  The stability of magnetic skyrmions has been investigated in the past, but
mostly in the absence of thermal fluctuations. However, thermal spin
fluctuations modify the magnetic properties (exchange stiffness,
Dzyaloshinskii-Moriya interaction (DMI) and anisotropy) that define skyrmion
stability. Thermal magnons also excite internal skrymion dynamics, deforming
the skyrmion shape. Entropy has also been shown to modify skyrmion lifetimes in
experiments, but is absent or approximated in previous studies. Here we use
metadynamics to calculate the free energy surface of a magnetic thin film in
terms of the topological charge and magnetization. We identify the free energy
minima corresponding to different spin textures and the lowest energy paths
between the ferromagnetic and single skyrmion states. We show that at low
temperatures the lowest free energy barrier is a skyrmion collapse process.
However, this energy barrier increases with temperature. An alternative path,
where a singularity forms on the skrymion edge, has a larger free energy
barrier at low temperatures but decreases with increasing temperature and
eventually becomes the lowest energy barrier.


  In this paper we study the finite element approximation of systems of
second-order nonlinear hyperbolic equations. The proposed numerical method
combines a $hp$-version discontinuous Galerkin finite element approximation in
the time direction with an $H^1(\Omega)$-conforming finite element
approximation in the spatial variables. Error bounds at the temporal nodal
points are derived under a weak restriction on the temporal step size in terms
of the spatial mesh size. Numerical experiments are presented to verify the
theoretical results.


  In a previous work (M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290) we
have addressed the mechanical foundations of equilibrium thermodynamics on the
basis of the Generalized Helmholtz Theorem. It was found that the volume
entropy provides a good mechanical analogue of thermodynamic entropy because it
satisfies the heat theorem and it is an adiabatic invariant. This property
explains the ``equal'' sign in Clausius principle ($S_f \geq S_i$) in a purely
mechanical way and suggests that the volume entropy might explain the ``larger
than'' sign (i.e. the Law of Entropy Increase) if non adiabatic transformations
were considered. Based on the principles of microscopic (quantum or classical)
mechanics here we prove that, provided the initial equilibrium satisfy the
natural condition of decreasing ordering of probabilities, the expectation
value of the volume entropy cannot decrease for arbitrary transformations
performed by some external sources of work on a insulated system. This can be
regarded as a rigorous quantum mechanical proof of the Second Law. We discuss
how this result relates to the Minimal Work Principle and improves over
previous attempts. The natural evolution of entropy is towards larger values
because the natural state of matter is at positive temperature. Actually the
Law of Entropy Decrease holds in artificially prepared negative temperature
systems.


  Obtaining complete information about the shape of an object by looking at it
from a single direction is impossible in general. In this paper, we
theoretically study obtaining differential geometric information of an object
from orthogonal projections in a number of directions. We discuss relations
between (1) a space curve and the projected curves from several distinct
directions, and (2) a surface and the apparent contours of projections from
several distinct directions, in terms of differential geometry and singularity
theory. In particular, formulae for recovering certain information on the
original curves or surfaces from their projected images are given.


  We compute the geometric phase for a spin-1/2 particle under the presence of
a composite environment, composed of an external bath (modeled by an infinite
set of harmonic oscillators) and another spin-1/2 particle. We consider both
cases: an initial entanglement between the spin-1/2 particles and an initial
product state in order to see if the initial entanglement has an enhancement
effect on the geometric phase of one of the spins. We follow the nonunitary
evolution of the reduced density matrix and evaluate the geometric phase for a
single two-level system. We also show that the initial entanglement enhances
the sturdiness of the geometric phase under the presence of an external
composite environment.


  Recent observations for a pressurized kagome superconductor through
transport, muon spin relaxation, nuclear magnetic resonance, and point contact
spectroscopy demonstrate striking fluctuating superconductivity at a magic
pressure. This discovery may hint at a new quantum dephasing mechanism, which
can be discussed from the perspectives of correlation and topology. Three
outstanding questions should be considered in decoding this mechanism: one is
the intrinsic phase fragile nature of kagome superconductivity; second is the
role of Coulomb interactions within different charge-ordered phases; third is
the geometrical phase compatibility between superconductivity and different
charge orders.


  Magnonics is a rapidly growing field, attracting much attention for its
potential applications in data transport and processing. Many individual
magnonic devices have been proposed and realized in laboratories. However, an
integrated magnonic circuit with several separate magnonic elements has yet not
been reported due to the lack of a magnonic amplifier to compensate for
transport and processing losses. The magnon transistor reported in [Nat.
Commun. 5, 4700, (2014)] could only achieve a gain of 1.8, which is
insufficient in many practical cases. Here, we use the stimulated three-magnon
splitting phenomenon to numerically propose a concept of magnon transistor in
which the energy of the gate magnons at 14.6 GHz is directly pumped into the
energy of the source magnons at 4.2 GHz, thus achieving the gain of 9. The
structure is based on the 100 nm wide YIG nano-waveguides, a directional
coupler is used to mix the source and gate magnons, and a dual-band magnonic
crystal is used to filter out the gate and idler magnons at 10.4 GHz frequency.
The magnon transistor preserves the phase of the signal and the design allows
integration into a magnon circuit.


  Large Hubbard U limit of the Kane-Mele model on a zigzag ribbon of honeycomb
lattice near half-filling is studied via a renormalized mean-field theory. The
ground state exhibits time-reversal symmetry (TRS) breaking d + i d'-wave
superconductivity. At large spin-orbit coupling, the Z2 phase with non-trivial
spin Chern number in the pure Kane-Mele model is persistent into the TRS broken
state (called spin-Chern phase), and has two pairs of counter-propagating
helical Majorana modes at the edges. As the spin-orbit coupling is reduced, the
system undergoes a topological quantum phase transition from the spin-Chern to
chiral superconducting states. Possible relevance of our results to
adatom-doped graphene and irridate compounds is discussed.


  We construct a bosonic quantum field on a general quantum graph. Consistency
of the construction leads to the calculation of the total scattering matrix of
the graph. This matrix is equivalent to the one already proposed using
generalized star product approach. We give several examples and show how they
generalize some of the scattering matrices computed in the mathematical or
condensed matter physics litterature.
  Then, we apply the construction for the calculation of the conductance of
graphs, within a small distance approximation. The consistency of the
approximation is proved by direct comparison with the exact calculation for the
`tadpole' graph.


  We investigate a family of Hopf algebras of dimension 72 whose coradical is
isomorphic to the algebra of functions on S_3. We determine the lattice of
submodules of the so-called Verma modules and as a consequence we classify all
simple modules. We show that these Hopf algebras are unimodular (as well as
their duals) but not quasitriangular; also, they are cocycle deformations of
each other.


  The control of a network of signalized intersections is considered. Previous
work demonstrates that the so-called back-pressure control provides stability
guarantees, assuming infinite queues capacities. In this paper, we highlight
the failing of current back-pressure control under finite capacities by
identifying sources of non work-conservation and congestion propagation. We
propose the use of a normalized pressure which guarantees work conservation and
mitigates congestion propagation, while ensuring fairness at low traffic
densities, and recovering original back-pressure as capacities grow to
infinity. This capacity-aware back-pressure control allows to improve
performance as congestion increases, as indicated by simulation results, and
keeps the key benefits of back-pressure: ability to be distributed over
intersections and O(1) complexity.


  Class I CH$_3$OH masers trace interstellar shocks. They have received little
attention mostly as a consequence of their low luminosities; this situation has
changed recently and Class I masers are now routinely used as signposts of
outflows. The recent detection of polarisation in Class I lines now makes it
possible to obtain information on magnetic fields in shocks. We make use of
newly calculated collisional rates to investigate the excitation of Class I
masers and to reconcile their observed properties with model results. We
performed LVG calculations with a plane-parallel slab geometry to compute the
pump and loss rates which regulate the interactions of the different maser
systems with the maser reservoir. We study the dependence of the pump rate, the
loss rate, and the inversion efficiency of the pumping scheme of Class I masers
on the physics of the gas. Bright Class I masers are mainly high-temperature
high-density structures with maser emission measures corresponding to high
CH$_3$OH abundances close to the limits set by collisional quenching. Our model
reproduces reasonably well most of the observed properties of Class I masers.
The 25 GHz masers are the most sensitive to the density and mase at higher
densities than other lines. Moreover, even at high density and high abundance,
their luminosity is lower than that of the 44 GHz and 36 GHz lines. By
comparison between observed isotropic photon luminosities and our model, we
infer beam solid angles of ~0.001 steradian. Class I masers can be separated
into 3 families: the $(J+1)_{-1}-J_{0}$-E type, the $(J+1)_0-J_1$-A type, and
the $J_2-J_1$-E lines. The 25 GHz lines behave in a different fashion from the
other masers as they are only inverted at densities above $10^6$ cm$^{-3}$ in
contrast to other Class I masers. Therefore, the detection of maser activity in
all 3 families is a clear indication of high densities.


  we construct a properly embedded minimal surface in the flat product R^2*S^1
which is quasi-periodic but is not periodic.


  Foundational models benefit from pre-training on large amounts of unlabeled
data and enable strong performance in a wide variety of applications with a
small amount of labeled data. Such models can be particularly effective in
analyzing brain signals, as this field encompasses numerous application
scenarios, and it is costly to perform large-scale annotation. In this work, we
present the largest foundation model in brain signals, Brant-2. Compared to
Brant, a foundation model designed for intracranial neural signals, Brant-2 not
only exhibits robustness towards data variations and modeling scales but also
can be applied to a broader range of brain neural data. By experimenting on an
extensive range of tasks, we demonstrate that Brant-2 is adaptive to various
application scenarios in brain signals. Further analyses reveal the scalability
of the Brant-2, validate each component's effectiveness, and showcase our
model's ability to maintain performance in scenarios with scarce labels.


  We analyze the collision of a high energy electron beam with an oscillating
electric and magnetic field configuration, which represents a three-dimensional
standing electromagnetic wave. The radiating electrons are stopped at the
distance of the order of or less than the electromagnetic wave wavelength, and
become trapped near the electric field local maxima due to the nonlinear
dependence of the radiation friction force on the electromagnetic field
strength, while the quantum effects on the radiation friction remain
negligible.


  Modern smartphones contain motion sensors, such as accelerometers and
gyroscopes. These sensors have many useful applications; however, they can also
be used to uniquely identify a phone by measuring anomalies in the signals,
which are a result from manufacturing imperfections. Such measurements can be
conducted surreptitiously in the browser and can be used to track users across
applications, websites, and visits.
  We analyze techniques to mitigate such device fingerprinting either by
calibrating the sensors to eliminate the signal anomalies, or by adding noise
that obfuscates the anomalies. To do this, we first develop a highly accurate
fingerprinting mechanism that combines multiple motion sensors and makes use of
(inaudible) audio stimulation to improve detection. We then collect
measurements from a large collection of smartphones and evaluate the impact of
calibration and obfuscation techniques on the classifier accuracy.


  One of the most critical tasks for startups is to validate their business
model. Therefore, entrepreneurs try to collect information such as feedback
from other actors to assess the validity of their assumptions and make
decisions. However, previous work on decisional guidance for business model
validation provides no solution for the highly uncertain and complex context of
earlystage startups. The purpose of this paper is, thus, to develop design
principles for a Hybrid Intelligence decision support system (HI-DSS) that
combines the complementary capabilities of human and machine intelligence. We
follow a design science research approach to design a prototype artifact and a
set of design principles. Our study provides prescriptive knowledge for HI-DSS
and contributes to previous work on decision support for business models, the
applications of complementary strengths of humans and machines for making
decisions, and support systems for extremely uncertain decision-making
problems.


  The operator product expansion (OPE) on the celestial sphere of conformal
primary gluons and gravitons is studied. Asymptotic symmetries imply recursion
relations between products of operators whose conformal weights differ by
half-integers. It is shown, for tree-level Einstein-Yang-Mills theory, that
these recursion relations are so constraining that they completely fix the
leading celestial OPE coefficients in terms of the Euler beta function. The
poles in the beta functions are associated with conformally soft currents.


  With the recent release of the black hole image of Sgr A* alongside the
earlier image of M87*, one can now really hope to acquire a better
understanding of the gravitational physics at the horizon scale. In this paper,
we investigate the prospect of the regular black hole scenario with a Minkowski
core in explaining the observed shadow of M87* and Sgr A*. Regular black holes
generally appear in Einstein gravity coupled to non-linear electrodynamics and
are interesting as they can evade the r = 0 curvature singularity arising in
general relativity. Using the previously determined mass and distance we
compute the observables associated with the black hole shadow. These when
compared with the observed angular diameter reveal that the shadow of M87* and
Sgr A* favor the regular black hole scenario with a small but non-zero charge.
The implications are discussed.


  In this work we find the Killing vector fields of the riemannian submanifolds
of the thermodynamic phase space of an ideal gas and show that the isometry
group corresponding to them is homomorphic to the euclidean group $E(2)$. We
also give the embedding of these submanifolds in the euclidean space $(R^{3},\
delta)$.


  A Sidon set is a subset of an Abelian group with the property that each sum
of two distinct elements is distinct. We construct a small maximal Sidon set of
size $O((n \cdot 2^n)^{1/3})$ in the group $\mathbb{Z}_2^n$, generalizing a
result of Ruzsa concerning maximal Sidon sets in the integers.


  We report VLA B-configuration observations of the HI 21 cm line on the close
disk galaxy pair NGC 5595 and NGC 5597. At the angular resolution of the
observations, $\sim7.1'' \times 4.2''$, while most of the HI 21 cm in NGC 5595
and in NGC 5597 has the same extent as the optical disk, we have detected for
the first time extended structures (streamers) to the north-east (NE), and
south-west (SW) of NGC 5595 with no counterparts in blue, red optical
(continuum), 20 cm radio continuum, or H$\alpha$ spectral-line emission. One
structure is extended by $\sim 45''$ to the NE with blue-shifted velocities,
and the other by $\sim 20''$ to the SW with red-shifted velocities with respect
to the systemic velocity. No HI 21 cm emission is detected from the innermost
central (nuclear) regions of either galaxy. Lower angular resolution HI 21 cm
imaging indicates the non-existence of any intergalactic HI 21 cm gas as tails
or bridges between the two galaxies. Our new 20 cm radio continuum emission
image of NGC 5597 shows a strong unresolved elongated structure at the central
region, in the north-east south-west direction, very similar to the spatial
location of the innermost H$\alpha$ spectral line emission. There is no 20 cm
continuum emission from its north spiral arm. In NGC 5595, the 20 cm radio
continuum image shows no continuum emission from the NE nor the SW extended
structures with HI 21 cm emission.


  We study the properties of discrete breathers, also known as intrinsic
localized modes, in the one-dimensional Frenkel-Kontorova lattice of
oscillators subject to damping and external force. The system is studied in the
whole range of values of the coupling parameter, from C=0 (uncoupled limit) up
to values close to the continuum limit (forced and damped sine-Gordon model).
As this parameter is varied, the existence of different bifurcations is
investigated numerically. Using Floquet spectral analysis, we give a complete
characterization of the most relevant bifurcations, and we find (spatial)
symmetry-breaking bifurcations which are linked to breather mobility, just as
it was found in Hamiltonian systems by other authors. In this way moving
breathers are shown to exist even at remarkably high levels of discreteness. We
study mobile breathers and characterize them in terms of the phonon radiation
they emit, which explains successfully the way in which they interact. For
instance, it is possible to form ``bound states'' of moving breathers, through
the interaction of their phonon tails. Over all, both stationary and moving
breathers are found to be generic localized states over large values of $C$,
and they are shown to be robust against low temperature fluctuations.


  We give a functional derivation of the Ward-Takahashi identity for Yang-Mills
theory in the framework of the exact renormalization group. The identity
realizes non-abelian gauge symmetry nontrivially despite the presence of a
momentum cutoff. The cutoff deforms the gauge transformation by introducing
composite operators. In our functional method, which is an extension of the
method used in our previous work on QED, these composite operators are
expressed in terms of the Wilson action that depends on both a UV cutoff and an
IR cutoff.


  Determining changes in global temperature and precipitation that may indicate
climate change is complicated by annual variations. One approach for finding
potential climate change indicators is to train a model that predicts the year
from annual means of global temperatures and precipitations. Such data is
available from the CMIP6 ensemble of simulations. Here a two-hidden-layer
neural network trained on this data successfully predicts the year. Differences
among temperature and precipitation patterns for which the model predicts
specific years reveal changes through time. To find these optimal patterns, a
new way of interpreting what the neural network has learned is explored.
Alopex, a stochastic correlative learning algorithm, is used to find optimal
temperature and precipitation maps that best predict a given year. These maps
are compared over multiple years to show how temperature and precipitations
patterns indicative of each year change over time.


  The standard Pirogov -- Sinai theory is generalized to the class of models
with two modes of interaction: longitudinal and transversal. Under rather
general assumptions about the longitudinal interaction and for one specific
form of the transversal interaction it is proved that such system has a variety
of phase transitions at any temperature: the parameter which plays the role of
inverse temperature is the strength of the transversal interaction. The
concrete examples of such systems are $(1+1)$-dimensional models.


  We introduce a method of reversing the execution of imperative concurrent
programs. Given an irreversible program, we describe the process of producing
two versions. The first performs forward execution and saves information
necessary for reversal. The second uses this saved information to simulate
reversal. We propose using identifiers to overcome challenges of reversing
concurrent programs. We prove this reversibility to be correct, showing that
the initial program state is restored and that all saved information is used
(garbage-free).


  We propose a neural network component, the regional aggregation layer, that
makes it possible to train a pixel-level density estimator using only
coarse-grained density aggregates, which reflect the number of objects in an
image region. Our approach is simple to use and does not require
domain-specific assumptions about the nature of the density function. We
evaluate our approach on several synthetic datasets. In addition, we use this
approach to learn to estimate high-resolution population and housing density
from satellite imagery. In all cases, we find that our approach results in
better density estimates than a commonly used baseline. We also show how our
housing density estimator can be used to classify buildings as residential or
non-residential.


  We reconstruct posterior distributions for the position (sky area and
distance) of a simulated set of binary neutron-star gravitational-waves signals
observed with Advanced LIGO and Advanced Virgo. We use a Dirichlet Process
Gaussian-mixture model, a fully Bayesian non-parametric method that can be used
to estimate probability density functions with a flexible set of assumptions.
The ability to reliably reconstruct the source position is important for
multimessenger astronomy, as recently demonstrated with GW170817. We show that
for detector networks comparable to the early operation of Advanced LIGO and
Advanced Virgo, typical localization volumes are
$\sim10^4$--$10^5~\mathrm{Mpc^3}$ corresponding to $\sim10^2$--$10^3$ potential
host galaxies. The localization volume is a strong function of the network
signal-to-noise ratio, scaling roughly $\propto \varrho_{net}^{-6}$. Fractional
localizations improve with the addition of further detectors to the network.
Our Dirichlet Process Gaussian-mixture model can be adopted for localizing
events detected during future gravitational-wave observing runs, and used to
facilitate prompt multimessenger follow-up.


  We study a model for the dynamics of vortices in type II superconductors. In
particular, we discuss glassy ``off equilibrium'' properties and ``aging'' in
magnetic creep. At low temperatures a crossover point is found, Tg, where
relaxation times seem to diverge a' la Vogel-Tamman-Fulcher. Magnetic creep
changes by crossing Tg: above Tg power law creep is found asymptotically
followed by stretched exponential saturation; below Tg the creep is logarithmic
and vortex motion strongly subdiffusive. In this region violation of time
translation invariance is found along with important dynamical scaling
properties. A thermodynamic glassy transition point can be found at a lower
temperature Tc.


  DDEBIFTOOL is a collection of Matlab routines for numerical bifurcation
analysis of systems of delay differential equations with discrete constant and
state-dependent delays. The package supports continuation and stability
analysis of steady state solutions and periodic solutions. Further one can
compute and continue several local and global bifurcations: fold and Hopf
bifurcations of steady states; folds, period doublings and torus bifurcations
of periodic orbits; and connecting orbits between equilibria. To analyse the
stability of steady state solutions, approximations are computed to the
rightmost, stability-determining roots of the characteristic equation which can
subsequently be used as starting values in a Newton procedure. For periodic
solutions, approximations to the Floquet multipliers are computed. The manual
describes the structure of the package, its routines, and its data and method
parameter structures.


  In usual (non-stochastic) tensor network calculations, the truncated singular
value decomposition (SVD) is often used for approximating a tensor, and it
causes systematic errors. By introducing stochastic noise in the approximation,
however, one can avoid such systematic errors at the expense of statistical
errors which can be straightforwardly controlled. Therefore in principle, exact
results can be obtained even at finite bond dimension up to the statistical
errors. A previous study of the unbiased method implemented in tensor
renormalization group (TRG) algorithm, however, showed that the statistical
errors for physical quantity are not negligible, and furthermore the
computational cost is linearly proportional to a system volume. In this paper,
we introduce a new way of stochastic noise such that the statistical error is
suppressed, and moreover, in order to reduce the computational cost we propose
common noise method whose cost is proportional to the logarithm of volume. We
find that the method provides better accuracy for the free energy compared with
the truncated SVD when applying to TRG for Ising model on square lattice.
Although the common noise method introduces systematic error originated from a
correlation of noises, we show that the error can be described by a simple
functional form in terms of the number of noises, thus the error can be
straightforwardly controlled in an actual analysis. We also apply the method to
the graph independent local truncation algorithm and show that the accuracy is
further improved.


  We have developed models of the fission barrier (barrier heights and
transition state spectra) that reproduce reasonably well the measured fission
cross section of $^{235}$U from neutron energy of 1 keV to 2 MeV. From these
models we have calculated the fission cross section of the 77 eV isomer of
$^{235}$U over the same energy range. We find that the ratio of the isomer
cross section to that of the ground state lies between about 0.45 and 0.55 at
low neutron energies. The cross sections become approximately equal above 1
MeV. The ratio of the neutron capture cross section to the fission cross
section for the isomer is predicted to be about a factor of 3 larger for the
isomer than for the ground state of $^{235}$U at keV neutron energies. We have
also calculated the cross section for the population of the isomer by inelastic
neutron scattering form the $^{235}$U ground state. We find that the isomer is
strongly populated, and for $E_n = 1 MeV$ the $(n,n'\gamma)$ cross section
leading to the population of the isomer is of the order of 0.5 barn. Thus,
neutron reaction network calculations involving the uranium isotopes in a high
neutron fluence are likely to be affected by the 77 eV isomer of $^{235}$U.
With these same models the fission cross sections of $^{233}$U and $^{237}$U
can be reproduced approximately using only minor adjustments to the barrier
heights. With the significant lowering of the outer barrier that is expected
for the outer barrier the general behavior of the fission cross section of
$^{239}$Pu can also be reproduced.


  We say a $d$-dimensional simplicial complex embeds into double dimension if
it embeds into the Euclidean space of dimension $2d$. For instance, a graph is
planar iff it embeds into double dimension. We study the conditions under which
the join of two simplicial complexes embeds into double dimension. Quite
unexpectedly, we show that there exist complexes which do not embed into double
dimension, however their join embeds into the respective double dimension. We
further derive conditions, in terms of the van Kampen obstructions of the two
complexes, under which the join will not be embeddable into the double
dimension. Our main tool in this study is the definition of the van Kampen
obstruction as a Smith class. We determine the Smith classes of the join of two
$\mathbb{Z}_p$-complexes in terms of the Smith classes of the factors. We show
that in general the Smith index is not stable under joins. This allows us to
prove our embeddability results.


  Root-zone soil moisture monitoring is essential for precision agriculture,
smart irrigation, and drought prevention. Modeling the spatiotemporal water
flow dynamics in soil is typically achieved by solving a hydrological model,
such as the Richards equation which is a highly nonlinear partial differential
equation (PDE). In this paper, we present a novel data-facilitated numerical
method for solving the mixed-form Richards equation. This numerical method,
which we call the D-GRW (Data-facilitated global Random Walk) method,
synergistically integrates adaptive linearization scheme, neural networks, and
global random walk in a finite volume discretization framework to produce
accurate numerical solutions of the Richards equation with guaranteed
convergence under reasonable assumptions. Through three illustrative examples,
we demonstrate and discuss the superior accuracy and mass conservation
performance of our D-GRW method and compare it with benchmark numerical methods
and commercial solver.


  We characterize the local (2-kpc sized) environments of Type Ia, II, and Ib/c
supernovae (SNe) that have recently occurred in nearby ($d\lesssim50$ Mpc)
galaxies. Using ultraviolet (UV, from GALEX) and infrared (IR, from WISE) maps
of 359 galaxies and a sample of 472 SNe, we measure the star formation rate
surface density ($\Sigma_{\rm SFR}$) and stellar mass surface density
($\Sigma_\star$) in a 2-kpc beam centered on each SN site. We show that
core-collapse SNe are preferentially located along the resolved galactic
star-forming main sequence, whereas Type Ia SNe are extended to lower values of
$\Sigma_{\rm SFR}$ at fixed $\Sigma_\star$, indicative of locations inside
quiescent galaxies or quiescent regions of galaxies. We also test how well the
radial distribution of each SN type matches the radial distributions of UV and
IR light in each host galaxy. We find that, to first order, the distributions
of all types of SNe mirror that of both near-IR light (3.4 and 4.5 microns,
tracing the stellar mass distribution) and mid-IR light (12 and 22 microns,
tracing emission from hot, small grains), and also resemble our best-estimate
$\Sigma_{\rm SFR}$. All types of SNe appear more radially concentrated than the
UV emission of their host galaxies. In more detail, the distributions of Type
II SNe show small statistical differences from that of near-IR light. We
attribute this overall structural uniformity to the fact that within any
individual galaxy, $\Sigma_{\rm SFR}$ and $\Sigma_\star$ track one another
well, with variations in $\Sigma_{\rm SFR}/\Sigma_\star$ most visible when
comparing between galaxies.


  A calorimeter was built to measure the heat from a porous capacitive working
electrode connected in a three-electrode configuration. This makes it possible
to detect differences between cathodic and anodic heat production. The
electrochemical cell contains a large electrolyte solution reservoir, ensuring
a constant concentration of the salt solution probed by the reference electrode
via a Luggin tube. A heat flux sensor is used to detect the heat, and its
calibration as a gauge of the total amount of heat produced by the electrode is
done on the basis of the net electrical work performed on the working electrode
during a full charging-discharging cycle. In principle, from the measured heat
and the electrical work, the change in internal energy of the working electrode
can be determined as a function of applied potential. Such measurements inform
about the potential energy and average electric potential of ions inside the
pores, giving insight into the electrical double layer inside electrode
micropores. Example measurements of the heat are shown for porous carbon
electrodes in aqueous salt solution.


  Absorption of electromagnetic energy by a material is a phenomenon that
underlies many applied problems, including molecular sensing, photocurrent
generation and photodetection. Commonly, the incident energy is delivered to
the system through a single channel, for example by a plane wave incident on
one side of an absorber. However, absorption can be made much more efficient by
exploiting wave interference. A coherent perfect absorber is a system in which
complete absorption of electromagnetic radiation is achieved by controlling the
interference of multiple incident waves. Here, we review recent advances in the
design and applications of such devices. We present the theoretical principles
underlying the phenomenon of coherent perfect absorption and give an overview
of the photonic structures in which it can be realized, including planar and
guided-mode structures, graphene-based systems, parity- and time-symmetric
structures, 3D structures and quantum-mechanical systems. We then discuss
possible applications of coherent perfect absorption in nanophotonics and,
finally, we survey the perspectives for the future of this field.


  The torsion anomalous conjecture states that for any variety V in an abelian
variety there are only finitely many maximal V-torsion anomalous varieties. We
prove this conjecture for V of codimension 2 in a product E^N of any elliptic
curve E. This was known only when E has CM. We also give an effective upper
bound for the normalized height of these maximal V-torsion anomalous varieties.


  Many transition-metal oxides show very large ("colossal") magnitudes of the
dielectric constant and thus have immense potential for applications in modern
microelectronics and for the development of new capacitance-based
energy-storage devices. In the present work, we thoroughly discuss the
mechanisms that can lead to colossal values of the dielectric constant,
especially emphasising effects generated by external and internal interfaces,
including electronic phase separation. In addition, we provide a detailed
overview and discussion of the dielectric properties of CaCu3Ti4O12 and related
systems, which is today's most investigated material with colossal dielectric
constant. Also a variety of further transition-metal oxides with large
dielectric constants are treated in detail, among them the system La2-xSrxNiO4
where electronic phase separation may play a role in the generation of a
colossal dielectric constant.


  Recent measurements of the temperature fluctuations of the cosmic microwave
background (CMB) radiation from the WMAP satellite provide indication of a
non-Gaussian behavior. Although the observed feature is small, it is detectable
and analyzable. Indeed, the temperature distribution P^{CMB}(Delta T) of these
data can be quite well fitted by the anomalous probability distribution
emerging within nonextensive statistical mechanics, based on the entropy S_q =
k (1 - \int dx [P(x)]^q)/(q - 1) (where in the limit case q -> 1 we obtain the
Boltzmann-Gibbs entropy S_1 = - k \int dx P(x) ln[P(x)]). For the CMB
frequencies analysed, \nu= 40.7, 60.8, and 93.5 GHz, P^{CMB}(Delta T) is well
described by P_q(Delta T) \propto 1/[1 + (q-1) B(\nu) (Delta T)^2]^{1/(q-1)},
with q = 1.04 \pm 0.01, the strongest non-Gaussian contribution coming from the
South-East sector of the celestial sphere. Moreover, Monte Carlo simulations
exclude, at the 99% confidence level, P_1(Delta T) \propto e^{- B(\nu) (Delta
T)^2} to fit the three-year WMAP data.


  We use the effects of mass segregation on the radial distribution of
different stellar populations in the core of 47 Tucanae to find estimates for
the masses of stars at different post main sequence evolutionary stages. We
take samples of main sequence (MS) stars from the core of 47 Tucanae, at
different magnitudes (i.e. different masses), and use the effects of this
dynamical process to develop a relation between the radial distance (RD) at
which the cumulative distribution reaches the 20th and 50th percentile, and
stellar mass. From these relations we estimate the masses of different post MS
populations. We find that mass remains constant for stars going through the
evolutionary stages between the upper MS up to the horizontal branch (HB). By
comparing RDs of the HB stars with stars of lower masses, we can exclude a mass
loss greater than 0.09M during the red giant branch (RGB) stage at nearly the
3{\sigma} level. The slightly higher mass estimates for the asymptotic giant
branch (AGB) are consistent with the AGB having evolved from somewhat more
massive stars. The AGB also exhibits evidence of contamination by more massive
stars, possibly blue stragglers (BSS), going through the RGB phase. We do not
include the BSS in this paper due to the complexity of these objects, instead,
the complete analysis of this population is left for a companion paper. The
process to estimate the masses described in this paper are exclusive to the
core of 47 Tuc.


  The LU-decomposition of Lehmer's tridiagonal matrix is first guessed, then
proved, which leads to an evaluation of the determinant.


  Generative adversarial networks (GANs) are one of the most widely used
generative models. GANs can learn complex multi-modal distributions, and
generate real-like samples. Despite the major success of GANs in generating
synthetic data, they might suffer from unstable training process, and mode
collapse. In this paper, we introduce a new GAN architecture called variance
enforcing GAN (VARGAN), which incorporates a third network to introduce
diversity in the generated samples. The third network measures the diversity of
the generated samples, which is used to penalize the generator's loss for low
diversity samples. The network is trained on the available training data and
undesired distributions with limited modality. On a set of synthetic and
real-world image data, VARGAN generates a more diverse set of samples compared
to the recent state-of-the-art models. High diversity and low computational
complexity, as well as fast convergence, make VARGAN a promising model to
alleviate mode collapse.


  Cluster-randomized experiments are increasingly used to evaluate
interventions in routine practice conditions, and researchers often adopt
model-based methods with covariate adjustment in the statistical analyses.
However, the validity of model-based covariate adjustment is unclear when the
working models are misspecified, leading to ambiguity of estimands and risk of
bias. In this article, we first adapt two conventional model-based methods,
generalized estimating equations and linear mixed models, with weighted
g-computation to achieve robust inference for cluster-average and
individual-average treatment effects. To further overcome the limitations of
model-based covariate adjustment methods, we propose an efficient estimator for
each estimand that allows for flexible covariate adjustment and additionally
addresses cluster size variation dependent on treatment assignment and other
cluster characteristics. Such cluster size variations often occur
post-randomization and, if ignored, can lead to bias of model-based estimators.
For our proposed efficient covariate-adjusted estimator, we prove that when the
nuisance functions are consistently estimated by machine learning algorithms,
the estimator is consistent, asymptotically normal, and efficient. When the
nuisance functions are estimated via parametric working models, the estimator
is triply-robust. Simulation studies and analyses of three real-world
cluster-randomized experiments demonstrate that the proposed methods are
superior to existing alternatives.


  A decomposition theorem for self-adjoint operators proved by Riesz and Lorch
is extended to normal operators. This extension gives a new proof of the
spectral theorem for unbounded normal operators.


  We consider the most commonly occurring circumstances which apply to
galaxies, namely membership in galaxy groups of about $10^{13}h^{-1} M_\odot$
total mass, and estimate the accompanying physical conditions of intergalactic
medium (IGM) density and the relative galaxy-IGM space velocity. We then
investigate the dynamical consequences of such a typical galaxy-IGM interaction
on a rotating gaseous disk within the galaxy potential. We find that the
rotating outer disk is systematically distorted into a characteristic "warp"
morphology, of the type that has been well-documented in the majority of
well-studied nearby systems. The distortion is established rapidly, within two
rotation periods, and is long-lived, surviving for at least ten. A second
consequence of the interaction is the formation of a one arm retrograde spiral
wave pattern that propagates in the disk. We suggest that the ubiquity of the
warp phenomenon might be used to reconstruct both the IGM density profile and
individual member orbits within galaxy groups.


  In a recent article (Auer et al, Algorithmica 2016) it was claimed that every
outer-1-planar graph has a planar visibility representation of area $O(n\log
n)$. In this paper, we show that this is wrong: There are outer-1-planar graphs
that require $\Omega(n^2)$ area in any planar drawing. Then wegive a
construction (using crossings, but preserving a given outer-1-planar embedding)
that results in an orthogonal box-drawing with O(n log n) area and at most two
bends per edge.


  We consider the exact recovery problem in the hypergraph stochastic block
model (HSBM) with $k$ blocks of equal size. More precisely, we consider a
random $d$-uniform hypergraph $H$ with $n$ vertices partitioned into $k$
clusters of size $s = n / k$. Hyperedges $e$ are added independently with
probability $p$ if $e$ is contained within a single cluster and $q$ otherwise,
where $0 \leq q < p \leq 1$. We present a spectral algorithm which recovers the
clusters exactly with high probability, given mild conditions on $n, k, p, q$,
and $d$. Our algorithm is based on the adjacency matrix of $H$, which is a
symmetric $n \times n$ matrix whose $(u, v)$-th entry is the number of
hyperedges containing both $u$ and $v$. To the best of our knowledge, our
algorithm is the first to guarantee exact recovery when the number of clusters
$k=\Theta(\sqrt{n})$.


  A family of continuous-time generalized autoregressive conditionally
heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$
process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004)
601--622], is introduced and studied. The resulting $\operatorname
{COGARCH}(p,q)$ processes, $q\ge p\ge 1$, exhibit many of the characteristic
features of observed financial time series, while their corresponding
volatility and squared increment processes display a broader range of
autocorrelation structures than those of the $\operatorname {COGARCH}(1,1)$
process. We establish sufficient conditions for the existence of a strictly
stationary nonnegative solution of the equations for the volatility process
and, under conditions which ensure the finiteness of the required moments,
determine the autocorrelation functions of both the volatility and the squared
increment processes. The volatility process is found to have the
autocorrelation function of a continuous-time autoregressive moving average
process.


  We provide necessary and sufficient conditions for a tempered distribution
$F\in S'(R)$ to be positive definite. A generalized Cauchy transform
$\widetilde{F}$ of $F$ is used as a numerical continuation of $F$ to the open
upper and lower complex half-planes in $C$. In fact, our necessary and
sufficient conditions for $F$ are determined completely by the properties of
the restriction of $\widetilde{F}$ to the imaginary axis in $C$. The main
result is given in terms of completely monotonic and absolutely monotonic
functions.


  The past decade has been especially creative for spintronics since the
(re)discovery of various two dimensional (2D) materials. Due to the unusual
physical characteristics, 2D materials have provided new platforms to probe the
spin interaction with other degrees of freedom for electrons, as well as to be
used for novel spintronics applications. This review briefly presents the most
important recent and ongoing research for spintronics in 2D materials.


  We consider an open quantum system described by the GKLS equation and we are
interested in the onset of decoherence. We are in particulary interested in
situations where only some degrees of freedom of the system are coupled to the
environment, and we want to understand if, and how fast, the noise travels
through the system and eventually affects all degrees of freedom. We find that
this can be understood in terms of the H\"ormander condition, a condition on
the commutators of the Hamiltonian vectorfields of the Lindblad operators and
the internal Hamiltonian, which is a condition for hypoellipticity known from
the theory of PDE's. We show that for Gaussian quantum channels this condition
leads to a delay in the onset of decoherence and can as well be used to detect
decoherence free subsystems.


  The goal of this article is to define an analogue of the Weil-pairing for
Drinfeld modules using explicit formulas and to deduce its main properties from
these formulas. Our result generalizes the formula currently known for rank 2
Drinfeld modules and works as a more explicit, elementary proof of the
Weil-pairing's existence than the one appearing in the current literature.


  Using the Atacama Large Millimetre/submillimeter Array (ALMA) and the Karl G.
Jansky Very Large Array (VLA), we observed the Extended Green Object (EGO)
G19.01$-$0.03 with sub-arcsecond resolution from 1.05 mm to 5.01 cm
wavelengths. Our $\sim0.4''\sim1600$ AU angular resolution ALMA observations
reveal a velocity gradient across the millimetre core MM1, oriented
perpendicular to the previously known bipolar molecular outflow, that is
consistently traced by 20 lines of 8 molecular species with a range of
excitation temperatures, including complex organic molecules (COMs). Kinematic
modelling shows the data are well described by models that include a disc in
Keplerian rotation and infall, with an enclosed mass of $40-70
\mathrm{M}_{\odot}$ (within a 2000 AU outer radius) for a disc inclination
angle of $i=40^{\circ}$, of which $5.4-7.2 \mathrm{M}_{\odot}$ is attributed to
the disc. Our new VLA observations show that the 6.7 GHz Class II methanol
masers associated with MM1 form a partial ellipse, consistent with an inclined
ring, with a velocity gradient consistent with that of the thermal gas. The
disc-to-star mass ratio suggests the disc is likely to be unstable and may be
fragmenting into as-yet-undetected low mass stellar companions. Modelling the
centimetre--millimetre spectral energy distribution of MM1 shows the ALMA 1.05
mm continuum emission is dominated by dust, whilst a free-free component,
interpreted as a hypercompact HII region, is required to explain the VLA
$\sim$5 cm emission. The high enclosed mass derived for a source with a
moderate bolometric luminosity ($\sim$10$^{4} \mathrm{L}_{\odot}$) suggests
that the MM1 disc may feed an unresolved high-mass binary system.


  In this short note we prove that the degree of the Gauss map {\nu} of a
closed 3-dimensional hypersurface of the Euclidean space is a lower bound for
the total bending functional B, introduced by G. Wiegmink. Consequently, the
energy functional E introduced by C. M. Wood admits a topological lower bound.


  As is well known, a varying effective gravitational "constant" is one of the
common features of most modified gravity theories. Of course, as a modified
gravity theory, $f(T)$ theory is not an exception. Noting that the
observational constraint on the varying gravitational "constant" is very tight,
in the present work we try to constrain $f(T)$ theories with the varying
gravitational "constant". We find that the allowed model parameter $n$ or
$\beta$ has been significantly shrunk to a very narrow range around zero. In
fact, the results improve the previous constraints by an order of magnitude.


  A key solution to visual question answering (VQA) exists in how to fuse
visual and language features extracted from an input image and question. We
show that an attention mechanism that enables dense, bi-directional
interactions between the two modalities contributes to boost accuracy of
prediction of answers. Specifically, we present a simple architecture that is
fully symmetric between visual and language representations, in which each
question word attends on image regions and each image region attends on
question words. It can be stacked to form a hierarchy for multi-step
interactions between an image-question pair. We show through experiments that
the proposed architecture achieves a new state-of-the-art on VQA and VQA 2.0
despite its small size. We also present qualitative evaluation, demonstrating
how the proposed attention mechanism can generate reasonable attention maps on
images and questions, which leads to the correct answer prediction.


  Magnetic skyrmions are topologically protected spin-whirl quasiparticles
currently considered as promising components for ultra-dense memory devices. In
the bulk they form lattices that are stable over just a few Kelvin below the
ordering temperature. This narrow stability range presents a key challenge for
applications, and finding ways to tune the SkL stability over a wider phase
space is a pressing issue. Here we show experimentally that the skyrmion phase
in the magnetoelectric insulator ${\text{Cu}_2 \text{O} \text{Se} \text{O}_3}$
can either expand or shrink substantially depending on the polarity of a
moderate applied electric field. The data are well-described by an expanded
mean-field model with fluctuations that show how the electric field provides a
direct control of the free energy difference between the skyrmion and the
surrounding conical phase. Our finding of the direct electric field control of
the skyrmion phase stability offers enormous potential for skyrmionic
applications based on a magnetoelectric coupling.


  Streaming interactive proofs (SIPs) are a framework for outsourced
computation. A computationally limited streaming client (the verifier) hands
over a large data set to an untrusted server (the prover) in the cloud and the
two parties run a protocol to confirm the correctness of result with high
probability. SIPs are particularly interesting for problems that are hard to
solve (or even approximate) well in a streaming setting. The most notable of
these problems is finding maximum matchings, which has received intense
interest in recent years but has strong lower bounds even for constant factor
approximations.
  In this paper, we present efficient streaming interactive proofs that can
verify maximum matchings exactly. Our results cover all flavors of matchings
(bipartite/non-bipartite and weighted). In addition, we also present streaming
verifiers for approximate metric TSP. In particular, these are the first
efficient results for weighted matchings and for metric TSP in any streaming
verification model.


  We study on the self-consistency of the pulsar polar cap model, i.e., the
problem of whether the field-aligned electric field is screened by
electron-positron pairs that are injected beyond the pair production front. We
solve the one-dimensional Poisson equation along a magnetic field line, both
analytically and numerically, for a given current density incorporating effects
of returning positrons, and we obtain the conditions for the electric-field
screening. The formula which we obtained gives the screening distance and the
return flux for given primary current density, field geometry and pair creation
rate at the pair production front.
  If the geometrical screening is not possible, for instance, on field lines
with a super-Goldreich-Julian current, then the electric field at the pair
production front is constrained to be fairly small in comparison with values
expected typically by the conventional polar cap models. This is because (1)
positive space charge by pair polarization is limited to a small value, and (2)
returning of positrons leave pair electrons behind. A previous belief that pair
creation with a pair density higher than the Goldreich-Julian density
immediately screens out the electric field is unjustified at least for for a
super Goldreich-Julian current density. We suggest some possibilities to
resolve this difficulty.


  Spin foams are candidate state-sum models for transition amplitudes in
quantum gravity. An active research subject is to identify the possible
divergences of spin foam models, or alternatively to show that models are
finite. We will discuss in detail the (non--occurrence of) divergences in the
Barrett-Crane model, formulated as an integral of delta function weights only.
We will furthermore present a simple method to estimate the divergence degree
of the so-called bubbles for general spin foam models. Divergences in spin
foams are expected to be related to the existence of gauge symmetries
(diffeomorphisms). Thus we have to conclude that such gauge symmetries are not
(fully) present in the model we consider. But we will identify a class of gauge
symmetries which occur at special solutions of the equations imposed by the
delta function weights. This situation is surprisingly similar to the case of
broken diffeomorphism symmetries in discrete gravity, which are present around
flat solutions. We introduce a method to derive (Ward-identity-like) equations
for the vertex amplitude of the model in the case of broken gauge symmetries.


  Complex networks have become increasingly popular for modeling various
real-world phenomena. Realistic generative network models are important in this
context as they avoid privacy concerns of real data and simplify complex
network research regarding data sharing, reproducibility, and scalability
studies. \emph{Random hyperbolic graphs} are a well-analyzed family of
geometric graphs. Previous work provided empirical and theoretical evidence
that this generative graph model creates networks with non-vanishing clustering
and other realistic features. However, the investigated networks in previous
applied work were small, possibly due to the quadratic running time of a
previous generator.
  In this work we provide the first generation algorithm for these networks
with subquadratic running time. We prove a time complexity of $O((n^{3/2}+m)
\log n)$ with high probability for the generation process. This running time is
confirmed by experimental data with our implementation. The acceleration stems
primarily from the reduction of pairwise distance computations through a polar
quadtree, which we adapt to hyperbolic space for this purpose. In practice we
improve the running time of a previous implementation by at least two orders of
magnitude this way. Networks with billions of edges can now be generated in a
few minutes.
  Finally, we evaluate the largest networks of this model published so far. Our
empirical analysis shows that important features are retained over different
graph densities and degree distributions.


  The JCMT Gould Belt Legacy Survey obtained SCUBA-2 observations of dense
cores within three sub-regions of Orion B: LDN 1622, NGC 2023/2024, and NGC
2068/2071, all of which contain clusters of cores. We present an analysis of
the clustering properties of these cores, including the two-point correlation
function and Cartwright's Q parameter. We identify individual clusters of dense
cores across all three regions using a minimal spanning tree technique, and
find that in each cluster, the most massive cores tend to be centrally located.
We also apply the independent M-Sigma technique and find a strong correlation
between core mass and the local surface density of cores. These two lines of
evidence jointly suggest that some amount of mass segregation in clusters has
happened already at the dense core stage.


  Recently, it has been known that the hidden Rashba (R-2) effect in
two-dimensional materials gives rise to a novel physical phenomenon called
spin-layer locking (SLL). However, not only has its underlying fundamental
mechanism been unclear, but also there are only a few materials exhibiting weak
SLL. Here, through the first-principles density functional theory and model
Hamiltonian calculation, we reveal that the R-2 SLL can be determined by the
competition between the sublayer-sublayer interaction and the spin-orbit
coupling (SOC), which is related to the Rashba strength. In addition, the
orbital angular momentum distribution is another crucial point to realize the
strong R-2 SLL. We propose that a novel 2D material Si$_2$Bi$_2$ possesses an
ideal condition for the strong R-2 SLL, whose Rashba strength is evaluated to
be 2.16 eV{\AA}, which is the greatest value ever observed in 2D R-2 materials
to the best of our knowledge. Furthermore, we reveal that the interlayer
interaction in a bilayer structure ensures R-2 states spatially farther apart,
implying a potential application in spintronics.


  Despite the frequent challenges posed by ambiguity when representing meaning
via natural language, it is often ignored or deliberately removed in tasks
mapping language to formally-designed representations, which generally assume a
one-to-one mapping between linguistic and formal representations. We attempt to
address this shortcoming by introducing AmP, a framework, dataset, and
challenge for translating ambiguous natural language to formal representations
like logic and code. We define templates and generate data for five
well-documented linguistic ambiguities. Using AmP, we investigate how several
few-shot text-to-code systems handle ambiguity, introducing three new metrics.
We find that large pre-trained models perform poorly at capturing the
distribution of possible meanings without deliberate instruction. However,
models are able to capture the distribution well when ambiguity is attested in
their inputs. These results motivate a call for including ambiguity explicitly
in datasets and promote considering the distribution of possible outputs when
evaluating systems. Data and code: https://github.com/esteng/ambiguous_parsing


  Let $\mathcal A$ be a unital $C^*$-algebra with the unit $e$. We consider the
elements $a\in \mathcal A$ which are Roberts orthogonal to the unit $e$. We
obtain a characterization of this orthogonality in terms of the Davis--Wielandt
shell of $a$ and show that, for certain classes of elements of $\mathcal A$,
the Roberts orthogonality of $a$ and $e$ is equivalent to the symmetry of the
numerical range of $a$ with respect to the origin.


  In this first paper we discuss the linear theory and the background evolution
of a new class of models we dub SCDEW: Strongly Coupled DE, plus WDM. In these
models, WDM dominates today's matter density; like baryons, WDM is uncoupled.
Dark Energy is a scalar field $\Phi$; its coupling to ancillary CDM, whose
today's density is $\ll 1\, \%$, is an essential model feature. Such coupling,
in fact, allows the formation of cosmic structures, in spite of very low WDM
particle masses ($\sim 100$ eV). SCDEW models yields Cosmic Microwave
Background and linear Large Scale features substantially undistinguishable from
$\Lambda$CDM, but thanks to the very low WDM masses they strongly alleviate
$\Lambda$CDM issues on small scales, as confirmed via numerical simulations in
the II associated paper. Moreover SCDEW cosmologies significantly ease the
coincidence and fine tuning problems of $\Lambda$CDM and, by using a field
theory approach, we also outline possible links with inflationary models. We
also discuss a possible fading of the coupling at low redshifts which prevents
non linearities on the CDM component to cause computational problems. The
(possible) low-$z$ coupling suppression, its mechanism, and its consequences
are however still open questions -not necessarily problems- for SCDEW models.
The coupling intensity and the WDM particle mass, although being extra
parameters in respect to $\Lambda$CDM, are found to be substantially
constrained a priori so that, if SCDEW is the underlying cosmology, we expect
most data to fit also $\Lambda$CDM predictions.


  Neural networks have been applied to tackle many-body electron correlations
for small molecules and physical models in recent years. Here we propose a new
architecture that extends molecular neural networks with the inclusion of
periodic boundary conditions to enable ab initio calculation of real solids.
The accuracy of our approach is demonstrated in four different types of
systems, namely the one-dimensional periodic hydrogen chain, the
two-dimensional graphene, the three-dimensional lithium hydride crystal, and
the homogeneous electron gas, where the obtained results, e.g. total energies,
dissociation curves, and cohesive energies, outperform many traditional ab
initio methods and reach the level of the most accurate approaches. Moreover,
electron densities of typical systems are also calculated to provide physical
intuition of various solids. Our method of extending a molecular neural network
to periodic systems can be easily integrated into other neural network
structures, highlighting a promising future of ab initio solution of more
complex solid systems using neural network ansatz, and more generally endorsing
the application of machine learning in materials simulation and condensed
matter physics.


  Performance of reliable communication over a coherent slow fading channel at
high SNR is succinctly captured as a fundamental tradeoff between diversity and
multiplexing gains. We study the problem of designing codes that optimally
tradeoff the diversity and multiplexing gains. Our main contribution is a
precise characterization of codes that are universally tradeoff-optimal, i.e.,
they optimally tradeoff the diversity and multiplexing gains for every
statistical characterization of the fading channel. We denote this
characterization as one of approximate universality where the approximation is
in the connection between error probability and outage capacity with diversity
and multiplexing gains, respectively. The characterization of approximate
universality is then used to construct new coding schemes as well as to show
optimality of several schemes proposed in the space-time coding literature.


  An ionization front expanding into a neutral medium can be slowed-down
significantly by recombinations. In cosmological numerical simulations the
recombination rate is often computed using a 'clumping factor', that takes into
account that not all scales in the simulated density field are resolved. Here
we demonstrate that using a single value of the clumping factor significantly
overestimates the recombination rate, and how a local estimate of the clumping
factor is both easy to compute, and gives significantly better numerical
convergence. We argue that this lower value of the recombination rate is more
relevant during the reionization process and hence that the importance of
recombinations during reionization has been overestimated.


  In this article, we study skew cyclic codes over ring
$R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is
an odd prime and $v^{3}=v$. We describe generator polynomials of skew cyclic
codes over this ring and investigate the structural properties of skew cyclic
codes over $R$ by a decomposition theorem. We also describe the generator
polynomials of the duals of skew cyclic codes. Moreover, the idempotent
generators of skew cyclic codes over $\mathbb{F}_{q}$ and $R$ are considered.


  The indirect, charge-carrier mediated coupling between localized magnetic
moments is studied for graphene nanoflakes of triangular shape and zig-zag
edge. The characteristic feature of such nanoflakes is the presence of a shell
of zero-energy states in the electronic spectrum. The tight-binding Hamiltonian
supplemented with a Hubbard term is used for electronic structure calculations.
The indirect RKKY (Ruderman-Kittel-Kasuya-Yosida) coupling energy is derived
from the total electronic energy of the system in a non-perturbative way. The
attention is focused on the on-site and plaquette impurities situated along the
edge. The charge doping is also taken into account. It is found that the
zero-energy states may give rise to a coupling mechanism which is describable
by a first-order perturbation calculus and can yield robust indirect coupling
of both ferro- and antiferromagnetic character, which dominates ovet the usual
RKKY mechanism. The numerical results obtained emphasize the importance of the
Hubbard term and the effect of the charge doping on the coupling.


  We show that bounded viscosity solutions of some nonlocal degenerate Isaacs
type operators of order $2s$ are H\"older continuous, provided $s$ is
sufficiently close to 1. As an application we obtain a Liouville theorem.


  The matrix factor model has drawn growing attention for its advantage in
achieving two-directional dimension reduction simultaneously for
matrix-structured observations. In this paper, we propose a simple iterative
least squares algorithm for matrix factor models, in contrast to the Principal
Component Analysis (PCA)-based methods in the literature. In detail, we first
propose to estimate the latent factor matrices by projecting the observations
with two deterministic weight matrices, which are chosen to diversify away the
idiosyncratic components. We show that the inferences on factors are still
asymptotically valid even if we overestimate both the row/column factor
numbers. We then estimate the row/column loading matrices by minimizing the
squared loss function under certain identifiability conditions. The resultant
estimators of the loading matrices are treated as the new weight/projection
matrices and thus the above update procedure can be iteratively performed until
convergence. Theoretically, given the true dimensions of the factor matrices,
we derive the convergence rates of the estimators for loading matrices and
common components at any $s$-th step iteration. Additionally, we propose an
eigenvalue-ratio method to estimate the pair of factor numbers consistently.
Thorough numerical simulations are conducted to investigate the finite-sample
performance of the proposed methods and two real datasets associated with
financial portfolios and multinational macroeconomic indices are used to
illustrate our algorithm's practical usefulness.


  While the global-average temperatures are rapidly rising, more researchers
have been shifting their focus towards the past mass-extinction events in order
to show the relations between temperature increase and temperature thresholds
which might trigger extinction of species. These temperature and
mass-extinction relation graphs are found practical by conservationists and
policy makers to determine temperature threshold values to set climate targets.
Unfortunately, this approach might be dangerous, because mass-extinction events
(MEEs) are related to many environmental parameters and temperature is only one
of them. Herein we provide a more comprehensive evaluation of the environmental
thresholds required to sustain a habitable planet. Besides, we suggest actions
within the sustainable-development goals (SDGs) to observe those critical
environmental parameters, in order to assure having an inhabitable planet for
the current living species.


  This work examines the breakup of a single drop of various low viscosity
fluids as it deforms in the presence of continuous horizontal air jet. Such a
fragmentation typically occurs after the bulk liquid has disintegrated upon
exiting the atomizer and is in the form of an ensemble of drops which undergo
further breakup. The drop deformation and its eventual disintegration is
important in evaluating the efficacy of a particular industrial process, be it
combustion in automobile engines or pesticide spraying in agricultural
applications. The interplay between competing influences of surface tension and
aerodynamic disruptive forces is represented by the Weber number, $We$, and
Ohnesorge number, $Oh$, and used to describe the breakup morphology. The
breakup pattern considered in our study corresponds to that of a bag attached
to a toroidal ring which occurs from $12 < We < 16$. We aim to address several
issues connected with this breakup process and their dependence on $We$ and
$Oh$ which have been hitherto unexplored. The $We$ boundary at which breakup
begins is theoretically determined and the expression obtained, $We = 12(1 +
2/3Oh^2)$, is found to match well with experimental data available in
literature. An exponential growth in the radial extent of the deformed drop and
the streamline dimension of the bag is predicted by a theoretical model and
confirmed by experimental findings. These quantities are observed to strongly
depend on $We$. However, their dependence on $Oh$ is weak.


  The Super-X Divertor (SXD) is an alternative divertor configuration
leveraging total flux expansion at the Outer Strike Point (OSP). While the
extended 2-Point Model (2PM) predicts facilitated detachment access and control
in the SXD configuration, these attractive features are not always retrieved
experimentally. These discrepancies are at least partially explained by the
effect of parallel flows which, when self-consistently included in the 2PM,
reveal the role of total flux expansion on the pressure balance and weaken the
total flux expansion effect on detachment access and control, compared to the
original predictions. This new model can partially explain the discrepancies
between the 2PM and experiments performed on tokamak \`a configuration variable
(TCV), in ohmic L-mode scenarios, which are particularly apparent when scanning
the OSP major radius Rt. In core density ramps in lower Single-Null (SN)
configuration, the impact of Rt on the CIII emission front movement in the
divertor outer leg - used as a proxy for the plasma temperature in the divertor
- is substantially weaker than 2PM predictions. Furthermore, in OSP radial
sweeps in lower and upper SN configurations, in ohmic L-mode scenarios with a
constant core density, the peak parallel particle flux density at the OSP is
almost independent of Rt, while the 2PM predicts a linear dependence. Finally,
analytical and numerical modeling of parallel flows in the divertor is
presented. It is shown that an increase in total flux expansion can favour
supersonic flows at the OSP. Parallel flows are also shown to be relevant by
analysing SOLPS-ITER simulations of TCV.


  In this paper, we tackle the problem of automatically generating algorithms
for linear algebra operations by taking advantage of problem-specific
knowledge. In most situations, users possess much more information about the
problem at hand than what current libraries and computing environments accept;
evidence shows that if properly exploited, such information leads to
uncommon/unexpected speedups. We introduce a knowledge-aware linear algebra
compiler that allows users to input matrix equations together with properties
about the operands and the problem itself; for instance, they can specify that
the equation is part of a sequence, and how successive instances are related to
one another. The compiler exploits all this information to guide the generation
of algorithms, to limit the size of the search space, and to avoid redundant
computations. We applied the compiler to equations arising as part of
sensitivity and genome studies; the algorithms produced exhibit, respectively,
100- and 1000-fold speedups.


  The logic of knowledge and justified assumptions, also known as logic of
grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for
nonmonotonic reasoning. To date, it has been used to embed in it default logic
(propositional case), autoepistemic logic, Turner's logic of universal
causation, and general logic programming under stable model semantics. Besides
showing the generality of GK as a logic for nonmonotonic reasoning, these
embeddings shed light on the relationships among these other logics. In this
paper, for the first time, we show how the logic of GK can be embedded into
disjunctive logic programming in a polynomial but non-modular translation with
new variables. The result can then be used to compute the extension/expansion
semantics of default logic, autoepistemic logic and Turner's logic of universal
causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.


  Let $G$ be a group and $\varphi$ be an automorphism of $G$. Two elements $x,
y$ of $G$ are said to be $\varphi$-twisted conjugate if $y=gx\varphi(g)^{-1}$
for some $g\in G$. A group $G$ has the $R_{\infty}$-property if the number of
$\varphi$-twisted conjugacy classes is infinite for every automorphism
$\varphi$ of $G$. In this paper we prove that the big mapping class group
$MCG(S)$ possesses the $R_{\infty}$-property under some suitable conditions on
the infinite-type surface $S$. As an application we also prove that the big
mapping class group possesses the $R_\infty$-property if and only if it
satisfies the $S_{\infty}$-property.


  In the uplink of multiuser multiple input multiple output (MU-MIMO) systems
operating over aging channels, pilot spacing is crucial for acquiring channel
state information and achieving high signal-to-interference-plus-noise ratio
(SINR). Somewhat surprisingly, very few works examine the impact of pilot
spacing on the correlation structure of subsequent channel estimates and the
resulting quality of channel state information considering channel aging. In
this paper, we consider a fast-fading environment characterized by its
exponentially decaying autocorrelation function, and model pilot spacing as a
sampling problem to capture the inherent trade-off between the quality of
channel state information and the number of symbols available for information
carrying data symbols. We first establish a quasi-closed form for the
achievable asymptotic deterministic equivalent SINR when the channel estimation
algorithm utilizes multiple pilot signals. Next, we establish upper bounds on
the achievable SINR and spectral efficiency, as a function of pilot spacing,
which helps to find the optimum pilot spacing within a limited search space.
Our key insight is that to maximize the achievable SINR and the spectral
efficiency of MU-MIMO systems, proper pilot spacing must be applied to control
the impact of the aging channel and to tune the trade-off between pilot and
data symbols.


  We study the optical response of a strongly correlated electron system near
the metal-insulator transition using a mapping to the sine-Gordon model. With
semiclassical quantization, the spectral weight is distributed between a Drude
peak and absorption lines due to breathers. We calculate the Drude weight, the
optical gap, and the lineshape of breather absorption.


  In statistical modelling of incomplete data, missingness is encoded as a
relation between datasets Y and response patterns R. The partitioning of Y into
observed and missing components is often denoted Yobs and Ymis. We point out a
mathematical defect in this notation which results from two different
mathematical relationships between Y and R not being distinguished, (Yobs,
Ymis, R) in which Yobs values are always observed, and Ymis values are always
missing, and the overlaying of a missingness pattern onto the marginal
distribution for Y, denoted (Yobs, Ymis). With the latter, Yobs and Ymis each
denote mixtures of observable and unobservable data. This overlaying of the
missingness pattern onto Y creates a link between the mathematics and the
meta-mathematics which violates the stochastic relationship encoded in (Y, R).
Additionally, in the theory there is a need to compare partitions of Y
according to different missingness patterns simultaneously. A simple remedy for
these problems is to use four symbols instead of two, and to make the
dependence on the missingness pattern explicit. We explain these and related
issues.


  Inspired by the topological insulator circuit proposed and experimentally
verified by Jia., et al. \cite{1}, we theoretically realized the topological
Lieb lattice, a line centered square lattice with rich topological properties,
in a radio-frequency circuit. We open the topological nontrivial band-gap
through specific capacitor-inductor network, which resembles adding intrinsic
spin orbit coupling term into the tight binding model. Finally, we discuss the
extension of the $\phi=\pi/2$ phase change of hopping between sites to
arbitrary value, and investigate the topological phase transition of the band
structure vary with capacitance, thereby paving the way for designing tunable
lattices using the presented framework.


  We present a quantum digital signature scheme whose security is based on
fundamental principles of quantum physics. It allows a sender (Alice) to sign a
message in such a way that the signature can be validated by a number of
different people, and all will agree either that the message came from Alice or
that it has been tampered with. To accomplish this task, each recipient of the
message must have a copy of Alice's "public key," which is a set of quantum
states whose exact identity is known only to Alice. Quantum public keys are
more difficult to deal with than classical public keys: for instance, only a
limited number of copies can be in circulation, or the scheme becomes insecure.
However, in exchange for this price, we achieve unconditionally secure digital
signatures. Sending an m-bit message uses up O(m) quantum bits for each
recipient of the public key. We briefly discuss how to securely distribute
quantum public keys, and show the signature scheme is absolutely secure using
one method of key distribution. The protocol provides a model for importing the
ideas of classical public key cryptography into the quantum world.


  We study analysis aspects of the sixth order GJMS operator $P_g^6$. Under
conformal normal coordinates around a point, the expansions of Green's function
of $P_g^6$ with pole at this point are presented. As a starting point of the
study of $P_g^6$, we manage to give some existence results of prescribed
$Q$-curvature problem on Einstein manifolds. One among them is that for $n \geq
10$, let $(M^n,g)$ be a closed Einstein manifold of positive scalar curvature
and $f$ a smooth positive function in $M$. If the Weyl tensor is nonzero at a
maximum point of $f$ and $f$ satisfies a vanishing order condition at this
maximum point, then there exists a conformal metric $\tilde g$ of $g$ such that
its $Q$-curvature $Q_{\tilde g}^6$ equals $f$.


  Criterion of the Jeans instability of interstellar gas clouds which are
gravitationally coupled with weakly interacting massive particles is revisited.
It is established that presence of the dark matter always reduces the Jeans
length, and in turn, Jeans mass of the interstellar gas clouds. Astrophysical
implications of this effect are discussed.


  Data sets of multivariate normal distributions abound in many scientific
areas like diffusion tensor imaging, structure tensor computer vision, radar
signal processing, machine learning, just to name a few. In order to process
those normal data sets for downstream tasks like filtering, classification or
clustering, one needs to define proper notions of dissimilarities between
normals and paths joining them. The Fisher-Rao distance defined as the
Riemannian geodesic distance induced by the Fisher information metric is such a
principled metric distance which however is not known in closed-form excepts
for a few particular cases. In this work, we first report a fast and robust
method to approximate arbitrarily finely the Fisher-Rao distance between
multivariate normal distributions. Second, we introduce a class of distances
based on diffeomorphic embeddings of the normal manifold into a submanifold of
the higher-dimensional symmetric positive-definite cone corresponding to the
manifold of centered normal distributions. We show that the projective Hilbert
distance on the cone yields a metric on the embedded normal submanifold and we
pullback that cone distance with its associated straight line Hilbert cone
geodesics to obtain a distance and smooth paths between normal distributions.
Compared to the Fisher-Rao distance approximation, the pullback Hilbert cone
distance is computationally light since it requires to compute only the extreme
minimal and maximal eigenvalues of matrices. Finally, we show how to use those
distances in clustering tasks.


  Signal processing of uniformly spaced data from stationary stochastic
processes with missing samples is investigated. Besides randomly and
independently occurring outliers also correlated data gaps are investigated.
Non-parametric estimators for the mean value, the signal variance, the
autocovariance and cross-covariance functions and the corresponding power
spectral densities are given, which are bias-free, independent of the spectral
composition of the data gaps. Bias-free estimation is obtained by averaging
over valid samples only from the data set. The procedures abstain from
interpolation of missing samples. An appropriate bias correction is used for
cases where the estimated mean value is subtracted out from the data. Spectral
estimates are obtained from covariance functions using Wiener-Khinchin's
theorem.


  We introduce DROID-SLAM, a new deep learning based SLAM system. DROID-SLAM
consists of recurrent iterative updates of camera pose and pixelwise depth
through a Dense Bundle Adjustment layer. DROID-SLAM is accurate, achieving
large improvements over prior work, and robust, suffering from substantially
fewer catastrophic failures. Despite training on monocular video, it can
leverage stereo or RGB-D video to achieve improved performance at test time.
The URL to our open source code is https://github.com/princeton-vl/DROID-SLAM.


  GRAVITY is a second generation VLTI instrument, combining the light of four
telescopes and two objects simultaneously. The main goal is to obtain
astrometrically accurate information. Besides correctly measured stellar phases
this requires the knowledge of the instrumental differential phase, which has
to be measured optically during the astronomical observations. This is the
purpose of a dedicated metrology system. The GRAVITY metrology covers the full
optical path, from the beam combiners up to the reference points in the beam of
the primary telescope mirror, minimizing the systematic uncertainties and
providing a proper baseline in astrometric terms. Two laser beams with a fixed
phase relation travel backward the whole optical chain, creating a fringe
pattern in any plane close to a pupil. By temporal encoding the phase
information can be extracted at any point by means of flux measurements with
photo diodes. The reference points chosen sample the pupil at typical radii,
eliminating potential systematics due differential focus. We present the final
design and the performance estimate, which is in accordance with the overall
requirements for GRAVITY.


  The bivariate distribution with exponential conditionals (BEC) is introduced
by Arnold and Strauss [Bivariate distributions with exponential conditionals,
J. Amer. Statist. Assoc. 83 (1988) 522--527]. This work presents a simple and
fast algorithm for simulating random variates from this density.


  The orbital distribution of transneptunian objects (TNOs) in the distant
Kuiper Belt (with semimajor axes beyond the 2:1 resonance, roughly $a$=50-100
au) provides constraints on the dynamical history of the outer solar system.
Recent studies show two striking features of this region: 1) a very large
population of objects in distant mean-motion resonances with Neptune, and 2)
the existence of a substantial detached population (non-resonant objects
largely decoupled from Neptune). Neptune migration models are able to implant
some resonant and detached objects during the planet migration era, but many
fail to match a variety of aspects of the orbital distribution. In this work,
we report simulations carried out using an improved version of the GPU-based
code GLISSE, following 100,000 test particles per simulation in parallel while
handling their planetary close encounters. We demonstrate for the first time
that a 2 Earth-mass rogue planet temporarily present during planet formation
can abundantly populate both the distant resonances and the detached
populations, surprisingly even without planetary migration. We show how weak
encounters with the rogue greatly increase the efficiency of filling the
resonances, while also dislodging TNOs out of resonance once they reach high
perihelia. The rogue's secular gravitational influence simultaneously generates
numerous detached objects observed at all semimajor axes. These results suggest
that the early presence of additional planet(s) reproduces the observed TNO
orbital structure in the distant Kuiper Belt.


  We report on an angle resolved photoemission (ARPES) study of bulk
electron-doped perovskite iridate, (Sr1-xLax)3Ir2O7. Fermi surface pockets are
observed with a total electron count in keeping with that expected from La
substitution. Depending on the energy and polarization of the incident photons,
these pockets show up in the form of disconnected "Fermi arcs", reminiscent of
those reported recently in surface electron-doped Sr2IrO4. Our observed
spectral variation is consistent with the coexistence of an electronic
supermodulation with structural distortion in the system.


  We study a restricted-height version of the one-dimensional Oslo sandpile
with conserved density, using periodic boundary conditions. Each site has a
limiting height which can be either two or three. When a site reaches its
limiting height it becomes active and may topple, loosing two particles, which
move randomly to nearest-neighbor sites. After a site topples it is randomly
assigned a new limiting height. We study the model using mean-field theory and
Monte Carlo simulation, focusing on the quasi-stationary state, in which the
number of active sites fluctuates about a stationary value. Using finite-size
scaling analysis, we determine the critical particle density and associated
critical exponents.


  The longitudes of perihelia and orbital poles of the solar system's dozen or
so most remote detected objects are clustered in a manner inconsistent with
that of a random sample of uniformly distributed orbits. While small number
statistics and observational biases may explain these features, the statistical
significance of the clustering has led to the recent development of the "Planet
Nine hypothesis." In the proposed scenario, orbits in the distant solar system
are shepherded via secular perturbations from an undetected massive planet on
an eccentric orbit. However, the precession of perihelia and nodes in the outer
Kuiper Belt and inner Oort Cloud are also affected by the the giant planets,
passing stars, and the galactic tide. We perform a large suite of numerical
simulations designed to study the orbital alignment of Extreme Trans-Neptunian
Objects (ETNOs) and Inner Oort Cloud Objects (IOCOs). In our various
integrations that include Planet Nine, we consistently find that >60% of ETNOs
and IOCOs that are detectable after 4 Gyr are also anti-aligned in perihelia
with the distant massive perturber. However, when we randomly select 17 objects
from this sample of remaining orbits, there is significant scatter in the
degree of longitude of perihelion and orbital pole clustering that might be
observed. Furthermore, we argue that, in the absence of Planet Nine, 17
randomly drawn orbits should still exhibit some clustering even if the
underlying distribution is uniform. Thus, we find that still more ETNO and IOCO
detections are required to confidently infer the presence of Planet Nine.


  PKS 1830$-$211 is a $\gamma$-ray emitting, high-redshift (z $= 2.507 \pm
0.002$), lensed flat-spectrum radio quasar. During the period mid-February to
mid-April 2019, this source underwent a series of strong $\gamma$-ray flares
that were detected by both AGILE-GRID and Fermi-LAT, reaching a maximum
$\gamma$-ray flux of $F_{\rm E>100 MeV}\approx 2.3\times10^{-5}$ ph cm$^{-2}$
s$^{-1}$. Here we report on a coordinated campaign from both on-ground
(Medicina, OVRO, REM, SRT) and orbiting facilities (AGILE, Fermi, INTEGRAL,
NuSTAR, Swift, Chandra), with the aim of investigating the multi-wavelength
properties of PKS 1830$-$211 through nearly simultaneous observations presented
here for the first time. We find a possible break in the radio spectra in
different epochs above 15 GHz, and a clear maximum of the 15 GHz data
approximately 110 days after the $\gamma$-ray main activity periods. The
spectral energy distribution shows a very pronounced Compton dominance (> 200)
which challenges the canonical one-component emission model. Therefore we
propose that the cooled electrons of the first component are re-accelerated to
a second component by, e.g., kink or tearing instability during the
$\gamma$-ray flaring periods. We also note that PKS 1830$-$211 could be a
promising candidate for future observations with both Compton satellites (e.g.,
e-ASTROGAM) and Cherenkov arrays (CTAO) which will help, thanks to their
improved sensitivity, in extending the data availability in energy bands
currently uncovered.


  This paper has been withdrawn since the material in these notes has been
updated, and extended, in hep-th/0409031 and hep-th/0409033, and in work to
follow.


  Plug-and-Play (PnP) methods are a class of efficient iterative methods that
aim to combine data fidelity terms and deep denoisers using classical
optimization algorithms, such as ISTA or ADMM, with applications in inverse
problems and imaging. Provable PnP methods are a subclass of PnP methods with
convergence guarantees, such as fixed point convergence or convergence to
critical points of some energy function. Many existing provable PnP methods
impose heavy restrictions on the denoiser or fidelity function, such as
non-expansiveness or strict convexity, respectively. In this work, we propose a
novel algorithmic approach incorporating quasi-Newton steps into a provable PnP
framework based on proximal denoisers, resulting in greatly accelerated
convergence while retaining light assumptions on the denoiser. By
characterizing the denoiser as the proximal operator of a weakly convex
function, we show that the fixed points of the proposed quasi-Newton PnP
algorithm are critical points of a weakly convex function. Numerical
experiments on image deblurring and super-resolution demonstrate 2--8x faster
convergence as compared to other provable PnP methods with similar
reconstruction quality.


  The statistical mechanics of a two-state Ising spin-glass model with finite
random connectivity, in which each site is connected to a finite number of
other sites, is extended in this work within the replica technique to study the
phase transitions in the three-state Ghatak-Sherrington (or random Blume-Capel)
model of a spin glass with a crystal field term. The replica symmetry ansatz
for the order function is expressed in terms of a two-dimensional
effective-field distribution which is determined numerically by means of a
population dynamics procedure. Phase diagrams are obtained exhibiting phase
boundaries which have a reentrance with both a continuous and a genuine
first-order transition with a discontinuity in the entropy. This may be seen as
"inverse freezing", which has been studied extensively lately, as a process
either with or without exchange of latent heat.


  There now exists preliminary experimental evidence for some fractions, such
as $\nu$ = 4/11 and 5/13, that do not belong to any of the sequences
$\nu=n/(2pn\pm 1)$, $p$ and $n$ being integers. We propose that these states
are mixed states of composite fermions of different flavors, for example,
composite fermions carrying two and four vortices. We also obtain an estimate
of the lowest-excitation dispersion curve as well as the transport gap; the
gaps for 4/11 are smaller than those for 1/3 by approximately a factor of 50.


  Recent advances in associative memory design through structured pattern sets
and graph-based inference algorithms have allowed reliable learning and recall
of an exponential number of patterns. Although these designs correct external
errors in recall, they assume neurons that compute noiselessly, in contrast to
the highly variable neurons in brain regions thought to operate associatively
such as hippocampus and olfactory cortex.
  Here we consider associative memories with noisy internal computations and
analytically characterize performance. As long as the internal noise level is
below a specified threshold, the error probability in the recall phase can be
made exceedingly small. More surprisingly, we show that internal noise actually
improves the performance of the recall phase while the pattern retrieval
capacity remains intact, i.e., the number of stored patterns does not reduce
with noise (up to a threshold). Computational experiments lend additional
support to our theoretical analysis. This work suggests a functional benefit to
noisy neurons in biological neuronal networks.


  Model independent formulae are derived for the beam analyzing power $A_y$ and
beam to meson spin transfers in $pp \to pp \omega$ taking into consideration
all the six threshold partial wave amplitudes covering the $Ss, Sp$ and $Ps$
channels. Attention is also focussed on the empirical determination of the
lowest three partial wave amplitudes $f_1, f_2, f_3$ without any discrete
ambiguities.


  Star formation is one of the least understood processes in cosmic evolution.
It is difficult to formulate a general theory for star formation in part
because of the wide range of physical processes involved. The interstellar gas
out of which stars form is a supersonically turbulent plasma governed by
magnetohydrodynamics. This is hard enough by itself, since we do not understand
even subsonic hydrodynamic turbulence very well, let alone supersonic non-ideal
MHD turbulence. However, the behavior of star-forming clouds in the ISM is also
obviously influenced by gravity, which adds complexity, and by both continuum
and line radiative processes. Finally, the behavior of star-forming clouds is
influenced by a wide variety of chemical processes, including formation and
destruction of molecules and dust grains (which changes the thermodynamic
behavior of the gas) and changes in ionization state (which alter how strongly
the gas couples to magnetic fields). As a result of these complexities, there
is nothing like a generally agreed-upon theory of star formation, as there is
for stellar structure. Instead, we are forced to take a much more
phenomenological approach. These notes provide an introduction to our current
thinking about how star formation works.


  An off-lattice Monte Carlo algorithm for solutions of equilibrium polymers
(EP) is proposed. At low and moderate densities this is shown to reproduce
faithfully the (static) properties found recently for flexible linear EP using
a lattice model. The molecular weight distribution (MWD) is well described in
the dilute limit by a Schultz-Zimm distribution and becomes purely exponential
in the semi-dilute limit.
  Additionally, very concentrated molten systems are studied. The MWD remains a
pure exponential in contrast to recent claims. The mean chain mass is found to
increase faster with density than in the semi-dilute regime due to additional
entropic interactions generated by the dense packing of spheres.
  We also consider systems in which the formation of rings is allowed so that
both the linear chains and the rings compete for the monomers. In agreement
with earlier predictions the MWD of the rings reveals a strong singularity
whereas the MWD of the coexisting linear chains remains essentially unaffected.


  Age-specific mortality rates are often disaggregated by different attributes,
such as sex, state, ethnic group and socioeconomic status. In making social
policies and pricing annuity at national and subnational levels, it is
important not only to forecast mortality accurately, but also to ensure that
forecasts at the subnational level add up to the forecasts at the national
level. This motivates recent developments in grouped functional time series
methods (Shang and Hyndman, 2017) to reconcile age-specific mortality
forecasts. We extend these grouped functional time series forecasting methods
to multivariate time series, and apply them to produce point forecasts of
mortality rates at older ages, from which fixed-term annuities for different
ages and maturities can be priced. Using the regional age-specific mortality
rates in Japan obtained from the Japanese Mortality Database, we investigate
the one-step-ahead to 15-step-ahead point-forecast accuracy between the
independent and grouped forecasting methods. The grouped forecasting methods
are shown not only to be useful for reconciling forecasts of age-specific
mortality rates at national and subnational levels, but they are also shown to
allow improved forecast accuracy. The improved forecast accuracy of mortality
rates is of great interest to the insurance and pension industries for
estimating annuity prices, in particular at the level of population subgroups,
defined by key factors such as sex, region, and socioeconomic grouping.