  We discuss two related principles for hypergeometric supercongrences, one
related to accelerated convergence and the other to the vanishing of Hodge
numbers. This is an extended abstract of a talk given at the workshop
"Hypergeometric motives and Calabi-Yau differential equations" at the
Mathematical Research Institute (MATRIX) of The University of Melbourne in
Creswick, Australia in January of 2017.


  The cross sections for exclusive muon pair production in nucleus - nucleus
collisions are calculated and several differential distributions are shown.
Realistic (Fourier transform of charge density) charge form factors of nuclei
are used and the corresponding results are compared with the cross sections
calculated with monopole form factor often used in the literature and discussed
recently in the context of higher-order QED corrections. Absorption effects are
discussed and quantified. The cross sections obtained with realistic form
factors are significantly smaller than those obtained with the monopole form
factor. The effect is bigger for large muon rapidities and/or large muon
transverse momenta. The predictions for the STAR and PHENIX collaboration
measurements at RHIC as well as the ALICE and CMS collaborations at LHC are
presented.


  Global Climate Models (GCM) are very useful tools to study theoretically the
general dynamics and specific phenomena in planetary atmospheres. In the case
of Venus, several GCMs succeeded in reproducing the atmosphere's superrotation
and the global temperature field. However, the highly variable polar
temperature and the permanent cold collar have not been reproduced
satisfactorily yet. Here we improve the radiative transfer scheme of the
Institut Pierre Simon Laplace Venus GCM in order to numerically simulate the
polar thermal features in Venus atmosphere. The main difference with the
previous model is that we now take into account the latitudinal variation of
the cloud structure. Both solar heating rates and infrared cooling rates have
been modified to consider the cloud top's altitude decrease toward the poles
and the variation in latitude of the different particle modes' abundances. A
new structure that closely resembles the observed cold collar appears in the
average temperature field at $2\times10^{4} - 4\times10^{3}$~Pa ($\sim62 -
66$~km) altitude range and $60^{\circ} - 90^{\circ}$ latitude band. It is not
isolated from the pole as in the observation-based maps, but the obtained
temperature values (220~K) are in good agreement with observed values.
Temperature polar maps across this region show an inner warm region where the
polar vortex is observed, but the obtained 230~K average value is colder than
the observed mean value and the simulated horizontal structure does not show
the fine-scale features present within the vortex. Our study shows that the
cloud structure is essential in the cold collar formation. Although our
analysis focuses on the improvement of the radiative forcing and the variations
it causes in the thermal structure, polar dynamics is definitely affected by
this modified environment and a noteworthy upwelling motion is found in the
cold collar area.


  We describe the results of a sequence of simulations of gravitational
collapse in a turbulent magnetized region. The parameters are chosen to be
representative of molecular cloud material. We find that several protostellar
cores and filamentary structures of higher than average density form. The
filaments inter-connect the high density cores. Furthermore, the magnetic field
strengths are found to correlate positively with the density, in agreement with
recent observations. We make synthetic channel maps of the simulations and show
that material accreting onto the cores is channelled along the magnetized
filamentary structures. This is compared with recent observations of S106, and
shown to be consistent with these data. We postulate that this mechanism of
accretion along filaments may provide a means for molecular cloud cores to grow
to the point where they become gravitationally unstable and collapse to form
stars.


  The article presents the result of an extended in silico experiment on
computational vibrational spectroscopy of graphene molecules performed using
the virtual vibrational spectrometer UHF VVS, previously proposed in the first
part of the study [1]. Since in vitro spectroscopy of such individual molecules
is practically impossible, the obtained spectra give the first idea of what
these spectra could be. A large set of studied molecules allows drawing the
first conclusions about the specific features of the vibrational dynamics of
the substances, caused by their radical structure and spin features of the
ground electronic state.


  Proton stability is one of the most perplexing puzzles in particle physics.
While the renormalizable Standard Model forbids proton decay mediating
operators due to accidental global symmetries, many of its extensions introduce
such dimension four, five and six operators. Furthermore, it is, in general,
expected that quantum gravity only respects local gauge, or discreet,
symmetries. String theory provides the arena to study particle physics in a
consistent framework of perturbative quantum gravity. An appealing proposition,
in this context, is that the dangerous operators are suppressed by an Abelian
gauge symmetry, which is broken near the TeV scale. A viable U(1) symmetry
should also be anomaly free, be family universal, and allow the generation of
fermion masses via the Higgs mechanism. We discuss such U(1) symmetries that
arise in quasi--realistic free fermionic heterotic--string derived models.
Ensuring that the U(1) symmetry is anomaly free at the low scale requires that
the Standard Model spectrum is augmented by additional states that are
compatible with the charge assignments in the string models. We construct such
string--inspired models and discuss some of their phenomenological
implications.


  In this paper we investigate a finite temperature generalization of survey
propagation, by applying it to the problem of finite temperature decoding of a
biased finite connectivity Sourlas code for temperatures lower than the
Nishimori temperature. We observe that the result is a shift of the location of
the dynamical critical channel noise to larger values than the corresponding
dynamical transition for belief propagation, as suggested recently by
Migliorini and Saad for LDPC codes. We show how the finite temperature 1-RSB SP
gives accurate results in the regime where competing approaches fail to
converge or fail to recover the retrieval state.


  A splitting BIBD is a type of combinatorial design that can be used to
construct splitting authentication codes with good properties. In this paper we
show that a design-theoretic approach is useful in the analysis of more general
splitting authentication codes. Motivated by the study of algebraic
manipulation detection (AMD) codes, we define the concept of a group generated
splitting authentication code. We show that all group-generated authentication
codes have perfect secrecy, which allows us to demonstrate that algebraic
manipulation detection codes can be considered to be a special case of an
authentication code with perfect secrecy.
  We also investigate splitting BIBDs that can be "equitably ordered". These
splitting BIBDs yield authentication codes with splitting that also have
perfect secrecy. We show that, while group generated BIBDs are inherently
equitably ordered, the concept is applicable to more general splitting BIBDs.
For various pairs $(k,c)$, we determine necessary and sufficient (or almost
sufficient) conditions for the existence of $(v, k \times c,1)$-splitting BIBDs
that can be equitably ordered. The pairs for which we can solve this problem
are $(k,c) = (3,2), (4,2), (3,3)$ and $(3,4)$, as well as all cases with $k =
2$.


  The subject of this paper is to study the decay of solutions for two systems
of laminated Timoshenko beams with interfacial slip in the whole space R
subject to a thermal effect of type III acting only on one component. When the
thermal effect is acting via the second or third component of the laminated
Timoshenko beam (rotation angle displacement or dynamic of the slip), we prove
that both systems are polynomially stable and obtain stability estimates in the
L2 -norm of solutions and their higher order derivatives with respect of the
space variable. The decay rates, as well as the absence and presence of the
regularity-loss type property, depend on the regularity of the initial data and
the speeds of wave propagations. However, when the thermal effect is acting via
the first comoponent (transversal displacement), we introduce a new stability
number \c{hi} and prove that the stability of systems is equivalent to \c{hi}
6= 0. An application to a case of lower order coupling terms will be also
given. To prove our results, we use the energy method in Fourier space combined
with well chosen weight functions to build appropriate Lyapunov functionals.


  For several hours on 2008 April 19 the T Tauri spectroscopic binary DQ Tau
was observed to brighten, reaching a maximum detected flux of 468 mJy and
likely making it (briefly) the brightest object at 3 mm in the Taurus
star-forming region. We present the light curve of a rarely before observed
millimeter flare originating in the region around a pre-main-sequence star, and
the first from a classical T Tauri star. We discuss the properties and nature
of the flaring behavior in the context of pulsed accretion flows (the current
picture based largely on studies of this object's optically variable spectrum),
as well as magnetospheric re-connection models (a separate theory that predicts
millimeter flares for close binaries of high orbital eccentricity). We believe
that the flare mechanism is linked to the binary orbit, and therefore periodic.
DQ Tau makes a strong case for multi-wavelength follow-up studies, performed in
parallel, of future flares to help determine whether magnetospheric and
dynamical interactions in a proto-binary system are independent.


  The inverse transfer in two-dimensional turbulence governed by the surface
quasi-geostrophic (SQG) equation is studied. The nonlinear transfer of this
system conserves the two quadratic quantities
$\Psi_1=<|(-\Delta)^{1/4}\psi|^2>/2$ and $\Psi_2=<|(-\Delta)^{1/2}\psi|^2>/2$
(kinetic energy), where $\psi$ is the streamfunction and $<\cdot>$ denotes a
spatial average. In the limit of infinite domain, the kinetic energy density
$\Psi_2$ remains bounded. For power-law inverse-transfer region, the inverse
flux of $\Psi_1$ diminishes as it proceeds toward sufficiently low wavenumbers,
implying that no persistent inverse cascade of $\Psi_1$ is sustainable. The
unrealizability of an inverse cascade of $\Psi_1$ implies that there is no
direct cascade of $\Psi_2$. Hence, the dual-cascade picture which is widely
believed to be realizable in two-dimensional Navier--Stokes turbulence does not
apply to SQG turbulence. Numerical results supporting the theoretical
predictions are presented.


  Complete deconvolution analysis for bulk RNAseq data is important and helpful
to distinguish whether the difference of disease-associated GEPs (gene
expression profiles) in tissues of patients and normal controls are due to
changes in cellular composition of tissue samples, or due to GEPs changes in
specific cells. One of the major techniques to perform complete deconvolution
is nonnegative matrix factorization (NMF), which also has a wide-range of
applications in the machine learning community. However, the NMF is a
well-known strongly ill-posed problem, so a direct application of NMF to RNAseq
data will suffer severe difficulties in the interpretability of solutions. In
this paper we develop an NMF-based mathematical model and corresponding
computational algorithms to improve the solution identifiability of
deconvoluting bulk RNAseq data. In our approach, we combine the biological
concept of marker genes with the solvability conditions of the NMF theories,
and develop a geometric structured guided optimization model. In this strategy,
the geometric structure of bulk tissue data is first explored by the spectral
clustering technique. Then, the identified information of marker genes is
integrated as solvability constraints, while the overall correlation graph is
used as manifold regularization. Both synthetic and biological data are used to
validate the proposed model and algorithms, from which solution
interpretability and accuracy are significantly improved.


  In this paper, I generalize the formula that the integration of Chern forms
of hermitian line bundles equals the algebraic intersection number of the
underlying line bundles. I generalize it to a formula on a quasi-projective
variety over a complete valuation field which might be archimedean or
non-archimedean. Our result has a close relation with the integration of Betti
forms and the notion of non-degeneracy of a closed subvariety.


  Polarisation states are described by spin expectation values, known as Stokes
parameters, whose trajectories in a rotationally symmetric system form a sphere
named after Poincar\'e. Here, we show that the trajectories of broken
rotational symmetric systems can exhibit distinct topological structures in
polarisation states. We use a phase-shifter to form a polarisation circle
(${\mathbb S}^1$), which interferes with the original input due to the phase
change of the output state upon the rotation. By rotating the circle using a
rotator, the trajectories become a polarisation torus (${\mathbb S}^1 \times
{\mathbb S}^1$), which was experimentally confirmed in a simple set-up using
passive optical components together with Mach-Zehnder interferometers. We also
discuss about realisations of other topological features, such as M\"obius
strip, Hopf-links, and topological Dirac bosons with a bulk-edge
correspondence.


  This article aims to give a short introduction into Hopf-algebraic aspects of
renormalization, enjoying growing attention for more than a decade by now. As
most available literature is concerned with the minimal subtraction scheme, we
like to point out properties of the kinematic subtraction scheme which is also
widely used in physics (under the names of MOM or BPHZ).
  In particular we relate renormalized Feynman rules $\phi_R$ in this scheme to
the universal property of the Hopf algebra $H_R$ of rooted trees, exhibiting a
refined renormalization group equation which is equivalent to $\phi_R: H_R
\rightarrow K[x]$ being a morphism of Hopf algebras to the polynomials in one
indeterminate.
  Upon introduction of analytic regularization this results in efficient
combinatorial recursions to calculate $\phi_R$ in terms of the Mellin
transform. We find that different Feynman rules are related by a distinguished
class of Hopf algebra automorphisms of $H_R$ that arise naturally from
Hochschild cohomology.
  Also we recall the known results for the minimal subtraction scheme and shed
light on the interrelationship of both schemes.
  Finally we incorporate combinatorial Dyson-Schwinger equations to study the
effects of renormalization on the physical meaningful correlation functions.
This yields a precise formulation of the equivalence of the two different
renormalization prescriptions mentioned before and allows for non-perturbative
definitions of quantum field theories in special cases.


  We develop the mathematical theory of a model, constructed by C. Gu, I.
Downes, O. Gnawali, and L. Guibas, of networks that diffuse continuously
acquired information from mobile sensor nodes. We prove new results on the
maximum, minimum, and expected capacity of their model of combinatorial and
geometric mobile sensor networks, as well as modified versions of these models.
We also give complexity results for the problem of deciding when a
combinatorial mobile sensor network is generated from a geometric mobile sensor
network.
  A more detailed description of the concerned concepts is the following. In a
restricted combinatorial mobile sensor network (RCMSN), there are n sensors
that continuously receive and store information from outside. Every two sensors
communicate exactly once, and at an event when two sensors communicate, they
receive and store additionally all information the other has stored. In a
geometric mobile sensor network (GMSN), a type of RCMSN, the sensors move with
constant speed on a straight line and communicate whenever a pair meet. For the
purpose of analysis, all information received by two sensors before a
communication event and after the previous communication events for each of
them is collected into one information packet, and the capacity is defined as
the ratio of the average number of sensors reached by the packets and the total
number of sensors.


  In this paper, we formally investigate two mathematical aspects of Hermite
splines which translate to features that are relevant to their practical
applications. We first demonstrate that Hermite splines are maximally localized
in the sense that their support sizes are minimal among pairs of functions with
identical reproduction properties. Then, we precisely quantify the
approximation power of Hermite splines for reconstructing functions and their
derivatives, and show that they are asymptotically identical to cubic B-splines
for these tasks. Hermite splines therefore combine optimal localization and
excellent approximation power, while retaining interpolation properties and
closed-form expression, in contrast to existing similar approaches. These
findings shed a new light on the convenience of Hermite splines for use in
computer graphics and geometrical design.


  Microwave spectroscopy within the Landau filling ($\nu$) range of the integer
quantum Hall effect (IQHE) has revealed pinning mode resonances signifying
Wigner solids (WSs) composed of quasi-particles or -holes. We study pinning
modes of WSs in wide quantum wells (WQWs) for $ 0.8\le\nu\le1.2$, varying the
density, $n$, and tilting the sample by angle $\theta$ in the magnetic field.
Three distinct WS phases are accessed. One phase, S1, is phenomenologically the
same as the WS observed in the IQHEs of narrow QWs. The second phase, S2,
exists at $\nu$ further from $\nu=1$ than S1, and requires a sufficiently large
$n$ or $\theta$, implying S2 is stabilized by the Zeeman energy. The melting
temperatures of S1 and S2, estimated from the disappearance of the pinning
mode, show different behavior vs $\nu$. At the largest $n$ or $\theta$, S2
disappears and the third phase, S1A, replaces S1, also exhibiting a pinning
mode. This occurs as the WQW $\nu=1$ IQHE becomes a two-component,
Halperin-Laughlin $\pone$ state. We interpret S1A as a WS of the excitations of
$\pone$, which has not been previously observed.


  In this note we observe that we can remove the hypothesis of resolution of
singularities from the isomorphism constructed by Suslin between the \'etale
cohomology with compact support and Bloch's higher Chow groups over an
algebraically closed field. We also show that this isomorphism can be obtained
using Ivorra's realisation functor.


  This paper concerns instruction sequences that contain probabilistic
instructions, i.e. instructions that are themselves probabilistic by nature. We
propose several kinds of probabilistic instructions, provide an informal
operational meaning for each of them, and discuss related work. On purpose, we
refrain from providing an ad hoc formal meaning for the proposed kinds of
instructions. We also discuss the approach of projection semantics, which was
introduced in earlier work on instruction sequences, in the light of
probabilistic instruction sequences.


  Both long-tailed and noisily labeled data frequently appear in real-world
applications and impose significant challenges for learning. Most prior works
treat either problem in an isolated way and do not explicitly consider the
coupling effects of the two. Our empirical observation reveals that such
solutions fail to consistently improve the learning when the dataset is
long-tailed with label noise. Moreover, with the presence of label noise,
existing methods do not observe universal improvements across different
sub-populations; in other words, some sub-populations enjoyed the benefits of
improved accuracy at the cost of hurting others. Based on these observations,
we introduce the Fairness Regularizer (FR), inspired by regularizing the
performance gap between any two sub-populations. We show that the introduced
fairness regularizer improves the performances of sub-populations on the tail
and the overall learning performance. Extensive experiments demonstrate the
effectiveness of the proposed solution when complemented with certain existing
popular robust or class-balanced methods.


  We demonstrate focusing of a plane microwave by a plano-concave lens
fabricated from a photonic crystal (PhC) having negative refractive index and
left-handed electromagnetic properties. An inverse experiment, in which a plane
wave is produced from a source placed at the focal point of the lens is also
reported. A frequency dependent negative refractive index, is obtained for the
lens from the experimental data which matches well with that determined from
band structure calculations.


  In its all-sky survey, Gaia will monitor astrometrically hundreds of
thousands of main-sequence stars within $\approx200$ pc, looking for the
presence of giant planetary companions within a few AUs from their host stars.
Indeed, Gaia observations will have great impact is the astrophysics of
planetary systems (e.g., Casertano et al. 2008), in particular when seen as a
complement to other techniques for planet detection and characterization (e.g.,
Sozzetti 2011). In this paper, I briefly address some of the relevant technical
issues associated with the precise and accurate determination of astrometric
orbits of planetary systems using Gaia data. I then highlight some of the
important synergies between Gaia high-precision astrometry and other ongoing
and planned, indirect and direct planet-finding and characterization programs,
both from the ground and in space, and over a broad range of wavelengths,
providing preliminary results related to one specific example of such
synergies.


  We consider a generalisation of a conjecture by Patterson and Wiedemann from
1983 on the Hamming distance of a function from $\mathbb{F}_q^n$ to
$\mathbb{F}_q$ to the set of affine functions from $\mathbb{F}_q^n$ to
$\mathbb{F}_q$. We prove the conjecture for each $q$ such that the
characteristic of $\mathbb{F}_q$ lies in a subset of the primes with density
$1$ and we prove the conjecture for all $q$ by assuming the generalised Riemann
hypothesis. Roughly speaking, we show the existence of functions for which the
distance to the affine functions is maximised when $n$ tends to infinity. This
also determines the asymptotic behaviour of the covering radius of the
$[q^n,n+1]$ Reed-Muller code over $\mathbb{F}_q$ and so answers a question
raised by Leducq in 2013. Our results extend the case $q=2$, which was recently
proved by the author and which corresponds to the original conjecture by
Patterson and Wiedemann. Our proof combines evaluations of Gauss sums in the
semiprimitive case, probabilistic arguments, and methods from discrepancy
theory.


  The results of our speckle interferometric observations of young binaries VY
Tau and XZ Tau are presented. For the first time, we found a relative
displacement of VY Tau components as well as a preliminary orbit for XZ Tau. It
appeared that the orbit is appreciably non-circular and is inclined by $i
\lesssim 47^o$ from the plane of the sky. It means that the rotation axis of XZ
Tau A and the axis of its jet are significantly non-perpendicular to the
orbital plane. We found that the average brightness of XZ Tau had been
increasing from the beginning of the last century up to the mid-thirties and
then it decreased by $\Delta B > 2$ mag. The maximal brightness has been
reached significantly later on the time of periastron passage. The total
brightness of XZ Tau's components varied in a non-regular way from 1970 to 1985
when eruptions of hot gas from XZ Tau A presumably had occurred. In the early
nineties the variations became regular following which a chaotic variability
had renewed. We also report that a flare activity of VY Tau has resumed after
40 yr pause, parameters of the previous and new flares are similar, and the
flares are related with the A component.


  In epidemiology, the effective reproduction number $R_e$ is used to
characterize the growth rate of an epidemic outbreak. In this paper, we
investigate properties of $R_e$ for a modified SEIR model of COVID-19 in the
city of Houston, TX USA, in which the population is divided into low-risk and
high-risk subpopulations. The response of $R_e$ to two types of control
measures (testing and distancing) applied to the two different subpopulations
is characterized. A nonlinear cost model is used for control measures, to
include the effects of diminishing returns. We propose three types of heuristic
strategies for mitigating COVID-19 that are targeted at reducing $R_e$, and we
exhibit the tradeoffs between strategy implementation costs and number of
deaths. We also consider two variants of each type of strategy: basic
strategies, which consider only the effects of controls on $R_e$, without
regard to subpopulation; and high-risk prioritizing strategies, which maximize
control of the high-risk subpopulation. Results showed that of the three
heuristic strategy types, the most cost-effective involved setting a target
value for $R_e$ and applying sufficient controls to attain that target value.
This heuristic led to strategies that begin with strict distancing of the
entire population, later followed by increased testing. Strategies that
maximize control on high-risk individuals were less cost-effective than basic
strategies that emphasize reduction of the rate of spreading of the disease.
The model shows that delaying the start of control measures past a certain
point greatly worsens strategy outcomes. We conclude that the effective
reproduction can be a valuable real-time indicator in determining
cost-effective control strategies.


  Motivated by problems arising in geometric flows, we prove several regularity
results for systems of local and nonlocal equations, adapting to the parabolic
case a neat argument due to Caffarelli. The geometric motivation of this work
comes from recent works arising in the theory harmonic maps with free boundary
in particular. We prove H\"older regularity of weak solutions.


  Micro-nanoparticle systems have wide applications in thermal science and
technology. In dense particulate system, the particle separation distance may
be less than the characteristic thermal wavelength and near field effect will
be significant and become a key factor to influence thermal radiation transfer
in the system. In this study, radiative heat transfer (RHT) between two
metallic nanoparticles clusters are explored using many-body radiative heat
transfer theory implemented with the coupled electric and magnetic dipole
(CEMD) approach, which effectively takes into account the contribution of
magnetic polarization of metallic nanoparticles on heat exchange. As the focus,
the effects of magnetic polarization and many-body interaction (MBI) on RHT
were analyzed. The effects of fractal dimension and relative orientation of the
clusters were also analyzed. Results show that the contribution of magnetically
polarized eddy-current Joule dissipation dominates the RHT between Ag
nanoparticle clusters. If only electric polarization (EP approach) is
considered, the heat conductance will be underestimated as compared with the
CEMD approach in both near field and far field regime. The effect of MBI on the
RHT between Ag nanoparticle clusters is unobvious at room temperature, which is
quite different from the SiC nanoparticle clusters. For the latter, MBI tends
to suppress RHT significantly. The relative orientation has remarkable effect
on radiative heat flux for clusters with lacy structure when the separation
distance is in the near field. While for the separation distance in far field,
both the relative orientation and the fractal dimension has a weak influence on
radiative heat flux. This work will help the understanding of thermal transport
in dense particulate system.


  We analyse a diffuse interface type approximation, known as the diffuse
domain approach, of a linear coupled bulk-surface elliptic partial differential
system. The well-posedness of the diffuse domain approximation is shown using
weighted Sobolev spaces and we prove that the solution to the diffuse domain
approximation converges weakly to the solution of the coupled bulk-surface
elliptic system as the approximation parameter tends to zero. Moreover, we can
show strong convergence for the bulk quantity, while for the surface quantity,
we can show norm convergence and strong convergence in a weighted Sobolev
space. Our analysis also covers a second order surface elliptic partial
differential equation and a bulk elliptic partial differential equation with
Dirichlet, Neumann and Robin boundary condition.


  We discuss dynamics of massive Klein-Gordon fields in two-dimensional Anti-de
Sitter spacetimes ($AdS_2$), in particular conserved quantities and non-modal
instability on the future Poincar\'e horizon called, respectively, the Aretakis
constants and the Aretakis instability. We find out the geometrical meaning of
the Aretakis constants and instability in a parallel-transported frame along a
null geodesic, i.e., some components of the higher-order covariant derivatives
of the field in the parallel-transported frame are constant or unbounded at the
late time, respectively. Because $AdS_2$ is maximally symmetric, any null
hypersurfaces have the same geometrical properties. Thus, if we prepare
parallel-transported frames along any null hypersurfaces, we can show that the
same instability emerges not only on the future Poincar\'e horizon but also on
any null hypersurfaces. This implies that the Aretakis instability in $AdS_2$
is the result of singular behaviors of the higher-order covariant derivatives
of the fields on the whole $AdS$ infinity, rather than a blow-up on a specific
null hypersurface. It is also discussed that the Aretakis constants and
instability are related to the conformal Killing tensors. We further explicitly
demonstrate that the Aretakis constants can be derived from ladder operators
constructed from the spacetime conformal symmetry.


  Stability of the boundary between epithelial tissues is key to preserve their
integrity and thus their biological functioning. We numerically investigate the
stability of the frontier between two confluent cell monolayers that divide at
constant rates. We show that even when the two tissues have the same mechanical
properties, the same cell division rate and the same homeostatic pressure, the
interface is unstable: the interface location is subject to fluctuations that
are of the same order of magnitude of the system size, leading eventually to
the disappearance of one or the other tissue. When these parameters differ, a
constant drift superimpose on this random walk of the boundary location. Our
results reveal that a regulation mechanism on cell division must exist to
guarantee the stability of the tissue boundaries.


  In spacetimes of dimension greater than four it is natural to consider higher
order (in R) corrections to the Einstein equations. In this letter generalized
Israel junction conditions for a membrane in such a theory are derived. This is
achieved by generalising the Gibbons-Hawking boundary term. The junction
conditions are applied to simple brane world models, and are compared to the
many contradictory results in the literature.


  We estimate the range of the radiative lifetime and energy of the anomalous,
low-energy $3/2^+(7.8 \pm 0.5$ eV) state in the $^{229}$Th nucleus. Our
phenomenological calculations are based on the available experimental data for
the intensities of $M1$ and $E2$ transitions between excited levels of the
$^{229}$Th nucleus in the $K^{\pi}[Nn_Z\Lambda]=5/2^+[633]$ and $3/2^+[631]$
rotational bands. We also discuss the influence of certain branching
coefficients, which affect the currently accepted measured energy of the
isomeric state. From this work, we establish a favored region where the
transition lifetime and energy should lie at roughly the 90% confidence level.
We also suggest new nuclear physics measurements, which would significantly
reduce the ambiguity in the present data.


  We present Acquisition Thompson Sampling (ATS), a novel technique for batch
Bayesian Optimization (BO) based on the idea of sampling multiple acquisition
functions from a stochastic process. We define this process through the
dependency of the acquisition functions on a set of model hyper-parameters. ATS
is conceptually simple, straightforward to implement and, unlike other batch BO
methods, it can be employed to parallelize any sequential acquisition function
or to make existing parallel methods scale further. We present experiments on a
variety of benchmark functions and on the hyper-parameter optimization of a
popular gradient boosting tree algorithm. These demonstrate the advantages of
ATS with respect to classical parallel Thompson Sampling for BO, its
competitiveness with two state-of-the-art batch BO methods, and its
effectiveness if applied to existing parallel BO algorithms.


  When a liquid droplet impacts a vibrated micro-structured surface with
asymmetric topology, the liquids perform a horizontal motion during its
bouncing. The moving effect is observed when the liquid is in contact with a
low surface energy surface (e.g. hydrophobic) and over a wide amplitude and
frequency range. We propose that the motion direction of liquid droplets is
driven by a force exerted by the unbalanced vapor flow between the contact of
solid and the liquid due to the asymmetric geometry. We observe the levitation
and movement dynamics of the droplet impacting on a vibrated micro-structured
surface to reveal the processes responsible for the transitional regime between
the moving, unmoved, and broken droplet as the vibration amplitude and
frequency increases. Based on the insight provided by the experiment and on the
analysis of the kinetic energy of the droplet, we develop a quantitative model
for the dynamic movement and its dependence on the vibration characteristics.


  We expose (without proofs) a unified computational approach to integrable
structures (including recursion, Hamiltonian, and symplectic operators) based
on geometrical theory of partial differential equations. We adopt a coordinate
based approach and aim to provide a tutorial to the computations.


  Is a commercial mass media, dependent on the market for its sustenance,
necessary, or even desirable, for liberal democracy? Yochai Benkler has argued
that a decentralized, peer-to-peer system of communications and information is
both possible with digital technology and preferable to a system based on
commercial mass media. He has contended in fact that the presence of
politically powerful, copyright-rich mass media imposes significant barriers to
the development of peer-to-peer information-sharing networks. In contrast, I
have argued that the commercial mass media play an important, and perhaps even
vital, role in liberal democracy by galvanizing public opinion, serving as a
watchdog against government and corporate wrongdoing, agenda-setting (which
enables public discourse), and serving as a relatively trustworthy source of
information. This paper seeks to push the ball forward on this issue. It first
isolates and enumerates the contributions that the commercial mass media are
said to make towards liberal democracy. It then briefly assesses the extent to
which the commercial mass media actually fulfills these constitutive functions.
It then asks whether alternative institutions might serve some or all of these
functions just as well or better. In so doing, it looks both to the past and
the future. First, it examines the political party-supported press that thrived
in the United States through much of the 19th century. Second, it examines
government-funded mass media. Third, it looks, skeptically, at possibilities
for peer-to-peer sharing of information and opinion in the digital network
environment. I conclude that, despite the weaknesses of commercial mass media,
an information policy suitable to liberal democracy should include a plurality
of types of voices, including commercial mass media.


  The Kepler Mission Science Operations Center (SOC) performs several critical
functions including managing the ~156,000 target stars, associated target
tables, science data compression tables and parameters, as well as processing
the raw photometric data downlinked from the spacecraft each month. The raw
data are first calibrated at the pixel level to correct for bias, smear induced
by a shutterless readout, and other detector and electronic effects. A
background sky flux is estimated from ~4500 pixels on each of the 84 CCD
readout channels, and simple aperture photometry is performed on an optimal
aperture for each star. Ancillary engineering data and diagnostic information
extracted from the science data are used to remove systematic errors in the
flux time series that are correlated with these data prior to searching for
signatures of transiting planets with a wavelet-based, adaptive matched filter.
Stars with signatures exceeding 7.1 sigma are subjected to a suite of
statistical tests including an examination of each star's centroid motion to
reject false positives caused by background eclipsing binaries. Physical
parameters for each planetary candidate are fitted to the transit signature,
and signatures of additional transiting planets are sought in the residual
light curve. The pipeline is operational, finding planetary signatures and
providing robust eliminations of false positives.


  Modal interpretations of quantum mechanics assign definite properties to
physical systems and specify single-time joint probabilities of these
properties. We show that a natural extension, applying to properties at several
times, can be given if a decoherence condition is satisfied. This extension
defines "consistent histories" of modal properties. We suggest a new form of
the modal scheme, that offers prospects of a more general applicability of the
histories concept. Finally, we discuss a possible way of applying these ideas
to relativistic quantum field theory.


  Negative superhumps are detected in the light curves of RW Tri collected in
September 1994 (Smak 1995) and November/December 1957 (Walker 1963). New system
parameters, obtained using $K_2$ and $V_{2,rot}\sin i$ (from Poole et al. 2003)
and $q$ (estimated from $P_{nSH}$), are $M_1=0.60\pm 0.20M\odot$, $M_2=0.48\pm
0.15M\odot$, $A=1.13\pm 0.09\times 10^{11}$cm and $i=72.5\pm 2.5$.


  Magnetic field induced ferroelectric hysteresis loop observed in
Bi0.75Sr0.25FeO3-delta is of prime importance. The coexistence of
antiferromagnetism and weak ferromagnetism is responsible for the original
magnetoelastic and magnetoferroelectric properties. Upon external magnetic
field application, the existence of a magnetostrictive effect supports a
structural transition towards a homogeneous antiferromagnetic and ferroelectric
phase. The magnetic field induced polarization is among the highest reported
for BiFeO3 based systems in either thin film or bulk forms (Pr=96 microC/cm2 at
10T) while the ferroelectric coercive field is among the lowest reported
(Hc=661(V/cm) at 10T). These properties make this material very attractive for
technical applications.


  Let $\mathcal{A}$ be a complex Banach algebra. An element $a\in \mathcal{A}$
has g-Drazin inverse if there exists $b\in \mathcal{A}$ such that $$b=bab,
ab=ba, a-a^2b\in \mathcal{A}^{qnil}.$$ Let $a,b\in \mathcal{A}$ have g-Drazin
inverses. If $$ab = \lambda a^\pi b^\pi b a b^\pi,$$ we prove that $a+b$ has
g-Drazin inverse and $$(a+b)^d = b^\pi a^d + b^da^\pi +
\sum\limits_{n=0}^\infty (b^d)^{n+1} a^n a^\pi + \sum\limits_{n=0}^\infty b^\pi
(a+b)^n b(a^d)^{n+2}.$$ The main results of Mosic (Bull. Malays. Sci. Soc.,
{\bf 40}(2017), 1465--1478) is thereby extended to the general case.
Applications to block operator matrices are given.


  We consider renormalizable couplings of neutral $\phi$, singly $\phi^\pm$,
and doubly charged $\phi^{\pm\pm}$ scalar bosons to leptons and the $Z$ gauge
boson and calculate the one-loop contributions to the anomalous weak magnetic
dipole moment (AWMDM) $a_\tau^W$ and the weak electric dipole moment (WEDM)
$d_\tau^W$ of a charged lepton in a model independent way. The analytic
expressions are presented in terms of both parametric integrals and
Passarino-Veltman scalar functions. Among the new contributions, there are
those arising from the vertices of the type $\phi^\pm W^\mp Z$ and $Z
\phi_i\phi_j$ ($i\ne j$), along with contributions from doubly charged scalar
bosons. Both $a_\tau$ and $d_\tau^W$ are evaluated in several scenarios , first
in a model independent way and then within some popular models, such as
two-Higgs doublet models (THDMs), multiple-Higgs doublet models and Higgs
triplet models. As far as $a_\tau^W$ is concerned, its real part reaches values
as high as $10^{-10}-10^{-9}$ for masses of the new scalar bosons in the 200
GeV range, whereas the imaginary part is one or two orders of magnitude below.
On the other hand, the most promising scenario for a nonvanishing WEDM is
offered by a $CP$-violating THDM in a scenario where the heavy neutral scalar
bosons are a mixture of $CP$ eigenstates. It is found that the real part of
$d_\tau^W$ is of the order of $10^{-24}$ ecm and its imaginary part can reach
the $10^{-26}$ ecm level for masses of the new scalar bosons of the order of a
few hundred of GeVs. Both the tau AWMDM and WEDM decrease dramatically as the
scalar boson masses increase.


  We give bounds on the average fidelity achievable by any quantum state
estimator, which is arguably the most prominently used figure of merit in
quantum state tomography. Moreover, these bounds can be computed online---that
is, while the experiment is running. We show numerically that these bounds are
quite tight for relevant distributions of density matrices. We also show that
the Bayesian mean estimator is ideal in the sense of performing close to the
bound without requiring optimization. Our results hold for all finite
dimensional quantum systems.


  We make use of publicly available results from N-body Millennium Simulation
to create mock samples of lensed supernovae type Ia and core-collapse.
Simulating galaxy-galaxy lensing we derive the rates of lensed supernovae and
find than at redshifts higher that 0.5 about 0.06 per cent of supernovae will
be lensed by a factor two or more. Future wide field surveys like Gaia or LSST
should be able to detect lensed supernovae in their unbiased sky monitoring.
Gaia (from 2013) will detect at least 2 cases whereas LSST (from 2018) will see
more than 500 a year. Large number of future lensed supernovae will allow to
verify results of cosmological simulations. The strong galaxy- galaxy lensing
gives an opportunity to reach high-redshift supernovae type Ia and extend the
Hubble diagram sample.


  We systematically develop a learning-based treatment of stochastic optimal
control (SOC), relying on direct optimization of parametric control policies.
We propose a derivation of adjoint sensitivity results for stochastic
differential equations through direct application of variational calculus.
Then, given an objective function for a predetermined task specifying the
desiderata for the controller, we optimize their parameters via iterative
gradient descent methods. In doing so, we extend the range of applicability of
classical SOC techniques, often requiring strict assumptions on the functional
form of system and control. We verify the performance of the proposed approach
on a continuous-time, finite horizon portfolio optimization with proportional
transaction costs.


  Truncating quantum field theories to a dominant mode offers a
non-perturbative approach to their solution. We consider here the interaction
of charged scalar matter with a single mode of the electromagnetic field. The
implied breaking of explicit Lorentz invariance prompts us to compare
instant-form quantisation and front-form, with the latter yielding significant
simplifications when light-front zero modes are included. Using these field
theory results we reassess the validity of existing first-quantised approaches
to depletion effects in strong laser fields, and propose an alternative
interpretation based on the dressing approach to QED and its infra-red
structure.


  Quantum mechanics is an extremely successful theory that agrees with every
experiment. However, the principle of linear superposition, a central tenet of
the theory, apparently contradicts a commonplace observation: macroscopic
objects are never found in a linear superposition of position states. Moreover,
the theory does not really explain as to why during a quantum measurement,
deterministic evolution is replaced by probabilistic evolution, whose random
outcomes obey the Born probability rule. In this article we review an
experimentally falsifiable phenomenological proposal, known as Continuous
Spontaneous Collapse: a stochastic non-linear modification of the
Schr\"{o}dinger equation, which resolves these problems, while giving the same
experimental results as quantum theory in the microscopic regime. Two
underlying theories for this phenomenology are reviewed: Trace Dynamics, and
gravity induced collapse. As one approaches the macroscopic scale, the
predictions of this proposal begin to differ appreciably from those of quantum
theory, and are being confronted by ongoing laboratory experiments that include
molecular interferometry and optomechanics. These experiments, which
essentially test the validity of linear superposition for large systems, are
reviewed here, and their technical challenges, current results, and future
prospects summarized. We conclude that it is likely that over the next two
decades or so, these experiments can verify or rule out the proposed stochastic
modification of quantum theory.


  We extensively characterize the electronic structure of ultra-narrow graphene
nanoribbons (GNRs) with armchair edges and zig-zag termini that have 5 carbon
atoms across their width (5-AGNRs), as synthesised on Au(111). Scanning
tunnelling spectroscopy measurements on the ribbons, recorded on both the
metallic substrate and a decoupling NaCl layer, show well-defined dispersive
bands and in-gap states. In combination with theoretical calculations, we show
how these in-gap states are topological in nature and localised at the zig-zag
termini of the nanoribbons. Besides rationalising the driving force behind the
topological class selection of 5-AGNRs, we also uncover the length-dependent
behaviour of these end states which transition from singly occupied spin-split
states to a closed-shell form as the ribbons become shorter. Finally, we
demonstrate the magnetic character of the end states via transport experiments
in a model two-terminal device structure in which the ribbons are suspended
between the scanning probe and the substrate that both act as leads.


  When one considers the collection $\mathcal{H}(\mathbb{R}^n)$ of all compact
subsets of $\mathbb{R}^n$ and equip it with a topology, many questions can be
asked about the topological space one ends up with. This is an example of a
hyperspace, a mathematical object which has been studied in a more abstract
setting since the beginning of the 20th century. Here we give an elementary
proof of the path-connectedness of $\mathcal{H}(\mathbb{R}^n)$, with the
topology induced by the Hausdoff metric, by exploring the vector structure of
$\mathbb{R}^n$ and using only basic ideas of topology of metric spaces that
undergraduate students with just a basic knowledge of these concepts will be
able to understand.


  The growing skill in the synthesis processes of new materials has intensified
the interest in exploring the properties of systems modeled by more complex
lattices. Two-dimensional super-honeycomb lattices, have been investigated in
metallic organic frameworks. They turned out as a significant route to the
emergence of localized electronic responses, manifested as flat bands in their
structure with topological isolating behavior. A natural inquiry is a complete
analysis of their topological phases in the presence of electronic correlation
effects. Here we analyse of the electron-electron correlation effects via
Hubbard mean-field approximation on the topological phases of 2D and quasi-1D
graphene-Kagome lattices. The 2D spin conductivity phase's diagrams describe
metallic, trivial and topological insulating behaviors, considering different
energy coupling and electronic occupations. Our results pave the way to
smart-engineered nanostructured devices with relevant applications in
spintronics and transport responses.


  The aim of this paper is to present an algorithm the complexity of which is
polynomial to compute the semi-simplified modulo $p$ of a semi-stable
$\Q_p$-representation of the absolute Galois group of a $p$-adic field
(\emph{i.e.} a finite extension of $\Q_p$). In order to do so, we use
abundantly the $p$-adic Hodge theory and, in particular, the Breuil-Kisin
modules theory.


  Many search-based quantum algorithms that achieve a theoretical speedup are
not practically relevant since they require extraordinarily long coherence
times, or lack the parallelizability of their classical counterparts.This
raises the question of how to divide computational tasks into a collection of
parallelizable sub-problems, each of which can be solved by a quantum computer
with limited coherence time. Here, we approach this question via hybrid
algorithms for the k-SAT problem. Our analysis is based on Sch\"oning's
algorithm, which solves instances of k-SAT by performing random walks in the
space of potential assignments. The search space of the walk allows for
"natural" partitions, where we subject only one part of the partition to a
Grover search, while the rest is sampled classically, thus resulting in a
hybrid scheme. In this setting, we argue that there exists a simple trade-off
relation between the total runtime and the coherence-time, which no such
partition based hybrid-scheme can surpass. For several concrete choices of
partitions, we explicitly determine the specific runtime coherence-time
relations, and show saturation of the ideal trade-off. Finally, we present
numerical simulations which suggest additional flexibility in implementing
hybrid algorithms with optimal trade-off.


  We develop $(\epsilon,\delta)$-differentially private projection-depth-based
medians using the propose-test-release (PTR) and exponential mechanisms. Under
general conditions on the input parameters and the population measure, (e.g. we
do not assume any moment bounds), we quantify the probability the test in PTR
fails, as well as the cost of privacy via finite sample deviation bounds. Next,
we show that when some observations are contaminated, the private
projection-depth-based median does not break down, provided its input location
and scale estimators do not break down. We demonstrate our main results on the
canonical projection-depth-based median, as well as on projection-depth-based
medians derived from trimmed estimators. In the Gaussian setting, we show that
the resulting deviation bound matches the known lower bound for private
Gaussian mean estimation. In the Cauchy setting, we show that the ``outlier
error amplification'' effect resulting from the heavy tails outweighs the cost
of privacy. This result is then verified via numerical simulations.
Additionally, we present results on general PTR mechanisms and a uniform
concentration result on the projected spacings of order statistics, which may
be of general interest.


  We deal with interval parametric systems of linear equations and the goal is
to solve such systems, which basically comes down to finding an enclosure for a
parametric solution set. Obviously we want this enclosure to be as tight as
possible. The review of the available literature shows that in order to make a
system more tractable most of the solution methods use left preconditioning of
the system by the midpoint inverse. Surprisingly, and in contrast to standard
interval linear systems, our investigations have shown that double
preconditioning can be more efficient than a single one, both in terms of
checking the regularity of the system matrix and enclosing the solution set.
Consequently, right (which was hitherto mentioned in the context of checking
regularity of interval parametric matrices) and double preconditioning together
with the p-solution concept enable us to solve a larger class of interval
parametric linear systems than most of existing methods. The applicability of
the proposed approach to solving interval parametric linear systems is
illustrated by several numerical examples.


  A primitive multiple scheme is a complex Cohen-Macaulay scheme $Y$ such that
the associated reduced scheme $X=Y_{red}$ is smooth, irreducible, and that $Y$
can be locally embedded in a smooth variety of dimension $\dim(X)+1$. If $n$ is
the multiplicity of $Y$, there is a canonical filtration $X=X_1\subset
X_2\subset\cdots\subset X_n=Y$, such that $X_i$ is a primitive multiple scheme
of multiplicity $i$. The simplest example is the trivial primitive multiple
scheme of multiplicity $n$ associated to a line bundle $L$ on $X$: it is the
$n$-th infinitesimal neighborhood of $X$, embedded if the line bundle $L^*$ by
the zero section.
  Let ${\bf Z}_n={spec}(C[t]/(t^n))$. The primitive multiple schemes of
multiplicity $n$ are obtained by taking an open cover $(U_i)$ of a smooth
variety $X$ and by gluing the schemes $U_i\times{\bf Z}_n$ using automorphisms
of $U_{ij}\times {\bf Z}_n$ that leave $U_{ij}$ invariant. This leads to the
study of the sheaf of nonabelian groups $G_n$ of automorphisms of $X\times {\bf
Z}_n$ that leave the $X$ invariant, and to the study of its first cohomology
set. If $n\geq 2$ there is an obstruction to the extension of $X_n$ to a
primitive multiple scheme of multiplicity $n+1$, which lies in the second
cohomology group $H^2(X,E)$ of a suitable vector bundle $E$ on $X$.
  In this paper we study these obstructions and the parametrization of
primitive multiple schemes. As an example we show that if $X=P_m$ with $m>=3$
all the primitive multiple schemes are trivial. If $X=P_2$, there are only two
non trivial primitive multiple schemes, of multiplicities $2$ and $4$, which
are not quasi-projective. On the other hand, if $X$ is a projective bundle over
a curve, we show that there are infinite sequences $X=X_1\subset
X_2\subset\cdots\subset X_n\subset X_{n+1}\subset\cdots$ of non trivial
primitive multiple schemes.


  Cuprous oxide (Cu$_2$O) is a semiconductor with large exciton binding energy
and significant technological importance in applications such as photovoltaics
and solar water splitting. It is also a superior material system for quantum
optics that enabled the observation of two intriguing phenomena, i.e. Rydberg
excitons as solid-state analogue to highly-excited atomic states and dense
exciton gases showing quantum degeneracy when approaching the phase transition
to Bose-Einstein condensation. Previous experiments focused on natural bulk
crystals due to major difficulties in growing high-quality synthetic samples.
Here, we present Cu$_2$O microcrystals with excellent optical material quality
capable of hosting both quantum-degenerate excitons and excited Rydberg states.
Growth of Cu$_2$O with exceedingly low point defect levels was achieved on
silicon by a scalable thermal oxidation process compatible with lithographic
patterning. Using the latter, we demonstrate Rydberg excitons in
site-controlled Cu$_2$O microstructures, paving the way for a plethora of
applications in integrated quantum photonics.


  We numerically analyze the evolution of a long-duration gamma-ray burst jet
as it leaves the progenitor star and propagates to the photospheric radius,
where radiation can be released. We find that the interaction of the
relativistic material with the progenitor star has influences well beyond the
stellar surface. Tangential collimation shocks are observed throughout the jet
evolution, out to about 100 stellar radii, which is the whole range of our
simulation. We find that the jet is internally hot at the photospheric radius
and we compute the photospheric emission. The photosphere is a very efficient
radiator, capable of converting more than half of the total energy of the jet
into radiation. We show that bright photospheres are a common feature of jets
born inside massive progenitor stars and that this effect can explain the high
radiative efficiency observed in long-duration bursts.


  The emerging field of vibro-polaritonic chemistry studies the impact of
light-matter hybrid states known as vibrational polaritons on chemical
reactivity and molecular properties. Here, we discuss vibro-polaritonic
chemistry from a quantum chemical perspective beyond the cavity
Born-Oppenheimer (CBO) approximation and examine the role of electron-photon
correlation in effective ground state Hamiltonians. We first quantitatively
review ab initio vibro-polaritonic chemistry based on the molecular Pauli-Fierz
Hamiltonian in dipole approximation and a vibrational strong coupling (VSC)
Born-Huang expansion. We then derive non-adiabatic coupling elements arising
from both ``slow'' nuclei and cavity modes compared to ``fast'' electrons via
the generalized Hellmann-Feynman theorem, discuss their properties and
re-evaluate the CBO approximation. In the second part, we introduce a crude VSC
Born-Huang expansion based on adiabatic electronic states, which provides a
foundation for widely employed effective Pauli-Fierz Hamiltonians in ground
state vibro-polaritonic chemistry. The latter do not strictly respect the CBO
approximation but an alternative scheme, which we name crude CBO approximation.
We argue that the crude CBO ground state misses electron-photon entanglement
relative to the CBO ground state due to neglected cavity-induced non-adiabatic
transition dipole couplings to excited states. A perturbative connection
between both ground state approximations is proposed, which identifies the
crude CBO ground state as first-order approximation to its CBO counterpart. We
provide an illustrative numerical analysis of the cavity Shin-Metiu model with
a focus on non-adiabatic coupling under VSC and electron-photon correlation
effects on classical activation barriers. We finally discuss potential
shortcomings of the electron-polariton Hamiltonian when employed in the VSC
regime.


  We reinterpret recent work on extremal Reissner- Nordstr\o m black holes to
argue that the mass is a measure of the gravitational entropy. We also find
that the entropy of scalar fields in this background has a stronger divergence
than usual.


  In this paper we develop a geometric version of the Hamilton-Jacobi equation
in the Poisson setting. Specifically, we "geometrize" what is usually called a
complete solution of the Hamilton-Jacobi equation. We use some well-known
results about symplectic groupoids, in particular cotangent groupoids, as a
keystone for the construction of our framework. Our methodology follows the
ambitious program proposed by A. Weinstein, [62], in order to develop geometric
formulations of the dynamical behavior of Lagrangian and Hamiltonian systems on
Lie algebroids and Lie groupoids. This procedure allows us to take symmetries
into account, and, as a by-product, we recover results from [14, 29, 31], but
even in these situations our approach is new. A theory of generating functions
for the Poisson structures considered here is also developed following the same
pattern, solving a longstanding problem of the area: how to obtain a generating
function for the identity tranformation and the nearby Poisson automorphisms of
Poisson manifolds. A direct application of our results give the construction of
a family of Poisson integrators, that is, integrators that conserve the
underlying Poisson geometry. These integrators are implemented in the paper in
benchmark problems. Some conclusions, current and future directions of research
are shown at the end of the paper.


  We show that the assignment of the (left) completely bounded multiplier
algebra $M_{cb}^l(L^1(\mathbb G))$ to a locally compact quantum group $\mathbb
G$, and the assignment of the intrinsic group, form functors between
appropriate categories. Morphisms of locally compact quantum groups can be
described by Hopf $*$-homomorphisms between universal $C^*$-algebras, by
bicharacters, or by special sorts of coactions. We show that the whole theory
of completely bounded multipliers can be lifted to the universal $C^*$-algebra
level, and that then the different pictures of both multipliers (reduced,
universal, and as centralisers) and morphisms interact in extremely natural
ways. The intrinsic group of a quantum group can be realised as a class of
multipliers, and so our techniques immediately apply. We also show how to think
of the intrinsic group using the universal $C^*$-algebra picture, and then,
again, show how the differing views on the intrinsic group interact naturally
with morphisms. We show that the intrinsic group is the "maximal classical"
quantum subgroup of a locally compact quantum group, show that it is even
closed in the strong Vaes sense, and that the intrinsic group functor is an
adjoint to the inclusion functor from locally compact groups to quantum groups.


  The purpose of this paper is twofold. First, we use a classical method to
establish Gaussian bounds of the fundamental matrix of a generalized parabolic
Lam\'{e} system with only bounded and measurable coefficients. Second, we
derive a maximal $L^1$ regularity result for the abstract Cauchy problem
associated with a composite operator. In a concrete example, we also obtain
maximal $L^1$ regularity for the Lam\'{e} system, from which it follows that
the Lipschitz seminorm of the solutions to the Lam\'{e} system is globally
$L^1$-in-time integrable. As an application, we use a Lagrangian approach to
prove a global-in-time well-posedness result for a viscous pressureless flow
provided that the initial velocity satisfies a scaling-invariant smallness
condition. The method established in this paper might be a powerful tool for
studying many issues arising from viscous fluids with truly variable densities.


  One of the main challenges for building the Semantic web is Ontology
Authoring. Controlled Natural Languages CNLs offer a user friendly means for
non-experts to author ontologies. This paper provides a snapshot of the
state-of-the-art for the core CNLs for ontology authoring and reviews their
respective evaluations.


  We experimentally demonstrate optomechanical motion and force measurements
near the quantum precision limits set by the quantum Cram\'er-Rao bounds
(QCRBs). Optical beams in coherent and phase-squeezed states are used to
measure the motion of a mirror under an external stochastic force. Utilizing
optical phase tracking and quantum smoothing techniques, we achieve position,
momentum, and force estimation accuracies close to the QCRBs with the coherent
state, while estimation using squeezed states shows clear quantum enhancements
beyond the coherent-state bounds.


  We propose a mechanism of unconventional superconductivity in two-dimensional
strongly-correlated electron systems. We consider a two-dimensional Kondo
lattice system or double-exchange system with spin-orbit coupling arising from
buckling of the plane. We show that a Chern-Simons term is induced for a gauge
field describing the phase fluctuations of the localized spins. Through the
induced Chern-Simons term, carriers behave like skyrmion excitations that lead
to a destruction mechanism of magnetic long-range order by carrier doping.
After magnetic long-range order is destroyed by carrier doping, the
Chern-Simons term plays a dominant role and the attractive interaction between
skyrmions leads to unconventional superconductivity. For the case of the
ferromagnetic interaction between the localized spins, the symmetry of the
Cooper pair is p-wave ($p_x \pm ip_y$). For the case of the antiferromagnetic
interaction between the localized spins, the symmetry of the Cooper pair is
d-wave ($d_{x^2-y^2}$). Applications to various systems are discussed, in
particular to the high-$T_c$ cuprates.


  The harmonic lasing free-electron laser amplifier, in which two wigglers is
employed in order for the fundamental resonance of the second wiggler to
coincide with the third harmonic of the first wiggler to generate ultraviolet
radiation, is studied. A set of coupled nonlinear first-order differential
equations describing the nonlinear evolution of the system, for a long electron
bunch, is solved numerically by CYRUS code. Solutions for the non-averaged and
averaged equations are compared. Remarkable agreement is found between the
averaged and non-averaged simulation for the evolution of the third harmonic.
Thermal effects in the form of longitudinal velocity spread are also
investigated. For efficiency enhancement, the second wiggler field is set to
decrease linearly and nonlinearly at the point where the radiation of the third
harmonic saturates. The optimum starting point and the slope of the tapering of
the amplitude of the wiggler are found by a successive run of the code. It is
found that tapering can increase the saturated power of the third harmonic
considerably. In order to reduce the length of the wiggler, the prebunched
electron beam is considered.


  Intent detection and slot filling are two main tasks for building a spoken
language understanding (SLU) system. The two tasks are closely related and the
information of one task can be utilized in the other task. Previous studies
either model the two tasks separately or only consider the single information
flow from intent to slot. None of the prior approaches model the bidirectional
connection between the two tasks simultaneously. In this paper, we propose a
Co-Interactive Transformer to consider the cross-impact between the two tasks.
Instead of adopting the self-attention mechanism in vanilla Transformer, we
propose a co-interactive module to consider the cross-impact by building a
bidirectional connection between the two related tasks. In addition, the
proposed co-interactive module can be stacked to incrementally enhance each
other with mutual features. The experimental results on two public datasets
(SNIPS and ATIS) show that our model achieves the state-of-the-art performance
with considerable improvements (+3.4% and +0.9% on overall acc). Extensive
experiments empirically verify that our model successfully captures the mutual
interaction knowledge.


  Deep learning models are increasingly popular in many machine learning
applications where the training data may contain sensitive information. To
provide formal and rigorous privacy guarantee, many learning systems now
incorporate differential privacy by training their models with (differentially)
private SGD. A key step in each private SGD update is gradient clipping that
shrinks the gradient of an individual example whenever its L2 norm exceeds some
threshold. We first demonstrate how gradient clipping can prevent SGD from
converging to stationary point. We then provide a theoretical analysis that
fully quantifies the clipping bias on convergence with a disparity measure
between the gradient distribution and a geometrically symmetric distribution.
Our empirical evaluation further suggests that the gradient distributions along
the trajectory of private SGD indeed exhibit symmetric structure that favors
convergence. Together, our results provide an explanation why private SGD with
gradient clipping remains effective in practice despite its potential clipping
bias. Finally, we develop a new perturbation-based technique that can provably
correct the clipping bias even for instances with highly asymmetric gradient
distributions.


  This article gives a formal definition of a lognormal family of probability
distributions on the set of symmetric positive definite (PD) matrices, seen as
a matrix-variate extension of the univariate lognormal family of distributions.
Two forms of this distribution are obtained as the large sample limiting
distribution via the central limit theorem of two types of geometric averages
of i.i.d. PD matrices: the log-Euclidean average and the canonical geometric
average. These averages correspond to two different geometries imposed on the
set of PD matrices. The limiting distributions of these averages are used to
provide large-sample confidence regions for the corresponding population means.
The methods are illustrated on a voxelwise analysis of diffusion tensor imaging
data, permitting a comparison between the various average types from the point
of view of their sampling variability.


  We use two different methods, the Hirsch-Fye quantum Monte Carlo simulation
and the slave-boson mean field analysis to estimate the effect of spin-orbit
coupling on the Kondo temperature in a quantum wire. In quantum Monte Carlo
simulation, we calculate the product of spin susceptibility and temperature for
different spin-orbit couplings and impurity energies. The variation of the
Kondo temperature is estimated via the low temperature universal curves. In the
mean field analysis, the Kondo temperature is estimated as the condensation
temperature of slave-boson. Both the two methods demonstrate that the Kondo
temperature is almost a linear function of the spin-orbit energy, and that the
Kondo temperature is suppressed by the spin-orbit coupling. Our results are
dramatically different from those given by the perturbative renormalization
group analysis.


  Market confidence is essential for successful investing. By incorporating
multi-market into the evolutionary minority game, we investigate the effects of
investor beliefs on the evolution of collective behaviors and asset prices.
When there exists another investment opportunity, market confidence, including
overconfidence and under-confidence, is not always good or bad for investment.
The roles of market confidence is closely related to market impact. For low
market impact, overconfidence in a particular asset makes an investor become
insensitive to losses and a delayed strategy adjustment leads to a decline in
wealth, and thereafter, one's runaway from the market. For high market impact,
under-confidence in a particular asset makes an investor over-sensitive to
losses and one's too frequent strategy adjustment leads to a large fluctuation
in asset prices, and thereafter, a decrease in the number of agents. At an
intermediate market impact, the phase transition occurs. No matter what the
market impact is, an equilibrium between different markets exists, which is
reflected in the occurrence of similar price fluctuations in different markets.
A theoretical analysis indicates that such an equilibrium results from the
coupled effects of strategy updating and shift in investment. The runaway of
the agents trading a specific asset will lead to a decline in the asset price
volatility and such a decline will be inhibited by the clustering of the
strategies. A uniform strategy distribution will lead to a large fluctuation in
asset prices and such a fluctuation will be suppressed by the decrease in the
number of agents in the market. A functional relationship between the price
fluctuations and the numbers of agents is found.


  The goal of this paper is to propose and study properties of multiwinner
voting rules which can be consider as generalisations of single-winner scoring
voting rules. We consider SNTV, Bloc, k-Borda, STV, and several variants of
Chamberlin--Courant's and Monroe's rules and their approximations. We identify
two broad natural classes of multiwinner score-based rules, and show that many
of the existing rules can be captured by one or both of these approaches. We
then formulate a number of desirable properties of multiwinner rules, and
evaluate the rules we consider with respect to these properties.


  On-line Precision scalability of the deep neural networks(DNNs) is a critical
feature to support accuracy and complexity trade-off during the DNN inference.
In this paper, we propose dual-precision DNN that includes two different
precision modes in a single model, thereby supporting an on-line precision
switch without re-training. The proposed two-phase training process optimizes
both low- and high-precision modes.


  As artificial intelligence, machine learning, and data science continue to
drive the data-centric economy, the challenges of implementing machine learning
on a single machine due to extensive data and computational needs have led to
the adoption of cloud computing solutions. This research paper explores the
design and implementation of a secure, cloud-native machine learning operations
(MLOPS) pipeline that supports multi-cloud environments. The primary objective
is to create a robust infrastructure that facilitates secure data collection,
real-time model inference, and efficient management of the machine learning
lifecycle. By leveraging cloud providers' capabilities, the solution aims to
streamline the deployment and maintenance of machine learning models, ensuring
high availability, scalability, and security. This paper details the network
topology, problem description, business and technical requirements, trade-offs,
and the provider selection process for achieving an optimal MLOPS environment.


  This article deals with the estimation of fractal dimension of
spatio-temporal patterns that are generated by numerically solving the Swift
Hohenberg (SH) equation. The patterns were converted into a spatial series
(analogous to time series) which were shown to be chaotic by evaluating the
largest Lyapunov exponent. We have applied several nonlinear time-series
analysis techniques like Detrended fluctuation and Rescaled range on these
spatial data to obtain Hurst exponent values that reveal spatial series data to
be long range correlated. We have estimated fractal dimension from the Hurst
and power law exponent and found the value lying between 1 and 2. The novelty
of our approach lies in estimating fractal dimension using image to data
conversion and spatial series analysis techniques, crucial for experimentally
obtained images.


  The widespread use of Batch Normalization has enabled training deeper neural
networks with more stable and faster results. However, the Batch Normalization
works best using large batch size during training and as the state-of-the-art
segmentation convolutional neural network architectures are very memory
demanding, large batch size is often impossible to achieve on current hardware.
We evaluate the alternative normalization methods proposed to solve this issue
on a problem of binary spine segmentation from 3D CT scan. Our results show the
effectiveness of Instance Normalization in the limited batch size neural
network training environment. Out of all the compared methods the Instance
Normalization achieved the highest result with Dice coefficient = 0.96 which is
comparable to our previous results achieved by deeper network with longer
training time. We also show that the Instance Normalization implementation used
in this experiment is computational time efficient when compared to the network
without any normalization method.


  It is known that, after a quench to zero temperature ($T=0$), two-dimensional
($d=2$) Ising ferromagnets with short-range interactions do not always relax to
the ordered state. They can also fall in infinitely long-lived striped
metastable states with a finite probability. In this paper, we study how the
abundance of striped states is affected by long-range interactions. We
investigate the relaxation of $d=2$ Ising ferromagnets with power-law
interactions by means of Monte Carlo simulations at both $T=0$ and $T \ne 0$.
For $T=0$ and the finite system size, the striped metastable states are
suppressed by long-range interactions. In the thermodynamic limit, their
occurrence probabilities are consistent with the short-range case. For $T \ne
0$, the final state is always ordered. Further, the equilibration occurs at
earlier times with an increase in the strength of the interactions.


  We systematically study the extension of the Supersymmetric Standard Model
(SSM) by an anomaly-free discrete gauge symmetry Z_N. We extend the work of
Ibanez and Ross with N=2,3 to arbitrary values of N. As new fundamental
symmetries, we find four Z_6, nine Z_9 and nine Z_18. We then place three
phenomenological demands upon the low-energy effective SSM: (i) the presence of
the mu-term in the superpotential, (ii) baryon-number conservation upto
dimension-five operators, and (iii) the presence of the see-saw neutrino mass
term LHLH. We are then left with only two anomaly-free discrete gauge
symmetries: baryon-triality, B_3, and a new Z_6, which we call proton-hexality,
P_6. Unlike B_3, P_6 prohibits the dimension-four lepton-number violating
operators. This we propose as the discrete gauge symmetry of the Minimal SSM,
instead of R-parity.


  We propose and compare various techiques available to produce smooth cubic
hypersurfaces over a non-algebraically-closed field which have rational points
but which are not stably rational over their ground field.


  We use laboratory experiments to investigate the entrainment of ambient fluid
into an axisymmetric turbulent plume that contains dense particles with a
settling velocity that is considerably smaller than the plume velocity. We
consider the effect of particle size, particle concentration, and the
orientation of the plume buoyancy flux - either in the same or opposite
direction to the particle buoyancy flux. When the plume buoyancy flux is in the
opposite direction to the particle buoyancy flux, entrainment into the plume
increases by up to 40%. The rate of entrainment increases linearly with the
ratio of particle buoyancy flux to fluid buoyancy flux but does not depend on
the particle size. In contrast, when the plume buoyancy flux is in the same
direction as the particle buoyancy flux, entrainment into the plume is
unaffected by the addition of particles. The observed increase in entrainment,
when the plume and particle buoyancy fluxes are in opposite directions, is
consistent with inertial clustering whereby particles are ejected from regions
of relatively high vorticity and accumulate in regions of relatively high
strain rate within the turbulent flow field. Regions with high particle
concentration can then experience convective instabilities that affect the
entrainment of ambient fluid into the plume. The differing behaviour observed
based on the plume buoyancy flux orientation is also consistent with the above
mechanism. Finally, based on the laboratory findings, we propose a new
expression for the entrainment coefficient to take into account the effect of
suspended particles of opposing buoyancy flux to the plume buoyancy flux.


  We have obtained deep imaging in the near-infrared J and K bands for 2 nearby
fields in the bar of the LMC with the ESO NTT telescope, under exquisite seeing
conditions. The K, J-K color-magnitude diagrams constructed from these data are
of outstanding photometric quality and reveal the presence of several hundreds
of red clump stars. Using the calibration of Alves for the K-band absolute
magnitude of Hipparcos-observed red clump stars in the solar neigbourhood we
derive a distance modulus to our observed LMC fields of 18.487 mag. Applying a
correction for the tilt of the LMC bar with respect to the line of sight
according to the geometrical model of van der Marel et al., the corresponding
LMC barycenter distance is 18.501 mag. If we adopt a K-band population
correction of -0.03 mag, as done by Alves et al. 2002, to account for the
difference in age and metallicity between the solar neighborhood and LMC red
clump star populations, we obtain an LMC barycenter distance modulus of 18.471
mag from our data. This is in excellent agreement with the result of Alves et
al., and of another very recent study of Sarajedini et al. (2002) obtained from
K-band photometry. However, we emphasize that current model predictions about
the uncertainties of population corrections seem to indicate that errors up to
about 0.12 mag may be possible, probably in any photometric band. Therefore,
work must continue to tighten the constraints on these corrections. We also
determine the mean red clump star magnitude in our LMC fields in the J band,
which could be a useful alternative to the K band should future work reveal
that population effect corrections for red clump stars in the J band are
smaller, or more reliably determined than those for the K band.


  A manifestly Lorentz invariant effective action for Yang-Mills theory
depending only on commuting fields is constructed. This action posesses a
bosonic symmetry, which plays a role analogous to the BRST symmetry in the
standard formalism.


  The instability of Liouville theory coupled to $c>1$ matter fields is shown
to persist even when the ``spikes'' which represent highly singular geometries
are allowed to interact in a natural way.


  A homogeneous ideal is robust if its universal Gr\"obner basis is also a
minimal generating set. For toric ideals, one has the stronger definition: A
toric ideal is strongly robust if its Graver basis equals the set of
indispensable binomials. We characterize the codimension 2 strongly robust
toric ideals by their Gale diagrams. This gives a positive answer to a question
of Petrovic, Thoma, and Vladoiu in the case of codimension 2 toric ideals.


  We study RR charge cancellation consistency conditions in string
compactifications with open string sectors, by introducing D-brane probes in
the configuration. We show that uncancelled charges manifest as chiral gauge
anomalies in the world-volume of suitable probes. RR tadpole cancellation can
therefore be described as the consistency of the effective compactified theory
not just in the vacuum, but also in all topological sectors (presence of
D-brane probes). The result explains why tadpole cancellation is usually much
stronger than anomaly cancellation of the compactified theory (in the vacuum
sector). We use the probe criterion to construct consistent six-dimensional
orientifolds of curved K3 spaces, where usual CFT techniques to compute
tadpoles are not valid. As a last application, we consider compactifications
where standard RR charge cancels but full K-theory charge does not. We show the
inconsistency of such models manifests as a global gauge anomaly on the
world-volume of suitable probes.


  This paper presents a stochastic three-dimensional (3D) focused transport
simulation of solar energetic particles (SEPs) produced by a data-driven
coronal mass ejection (CME) shock propagating through a data-driven model of
coronal and heliospheric magnetic fields. The injection of SEPs at the CME
shock is treated using diffusive shock acceleration of post-shock superthermal
solar wind ions. A time backward stochastic simulation is employed to solve the
transport equation to obtain the SEP time-intensity profile at any location,
energy, and pitch angle. The model is applied to a SEP event on 2020 May 29,
observed by STEREO-A close to 1 au and by Parker Solar Probe (PSP) when it was
about 0.33 au away from the Sun. The SEP event was associated with a very slow
CME with a plane-of-sky speed of 337 km/s at a height below 6 $\rm R_S$ as
reported in the SOHO/LASCO CME catalog. We compute the time profiles of
particle flux at PSP and STEREO-A locations, and estimate both the spectral
index of the proton energy spectrum for energies between 2 and 16 MeV and the
equivalent path length of the magnetic field lines experienced by the first
arriving SEPs. We found that the simulation results are well correlated with
observations. The SEP event could be explained by the acceleration of particles
by a weak CME shock in the low solar corona that is not magnetically connected
to the observers.


  Dynamic model atmospheres of Mira stars predict variabilities in the
photospheric radius and in atmospheric molecular layers which are not yet
strongly constrained by observations. Here we measure the variability of the
oxygen-rich Mira star R Peg. We used K band spectro-interferometry with a
spectral resolution of about 4000 obtained at four epochs between post-maximum
and minimum visual phases employing the newly available GRAVITY beam combiner
at the VLTI. Our observations show a continuum radius that is anti-correlated
with the visual lightcurve. Uniform disc (UD) angular diameters at a
near-continuum wavelength of 2.25 mu are steadily increasing with values of 8.7
mas, 9.4 mas, 9.8 mas, and 9.9 mas at visual phases of 0.15, 0.36, 0,45, 0.53,
respectively. UD diameters at a bandpass around 2.05 mu, dominated by water
vapour, follow the near-continuum variability at larger UD diameters. UD
diameters at the CO 2-0 bandhead, instead, are correlated with the visual
lightcurve and anti-correlated with the near-continuum UD diameters. The
observed anti-correlation between continuum radius and visual lightcurve is
consistent with an earlier study of the oxygen-rich Mira S Lac, and with recent
1D CODEX dynamic model atmosphere predictions. The amplitude of the variation
is comparable to the earlier observations of S Lac, and smaller than predicted
by CODEX models. The wavelength-dependent visibility variations at our epochs
can be reproduced by a set of CODEX models at model phases between 0.3 and 0.6.
The anti-correlation of water vapour and CO contributions at our epochs
suggests that these molecules undergo different processes along the stellar
cycle. The newly available GRAVITY instrument is suited to conducting longer
time series observations, which are needed to provide strong constraints on the
model-predicted intra- and inter-cycle variability.


  Quantum sensors based on light-pulse atom interferometers allow for
high-precision measurements of inertial and electromagnetic forces such as the
accurate determination of fundamental constants as the fine structure constant
or testing foundational laws of modern physics as the equivalence principle.
These schemes unfold their full performance when large interrogation times
and/or large momentum transfer can be implemented. In this article, we
demonstrate how precision interferometry can benefit from the use of
Bose-Einstein condensed sources when the state of the art is challenged. We
contrast systematic and statistical effects induced by Bose-Einstein condensed
sources with thermal sources in three exemplary science cases of Earth- and
space-based sensors.


  To ensure fulfilling stakeholder wishes, it is crucial to validate the
documented requirements. This is often complicated by the fact that the wishes
and intentions of different stakeholders are somewhat contradictory, which
manifests itself in inconsistent requirements. To aid requirements engineers in
identifying and resolving inconsistent requirements, we investigated the
usefulness for manual reviews of two different model-based representation
formats for inconsistent requirements; one that represent the inconsistent
requirements in separate diagrams and one that represents them integrated into
one diagram using annotations. The results from a controlled experiment show
that the use of such integrated review diagrams can significantly increase
efficiency of manual reviews, without sacrificing effectiveness.


  We present a parameter-free scheme to combine fixed-order multi-jet results
with parton-shower evolution. The scheme produces jet cross sections with
leading-order accuracy in the complete phase space of multiple emissions,
resumming large logarithms when appropriate, while not arbitrarily enforcing
ordering on momentum configurations beyond the reach of the parton-shower
evolution equation. This requires the development of a matrix-element
correction scheme for complex phase-spaces including ordering conditions as
well as a systematic scale-setting procedure for unordered phase-space points.
The resulting algorithm does not require a merging-scale parameter. We
implement the new method in the Vincia framework and compare to LHC data.


  We make a number of small changes, including correcting an error in our
heavy-neutrino decay rate. None of our analysis is changed, either in substance
or detail.


  The recent extension of the standard model to include massive neutrinos in
the framework of noncommutative geometry and the spectral action principle
involves new scalar fields and their interactions with the usual complex scalar
doublet. After ensuring that they bring no unphysical consequences, we address
the question of how these fields affect the physics predicted in Weinberg-Salam
theory, particularly in the context of the Electroweak phase transition.
Applying the Dolan-Jackiw procedure, we calculate the finite temperature
corrections, and find that the phase transition is first order. The new scalar
interactions significantly improve the stability of the Electroweak Z string,
through the ``bag'' phenomenon described by Watkins and Vachaspati. (Recently
cosmic strings have climbed back into interest due to new evidence). Sourced by
static embedded strings, an internal space analogy of Cartan's torsion is
drawn, and a possible Higgs-force-like `gravitational' effect of this
non-propagating torsion on the fermion masses is described. We also check that
the field generating the Majorana mass for the $\nu_R$ is non-zero in the
physical vacuum.


  Quasars are variable on timescales from days to years in UV/optical, and
generally appear bluer while they brighten. The physics behind the variations
in fluxes and colors remains unclear. Using SDSS g and r band photometric
monitoring data of quasars in Stripe 82, we find that although the flux
variation amplitude increases with timescale, the color variability exhibits
opposite behavior. The color variability of quasars is prominent at timescales
as short as ~ 10 days, but gradually reduces toward timescales up to years. In
other words, the variable emission at shorter timescales is bluer than that at
longer timescales. This timescale dependence is clearly and consistently
detected at all redshifts from z = 0 to 3.5, thus can not be due to
contaminations to broadband photometry from emission lines which do not respond
to fast continuum variations. The discovery directly rules out the possibility
that simply attributes the color variability to contamination from a
non-variable redder component, such as the host galaxy. It can not be
interpreted as changes in global accretion rate either. The thermal accretion
disk fluctuation model is favored, in the sense that fluctuations in the inner
hotter region of the disk are responsible for short term variations, while
longer term and stronger variations are expected from larger and cooler disk
region. An interesting implication is that one can use quasar variations at
different timescales to probe disk emission at different radii.


  In this note various geometric properties of a Banach space $X$ are
characterized by means of weaker corresponding geometric properties involving
an ultrapower $X^\mathcal{U}$. The characterizations do not depend on the
particular choice of the free ultrafilter $\mathcal{U}$. For example, a point
$x\in S_X$ is an MLUR point if and only if $j(x)$ (given by the canonical
inclusion $j\colon X \to X^\mathcal{U}$) in $B_{X^\mathcal{U}}$ is an extreme
point; a point $x\in S_X$ is LUR if and only if $j(x)$ is not contained in any
non-degenerate line segment of $S_{X^\mathcal{U}}$; a Banach space $X$ is URED
if and only if there are no $x,y \in S_{X^\mathcal{U}}$, $x\neq y$, with $x-y
\in j(X)$.


  The ground state critical properties of the Random Field Ising Model (RFIM)
on the diamond hierarchical lattice are investigated via a combining method
encompassing real space renormalization group and an exact recurrence
procedure. The local magnetization and the nearest neighbors pair correlation
function are exactly calculated. The fixed-point joint probability distribution
of couplings and local fields are numerically obtained and analyzed, indicating
that the critical behavior of the model is governed by the zero temperature
disorder fixed point. The critical exponents associated with the order
parameter and correlation length are estimated showing an universal behavior
regarding the choice of the initial probability distribution for initial local
fields being the symmetric continuous Gaussian or discrete delta-bimodal.


  Scale free dynamics are observed in a variety of physical and biological
systems. These include neural activity in which evidence for scale freeness has
been reported using a range of imaging modalities. Here, we derive the ways in
which connections within a network must transform - relative to system size -
in order to maintain scale freeness and test these theoretical transformations
via simulations. First, we explore the known invariance of planetary motion for
orbits varying in size. Using parametric empirical Bayesian modelling and a
generic dynamical systems model, we show that we recover Kepler's third law
from orbital timeseries, using our proposed transformations; thereby providing
construct validation. We then demonstrate that the dynamical critical exponent
is inversely proportional to the time rescaling exponent, in the context of
coarse graining operations. Using murine calcium imaging data, we then show
that the dynamical critical exponent can be estimated in an empirical
biological setting. Specifically, we compare dynamical critical exponents -
associated with spontaneous and task states in two regions of imaged cortex -
that are classified as task-relevant and task-irrelevant. We find, consistently
across animals, that the task-irrelevant region exhibits higher dynamical
critical exponents during spontaneous activity than during task performance.
Conversely, the task-relevant region is associated with higher dynamical
critical exponents in task vs. spontaneous states. These data support the idea
that higher dynamical critical exponents, within relevant cortical structures,
underwrite neuronal processing due to the implicit increase in cross-scale
information transmission.


  We provide the first evidence of a walking dynamics for two color lattice
Yang-Mills theory with two Dirac flavors in the symmetric representation of the
gauge group.


  Approximate subgraph matching, which is an important primitive for many
applications like question answering, community detection, and motif discovery,
often involves large labeled graphs such as knowledge graphs, social networks,
and protein sequences. Effective methods for extracting matching subgraphs, in
terms of label and structural similarities to a query, should depict accuracy,
computational efficiency, and robustness to noise. In this paper, we propose
VerSaChI for finding the top-k most similar subgraphs based on 2-hop label and
structural overlap similarity with the query. The similarity is characterized
using Chebyshev's inequality to compute the chi-square statistical significance
for measuring the degree of matching of the subgraphs. Experiments on real-life
graph datasets showcase significant improvements in terms of accuracy compared
to state-of-the-art methods, as well as robustness to noise.


  Learning effective visual representations that generalize well without human
supervision is a fundamental problem in order to apply Machine Learning to a
wide variety of tasks. Recently, two families of self-supervised methods,
contrastive learning and latent bootstrapping, exemplified by SimCLR and BYOL
respectively, have made significant progress. In this work, we hypothesize that
adding explicit information compression to these algorithms yields better and
more robust representations. We verify this by developing SimCLR and BYOL
formulations compatible with the Conditional Entropy Bottleneck (CEB)
objective, allowing us to both measure and control the amount of compression in
the learned representation, and observe their impact on downstream tasks.
Furthermore, we explore the relationship between Lipschitz continuity and
compression, showing a tractable lower bound on the Lipschitz constant of the
encoders we learn. As Lipschitz continuity is closely related to robustness,
this provides a new explanation for why compressed models are more robust. Our
experiments confirm that adding compression to SimCLR and BYOL significantly
improves linear evaluation accuracies and model robustness across a wide range
of domain shifts. In particular, the compressed version of BYOL achieves 76.0%
Top-1 linear evaluation accuracy on ImageNet with ResNet-50, and 78.8% with
ResNet-50 2x.


  We consider relatively heavy neutrinos $\nu_H$, mostly contributing to a
sterile state $\nu_s$, with mass in the range 10 MeV $\lesssim m_s \lesssim
m_{\pi} \sim 135$ MeV, which are thermally produced in the early universe in
collisional processes involving active neutrinos, and freezing out after the
QCD phase transition. If these neutrinos decay after the active neutrino
decoupling, they generate extra neutrino radiation, but also contribute to
entropy production. Thus, they alter the value of the effective number of
neutrino species $N_{\rm eff}$ as for instance measured by the cosmic microwave
background (CMB), as well as affect primordial nucleosynthesis (BBN), notably
${}^4$He production. We provide a detailed account of the solution of the
relevant Boltzmann equations. We also identify the parameter space allowed by
current Planck satellite data and forecast the parameter space probed by future
Stage-4 ground-based CMB observations, expected to match or surpass BBN
sensitivity.


  Deep generative models for graphs have shown great promise in the area of
drug design, but have so far found little application beyond generating
graph-structured molecules. In this work, we demonstrate a proof of concept for
the challenging task of road network extraction from image data. This task can
be framed as image-conditioned graph generation, for which we develop the
Generative Graph Transformer (GGT), a deep autoregressive model that makes use
of attention mechanisms for image conditioning and the recurrent generation of
graphs. We benchmark GGT on the application of road network extraction from
semantic segmentation data. For this, we introduce the Toulouse Road Network
dataset, based on real-world publicly-available data. We further propose the
StreetMover distance: a metric based on the Sinkhorn distance for effectively
evaluating the quality of road network generation. The code and dataset are
publicly available.