state. Finally, we numerically
demonstrate that the cascaded NMZI can be very efficient in both the input
power and the level of cascade. The protocol of quantum state preparation with
NMZI can be extended to various systems of bosonic modes.


  Bound states in the continuum (BICs) are localized modes residing in the
radiation continuum. They were first predicted for single-particle states, and
became a general feature of many wave systems. In many-body quantum physics, it
is still unclear what would be a close analog of BICs, and whether
interparticle interaction may induce BICs. Here, we predict a novel type of
multiparticle states in the interaction-modulated Bose-Hubbard model that can
be associated with the BIC concept. Under periodic boundary conditions, a
so-called quasi-BIC appears as a bounded pair residing in a standing wave
formed by the third particle. Under open boundary conditions, such a hybrid
state becomes an eigenstate of the system. We demonstrate that the Thouless
pumping of the quasi-BICs can be realized by modulating the on-site
interactions in space and time. Surprisingly, while the center-of-mass of the
quasi-BIC is shifted by a unit cell in one cycle, the bounded pair moves into
the opposite direction with the standing wave.


  We consider the dynamics of systems of self propelling particles with
nonholonomic constraints. A continuum model for a discrete algorithm used in
works by T. Vicsek et al. is proposed. For a case of planar geometry the finite
flocking behavior is obtained. The circulation of the velocity field is found
not to be conserved as a consequence of the nonholomicity. The stability of
ordered motion with respect to noise is discussed. An analogy with the kinetics
of charges in superconductors is noted.


  Shell ferromagnetism is a new functional property of certain Heusler alloys
which has been recently observed in
$\mathrm{Ni}_{50}\mathrm{Mn}_{45}\mathrm{In}_{5}$. We report the results of a
comparative study of the magnetic microstructure of bulk
$\mathrm{Ni}_{50}\mathrm{Mn}_{45}\mathrm{In}_{5}$ Heusler alloys using
magnetometry, synchrotron x-ray diffraction, and magnetic small-angle neutron
scattering (SANS). By combining unpolarized and spin-polarized SANS (POLARIS)
we demonstrate that a number of important conclusions regarding the mesoscopic
spin structure can be made. In particular, the analysis of the magnetic neutron
data suggests that nanoprecipitates with an effective ferromagnetic component
form in an antiferromagnetic matrix on field annealing at $700 \, \mathrm{K}$.
These particles represent sources of perturbation, which seem to give rise to
magnetically disordered regions in the vicinity of the particle-matrix
interface. Analysis of the spin-flip SANS cross section via the computation of
the correlation function yields a value of $\sim 55 \, \mathrm{nm}$ for the
particle size and $\sim 20 \, \mathrm{nm}$ for the size of the spin-canted
region.


  Although dust content is usually assumed to depend uniquely on metallicity,
recent observations of two extremely metal-poor dwarf galaxies have suggested
that this may not always be true. At a similar oxygen abundance of ~ 3% Zsun,
the dust-to-gas and dust-to-stellar mass ratios in SBS 0335-052 and IZw 18
differ by a factor 40-70 according to including molecular gas or excluding it.
Here we investigate a possible reason for this dramatic difference through
models based on a semi-analytical formulation of chemical evolution including
dust. Results suggest that the greater dust mass in SBS 0335-052 is due to the
more efficient grain growth allowed by the high density in the cold
interstellar medium (ISM), observationally inferred to be almost 20 times
higher than in IZw 18. Our models are able to explain the difference in dust
masses, suggesting that efficient dust formation and dust content in galaxies,
including those with the highest measured redshifts, depend sensitively on the
ISM density, rather than only on metallicity.


  A harmonic cycle $\lambda$, also called a discrete harmonic form, is a
solution of the Laplace's equation with the combinatorial Laplace operator
obtained from the boundary operators of a chain complex. By the combinatorial
Hodge theory, harmonic spaces are isomorphic to the homology groups with real
coefficients. In particular, if a cell complex has a one dimensional reduced
homology, it has a unique harmonic cycle up to scalar, which we call the
\emph{standard harmonic cycle}. In this paper, we will present a formula for
the standard harmonic cycle $\lambda$ of a cell complex based on a
high-dimensional generalization of cycletrees. Moreover, by using duality, we
will define the standard harmonic cocycle $\lambda^*$, and show intriguing
combinatorial properties of $\lambda$ and $\lambda^*$ in relation to (dual)
spanning trees, (dual) cycletrees, winding numbers $w(\cdot)$ and cutting
numbers $c(\cdot)$ in high dimensions.


  A classical theorem due to Mattila (see \cite{Mat84}; see also \cite{M95},
Chapter 13) says that if $A,B \subset {\Bbb R}^d$ of Hausdorff dimension $s_A,
s_B$, respectively, with $s_A+s_B \ge d$, $s_B>\frac{d+1}{2}$ and
$dim_{{\mathcal H}}(A \times B)=s_A+s_B\ge d$, then $$ dim_{{\mathcal H}}(A
\cap (z+B)) \leq s_A+s_B-d$$ for almost every $z \in {\Bbb R}^d$, in the sense
of Lebesgue measure.
  In this paper, we replace the Hausdorff dimension on the left hand side of
the first inequality above by the upper Minkowski dimension, replace the
Lebesgue measure of the set of translates by a Hausdorff measure on a set of
sufficiently large dimension and replace the translation and rotation group by
a more general variable coefficient family of transformations. Interesting
arithmetic issues arise in the consideration of sharpness examples. These
results are partly motivated by those in \cite{EIT11} and \cite{IJL10} where in
the former the classical regular value theorem from differential geometry was
investigated in a fractal setting and in the latter discrete incidence theory
is explored from an analytic standpoint. Fourier Integral Operator bounds and
other techniques of harmonic analysis play a crucial role in our investigation.
  We also consider, in the spirit of the Furstenberg conjecture, inverse
problems for intersections by asking how small a dimension of a set can be
given that the dimension of its intersections with a suitably well-curved
family of manifolds is bounded from below by a given threshold.
  Finally, we shall discuss applications of our estimates to the problem of
estimating the number of solutions of systems of diophantine equations over
integers.


  In this paper we study the dynamics of a soliton in the generalized NLS with
a small external potential $\epsilon V$ of Schwartz class. We prove that there
exists an effective mechanical system describing the dynamics of the soliton
and that, for any positive integer $r$, the energy of such a mechanical system
is almost conserved up to times of order $\epsilon^{-r}$. In the rotational
invariant case we deduce that the true orbit of the soliton remains close to
the mechanical one up to times of order $\epsilon^{-r}$.


  We compute the proton-neutron entanglement entropy in the interacting nuclear
shell model for a variety of nuclides and interactions. Some results make
intuitive sense, for example that the shell structure, as governed by
single-particle and monopole energies, strongly affects the energetically
available space and thus the entanglement entropy. We also find a surprising
result: that the entanglement entropy at low excitation energy tends to
decrease for nuclides when $N \neq Z$. While we provide evidence this arises
from the physical nuclear force by contrasting with random two-body
interactions which shows no such decrease, the exact mechanism is unclear.
Nonetheless, the low entanglement suggests that in models of neutron-rich
nuclides, the coupling between protons and neutrons may be less computationally
demanding than one might otherwise expect.


  The vertical alignment optimization problem for road design aims to generate
a vertical alignment of a new road with a minimum cost, while satisfying safety
and design constraints. We present a new model called multi-haul quasi network
flow (MH-QNF) for vertical alignment optimization that improves the accuracy
and reliability of previous mixed integer linear programming models. We
evaluate the performance of the new model compared to two state-of-the-art
models in the field: the complete transportation graph (CTG) and the quasi
network flow (QNF) models. The numerical results show that, within a 1%
relative error, the proposed model is robust and solves more than 93% of test
problems compared to 82% for the CTG and none for the QNF. Moreover, the MH-QNF
model solves the problems approximately 8 times faster than the CTG model.


  Contemporary data assimilation often involves more than a million prediction
variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists.
They are successful indispensable tools in science and engineering, because
they allow for computationally cheap low ensemble state approximation for
extremely large dimensional turbulent dynamical systems. The practical finite
ensemble filter like EnKF necessarily involve modifications such as covariance
inflation and localization, and it is a genuine mystery why they perform so
well with small ensemble sizes in large dimensions. This paper provides the
first rigorous stochastic analysis of the accuracy and covariance fidelity of
EnKF in the practical regime where the ensemble size is much smaller than the
large ambient dimension for EnKFs with random coefficients. A challenging issue
overcome here is that EnKF in huge dimensions introduces unavoidable bias and
model errors which need to be controlled and estimated.


  Unconstrained lip-to-speech synthesis aims to generate corresponding speeches
from silent videos of talking faces with no restriction on head poses or
vocabulary. Current works mainly use sequence-to-sequence models to solve this
problem, either in an autoregressive architecture or a flow-based
non-autoregressive architecture. However, these models suffer from several
drawbacks: 1) Instead of directly generating audios, they use a two-stage
pipeline that first generates mel-spectrograms and then reconstructs audios
from the spectrograms. This causes cumbersome deployment and degradation of
speech quality due to error propagation; 2) The audio reconstruction algorithm
used by these models limits the inference speed and audio quality, while neural
vocoders are not available for these models since their output spectrograms are
not accurate enough; 3) The autoregressive model suffers from high inference
latency, while the flow-based model has high memory occupancy: neither of them
is efficient enough in both time and memory usage. To tackle these problems, we
propose FastLTS, a non-autoregressive end-to-end model which can directly
synthesize high-quality speech audios from unconstrained talking videos with
low latency, and has a relatively small model size. Besides, different from the
widely used 3D-CNN visual frontend for lip movement encoding, we for the first
time propose a transformer-based visual frontend for this task. Experiments
show that our model achieves $19.76\times$ speedup for audio waveform
generation compared with the current autoregressive model on input sequences of
3 seconds, and obtains superior audio quality.


  Future direct observations of extrasolar Earth-sized planets in the habitable
zone could be hampered by a worrisome source of noise, starlight-reflecting
exozodiacal dust. Mid-infrared surveys are currently underway to constrain the
amount of exozodiacal dust in the habitable zones around nearby stars. However,
at visible wavelengths another source of dust, invisible to these surveys, may
dominate over exozodiacal dust. For systems observed near edge-on, a cloud of
dust with face-on optical depth 10^-7 beyond ~5 AU can mimic the surface
brightness of a cloud of exozodiacal dust with equal optical depth if the dust
grains are sufficiently forward-scattering. We posit that dust migrating inward
from cold debris belts via Poynting-Robertson drag could produce this
"pseudo-zodiacal" effect, potentially making it ~50% as common as exozodiacal
clouds. We place constraints on the disk radii and scattering phase function
required to produce the effect.


  We revisit the notion of nonclassical distance of states of bosonic quantum
systems introduced in [M. Hillery, Phys. Rev. A 35, 725 (1987)] in a general
multimode setting. After reviewing its definition, we establish some of its
general properties. We obtain new upper and lower bounds on the nonclassical
distance in terms of the supremum of the Husimi function of the state.
Considering several examples, we elucidate the cases for which our lower bound
is tight, which include the multimode number states and a class of multimode
N00N states. The latter provide examples of states of definite photon number $n
\geq 2$ whose nonclassical distance can be made arbitrarily close to the upper
limit of $1$ by increasing the number of modes. We show that the nonclassical
distance of the even and odd Schr\"odinger cat states is bounded away from
unity regardless of how macroscopic the superpositions are, and that the
nonclassical distance is not necessarily monotonically increasing with respect
to macroscopicity.


  For a projective hypersurface $X \subset \P^n$, the images of the polar maps
of degree $k$ are studied. The cohomology class defined by these maps is
calculated and classical results on dual varieties are presented as
applications.


  In nanoscale junctions the interaction between charge carriers and the local
vibrations results in renormalization, damping and heating of the vibrational
modes. We here formulate a nonequilibrium Green's functions based theory to
describe such effects. Studying a generic junction model with an off-resonant
electronic level, we find a strong bias dependence of the frequency
renormalization and vibrational damping accompanied by pronounced nonlinear
vibrational heating in junctions with intermediate values of the coupling to
the leads. Combining our theory with ab-initio calculations we furthermore show
that the bias dependence of the Raman shifts and linewidths observed
experimentally in an OPV3 junction [D. Ward et al., Nature Nano. 6, 33 (2011)]
may be explained by a combination of dynamic carrier screening and molecular
charging.


  In open-retrieval conversational machine reading (OR-CMR) task, machines are
required to do multi-turn question answering given dialogue history and a
textual knowledge base. Existing works generally utilize two independent
modules to approach this problem's two successive sub-tasks: first with a
hard-label decision making and second with a question generation aided by
various entailment reasoning methods. Such usual cascaded modeling is
vulnerable to error propagation and prevents the two sub-tasks from being
consistently optimized. In this work, we instead model OR-CMR as a unified
text-to-text task in a fully end-to-end style. Experiments on the OR-ShARC
dataset show the effectiveness of our proposed end-to-end framework on both
sub-tasks by a large margin, achieving new state-of-the-art results. Further
ablation studies support that our framework can generalize to different
backbone models.


  Pulsars typically exhibit radio emission in the form of narrow pulses
originated from confined regions of their magnetospheres. A potential presence
of magnetospherically originated emission outside this region, the so-called
off-pulse emission, would challenge the existing theories. Detection of
significant off-pulse emission has been reported so far from only two pulsars,
B0525+21 and B2045-16, at 325 and 610 MHz. However, the nature of this newly
uncovered off-pulse emission remains unclear. To probe its origin we conducted
very high resolution radio observations of B0525+21 and B2045-16 with the
European VLBI Network (EVN) at 1.39 GHz. Whereas the pulsed emission is
detected at a level consistent with previous observations, we report absence of
any off-pulse emission above $42$ and $96\ \mathrm{\mu Jy\ beam^{-1}}$ (three
times the rms noise levels) for B0525+21 and B2045-16, respectively. Our
stringent upper limits imply the off-pulse emission to be less than $0.4$ and
$0.3\%$ of the period-averaged pulsed flux density, i.e., much fainter than the
previously suggested values of $1$-$10\%$. Since the EVN data are most
sensitive to extremely compact angular scales, our results suggest a
non-magnetospheric origin for the previously reported off-pulse emission.
Presence of extended emission that is resolved out on these milliarcsecond
scales still remains plausible. In this case, we constrain the emission to
arise from structures with sizes of $\sim (0.61$-$19) \times 10^3\ \mathrm{au}$
for B0525+21 and $\sim (0.48$-$8.3) \times 10^3\ \mathrm{au}$ for B2045-16.
These constraints might indicate that the two pulsars are accompanied by
compact bow-shock pulsar wind nebulae. Future observations probing intermediate
angular scales ($\sim 0.1$-$5\ \mathrm{arcsec}$) will help in clarifying the
actual origin of the off-pulse emission.


  In dyadic interaction, predicting the listener's facial reactions is
challenging as different reactions may be appropriate in response to the same
speaker's behaviour. This paper presents a novel framework called ReactFace
that learns an appropriate facial reaction distribution from a speaker's
behaviour rather than replicating the real facial reaction of the listener.
ReactFace generates multiple different but appropriate photo-realistic human
facial reactions by (i) learning an appropriate facial reaction distribution
representing multiple appropriate facial reactions; and (ii) synchronizing the
generated facial reactions with the speaker's verbal and non-verbal behaviours
at each time stamp, resulting in realistic 2D facial reaction sequences.
Experimental results demonstrate the effectiveness of our approach in
generating multiple diverse, synchronized, and appropriate facial reactions
from each speaker's behaviour, with the quality of the generated reactions
being influenced by the speaker's speech and facial behaviours. Our code is
made publicly available at \url{https://github.com/lingjivoo/ReactFace}.


  In this article, we study the limiting behavior of Bai (2009)'s interactive
fixed effects estimator in the presence of randomly missing data. In extensive
simulation experiments, we show that the inferential theory derived by Bai
(2009) and Moon and Weidner (2017) approximates the behavior of the estimator
fairly well. However, we find that the fraction and pattern of randomly missing
data affect the performance of the estimator. Additionally, we use the
interactive fixed effects estimator to reassess the baseline analysis of
Acemoglu et al. (2019). Allowing for a more general form of unobserved
heterogeneity as the authors, we confirm significant effects of democratization
on growth.


  We show that null surfaces defined by the outgoing and infalling wave fronts
emanating from and arriving at a sphere in Minkowski spacetime have
thermodynamical properties that are in strict formal correspondence with those
of black hole horizons in curved spacetimes. Such null surfaces, made of pieces
of light cones, are bifurcate conformal Killing horizons for suitable
conformally stationary observers. They can be extremal and non-extremal
depending on the radius of the shining sphere. Such conformal Killing horizons
have a constant light cone (conformal) temperature, given by the standard
expression in terms of the generalisation of surface gravity for conformal
Killing horizons. Exchanges of conformally invariant energy across the horizon
are described by a first law where entropy changes are given by $1/(4\ell_p^2)$
of the changes of a geometric quantity with the meaning of horizon area in a
suitable conformal frame. These conformal horizons satisfy the zeroth to the
third laws of thermodynamics in an appropriate way. In the extremal case they
become light cones associated with a single event; these have vanishing
temperature as well as vanishing entropy.


  We show that four exceptional Fuchsian equations, each determined by the four
parabolic singularities, known as the Chudnovsky equations, are transformed
into each other by algebraic transformations. We describe equivalence of these
equations and their counterparts on tori. The latter are the Fuchsian equations
on elliptic curves and their equivalence is characterized by transcendental
transformations which are represented explicitly in terms of elliptic and theta
functions.


  Let $\mathcal{S}^*_t(\alpha_1,\alpha_2)$ denote the class of functions $f$
analytic in the open unit disc $\Delta$, normalized by the condition
$f(0)=0=f'(0)-1$ and satisfying the following two--sided inequality:
\begin{equation*}
  -\frac{\pi\alpha_1}{2}< \arg\left\{\frac{zf'(z)}{f(z)}\right\}
  <\frac{\pi\alpha_2}{2} \quad (z\in\Delta), \end{equation*} where
$0<\alpha_1,\alpha_2\leq1$. The class $\mathcal{S}^*_t(\alpha_1,\alpha_2)$ is a
subclass of strongly starlike functions of order $\beta$ where
$\beta=\max\{\alpha_1,\alpha_2\}$. The object of the present paper is to derive
some certain inequalities including (for example), upper and lower bounds for
${\rm Re}\{zf'(z)/f(z)\}$, growth theorem, logarithmic coefficient estimates
and coefficient estimates for functions $f$ belonging to the class
$\mathcal{S}^*_t(\alpha_1,\alpha_2)$.


  Superconducting metamaterials comprising rf SQUIDs (Superconducting QUantum
Interference Devices) have been recently realized and investigated with respect
to their tuneability, permeability and dynamic multistability properties. These
properties are a consequence of intrinsic nonlinearities due to the sensitivity
of the superconducting state to external stimuli. SQUIDs, made of a
superconducting ring interrupted by a Josephson junction, possess yet another
source of nonlinearity, which makes them widely tuneable with an applied dc
dlux. A model SQUID metamaterial, based on electric equivalent circuits, is
used in the weak coupling approximation to demonstrate the dc flux tuneability,
dynamic multistability, and nonlinear transmission in SQUID metamaterials
comprising non-hysteretic SQUIDs. The model equations reproduce the
experimentally observed tuneability patterns, and predict tuneability with the
power of an applied ac magnetic magnetic field. Moreover, the results indicate
the opening of nonlinear frequency bands for energy transmission through SQUID
metamaterials, for sufficiently strong ac fields.


  The Hubble Deep Field images have provided us with a unique chance to relate
statistical properties of high-redshift galaxies to statistical properties of
\lya absorption systems. Combining an {\em empirical} measure of the galaxy
surface density versus redshift with an {\em empirical} measure of the gaseous
extent of galaxies, we predict the number density of \lya absorption systems
that originate in extended gaseous envelopes of galaxies versus redshift. We
show that at least 50% and as much as 100% of observed \lya absorption systems
of $W\apg0.32$ \AA can be explained by extended gaseous envelops of galaxies.
Therefore, we conclude that known galaxies of known gaseous extent must produce
a significant fraction and perhaps all of \lya absorption systems over a large
redshift range.


  The theory of summability of divergent series is a major branch of
mathematical analysis that has found important applications in engineering and
science. It addresses methods of assigning natural values to divergent sums,
whose prototypical examples include the Abel summation method, the Cesaro
means, and Borel summability method. In this paper, we introduce a new
summability method for divergent series, and derive an asymptotic expression to
its error term. We show that it is both regular and linear, and that it arises
quite naturally in the study of local polynomial approximations of analytic
functions. Because the proposed summability method is conceptually simple and
can be implemented in a few lines of code, it can be quite useful in practice
for computing the values of divergent sums.


  The special isothermic surfaces, discovered by Darboux in connection with
deformations of quadrics, admit a simple explanation via the gauge-theoretic
approach to isothermic surfaces. We find that they fit into a heirarchy of
special classes of isothermic surface and extend the theory to arbitrary
codimension.


  We investigate the open dynamics of a probe qubit weakly interacting with
distinct qubit environments bearing quantum information. We show that the
proposed dissipative model yields a binary classification of the reservoir
qubits' quantum information in the steady state in the Bloch qubit parameter
space, depending on the coupling rates. To describe the dissipation model
dynamics, we have adopted the collision model, in which the input information
parameters of the reservoir qubits are easily determined. We develop a
generalized classification rule based on the results of the micromaser-like
master equation where the classification can be described in terms of the Bloch
parameters. Moreover, we show that the proposed classification scheme can also
be achieved through quantum parameter estimation. Finally, we demonstrate that
the proposed dissipative classification scheme is suitable for gradient descent
based supervised learning tasks.


  The Colle and Salvetti approach [Theoret. Chim. Acta, 37, 329 (1975)] to the
calculation of the correlation energy of a system is modified in order to
explicitly include into the theory the kinetic contribution to the correlation
energy. This is achieved by deducing from a many electrons wave function,
including the correlation effects via a Jastrow factor, an approximate
expression of the one-electron reduced density matrix. Applying the latter to
the homogeneous electron gas, an analytic expression of the correlation kinetic
energy is derived. The total correlation energy of such a system is then
deduced from its kinetic contribution inverting a standard procedure. At
variance of the original Colle-Salvetti theory, the parameters entering in both
the kinetic correlation and the total correlation energies are determined
analytically, leading to a satisfactory agreement with the results of Perdew
and Wang [Phys. Rev. B 45, 13244 (1992)]. The resulting (parameter-free)
expressions give rise to a modified-local-density approximation that can be
used in self-consistent density-functional calculations. We have performed such
calculations for a large set of atoms and ions and we have found results for
the correlation energies and for the ionization potentials which improve those
of the standard local-density approximation.


  We study functions defined on the vertices of the Hamming graphs $H(n,q)$.
The adjacency matrix of $H(n,q)$ has $n+1$ distinct eigenvalues $n(q-1)-q\cdot
i$ with corresponding eigenspaces $U_{i}(n,q)$ for $0\leq i\leq n$. In this
work, we consider the problem of finding the minimum possible support (the
number of nonzeros) of functions belonging to a direct sum $U_i(n,q)\oplus
U_{i+1}(n,q)\oplus\ldots\oplus U_j(n,q)$ for $0\leq i\leq j\leq n$. For the
case $n\geq i+j$ and $q\geq 3$ we find the minimum cardinality of the support
of such functions and obtain a characterization of functions with the minimum
cardinality of the support. In the case $n<i+j$ and $q\geq 4$ we also find the
minimum cardinality of the support of functions, and obtain a characterization
of functions with the minimum cardinality of the support for $i=j$, $n<2i$ and
$q\geq 5$. In particular, we characterize eigenfunctions from the eigenspace
$U_{i}(n,q)$ with the minimum cardinality of the support for cases $i\le
\frac{n}{2}$,$q\ge 3$ and $i> \frac{n}{2}$,$\,q\ge 5$.


  Many complex systems respond to a continuous input of energy by an
accumulation of stress over time, interrupted by sudden energy releases called
avalanches. Recently, it has been pointed out that several basic features of
avalanche dynamics are induced at the microscopic level by relaxation
processes, which are neglected by most models. During my thesis, I studied two
well-known models of avalanche dynamics, modified minimally by the inclusion of
some forms of relaxation.
  The first system is that of a viscoelastic interface driven in a disordered
medium. In mean-field, we prove that the interface has a periodic behaviour
(with a new, emerging time scale), with avalanche events that span the whole
system. We compute semi-analytically the friction force acting on this surface,
and find that it is compatible with classical friction experiments. In finite
dimensions (2D), the mean-field system-sized events become local, and numerical
simulations give qualitative and quantitative results in good agreement with
several important features of real earthquakes.
  The second system including a minimal form of relaxation consists in a toy
model of avalanches: the Directed Percolation process. In our study of a
non-Markovian variant of Directed Percolation, we observed that the
universality class was modified but not completely. In particular, in the
non-Markov case an exponent changes of value while several scaling relations
still hold. This picture of an extended universality class obtained by the
addition of a non-Markovian perturbation to the dynamics provides promising
prospects for our first system.


  In this study, by combining the equal spacing rule with recent observations
of $\Omega_c(X)$ and $\Xi_c(X)$ baryons, we predict the spectrum of the
low-lying $\lambda$-mode $1P$-wave excited $\Sigma_c$ states. Furthermore,
their strong decay properties are predicted using the chiral quark model and
the nature of $\Sigma_c(2800)$ is investigated by analyzing the $\Lambda_c\pi$
invariant mass spectrum. The $\Sigma_c(2800)$ structure observed in the
$\Lambda_c \pi$ mass spectrum was found to potentially arise from two
overlapping $P$-wave $\Sigma_c$ resonances, $\Sigma_c(2813)3/2^-$ and
$\Sigma_c(2840)5/2^-$. These resonances have similar decay widths of
$\Gamma\sim 40$ MeV and predominantly decay into the $\Lambda_c \pi$ channel.
The $\Sigma_c(2755)1/2^-$ state is likely to be a very narrow state with a
width of $\Gamma\sim 15$ MeV, with its decays almost saturated by the
$\Lambda_c \pi$ channel. Additionally, evidence of the
$\Sigma_c(2755)\frac{1}{2}^-$ resonance as a very narrow peak may be seen in
the $\Lambda_c\pi$ invariant mass spectrum. The other two $P$-wave states,
$\Sigma_c(2746)\frac{1}{2}^-$ and $\Sigma_c(2796)\frac{3}{2}^-$, are relatively
narrow states with similar widths of $\Gamma\sim 30$ MeV and predominantly
decay into $\Sigma_c\pi$ and $\Sigma^{*}_c\pi$, respectively. We hope our study
can provide useful references for discovering these low-lying $P$-wave states
in forthcoming experiments.


  The challenge to in-band full-duplex wireless communication is managing
self-interference. Many designs have employed spatial isolation mechanisms,
such as shielding or multi-antenna beamforming, to isolate the
self-interference wave from the receiver. Such spatial isolation methods are
effective, but by confining the transmit and receive signals to a subset of the
available space, the full spatial resources of the channel be under-utilized,
expending a cost that may nullify the net benefit of operating in full-duplex
mode. In this paper we leverage an antenna-theory-based channel model to
analyze the spatial degrees of freedom available to a full-duplex capable base
station, and observe that whether or not spatial isolation out-performs
time-division (i.e. half-duplex) depends heavily on the geometric distribution
of scatterers. Unless the angular spread of the objects that scatter to the
intended users is overlapped by the spread of objects that backscatter to the
base station, then spatial isolation outperforms time division, otherwise time
division may be optimal.


  Identifying intrinsic low-dimensional ferromagnets with high transition
temperature and electrically tunable magnetism is crucial for the development
of miniaturized spintronics and magnetoelectrics. Recently long-range 2D
ferromagnetism was observed in van der Waals crystals CrI$_3$ and
Cr$_2$Ge$_2$Te$_6$, however their Curie temperature is significantly lowered
when reducing down to monolayer/few layers. Herein, using renormalized
spin-wave theory and first-principles electronic structure theory, we present a
theoretical study of electrically tunable 2D ferromagnetism in van der Waals
layered CrSBr and CrSeBr semiconductors with high Curie temperature of ~150K
and sizable band gap. High transition temperature is attributed to strong
anion-mediated superexchange interaction and a sizable spin-wave excitation gap
due to large exchange and single-ion anisotropy. Remarkably, hole and electron
doping can switch magnetization easy axis from in-plane to out-of-plane
direction. These unique characteristics establish monolayer CrSBr and CrSeBr as
promising platform for realizing 2D spintronics and magnetoelectrics such as 2D
spin field effect transistor.


  We consider two-stage inflationary models in which a superheavy scale F-term
hybrid inflation is followed by an intermediate scale modular inflation. We
confront these models with the restrictions on the power spectrum P_R of
curvature perturbations and the spectral index n_s implied by the recent data
within the power-law cosmological model with cold dark matter and a
cosmological constant. We show that these restrictions can be met provided that
the number of e-foldings N_HI* suffered by the pivot scale k_*=0.002/Mpc during
hybrid inflation is appropriately restricted. The additional e-foldings
required for solving the horizon and flatness problems can be naturally
generated by the subsequent modular inflation. For central values of P_R and
n_s, we find that, in the case of standard hybrid inflation, the values
obtained for the grand unification scale are close to its supersymmetric value
M_GUT=2.86 x 10^16 GeV, the relevant coupling constant is relatively large
(0.005-0.14), and N_HI* between about 10 and 21.7. In the case of shifted
[smooth] hybrid inflation, the grand unification scale can be identified with
M_GUT provided that N_HI*=21 [N_HI*=18].


  In AI research, so far, the attention paid to the characterization and
representation of function and affordance has been sporadic and sparse, even
though this aspect features prominently in an intelligent system's functioning.
In the sporadic and sparse, though commendable efforts so far devoted to the
characterization and understanding of function and affordance, there has also
been no general framework that could unify all the different use domains and
situations related to the representation and application of functional
concepts. This paper develops just such a general framework, with an approach
that emphasizes the fact that the representations involved must be explicitly
cognitive and conceptual, and they must also contain causal characterizations
of the events and processes involved, as well as employ conceptual constructs
that are grounded in the referents to which they refer, in order to achieve
maximal generality. The basic general framework is described, along with a set
of basic guiding principles with regards to the representation of
functionality. To properly and adequately characterize and represent
functionality, a descriptive representation language is needed. This language
is defined and developed, and many examples of its use are described. The
general framework is developed based on an extension of the general language
meaning representational framework called conceptual dependency. To support the
general characterization and representation of functionality, the basic
conceptual dependency framework is enhanced with representational devices
called structure anchor and conceptual dependency elaboration, together with
the definition of a set of ground level concepts. These novel representational
constructs are defined, developed, and described. A general framework dealing
with functionality would represent a major step toward achieving Artificial
General Intelligence.