  We study the mixing time of a random walker who moves inside a dynamical
random cluster model on the d-dimensional torus of side-length n. In this
model, edges switch at rate \mu between open and closed, following a Glauber
dynamics for the random cluster model with parameters p,q. At the same time,
the walker jumps at rate 1 as a simple random walk on the torus, but is only
allowed to traverse open edges. We show that for small enough p the mixing time
of the random walker is of order n^2/\mu. In our proof we construct of a
non-Markovian coupling through a multi-scale analysis of the environment, which
we believe could be more widely applicable.


  Suppose that $\tilde{G}$ is a connected reductive group defined over a field
$k$, and $\Gamma$ is a finite group acting via $k$-automorphisms of $\tilde{G}$
satisfying a certain quasi-semisimplicity condition. Then the connected part of
the group of $\Gamma$-fixed points in $\tilde{G}$ is reductive. We axiomatize
the main features of the relationship between this fixed-point group and the
pair $(\tilde{G},\Gamma)$, and consider any group $G$, not just the
$\Gamma$-fixed points of $\tilde{G}$, satisfying the axioms. (In fact, the
axioms do not require $\Gamma$ to act on all of $\tilde{G}$.) If both
$\tilde{G}$ and $G$ are $k$-quasisplit, then we can consider their duals
$\tilde{G}^*$ and $G^*$. We show the existence of and give an explicit formula
for a natural map from semisimple stable conjugacy classes in $G^*(k)$ to those
in $\tilde{G}^*(k)$. If $k$ is finite, then our groups are automatically
quasisplit, and our result specializes to give a map from semisimple conjugacy
classes in $G^*(k)$ to those in $\tilde{G}^*(k)$. Since such classes
parametrize packets of irreducible representations of $G(k)$ and
$\tilde{G}(k)$, one obtains a mapping of such packets.


  We start by reviewing some interesting results in mesoscopic physics
illustrating nontrivial insights on Quantum Mechanics. We then review the
general principles of dephasing (sometimes called "decoherence") of
Quantum-Mechanical interference by coupling to the environment degrees of
freedom. A particular recent example of dephasing by a current-carrying
(nonequilibrium) system is then discussed in some detail. This system is itself
a manifestly Quantum Mechanical one and this is another illustration of
detection without the need for "classical observers" etc. We conclude by
describing briefly a recent problem having to do with the orbital magnetic
response of conduction electrons (another manifestly Quantum Mechanical
property): The magnetic response of a normal layer (N) coating a
superconducting cylinder (S). Some recent very intriguing experimental results
on a giant paramagnetic component of this response are explained using special
states in the normal layer. It is hoped that these discussions illustrate not
only the vitality and interest of mesoscopic physics\cite{book} but also its
extreme relevance to fundamental issues in Quantum Mechanics.


  Let $L$ be a nef line bundle on a smooth complex projective variety $X$ of
dimension $n$. Demailly has introduced a very interesting invariant --- the
Seshadri constant $\epsilon(L,x)$ --- which in effect measures how positive $L$
is locally near a given point $x \in X$. For instance, Seshadri's criterion for
ampleness may be phrased as stating that $L$ is ample if and only if there
exists a positive number $e > 0$ such that $\epsilon(L,x) > e$ for all $x \in
X$, and if $L$ is VERY ample, then $\epsilon(L,x) \ge 1$ for every $x$. We
prove the somewhat surprising result that in each dimension $n$ there is a
uniform lower bound on the Seshadri constant of an ample line bundle $L$ at a
very general point of $X$. Specifically, $\epsilon(L,x) \ge (1/n) $ for all $x
\in X$ outside the union of countably many proper subvarieties of $X$. Examples
of Miranda show that there cannot exist a bound (independent of $X$ and $L$)
that holds at every point. The proof draws inspiration from two sources: first,
the arguments used to prove boundedness of Fano manifolds of Picard number one;
and secondly some of the geometric ideas involving zero-estimates appearing in
the work of Faltings and others on Diophantine approximation and transcendence
theory. We give some elementary applications of the main theorem to adjoint and
pluricanonical linear series.


  We report on near-infrared and optical observations of the GRB 970616 error
box and of the X-ray sources discovered by ASCA and ROSAT in the region. No
optical transient was found either within the IPN band or in the X-ray error
boxes, similarly to other bursts, and we suggest that either considerable
intrinsic absorption was present (like GRB 970828) or that the optical
transient displayed a very fast decline (like GRB 980326 and GRB 980519).


  We show that in Gauss-Bonnet gravity with negative Gauss-Bonnet coefficient
and without a cosmological constant, one can explain the acceleration of the
expanding Universe. We first introduce a solution of the Gauss-Bonnet gravity
with negative Gauss-Bonnet coefficient and no cosmological constant term in an
empty $(n+1)$-dimensional bulk. This solution can generate a de Sitter
spacetime with curvature $n(n+1)/\{(n-2)(n-3)|\alpha|\}$. We show that an
$(n-1)$-dimensional brane embedded in this bulk can have an expanding feature
with acceleration. We also considered a 4-dimensional brane world in a
5-dimensional empty space with zero cosmological constant and obtain the
modified Friedmann equations. The solution of these modified equations in
matter-dominated era presents an expanding Universe with negative deceleration
and positive jerk which is consistent with the recent cosmological data. We
also find that for this solution, the $"n"th$ derivative of the scale factor
with respect to time can be expressed only in terms of Hubble and deceleration
parameters.


  We investigate the mass spectrum of Nucleon and Delta (and its counterparts
with strange and charm), and their excited states, in quenched lattice QCD with
exact chiral symmetry. For each light baryon, we use 23 masses to determine the
coefficients of the mass formula in quenched chiral perturbation theory. By
chiral extrapolation to m_\pi=135 MeV, we obtain M_N=958(26) MeV,
M_{N*}=1553(42) MeV, M_{Delta}=1216(32) MeV and M_{Delta*}=1611(17) MeV, which
are identified with N(939)P_{11},N(1535)S_{11}, Delta(1232)P_{33} and
Delta(1620)S_{31} respectively. Further, we directly measure the masses of
Omega^{-}, M_{Omega}=1648(60) MeV, and its excited state, M_{Omega*}=1935(48)
MeV; as well as the triply charmed baryon Omega_{ccc}^{++},
M_{Omega_{ccc}^{++}}=4931(22) MeV, and its excited state,
M_{{\Omega^{++}_{ccc}}^*}=5185(35) MeV.


  FU Orionis stars (FUORS) are eruptive pre-main sequence objects thought to
represent quasi-periodic or recurring stages of enhanced accretion during the
low-mass star-forming process. We characterize the sample of known and
candidate FUORS in an homogeneous and consistent way, deriving stellar and
circumstellar parameters for each object. We emphasize the analysis in those
parameters that are supposed to vary during the FUORS stage. We modeled the
SEDs of 24 of the 26 currently known FUORS, using the radiative transfer code
of Whitney et al (2003b). We compare our models with those obtained by
Robitaille et al. (2007) for Taurus class II and I sources in quiescence
periods, by calculating the cumulative distribution of the different
parameters. FUORS have more massive disks: we find that $\sim80\%$ of the disks
in FUORS are more massive than any Taurus class II and I sources in the sample.
Median values for the disk mass accretion rates are ~ 1.e-7 Msun/yr vs ~ 1.e-5
Msun/yr for standard YSOs (young stellar objects) and FUORS, respectively.
While the distributions of envelope mass accretion rates for class I FUORS and
for standard class I objects are similar, FUORS, on average, have higher
envelope mass accretion rates than standard class II and class I sources. Most
FUORS (~ 70%) have envelope mass accretion rates above 1.e-7 Msun/yr. In
contrast, 60% of the classical YSO sample have accretion rates below this
value. Our results support the current scenario in which changes experimented
by the circumstellar disk explain the observed properties of these stars.
However, the increase in the disk mass accretion rate is smaller than
theoretically predicte (Frank et al. 1992; Hartmann & Kenyon 1996), though in
good agreement with previous determinations.


  Bagging and boosting are proved to be the best methods of building multiple
classifiers in classification combination problems. In the area of "flat
clustering" problems, it is also recognized that multi-clustering methods based
on boosting provide clusterings of an improved quality. In this paper, we
introduce a novel multi-clustering method for "hierarchical clusterings" based
on boosting theory, which creates a more stable hierarchical clustering of a
dataset. The proposed algorithm includes a boosting iteration in which a
bootstrap of samples is created by weighted random sampling of elements from
the original dataset. A hierarchical clustering algorithm is then applied to
selected subsample to build a dendrogram which describes the hierarchy.
Finally, dissimilarity description matrices of multiple dendrogram results are
combined to a consensus one, using a hierarchical-clustering-combination
approach. Experiments on real popular datasets show that boosted method
provides superior quality solutions compared to standard hierarchical
clustering methods.


  This work describes a simple agent model for the spread of an epidemic
outburst, with special emphasis on mobility and geographical considerations,
which we characterize via statistical mechanics and numerical simulations. As
the mobility is decreased, a percolation phase transition is found separating a
free-propagation phase in which the outburst spreads without finding spatial
barriers and a localized phase in which the outburst dies off. Interestingly,
the number of infected agents is subject to maximal fluctuations at the
transition point, building upon the unpredictability of the evolution of an
epidemic outburst. Our model also lends itself to testing vaccination
schedules. Indeed, it has been suggested that if a vaccine is available but
scarce it is convenient to carefully select the vaccination program to maximize
the chances of halting the outburst. We discuss and evaluate several schemes,
with special interest on how the percolation transition point can be shifted,
allowing for higher mobility without epidemiological impact.


  We establish the local H\"older continuity for the nonnegative weak solutions
of certain doubly nonlinear parabolic equations possessing a singularity in the
time derivative part and a degeneracy in the principal part. The proof involves
the method of intrinsic scaling and the setting is a measure space equipped
with a doubling non-trivial Borel measure supporting a Poincar\'e inequality.


  The convergence of HPC and data-intensive methodologies provide a promising
approach to major performance improvements. This paper provides a general
description of the interaction between traditional HPC and ML approaches and
motivates the Learning Everywhere paradigm for HPC. We introduce the concept of
effective performance that one can achieve by combining learning methodologies
with simulation-based approaches, and distinguish between traditional
performance as measured by benchmark scores. To support the promise of
integrating HPC and learning methods, this paper examines specific examples and
opportunities across a series of domains. It concludes with a series of open
computer science and cyberinfrastructure questions and challenges that the
Learning Everywhere paradigm presents.


  There is an increasing need to hold players responsible for negative or
positive impact that take place elsewhere in a value chain or a network. For
example, countries or companies are held more and more responsible for their
indirect carbon emissions. We introduce a responsibility value that allocates
the total impact of the value chain among the players, taking into account
their direct impact and their indirect impact through the underlying graph.
Moreover, we show that the responsibility value satisfies a set of natural yet
important properties.


  The $j = 3/2$ fermions in cubic crystals or cold atomic gases can form Cooper
pairs in both singlet ($J = 0$) and unconventional quintet ($J = 2$) $s$-wave
states. Our study utilizes analytical field theory to examine fluctuations in
these states within the framework of the Luttinger-Kohn model. We investigate
how collective modes evolve with varying spin-orbit coupling (SOC) strength. In
the singlet state, quintet Bardasis-Schrieffer modes soften at a finite
wavevector, hinting at Fulde-Ferrell-Larkin-Ovchinnikov physics. In the quintet
state, we identify additional gapless and gapped modes originating from the
partially broken symmetry due to SOC. Our results can be readily detected using
current experimental techniques.


  Magnetic skyrmions are compact chiral spin textures that exhibit a rich
variety of topological phenomena and hold potential for developing high-density
memory devices and novel computing schemes driven by spin currents. Here, we
demonstrate room temperature interfacial stabilization and current-driven
control of skyrmion bubbles in the ferrimagnetic insulator Tm3Fe5O12 (TmIG)
coupled to Pt. We track the current-induced motion of individual skyrmion
bubbles. The ferrimagnetic order of the crystal together with the interplay of
spin-orbit torques and pinning determine the skyrmion dynamics in TmIG and
result in a strong skyrmion Hall effect characterized by a negative deflection
angle and hopping motion. Further, we show that the velocity and depinning
threshold of the skyrmion bubbles can be modified by exchange coupling TmIG to
an in-plane magnetized Y3Fe5O12 layer, which distorts the spin texture of the
skyrmions and leads to a directional-dependent rectification of their dynamics.
This effect, which is equivalent to a magnetic ratchet, is exploited to control
the skyrmion flow in a racetrack-like device.


  We prove that "unitary deformation K-theory" takes products of finitely
generated groups to coproducts of algebra spectra over ku, the connective
K-theory spectrum. Additionally, we give spectral sequences for computing the
homotopy groups of the unitary deformation K-theory of a group G and the
cofiber of the Bott map in terms of PU(n)-equivariant K-theory and homology of
spaces of G-representations.


  A theory of the IR-field-induced single-photon generation by the narrow
thin-film superconducting rings made of the isotropic s-wave pairing type-II
superconductors is presented. It is shown that statistical measurements of the
energies of photons emitted by the same current-carrying ring prepared
initially in the same quantum state, allow to find the number distribution of
Cooper pairs in the superconductor.


  We present a catalog of mid-infrared (MIR) spectra of 150 infrared (IR)
luminous galaxies in the Spitzer extragalactic first look survey obtained with
IRS on board Spitzer. The sample is selected to be brighter than ~0.9 mJy at 24
micron and it has a z distribution in the range [0.3,3.5] with a peak at z=1.
It primarily comprises ultraluminous IR galaxies at z>1 and luminous IR
galaxies at z<1, as estimated from their monochromatic 14 micron luminosities.
The number of sources with spectra that are dominated by an active galactic
nucleus (AGN) continuum is 49, while 39 sources have strong, star-formation
related features. For this classification, we used the equivalent width (EW) of
the 11.3 micron polycyclic aromatic hydrocarbon (PAH) feature. Several
intermediate/high z starbursts have higher PAH EW than local ULIRGs. An
increase in the AGN activity is observed with increasing z and luminosity,
based on the decreasing EW of PAHs and the increasing [NeIII]/[NeII] ratio.
Spectral stacking leads to the detection of the 3.3 micron PAH, the H2 0-0 S(1)
and S(3) lines, and the [NeV] line. We observe differences in the flux ratios
of PAHs in the stacked spectra of IR-luminous galaxies with z or luminosity,
which are not due to extinction effects. When placing the observed galaxies on
IR color-color diagrams, we find that the wedge defining AGN comprises most
sources with continuum-dominated spectra, but also contains many starbursts.
The comparison of the 11.3 micron PAH EW and the H-band effective radius,
measured from HST data, indicates that sources with EW>2 micron, are typically
more extended than ~3 kpc. However, there is no strong correlation between the
MIR spectral type and the near-IR extent of the sources. [Abridged].


  We present a novel method to perform quantum state tomography for
many-particle systems which are particularly suitable for estimating states in
lattice systems such as of ultra-cold atoms in optical lattices. We show that
the need for measuring a tomographically complete set of observables can be
overcome by letting the state evolve under some suitably chosen random circuits
followed by the measurement of a single observable. We generalize known results
about the approximation of unitary 2-designs, i.e., certain classes of random
unitary matrices, by random quantum circuits and connect our findings to the
theory of quantum compressed sensing. We show that for ultra-cold atoms in
optical lattices established techniques like optical super-lattices, laser
speckles, and time-of-flight measurements are sufficient to perform fully
certified, assumption-free tomography. Combining our approach with tensor
network methods - in particular the theory of matrix-product states - we
identify situations where the effort of reconstruction is even constant in the
number of lattice sites, allowing in principle to perform tomography on
large-scale systems readily available in present experiments.


  Based on the work of Durhuus-J{\'o}nsson and Benedetti-Ziegler, we revisit
the question of the number of triangulations of the 3-ball. We introduce a
notion of nucleus (a triangulation of the 3-ball without internal nodes, and
with each internal face having at most 1 external edge). We show that every
triangulation can be built from trees of nuclei. This leads to a new
reformulation of Gromov's question: We show that if the number of rooted nuclei
with $t$ tetrahedra has a bound of the form $C^t$, then the number of rooted
triangulations with $t$ tetrahedra is bounded by $C_*^t$.


  We investigate multi-spacecraft observations of the January 17, 2010 solar
energetic particle event. Energetic electrons and protons have been observed
over a remarkable large longitudinal range at the two STEREO spacecraft and
SOHO suggesting a longitudinal spread of nearly 360 degrees at 1AU. The flaring
active region, which was on the backside of the Sun as seen from Earth, was
separated by more than 100 degrees in longitude from the magnetic footpoints of
each of the three spacecraft. The event is characterized by strongly delayed
energetic particle onsets with respect to the flare and only small or no
anisotropies in the intensity measurements at all three locations. The presence
of a coronal shock is evidenced by the observation of a type II radio burst
from the Earth and STEREO B. In order to describe the observations in terms of
particle transport in the interplanetary medium, including perpendicular
diffusion, a 1D model describing the propagation along a magnetic field line
(model 1) (Dr\"oge, 2003) and the 3D propagation model (model 2) by (Dr\"oge et
al., 2010) including perpendicular diffusion in the interplanetary medium have
been applied, respectively. While both models are capable of reproducing the
observations, model 1 requires injection functions at the Sun of several hours.
Model 2, which includes lateral transport in the solar wind, reveals high
values for the ratio of perpendicular to parallel diffusion. Because we do not
find evidence for unusual long injection functions at the Sun we favor a
scenario with strong perpendicular transport in the interplanetary medium as
explanation for the observations.


  We study vanishing viscosity solutions to the axisymmetric Euler equations
with (relative) vorticity in $L^p$ with $p>1$. We show that these solutions
satisfy the corresponding vorticity equations in the sense of renormalized
solutions. Moreover, we show that the kinetic energy is preserved provided that
$p>3/2$ and the vorticity is nonnegative and has finite second moments.


  Blueworks - Medical Expert Diagnosis is developing an application, BWEye, to
be used as an ophthalmology consultation decision support system. The
implementation of this application involves several different tasks and one of
them is the implementation of an ophthalmology images registration algorithm.
The work reported in this document is related with the implementation of an
algorithm to register images of angiography, colour retinography and redfree
retinography. The implementations described were developed in the software
MATLAB.
  The implemented algorithm is based in the detection of the bifurcation points
(y-features) of the vascular structures of the retina that usually are visible
in the referred type of images. There are proposed two approaches to establish
an initial set of features correspondences. The first approach is based in the
maximization of the mutual information of the bifurcation regions of the
features of images. The second approach is based in the characterization of
each bifurcation point and in the minimization of the Euclidean distance
between the descriptions of the features of the images in the descriptors
space. The final set of the matching features for a pair of images is defined
through the application of the RANSAC algorithm.
  Although, it was not achieved the implementation of a full functional
algorithm, there were made several analysis that can be important to future
improvement of the current implementation.


  Microstrctural, vibrational, ferroelectric and dielectric properties
investigation reveals non-stoichiometric chemical ordered regions (CORs) and
relaxor like dielectric characteristics in lead magnesium niobate (PMN)
ceramics uniaxially hot pressed (HP) at 800 oC to 1200 oC. Occurance of (1/2
1/2 1/2) superlattice reflections along <111> in <110> zone axis SAED pattern
as well as the presence of bright nano-meter regions in corresponding
dark-field images in 800 oC hot pressed PMN demonstrates formation of the CORs
as soon as perovskite phase is formed during calcination and remains unaffected
with HP sintering tempreature. Separation between two broad peaks of Nb-O-Nb
stretching mode and the red-shift of O-B-O bending modes suggest an increase in
the polar nano-size regions. Grain size dependence of the em and shifting of
the Tm from 278 K to 263 K is explained by the core-shell model. Polarization
switching and impedance spectroscopy is observed to be consistent with the
grain size analysis.


  The assumption that a parametric class of functions fits the data structure
sufficiently well is common in fitting curves and surfaces to regression data.
One then derives a parameter estimate resulting from a least squares fit, say,
and in a second step various kinds of chi^2 goodness of fit measures, to assess
whether the deviation between data and estimated surface is due to random noise
and not to systematic departures from the model. In this paper we show that
commonly-used chi^2-measures are invalid in regression models, particularly
when inhomogeneous noise is present. Instead we present a bootstrap algorithm
which is applicable in problems described by noisy versions of Fredholm
integral equations. of the first kind. We apply the suggested method to the
problem of recovering the luminosity density in the Milky Way from data of the
DIRBE experiment on board the COBE satellite.


  In this paper, by using the atomic decomposition theory of Hardy space and
weak Hardy space, we discuss the boundedness of parameterized Littlewood-Paley
operator with variable kernel on these spaces.


  We report on the results of a simulation based study of colliding magnetized
plasma flows. Our set-up mimics pulsed power laboratory astrophysical
experiments but, with an appropriate frame change, are relevant to
astrophysical jets with internal velocity variations. We track the evolution of
the interaction region where the two flows collide. Cooling via radiative loses
are included in the calculation. We systematically vary plasma beta ($\beta_m$)
in the flows, the strength of the cooling ($\Lambda_0$) and the exponent
($\alpha$) of temperature-dependence of the cooling function. We find that for
strong magnetic fields a counter-propagating jet called a "spine" is driven by
pressure from shocked toroidal fields. The spines eventually become unstable
and break apart. We demonstrate how formation and evolution of the spines
depends on initial flow parameters and provide a simple analytic model that
captures the basic features of the flow.


  The Hilbert class field of the quaternion algebra $B$ is an algebra
$\mathscr{H}(B)$ such that every two-sided ideal of $B$ is principal in
$\mathscr{H}(B)$. We study the avatars of $B$ and $\mathscr{H}(B)$, i.e.
algebraic surfaces attached to the quaternion algebras. It is proved that the
avatar of $\mathscr{H}(B)$ is obtained from the avatar of $B$ by a birational
map (blow-up). We apply this result to the function field analogy.


  We consider both geometric and measure-theoretic shrinking targets for
ergodic maps, investigating when they are visible or invisible. Some Baire
category theorems are proved, and particular constructions are given when the
underlying map is fixed. Open questions about shrinking targets are also
described.


  We propose in this paper a method for measuring the similarity between
ontological concepts and terms. Our metric can take into account not only the
common words of two strings to compare but also other features such as the
position of the words in these strings, or the number of deletion, insertion or
replacement of words required for the construction of one of the two strings
from each other. The proposed method was then used to determine the ontological
concepts which are equivalent to the terms that qualify toponymes. It aims to
find the topographical type of the toponyme.


  Cyber-Physical Systems (CPSs), comprising both software and physical
components, arise in many industry-relevant domains and are often mission- or
safety-critical.
  System-Level Verification (SLV) of CPSs aims at certifying that given (e.g.,
safety or liveness) specifications are met, or at estimating the value of some
KPIs, when the system runs in its operational environment, i.e., in presence of
inputs (from users or other systems) and/or of additional, uncontrolled
disturbances.
  To enable SLV of complex systems from the early design phases, the currently
most adopted approach envisions the simulation of a system model under the
(time bounded) operational scenarios of interest. Simulation-based SLV can be
computationally prohibitive (years of sequential simulation), since model
simulation is computationally intensive and the set of scenarios of interest
can huge.
  We present a technique that, given a collection of scenarios of interest
(extracted from mass-storage databases or from symbolic structures, e.g.,
constraint-based scenario generators), computes parallel shortest simulation
campaigns, which drive a possibly large number of system model simulators
running in parallel in a HPC infrastructure through all (and only) those
scenarios in the user-defined (possibly random) order, by wisely avoiding
multiple simulations of repeated trajectories, thus minimising the overall
completion time, compatibly with the available simulator memory capacity.
  Our experiments on Modelica/FMU and Simulink case study models with up to
~200 million scenarios show that our optimisation yields speedups as high as
8x. This, together with the enabled massive parallelisation, makes practically
viable (a few weeks in a HPC infrastructure) verification tasks (both
statistical and exhaustive, with respect to the given set of scenarios) which
would otherwise take inconceivably long time.


  In the quest to determine fault weakening processes that govern earthquake
mechanics, it is common to infer the earthquake breakdown energy from
seismological measurements. Breakdown energy is observed to scale with slip,
which is often attributed to enhanced fault weakening with continued slip or at
high slip rates, possibly caused by flash heating and thermal pressurization.
However, breakdown energy varies by more than six orders of magnitude, which is
physically irreconcilable with prevailing material properties. We present a
dynamic model that demonstrates that breakdown energy scaling can occur despite
constant fracture energy and does not require thermal pressurization or other
enhanced weakening. Instead, earthquake breakdown energy scaling occurs simply
due to scale-invariant stress drop overshoot, which is affected more directly
by the overall rupture mode -- crack-like or pulse-like -- rather than from a
specific slip-weakening relationship. Our findings suggest that breakdown
energy may be used to discern crack-like earthquakes from self-healing pulses
with negative breakdown energy.


  The hybrid high-order method is a modern numerical framework for the
approximation of elliptic PDEs. We present here an extension of the hybrid
high-order method to meshes possessing curved edges/faces. Such an extension
allows us to enforce boundary conditions exactly on curved domains, and capture
curved geometries that appear internally in the domain e.g. discontinuities in
a diffusion coefficient. The method makes use of non-polynomial functions on
the curved faces and does not require any mappings between reference
elements/faces. Such an approach does not require the faces to be polynomial,
and has a strict upper bound on the number of degrees of freedom on a curved
face for a given polynomial degree. Moreover, this approach of enriching the
space of unknowns on the curved faces with non-polynomial functions should
extend naturally to other polytopal methods. We show the method to be stable
and consistent on curved meshes and derive optimal error estimates in $L^2$ and
energy norms. We present numerical examples of the method on a domain with
curved boundary, and for a diffusion problem such that the diffusion tensor is
discontinuous along a curved arc.


  We estimate the sums \[ \sum_{c\leq x} \frac{S(m,n,c,\chi)}{c}, \] where the
$S(m,n,c,\chi)$ are Kloosterman sums of half-integral weight on the modular
group. Our estimates are uniform in $m$, $n$, and $x$ in analogy with Sarnak
and Tsimerman's improvement of Kuznetsov's bound for the ordinary Kloosterman
sums. Among other things this requires us to develop mean value estimates for
coefficients of Maass cusp forms of weight $1/2$ and uniform estimates for
$K$-Bessel integral transforms. As an application, we obtain an improved
estimate for the classical problem of estimating the size of the error term in
Rademacher's formula for the partition function $p(n)$.


  Dropout is commonly used to help reduce overfitting in deep neural networks.
Sparsity is a potentially important property of neural networks, but is not
explicitly controlled by Dropout-based regularization. In this work, we propose
Sparseout a simple and efficient variant of Dropout that can be used to control
the sparsity of the activations in a neural network. We theoretically prove
that Sparseout is equivalent to an $L_q$ penalty on the features of a
generalized linear model and that Dropout is a special case of Sparseout for
neural networks. We empirically demonstrate that Sparseout is computationally
inexpensive and is able to control the desired level of sparsity in the
activations. We evaluated Sparseout on image classification and language
modelling tasks to see the effect of sparsity on these tasks. We found that
sparsity of the activations is favorable for language modelling performance
while image classification benefits from denser activations. Sparseout provides
a way to investigate sparsity in state-of-the-art deep learning models. Source
code for Sparseout could be found at
\url{https://github.com/najeebkhan/sparseout}.


  We prove fine higher regularity results of Calder\'on-Zygmund-type for
equations involving nonlocal operators modelled on the fractional $p$-Laplacian
with possibly discontinuous coefficients of VMO-type. We accomplish this by
establishing precise pointwise bounds in terms of certain fractional sharp
maximal functions. This approach is new already in the linear setting and
enables us to deduce sharp regularity results also in borderline cases.


  A real-world graph has a complex topological structure, which is often formed
by the interaction of different latent factors. However, most existing methods
lack consideration of the intrinsic differences in relations between nodes
caused by factor entanglement. In this paper, we propose an
\underline{\textbf{A}}dversarial \underline{\textbf{D}}isentangled
\underline{\textbf{G}}raph \underline{\textbf{C}}onvolutional
\underline{\textbf{N}}etwork (ADGCN) for disentangled graph representation
learning. To begin with, we point out two aspects of graph disentanglement that
need to be considered, i.e., micro-disentanglement and macro-disentanglement.
For them, a component-specific aggregation approach is proposed to achieve
micro-disentanglement by inferring latent components that cause the links
between nodes. On the basis of micro-disentanglement, we further propose a
macro-disentanglement adversarial regularizer to improve the separability among
component distributions, thus restricting the interdependence among components.
Additionally, to reveal the topological graph structure, a diversity-preserving
node sampling approach is proposed, by which the graph structure can be
progressively refined in a way of local structure awareness. The experimental
results on various real-world graph data verify that our ADGCN obtains more
favorable performance over currently available alternatives. The source codes
of ADGCN are available at \textit{\url{https://github.com/SsGood/ADGCN}}.


  We investigate interacting phase oscillators whose mean field is at a
different frequency from the mean or mode of their natural frequencies. The
associated asymmetries lead to a macroscopic travelling wave. We show that the
mean ensemble frequency of such systems differs from their entrainment
frequency. In some scenarios these frequencies take values that,
counter-intuitively, lie beyond the limits of the natural frequencies. The
results indicate that a clear distinction should be drawn between the two
variables describing the macroscopic dynamics of cooperative systems. This has
important implications for real systems where a non-trivial distribution of
parameters is common.


  M105 is an early-type galaxy in the nearby Leo I group, the closest galaxy
group to contain all galaxy types and therefore an excellent environment to
explore the low-mass end of intra-group light (IGL) assembly. We present a new
extended kinematic survey of planetary nebulae (PNe) in M105 and the
surrounding 30'x30' in the Leo I group with the Planetary Nebula Spectrograph.
We use PNe as kinematic tracers of the diffuse stellar light in the halo and
IGL and employ Gaussian mixture models to separate contributions from the
companion galaxy NGC 3384 and associate PNe with halo and IGL components around
M105. We present a catalogue of 314 PNe and firmly associate 93 with NGC 3384
and 169 with M105. The PNe in M105 are further associated with its halo and the
surrounding exponential envelope. We construct smooth velocity and velocity
dispersion fields and calculate projected rotation, velocity dispersion, and
$\lambda_R$ profiles for each component. Halo PNe exhibit declining velocity
dispersion and rotation profiles, while the velocity dispersion and rotation of
the exponential envelope increase notably at large radii. We identify three
regimes with distinct kinematics that are linked to distinct stellar population
properties: (i) the rotating core (within $1~R_\mathrm{eff}$) formed in situ
and dominated by metal-rich ([M/H]~0) stars likely formed in situ, (ii) the
halo from 1 to $7.5~R_\mathrm{eff}$ consisting of intermediate-metallicity
stars ([M/H]>-1), either formed in situ or brought in through major mergers,
and (iii) the exponential envelope reaching beyond our farthest data point at
16 $R_\mathrm{eff}$, predominately composed of metal-poor ([M/H]<-1) stars. The
high velocity dispersion and moderate rotation of the latter are consistent
with that measured for dwarf satellite galaxies in the Leo I group, indicating
that the exponential envelope traces the transition to the IGL.


  Effective teams are crucial for organisations, especially in environments
that require teams to be constantly created and dismantled, such as software
development, scientific experiments, crowd-sourcing, or the classroom. Key
factors influencing team performance are competences and personality of team
members. Hence, we present a computational model to compose proficient and
congenial teams based on individuals' personalities and their competences to
perform tasks of different nature. With this purpose, we extend Wilde's
post-Jungian method for team composition, which solely employs individuals'
personalities. The aim of this study is to create a model to partition agents
into teams that are balanced in competences, personality and gender. Finally,
we present some preliminary empirical results that we obtained when analysing
student performance. Results show the benefits of a more informed team
composition that exploits individuals' competences besides information about
their personalities.


  Multiple robotic systems, working together, can provide important solutions
to different real-world applications (e.g., disaster response), among which
task allocation problems feature prominently. Very few existing decentralized
multi-robotic task allocation (MRTA) methods simultaneously offer the following
capabilities: consideration of task deadlines, consideration of robot range and
task completion capacity limitations, and allowing asynchronous decision-making
under dynamic task spaces. To provision these capabilities, this paper presents
a computationally efficient algorithm that involves novel construction and
matching of bipartite graphs. Its performance is tested on a multi-UAV flood
response application.


  Given an abelian surface, the number of its distinct decompositions into a
product of elliptic curves has been described by Ma. Moreover, Ma himself
classified the possible decompositions for abelian surfaces of Picard number $1
\leq \rho \leq 3$. We explicitly find all such decompositions in the case of
abelian surfaces of Picard number $\rho= 4$. This is done by computing the
transcendental lattice of products of isogenous elliptic curves with complex
multiplication, generalizing a technique of Shioda and Mitani, and by studying
the action of a certain class group on the factors of a given decomposition. We
also provide an alternative and simpler proof of Ma's formula, and an
application to singular K3 surfaces.


  Keyphrase generation is the task consisting in generating a set of words or
phrases that highlight the main topics of a document. There are few datasets
for keyphrase generation in the biomedical domain and they do not meet the
expectations in terms of size for training generative models. In this paper, we
introduce kp-biomed, the first large-scale biomedical keyphrase generation
dataset with more than 5M documents collected from PubMed abstracts. We train
and release several generative models and conduct a series of experiments
showing that using large scale datasets improves significantly the performances
for present and absent keyphrase generation. The dataset is available under
CC-BY-NC v4.0 license at https://huggingface.co/ datasets/taln-ls2n/kpbiomed.


  We present new investigation of the Lamb shift (2P_{1/2}-2S_{1/2}) in muonic
deuterium (mu d) atom using the three-dimensional quasipotential method in
quantum electrodynamics. The vacuum polarization, nuclear structure and recoil
effects are calculated with the account of contributions of orders alpha^3,
alpha^4, alpha^5 and alpha^6. The results are compared with earlier performed
calculations. The obtained numerical value of the Lamb shift 202.4139 meV can
be considered as a reliable estimate for the comparison with forthcoming
experimental data.


  We consider a Lindley process with Laplace distributed space increments. We
obtain closed form recursive expressions for the density function of the
position of the process and for its first exit time distribution from the
domain $[0,h]$. We illustrate the results in terms of the parameters of the
process. The work is completed by an open source version of the software.


  Convolutional Neural Networks (CNNs) work very well for supervised learning
problems when the training dataset is representative of the variations expected
to be encountered at test time. In medical image segmentation, this premise is
violated when there is a mismatch between training and test images in terms of
their acquisition details, such as the scanner model or the protocol.
Remarkable performance degradation of CNNs in this scenario is well documented
in the literature. To address this problem, we design the segmentation CNN as a
concatenation of two sub-networks: a relatively shallow image normalization
CNN, followed by a deep CNN that segments the normalized image. We train both
these sub-networks using a training dataset, consisting of annotated images
from a particular scanner and protocol setting. Now, at test time, we adapt the
image normalization sub-network for \emph{each test image}, guided by an
implicit prior on the predicted segmentation labels. We employ an independently
trained denoising autoencoder (DAE) in order to model such an implicit prior on
plausible anatomical segmentation labels. We validate the proposed idea on
multi-center Magnetic Resonance imaging datasets of three anatomies: brain,
heart and prostate. The proposed test-time adaptation consistently provides
performance improvement, demonstrating the promise and generality of the
approach. Being agnostic to the architecture of the deep CNN, the second
sub-network, the proposed design can be utilized with any segmentation network
to increase robustness to variations in imaging scanners and protocols. Our
code is available at:
\url{https://github.com/neerakara/test-time-adaptable-neural-networks-for-domain-generalization}.


  Recent tunneling conductance measurements on semiconductor-superconductor
nanowires find zero-bias peaks to be ubiquitous across wide ranges of chemical
potential and Zeeman energy. Motivated by this, we demonstrate that
topologically-trivial Andreev abound states (ABSs) pinned near zero energy are
produced rather generically in inhomogeneous systems with multi-band occupancy
in the presence of inter-band coupling. We first investigate the inter-band
coupling mechanism responsible for the pinning within a multi-band 1D toy
model, then we confirm the findings using a 3D Schr\"{o}dinger-Poisson approach
that incorporates the geometric and electrostatic details of the actual device.
Our analysis shows that level-repulsion generated by inter-band coupling can
lead to a rather spectacular pinning of the lowest-energy mode near zero energy
in systems (or regions) characterized by very-short length scales
($\sim100~$nm).We show that level repulsion between the lowest energy levels
can mimic the gap opening feature (simultaneous with the emergence of a
near-zero energy mode) predicted to occur in Majorana hybrid systems. We also
demonstrate that nearly-zero bias differential conductance features exhibiting
particle-hole asymmetry are due to the presence of (topologically-trivial) ABSs
pinned near zero-energy by level repulsion, not to Majorana zero modes,
quasi-Majoranas, or any other low-energy mode that involves (partially)
separated Majorana bound states. Our findings demonstrate the importance of
understanding in detail multi-band physics and electrostatic effects in the
context of the ongoing search for Majorana modes in
semiconductor-superconductor heterostructures.


  Graph neural networks have emerged as a powerful tool for graph
representation learning, but their performance heavily relies on abundant
task-specific supervision. To reduce labeling requirement, the "pre-train,
prompt" paradigms have become increasingly common. However, existing study of
prompting on graphs is limited, lacking a universal treatment to appeal to
different downstream tasks. In this paper, we propose GraphPrompt, a novel
pre-training and prompting framework on graphs. GraphPrompt not only unifies
pre-training and downstream tasks into a common task template but also employs
a learnable prompt to assist a downstream task in locating the most relevant
knowledge from the pre-trained model in a task-specific manner. To further
enhance GraphPrompt in these two stages, we extend it into GraphPrompt+ with
two major enhancements. First, we generalize several popular graph pre-training
tasks beyond simple link prediction to broaden the compatibility with our task
template. Second, we propose a more generalized prompt design that incorporates
a series of prompt vectors within every layer of the pre-trained graph encoder,
in order to capitalize on the hierarchical information across different layers
beyond just the readout layer. Finally, we conduct extensive experiments on
five public datasets to evaluate and analyze GraphPrompt and GraphPrompt+.


  Recently, a link between Lorentzian and Finslerian Geometries has been
carried out, leading to the notion of wind Riemannian structure (WRS), a
generalization of Finslerian Randers metrics. Here, we further develop this
notion and its applications to spacetimes, by introducing some
characterizations and criteria for the completeness of WRS's.
  As an application, we consider a general class of spacetimes admitting a time
function $t$ generated by the flow of a complete Killing vector field
(generalized standard stationary spacetimes or, more precisely, SSTK ones) and
derive simple criteria ensuring that its slices $t=$ constant are Cauchy.
Moreover, a brief summary on the Finsler/Lorentz link for readers with some
acquaintance in Lorentzian Geometry, plus some simple examples in Mathematical
Relativity, are provided.


  We investigate an averaging process that describes how interacting agents
approach consensus through binary interactions. In each elementary step, two
agents are selected at random and they reach compromise by adopting their
opinion average. We show that the fraction of agents with a monotonically
decreasing opinion decays as $e^{-\alpha t}$, and that the exponent
$\alpha=\tfrac{1}{2}-\tfrac{1+\ln \ln 2}{4\ln 2}$ is selected as the extremum
from a continuous spectrum of possible values. The opinion distribution of
monotonic agents is asymmetric, and it becomes self-similar at large times.
Furthermore, the tails of the opinion distribution are algebraic, and they are
characterized by two distinct and nontrivial exponents. We also explore
statistical properties of agents with an opinion strictly above average.


  The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest
integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i$,
$i\in [k]$, where each $V_i$ is an $i$-packing. In this paper, we investigate
for a given triple $(a,b,c)$ of positive integers whether there exists a graph
$G$ such that $\omega(G) = a$, $\chi(G) = b$, and $\chi_{\rho}(G) = c$. If so,
we say that $(a, b, c)$ is realizable. It is proved that $b=c\ge 3$ implies
$a=b$, and that triples $(2,k,k+1)$ and $(2,k,k+2)$ are not realizable as soon
as $k\ge 4$. Some of the obtained results are deduced from the bounds proved on
the packing chromatic number of the Mycielskian. Moreover, a formula for the
independence number of the Mycielskian is given. A lower bound on
$\chi_{\rho}(G)$ in terms of $\Delta(G)$ and $\alpha(G)$ is also proved.


  The BNL and FNAL measurements of the anomalous magnetic moment of the muon
disagree with the Standard Model (SM) prediction by more than $4\sigma$. The
hadronic vacuum polarization (HVP) contributions are the dominant source of
uncertainty in the SM prediction. There are, however, tensions between
different estimates of the HVP contributions, including data-driven estimates
based on measurements of the $R$-ratio. To investigate that tension, we modeled
the unknown $R$-ratio as a function of CM energy with a treed Gaussian process
(TGP). This is a principled and general method grounded in data-science that
allows complete uncertainty quantification and automatically balances over- and
under-fitting to noisy data. Our tool yields exploratory results are similar to
previous ones and we find no indication that the $R$-ratio was previously
mismodeled. Whilst we advance some aspects of modeling the $R$-ratio and
develop new tools for doing so, a competitive estimate of the HVP contributions
requires domain-specific expertise and a carefully curated database of
measurements.


  We propose a particle-based method to simulate thin-film fluid that jointly
facilitates aggressive surface deformation and vigorous tangential flows. We
build our dynamics model from the surface tension driven Navier-Stokes equation
with the dimensionality reduced using the asymptotic lubrication theory and
customize a set of differential operators based on the weakly compressible
Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key
insight is that the compressible nature of SPH, which is unfavorable in its
typical usage, is helpful in our application to co-evolve the thickness,
calculate the surface tension, and enforce the fluid incompressibility on a
thin film. In this way, we are able to two-way couple the surface deformation
with the in-plane flows in a physically based manner. We can simulate complex
vortical swirls, fingering effects due to Rayleigh-Taylor instability,
capillary waves, Newton's interference fringes, and the Marangoni effect on
liberally deforming surfaces by presenting both realistic visual results and
numerical validations. The particle-based nature of our system also enables it
to conveniently handle topology changes and codimension transitions, allowing
us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as
pinch-off of unstable catenoids, dripping under gravity, merging of droplets,
as well as bubble rupture.


  The quantum dynamics of a two-dimensional charged spin $1/2$ particle is
studied for general, symmetry--free curved surfaces and general, nonuniform
magnetic fields that are, when different from zero, orthogonal to the defining
two surface. Although higher Landau levels generally lose their degeneracy
under such general conditions, the lowest Landau level, the ground state,
remains degenerate. Previous discussions of this problem have had less
generality and/or used supersymmetry, or else have appealed to very general
mathematical theorems from differential geometry. In contrast our discussion
relies on simple and standard quantum mechanical concepts.
  The mathematical similarity of the physical problem at hand and that of a
phase-space path integral quantization scheme of a general classical system is
emphasized. Adopting this analogy in the general case leads to a general
quantization procedure that is invariant under general coordinate
transformations-- completely unlike any of the conventional quantization
prescriptions -- and therefore generalizes the concept of quantization to new
and hitherto inaccesible situations.
  In a complementary fashion , the so-obtained picture of general quantization
helps to derive useful semiclassical formulas for the Hall current in the case
of a filling factor equal to one for a general surface and magnetic field.


  The scattering of bright quantum solitons at barrier potentials in
one-dimensional geometries is investigated. Such protocols have been predicted
to lead to the creation of nonlocal quantum superpositions. The centre-of-mass
motion of these bright matter-wave solitons generated from attractive
Bose-Einstein condensates can be analysed with the effective potential
approach. An application to the case of two particles being scattered at a
delta potential allows analytical calculations not possible for higher particle
numbers as well as a comparison with numerical results. Both for the dimer and
a soliton with particle numbers on the order of N = 100, we investigate the
signatures of the coherent superposition states in an interferometric setup and
argue that experimentally an interference pattern would be particularly well
observable in the centre-of-mass density. Quantum superposition states of
ultra-cold atoms are interesting as input states for matter-wave interferometry
as they could improve signal-to-noise ratios.


  We study the prolate-shape predominance of the nuclear ground-state
deformation by calculating the masses of more than two thousand even-even
nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The
influences of the surface thickness of the single-particle potentials, the
strength of the spin-orbit potential, and the pairing correlations are
investigated by varying the parameters of the Woods-Saxon potential and the
pairing interaction. The strong interference between the effects of the surface
thickness and the spin-orbit potential is confirmed to persist for six sets of
the Woods-Saxon potential parameters. The observed behavior of the ratios of
prolate, oblate, and spherical nuclei versus potential parameters are rather
different in different mass regions. It is also found that the ratio of
spherical nuclei increases for weakly bound unstable nuclei. Differences of the
results from the calculations with the Nilsson potential are described in
detail.


  Removing information from a machine learning model is a non-trivial task that
requires to partially revert the training process. This task is unavoidable
when sensitive data, such as credit card numbers or passwords, accidentally
enter the model and need to be removed afterwards. Recently, different concepts
for machine unlearning have been proposed to address this problem. While these
approaches are effective in removing individual data points, they do not scale
to scenarios where larger groups of features and labels need to be reverted. In
this paper, we propose the first method for unlearning features and labels. Our
approach builds on the concept of influence functions and realizes unlearning
through closed-form updates of model parameters. It enables to adapt the
influence of training data on a learning model retrospectively, thereby
correcting data leaks and privacy issues. For learning models with strongly
convex loss functions, our method provides certified unlearning with
theoretical guarantees. For models with non-convex losses, we empirically show
that unlearning features and labels is effective and significantly faster than
other strategies.


  I review the status of perturbative QCD calculations for jet production in
eP-scattering at HERA. I will discuss possibilities of combining fixed order,
especially higher order, calculations and parton showers.


  We show the consistency of "there is a nice sigma --ideal I on the reals with
add(I)= omega_1 which cannot be represented as the union of a strictly
increasing sequence of length omega_1 of sigma-subideals". This answers a
question by Borodulin-Nadzieja and Glab.


  Using the method of ``reduced parallaxes'' for the Halo RR Lyrae stars in the
Hipparcos catalogue we derive a zero point of 0.77 $\pm$ 0.26 mag for an
assumed slope of 0.18 in the $M_{\rm V}$-[Fe/H] relation. This is 0.28
magnitude brighter than the value Fernley et al. (1998a) derived by employing
the method of statistical parallax for the {\it identical} sample and using the
same slope.
  We point out that a similar difference exists between the ``reduced
parallaxes'' method and the statistical parallax method for the Cepheids in the
Hipparcos catalogue.
  We also determine the zero point for the $M_{\rm K}$-$\log P_{0}$ relation,
and obtain a value of -1.16 $\pm$ 0.27 mag (for a slope of -2.33). The distance
moduli to the Hipparcos RR Lyrae stars derived from the two relations agree
well.
  The derived distance scale is in good agreement with the results from the
Main Sequence fitting distances of Galactic globular clusters and with the
results of theoretical Horizontal Branch models, and implies a distance modulus
to the LMC of 18.61 $\pm$ 0.28 mag.


  Time Series Classification and Extrinsic Regression are important and
challenging machine learning tasks. Deep learning has revolutionized natural
language processing and computer vision and holds great promise in other fields
such as time series analysis where the relevant features must often be
abstracted from the raw data but are not known a priori. This paper surveys the
current state of the art in the fast-moving field of deep learning for time
series classification and extrinsic regression. We review different network
architectures and training methods used for these tasks and discuss the
challenges and opportunities when applying deep learning to time series data.
We also summarize two critical applications of time series classification and
extrinsic regression, human activity recognition and satellite earth
observation.


  A self-consistent calculation scheme for correlated electron systems is
created based on the density-functional theory (DFT). Our scheme is a
multi-reference DFT (MR-DFT) calculation in which the electron charge density
is reproduced by an auxiliary interacting Fermion system. A short-range
Hubbard-type interaction is introduced by a rigorous manner with a residual
term for the exchange-correlation energy. The Hubbard term is determined
uniquely by referencing the density fluctuation at a selected localized
orbital. This strategy to obtain an extension of the Kohn-Sham scheme provides
a self-consistent electronic structure calculation for the materials design.
Introducing an approximation for the residual exchange-correlation energy
functional, we have the LDA+U energy functional. Practical self-consistent
calculations are exemplified by simulations of Hydrogen systems, i.e. a
molecule and a periodic one-dimensional array, which is a proof of existence of
the interaction strength U as a continuous function of the local fluctuation
and structural parameters of the system.


  Since horizon formation in global anti-de Sitter spacetime is dual to
thermalization of a conformal field theory on a compact space, whether generic
initial data is stable or unstable against gravitational collapse is of great
interest. We argue that all the known stable initial data for massless scalars
are dominated by single scalar eigenmodes, specifically providing strong
numerical evidence consistent with the interpretation that initial data with
equal energies in two modes collapse on time scales of order the inverse square
of the amplitude. We further scan the parameter space for massive scalar field
initial data and present evidence for a novel class of stable or quasi-stable
solutions for massive scalars with energy spread through several eigenmodes.


  Assigning a satisfactory truly concurrent semantics to Petri nets with
confusion and distributed decisions is a long standing problem, especially if
one wants to resolve decisions by drawing from some probability distribution.
Here we propose a general solution based on a recursive, static decomposition
of (occurrence) nets in loci of decision, called structural branching cells
(s-cells). Each s-cell exposes a set of alternatives, called transactions. Our
solution transforms a given Petri net into another net whose transitions are
the transactions of the s-cells and whose places are those of the original net,
with some auxiliary structure for bookkeeping. The resulting net is
confusion-free, and thus conflicting alternatives can be equipped with
probabilistic choices, while nonintersecting alternatives are purely concurrent
and their probability distributions are independent. The validity of the
construction is witnessed by a tight correspondence with the recursively
stopped configurations of Abbes and Benveniste. Some advantages of our approach
are that: i) s-cells are defined statically and locally in a compositional way;
ii) our resulting nets faithfully account for concurrency.


  The WMAP satellite has completed 3 years of observations of the cosmic
microwave background radiation. The 3-year data products include several sets
of full sky maps of the Stokes I, Q and U parameters in 5 frequency bands,
spanning 23 to 94 GHz, and supporting items, such as beam window functions and
noise covariance matrices. The processing used to produce the current sky maps
and supporting products represents a significant advancement over the first
year analysis, and is described herein. Improvements to the pointing
reconstruction, radiometer gain modeling, window function determination and
radiometer spectral noise parametrization are presented. A detailed description
of the updated data processing that produces maximum likelihood sky map
estimates is presented, along with the methods used to produce reduced
resolution maps and corresponding noise covariance matrices. Finally two
methods used to evaluate the noise of the full resolution sky maps are
presented along with several representative year-to-year null tests,
demonstrating that sky maps produced from data from different observational
epochs are consistent.


  Within a microscopic approach the structure of Neutron Stars is usually
studied by modelling the homogeneous nuclear matter of the core by a suitable
Equation of State, based on a many-body theory, and the crust by a functional
based on a more phenomenological approach. We present the first calculation of
Neutron Star overall structure by adopting for the core an Equation of State
derived from the Brueckner-Hartree-Fock theory and for the crust, including the
pasta phase, an Energy Density Functional based on the same Equation of State,
and which is able to describe accurately the binding energy of nuclei
throughout the mass table. Comparison with other approaches is discussed. The
relevance of the crust Equation of state for the Neutron Star radius is
particularly emphasised.


  We address the question: Why may reaction-diffusion equations with hysteretic
nonlinearities become ill-posed and how to amend this? To do so, we discretize
the spatial variable and obtain a lattice dynamical system with a hysteretic
nonlinearity. We analyze a new mechanism that leads to appearance of a
spatio-temporal pattern called {\it rattling}: the solution exhibits a
propagation phenomenon different from the classical traveling wave, while the
hysteretic nonlinearity, loosely speaking, takes a different value at every
second spatial point, independently of the grid size. Such a dynamics indicates
how one should redefine hysteresis to make the continuous problem well-posed
and how the solution will then behave. In the present paper, we develop main
tools for the analysis of the spatially discrete model and apply them to a
prototype case. In particular, we prove that the propagation velocity is of
order $a t^{-1/2}$ as $t\to\infty$ and explicitly find the rate $a$.


  In this work, the generalization of Friedel formula and Krein's theorem in
complex potential scattering theory is presented. The consequence of various
symmetry constraints on dynamical system are discussed. In addition,
Muskhelishvili-Omn\`es representation of Krein's theorem is also given and
discussed.


  We develop novel compressive coded rotating mirror (CCRM) camera to capture
events at high frame rates in passive mode with a compact instrument design at
the fraction of the cost compared to other high-speed imaging cameras.
Operation of CCRM camera is based on the amplitude optical encoding (grey
scale) and a continuous frame sweep across a low-cost detector using a
motorized rotating mirror system which can achieve single pixel shift between
adjacent frames. Amplitude encoding and continuous frame overlapping enable the
CCRM camera to achieve high number of captured frames and high temporal
resolution without making sacrifices in the spatial resolution. Two sets of
dynamic scenes have been captured at up to 120 Kfps frame rate in both
monochrome and colored scales in the experimental demonstrations. The obtained
heavily compressed data from the experiment are reconstructed using the
optimization algorithm under the compressive sensing (CS) paradigm and the
highest sequence depth of 1400 captured frames in single exposure has been
achieved with the highest compression ratio of 368 compared to other CS-based
high-speed imaging technologies. Under similar conditions CCRM camera is
700$\times$ faster than conventional rotating mirror based imaging devices and
could reach frame rate of up to 20 Gfps.


  Balogh, Bollobas and Weinreich showed that a parameter that has since been
termed the distinguishing number can be used to identify a jump in the possible
speeds of hereditary classes of graphs at the sequence of Bell numbers.
  We prove that every hereditary class that lies above the Bell numbers and has
finite distinguishing number contains a boundary class for well-quasi-ordering.
This means that any such hereditary class which in addition is defined by
finitely many minimal forbidden induced subgraphs must contain an infinite
antichain. As all hereditary classes below the Bell numbers are
well-quasi-ordered, our results complete the answer to the question of
well-quasi-ordering for hereditary classes with finite distinguishing number.
  We also show that the decision procedure of Atminas, Collins, Foniok and
Lozin to decide the Bell number (and which now also decides well-quasi-ordering
for classes of finite distinguishing number) has run time bounded by an
explicit (quadruple exponential) function of the order of the largest minimal
forbidden induced subgraph of the class.


  Qualifying gene and isoform expression is one of the primary tasks for
RNA-Seq experiments. Given a sequence of counts representing numbers of reads
mapped to different positions (exons and junctions) of isoforms, methods based
on Poisson generalized linear models (GLM) with the identity link function have
been proposed to estimate isoform expression levels from these counts. These
Poisson based models have very limited ability in handling the overdispersion
in the counts brought by various sources, and some of them are not robust to
outliers. We propose a negative binomial based GLM with identity link, and use
a set of robustified quasi-likelihood equations to make it resistant to
outliers. An efficient and reliable numeric algorithm has been identified to
solve these equations. In simulations, we find that our approach seems to
outperform existing approaches. We also find evidence supporting this
conclusion in real RNA-Seq data.


  We present highly accurate, dimensionally-reduced gravitational waveforms for
binary inspirals whose components have large spin-induced quadrupole moments.
The spin-induced quadrupole of a body first appears in the phase of a waveform
at the early inspiral stage of the binary coalescence, making it a relatively
clean probe of the internal structure of the body. However, for objects with
large quadrupolar deviations from Kerr, searches using binary black hole (BBH)
models would be ineffective. In order to perform a computationally-feasible
search, we present two dimensionally-reduced models which are derived from the
original six-dimensional post-Newtonian waveform for such systems. Our
dimensional reduction method is guided by power counting in the post-Newtonian
expansion, suitable reparameterizations of the source physics, and truncating
terms in the phase that are small in most physically well-motivated regions of
parameter space. In addition, we note that large quadrupolar deviations cause
the frequency at which a binary system reaches its minimum binding energy to be
reduced substantially. This minimum signals the end of the inspiral regime and
provides a natural cutoff for the PN waveform. We provide accurate analytic
estimates for these frequency cutoffs. Finally, we perform injection studies to
test the effectualness of the dimensionally reduced waveforms. We find that
over $80\%$ of the injections have an effectualness of $\varepsilon > 0.999$,
significantly higher than is typically required for standard BBH banks, for
systems with component spins of $|\chi_i| \lesssim 0.6$ and dimensionless
quadrupole of $\kappa_i \lesssim 10^3$. Importantly, these waveforms represent
an essential first step towards enabling an effective search for astrophysical
objects with large quadrupoles.


  To construct realistic mathematical models from the first principles, the
authors suggest using the stochastization method. In a number of works
different approaches to stochastization of mathematical models were considered.
In the end, the whole variety of approaches was reduced to two formalisms:
combinatorial (state vectors) and operator (occupation numbers). In the article
the authors briefly describe these formalisms with an emphasis on their
practical application.


  Metastable nanostructures are kinetically trapped in local energy minima
featuring intriguing surface and material properties. To unleash their
potential, there is a need for non-equilibrium processes capable of stabilizing
a large range of crystal phases outside thermodynamic equilibrium conditions by
closely and flexibly controlling atomic reactant composition, spatial
temperature distribution and residence time. Here, we demonstrate the capture
of metastable pseudo-binary metal oxides at room temperature with scalable
combustion-aerosol processes. By a combination of X-ray diffraction, electron
microscopy and online flame characterization, we investigate the occurrence of
metastable CoCu$_2$O$_3$ with controlled crystal size (4-16 nm) over
thermodynamically stable CuO and Co$_3$O$_4$. Immediate practical impact is
demonstrated by exceptional sensing and catalytic performance for air pollutant
detection (e.g., 15 parts-per-billion benzene). This approach can be extended
to various binary, ternary and high entropy oxides with even more components to
access novel materials also promising for actuators, energy storage or solar
cells.


  We study a quite general family of dynamical $r$-matrices for an auxiliary
loop algebra ${\cal L}({su(2)})$ related to restricted flows for equations of
the KdV type. This underlying $r$-matrix structure allows to reconstruct Lax
representations and to find variables of separation for a wide set of the
integrable natural Hamiltonian systems. As an example, we discuss the
Henon-Heiles system and a quartic system of two degrees of freedom in detail.


  In this paper, conformal motions are studied in plane symmetric static
spacetimes. The general solution of conformal Killing equations and the general
form of the conformal Killing vector for these spacetimes are presented. All
possibilities for the existence of conformal motions in these spacetimes are
exhausted.


  We develop a location analysis spatial model of firms' competition in
multi-characteristics space, where consumers' opinions about the firms'
products are distributed on multilayered networks. Firms do not compete on
price but only on location upon the products' multi-characteristics space, and
they aim to attract the maximum number of consumers. Boundedly rational
consumers have distinct ideal points/tastes over the possible available firm
locations but, crucially, they are affected by the opinions of their neighbors.
Proposing a dynamic agent-based analysis on firms' location choice we
characterize multi-dimensional product differentiation competition as adaptive
learning by firms' managers and we argue that such a complex systems approach
advances the analysis in alternative ways, beyond game-theoretic calculations.


  Graphite and diamond have comparable free energies, yet forming diamond from
graphite is far from easy. In the absence of a catalyst, pressures that are
significantly higher than the equilibrium coexistence pressures are required to
induce the graphite-to-diamond transition. Furthermore, the formation of the
metastable hexagonal polymorph of diamond instead of the more stable cubic
diamond is favored at lower temperatures. The concerted mechanism suggested in
previous theoretical studies cannot explain these phenomena. Using an ab initio
quality neural-network potential we performed a large-scale study of the
graphite-to-diamond transition assuming that it occurs via nucleation. The
nucleation mechanism accounts for the observed phenomenology and reveals its
microscopic origins. We demonstrated that the large lattice distortions that
accompany the formation of the diamond nuclei inhibit the phase transition at
low pressure and direct it towards the hexagonal diamond phase at higher
pressure. The nucleation mechanism proposed in this work is an important step
towards a better understanding of structural transformations in a wide range of
complex systems such as amorphous carbon and carbon nanomaterials.


  We discuss In\"on\"u-Wigner contractions of affine Kac-Moody algebras. We
show that the Sugawara construction for the contracted affine algebra exists
only for a fixed value of the level $k$, which is determined in terms of the
dimension of the uncontracted part of the starting Lie algebra, and the
quadratic Casimir in the adjoint representation. Further, we discuss
contractions of $G/H$ coset spaces, and obtain an affine {\it translation}
algebra, which yields a Virasoro algebra (via a GKO construction) with a
central charge given by $dim(G/H)$.


  Engineering simulations using boundary-value partial differential equations
often implicitly assume that the uncertainty in the location of the boundary
has a negligible impact on the output of the simulation. In this work, we
develop a novel method for describing the geometric uncertainty in
image-derived models and use a naive method for subsequently quantifying a
simulation's sensitivity to that uncertainty. A Gaussian random field is
constructed to represent the space of possible geometries, based on
image-derived quantities such as pixel size, which can then be used to probe
the simulation's output space. The algorithm is demonstrated with examples from
biomechanics where patient-specific geometries are often segmented from
low-resolution, three-dimensional images. These examples show the method's wide
applicability with examples using linear elasticity and fluid dynamics. We show
that important biomechanical outputs of these example simulations, namely
maximum principal stress and wall shear stress, can be highly sensitive to
realistic uncertainties in geometry.


  A Hamiltonian cycle in a graph is a spanning subgraph that is homeomorphic to
a circle. With this in mind, it is natural to define a Hamiltonian d-sphere in
a d-dimensional simplicial complex as a spanning subcomplex that is
homeomorphic to a d-dimensional sphere.
  We consider the Linial-Meshulam model for random simplicial complexes, and
prove that there is a sharp threshold at $p=\sqrt{\frac{e}{\gamma n}}$ for the
appearance of a Hamiltonian $2$-sphere in a random $2$-complex, where $\gamma =
4^4/3^3$.


  Regional aggregates of health outcomes over delineated administrative units
(e.g., states, counties, zip codes), or areal units, are widely used by
epidemiologists to map mortality or incidence rates and capture geographic
variation. To capture health disparities over regions, we seek "difference
boundaries" that separate neighboring regions with significantly different
spatial effects. Matters are more challenging with multiple outcomes over each
unit, where we capture dependence among diseases as well as across the areal
units. Here, we address multivariate difference boundary detection for
correlated diseases. We formulate the problem in terms of Bayesian pairwise
multiple comparisons and seek the posterior probabilities of neighboring
spatial effects being different. To achieve this, we endow the spatial random
effects with a discrete probability law using a class of multivariate
areally-referenced Dirichlet process (MARDP) models that accommodate spatial
and inter-disease dependence. We evaluate our method through simulation studies
and detect difference boundaries for multiple cancers using data from the
Surveillance, Epidemiology, and End Results (SEER) Program of the National
Cancer Institute.


  We develop some new analytic bounds on transmission probabilities (and the
related reflection probabilities and Bogoliubov coefficients) for generic
one-dimensional scattering problems. To do so we rewrite the Schrodinger
equation for some complicated potential whose properties we are trying to
investigate in terms of some simpler potential whose properties are assumed
known, plus a (possibly large) "shift" in the potential. Doing so permits us to
extract considerable useful information without having to exactly solve the
full scattering problem.


  We demonstrate from first principles a core fallacy employed by a coterie of
authors who claim that data from the Vaccine Adverse Reporting System (VAERS)
show that hundreds of thousands of U.S. deaths are attributable to COVID
vaccination.


  In this paper, we extend the QMRDT probabilistic model for the domain of
internal medicine to include decisions about treatments. In addition, we
describe how we can use the comprehensive decision model to construct a simpler
decision model for a specific patient. In so doing, we transform the task of
problem formulation to that of narrowing of a larger problem.


  Effects of predators of juvenile mice on the spread of the Hantavirus are
analyzed in the context of a recently proposed model. Two critical values of
the predation probability are identified. When the smaller of them is exceeded,
the hantavirus infection vanishes without extinguishing the mice population.
When the larger is exceeded, the entire mice population vanishes. These results
suggest the possibility of control of the spread of the epidemic by introducing
predators in areas of mice colonies in a suitable way so that such control does
not kill all the mice but lowers the epidemic spread.


  We give a simple statistical proof of a binomial identity, by evaluating the
Laplace transform of the maximum of n independent exponential random variables
in two different ways. As a by product, we obtain a simple proof of an
interesting result concerning the exponential distribution. The connections
between a probabilistic approach and the statistical approach are discussed,
which explains why certain binomial identities admit probabilistic
interpretations. In the process, several new binomial identities are also
obtained and discussed.


  I develop a model of a randomized experiment with a binary intervention and a
binary outcome. Potential outcomes in the intervention and control groups give
rise to four types of participants. Fixing ideas such that the outcome is
mortality, some participants would live regardless, others would be saved,
others would be killed, and others would die regardless. These potential
outcome types are not observable. However, I use the model to develop
estimators of the number of participants of each type. The model relies on the
randomization within the experiment and on deductive reasoning. I apply the
model to an important clinical trial, the PROWESS trial, and I perform a Monte
Carlo simulation calibrated to estimates from the trial. The reduced form from
the trial shows a reduction in mortality, which provided a rationale for FDA
approval. However, I find that the intervention killed two participants for
every three it saved.


  Though achieving impressive results on many NLP tasks, the BERT-like masked
language models (MLM) encounter the discrepancy between pre-training and
inference. In light of this gap, we investigate the contextual representation
of pre-training and inference from the perspective of word probability
distribution. We discover that BERT risks neglecting the contextual word
similarity in pre-training. To tackle this issue, we propose an auxiliary gloss
regularizer module to BERT pre-training (GR-BERT), to enhance word semantic
similarity. By predicting masked words and aligning contextual embeddings to
corresponding glosses simultaneously, the word similarity can be explicitly
modeled. We design two architectures for GR-BERT and evaluate our model in
downstream tasks. Experimental results show that the gloss regularizer benefits
BERT in word-level and sentence-level semantic representation. The GR-BERT
achieves new state-of-the-art in lexical substitution task and greatly promotes
BERT sentence representation in both unsupervised and supervised STS tasks.


  A machine learning (ML) design framework is proposed for dynamically
adjusting clock frequency based on propagation delay of individual
instructions. A Random Forest model is trained to classify propagation delays
in real-time, utilizing current operation type, current operands, and
computation history as ML features. The trained model is implemented in Verilog
as an additional pipeline stage within a baseline processor. The modified
system is simulated at the gate-level in 45 nm CMOS technology, exhibiting a
speed-up of 68% and energy reduction of 37% with coarse-grained ML
classification. A speed-up of 95% is demonstrated with finer granularities at
additional energy costs.


  We present a sensor misalignment-tolerant AUV navigation method that
leverages measurements from an acoustic array and dead reckoned information.
Recent studies have demonstrated the potential use of passive acoustic
Direction of Arrival (DoA) measurements for AUV navigation without requiring
ranging measurements. However, the sensor misalignment between the acoustic
array and the attitude sensor was not accounted for. Such misalignment may
deteriorate the navigation accuracy. This paper proposes a novel approach that
allows simultaneous AUV navigation, beacon localization, and sensor alignment.
An Unscented Kalman Filter (UKF) that enables the necessary calculations to be
completed at an affordable computational load is developed. A Nonlinear Least
Squares (NLS)-based technique is employed to find an initial solution for
beacon localization and sensor alignment as early as possible using a
short-term window of measurements. Experimental results demonstrate the
performance of the proposed method.


  Fourier single-pixel imaging (FSI) is a branch of single-pixel imaging
techniques. It uses Fourier basis patterns as structured patterns for spatial
information acquisition in the Fourier domain. However, the spatial resolution
of the image reconstructed by FSI mainly depends on the number of Fourier
coefficients sampled. The reconstruction of a high-resolution image typically
requires a number of Fourier coefficients to be sampled, and therefore takes a
long data acquisition time. Here we propose a new sampling strategy for FSI. It
allows FSI to reconstruct a clear and sharp image with a reduced number of
measurements. The core of the proposed sampling strategy is to perform a
variable density sampling in the Fourier space and, more importantly, the
density with respect to the importance of Fourier coefficients is subject to a
one-dimensional Gaussian function. Combined with compressive sensing, the
proposed sampling strategy enables better reconstruction quality than
conventional sampling strategies, especially when the sampling ratio is low. We
experimentally demonstrate compressive FSI combined with the proposed sampling
strategy is able to reconstruct a sharp and clear image of 256-by-256 pixels
with a sampling ratio of 10%. The proposed method enables fast single-pixel
imaging and provides a new approach for efficient spatial information
acquisition.


  This paper introduces and formalizes the classical view on supply and demand,
which, we argue, has an integrity independent and distinct from the
neoclassical theory. Demand and supply, before the marginal revolution, are
defined not by an unobservable criterion such as a utility function, but by an
observable monetary variable, the reservation price: the buyer's (maximum)
willingness to pay (WTP) value (a potential price) and the seller's (minimum)
willingness to accept (WTA) value (a potential price) at the marketplace.
Market demand and supply are the cumulative distribution of the buyers' and
sellers' reservation prices, respectively. This WTP-WTA classical view of
supply and demand formed the means whereby market participants were motivated
in experimental economics although experimentalists (trained in neoclassical
economics) were not cognizant of their link to the past. On this foundation was
erected a vast literature on the rules of trading for a host of institutions,
modern and ancient. This paper documents textually this reappraisal of
classical economics and then formalizes it mathematically. A follow-up paper
will articulate a theory of market price formation rooted in this classical
view on supply and demand and in experimental findings on market behavior.


  This paper presents a novel Fully Binary Point Cloud Transformer (FBPT) model
which has the potential to be widely applied and expanded in the fields of
robotics and mobile devices. By compressing the weights and activations of a
32-bit full-precision network to 1-bit binary values, the proposed binary point
cloud Transformer network significantly reduces the storage footprint and
computational resource requirements of neural network models for point cloud
processing tasks, compared to full-precision point cloud networks. However,
achieving a fully binary point cloud Transformer network, where all parts
except the modules specific to the task are binary, poses challenges and
bottlenecks in quantizing the activations of Q, K, V and self-attention in the
attention module, as they do not adhere to simple probability distributions and
can vary with input data. Furthermore, in our network, the binary attention
module undergoes a degradation of the self-attention module due to the uniform
distribution that occurs after the softmax operation. The primary focus of this
paper is on addressing the performance degradation issue caused by the use of
binary point cloud Transformer modules. We propose a novel binarization
mechanism called dynamic-static hybridization. Specifically, our approach
combines static binarization of the overall network model with fine granularity
dynamic binarization of data-sensitive components. Furthermore, we make use of
a novel hierarchical training scheme to obtain the optimal model and
binarization parameters. These above improvements allow the proposed
binarization method to outperform binarization methods applied to convolution
neural networks when used in point cloud Transformer structures. To demonstrate
the superiority of our algorithm, we conducted experiments on two different
tasks: point cloud classification and place recognition.


  The $B_{c}^{\ast}$ ${\to}$ $B_{u,d,s}V$, $B_{u,d,s}P$ decays are investigated
with the QCD factorization approach, where $V$ and $P$ denote the ground
$SU(3)$ vector and pseudoscalar mesons, respectively. The $B_{c}^{\ast}$
${\to}$ $B_{u,d,s}$ transition form factors are calculated with the
Wirbel-Stech-Bauer model. It is found that branching ratios for the
color-favored and Cabibbo-favored $B_{c}^{\ast}$ ${\to}$ $B_{s}{\rho}$,
$B_{s}{\pi}$ decays can reach up to ${\cal O}(10^{-7})$, which might be
measurable in the future LHC experiments.


  We introduce and describe relations between Sobolev, Besov and Paley-Wiener
spaces associated with three representations of the Lie group of affine
transformations of the line. These representations are left and right regular
representations and a representation in a space of functions defined on the
half-line. The Besov spaces are described as interpolation spaces between
respective Sobolev spaces in terms of the Petree's real interpolation method
and in terms of a relevant moduli of continuity. By using a Laplace operators
associated with these representations a scales of relevant Paley-Wiener spaces
are developed and a corresponding $L_{2}$-approximation theory is constructed
in which our Besov spaces appear as approximation spaces. Another description
of our Besov spaces is given in terms of a frequency-localized Hilbert frames.
A Jackson-type inequalities are also proven.


  The dynamics and stability of magnetic skyrmions within a nano-track with
multiple confinements are investigated. Firstly, the motion of a single
skyrmion under spin transfer torque (STT) is studied. By accurately adjusting
the current pulse magnitude and width, the study reveals the possibility to pin
and stabilize the skyrmion in each confinement. Due to the Hall angle, the
depining of the skyrmion from the top confinement requires two pulses with
adjustable time delay while a single pulse is enough to depin it for the case
of bottom confinement. In the case of two skyrmions, once one is pinned in one
confinement, the second one stabilizes in the nearest available empty state and
no more than one skyrmion could be seen in single confinement. Finally and for
further confirmation of this behavior, the motion of a large number of
skyrmions is investigated under the same conditions. The results show that a
multistate device could be obtained with still the existence of only one
skyrmion per state. The skyrmions could be displaced along the nano-track until
their annihilation at the end of the device.


  We study quantum annealing for combinatorial optimization with Hamiltonian $H
= z H_f + H_0$ where $H_f$ is diagonal, $H_0=-|\phi \rangle \langle \phi|$ is
the equal superposition state projector and $z$ the annealing parameter. We
analytically compute the minimal spectral gap as $\mathcal{O}(1/\sqrt{N})$ with
$N$ the total number of states and its location $z_*$. We show that quantum
speed-up requires an annealing schedule which demands a precise knowledge of
$z_*$, which can be computed only if the density of states of the optimization
problem is known. However, in general the density of states is intractable to
compute, making quadratic speed-up unfeasible for any practical combinatoric
optimization problems. We conjecture that it is likely that this negative
result also applies for any other instance independent transverse Hamiltonians
such as $H_0 = -\sum_{i=1}^n \sigma_i^x$.


  We present new synthetic models of the TP-AGB evolution. They are computed
for 7 values of initial metal content (Z from 0.0001 to 0.03) and for initial
masses between 0.5 and 5.0 Msun, thus extending the low- and intermediate-mass
tracks of Girardi et al. (2000) until the beginning of the post-AGB phase. The
calculations are performed by means of a synthetic code that incorporates many
recent improvements, among which we mention: (1) the use of detailed and
revised analytical relations to describe the evolution of quiescent luminosity,
inter-pulse period, third dredge-up, hot bottom burning, pulse cycle luminosity
variations, etc.; (2) the use of variable molecular opacities -- i.e. opacities
consistent with the changing photospheric chemical composition -- in the
integration of a complete envelope model, instead of the standard choice of
scaled-solar opacities; (3) the use of formalisms for the mass-loss rates
derived from pulsating dust-driven wind models of C- and O-rich AGB stars; and
(4) the switching of pulsation modes between the first overtone and the
fundamental one along the evolution, which has consequences in terms of the
history of mass loss. It follows that, in addition to the time evolution on the
HR diagram, the new models predict in a consistent fashion also variations in
surface chemical compositions, pulsation modes and periods, and mass-loss
rates. The onset and efficiency of the third dredge-up process are calibrated
in order to reproduce basic observables like the carbon star luminosity
functions in the Magellanic Clouds, and TP-AGB lifetimes (star counts) in
Magellanic Cloud clusters. Forthcoming papers will present the theoretical
isochrones and chemical yields derived from these tracks, and additional tests
performed with the aid of a complete population synthesis code.


  At high temperature, the overlap of two particles chosen independently
according to the Gibbs measure of the branching Brownian motion converges to
zero as time goes to infinity. We investigate the precise decay rate of the
probability to obtain an overlap greater than $a$, for some $a>0$, in the whole
subcritical phase of inverse temperatures $\beta \in [0,\beta_c)$. Moreover, we
study this probability both conditionally on the branching Brownian motion and
non-conditionally. Two sub-phases of inverse temperatures appear, but
surprisingly the threshold is not the same in both cases.


  The Sagnac Interferometer has historically been used for detecting
non-reciprocal phenomena, such as rotation. We demonstrate an apparatus in
which this technique is employed for high resolution measurements of the
Magneto-Optical Polar Kerr effect--a direct indicator of magnetism. Previous
designs have incorporated free-space components which are bulky and difficult
to align. We improve upon this technique by using all fiber-optic coupled
components and demonstrate operation at a new wavelength, 820 nm, with which we
can achieve better than 1 $\mu$rad resolution. Mounting the system on a
piezo-electric scanner allows us to acquire diffraction limited images with 1.5
$\mu$m spatial resolution. We also provide extensive discussion on the details
and of the Sagnac Interferometer's construction.


  Language models (LMs) have long been used to improve results of automatic
speech recognition (ASR) systems, but they are unaware of the errors that ASR
systems make. Error correction models are designed to fix ASR errors, however,
they showed little improvement over traditional LMs mainly due to the lack of
supervised training data. In this paper, we present Denoising LM (DLM), which
is a $\textit{scaled}$ error correction model trained with vast amounts of
synthetic data, significantly exceeding prior attempts meanwhile achieving new
state-of-the-art ASR performance. We use text-to-speech (TTS) systems to
synthesize audio, which is fed into an ASR system to produce noisy hypotheses,
which are then paired with the original texts to train the DLM. DLM has several
$\textit{key ingredients}$: (i) up-scaled model and data; (ii) usage of
multi-speaker TTS systems; (iii) combination of multiple noise augmentation
strategies; and (iv) new decoding techniques. With a Transformer-CTC ASR, DLM
achieves 1.5% word error rate (WER) on $\textit{test-clean}$ and 3.3% WER on
$\textit{test-other}$ on Librispeech, which to our knowledge are the best
reported numbers in the setting where no external audio data are used and even
match self-supervised methods which use external audio data. Furthermore, a
single DLM is applicable to different ASRs, and greatly surpassing the
performance of conventional LM based beam-search rescoring. These results
indicate that properly investigated error correction models have the potential
to replace conventional LMs, holding the key to a new level of accuracy in ASR
systems.


  Recent advancements in nanofabrication have enabled the creation of vacuum
electronic devices with nanoscale free space gaps. These nanoelectronic devices
promise the benefits of cold-field emission and transport through free-space,
such as high nonlinearity and relative insensitivity to temperature and
ionizing radiation, all the while drastically reducing the footprint,
increasing the operating bandwidth and reducing the power consumption of each
device. Furthermore, planarized vacuum nanoelectronics could easily be
integrated at scale similar to typical micro and nanoscale semiconductor
electronics. However, the interplay between different electron emission
mechanisms from these devices are not well understood, and inconsistencies with
pure Fowler-Nordheim emission have been noted by others. In this work, we
systematically study the current-voltage characteristics of planar vacuum
nano-diodes having few-nanometer radii of curvature and free-space gaps between
the emitter and collector. By investigating the current-voltage characteristics
of nearly identical diodes fabricated from two different materials and under
various environmental conditions, such as temperature and atmospheric pressure,
we were able to clearly isolate three distinct emission regimes within a single
device: Schottky, Fowler-Nordheim, and saturation. Our work will enable robust
and accurate modeling of vacuum nanoelectronics which will be critical for
future applications requiring high-speed and low-power electronics capable of
operation in extreme conditions.


  We prove $L^p\to L^q$ estimates for the local maximal operator associated
with dilates of the K\'oranyi sphere in Heisenberg groups. These estimates are
sharp up to endpoints and imply new bounds on sparse domination for the
corresponding global maximal operator. We also prove sharp $L^p\to L^q$
estimates for spherical means over the Kor\'anyi sphere, which can be used to
improve the sparse domination bounds for the associated lacunary maximal
operator.


  In this paper we propose a method that imitates a translation expert using
the Korean translation information and analyse the performance. Korean is good
at tagging than Chinese, so we can use this property in Chinese POS tagging.


  We study the distribution of the Brauer group and the frequency of the
Brauer--Manin obstruction to the Hasse principle and weak approximation in a
family of smooth del Pezzo surfaces of degree four over the rationals.