  Recent generalizations of the Hopfield model of associative memories are able
to store a number $P$ of random patterns that grows exponentially with the
number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity,
another interesting feature of these networks is their connection to the
attention mechanism which is part of the Transformer architectures widely
applied in deep learning. In this work, we study a generic family of pattern
ensembles using a statistical mechanics analysis which gives exact asymptotic
thresholds for the retrieval of a typical pattern, $\alpha_1$, and lower bounds
for the maximum of the load $\alpha$ for which all patterns can be retrieved,
$\alpha_c$, as well as sizes of attraction basins. We discuss in detail the
cases of Gaussian and spherical patterns, and show that they display rich and
qualitatively different phase diagrams.


  The atmospheric circulation of tidally locked planets is dominated by a
superrotating eastward equatorial jet. We develop a predictive theory for the
formation of this jet, proposing a mechanism in which the three-dimensional
stationary waves induced by the day-night forcing gradient produce an
equatorial acceleration. This is balanced in equilibrium by an interaction
between the resulting jet and the vertical motion of the atmosphere. The
three-dimensional structure of the zonal acceleration is vital to this
mechanism.
  We demonstrate this mechanism in a hierarchy of models. We calculate the
three-dimensional stationary waves induced by the forcing on these planets, and
show the vertical structure of the zonal acceleration produced by these waves,
which we use to suggest a mechanism for how the jet forms. GCM simulations are
used to confirm the equilibrium state predicted by this mechanism, where the
acceleration from these waves is balanced by an interaction between the
zonal-mean vertical velocity and the jet. We derive a simple model of this
using the "Weak Temperature Gradient" approximation, which gives an estimate of
the jet speed on a terrestrial tidally locked planet.
  We conclude that the proposed mechanism is a good description of the
formation of an equatorial jet on a terrestrial tidally locked planet, and
should be useful for interpreting observations and simulations of these
planets. The mechanism requires assumptions such as a large equatorial Rossby
radius and weak acceleration due to transient waves, and a different mechanism
may produce the equatorial jets on gaseous tidally locked planets.


  We study two body dipolar scattering in two dimensions with a tilted
polarization axis. This tilt reintroduces the anisotropic interaction in a
controllable manner. As a function of this polarization angle we present the
scattering results in both the threshold and semi-classical regimes. We find a
series of resonances as a function of the angle which allows the scattering to
be tuned. However the character of the resonances varies strongly as a function
angle. Additionally we study the properties of the molecular bound states as a
function of the polarization angle.


  Electromagnetic vacuum fluctuations have observable consequences, like the
Casimir force between mirrors in vacuum. This force is now measured with good
accuracy and agreement with theory when the effect of imperfect reflection of
mirrors is properly taken into account. We discuss the simple case of bulk
metallic mirrors described by a plasma model and show that simple scaling laws
are obtained at the limits of long and short distances. The crossover between
the short and long-distance laws is quite similar to the crossover between Van
der Waals and Casimir-Polder forces for two atoms in vacuum. The result
obtained at short distances can be understood as the London interaction between
plasmon excitations at the surface of each bulk mirror.


  We study the resonance properties within chiral perturbation theory by
explicitly taking into account the U_A(1) anomaly effect. This assures we have
the appropriate degrees of freedom of low energy QCD in the large Nc limit. We
calculate the various resonance properties, such as mass, width and residues,
for the physical case, i.e. Nc=3. Then we extrapolate the values of Nc to study
the trajectories of resonance poles.


  This study presents a spatiotemporal traffic prediction approach for NextG
mobile networks, ensuring the service-level agreements (SLAs) of each network
slice. Our approach is multivariate, multi-step, and spatiotemporal. Leveraging
20 radio access network (RAN) features, peak traffic hour data, and
mobility-based clustering, we propose a parametric SLA-based loss function to
guarantee an SLA violation rate. We focus on single-cell, multi-cell, and
slice-based prediction approaches and present a detailed comparative analysis
of their performances, strengths, and limitations.
  First, we address the application of single-cell and multi-cell training
architectures. While single-cell training offers individual cell-level
prediction, multi-cell training involves training a model using traffic from
multiple cells from the same or different base stations. We show that the
single-cell approach outperforms the multi-cell approach and results in test
loss improvements of 11.4% and 38.1% compared to baseline SLA-based and
MAE-based models, respectively.
  Next, we explore slice-based traffic prediction. We present single-slice and
multi-slice methods for slice-based downlink traffic volume prediction, arguing
that multi-slice prediction offers a more accurate forecast. The slice-based
model we introduce offers substantial test loss improvements of 28.2%, 36.4%,
and 55.6% compared to our cell-based model, the baseline SLA-based model, and
the baseline MAE-based model, respectively.


  A time-dependent double-barrier option is a derivative security that delivers
the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous
time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time
interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of
the barrier option price into the corresponding European option price minus the
barrier premium for a wide class of payoff functions $\phi$, barrier functions
$b_\pm$ and linear diffusions $(S_t)_{t\in[0,T]}$. We show that the barrier
premium can be expressed as a sum of integrals along the barriers $b_\pm$ of
the option's deltas $\Delta_\pm:[0,T]\to\RR$ at the barriers and that the pair
of functions $(\Delta_+,\Delta_-)$ solves a system of Volterra integral
equations of the first kind. We find a semi-analytic solution for this system
in the case of constant double barriers and briefly discus a numerical
algorithm for the time-dependent case.


  The information contained in the Gaia Second Data Release (DR2) allows to
search for the unusual objects with the pre-selected properties, literally
constructing the stars with the desired characteristics. This work describes
the idea of method, its implementation and the results of searching for the
ultracool compact binaries within 200 parsec distance. The search in the
selected range of absolute magnitudes (M=11..13) has yielded the discovery of
both expected and unexpected objects. We found two cataclysmic variables with
the extreme IR versus UV color index at 126 and 103 parsecs, two eclipsing
pre-cataclysmic systems in the period gap and a candidate young stellar object.
We analyze the new variable stars using the data from synoptic surveys and
compare their properties to the known stars of these types. Applications to the
galactic population density of compact binaries are also discussed.


  We investigate the second harmonic generation of light field carrying orbital
angular momentum in bulk $\chi^{(2)}$ material. We show that due to
conservation of energy and momentum, the frequency doubled beam light has a
modified spatial distribution and mode characteristics. Through rigorous phase
matching conditions, we demonstrate efficient mode and frequency conversion
based on three wave nonlinear optical mixing.


  With increasing sensitivity, angular resolution, and frequency coverage,
future cosmic microwave background (CMB) experiments like PICO will allow us to
access new information about galaxy clusters through the relativistic thermal
Sunyaev-Zeldovich (SZ) effect. We will be able to map the temperature of
relativistic electrons across the entire sky, going well beyond a simple
detection of the relativistic SZ effect by cluster stacking methods that
currently define the state-of-the-art. Here, we propose a new map-based
approach utilizing SZ-temperature moment expansion and constrained-ILC methods
to extract electron gas temperature maps from foreground-obscured CMB data.
This delivers a new independent map-based observable, the electron temperature
power spectrum $T_{\rm e}^{yy}(\ell)$, which can be used to constrain cosmology
in addition to the Compton-$y$ power spectrum $C_\ell^{yy}(\ell)$ . We find
that PICO has the required sensitivity, resolution, and frequency coverage to
accurately map the electron gas temperature of galaxy clusters across the full
sky, covering a broad range of angular scales. Frequency-coverage at
$\nu\gtrsim 300\,{\rm GHz}$ plays an important role for extracting the
relativistic SZ effect in the presence of foregrounds. For Coma, PICO will
allow us to directly reconstruct the electron temperature profile using the
relativistic SZ effect. Coma's average electron temperature will be measured to
$10\sigma$ significance after foreground removal using PICO. Low-angular
resolution CMB experiment like LiteBIRD could achieve $2\sigma$ to $3\sigma$
measurement of the electron temperature of this largest cluster. Our analysis
highlights a new spectroscopic window into the thermodynamic properties of
galaxy clusters and the diffuse electron gas at large angular scales.


  The relatively low concentration of pathogen indicators, such Salmonella, in
composting sometimes causes a problem with detection when using the
conventional techniques. The presence of viable but non-culturable (VBNC)
organisms is also a potential problem with Salmonella detection when using
conventional techniques. In this study, the molecular approach for organism
recognition, known as Polymerase Chain Reaction (PCR), was used for
characterisation the Salmonella spp. used as inoculums in composting. This
study also provides a better understand about selecting the suitable primer for
Salmonella spp. The specificity of the probes and primers at the species level
were verified by performing NCBI-BLAST2 (Basic Local Alignment Search Tool).
Primers that target the invA gene for Salmonella were selected which produce
fragment lengths around 285bp (shown in Figure 1). The Salmonella spp.
solutions were tested and proved contained the sequences of invA gene by using
several steps of molecular techniques before used it as inoculums in
composting. The laboratory scale batch composting reactors were used to examine
the inactivation of Salmonella spp. The inoculate solution of Salmonella was
prepared by culturing Salmonella enteritidis (ATCC13076) in tryptone broth
solution for 24 hours before adding it directly into the compost material. The
reduction rate of Salmonella spp. was enumerated by conventional method
accordingly to the standard compost guidelines (Figure 2). The laboratory scale
study showed that after composting for 8 days the numbers of Salmonella spp.
were below the limits in the UK compost standard (PAS 100) which requires the
compost to be free of Salmonella spp.


  We consider finite extensions of the rationals which are unramified except
for at 2 and infinity. We show there are no such extensions of degrees 9
through 15.


  Imagine an under water factory which is about $10 \mu$m long in each
direction. The factory is filled with machines, each typically a few tens of
nanometers long, which perform specfic tasks and operate in a well coordinated
manner. A cell, the structural and functional unit of life, is not very
different from this micro-factory. In this article, I begin with Alice's guided
tour of this micro-factory in her dream during which the guide shows her wide
varieties of the nano-machines in this factory. The style of presentation of
the first half of this article is inspired by Lewis Carrol's {\it Alice in
Wonderland}. In the second half, I introduce the methods of studying the
materials and mechanisms of the molecular machines through dialogues; the three
participants in this discussion are Alice, her elder brother Alex and her
father Albert. The style of presentation of the second half of this article, in
terms of a dialogue, is adapted from Galileo's {\it Dialogue Concerning the Two
Chief World Systems}. Albert, a professor of biophysics, emphasizes the crucial
differences between the mechanisms of the natural nano-machines and those of
their macroscopic counterparts. He also points out some practical applications
of this interdisciplinary research in biomedical science and nano-technology.


  Solar cells have generated a lot of interest as a potential source of clean
renewable energy for the future. However a big bottleneck in wide scale
deployment of these energy sources remain the low efficiency of these
conversion devices. Recently the use of nanostructures and the strategy of
quantum confinement have been as a general approach towards better charge
carrier generation and capture. In this article we have presented calculations
on the optical characteristics of nanowires made out of Silicon. Our
calculations show these nanowires form excellent optoelectronic materials and
may yield efficient photovoltaic devices.


  We extend the complete Mellin (CM) representation of Feynman amplitudes to
the non-commutative quantum field theories. This representation is a versatile
tool. It provides a quick proof of meromorphy of Feynman amplitudes in
parameters such as the dimension of space-time. In particular it paves the road
for the dimensional renormalization of these theories. This complete Mellin
representation also allows the study of asymptotic behavior under rescaling of
arbitrary subsets of external invariants of any Feynman amplitude.


  In today's global business market place, individual firms no longer compete
as independent entities with unique brand names but as integral part of supply
chain links. Key to success of any business is satisfying customer's demands on
time which may result in cost reductions and increase in service level. In
supply chain networks decisions are made with uncertainty about product's
demands, costs, prices, lead times, quality in a competitive and collaborative
environment. If poor decisions are made, they may lead to excess inventories
that are costly or to insufficient inventory that cannot meet customer's
demands. In this work we developed a bi-objective model that minimizes system
wide costs of the supply chain and delays on delivery of products to
distribution centers for a three echelon supply chain. Picking a set of Pareto
front for multi-objective optimization problems require robust and efficient
methods that can search an entire space. We used evolutionary algorithms to
find the set of Pareto fronts which have proved to be effective in finding the
entire set of Pareto fronts.


  It is an open question whether glitch activity in individual pulsars varies
on decadal time-scales. The Crab pulsar has experienced 23 spin-up glitches in
the last 36 years, interrupting an otherwise monotonic deceleration. A
homogeneous Poisson process, i.e. a process with constant rate, is not
sufficient to describe the time-ordered distribution of glitch epochs in the
Crab pulsar. There are signs of clustering at the $2\sigma$ level when testing
with Ripley's $K$ function. Two alternative, inhomogeneous models with one and
two step-wise rate changes are found to have higher relative evidence (Bayes
factors of 1.74 and 2.86 respectively) than the homogeneous Poisson process.
The distinction between clustering, where events are correlated, and rate
variation is discussed. The implications for glitch microphysics, in particular
trigger mechanisms based on avalanche processes, are briefly discussed.


  We present variational and numerical solutions of the generalized
Gross--Pitaevskii equation for an atomic Bose--Einstein condensate with
time-dependent, laser-induced dipole-dipole interactions (LIDDI). The formation
of a supersolid ground state due to LIDDI in an elongated (cigar-shaped) BEC is
investigated. It is found that the supersolid structure emerges if the laser
intensity exceeds a critical value, which depends on the linear density of
atoms in the BEC.


  Subgraph representation learning based on Graph Neural Network (GNN) has
exhibited broad applications in scientific advancements, such as predictions of
molecular structure-property relationships and collective cellular function. In
particular, graph augmentation techniques have shown promising results in
improving graph-based and node-based classification tasks. Still, they have
rarely been explored in the existing GNN-based subgraph representation learning
studies. In this study, we develop a novel multi-view augmentation mechanism to
improve subgraph representation learning models and thus the accuracy of
downstream prediction tasks. Our augmentation technique creates multiple
variants of subgraphs and embeds these variants into the original graph to
achieve highly improved training efficiency, scalability, and accuracy.
Benchmark experiments on several real-world biological and physiological
datasets demonstrate the superiority of our proposed multi-view augmentation
techniques in subgraph representation learning.


  Experiments reveal that structural transitions in thin sheets are mediated by
the passage of transient and stable mobile localized elastic excitations. These
``crumples'' or ``d-cones'' nucleate, propagate, interact, annihilate, and
escape. Much of the dynamics occurs on millisecond time scales. Nucleation
sites correspond to regions where generators of the ideal unstretched surface
converge. Additional stable intermediate states illustrate two forms of
quasistatic inter-crumple interaction through ridges or valleys. These
interactions create pairs from which extended patterns may be constructed in
larger specimens. The onset of localized transient deformation with increasing
sheet size is correlated with a characteristic stable crumple size, whose
measured scaling with thickness is consistent with prior theory and experiment
for localized elastic features in thin sheets. We offer a new theoretical
justification of this scaling.


  We study the conformal structure of exotic (non-big-bang) singularity
universes using the hybrid big-bang/exotic singularity/big-bang and
big-rip/exotic singularity/big-rip models by investigating their appropriate
Penrose diagrams. We show that the diagrams have the standard structure for the
big-bang and big-rip and that exotic singularities appear just as the constant
time hypersurfaces for the time of a singularity and because of their geodesic
completeness are potentially transversable. We also comment on some
applications and extensions of the Penrose diagram method in studying exotic
singularities.


  Let $C$ be a smooth projective curve over the field of complex numbers
$\mathbb{C}$ of genus $g(C)>0$. Let $E$ be a locally free sheaf on $C$ of rank
$r$ and degree $e$. Let $\mathcal{Q}:={\rm Quot}_{C/\mathbb{C}}(E,k,d)$ denote
the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. For $k>0$ and
$d\gg 0$ we compute the Picard group of $\mathcal{Q}$.


  We employ matrix-product state techniques to numerically study the
zero-temperature spin transport in a finite spin-1/2 XXZ chain coupled to
fermionic leads with a spin bias voltage. Current-voltage characteristics are
calculated for parameters corresponding to the gapless XY phase and the gapped
N\'eel phase. In both cases, the low-bias spin current is strongly suppressed
unless the parameters of the model are fine-tuned. For the XY phase, this
corresponds to a conducting fixed point where the conductance agrees with the
Luttinger-liquid prediction. In the N\'eel phase, fine-tuning the parameters
similarly leads to an unsuppressed spin current with a linear current-voltage
characteristic at low bias voltages. However, with increasing the bias voltage,
there occurs a sharp crossover to a region where a current-voltage
characteristic is no longer linear and the smaller differential conductance is
observed. We furthermore show that the parameters maximizing the spin current
minimize the Friedel oscillations at the interface, in agreement with the
previous analyses of the charge current for inhomogeneous Hubbard and spinless
fermion chains.


  We investigate which planar point sets allow simultaneous straight-line
embeddings of all planar graphs on a fixed number of vertices. We first show
that $(1.293-o(1))n$ points are required to find a straight-line drawing of
each $n$-vertex planar graph (vertices are drawn as the given points); this
improves the previous best constant $1.235$ by Kurowski (2004).
  Our second main result is based on exhaustive computer search: We show that
no set of 11 points exists, on which all planar 11-vertex graphs can be
simultaneously drawn plane straight-line. This strengthens the result by
Cardinal, Hoffmann, and Kusters (2015), that all planar graphs on $n \le 10$
vertices can be simultaneously drawn on particular `universal' sets of $n$
points while there are no universal sets for $n \ge 15$. Moreover, we provide a
set of 49 planar 11-vertex graphs which cannot be simultaneously drawn on any
set of 11 points. This, in fact, is another step towards a (negative) answer of
the question, whether every two planar graphs can be drawn simultaneously -- a
question raised by Brass, Cenek, Duncan, Efrat, Erten, Ismailescu, Kobourov,
Lubiw, and Mitchell (2007).


  A family of effective equations for wave propagation in periodic media for
arbitrary timescales $\mathcal{O}(\varepsilon^{-\alpha})$, where
$\varepsilon\ll1$ is the period of the tensor describing the medium, is
proposed. The well-posedness of the effective equations of the family is
ensured without requiring a regularization process as in previous models [A.
Benoit and A. Gloria, arXiv:1701.08600, 2017], [G. Allaire, A. Lamacz, and J.
Rauch, arXiv:1803.09455, 2018]. The effective solutions in the family are
proved to be $\varepsilon$ close to the original wave in a norm equivalent to
the $L^\infty(0,\varepsilon^{-\alpha}T;L^2(\Omega))$ norm. In addition, a
numerical procedure for the computation of the effective tensors of arbitrary
order is provided. In particular, we present a new relation between the
correctors of arbitrary order, which allows to substantially reduce the
computational cost of the effective tensors of arbitrary order. This relation
is not limited to the effective equations presented in this paper and can be
used to compute the effective tensors of alternative effective models.


  We study the point spectrum of the linearization at a solitary wave solution
$\phi_\omega(x)e^{-\mathrm{i}\omega t}$ to the nonlinear Dirac equation in
$\mathbb{R}^n$, $n\ge 1$, with the nonlinear term given by
$f(\psi^*\beta\psi)\beta\psi$ (known as the Soler model). We focus on the
spectral stability, that is, the absence of eigenvalues with nonzero real part,
in the non-relativistic limit $\omega\lesssim m$, in the case when $f\in
C^1(\mathbb{R}\setminus\{0\})$, $f(\tau)=|\tau|^k+O(|\tau|^K)$ for $\tau\to 0$,
with $0<k<K$. For $n\ge 1$, we prove the spectral stability of small amplitude
solitary waves ($\omega\lesssim m$) for the charge-subcritical cases $k\lesssim
2/n$ ($1<k\le 2$ when $n=1$) and for the "charge-critical case" $k=2/n$,
$K>4/n$.
  An important part of the stability analysis is the proof of the absence of
bifurcations of nonzero-real-part eigenvalues from the embedded threshold
points at $\pm 2m\mathrm{i}$. Our approach is based on constructing a new
family of exact bi-frequency solitary wave solutions in the Soler model, using
this family to determine the multiplicity of $\pm 2\omega\mathrm{i}$
eigenvalues of the linearized operator, and the analysis of the behaviour of
"nonlinear eigenvalues" (characteristic roots of holomorphic operator-valued
functions).


  This paper addresses the problem of unknown delays in adversarial multi-armed
bandit (MAB) with multiple play. Existing work on similar game setting focused
on only the case where the learner selects an arm in each round. However, there
are lots of applications in robotics where a learner needs to select more than
one arm per round. It is therefore worthwhile to investigate the effect of
delay when multiple arms are chosen. The multiple arms chosen per round in this
setting are such that they experience the same amount of delay. There can be an
aggregation of feedback losses from different combinations of arms selected at
different rounds, and the learner is faced with the challenge of associating
the feedback losses to the arms producing them. To address this problem, this
paper proposes a delayed exponential, exploitation and exploration for multiple
play (DEXP3.M) algorithm. The regret bound is only slightly worse than the
regret of DEXP3 already proposed for the single play setting with unknown
delay.


  In this article, we study the masses and pole residues of the
pseudoscalar-diquark-pseudoscalar-antidiquark type and
vector-diquark-vector-antidiquark type scalar hidden-charm $cu\bar{c}\bar{d}$
($cu\bar{c}\bar{s}$) tetraquark states with QCD sum rules by taking into
account the contributions of the vacuum condensates up to dimension-10 in the
operator product expansion. The predicted masses can be confronted with the
experimental data in the future. Possible decays of those tetraquark states are
also discussed.


  We report the first extensive set of optical photometric observations of the
counterpart to SAX J1808.4-3658 (V4580 Sagittarius) in quiescence. The source
was detected at V~21, 5 magnitudes fainter than at the peak of its 1998
outburst. However, a comparable ~6% semi-amplitude 2hr modulation of its flux
is revealed. This has the same phasing and approximately sinusoidal modulation
as seen during outburst and with photometric minimum when the pulsar is behind
the companion. The lack of a double-humped morphology rules out an ellipsoidal
origin, implying that the bulk of the optical flux does not arise from the
companion. Moreover, applying crude modelling to the disc and X-ray irradiated
face of the donor shows that the internal energy release of a remnant disc
(with mass transfer driven by gravitational radiation) is sufficient to explain
most of the optical emission, and with the modulation due to the varying
contribution of the heated star's face. We note that this model is also
consistent with the much lower X-ray to optical flux ratio in quiescence versus
outburst, and with the phasing of the optical modulation.


  The orthogonality of cat and displaced cat states, underlying Heisenberg
limited measurement in quantum metrology, is studied in the limit of large
number of states. The asymptotic expression for the corresponding state overlap
function, controlled by the sub-Planck structures arising from phase space
interference, is obtained exactly. The validity of large phase space support,
in which context the asymptotic limit is achieved, is discussed in detail. For
large number of coherent states, uniformly located on a circle, it identically
matches with the diffraction pattern for a circular ring with uniform angular
source strength. This is in accordance with the van Cittert-Zernike theorem,
where the overlap function, similar to the mutual coherence function matches
with a diffraction pattern.


  We present a brief review of power laws and correlation functions as measures
of criticality and the relation between them. By comparing phenomenology from
rain, brain and the forest fire model we discuss the relevant features of
self-organisation to the vicinity about a critical state. We conclude that
organisation to a region of extended correlations and approximate power laws
may be behaviour of interest shared between the three considered systems.


  We derive exact expressions for the finite-time statistics of extrema
(maximum and minimum) of the spatial displacement and the fluctuating entropy
flow of biased random walks. Our approach captures key features of extreme
events in molecular motor motion along linear filaments. Our results generalize
the infimum law for entropy production and reveal a symmetry of the
distribution of its maxima and minima. We also show that the relaxation
spectrum of the full generating function, and hence of any moment, of the
finite-time extrema distributions can be written in terms of the
Mar{\v{c}}enko-Pastur distribution of random-matrix theory. Using this result,
we obtain estimates for the extreme-value statistics of stochastic transport
from the eigenvalue distributions of suitable Wishart and Laguerre random
matrices. We confirm our results by numerical simulations of stochastic models
of molecular motors and discuss as illustrative example our theory in the
context of sports.


  Information Flow Control (IFC) is a collection of techniques for ensuring a
no-write-down no-read-up style security policy known as noninterference.
Traditional methods for both static and dynamic IFC suffer from untenable
numbers of false alarms on real-world programs. Secure Multi-Execution (SME)
promises to provide secure IFC without modifying the behaviour of already
secure programs, a property known as transparency. Implementations of SME exist
for the web and as plug-ins to several programming languages. Furthermore, SME
can in theory work in a black-box manner, meaning that it can be programming
language agnostic, making it perfect for securing legacy or third-party
systems. As such SME, and its variants like Multiple Facets (MF) and Faceted
Secure Multi-Execution (FSME), appear to be a family of panaceas for the
security engineer. The question is, how come, given all these advantages, that
these techniques are not ubiquitous in practice? The answer lies, partially, in
the issue of runtime and memory overhead. SME and its variants are
prohibitively expensive to deploy in many non-trivial situations. Why is this
the case? On the surface, the reason is simple. The techniques in the SME
family all rely on the idea of multi-execution, running all or parts of a
program multiple times to achieve noninterference. Naturally, this causes
overhead. However, the goal in the IFC community has been to overcome these
overheads. In this paper we argue that there are fundamental reasons to expect
this not to be possible and prove two key theorems: 1. All transparent
enforcement is polynomial time equivalent to multi-execution. 2. All black-box
enforcement takes time exponential in the number of principals in the security
lattice. We also answer, in the affirmative, an open question about the
possibility of transparently enforcing the TINI security condition.


  High dimensional hypothesis test deals with models in which the number of
parameters is significantly larger than the sample size. Existing literature
develops a variety of individual tests. Some of them are sensitive to the dense
and small disturbance, and others are sensitive to the sparse and large
disturbance. Hence, the powers of these tests depend on the assumption of the
alternative scenario. This paper provides a unified framework for developing
new tests which are adaptive to a large variety of alternative scenarios in
high dimensions. In particular, our framework includes arbitrary hypotheses
which can be tested using high dimensional $U$-statistic based vectors. Under
this framework, we first develop a broad family of tests based on a novel
variant of the $L_p$-norm with $p\in \{1,\dots,\infty\}$. We then combine these
tests to construct a data-adaptive test that is simultaneously powerful under
various alternative scenarios. To obtain the asymptotic distributions of these
tests, we utilize the multiplier bootstrap for $U$-statistics. In addition, we
consider the computational aspect of the bootstrap method and propose a novel
low-cost scheme. We prove the optimality of the proposed tests. Thorough
numerical results on simulated and real datasets are provided to support our
theory.


  In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a
randomly forced particle which collides inelastically with a boundary can
undergo inelastic collapse and come to rest in a finite time. Here we discuss
the survival probability for the inelastic collapse transition. It is found
that the collapse-time distribution behaves asymptotically as a power-law in
time, and that the exponent governing this decay is non-universal. An
approximate calculation of the collapse-time exponent confirms this behaviour
and shows how inelastic collapse can be viewed as a generalised persistence
phenomenon.


  We study theoretically how electron-phonon interaction affects the energies
and level broadening (inverse lifetime) of Majorana bound states (MBSs) in a
clean topological nanowire at low temperatures. At zero temperature, the energy
splitting between the right and left MBSs remains exponentially small with
increasing nanowire length $L$. At finite temperatures, however, the absorption
of thermal phonons leads to the broadening of energy levels of the MBSs that
does not decay with system length, and the coherent absorption/emission of
phonons at opposite ends of the nanowire results in MBSs energy splitting that
decays only as an inverse power-law in $L$. Both effects remain exponential in
temperature. In the case of quantized transverse motion of phonons, the
presence of Van Hove singularities in the phonon density of states causes
additional resonant enhancement of both the energy splitting and the level
broadening of the MBSs. This is the most favorable case to observe the
phonon-induced energy splitting of MBSs as it becomes much larger than the
broadening even if the topological nanowire is much longer than the coherence
length. We also calculate the charge and spin associated with the energy
splitting of the MBSs induced by phonons. We consider both a spinless
low-energy continuum model, which we evaluate analytically, as well as a
spinful lattice model for a Rashba nanowire, which we evaluate numerically.


  This paper explores the use of geometric algebra to study the Galilean
spacetime and its physical implications. The authors introduce the concept of
geometric algebra and its advantages over tensor algebra for describing
physical phenomena. They define the Galilean-spacetime algebra (GSTA) as a
geometric algebra generated by a four-dimensional vector space with a
degenerate metric. They show how the GSTA can be used to represent Galilean
transformations, rotations, translations, and boosts. The authors also derive
the general form of Galilean transformations in the GSTA and show how they
preserve the scalar product and the pseudoscalar. They develop a tensor
formulation of Galilean electromagnetism using the GSTA and show how it reduces
to the usual Maxwell equations in the non-relativistic limit. They introduce
the concept of Galilean spinors as elements of the minimal left ideals of the
GSTA and show how the Galilean spinors can be used to construct the
Levy-Leblond equation for a free electron and its matrix representation. They
provide a suitable matrix representation for the Galilean gamma matrices and
the Galilean pseudoscalar. They relate the GSTA to the four component dual
numbers introduced by Majernik to express Galilean transformations and show how
the dual numbers can be used to develop a Newton-Cartan theory of gravity. The
paper concludes by summarizing the main results and suggesting some possible
applications and extensions of the GSTA.


  In this paper, we study stable constant mean curvature $H$ surfaces in
$\R^3$. We prove that, in such a surface, the distance from a point to the
boundary is less that $\pi/(2H)$. This upper-bound is optimal and is extended
to stable constant mean curvature surfaces in space forms.


  This paper is devoted to the memory of Professor George M. Zaslavsky passed
away on November 25, 2008. In the field of discrete maps, George M. Zaslavsky
introduced a dissipative standard map which is called now the Zaslavsky map. G.
Zaslavsky initialized many fundamental concepts and ideas in the fractional
dynamics and kinetics. In this paper, starting from kicked damped equations
with derivatives of non-integer orders we derive a fractional generalization of
discrete maps. These fractional maps are generalizations of the Zaslavsky map
and the Henon map. The main property of the fractional differential equations
and the correspondent fractional maps is a long-term memory and dissipation.
The memory is realized by the fact that their present state evolution depends
on all past states with special forms of weights.


  DNA Copy number variation (CNV) has recently gained considerable interest as
a source of genetic variation that likely influences phenotypic differences.
Many statistical and computational methods have been proposed and applied to
detect CNVs based on data that generated by genome analysis platforms. However,
most algorithms are computationally intensive with complexity at least
$O(n^2)$, where $n$ is the number of probes in the experiments. Moreover, the
theoretical properties of those existing methods are not well understood. A
faster and better characterized algorithm is desirable for the ultra high
throughput data. In this study, we propose the Screening and Ranking algorithm
(SaRa) which can detect CNVs fast and accurately with complexity down to O(n).
In addition, we characterize theoretical properties and present numerical
analysis for our algorithm.


  Recent observations revealed a coherence between the spin vector of a galaxy
and the orbital motion of its neighbors. We refer to the phenomenon as "the
spin$-$orbit alignment (SOA)" and explore its physical origin via the
IllustrisTNG simulation. This is the first study to utilize a cosmological
hydrodynamic simulation to investigate the SOA of galaxy pairs. In particular,
we identify paired galaxies at $z = 0$ having the nearest neighbor with mass
ratios from 1/10 to 10 and calculate the spin$-$orbit angle for each pair. Our
results are as follows. (a) There exists a clear preference for prograde
orientations (i.e., SOA) for galaxy pairs, qualitatively consistent with
observations. (b) The SOA is significant for both baryonic and dark matter
spins, being the strongest for gas and the weakest for dark matter. (c) The SOA
is stronger for less massive targets and for targets having closer neighbors.
(d) The SOA strengthens for galaxies in low-density regions, and the signal is
dominated by central$-$satellite pairs in low-mass halos. (e) There is an
explicit dependence of the SOA on the duration of interaction with its current
neighbor. Taken together, we propose that the SOA witnessed at $z = 0$ has been
developed mainly by interactions with a neighbor for an extended period of
time, rather than tidal torque from the ambient large-scale structure.


  Let $M$ be a pseudo-Hermitian homogeneous space of finite volume. We show
that $M$ is compact and the identity component $G$ of the group of holomorphic
isometries of $M$ is compact. If $M$ is simply connected, then even the full
group of holomorphic isometries is compact. These results stem from a careful
analysis of the Tits fibration of $M$, which is shown to have a torus as its
fiber. The proof builds on foundational results on the automorphisms groups of
compact almost pseudo-Hermitian homogeneous spaces. It is known that a compact
homogeneous pseudo-K\"ahler manifold splits as a product of a complex torus and
a rational homogeneous variety, according to the Levi decomposition of $G$.
Examples show that compact homogeneous pseudo-Hermitian manifolds in general do
not split in this way.


  We study the Landau-Ginzburg (LG) mirror theory of the non-linear sigma model
on the ALE space ${\cal M}$ obtained by resolving the singularity of the
orbifold ${\bf C}^2/{\bf Z}_N$. In the LG description, the data of the BPS
spectrum and the lines of marginal stability are encoded in the special
Lagrangian submanifolds of the mirror manifold $\hat{{\cal M}}$. Our LG
description is quite simple as compared with the quiver gauge theory analysis
near the orbifold point. Furthermore our mirror analysis can be applied to any
point on the moduli space of ${\cal M}$.


  Mini-batch sub-sampling (MBSS) is favored in deep neural network training to
reduce the computational cost. Still, it introduces an inherent sampling error,
making the selection of appropriate learning rates challenging. The sampling
errors can manifest either as a bias or variances in a line search. Dynamic
MBSS re-samples a mini-batch at every function evaluation. Hence, dynamic MBSS
results in point-wise discontinuous loss functions with smaller bias but larger
variance than static sampled loss functions. However, dynamic MBSS has the
advantage of having larger data throughput during training but requires the
complexity regarding discontinuities to be resolved. This study extends the
gradient-only surrogate (GOS), a line search method using quadratic
approximation models built with only directional derivative information, for
dynamic MBSS loss functions. We propose a gradient-only approximation line
search (GOALS) with strong convergence characteristics with defined optimality
criterion. We investigate GOALS's performance by applying it on various
optimizers that include SGD, RMSprop and Adam on ResNet-18 and EfficientNetB0.
We also compare GOALS's against the other existing learning rate methods. We
quantify both the best performing and most robust algorithms. For the latter,
we introduce a relative robust criterion that allows us to quantify the
difference between an algorithm and the best performing algorithm for a given
problem. The results show that training a model with the recommended learning
rate for a class of search directions helps to reduce the model errors in
multimodal cases.


  Non-compact QED3 is simulated both in the quenched and unquenched cases. In
particular, we investigate the restoration of chiral symmetry at finite
temperature. We also compute the zero temperature spectrum of the theory,
including (in the quenched case) the dynamical fermion mass. From these two set
of data, one can obtain estimates for the ratio of the mass gap to the critical
temperature, of particular interest for applications to high-Tc
superconductivity.


  Dimension reduction lies at the heart of many statistical methods. In
regression, dimension reduction has been linked to the notion of sufficiency
whereby the relation of the response to a set of predictors is explained by a
lower dimensional subspace in the predictor space. In this paper, we consider
the notion of a dimension reduction in regression on subspaces that are
sufficient to explain interaction effects between predictors and another
variable of interest. The motivation for this work is from precision medicine
where the performance of an individualized treatment rule, given a set of
pretreatment predictors, is determined by interaction effects.


  We describe a simple experimental apparatus for laser ablation of barium
monohydride (BaH) molecules and the study of their rovibrational spectra that
are relevant to direct laser cooling. We present a detailed analysis of the
properties of ablation plumes that can improve the understanding of surface
ablation and deposition technologies. A range of absorption spectroscopy and
collisional thermalization regimes has been studied. We directly measured the
Franck-Condon factor of the
$\mathrm{B}^2\Sigma^+(v'=0)\leftarrow\mathrm{X}^2\Sigma^+(v"=1)$ transition.
Prospects for production of a high luminosity cryogenic BaH beam are outlined.
This molecule is a promising candidate for laser cooling and ultracold
fragmentation, both of which are precursors to novel experiments in many-body
physics and precision measurement.


  We present detailed neutron scattering studies of the static and dynamic
stripes in an optimally doped high-temperature superconductor,
La$_2$CuO$_{4+y}$. We find that the dynamic stripes do not disperse towards the
static stripes in the limit of vanishing energy transfer. We conclude that the
dynamic stripes observed in neutron scattering experiments are not the
Goldstone modes associated with the broken symmetry of the simultaneously
observed static stripes, but rather that the signals originate from different
domains in the sample. These domains may be related by structural twinning, or
may be entirely different phases, where the static stripes in one phase are
pinned versions of the dynamic stripes in the other. Our results explain
earlier observations of unusual dispersions in underdoped
La$_{2-x}$Sr$_x$CuO$_{4}$ ($x=0.07$) and La$_{2-x}$Ba$_x$CuO$_{4}$ ($x=0.095$).
Our findings are relevant for all compounds exhibiting magnetic stripes, and
may thus be a vital part in unveiling the nature of high temperature
superconductivity.


  Isometries are ubiquitous in nature; isometries of discrete (quantized)
objects---abstracted as the group of isometries of $\mathbb{Z}^n$ denoted by
$\mathsf{ISO}(\mathbb{Z}^n)$---are important concepts in the computational
world. In this paper, we compute various isometric invariances which
mathematically are orbit-computation problems under various isometry-subgroup
actions $H \curvearrowright \mathbb{Z}^n, H \leq \mathsf{ISO}(\mathbb{Z}^n)$.
One computational challenge here is about the \emph{infinite}: in general, we
can have an infinite subgroup acting on $\mathbb{Z}^n$, resulting in possibly
an infinite number of orbits of possibly infinite size. In practice, we
restrict the set of orbits (a partition of $\mathbb{Z}^n$) to a finite subset
$Z \subseteq \mathbb{Z}^n$ (a partition of $Z$), where $Z$ is specified a
priori by an application domain or a data set. Our main contribution is an
efficient algorithm to solve this \emph{restricted} orbit-computation problem
in the special case of \emph{atomically generated subgroups}---a new notion
partially motivated from interpretable AI. The atomic property is key to
preserving the \emph{semidirect-product structure}---the core structure we
leverage to make our algorithm outperform generic approaches. Besides
algorithmic merit, our approach enables \emph{parallel-computing}
implementations in many subroutines, which can further benefit from hardware
boosts. Moreover, our algorithm works efficiently for \emph{any} finite subset
($Z$) regardless of the shape (continuous/discrete, (non)convex) or location;
so it is application-independent.


  We consider some metrics and weak metrics defined on the Teichmueller space
of a surface of finite type with nonempty boundary, that are defined using the
hyperbolic length spectrum of simple closed curves and of properly embedded
arcs, and we compare these metrics and weak metrics with the Teichm\"uller
metric. The comparison is on subsets of Teichm\"uller space which we call
"$\epsilon_0$-relative $\epsilon$-thick parts", and whose definition depends on
the choice of some positive constants $\epsilon_0$ and $\epsilon$. Meanwhile,
we give a formula for the Teichm\"uller metric of a surface with boundary in
terms of extremal lengths of families of arcs.


  We apply Vojta's conjecture to blowups and deduce a number of deep statements
regarding (generalized) greatest common divisors on varieties, in particular on
projective space and on abelian varieties. Special cases of these statements
generalize earlier results and conjectures. We also discuss the relationship
between generalized greatest common divisors and the divisibility sequences
attached to algebraic groups, and we apply Vojta's conjecture to obtain a
strong bound on the divisibility sequences attached to abelian varieties of
dimension at least two.


  The Trojan Horse (TH) method is a powerful indirect technique that provides
information to determine astrophysical factors for rearrangement processes at
astrophysically relevant energies. A short coming for understanding the
reliability of the technique has been determining the importance of nuclear and
Coulomb effects on the energy dependence of the yield. Using a simple model, we
demonstrate that off-energy-shell and Coulomb effects in the entry channel and
the final state nuclear interactions do not change the energy dependence of the
astrophysical factor extracted from the TH reaction. Some examples are
presented.


  The speed-up provided by quantum algorithms with respect to their classical
counterparts is at the origin of scientific interest in quantum computation.
However, the fundamental reasons for such a speed-up are not yet completely
understood and deserve further attention. In this context, the classical
simulation of quantum algorithms is a useful tool that can help us in gaining
insight. Starting from the study of general conditions for classical
simulation, we highlight several important differences between two
non-equivalent classes of quantum algorithms. We investigate their performance
under realistic conditions by quantitatively studying their resilience with
respect to static noise. This latter refers to errors affecting the inital
preparation of the register used to run an algorithm. We also compare the
evolution of the entanglement involved in the different computational
processes.


  The meson eigenstates of the light-cone Hamiltonian in a coarse transverse
lattice gauge theory are investigated. Building upon previous work in pure
gauge theory, the Hamiltonian and its Fock space are expanded in powers of
dynamical fields. In the leading approximation, the couplings appearing in the
Hamiltonian are renormalised by demanding restoration of space-time symmetries
broken by the cut-off. Additional requirements from chiral symmetry are
discussed and difficulties in imposing them from first principles in the
leading approximation are noted. A phenomenological calculation is then
performed, in which chiral symmetry in spontaneously broken form is modelled by
imposing the physical pion-rho mass splitting as a constraint. The light-cone
wavefunctions of the resulting Hamiltonian are used to compute decay constants,
form factors and quark momentum and spin distributions for the pion and rho
mesons. Extensions beyond leading order, and the implications for first
principles calculations, are briefly discussed.


  Let f(m,n) denote the number of relatively prime subsets of {m+1,m+2,...,n},
and let Phi(m,n) denote the number of subsets A of {m+1,m+2,...,n} such that
gcd(A) is relatively prime to n. Let f_k(m,n) and Phi_k(m,n) be the analogous
counting functions restricted to sets of cardinality k. Simple explicit
formulas and asymptotic estimates are obtained for these four functions.


  We discuss results stemming from observations of the white-light and [Fe XIV]
emission corona during the total eclipse of the Sun of 2008 August 1, in
Mongolia (Altaj region) and in Russia (Akademgorodok, Novosibirsk, Siberia).
Corresponding to the current extreme solar minimum, the white-light corona,
visible up to 20 solar radii, was of a transient type with well-pronounced
helmet streamers situated above a chain of prominences at position angles 48,
130, 241 and 322 degrees. A variety of coronal holes, filled with a number of
thin polar plumes, were seen around the poles. Furthering an original method of
image processing, stars up to 12 magnitude, a Kreutz-group comet (C/2008 O1),
and a coronal mass ejection (CME) were also detected, with the smallest
resolvable structures being of, and at some places even less than, 1 arcsec.
Differences, presumably motions, in the corona and prominences are seen even
with the 19-min time difference between our sites. In addition to the
high-resolution coronal images, which show the continuum corona (K-corona) that
results from electron scattering of photospheric light, images of the
overlapping green-emission-line (530.3 nm, [Fe XIV]) corona were obtained with
the help of two narrow-passband filters (centered on the line itself and for
the continuum in the vicinity of 529.1 nm, respectively), each with FWHM of
0.15 nm. Through solar observations, on whose scheduling and details we
consulted, with the Solar and Heliospheric Observatory, Hinode's XRT and SOT,
TRACE, and STEREO, as well as Wilcox Solar Observatory and SOHO/MDI
magnetograms, we set our eclipse observations in the context of the current
unusually low and prolonged solar minimum.


  The applicability of the effective models to the description of baryons and
the behaviour of ratios of strange baryons to pions is discussed. In the
framework of the EPNJL model, the Bethe - Salpeter equation is used to find
masses of baryons, which are considered as diquark-quark state. Baryon melting
is discussed at a finite chemical potential and a flavor dependence of the
hadronic deconfinement temperature is pointed. It is shown that the description
of the diquark-quark state at finite chemical potential is limited due to the
occurrence of the Bose condensate. This effect is strongly manifested in the
description of light diquarks and baryons. Both $\Lambda^0/\pi^+$ and
$\Xi^-/\pi^+$ ratios show a sharp behaviour as functions of $T/\mu_B$ variable,
where T and $\mu_B$ are calculated along the melting lines.


  In this paper we explore the life expectancy at birth in the Netherlands by
based on a recent theory and a new methodology but also a classical theory of
fitting and forecasting. We use the data from 1850 to 2006 provided by the
Human Mortality Database (HMD) for the annual deaths per year of age and the
structure of the population per year of age. We apply the IM first exit time
model which includes also the infant mortality by using the appropriate
non-linear regression analysis program that we have developed in Excel. We
provide all the related material from the website: http://www.cmsim.net


  Let $S$ be a locally Noetherian normal scheme and $\blacklozenge/S$ a set of
properties of $S$-schemes. Then we shall write Sch$_{\blacklozenge/S}$ for the
full subcategory of the category of $S$-schemes Sch$_{/S}$ determined by the
objects $X\in {\rm Sch}_{\blacklozenge/S}$ that satisfy every property of
$\blacklozenge/S$. In the present paper, we shall mainly be concerned with the
properties "reduced", "quasi-compact over $S$", "quasi-separated over $S$", and
"separated over $S$". We give a functorial category-theoretic algorithm for
reconstructing $S$ from the intrinsic structure of the abstract category
Sch$_{\blacklozenge/S}$. This result is analogous to a result of Mochizuki
\cite{Mzk04} and may be regarded as a partial generalization of a result of de
Bruyn \cite{deBr19} in the case where $S$ is a locally Noetherian normal
scheme.


  Large deviation theory and instanton calculus for stochastic systems are
widely used to gain insight into the evolution and probability of rare events.
At its core lies the realization that rare events are, under the right
circumstances, dominated by their least unlikely realization. Their computation
through a saddle-point approximation of the path integral for the corresponding
stochastic field theory then reduces an inefficient stochastic sampling problem
into a deterministic optimization problem: finding the path of smallest action,
the instanton. In the presence of heavy tails, though, standard algorithms to
compute the instanton critically fail to converge. The reason for this failure
is the divergence of the scaled cumulant generating function (CGF) due to a
non-convex large deviation rate function. We propose a solution to this problem
by "convexifying" the rate function through nonlinear reparametrization of the
observable, which allows us to compute instantons even in the presence of
super-exponential or algebraic tail decay. The approach is generalizable to
other situations where the existence of the CGF is required, such as
exponential tilting in importance sampling for Monte-Carlo algorithms. We
demonstrate the proposed formalism by applying it to rare events in several
stochastic systems with heavy tails, including extreme power spikes in fiber
optics induced by soliton formation.


  We describe the isomorphism classes of infinite-dimensional graded Lie
algebras of maximal class, generated by elements of weight one, over fields of
odd characteristic.


  Crisis response is a critical area of research, with encouraging progress in
the past view yeas. The aim of the research is to contribute to building future
crisis environment where software agents, robots, responders, crisis managers,
and crisis organizations interact to provide advice, protection and aid. This
paper discusses the crisis response domain requirements, and provides analysis
of five crisis response systems namely: DrillSim [2], DEFACTO [15], ALADDIN
[1], RoboCup Rescue [18], and FireGrid [3]. Analysis of systems includes
systems architecture and methodology. In addition, we identified features and
limitations of systems based on crisis response domain requirements.


  The spectral features observed in kilonovae (KNe) reveal the elemental
composition and the velocity structures of matter ejected from neutron star
mergers. In the spectra of the kilonova AT2017gfo, a P Cygni line at about
1$\mu$m has been linked to Sr II, providing the first direct evidence of
freshly synthesised $r$-process material. An alternative explanation to Sr II
was proposed - He I $\lambda 1083.3$nm under certain
non-local-thermodynamic-equilibrium (NLTE) conditions. A key way to robustly
discriminate between these identifications, and indeed other proposed
identifications, is to analyse the temporal emergence and evolution of the
feature. In this analysis we trace the earliest appearance of the observed
feature and detail its spectro-temporal evolution, which we compare with a
collisional-radiative model of helium. We show that the 1$\mu$m P Cygni line is
inconsistent with a He I interpretation both in emergence time and in
subsequent spectral evolution. Self-consistent helium masses cannot reproduce
the observed feature, due to the diminishing strength of radiative pathways
leaving triplet helium.


  Let $X$ be a compact hyperk\"ahler manifold with a Lagrangian fibration
$\pi\colon X\to B$. A Shafarevich-Tate twist of $X$ is a holomorphic symplectic
manifold with a Lagrangian fibration $\pi^\varphi\colon X^\varphi\to B$ which
is isomorphic to $\pi$ locally over the base. In particular, $\pi^\varphi$ has
the same fibers as $\pi$. A twist $X^\varphi$ corresponds to an element
$\varphi$ in the Shafarevich-Tate group of $X$. We show that $X^\varphi$ is
K\"ahler when a multiple of $\varphi$ lies in the connected component of unity
of the Shafarevich-Tate group and give a necessary condition for $X^\varphi$ to
be bimeromorphic to a K\"ahler manifold.


  The process of a positron $\unicode{x2013}$ bound-electron annihilation with
simultaneous emission of two photons is investigated theoretically. A fully
relativistic formalism based on $\textit{ab initio}$ QED description of the
process is worked out. The developed approach is applied to evaluate the
annihilation of a positron with $K$-shell electrons of a silver atom, for which
a strong contradiction between theory and experiment was previously stated. The
results obtained here resolve this long-standing disagreement and, moreover,
demonstrate a sizeable difference with approaches so far used for calculations
of the positron $\unicode{x2013}$ bound-electron annihilation process, namely,
the $\textit{Lee's}$ and $\textit{impulse}$ approximations.


  New developments concerning the extension of the Feynman diagram analyzer
DIANA are presented. We discuss new graphics facilities, different approaches
to automation of momenta distribution and parallel processing facilities.
Furthermore applications to $t\bar t$ production and Bhabha scattering are
shortly discussed.


  The force induced unzipping transition of a double stranded DNA is considered
from a purely thermodynamic point of view. This analysis provides us with a set
of relations that can be used to test microscopic theories and experiments. The
thermodynamic approach is based on the hypothesis of impenetrability of the
force in the zipped state. The melting and the unzipping transitions are
considered in the same framework and compared with the existing statistical
model results. The analysis is then extended to a possible continuous unzipping
transition.


  A phenomenological model of the Landau type forms the basis for a study of
elastic distortions near the spin-Peierls transition $T_c$ in $CuGeO_3$. The
atomic displacements proposed by Hirota {\it et al.} [Phys. Rev. Lett. {\bf
73}, 736 (1994)] are accounted for by the model which includes linear coupling
between $Cu$ and $O$ distortions. $Cu$ displacements are seen to be responsible
for anomalies in the elastic properties {\it at} $T_c$, whereas incipient $O$
distortions give rise to temperature dependence below $T_c$. A discussion of
possible critical behavior is also made.


  Deposition of Au on vicinal Si(553) surfaces results in the self-assembly of
one-dimensional (1D) Au atomic wires. Charge transfer from the Au wire to the
Si step edge leads to a chain of Si danglingbond orbitals with a long range
ordered threefold periodicity along the steps and infinite interchain
interaction perpendicular to the steps. Employing spot-profile analysis
low-energy electron diraction (SPA-LEED) we observed a broadening of spot width
with time, reflecting the degradation of Si dangling bond chain and Au wire
length. Adsorbates were identified as primary source for spot broadening. They
force the generation of solitons and anti-solitons which immediately destroy
the long-range order along and perpendicular to the steps, respectively. From
the temporal evolution of broadening, we conclude that the Au wires are less
reactive to adsorption than the Si dangling bond chains.


  We theoretically analyze a scheme for fast stabilization of arbitrary qubit
states with high fidelities, extending a protocol recently demonstrated
experimentally [Lu et al., Phys. Rev. Lett. 119, 150502 (2017)]. That
experiment utilized red and blue sideband transitions in a system composed of a
fluxonium qubit, a low-Q LC-oscillator, and a coupler enabling us to tune the
interaction between them. Under parametric modulations of the coupling
strength, the qubit can be steered into any desired pure or mixed single-qubit
state. For realistic circuit parameters, we predict that stabilization can be
achieved within 100 ns. By varying the ratio between the oscillator's damping
rate and the effective qubit-oscillator coupling strength, we can switch
between under-damped, critically-damped, and over-damped stabilization and find
optimal working points. We further analyze the effect of thermal fluctuations
and show that the stabilization scheme remains robust for realistic
temperatures.


  The study of fast radio bursts (FRBs) is of great importance, and is a topic
that has been extensively researched, particularly in recent years. While the
extreme nature of FRBs can serve as a tool for researchers to probe the
intergalactic medium and study exotic aspects of the Universe, keeping track of
FRB properties is challenged by the frequent detection of new bursts. We
introduce the FRBSTATS platform, which provides an up-to-date and user-friendly
web interface to an open-access catalogue of published FRBs, along with a
statistical overview of the observed events. The platform supports the
retrieval of fundamental FRB data either directly through the FRBSTATS API, or
in the form of a CSV/JSON-parsed database, while enabling the plotting of
parameters and their distributions, for a variety of visualizations. These
features allow researchers to conduct population studies and comparisons with
astrophysical models, describing the origin and emission mechanism behind these
sources. So far, the inferred redshift estimates of 813 bursts have been
computed, providing the first public database that includes redshift estimates
inferred from dispersion measure entries for nearly all observed FRBs, as well
as host redshifts (where available). Lastly, the platform provides a
visualization tool that illustrates associations between primary bursts and
repeaters, complementing basic repeater information provided by the Transient
Name Server. In this work, we present the structure of the platform, the
established version control system, as well as the strategy for keeping such an
open database up to date. Additionally, we introduce a novel,
computationally-efficient, clustering-based approach that enables unsupervised
classification of hundreds of bursts into repeaters and non-repeaters,
resulting in the discovery of one new FRB repeater.


  We demonstrate how a morphological veto involving Bayesian statistics can
improve the receiver-operating characteristic (ROC) curves of the current
search for core-collapse supernovae (CCSNe) as implemented by the coherent
Waveburst (cWB) algorithm. Examples involving two implementations of BayesWave
(BW), one that makes no assumption of the polarization state of the
gravitational wave (GW) and one that uses the same elliptical polarization
settings adopted in previous usages for Binary systems are provided on the set
of waveforms currently adopted for the first and second Advanced LIGO (aLIGO)
science runs for the targeted CCSNe search. A comparison of the performance for
all-sky searches versus the targeted searches with optical triggers is
provided. The average cWB+BW ROC range improvements with respect to a fixed
false-alarm rate (FAR) for slowly-rotating waveforms ranged from [+1.30%,
+15.76%] while the improvement for rapidly-rotating waveforms were on the order
of [+1.19%, +22.05%]. The application of BW to CCSN GW triggers also shows a
significant reduction of the FAR while maintaining detection efficiency and
remaining sensitive to a wide range of morphological CCSNe signals. It appears
that the code developed for arbitrarily polarized signals outperforms the
previous code for the GW morphologies tested.


  We study isovector collective excitations in nuclear matter by employing the
linearized Landau-Vlasov equation with and without a non-Markovian binary
collision term at finite temperature. We calculate the giant dipole resonance
(GDR) strength function for finite nuclei using Steinwedel-Jensen model and
also by Thomas-Fermi approximation, and we compare them for 120Sn and 208Pb
with experimental results.


  In this paper, we propose an outlier-robust regularized kernel-based method
for linear system identification. The unknown impulse response is modeled as a
zero-mean Gaussian process whose covariance (kernel) is given by the recently
proposed stable spline kernel, which encodes information on regularity and
exponential stability. To build robustness to outliers, we model the
measurement noise as realizations of independent Laplacian random variables.
The identification problem is cast in a Bayesian framework, and solved by a new
Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the
representation of the Laplacian random variables as scale mixtures of
Gaussians, we design a Gibbs sampler which quickly converges to the target
distribution. Numerical simulations show a substantial improvement in the
accuracy of the estimates over state-of-the-art kernel-based methods.


  The method of nonlinear realizations is used to clarify some conceptual and
technical issues related to the Schwarzian mechanics. It is shown that the
Schwarzian derivative arises naturally, if one applies the method to SL(2,R)
times R group and decides to keep the number of the independent Goldstone
fields to a minimum. The Schwarzian derivative is linked to the invariant
Maurer-Cartan one-forms, which make its SL(2,R)-invariance manifest. A
Lagrangian formulation for a variant of the Schwarzian mechanics studied
recently in [Nucl. Phys. B 936 (2018) 661] is built and its geometric
description in terms of 4d metric of the ultrahyperbolic signature is given.


  We study the interpolation sets for the Hardy-Sobolev spaces defined on the
unit ball of ${\bf C}^n$. We begin by giving a natural extension to ${\bf C}^n$
of the condition that is known to be necessay and sufficient for interpolation
sets lying on the boundary of the unit disc. We show that under this condition
the restriction of a function in the Hardy-Sobolev space to the set always
exists, and lies in a Besov space. We then show that under the assumption that
there is an holomorphic distance function for the set, there is an extension
operator from these spaces to the Hardy-Sobolev ones.


  We present two versions of the Egorov theorem for orbifolds. The first one is
a straightforward extension of the classical theorem for smooth manifolds. The
second one considers an orbifold as a singular manifold, the orbit space of a
Lie group action, and deals with the corresponding objects in noncommutative
geometry.


  Knowledge distillation facilitates the training of a compact student network
by using a deep teacher one. While this has achieved great success in many
tasks, it remains completely unstudied for image-based 6D object pose
estimation. In this work, we introduce the first knowledge distillation method
driven by the 6D pose estimation task. To this end, we observe that most modern
6D pose estimation frameworks output local predictions, such as sparse 2D
keypoints or dense representations, and that the compact student network
typically struggles to predict such local quantities precisely. Therefore,
instead of imposing prediction-to-prediction supervision from the teacher to
the student, we propose to distill the teacher's \emph{distribution} of local
predictions into the student network, facilitating its training. Our
experiments on several benchmarks show that our distillation method yields
state-of-the-art results with different compact student models and for both
keypoint-based and dense prediction-based architectures.


  We present two independent measurements of stellar velocity dispersions (
$\sigma_\rm{\star}$ ) from the Ca\,H+K \& Mg\,\textsc{i} region
(3880--5550~\AA) and the Calcium Triplet region (CaT, 8350--8750~\AA) for 173
hard X-ray-selected Type 1 AGNs ($z \leq$ 0.08) from the 105-month Swift-BAT
catalog. We construct one of the largest samples of local Type 1 AGNs that have
both single-epoch (SE) 'virial' black hole mass ($M_\rm{BH}$) estimates and
$\sigma_\rm{\star}$ measurements obtained from high spectral resolution data,
allowing us to test the usage of such methods for SMBH studies. We find that
the two independent $\sigma_\rm{\star}$ measurements are highly consistent with
each other, with an average offset of only $0.002\pm0.001$ dex. Comparing
$M_\rm{BH}$ estimates based on broad emission lines and stellar velocity
dispersion measurements, we find that the former is systematically lower by
$\approx$0.12 dex. Consequently, Eddington ratios estimated through broad-line
$M_\rm{BH}$ determinations are similarly biased (but in the opposite way). We
argue that the discrepancy is driven by extinction in the broad-line region
(BLR). We also find an anti-correlation between the offset from the $M_\rm{BH}$
- $\sigma_\rm{\star}$ relation and the Eddington ratio. Our sample of Type 1
AGNs shows a shallower $M_\rm{BH}$ - $\sigma_\rm{\star}$ relation (with a power
law exponent of $\approx$3.5) compared with that of inactive galaxies (with a
power-law exponent of $\approx$4.5), confirming earlier results obtained from
smaller samples.


  For each $n \geq -1$, a quasi-category is said to be $n$-truncated if its
hom-spaces are $(n-1)$-types. In this paper we study the model structure for
$n$-truncated quasi-categories, which we prove can be constructed as the
Bousfield localisation of Joyal's model structure for quasi-categories with
respect to the boundary inclusion of the $(n+2)$-simplex. Furthermore, we prove
the expected Quillen equivalences between categories and $1$-truncated
quasi-categories and between $n$-truncated quasi-categories and Rezk's
$(n,1)$-$\Theta$-spaces.


  Effective machine learning models can automatically learn useful information
from a large quantity of data and provide decisions in a high accuracy. These
models may, however, lead to unfair predictions in certain sense among the
population groups of interest, where the grouping is based on such sensitive
attributes as race and gender. Various fairness definitions, such as
demographic parity and equalized odds, were proposed in prior art to ensure
that decisions guided by the machine learning models are equitable.
Unfortunately, the "fair" model trained with these fairness definitions is
threshold sensitive, i.e., the condition of fairness may no longer hold true
when tuning the decision threshold. This paper introduces the notion of
threshold invariant fairness, which enforces equitable performances across
different groups independent of the decision threshold. To achieve this goal,
this paper proposes to equalize the risk distributions among the groups via two
approximation methods. Experimental results demonstrate that the proposed
methodology is effective to alleviate the threshold sensitivity in machine
learning models designed to achieve fairness.


  We present SU(3) gluon propagators calculated on 48*48*48*N_t lattices at
beta=6.8 where N_t=64 (corresponding the confinement phase) and N_t=16
(deconfinement) with the bare gauge parameter,alpha, set to be 0.1. In order to
avoid Gribov copies, we employ the stochastic gauge fixing algorithm. Gluon
propagators show quite different behavior from those of massless gauge fields:
(1) In the confinement phase, G(t) shows massless behavior at small and large
t, while around 5<t<15 it behaves as massive particle, and (2) effective mass
observed in G(z) becomes larger as z increases. (3) In the deconfinement phase,
G(z) shows also massive behavior but effective mass is less than in the
confinement case. In all cases, slope masses are increasing functions of t or
z, which can not be understood as addtional physical poles.


  Due to its proximity, the mass of the supermassive black hole in the nucleus
of Andromeda galaxy (M31), the most massive black hole in the Local Group of
galaxies, has been measured by several methods involving the kinematics of a
stellar disk that surrounds it. We report here the discovery of an eccentric
Halpha emitting disk around the black hole at the center of M31 and show how
modeling this disk can provide an independent determination of the mass of the
black hole. Our model implies a mass of 5.0_{-1.0}^{+0.8} x 10^7 Mo for the
central black hole, consistent with the average of determinations by methods
involving stellar dynamics, and compatible (at 1-sigma level) with measurements
obtained from the most detailed models of the stellar disk around the central
black hole. This value is also consistent with the M-sigma relation. In order
to make a comparison, we applied our simulation on the stellar kinematics in
the nucleus of M31 and concluded that the parameters obtained for the stellar
disk are not formally compatible with the parameters obtained for the Halpha
emitting disk. This result suggests that the stellar and the Halpha emitting
disks are intrinsically different from each other. A plausible explanation is
that the Halpha emission is associated with a gaseous disk. This hypothesis is
supported by the detection of traces of weaker nebular lines in the nuclear
region of M31. However, we cannot exclude the possibility that the Halpha
emission is, at least partially, generated by stars.


  We explore the occurrence and detectability of planet-planet occultations
(PPOs) in exoplanet systems. These are events during which a planet occults the
disk of another planet in the same system, imparting a small photometric signal
as its thermal or reflected light is blocked. We focus on the planets in
TRAPPIST-1, whose orbital planes we show are aligned to within 0.3 degrees at
90% confidence. We present a photodynamical model for predicting and computing
PPOs in TRAPPIST-1 and other systems for various assumptions of the planets'
atmospheric states. When marginalizing over the uncertainties on all orbital
parameters, we find that the rate of PPOs in TRAPPIST-1 is about 1.4 per day.
We investigate the prospects for detection of these events with the James Webb
Space Telescope, finding that ~10-20 occultations per year of b and c should be
above the noise level at 12-15 microns. Joint modeling of several of these PPOs
could lead to a robust detection. Alternatively, observations with the proposed
Origins Space Telescope should be able to detect individual PPOs at high
signal-to-noise. We show how PPOs can be used to break transit timing variation
degeneracies, imposing strong constraints on the eccentricities and masses of
the planets, as well as to constrain the longitudes of nodes and thus the
complete three-dimensional structure of the system. We further show how
modeling of these events can be used to reveal a planet's day/night temperature
contrast and construct crude surface maps. We make our photodynamical code
available on github.


  We present the ETMC results for the bag parameters describing the neutral
kaon mixing in the Standard Model and beyond and preliminary results for the
bag parameters controlling the short distance contributions in the
D^0-\bar{D}^0 oscillations. We also present preliminary results for the B_{Bd},
B_{Bs}, B_{Bs}/B_{Bd} and \xi -parameter controlling B^0_-\bar{B}^0
oscillations in the Standard Model employing the so-called ratio method. Using
Nf=2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks we
achieve both O(a)-improvement and continuum like renormalization pattern.
Simulations are performed at three-values of the lattice spacing and several
values of quark masses in the light, strange, charm region and above charm up
to ~2.5m_c. Our results are extrapolated to the continuum limit and
extrapolated/interpolated to the physical quark masses.


  An integrated microscope that combines different optical techniques for
simultaneous imaging is demonstrated. The microscope enables spectral-domain
optical coherence microscopy based on optical backscatter, and multi-photon
microscopy for the detection of two-photon fluorescence and second harmonic
generation signals. The unique configuration of this integrated microscope
allows for the simultaneous acquisition of both anatomical (structural) and
functional imaging information with particular emphasis for applications in the
fields of tissue engineering and cell biology. In addition, the contemporary
analysis of the spectroscopic features can enhance contrast by differentiating
among different tissue components.


  In the realistic model of cosmic inflation the inflaton potential should be
flat and stable under quantum corrections. It is natural to imagine that there
is some symmetry behind and an idea of the inflaton as a Nambu-Goldstone boson
of spontaneous breaking of some symmetry has been examined. We give a general
formulation of this idea using the non-linear realization of Nambu-Goldstone
boson in low-energy effective theory with some explicit symmetry breaking to
generate non-trivial potential. The potential is naturally a simple function,
typically the mass term of inflaton, and the scenario of "warm inflation"
should necessarily be applied under the present observational constraints. We
investigate the generation mechanism of necessary thermal dissipation term in
inflaton field equation for "warm inflation" without large thermal corrections
to inflaton potential. A simple numerical analysis is given to investigate the
viability of this scenario.


  Compute-and-forward (CF) harnesses interference in wireless communications by
exploiting structured coding. The key idea of CF is to compute integer
combinations of codewords from multiple source nodes, rather than to decode
individual codewords by treating others as noise. Compute-compress-and-forward
(CCF) can further enhance the network performance by introducing compression
operations at receivers. In this paper, we develop a more general compression
framework, termed generalized compute-compress-and-forward (GCCF), where the
compression function involves multiple quantization-and-modulo lattice
operations. We show that GCCF achieves a broader compression rate region than
CCF. We also compare our compression rate region with the fundamental
Slepian-Wolf (SW) region. We show that GCCF is optimal in the sense of
achieving the minimum total compression rate. We also establish the criteria
under which GCCF achieves the SW region. In addition, we consider a two-hop
relay network employing the GCCF scheme. We formulate a sum-rate maximization
problem and develop an approximate algorithm to solve the problem. Numerical
results are presented to demonstrate the performance superiority of GCCF over
CCF and other schemes.


  The possibility of thermal and quantum fluctuations induced attractive
interaction leading to a pairing gap \Delta_tq in the single-particle spectrum
of d-p model in the limit of a large N of fermion flavor is investigated
analytically. This is an anomalous pairing gap in addition to the one with
d-wave symmetry originating from partially screened, inter-site coulomb
interaction. The motivation was to search for a hierarchy of multiple many-body
interaction scales in high-Tc superconductor as suggested by recent
experimental findings. The pairing gap anisotropy stems from more than one
sources, namely, nearest neighbour hoppings and the p-d hybridization but not
the coupling of the effective interaction. The temperature at which \Delta_tq
vanishes may be driven to zero by using a tuning parameter to have access to
quantum criticality only when N >> 1. For the physical case N = 2, the usual
coherent quasi-particle feature surfaces in the spectral weight everywhere in
the momentum space below the pairing gap \Delta_tq. Thus it appears that the
reduction in spin degeneracy has the effect of masking quantum criticality.


  The paradigms of transformational planning, case-based planning, and plan
debugging all involve a process known as plan adaptation - modifying or
repairing an old plan so it solves a new problem. In this paper we provide a
domain-independent algorithm for plan adaptation, demonstrate that it is sound,
complete, and systematic, and compare it to other adaptation algorithms in the
literature. Our approach is based on a view of planning as searching a graph of
partial plans. Generative planning starts at the graph's root and moves from
node to node using plan-refinement operators. In planning by adaptation, a
library plan - an arbitrary node in the plan graph - is the starting point for
the search, and the plan-adaptation algorithm can apply both the same
refinement operators available to a generative planner and can also retract
constraints and steps from the plan. Our algorithm's completeness ensures that
the adaptation algorithm will eventually search the entire graph and its
systematicity ensures that it will do so without redundantly searching any
parts of the graph.


  Time series are characterized by complex memory and/or distribution patterns.
In this letter we show that models obeying to different statistics may equally
reproduce some pattern of a time series. In particular we discuss the
difference between L\'evy-walk and fractal Gaussian intermittent signals and
show that the adoption of complementary scaling analysis techniques may be
useful to distinguish the two cases. Finally, we apply this methodology to the
earthquake occurrences in California and suggest the possibility that
earthquake occurrences are described by a \textit{colored} (= `long-range
correlated') Generalized Poisson model.


  We establish a relation between two hallmarks of integrable systems: the
relaxation towards the generalized Gibbs ensemble (GGE) and the dissipationless
charge transport. We show that the former one is possible only if the so called
Mazur bound on the charge stiffness is saturated by local conserved quantities.
As an example we show how a non--GGE steady state with a current can be
generated in the one-dimensional model of interacting spinless fermions with a
flux quench. Moreover an extended GGE involving the quasi-local conserved
quantities can be formulated for this case.


  Non-deterministic measurements are common in real-world scenarios: the
performance of a stochastic optimization algorithm or the total reward of a
reinforcement learning agent in a chaotic environment are just two examples in
which unpredictable outcomes are common. These measures can be modeled as
random variables and compared among each other via their expected values or
more sophisticated tools such as null hypothesis statistical tests. In this
paper, we propose an alternative framework to visually compare two samples
according to their estimated cumulative distribution functions. First, we
introduce a dominance measure for two random variables that quantifies the
proportion in which the cumulative distribution function of one of the random
variables stochastically dominates the other one. Then, we present a graphical
method that decomposes in quantiles i) the proposed dominance measure and ii)
the probability that one of the random variables takes lower values than the
other. With illustrative purposes, we re-evaluate the experimentation of an
already published work with the proposed methodology and we show that
additional conclusions (missed by the rest of the methods) can be inferred.
Additionally, the software package RVCompare was created as a convenient way of
applying and experimenting with the proposed framework.


  We discuss how small neutrino rest masses can increase the expansion rate
near the photon decoupling epoch in the early universe, causing an earlier,
higher temperature freeze-out for ionization equilibrium compared to the
massless neutrino case. This yields a larger free-electron fraction. A larger
ratio of the sound horizon to the photon diffusion length follows, implying a
smaller inferred Neff. This neutrino-mass/recombination effect depends strongly
on the neutrino rest masses. Though below current sensitivity, this effect
could be probed by next-generation cosmic microwave background experiments,
giving an observational handle of neutrino mass physics.


  The distinct methods for measuring topological charge in a non-abelian
anyonic system have been discussed in the literature: projective measurement of
a single point-like quasiparticle and interferometric measurement of the total
topological charge of a group of quasiparticles. Projective measurement by
definition is only applied near a point and will project to a topological
charge sector near that point. Thus, if it is to be applied to a \emph{group}
of anyons to project to a \emph{total} charge, then the anyons must first be
fused one by one to obtain a single anyon carrying the collective charge. We
show that interferometric measurement is strictly stronger: Any protocol
involving projective measurement can be simulated at low overhead by another
protocol involving only interferometric measurement.


  Systems of on-off detectors are well established for measuring radiation
fields in the regime of small photon numbers. We propose to combine these
detector systems with unbalanced homodyning with a weak local oscillator. This
approach yields phase-space functions, which represent the click counterpart of
the s parametrized quasiprobabilities of standard photoelectric detection
theory. This introduced class of distributions can be directly sampled from the
measured click counting statistics. Therefore, our technique visualizes
nonclassical effects without further data processing. Surprisingly, a small
number of on-off diodes can yield more insight than perfect photon number
resolution. Quantum signatures in the particle and wave domain of the quantized
radiation field, as shown by photon number and squeezed states, respectively,
will be uncovered in terms of negativities of the sampled phase-space
functions. Application in the vast fields of quantum optics and quantum
technology will benefit from our efficient nonclassicality characterization
approach.


  The Horvitz-Thompson (HT) estimator is widely used in survey sampling.
However, the variance of the HT estimator becomes large when the inclusion
probabilities are highly heterogeneous. To overcome this shortcoming, in this
paper, a hard-threshold method is used for the first-order inclusion
probabilities, that is, we carefully choose a threshold value, then replace the
inclusion probabilities smaller than the threshold by the threshold. By this
shrinkage strategy, we propose a new estimator called improved Horvitz-Thompson
(IHT) estimator to estimate the population total. The IHT estimator increases
the estimation accuracy although it brings bias which is relatively small. We
derive the IHT estimator's MSE and its unbiased estimator, and theoretically
compare the IHT estimator with the HT estimator. We also apply our idea to
construct the improved ratio estimator. We numerically analyze simulated and
real data sets to illustrate that the proposed estimators are more efficient
and robust than the classical estimators.


  Quantum molecular dynamic simulations are introduced to study the dynamical,
electrical, and optical properties of carbon dioxide under dynamic
compressions. The principal Hugoniot derived from the calculated equation of
states is demonstrated to be well accordant with experimental results.
Molecular dissociation and recombination are investigated through pair
correlation functions, and decomposition of carbon dioxide is found to be
between 40 and 50 GPa along the Hugoniot, where nonmetal-metal transition is
observed. In addition, the optical properties of shock compressed carbon
dioxide are also theoretically predicted along the Hugoniot.


  We prove the existence of a limit shape for the dimer model on planar
periodic bipartite graphs with an arbitrary fundamental domain and arbitrary
periodic weights. This proof is based on a variational principle that uses the
locality of the model and the compactness of the space of states.


  This paper presents a novel control protocol for robust distance-based
formation control with prescribed performance in which agents are subjected to
unknown external disturbances. Connectivity maintenance and collision avoidance
among neighboring agents are also handled by the appropriate design of certain
performance bounds that constrain the inter-agent distance errors. As an
extension to the proposed scheme, distance-based formation centroid maneuvering
is also studied for disturbance-free agents, in which the formation centroid
tracks a desired time-varying velocity. The proposed control laws are
decentralized, in the sense that each agent employs local relative information
regarding its neighbors to calculate its control signal. Therefore, the control
scheme is implementable on the agents' local coordinate frames. Using rigid
graph theory, input-to-state stability, and Lyapunov based analysis, the
results are established for minimally and infinitesimally rigid formations in
2-D or 3-D space. Furthermore, it is argued that the proposed approach
increases formation robustness against shape distortions and can prevent
formation convergence to incorrect shapes, which is likely to happen in
conventional distance-based formation control methods. Finally, extensive
simulation studies clarify and verify the proposed approach.


  The time-reversal and parity violating superconducting(SC) phase of
Bi2Sr2CaCu2O8 induced by a magnetic field (B), reported by Krishana et al[K.
Krishana et al, Science 277, 83 (1997)] over the limited field range of 0.6T <
B < 5T, is examined starting with the model free-energy functional predicted by
Laughlin [R. B. Laughlin, Physica C 234, 280 (1994)]. On the basis of entropy
considerations we show that the passage from the normal to this field-driven SC
state at a non-zero temperatures (T) is possible if kBT \leq \Delta 0 where the
zero-temperature gap \Delta0 ~ \hbarv/lB, v is the root-mean-square velocity of
the d-wave node, and lB = \surd(\hbar/eB) is the magnetic length. The
restriction may be construed as setting lower limit on the required field
strength at a given temperature. We find that, over the field range mentioned,
the specific heat coefficient exhibits \surd B- and the B-linear dependence
(Volovick effect).


  We show that total multiplicities of negative and positive spectra of a
self-adjoint Hankel operator $H$ with kernel $h(t)$ and of an operator of
multiplication by some real function $s(x)$ coincide. In particular, $\pm H\geq
0$ if and only if $\pm s(x)\geq 0$. The kernel $h(t)$ and its "sign-function"
$s(x)$ are related by an explicit formula. An expression of $h(t)$ in terms of
$s(x)$ leads to an exponential representation of $h(t)$.
  Our approach directly applies to various classes of Hankel operators. In
particular, for Hankel operators of finite rank, we find an explicit formula
for the total multiplicity of their negative and positive spectra.


  We present a criterion for a family of random distributions to be tight in
local H\"older and Besov spaces of possibly negative regularity. We then apply
this criterion to the magnetization field of the two-dimensional Ising model at
criticality, answering a question of Camia, Garban and Newman.


  We show that local PT-symmetric evolutions can lead to violation of the
no-signaling principle for separable and even classically correlated bipartite
shared quantum states. For classically correlated states, specially chosen
PT-symmetric operations from a set of zero volume can also preserve the
principle. The violations can be removed by using a CPT inner product instead
of the traditional one.


  This paper considers the partial decode-and-forward (PDF) strategy for the
Gaussian multiple-input multiple-output (MIMO) relay channel. Unlike for the
decode-and-forward (DF) strategy or point-to-point (P2P) transmission, for
which Gaussian channel inputs are known to be optimal, the input distribution
that maximizes the achievable PDF rate for the Gaussian MIMO relay channel has
remained unknown so far. For some special cases, e.g., for relay channels where
the optimal PDF strategy reduces to DF or P2P transmission, it could be deduced
that Gaussian inputs maximize the PDF rate. For the general case, however, the
problem has remained open until now. In this work, we solve this problem by
proving that the maximum achievable PDF rate for the Gaussian MIMO relay
channel is always attained by Gaussian channel inputs. Our proof relies on the
channel enhancement technique, which was originally introduced by Weingarten et
al. to derive the (private message) capacity region of the Gaussian MIMO
broadcast channel. By combining this technique with a primal decomposition
approach, we first establish that jointly Gaussian source and relay inputs
maximize the achievable PDF rate for the aligned Gaussian MIMO relay channel.
Subsequently, we use a limiting argument to extend this result from the aligned
to the general Gaussian MIMO relay channel.


  Books have been widely used to share information and contribute to human
knowledge. However, the quantitative use of books as a method of scholarly
communication is relatively unexamined compared to journal articles and
conference papers. This study uses the COCI dataset (a comprehensive open
citation dataset provided by OpenCitations) to explore books' roles in
scholarly communication. The COCI data we analyzed includes 445,826,118
citations from 46,534,705 bibliographic entities. By analyzing such a large
amount of data, we provide a thorough, multifaceted understanding of books.
Among the investigated factors are 1) temporal changes to book citations; 2)
book citation distributions; 3) years to citation peak; 4) citation half-life;
and 5) characteristics of the most-cited books. Results show that books have
received less than 4% of total citations, and have been cited mainly by journal
articles. Moreover, 97.96% of books have been cited fewer than ten times. Books
take longer than other bibliographic materials to reach peak citation levels,
yet are cited for the same duration as journal articles. Most-cited books tend
to cover general (yet essential) topics, theories, and technological concepts
in mathematics and statistics.


  The theory of entropic gravity conjectures that gravity emerges
thermodynamically rather than being a fundamental force. One of the main
criticisms of entropic gravity is that it would lead to quantum massive
particles losing coherence in free fall, which is not observed experimentally.
This criticism was refuted in [Phys. Rev. Res. 3, 033065 (2021)], where a
nonrelativistic master equation modeling gravity as an open quantum system
interaction demonstrated that in the strong coupling limit, coherence could be
maintained and reproduce conventional free-fall dynamics. Moreover, the
nonrelativistic master equation was shown to be fully compatible with the
qBounce experiment for ultracold neutrons. Motivated by this, we extend these
results to gravitationally accelerating Dirac fermions. We achieve this by
using the Dirac equation in Rindler space and modeling entropic gravity as a
thermal bath thus adopting the open quantum systems approach as well. We
demonstrate that in the strong coupling limit, our entropic gravity model
maintains quantum coherence for Dirac fermions. In addition, we demonstrate
that spin is not affected by entropic gravity. We use the Foldy-Wouthysen
transformation to demonstrate that it reduces to the nonrelativistic master
equation, supporting the entropic gravity hypothesis for Dirac fermions. Also,
we demonstrate how antigravity seemingly arises from the Dirac equation for
free-falling antiparticles but use numerical simulations to show that this
phenomenon originates from zitterbewegung thus not violating the equivalence
principle.