title:
Parameter Estimation of Gaussian-Damped Sinusoids from a Geometric
  Perspective

abstract:
  The five parameter gaussian damped sinusoid equation is a reasonable model
for betatron motion with chromatic decoherence of the proton bunch centroid
signal in the ring at the Spallation Neutron Source. A geometric method for
efficiently fitting this equation to the turn by turn signals to extract the
betatron tune and damping constant will be presented. This method separates the
parameters into global and local parameters and allows the use of vector
arithmetic to eliminate the local parameters from the parameter search space.
Furthermore, this method is easily generalized to reduce the parameter search
space for a larger class of problems.


title:
General Analytic Solutions of Scalar Field Cosmology with Arbitrary
  Potential

abstract:
  We present the solution space for the case of a minimally coupled scalar
field with arbitrary potential in a FLRW metric. This is made possible due to
the existence of a nonlocal integral of motion corresponding to the conformal
Killing field of the two-dimensional minisuperspace metric. The case for both
spatially flat and non flat are studied first in the presence of only the
scalar field and subsequently with the addition of non interacting perfect
fluids. It is verified that this addition does not change the general form of
the solution, but only the particular expressions of the scalar field and the
potential. The results are applied in the case of parametric dark energy models
where we derive the scalar field equivalence solution for some proposed models
in the literature.


title:
Lattice Partition Multiple Access: A New Method of Downlink
  Non-orthogonal Multiuser Transmissions

abstract:
  In this paper, we propose a new downlink non-orthogonal multiuser
superposition transmission scheme for future 5G cellular networks, which we
refer to as the lattice partition multiple access (LPMA). In this proposed
design, the base station transmits multilevel lattice codes for multiple users.
Each user's code level corresponds to a distinct prime and is weighted by a
product of all distinct primes of the other users excluding its own. Due to the
structural property of lattice codes, each user can cancel out the interference
from the other code levels by using the modulo lattice operation in a
successive/parallel manner. LPMA can overcome the drawback of non-orthogonal
multiple access (NOMA), which arises when users have similar channel
conditions. We demonstrate that the proposed LPMA shows a clear throughput
enhancement over the current NOMA scheme.


title: A Repeated Signal Difference for Recognising Patterns

abstract:
  This paper describes a new mechanism that might help with defining pattern
sequences, by the fact that it can produce an upper bound on the ensemble value
that can persistently oscillate with the actual values produced from each
pattern. With every firing event, a node also receives an on/off feedback
switch. If the node fires, then it sends a feedback result depending on the
input signal strength. If the input signal is positive or larger, it can store
an 'on' switch feedback for the next iteration. If the signal is negative or
smaller, it can store an 'off' switch feedback for the next iteration. If the
node does not fire, then it does not affect the current feedback situation and
receives the switch command produced by the last active pattern event for the
same neuron. The upper bound therefore also represents the largest or most
enclosing pattern set and the lower value is for the actual set of firing
patterns. If the pattern sequence repeats, it will oscillate between the two
values, allowing them to be recognised and measured more easily, over time.
Tests show that changing the sequence ordering produces different value sets,
which can also be measured.


title:
Physical description of the blood flow from the internal jugular vein to
  the right atrium of the heart: new ultrasound application perspectives

abstract:
  This is a self-published methodological note distributed under the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),
which permits unrestricted use, distribution, and reproduction in any medium,
provided the original work is properly cited. The note contains an original
reasoning of mine and the goal to share thoughts and methodologies, not
results. Therefore before using the contents of these notes, everyone is
invited to verify the accuracy of the assumptions and conclusions.


title: Online Dominating Set

abstract:
  This paper is devoted to the online dominating set problem and its variants.
We believe the paper represents the first systematic study of the effect of two
limitations of online algorithms: making irrevocable decisions while not
knowing the future, and being incremental, i.e., having to maintain solutions
to all prefixes of the input. This is quantified through competitive analyses
of online algorithms against two optimal algorithms, both knowing the entire
input, but only one having to be incremental. We also consider the competitive
ratio of the weaker of the two optimal algorithms against the other.
  We consider important graph classes, distinguishing between connected and not
necessarily connected graphs. For the classic graph classes of trees,
bipartite, planar, and general graphs, we obtain tight results in almost all
cases. We also derive upper and lower bounds for the class of bounded-degree
graphs. From these analyses, we get detailed information regarding the
significance of the necessary requirement that online algorithms be
incremental. In some cases, having to be incremental fully accounts for the
online algorithm's disadvantage.


title:
Relaxation of nonconvex unbounded integrals with general growth
  conditions in Cheeger-Sobolev spaces

abstract:
  We study relaxation of nonconvex integrals of the calculus of variations in
the setting of Cheeger-Sobolev spaces when the integrand has not polynomial
growth and can take infinite values.


title: Symmetry and transformation of waves in optics and acoustics of crystals

abstract:
  It is show that in group representation by non-traditionally determining by
the Maxwell equations, instead of wave, linear differential operator of
momentous type from the common point of view the transformation of
electromagnetic and ultrasonic radiation as well as the formation of caustics
generation of solitons in crystals is represented. It is established that
forming operator structural constants determine bias current with the connected
charge and group velocity and also optical and acoustic axes of a crystal,
which characterize its wave properties, moreover crystals are classified on
common electromagnetic base. It is discovered that at change of crystal
symmetry and representation of different wave process the problems also take
place, which are similar to others spheres of physics and are constructed on
the same aximatical base.


title:
Message passing theory for percolation models on multiplex networks with
  link overlap

abstract:
  Multiplex networks describe a large variety of complex systems including
infrastructures, transportation networks and biological systems. Most of these
networks feature a significant link overlap. It is therefore of particular
importance to characterize the mutually connected giant component in these
networks. Here we provide a message passing theory for characterizing the
percolation transition in multiplex networks with link overlap and an arbitrary
number of layers $M$. Specifically we propose and compare two message passing
algorithms, that generalize the algorithm widely used to study the percolation
transition in multiplex networks without link overlap. The first algorithm
describes a directed percolation transition and admits an epidemic spreading
interpretation. The second algorithm describes the emergence of the mutually
connected giant component, that is the percolation transition, but does not
preserve the epidemic spreading interpretation. We obtain the phase diagrams
for the percolation and directed percolation transition in simple
representative cases. We demonstrate that for the same multiplex network
structure, in which the directed percolation transition has non-trivial
tricritical points, the percolation transition has a discontinuous phase
transition, with the exception of the trivial case in which all the layers
completely overlap.


title: Observation of Fermi Arcs in Type-II Weyl Semimetal Candidate WTe2

abstract:
  We use ultrahigh resolution, tunable, vacuum ultraviolet laser angle-resolved
photoemission spectroscopy (ARPES) to study the electronic properties of
WTe$_2$, a material that was predicted to be a type-II Weyl semimetal. The Weyl
fermion states in WTe2 were proposed to emerge at the crossing points of
electron and hole pockets; and Fermi arcs connecting electron and hole pockets
would be visible in the spectral function on (001) surface. Here we report the
observation of such Fermi arcs in WTe2 confirming the theoretical predictions.
This provides strong evidence for type-II Weyl semimetallic states in WTe2.


title:
Quantitative analysis of jugular venous pulse obtained by using a
  general-purpose ultrasound scanner


title:
High order finite difference schemes on non-uniform meshes for the
  time-fractional Black-Scholes equation

abstract:
  We construct a three-point compact finite difference scheme on a non-uniform
mesh for the time-fractional Black-Scholes equation. We show that for special
graded meshes used in finance, the Tavella-Randall and the quadratic meshes the
numerical solution has a fourth-order accuracy in space. Numerical experiments
are discussed.


title: On zeros of some entire functions

abstract:
  Let \begin{equation*} A_{q}^{(\alpha)}(a;z) = \sum_{k=0}^{\infty}
\frac{(a;q)_{k} q^{\alpha k^2} z^k} {(q;q)_{k}}, \end{equation*} where $\alpha
>0,~0<q<1.$ In a paper of Ruiming Zhang, he asked under what conditions the
zeros of the entire function $A_{q}^{(\alpha)}(a;z)$ are all real and
established some results on the zeros of $A_{q}^{(\alpha)}(a;z)$ which present
a partial answer to that question. In the present paper, we will set up some
results on certain entire functions which includes that
$A_{q}^{(\alpha)}(q^l;z),~l\geq 2$ has only infinitely many negative zeros that
gives a partial answer to Zhang's question. In addition, we establish some
results on zeros of certain entire functions involving the Rogers-Szeg\H{o}
polynomials and the Stieltjes-Wigert polynomials.


title: Cryptographically secure multiparty evaluation of system reliability

abstract:
  The precise design of a system may be considered a trade secret which should
be protected, whilst at the same time component manufacturers are sometimes
reluctant to release full test data (perhaps only providing mean time to
failure data). In this situation it seems impractical to both produce an
accurate reliability assessment and satisfy all parties' privacy requirements.
However, we present recent developments in cryptography which, when combined
with the recently developed survival signature in reliability theory, allows
almost total privacy to be maintained in a cryptographically strong manner in
precisely this setting. Thus, the system designer does not have to reveal their
trade secret design and the component manufacturer can retain component test
data in-house.


title: From Basu-Harvey to Nahm equation via 3-Lie bialgebra

abstract:
  Using the concept of 3-Lie bialgebra; we construct the Bagger- Lambert-
Gustavson (BLG) model on the Manin triple $\cal D$ of the especial 3-Lie
bialgebra $({\cal D},{\cal A}_{\cal G},{\cal A}_{{\cal G}^*}^*)$ which is in
correspondence with Manin triple of Lie bialgebra $({\cal D},{\cal G},{\cal
G}^*)$. We have shown that the Nahm equation (with Lie bialgebra ${\cal G}$)
can be obtained from the Basu-Harvey equation as a boundary condition of BLG
model (with 3-Lie bialgebra ${\cal D}$) and vice versa.


title: Brownian bridges to submanifolds

abstract:
  We introduce and study Brownian bridges to submanifolds. Our method involves
proving a general formula for the integral over a submanifold of the minimal
heat kernel on a complete Riemannian manifold. We use the formula to derive
lower bounds, an asymptotic relation and derivative estimates. We also see a
connection to hypersurface local time. This work is motivated by the desire to
extend the analysis of path and loop spaces to measures on paths which
terminate on a submanifold.


title: M2 to D2 and vice versa by 3-Lie and Lie bialgebra

abstract:
  Using the concept of 3-Lie bialgebra, which has recently been defined in
arXiv:1604.04475, we construct Bagger-Lambert-Gustavson (BLG) model for
M2-brane on Manin triple of a special 3-Lie bialgebra. Then by using the
correspondence and relation between those 3-Lie bialgebra with Lie bialgebra,
we reduce this model to an $N=(4,4)$ WZW model (D2-brane), such that, its
algebraic structure is a Lie bialgebra with one 2-cocycle. In this manner by
using correspondence of 3-Lie bialgebra and Lie bialgebra (for this special
3-Lie algebra) one can construct M2-brane from a D2-brane and vice versa.


title:
Derivative with two fractional orders: New door of investigation toward
  revolution in fractional calculus

abstract:
  In order to describe more complex problem using the concept of fractional
derivatives, we introduce in this paper the concept of fractional derivatives
with orders. The new definitions are based upon the concept of power law
together with the generalized Mittag-Leffler function. The first order is
included in the power law function and the second is in the generalized
Mittag-Leffler function. Each order therefore plays an important rule while
modelling for instance problems with two layers with different properties. This
is the case for instance in thermal science for a reaction diffusion within a
media with two different layers with different properties. Another case is that
of groundwater flowing within an aquifer where geological formation is formed
with two layers with different properties. The paper presents new useful
information within the scope of fractional calculus that will open new doors
for research and investigations in modelling real world problems.


title: Three nontrivial solutions for nonlinear fractional Laplacian equations

abstract:
  We study a Dirichlet-type boundary value problem for a pseudodifferential
equation driven by the fractional Laplacian, proving the existence of three
nonzero solutions. When the reaction term is sublinear at infinity, we apply
the second deformation theorem and spectral theory. When the reaction term is
superlinear at infinity, we apply the mountain pass theorem and Morse theory.


title: Prescribing metrics on the boundary of AdS 3-manifolds

abstract:
  We prove that given two metrics $g_{+}$ and $g_{-}$ with curvature $\kappa
<-1$ on a closed, oriented surface $S$ of genus $\tau\geq 2$, there exists an
$AdS$ manifold $N$ with smooth, space-like, strictly convex boundary such that
the induced metrics on the two connected components of $\partial N$ are equal
to $g_{+}$ and $g_{-}$. Using the duality between convex space-like surfaces in
$AdS_{3}$, we obtain an equivalent result about the prescription of the third
fundamental form.


title:
Statistics and properties of low-frequency vibrational modes in
  structural glasses

abstract:
  Low-frequency vibrational modes play a central role in determining various
basic properties of glasses, yet their statistical and mechanical properties
are not fully understood. Using extensive numerical simulations of several
model glasses in three dimensions, we show that in systems of linear size $L$
sufficiently smaller than a crossover size $L_{D}$, the low-frequency tail of
the density of states follows $D(\omega)\!\sim\!\omega^4$ up to the vicinity of
the lowest Goldstone mode frequency. We find that the sample-to-sample
statistics of the minimal vibrational frequency in systems of size $L\!<\!L_D$
is Weibullian, with scaling exponents in excellent agreement with the
$\omega^4$ law. We further show that the lowest frequency modes are spatially
quasi-localized, and that their localization and associated quartic
anharmonicity are largely frequency-independent. The effect of preparation
protocols on the low-frequency modes is elucidated and a number of glassy
lengthscales are briefly discussed.


title:
Excitation of ship waves by a submerged object: new solution to the
  classical problem

abstract:
  We have proposed a new method for solving the problem of ship waves excited
on the surface of a non-viscous liquid by a submerged object that moves at a
variable speed. As a first application of this method, we have obtained a new
solution to the classic problem of ship waves generated by a submerged ball
that moves rectilinearly with constant velocity parallel to the equilibrium
surface of the liquid. For this example, we have derived asymptotic expressions
describing the vertical displacement of the liquid surface in the limit of
small and large values of the Froude number. The exact solution is presented in
the form of two terms, each of which is reduced to one-dimensional integrals.
One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As
a second example, we considered vertical oscillation of the submerged ball. In
this case, the solution leads to the calculation of one-dimensional integral
and describes surface waves propagating from the epicenter above the ball.


title:
Understanding the Systems Biology of Pathogen Virulence Using Semantic
  Methodologies

abstract:
  Systems biology approaches to the integrative study of cells, organs and
organisms offer the best means of understanding in a holistic manner the
diversity of molecular assays that can be now be implemented in a high
throughput manner. Such assays can sample the genome, epigenome, proteome,
metabolome and microbiome contemporaneously, allowing us for the first time to
perform a complete analysis of physiological activity. The central problem
remains empowering the scientific community to actually implement such an
integration, across seemingly diverse data types and measurements. One
promising solution is to apply semantic techniques on a self-consistent and
implicitly correct ontological representation of these data types. In this
paper we describe how we have applied one such solution, based around the
InterMine data warehouse platform which uses as its basis the Sequence
Ontology, to facilitate a systems biology analysis of virulence in the
apicomplexan pathogen $Toxoplasma~gondii$, a common parasite that infects up to
half the worlds population, with acute pathogenic risks for immuno-compromised
individuals or pregnant mothers. Our solution, which we named `toxoMine', has
provided both a platform for our collaborators to perform such integrative
analyses and also opportunities for such cyberinfrastructure to be further
developed, particularly to take advantage of possible semantic similarities of
value to knowledge discovery in the Omics enterprise. We discuss these
opportunities in the context of further enhancing the capabilities of this
powerful integrative platform.


title: Majorana approach to the stochastic theory of lineshapes

abstract:
  Motivated by recent Mossbauer experiments on strongly correlated
mixed-valence systems, we revisit the Kubo-Anderson stochastic theory of
spectral lineshapes. Using a Majorana representation for the nuclear spin we
demonstrate how to recast the classic lineshape theory in a field-theoretic and
diagrammatic language. We show that the leading contribution to the self-energy
can reproduce most of the observed lineshape features including splitting and
lineshape narrowing, while the vertex and the self-consistency corrections can
be systematically included in the calculation. This new approach permits us to
predict the line-shape produced by an arbitrary bulk charge fluctuation
spectrum providing a model-independent way to extract the local charge
fluctuation spectrum of the surrounding medium. We also derive an inverse
formula to extract the charge fluctuation from the measured lineshape.


title: Giant planet formation in radially structured protoplanetary discs

abstract:
  Our recent N-body simulations of planetary system formation, incorporating
models for the main physical processes thought to be important during the
building of planets (i.e. gas disc evolution, migration, planetesimal/boulder
accretion, gas accretion onto cores, etc.), have been successful in reproducing
some of the broad features of the observed exoplanet population (e.g. compact
systems of low mass planets, hot Jupiters), but fail completely to form any
surviving cold Jupiters. The primary reason for this failure is rapid inward
migration of growing protoplanets during the gas accretion phase, resulting in
the delivery of these bodies onto orbits close to the star. Here, we present
the results of simulations that examine the formation of gas giant planets in
protoplanetary discs that are radially structured due to spatial and temporal
variations in the effective viscous stresses, and show that such a model
results in the formation of a population of cold gas giants. Furthermore, when
combined with models for disc photoevaporation and a central magnetospheric
cavity, the simulations reproduce the well-known hot-Jupiter/cold-Jupiter
dichotomy in the observed period distribution of giant exoplanets, with a
period valley between 10-100 days.


title: A note on the differences of computably enumerable reals

abstract:
  We show that given any non-computable left-c.e. real $\alpha$ there exists a
left-c.e. real $\beta$ such that $\alpha\neq \beta+\gamma$ for all left-c.e.
reals and all right-c.e. reals $\gamma$. The proof is non-uniform, the
dichotomy being whether the given real $\alpha$ is Martin-Loef random or not.
It follows that given any universal machine $U$, there is another universal
machine $V$ such that the halting probability of U is not a translation of the
halting probability of V by a left-c.e. real. We do not know if there is a
uniform proof of this fact.


title: Simulations of ram-pressure stripping in galaxy-cluster interactions

abstract:
  Observationally, the quenching of star-forming galaxies appears to depend
both on their mass and environment. The exact cause of the environmental
dependence is still poorly understood, yet semi-analytic models (SAMs) of
galaxy formation need to parameterise it to reproduce observations of galaxy
properties. In this work, we use hydrodynamical simulations to investigate the
quenching of disk galaxies through ram-pressure stripping (RPS) as they fall
into galaxy clusters with the goal of characterising the importance of this
effect for the reddening of disk galaxies. Our set-up employs a live model of a
galaxy cluster that interacts with infalling disk galaxies on different orbits.
We use the moving-mesh code AREPO, augmented with a special refinement strategy
to yield high resolution around the galaxy on its way through the cluster in a
computationally efficient way. Our direct simulations differ substantially from
stripping models employed in current SAMs, which in most cases overpredict the
mass loss from RPS. Furthermore, after pericentre passage, as soon as ram
pressure becomes weaker, gas that remains bound to the galaxy is redistributed
to the outer parts, an effect that is not captured in simplified treatements of
RPS. Star formation in our model galaxies is quenched mainly because the hot
gas halo is stripped, depriving the galaxy of its gas supply. The cold gas disk
is only stripped completely in extreme cases, leading to full quenching and
significant reddening on timescale of ~200 Myr. On the other hand, galaxies
experiencing only mild ram pressure actually show an enhanced star formation
rate that is consistent with observations and are quenched on timescales > 1
Gyr. Stripped gas in the wake is mixed efficiently with intracluster gas
already a few tens of kpc behind the disk, and this gas is free of residual
star formation.


title: Preference Elicitation For Single Crossing Domain

abstract:
  Eliciting the preferences of a set of agents over a set of alternatives is a
problem of fundamental importance in social choice theory. Prior work on this
problem has studied the query complexity of preference elicitation for the
unrestricted domain and for the domain of single peaked preferences. In this
paper, we consider the domain of single crossing preference profiles and study
the query complexity of preference elicitation under various settings. We
consider two distinct situations: when an ordering of the voters with respect
to which the profile is single crossing is known versus when it is unknown. We
also consider different access models: when the votes can be accessed at
random, as opposed to when they are coming in a pre-defined sequence. In the
sequential access model, we distinguish two cases when the ordering is known:
the first is that sequence in which the votes appear is also a single-crossing
order, versus when it is not.
  The main contribution of our work is to provide polynomial time algorithms
with low query complexity for preference elicitation in all the above six
cases. Further, we show that the query complexities of our algorithms are
optimal up to constant factors for all but one of the above six cases. We then
present preference elicitation algorithms for profiles which are close to being
single crossing under various notions of closeness, for example, single
crossing width, minimum number of candidates | voters whose deletion makes a
profile single crossing.


title: Quantum gravity kinematics from extended TQFTs

abstract:
  We show how extended topological quantum field theories (TQFTs) can be used
to obtain a kinematical setup for quantum gravity, i.e. a kinematical Hilbert
space together with a representation of the observable algebra including
operators of quantum geometry. In particular, we consider the holonomy-flux
algebra of (2+1)-dimensional Euclidean loop quantum gravity, and construct a
new representation of this algebra that incorporates a positive cosmological
constant. The vacuum state underlying our representation is defined by the
Turaev-Viro TQFT. We therefore construct here a generalization, or more
precisely a quantum deformation at root of unity, of the previously-introduced
SU(2) BF representation. The extended Turaev-Viro TQFT provides a description
of the excitations on top of the vacuum, which are essential to allow for a
representation of the holonomies and fluxes. These excitations agree with the
ones induced by massive and spinning particles, and therefore the framework
presented here allows automatically for a description of the coupling of such
matter to (2+1)-dimensional gravity with a cosmological constant. The new
representation presents a number of advantages over the representations which
exist so far. It possesses a very useful finiteness property which guarantees
the discreteness of spectra for a wide class of quantum (intrinsic and
extrinsic) geometrical operators. The notion of basic excitations leads to a
fusion basis which offers exciting possibilities for constructing states with
interesting global properties. The work presented here showcases how the
framework of extended TQFTs can help design new representations and understand
the associated notion of basic excitations. This is essential for the
construction of the dynamics of quantum gravity, and will enable the study of
possible phases of spin foam models and group field theories from a new
perspective.

categories: hep-th cond-mat.str-el gr-qc math-ph math.MP math.QA


title: The Legendrian knot complement problem

abstract:
  We prove that every Legendrian knot in the tight contact structure of the
3-sphere is determined by the contactomorphism type of its exterior. Moreover,
by giving counterexamples we show this to be not true for Legendrian links in
the tight 3-sphere. On the way a new user-friendly formula for computing the
Thurston-Bennequin invariant of a Legendrian knot in a surgery diagram is
given.


title:
p-adic uniformization and the action of Galois on certain affine
  correspondences

abstract:
  Given two monic polynomials f and g with coefficients in a number field K,
and some a in K, we examine the action of the absolute Galois group of K on the
directed graph of iterated preimages of a under the correspondence g(y)=f(x),
assuming that deg(f)>deg(g) and that gcd(deg(f), deg(g))=1. If a prime of K
exists at which f and g have integral coefficients, and at which a is not
integral, we show that this directed graph of preimages consists of finitely
many Galois-orbits. We obtain this result by establishing a p-adic
uniformization of such correspondences, tenuously related to Bottcher's
uniformization of polynomial dynamical systems over the complex numbers.


title:
Locally Imposing Function for Generalized Constraint Neural Networks - A
  Study on Equality Constraints

abstract:
  This work is a further study on the Generalized Constraint Neural Network
(GCNN) model [1], [2]. Two challenges are encountered in the study, that is, to
embed any type of prior information and to select its imposing schemes. The
work focuses on the second challenge and studies a new constraint imposing
scheme for equality constraints. A new method called locally imposing function
(LIF) is proposed to provide a local correction to the GCNN prediction
function, which therefore falls within Locally Imposing Scheme (LIS). In
comparison, the conventional Lagrange multiplier method is considered as
Globally Imposing Scheme (GIS) because its added constraint term exhibits a
global impact to its objective function. Two advantages are gained from LIS
over GIS. First, LIS enables constraints to fire locally and explicitly in the
domain only where they need on the prediction function. Second, constraints can
be implemented within a network setting directly. We attempt to interpret
several constraint methods graphically from a viewpoint of the locality
principle. Numerical examples confirm the advantages of the proposed method. In
solving boundary value problems with Dirichlet and Neumann constraints, the
GCNN model with LIF is possible to achieve an exact satisfaction of the
constraints.


title: Majorana spectroscopy of 3D Kitaev spin-liquids

abstract:
  We analyse the dynamical response of a range of 3D Kitaev quantum
spin-liquids, using lattice models chosen to explore the different possible
low-energy spectra for gapless Majorana fermions, with either Fermi surfaces,
nodal lines or Weyl points. We find that the behaviour of the dynamical
structure factor is distinct in all three cases, reflecting the quasiparticle
density of states in two fundamentally different ways. First, the low-energy
response is either straightforwardly related to the power with which the
low-energy density of states vanishes; or for a non-vanishing density of
states, to the phase shifts encountered in the corresponding X-ray edge
problem, whose phenomenology we extend to the case of Majorana fermions.
Second, at higher energies, there is a rich fine-structure, determined by
microscopic features of the Majorana spectrum. Our theoretical results test the
usefulness of inelastic neutron scattering as a probe of these quantum spin
liquids: we find that although spin flips fractionalise, the main features of
the dynamical spin response nevertheless admit straightforward interpretations
in terms of Majorana and flux loop excitations.


title:
A unifying energy-based approach to stability of power grids with market
  dynamics

abstract:
  In this paper a unifying energy-based approach is provided to the modeling
and stability analysis of power systems coupled with market dynamics. We
consider a standard model of the power network with a third-order model for the
synchronous generators involving voltage dynamics. By applying the primal-dual
gradient method to a social welfare optimization, a distributed dynamic pricing
algorithm is obtained, which can be naturally formulated in port-Hamiltonian
form. By interconnection with the physical model a closed-loop port-Hamiltonian
system is obtained, whose properties are exploited to prove asymptotic
stability to the set of optimal points. This result is extended to the case
that also general nodal power constraints are included into the social welfare
problem. Additionally, the case of line congestion and power transmission costs
in acyclic networks is covered. Finally, a dynamic pricing algorithm is
proposed that does not require knowledge about the power supply and demand.


title:
Two-grid algorithms for singularly perturbed reaction-diffusion problems
  on layer adapted meshes

abstract:
  We propose a new two-grid approach based on Bellman-Kalaba quasilinearization
and Axelsson-Xu finite element two-grid method for the solution of singularly
perturbed reaction-diffusion equations. The algorithms involve solving one
inexpensive problem on coarse grid and solving on fine grid one linear problem
obtained by quasilinearization of the differential equation about an
interpolant of the computed solution on the coarse grid. Different meshes (of
Bakhvalov, Shishkin and Vulanovi\'c types) are examined. All the schemes are
uniformly convergent with respect to the small parameter. We show theoretically
and numerically that the global error of the two-grid method is the same as of
the nonlinear problem solved directly on the fine layer-adapted mesh.


title: A note on the birefringence angle estimation in CMB data analysis

abstract:
  Parity violating physics beyond the standard model of particle physics
induces a rotation of the linear polarization of photons. This effect, also
known as cosmological birefringence (CB), can be tested with the observations
of the cosmic microwave background (CMB) anisotropies which are linearly
polarized at the level of $5-10\%$. In particular CB produces non-null CMB
cross correlations between temperature and B mode-polarization, and between E-
and B-mode polarization. Here we study the properties of the so called
D-estimators, often used to constrain such an effect. After deriving the
framework of both frequentist and Bayesian analysis, we discuss the interplay
between birefringence and weak-lensing, which, albeit parity conserving,
modifies pre-existing TB and EB cross correlation.


title:
Three-flavor chiral effective model with four baryonic multiplets within
  the mirror assignment

abstract:
  We study three-flavor octet baryons by using the so-called extended Linear
Sigma Model (eLSM). Within a quark-diquark picture, the requirement of a mirror
assignment naturally leads to the consideration of four spin-$\frac{1}{2}$
baryon multiplets. A reduction of the Lagrangian to the two-flavor case leaves
four doublets of nucleonic states which mix to form the experimentally observed
states $N(939)$, $N(1440)$, $N(1535)$ and $N(1650)$. We determine the
parameters of the nucleonic part of the Lagrangian from a fit to masses and
decay properties of the aforementioned states. By tracing their masses when
chiral symmetry is restored, we conclude that the pairs $N(939)$, $N(1535)$ and
$N(1440)$, $N(1650)$ form chiral partners.


title: Temperature dependence of spin-orbit torques in W/CoFeB bilayers

abstract:
  We report on the temperature and layer thickness variation of spin-orbit
torques in perpendicularly magnetized W/CoFeB bilayers. Harmonic Hall voltage
measurements reveal dissimilar temperature evolutions of longitudinal and
transverse effective magnetic field components. The transverse effective field
changes sign at 250 K for a 2 nm thick W buffer layer, indicating a much
stronger contribution from interface spin-orbit interactions compared to, for
example, Ta. Transmission electron microscopy measurements reveal that
considerable interface mixing between W and CoFeB is primarily responsible for
this effect.


title:
Maximizing the Probability of Detecting an Electromagnetic Counterpart
  of Gravitational-wave Events

abstract:
  Compact binary coalescences are a promising source of gravitational waves for
second-generation interferometric gravitational-wave detectors such as advanced
LIGO and advanced Virgo. These are among the most promising sources for joint
detection of electromagnetic (EM) and gravitational-wave (GW) emission. To
maximize the science performed with these objects, it is essential to undertake
a followup observing strategy that maximizes the likelihood of detecting the EM
counterpart. We present a follow-up strategy that maximizes the counterpart
detection probability, given a fixed investment of telescope time. We show how
the prior assumption on the luminosity function of the electro-magnetic
counterpart impacts the optimized followup strategy. Our results suggest that
if the goal is to detect an EM counterpart from among a succession of GW
triggers, the optimal strategy is to perform long integrations in the highest
likelihood regions, with a time investment that is proportional to the $2/3$
power of the surface density of the GW location probability on the sky. In the
future, this analysis framework will benefit significantly from the
3-dimensional localization probability.


title:
Influence of the biquadratic exchange interaction in the classical
  ground state magnetic response of the antiferromagnetic icosahedron

abstract:
  The icosahedron has a ground state magnetization discontinuity in an external
magnetic field when classical spins mounted on its vertices are coupled
according to the antiferromagnetic Heisenberg model. This is so even if there
is no magnetic anisotropy in the Hamiltonian. The discontinuity is a
consequence of the frustrated nature of the interactions, which originates in
the topology of the cluster. Here it is found that the addition of the next
order isotropic spin exchange interaction term in the Hamiltonian, the
biquadratic exchange interaction, significantly enriches the classical ground
state magnetic response. For relatively weak biquadratic interaction new
discontinuities emerge, while for even stronger the number of discontinuities
for this small molecule can go up to seven, accompanied by a susceptibility
discontinuity. These results demonstrate the possibility of using a small
entity like the icosahedron as a magnetic unit whose ground state spin
configuration and magnetization can be tuned between many different
non-overlapping regimes with the application of an external field.


title:
Novel Approach to the Dark Matter Problem: Primordial Intermediate-Mass
  Black Holes

abstract:
  A discussion at a Scientific American level of the idea that the constituents
of the dark mater in galactic halos are primordial intermediate-mass black
holes with masses between ten and one hundred thousand times the solar mass.


title:
Phase field modelling of interfacial anisotropy driven faceting of
  precipitates

abstract:
  We use extended Cahn-Hilliard (ECH) equations to study faceted precipitate
morphologies; specifically, we obtain four sided precipitates (in 2-D) and
dodecahedron (in 3-D) in a system with cubic anisotropy, and, six-sided
precipitates (in 2-D, in the basal plane), hexagonal dipyramids and hexagonal
prisms (in 3-D) in systems with hexagonal anisotropy. Our listing of these ECH
equations is fairly comprehensive and complete (upto sixth rank tensor terms of
the Taylor expansion of the free energy). We also show how the parameters that
enter the model are to be obtained if either the interfacial energy anisotropy
or the equilibrium morphology of the precipitate is known.


title:
Roles of the spreading scope and effectiveness in spreading dynamics on
  multiplex networks

abstract:
  Comparing with single networks, the multiplex networks bring two main effects
on the spreading process among individuals. First, the pathogen or information
can be transmitted to more individuals through different layers at one time,
which enlarges the spreading scope. Second, through different layers, an
individual can also transmit the pathogen or information to the same
individuals more than once at one time, which makes the spreading more
effective. To understand the different roles of the spreading scope and
effectiveness, we propose an epidemic model on multiplex networks with link
overlapping, where the spreading effectiveness of each interaction as well as
the variety of channels (spreading scope) can be controlled by the number of
overlapping links. We find that for Poisson degree distribution, increasing the
epidemic scope (the first effect) is more efficient than enhancing epidemic
probability (the second effect) to facilitate the spreading process. However,
for power-law degree distribution, the effects of the two factors on the
spreading dynamics become complicated. Enhancing epidemic probability makes
pathogen or rumor easier to outbreak in a finite system. But after that
increasing epidemic scopes is still more effective for a wide spreading.
Theoretical results along with reasonable explanation for these phenomena are
all given in this paper, which indicates that the epidemic scope could play an
important role in the spreading dynamics.


title:
Pieces-of-parts for supervoxel segmentation with global context:
  Application to DCE-MRI tumour delineation

abstract:
  Rectal tumour segmentation in dynamic contrast-enhanced MRI (DCE-MRI) is a
challenging task, and an automated and consistent method would be highly
desirable to improve the modelling and prediction of patient outcomes from
tissue contrast enhancement characteristics - particularly in routine clinical
practice. A framework is developed to automate DCE-MRI tumour segmentation, by
introducing: perfusion-supervoxels to over-segment and classify DCE-MRI volumes
using the dynamic contrast enhancement characteristics; and the pieces-of-parts
graphical model, which adds global (anatomic) constraints that further refine
the supervoxel components that comprise the tumour. The framework was evaluated
on 23 DCE-MRI scans of patients with rectal adenocarcinomas, and achieved a
voxelwise area-under the receiver operating characteristic curve (AUC) of 0.97
compared to expert delineations. Creating a binary tumour segmentation, 21 of
the 23 cases were segmented correctly with a median Dice similarity coefficient
(DSC) of 0.63, which is close to the inter-rater variability of this
challenging task. A sec- ond study is also included to demonstrate the method's
generalisability and achieved a DSC of 0.71. The framework achieves promising
results for the underexplored area of rectal tumour segmentation in DCE-MRI,
and the methods have potential to be applied to other DCE-MRI and supervoxel
segmentation problems


title: Distributed chaos and helicity in turbulence

abstract:
  The distributed chaos driven by Levich-Tsinober (helicity) integral: $I=\int
\langle h({\bf x},t)~h({\bf x}+{\bf r}, t)\rangle d{\bf r}$ has been studied.
It is shown that the helical distributed chaos can be considered as basis for
complex turbulent flows with interplay between large-scale coherent structures
and small-scale turbulence, such as Cuette-Taylor flow, wake behind cylinder
and turbulent flow in the Large Plasma Device (LAPD) with inserted limiters. In
the last case appearance of the helical distributed chaos, caused by the
limiters, results in improvement of radial particle confinement.


title:
Convolution quadrature for the wave equation with a nonlinear impedance
  boundary condition

abstract:
  A rarely exploited advantage of time-domain boundary integral equations
compared to their frequency counterparts is that they can be used to treat
certain nonlinear problems. In this work we investigate the scattering of
acoustic waves by a bounded obstacle with a nonlinear impedance boundary
condition. We describe a boundary integral formulation of the problem and prove
without any smoothness assumptions on the solution the convergence of a full
discretization: Galerkin in space and convolution quadrature in time. If the
solution is sufficiently regular, we prove that the discrete method converges
at optimal rates. Numerical evidence in 3D supports the theory.


title:
Non-contact hemodynamic imaging reveals the jugular venous pulse
  waveform

abstract:
  Cardiovascular monitoring is important to prevent diseases from progressing.
The jugular venous pulse (JVP) waveform offers important clinical information
about cardiac health, but is not routinely examined due to its invasive
catheterisation procedure. Here, we demonstrate for the first time that the JVP
can be consistently observed in a non-contact manner using a novel light-based
photoplethysmographic imaging system, coded hemodynamic imaging (CHI). While
traditional monitoring methods measure the JVP at a single location, CHI's
wide-field imaging capabilities were able to observe the jugular venous pulse's
spatial flow profile for the first time. The important inflection points in the
JVP were observed, meaning that cardiac abnormalities can be assessed through
JVP distortions. CHI provides a new way to assess cardiac health through
non-contact light-based JVP monitoring, and can be used in non-surgical
environments for cardiac assessment.


title: Inverse Problems under Sarmanov dependence structure

abstract:
  Consider a sequence $\{(X_{i}, Y_{i})\}$ of independent and identically
distributed random vectors, with joint distribution bivariate Sarmanov. This is
a natural set-up for discrete time financial risk models with insurance risks.
Of particular interest are the infinite time ruin probabilities $P\left[\sup_{n
\geq 1}\sum_{i=1}^{n} X_i \prod_{j=1}^{i}Y_{j} > x\right]$. When the $Y_{i}$'s
are assumed to have lighter tails than the $X_{i}$'s, we investigate sufficient
conditions that ensure each $X_{i}$ has a regularly varying tail, given that
the ruin probability is regularly varying. This is an inverse problem to the
more traditional analysis of the ruin probabilities based on the tails of the
$X_{i}$'s. We impose moment-conditions as well as non-vanishing Mellin
transform assumptions on the $Y_{i}$'s in order to achieve the desired results.
But our analysis departs from the more conventional assumption of independence
between the sequences $\{X_{i}\}$ and $\{Y_{i}\}$, instead assuming each
$(X_{i}, Y_{i})$ to be jointly distributed as bivariate Sarmanov, a fairly
broad class of bivariate distributions.


title: Evolution of the free volume between rough surfaces in contact

abstract:
  The free volume comprised between rough surfaces in contact governs the
fluid/gas transport properties across networks of cracks and the
leakage/percolation phenomena in seals. In this study, a fundamental insight
into the evolution of the free volume depending on the mean plane separation,
on the real contact area and on the applied pressure is gained in reference to
fractal surfaces whose contact response is solved using the boundary element
method. Particular attention is paid to the effect of the surface fractal
dimension and of the surface resolution on the predicted results. The free
volume domains corresponding to different threshold levels are found to display
fractal spatial distributions whose bounds to their fractal dimensions are
theoretically derived. A synthetic formula based on the probability
distribution function of the free volumes is proposed to synthetically
interpret the numerically observed trends.


title:
Gas and grain chemical composition in cold cores as predicted by the
  Nautilus 3-phase model

abstract:
  We present an extended version of the 2-phase gas-grain code NAUTILUS to the
3-phase modelling of gas and grain chemistry of cold cores. In this model, both
the mantle and the surface are considered as chemically active. We also take
into account the competition among reaction, diffusion and evaporation. The
model predictions are confronted to ice observations in the envelope of
low-mass and massive young stellar objects as well as toward background stars.
Modelled gas-phase abundances are compared to species observed toward TMC-1
(CP) and L134N dark clouds. We find that our model successfully reproduces the
observed ice species. It is found that the reaction-diffusion competition
strongly enhances reactions with barriers and more specifically reactions with
H2, which is abundant on grains. This finding highlights the importance to have
a good approach to determine the abundance of H2 on grains. Consequently, it is
found that the major N-bearing species on grains go from NH3 to N2 and HCN when
the reaction-diffusion competition is accounted. In the gas-phase and before
few 10^5 yrs, we find that the 3-phase model does not have a strong impact on
the observed species compared to the 2-phase model. After this time, the
computed abundances dramatically decrease due to the strong accretion on dust,
which is not counterbalanced by the desorption less efficient than in the
2-phase model. This strongly constrains the chemical-age of cold cores to be of
the order of few 10^5 yrs.


title: Simulations in the field of power converters for particle accelerators

abstract:
  The complexity and cost of building and running high-power electrical systems
make the use of simulations unavoidable. The simulations available today
provide great understanding about how systems really operate. This paper helps
the reader to gain an insight into simulation in the field of power converters
for particle accelerators. Starting with the definition and basic principles of
simulation, two simulation types, as well as their leading tools, are
presented: analog and numerical simulations. Some practical applications of
each simulation type are also considered. The final conclusion then summarizes
the main important items to keep in mind before opting for a simulation tool or
before performing a simulation.


title: Stabilization of Damped Waves on Spheres and Zoll Surfaces of Revolution

abstract:
  We study the strong stabilization of wave equations on some sphere-like
manifolds, with rough damping terms which do not satisfy the geometric control
condition posed by Rauch-Taylor and Bardos-Lebeau-Rauch. We begin with an
unpublished result of G. Lebeau, which states that on S^d , the indicator
function of the upper hemisphere strongly stabilizes the damped wave equation,
even though the equators, which are geodesics contained in the boundary of the
upper hemisphere, do not enter the damping region. Then we extend this result
on dimension 2, to Zoll surfaces of revolution, whose geometry is similar to
that of S^2 . In particular, geometric objects such as the equator, and the
hemi-surfaces are well defined. Our result states that the indicator function
of the upper hemi-surface strongly stabilizes the damped wave equation, even
though the equator, as a geodesic, does not enter the upper hemi-surface
either.


title:
A Multigrid Method for the Ground State Solution of Bose-Einstein
  Condensates Based on Newton Iteration

abstract:
  In this paper, a new kind of multigrid method is proposed for the ground
state solution of Bose-Einstein condensates based on Newton iteration method.
Instead of treating eigenvalue $\lambda$ and eigenvector $u$ respectively, we
regard the eigenpair $(\lambda, u)$ as one element in the composite space $\R
\times H_0^1(\Omega)$ and then Newton iteration method is adopted for the
nonlinear problem. Thus in this multigrid scheme, we only need to solve a
linear discrete boundary value problem in every refined space, which can
improve the overall efficiency for the simulation of Bose-Einstein
condensations.


title: Hot super-Earths stripped by their host stars

abstract:
  Simulations predict that hot super-Earth sized exoplanets can have their
envelopes stripped by photo-evaporation, which would present itself as a lack
of these exoplanets. However, this absence in the exoplanet population has
escaped a firm detection. Here we demonstrate, using asteroseismology on a
sample of exoplanets and exoplanet candidates observed during the Kepler
mission that, while there is an abundance of super-Earth sized exoplanets with
low incident fluxes, none are found with high incident fluxes. We do not find
any exoplanets with radii between 2.2 and 3.8 Earth radii with incident flux
above 650 times the incident flux on Earth. This gap in the population of
exoplanets is explained by evaporation of volatile elements and thus supports
the predictions. The confirmation of a hot-super-Earth desert caused by
evaporation will add an important constraint on simulations of planetary
systems, since they must be able to reproduce the dearth of close-in
super-Earths.


title: Fixed-Field Alternating-Gradient Accelerators

abstract:
  These notes provide an overview of Fixed-Field Alternating-Gradient (FFAG)
accelerators for medical applications. We begin with a review of the basic
principles of this type of accelerator, including the scaling and non-scaling
types, highlighting beam dynamics issues that are of relevance to hadron ac-
celerators. The potential of FFAG accelerators in the field of hadron therapy
is discussed in detail, including an overview of existing medical FFAG designs.
The options for FFAG treatment gantries are also considered.


title: On the Hilbert Polynomial of the HOMFLYPT Homology

abstract:
  We prove that the degree of the Hilbert polynomial of the HOMFLYPT homology
of a closed braid $B$ is $l-1$, where $l$ is the number of components of $B$.
This controls the growth of the HOMFLYPT homology with respect to its
polynomial grading. The Hilbert polynomial also reveals a link polynomial
hidden in the HOMFLYPT polynomial.


title: On sets of irreducible polynomials closed by composition

abstract:
  Let $\mathcal S$ be a set of monic degree $2$ polynomials over a finite field
and let $C$ be the compositional semigroup generated by $\mathcal S$. In this
paper we establish a necessary and sufficient condition for $C$ to be
consisting entirely of irreducible polynomials. The condition we deduce depends
on the finite data encoded in a certain graph uniquely determined by the
generating set $\mathcal S$. Using this machinery we are able both to show
examples of semigroups of irreducible polynomials generated by two degree $2$
polynomials and to give some non-existence results for some of these sets in
infinitely many prime fields satisfying certain arithmetic conditions.


title: BFDA: A Matlab Toolbox for Bayesian Functional Data Analysis

abstract:
  We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical
model to smooth multiple functional data with the assumptions of the same
underlying Gaussian process distribution, a Gaussian process prior for the mean
function, and an Inverse-Wishart process prior for the covariance function.
This model-based approach can borrow strength from all functional data to
increase the smoothing accuracy, as well as estimate the mean-covariance
functions simultaneously. An option of approximating the Bayesian inference
process using cubic B-spline basis functions is integrated in BFDA, which
allows for efficiently dealing with high-dimensional functional data. Examples
of using BFDA in various scenarios and conducting follow-up functional
regression are provided. The advantages of BFDA include: (1) Simultaneously
smooths multiple functional data and estimates the mean-covariance functions in
a nonparametric way; (2) flexibly deals with sparse and high-dimensional
functional data with stationary and nonstationary covariance functions, and
without the requirement of common observation grids; (3) provides accurately
smoothed functional data for follow-up analysis.


title:
Annotation Order Matters: Recurrent Image Annotator for Arbitrary Length
  Image Tagging

abstract:
  Automatic image annotation has been an important research topic in
facilitating large scale image management and retrieval. Existing methods focus
on learning image-tag correlation or correlation between tags to improve
annotation accuracy. However, most of these methods evaluate their performance
using top-k retrieval performance, where k is fixed. Although such setting
gives convenience for comparing different methods, it is not the natural way
that humans annotate images. The number of annotated tags should depend on
image contents. Inspired by the recent progress in machine translation and
image captioning, we propose a novel Recurrent Image Annotator (RIA) model that
forms image annotation task as a sequence generation problem so that RIA can
natively predict the proper length of tags according to image contents. We
evaluate the proposed model on various image annotation datasets. In addition
to comparing our model with existing methods using the conventional top-k
evaluation measures, we also provide our model as a high quality baseline for
the arbitrary length image tagging task. Moreover, the results of our
experiments show that the order of tags in training phase has a great impact on
the final annotation performance.


title:
A constructive characterisation of circuits in the simple $(2,1)$-sparse
  matroid

abstract:
  A simple graph $G=(V,E)$ is a $(2,1)$-circuit if $|E|=2|V|$ and $|E(H)|\leq
2|V(H)|-1$ for every proper subgraph $H$ of $G$. Motivated, in part, by ongoing
work to understand unique realisations of graphs on surfaces, we derive a
constructive characterisation of $(2,1)$-circuits. The characterisation uses
the well known 1-extension and $X$-replacement operations as well as several
summation moves to glue together $(2,1)$-circuits over small cutsets.


title:
A discontinuous Galerkin method for a new class of Green-Naghdi
  equations on simplicial unstructured meshes

abstract:
  In this paper, we introduce a discontinuous Finite Element formulation on
simplicial unstructured meshes for the study of free surface flows based on the
fully nonlinear and weakly dispersive Green-Naghdi equations. Working with a
new class of asymptotically equivalent equations, which have a simplified
analytical structure, we consider a decoupling strategy: we approximate the
solutions of the classical shallow water equations supplemented with a source
term globally accounting for the non-hydrostatic effects and we show that this
source term can be computed through the resolution of scalar elliptic
second-order sub-problems. The assets of the proposed discrete formulation are:
(i) the handling of arbitrary unstructured simplicial meshes, (ii) an arbitrary
order of approximation in space, (iii) the exact preservation of the motionless
steady states, (iv) the preservation of the water height positivity, (v) a
simple way to enhance any numerical code based on the nonlinear shallow water
equations. The resulting numerical model is validated through several
benchmarks involving nonlinear wave transformations and run-up over complex
topographies.


title:
Computable Error Estimates for Ground State Solution of Bose-Einstein
  Condensates

abstract:
  In this paper, we propose a computable error estimate of the Gross-Pitaevskii
equation for ground state solution of Bose-Einstein condensates by general
conforming finite element methods on general meshes. Based on the proposed
error estimate, asymptotic lower bounds of the smallest eigenvalue and ground
state energy can be obtained. Several numerical examples are presented to
validate our theoretical results in this paper.


title:
On the pressureless damped Euler-Poisson equations with non-local
  forces: Critical thresholds and large-time behavior

abstract:
  We analyse the one-dimensional pressureless Euler-Poisson equations with a
linear damping and non-local interaction forces. These equations are relevant
for modelling collective behavior in mathematical biology. We provide a sharp
threshold between the supercritical region with finite-time breakdown and the
subcritical region with global-in-time existence of the classical solution. We
derive an explicit form of solution in Lagrangian coordinates which enables us
to study the time-asymptotic behavior of classical solutions with the initial
data in the subcritical region.


title: Extremal decomposition problems for p-harmonic radius

abstract:
  We extend classical results by Lavrent'ev and Kufarev concerning the product
of the conformal radii of planar non-overlapping domains. We also extend
relatively recent results for the case of domains in the $n$-dimensional
Euclidean space, $n \geq 3$, with conformal radii replaced by harmonic ones.
Namely, we get analogues of these results in $n$-dimensional Euclidean space in
terms of $p$-harmonic radius. The proofs are based on technique of modulii of
curve families and dissymmetrization of such families.


title: Transient error approximation in a L\'evy queue

abstract:
  Motivated by a capacity allocation problem within a finite planning period,
we conduct a transient analysis of a single-server queue with L\'evy input.
From a cost minimization perspective, we investigate the error induced by using
stationary congestion measures as opposed to time-dependent measures. Invoking
recent results from fluctuation theory of L\'evy processes, we derive a refined
cost function, that accounts for transient effects. This leads to a corrected
capacity allocation rule for the transient single-server queue. Extensive
numerical experiments indicate that the cost reductions achieved by this
correction can by significant.


title:
Measurements of $Z\gamma$ and $Z\gamma\gamma$ production in $pp$
  collisions at $\sqrt{s}=$ 8 TeV with the ATLAS detector

abstract:
  The production of $Z$ bosons with one or two isolated high-energy photons is
studied using $pp$ collisions at $\sqrt{s}$ = 8 TeV. The analyses use a data
sample with an integrated luminosity of 20.3 fb$^{-1}$ collected by the ATLAS
detector during the 2012 LHC data taking. The $Z\gamma$ and $Z\gamma\gamma$
production cross sections are measured with leptonic ($e^{+}e^{-}$,
$\mu^{+}\mu^{-}$, $\nu\bar{\nu}$) decays of the $Z$ boson, in extended fiducial
regions defined in terms of the lepton and photon acceptance. They are then
compared to cross-section predictions from the Standard Model, where the
sources of the photons are radiation off initial-state quarks and radiative
$Z$-boson decay to charged leptons, and from fragmentation of final-state
quarks and gluons into photons. The yields of events with photon transverse
energy $E_T >$ 250 GeV from $\ell^{+}\ell^{-}\gamma$ events and with $E_T >$
400 GeV from $\nu\bar{\nu}\gamma$ events are used to search for anomalous
triple gauge-boson couplings $ZZ\gamma$ and $Z\gamma\gamma$. The yields of
events with diphoton invariant mass $m_{\gamma\gamma} >$ 200 GeV from
$\ell^{+}\ell^{-}\gamma\gamma$ events and with $m_{\gamma\gamma} > $ 300 GeV
from $\nu\bar{\nu}\gamma\gamma$ events are used to search for anomalous quartic
gauge-boson couplings $ZZ\gamma\gamma$ and $Z\gamma\gamma\gamma$. No deviations
from Standard Model predictions are observed and limits are placed on
parameters used to describe anomalous triple and quartic gauge-boson couplings.


title:
On the possibility of determining the distance to the Galactic center
  from the geometry of spiral arm segments

abstract:
  A new approach to determining the solar galactocentric distance, $R_0$, from
the geometry of spiral-arm segments is proposed. Geometric aspects of the
problem are analyzed and a simplified three-point method for estimating $R_0$
from objects in a spiral segment is developed in order to test the proposed
approach. An estimate of $R_0 = 8.44 \pm 0.45$ kpc is obtained by applying the
method to masers with measured trigonometric parallaxes, and statistical
properties of the $R_0$ estimation from spiral segments are analyzed.


title: Particle Acceleration and Heating by Turbulent Reconnection

abstract:
  Turbulent flows in the solar wind, large scale current sheets, multiple
current sheets, and shock waves lead to the formation of environments in which
a dense network of current sheets is established and sustains "turbulent
reconnection". We constructed a 2D grid on which a number of randomly chosen
grid points are acting as scatterers (i.e. magnetic clouds or current sheets).
Our goal is to examine how test particles respond inside this large scale
collection of scatterers. We study the energy gain of individual particles, the
evolution of their energy distribution and their escape time distribution. We
have developed a new method to estimate the transport coefficients from the
dynamics of the interaction of the particles with the scatterers. Replacing the
"magnetic clouds" with current sheets, we have proven that the energization
processes can be more efficient depending on the strength of the effective
electric fields inside the current sheets and their statistical properties.
Using the estimated transport coefficients and solving the Fokker-Planck (FP)
equation we can recover the energy distribution of the particles only for the
sstochastic Fermi process. We have shown that the evolution of the particles
inside a turbulent reconnecting volume is not a solution of the FP equation,
since the interaction of the particles with the current sheets is "anomalous",
in contrast to the case of the second order Fermi process.


title: Some probabilistic properties of fractional point processes

abstract:
  This paper studies the first hitting times of generalized Poisson processes
$N^f(t)$, related to Bernstein functions $f$. For the space-fractional Poisson
processes, $N^\alpha(t)$, $t>0$ (corresponding to $f= x^\alpha$), the hitting
probabilities $P\{T_k^\alpha<\infty\}$ are explicitly obtained and analyzed.
The processes $N^f(t)$ are time-changed Poisson processes $N(H^f(t))$ with
subordinators $H^f(t)$ and here we study $N\left(\sum_{j=1}^n
H^{f_j}(t)\right)$ and obtain probabilistic features of these extended counting
processes. A section of the paper is devoted to processes of the form
$N(|\mathcal{G}_{H,\nu}(t)|)$ where $\mathcal{G}_{H,\nu}(t)$ are generalized
grey Brownian motions. This involves the theory of time-dependent fractional
operators of the McBride form. While the time-fractional Poisson process is a
renewal process, we prove that the space-time Poisson process is no longer a
renewal process.


title:
Node-to-segment and node-to-surface interface finite elements for
  fracture mechanics

abstract:
  The topologies of existing interface elements used to discretize cohesive
cracks are such that they can be used to compute the relative displacements
(displacement discontinuities) of two opposing segments (in 2D) or of two
opposing facets (in 3D) belonging to the opposite crack faces and enforce the
cohesive traction-separation relation. In the present work we propose a novel
type of interface element for fracture mechanics sharing some analogies with
the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact
elements. The displacement gap of a node belonging to the finite element
discretization of one crack face with respect to its projected point on the
opposite face is used to determine the cohesive tractions, the residual vector
and its consistent linearization for an implicit solution scheme. The following
advantages with respect to classical interface finite elements are
demonstrated: (i) non-matching finite element discretizations of the opposite
crack faces is possible; (ii) easy modelling of cohesive cracks with
non-propagating crack tips; (iii) the internal rotational equilibrium of the
interface element is assured. Detailed examples are provided to show the
usefulness of the proposed approach in nonlinear fracture mechanics problems.


title: The spaces of non-contractible closed curves in compact space forms

abstract:
  We calculate the rational equivariant cohomology of the spaces of
non-contractible loops in compact space forms and show how to apply these
calculations for proving the existence of closed geodesics.


title: Shadows of graphical mean curvature flow

abstract:
  We consider mean curvature flow of an initial surface that is the graph of a
function over some domain of definition in $R^n$. If the graph is not complete
then we impose a constant Dirichlet boundary condition at the boundary of the
surface. We establish longtime-existence of the flow and investigate the
projection of the flowing surface onto $R^n$, the shadow of the flow. This
moving shadow can be seen as a weak solution for mean curvature flow of
hypersurfaces in $R^n$ with a Dirichlet boundary condition. Furthermore, we
provide a lemma of independent interest to locally mollify the boundary of an
intersection of two smooth open sets in a way that respects curvature
conditions.


title:
Search for lepton flavour violating decays of heavy resonances and
  quantum black holes to an e-mu pair in proton-proton collisions at sqrt(s) =
  8 TeV

abstract:
  A search for narrow resonances decaying to an electron and a muon is
presented. The e-mu mass spectrum is also investigated for non-resonant
contributions from the production of quantum black holes (QBHs). The analysis
is performed using data corresponding to an integrated luminosity of 19.7
inverse femtobarns collected in proton-proton collisions at a centre-of-mass
energy of 8 TeV with the CMS detector at the LHC. With no evidence for physics
beyond the standard model in the invariant mass spectrum of selected e-mu
pairs, upper limits are set at 95% confidence level on the product of cross
section and branching fraction for signals arising in theories with charged
lepton flavour violation. In the search for narrow resonances, the resonant
production of a tau sneutrino in R-parity violating supersymmetry is
considered. The tau sneutrino is excluded for masses below 1.28 TeV for
couplings lambda[132] = lambda[231] = lambda'[311] = 0.01, and below 2.30 TeV
for lambda[132] = lambda[231] = 0.07 and lambda'[311] = 0.11. These are the
most stringent limits to date from direct searches at high-energy colliders. In
addition, the resonance searches are interpreted in terms of a model with heavy
partners of the Z boson and the photon. In a framework of TeV-scale quantum
gravity based on a renormalization of Newton's constant, the search for
non-resonant contributions to the e-mu mass spectrum excludes QBH production
below a threshold mass M[th] of 1.99 TeV. In models that invoke extra
dimensions, the bounds range from 2.36 TeV for one extra dimension to 3.63 TeV
for six extra dimensions. This is the first search for QBHs decaying into the
e-mu final state.


title: A note on the validity of Bogoliubov correction to mean-field dynamics

abstract:
  We study the norm approximation to the Schr\"odinger dynamics of $N$ bosons
in $\mathbb{R}^3$ with an interaction potential of the form
$N^{3\beta-1}w(N^{\beta}(x-y))$. Assuming that in the initial state the
particles outside of the condensate form a quasi-free state with finite kinetic
energy, we show that in the large $N$ limit, the fluctuations around the
condensate can be effectively described using Bogoliubov approximation for all
$0\le \beta<1/2$. The range of $\beta$ is expected to be optimal for this large
class of initial states.


title:
The Poincar\'e-Bendixson Theorem and the Non-linear Cauchy-Riemann
  Equations

abstract:
  Fiedler and Mallet-Paret prove a version of the classical
Poincar\'e-Bendixson Theorem for scalar parabolic equations. We prove that a
similar result holds for bounded solutions of the non-linear Cauchy-Riemann
equations. The latter is an application of an abstract theorem for flows with
a(n) (unbounded) discrete Lyapunov function.


title: Can Boosting with SVM as Week Learners Help?

abstract:
  Object recognition in images involves identifying objects with partial
occlusions, viewpoint changes, varying illumination, cluttered backgrounds.
Recent work in object recognition uses machine learning techniques SVM-KNN,
Local Ensemble Kernel Learning, Multiple Kernel Learning. In this paper, we
want to utilize SVM as week learners in AdaBoost. Experiments are done with
classifiers like near- est neighbor, k-nearest neighbor, Support vector
machines, Local learning(SVM- KNN) and AdaBoost. Models use Scale-Invariant
descriptors and Pyramid his- togram of gradient descriptors. AdaBoost is
trained with set of week classifier as SVMs, each with kernel distance function
on different descriptors. Results shows AdaBoost with SVM outperform other
methods for Object Categorization dataset.


title:
Better Strategyproof Mechanisms without Payments or Prior --- An
  Analytic Approach

abstract:
  We revisit the problem of designing strategyproof mechanisms for allocating
divisible items among two agents who have linear utilities, where payments are
disallowed and there is no prior information on the agents' preferences. The
objective is to design strategyproof mechanisms which are competitive against
the most efficient (but not strategyproof) mechanism.
  For the case with two items:
  (1) We provide a set of sufficient conditions for strategyproofness.
  (2) We use an analytic approach to derive strategyproof mechanisms which are
more competitive than all prior strategyproof mechanisms.
  (3) We improve the linear-program-based proof of Guo and Conitzer to show new
upper bounds on competitive ratios.
  (4) We provide the first "mathematical" upper bound proof.
  For the cases with any number of items:
  (1) We build on the Partial Allocation mechanisms introduced by Cole et al.
to design a strategyproof mechanism which is 0.67776-competitive, breaking the
2/3 barrier.
  (2) We propose a new subclass of strategyproof mechanisms called
Dynamical-Increasing-Price mechanisms, where each agent purchases the items
using virtual money, and the prices of the items depend on other agents'
preferences.


title:
Large Enhancement of Circular Dichroism Using an Embossed Chiral
  Metamaterial

abstract:
  In the close vicinity of a chiral nanostructure, the circular dichroism of a
biomolecule could be greatly enhanced, due to the interaction with the local
superchiral fields. Modest enhancement of optical activity using a planar
metamaterial, with some chiral properties, and achiral nanoparticles has been
previously reported. A more substantial chirality enhancement can be achieved
in the local filed of a chiral nanostructure with a three-dimensional
arrangement. Using an embossed chiral nanostructure designed for chiroptical
sensing, we measure the circular dichroism spectra of two biomolecules,
Chlorophylls A and B, at the molecular level, using a simple polarization
resolved reflection measurement. This experiment is the first realization of
the on-resonance surface-enhanced circular dichroism, achieved by matching the
chiral resonances of a strongly chiral metamaterial with that of a chiral
molecule, resulting in an unprecedentedly large differential CD spectrum from a
monolayer of a chiral material.


title:
Principal Component Analysis: Resources for an Essential Application of
  Linear Algebra

abstract:
  Principal Component Analysis (PCA) is a highly useful topic within an
introductory Linear Algebra course, especially since it can be used to
incorporate a number of applied projects. This method represents an essential
application and extension of the Spectral Theorem and is commonly used within a
variety of fields, including statistics, neuroscience, and image compression.
We present a synopsis of PCA and include a number of examples that can be used
within upper-level mathematics courses to engage undergraduate students while
introducing them to one of the most widely-used applications of linear algebra.


title: Odd Khovanov's arc algebra

abstract:
  We construct an odd version of Khovanov's arc algebra $H^n$. Extending the
center to elements that anticommute, we get a subalgebra that is isomorphic to
the oddification of the cohomology of the $(n,n)$-Springer varieties. We also
prove that the odd arc algebra can be twisted into an associative algebra.


title: Search for a Dark Matter component

abstract:
  In this paper, after reviewing some of the most important concepts about Dark
Matter (DM) and methods of its registration, in particular by using SQUIDs, we
focus on two main problems. First, the possible mechanism of magnetic moment
origin for DM particles, in the form of neutralino, is discussed: the presence
of a magnetic moment means the existence of a new kind of interaction, whose
corresponding cross section is estimated. Second, a simple uniform model for DM
and Dark Energy (DE) is proposed. Two types of devices based on SQUID, in
particular the SQUID-paramagnetic absorber and the SQUID-magnetostrictor
systems, both suitable for investigations of above problems, are considered.


title:
Weighted sums of the squares of the distances of a point to the
  sidelines of a triangle

abstract:
  We study a function, which is a weighted sum of the squares of the distances
of an arbitrary point to the sidelines of a triangle. The given weights,
considered as barycentric coordinates, determine a point $M$. We prove that the
function reaches its minimum (maximum) at a point, which is isogonal conjugate
to $M$.


title: Strongly Proximal Edelsbrunner-Harer Nerves in Voronoi Tessellations

abstract:
  This paper introduces Edelsbrunner-Harer nerve in collections of Voronoi
regions (called nucleus clusters) endowed with one or more proximity relations.
The main results in this paper are that a maximal nucleus cluster (MNC) in a
Voronoi Tessellation is a strongly proximal Edelsbrunner-Harer nerve, each MNC
nerve and the union of the sets in the MNC have the same homotopy type.


title:
The Numerical Approximation of Nonlinear Functionals and Functional
  Differential Equations

abstract:
  The fundamental importance of functional differential equations has been
recognized in many areas of mathematical physics, such as fluid dynamics (Hopf
characteristic functional equation), quantum field theory (Schwinger-Dyson
equations) and statistical physics (equations for generating functionals and
effective Fokker-Planck equations). However, no effective numerical method has
yet been developed to compute their solution. The purpose of this report is to
fill this gap, and provide a new perspective on the problem of numerical
approximation of nonlinear functionals and functional differential equations.

categories: math.NA math-ph math.MP physics.comp-ph physics.flu-dyn


title:
Kernel Distribution Embeddings: Universal Kernels, Characteristic
  Kernels and Kernel Metrics on Distributions

abstract:
  Kernel mean embeddings have recently attracted the attention of the machine
learning community. They map measures $\mu$ from some set $M$ to functions in a
reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of
two mapped measures is a semi-metric $d_k$ over $M$. We study three questions.
(I) For a given kernel, what sets $M$ can be embedded? (II) When is the
embedding injective over $M$ (in which case $d_k$ is a metric)? (III) How does
the $d_k$-induced topology compare to other topologies on $M$? The existing
machine learning literature has addressed these questions in cases where $M$ is
(a subset of) the finite regular Borel measures. We unify, improve and
generalise those results. Our approach naturally leads to continuous and
possibly even injective embeddings of (Schwartz-) distributions, i.e.,
generalised measures, but the reader is free to focus on measures only. In
particular, we systemise and extend various (partly known) equivalences between
different notions of universal, characteristic and strictly positive definite
kernels, and show that on an underlying locally compact Hausdorff space, $d_k$
metrises the weak convergence of probability measures if and only if $k$ is
continuous and characteristic.


title:
Dichotomy between Attractive and Repulsive Tomonaga-Luttinger Liquids in
  Spin Ladders

abstract:
  We present two methods to determine whether the interactions in a
Tomonaga-Luttinger liquid (TLL) state of a spin-$1/2$ Heisenberg
antiferromagnetic ladder are attractive or repulsive. The first method combines
two bulk measurements, of magnetization and specific heat, to deduce the TLL
parameter that distinguishes between the attraction and repulsion. The second
one is based on a local-probe, NMR measurements of the spin-lattice relaxation.
For the strong-leg spin ladder compound $\mathrm{(C_7H_{10}N)_2CuBr_4}$ we find
that the isothermal magnetic field dependence of the relaxation rate,
$T_1^{-1}(H)$, displays a concave curve between the two critical fields that
bound the TLL regime. This is in sharp contrast to the convex curve previously
reported for a strong-rung ladder $\mathrm{(C_5H_{12}N)_2CuBr_4}$. Within the
TLL description, we show that the concavity directly reflects the attractive
interactions, while the convexity reflects the repulsive ones.


title:
Thermodynamic optimization of an electric circuit as a non-steady energy
  converter

abstract:
  Electrical circuits with transient elements can be good examples of systems
where non--steady irreversible processes occur, so in the same way as a steady
state energy converter, we use the formal construction of the first order
irreversible thermodynamic (FOIT) to describe the energetics of these circuits.
In this case, we propose an isothermic model of two meshes with transient and
passive elements, besides containing two voltage sources (which can be
functions of time); this is a non--steady energy converter model. Through the
Kirchhoff equations, we can write the circuit phenomenological equations. Then,
we apply an integral transformation to linearise the dynamic equations and
rewrite them in algebraic form, but in the frequency space. However, the same
symmetry for steady states appears (cross effects). Thus, we can study the
energetic performance of this converter model by means of two parameters: the
"force ratio" and the "coupling degre". Furthermore, it is possible to obtain
the characteristic functions (dissipation function, power output, efficiency,
etc.). They allow us to establish a simple optimal operation regime of this
energy converter. As an example, we obtain the converter behavior for the
maximum efficient power regime (MPE).


title:
Observation of two distinct superconducting domes under pressure in
  tetragonal FeS

abstract:
  As the simplest iron-based superconductor, FeSe forms a tetragonal structure
with transition temperature Tc ~ 8 K. With assistance of pressure, or other
techniques, Tc can be greatly enhanced, even to above liquid nitrogen
temperature. The newly discovered superconducting tetragonal FeS (Tc ~ 4.5 K),
a sulfide counterpart of FeSe, promotes us on its high pressure investigation.
The transport and structure evolution of FeS with pressure have been studied. A
rapid suppression of Tc and vanishing of superconductivity at 4.0 GPa are
observed, followed by a second superconducting dome with a 30% enhancement in
maximum Tc. An onsite tetragonal to hexagonal phase transition occurs around
7.0 GPa, followed by a broad pressure range of phase coexistence. The residual
deformed tetragonal phase is considered as the source of second superconducting
dome. The observation of two superconducting domes in iron-based
superconductors poses great challenges for understanding their pairing
mechanism.


title: Cascading Denial of Service Attacks on Wi-Fi Networks

abstract:
  We unveil the existence of a vulnerability in Wi-Fi, which allows an
adversary to remotely launch a Denial-of-Service (DoS) attack that propagates
both in time and space. This vulnerability stems from a coupling effect induced
by hidden nodes. Cascading DoS attacks can congest an entire network and do not
require the adversary to violate any protocol. We demonstrate the feasibility
of such attacks through experiments with real Wi-Fi cards, extensive ns-3
simulations, and theoretical analysis. The simulations show that the attack is
effective both in networks operating under fixed and varying bit rates, as well
as ad hoc and infrastructure modes. To gain insight into the root-causes of the
attack, we model the network as a dynamical system and analyze its limiting
behavior. The model predicts that a phase transition (and hence a cascading
attack) is possible when the retry limit parameter of Wi-Fi is greater or equal
to 7, and explicitly characterizes the phase transition region in terms of the
system parameters.


title:
Check-hybrid GLDPC Codes: Systematic Elimination of Trapping Sets and
  Guaranteed Error Correction Capability

abstract:
  In this paper, we propose a new approach to construct a class of check-hybrid
generalized low-density parity-check (CH-GLDPC) codes which are free of small
trapping sets. The approach is based on converting some selected check nodes
involving a trapping set into super checks corresponding to a 2-error
correcting component code. Specifically, we follow two main purposes to
construct the check-hybrid codes; first, based on the knowledge of the trapping
sets of the global LDPC code, single parity checks are replaced by super checks
to disable the trapping sets. We show that by converting specified single check
nodes, denoted as critical checks, to super checks in a trapping set, the
parallel bit flipping (PBF) decoder corrects the errors on a trapping set and
hence eliminates the trapping set. The second purpose is to minimize the rate
loss caused by replacing the super checks through finding the minimum number of
such critical checks. We also present an algorithm to find critical checks in a
trapping set of column-weight 3 LDPC code and then provide upper bounds on the
minimum number of such critical checks such that the decoder corrects all error
patterns on elementary trapping sets. Moreover, we provide a fixed set for a
class of constructed check-hybrid codes. The guaranteed error correction
capability of the CH-GLDPC codes is also studied. We show that a CH-GLDPC code
in which each variable node is connected to 2 super checks corresponding to a
2-error correcting component code corrects up to 5 errors. The results are also
extended to column-weight 4 LDPC codes. Finally, we investigate the eliminating
of trapping sets of a column-weight 3 LDPC code using the Gallager B decoding
algorithm and generalize the results obtained for the PBF for the Gallager B
decoding algorithm.


title: Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure

abstract:
  The multi-armed bandit problems have been studied mainly under the measure of
expected total reward accrued over a horizon of length $T$. In this paper, we
address the issue of risk in multi-armed bandit problems and develop parallel
results under the measure of mean-variance, a commonly adopted risk measure in
economics and mathematical finance. We show that the model-specific regret and
the model-independent regret in terms of the mean-variance of the reward
process are lower bounded by $\Omega(\log T)$ and $\Omega(T^{2/3})$,
respectively. We then show that variations of the UCB policy and the DSEE
policy developed for the classic risk-neutral MAB achieve these lower bounds.


title:
Theoretically Optimal Datalog Rewritings for OWL 2 QL Ontology-Mediated
  Queries

abstract:
  We show that, for OWL 2 QL ontology-mediated queries with (i) ontologies of
bounded depth and conjunctive queries of bounded treewidth, (ii) ontologies of
bounded depth and bounded-leaf tree-shaped conjunctive queries, and (iii)
arbitrary ontologies and bounded-leaf tree-shaped conjunctive queries, one can
construct and evaluate nonrecursive datalog rewritings by, respectively,
LOGCFL, NL and LOGCFL algorithms, which matches the optimal combined
complexity.


title:
A Second-Quantized Kolmogorov-Chentsov Theorem via the Operator Product
  Expansion

abstract:
  We establish a direct connection between two fundamental topics: one in
probability theory and one in quantum field theory. The first topic is the
problem of pointwise multiplication of random Schwartz distributions which has
been the object of recent progress thanks to Hairer's theory of regularity
structures and the theory of paracontrolled distributions introduced by
Gubinelli, Imkeller and Perkowski. The second topic is Wilson's operator
product expansion which is a general property of models of quantum field theory
and a cornerstone of the bootstrap approach to conformal field theory. Our main
result is a general theorem for the almost sure construction of products of
random distributions by mollification and suitable additive as well as
multiplicative renormalizations. The hypothesis for this theorem is the
operator product expansion with precise bounds for pointwise correlations. We
conjecture these bounds to be universal features of quantum field theories with
gapped dimension spectrum. Our theorem can accommodate logarithmic corrections,
anomalous scaling dimensions and even lack of translation invariance. However,
it only applies to fields with short distance singularities that are milder
than white noise. As an application, we provide a detailed treatment of a
scalar conformal field theory of mean field type, i.e., the fractional massless
free field also known as the fractional Gaussian field.


title: Forces in the complex octonion curved space

abstract:
  The paper aims to extend major equations in the electromagnetic and
gravitational theories from the flat space into the complex octonion curved
space. Maxwell applied simultaneously the quaternion analysis and vector
terminology to describe the electromagnetic theory. It inspires subsequent
scholars to study the electromagnetic and gravitational theories with the
complex quaternions/octonions. Furthermore Einstein was the first to depict the
gravitational theory by means of tensor analysis and curved four-space-time.
Nowadays some scholars investigate the electromagnetic and gravitational
properties making use of the complex quaternion/octonion curved space. From the
orthogonality of two complex quaternions, it is possible to define the
covariant derivative of the complex quaternion curved space, describing the
gravitational properties in the complex quaternion curved space. Further it is
possible to define the covariant derivative of the complex octonion curved
space by means of the orthogonality of two complex octonions, depicting
simultaneously the electromagnetic and gravitational properties in the complex
octonion curved space. The result reveals that the connection coefficient and
curvature of the complex octonion curved space will exert an influence on the
field strength and field source of the electromagnetic and gravitational
fields, impacting the linear momentum, angular momentum, torque, energy, and
force and so forth.


title:
On the primitivity of birational transformations of irreducible
  symplectic manifolds

abstract:
  Let $f\colon X\dashrightarrow X$ be a bimeromorphic transformation of a
complex irreducible symplectic manifold $X$. Some important dynamical
properties of $f$ are encoded by the induced linear automorphism $f^*$ of
$H^2(X,\mathbb Z)$. Our main result is that a bimeromorphic transformation such
that $f^*$ has at least one eigenvalue with modulus $>1$ doesn't admit any
invariant fibration (in particular its generic orbit is Zariski-dense).


title: A note on the double-critical graph conjecture

abstract:
  A connected $n$-chromatic graph $G$ is double-critical if for all the edges
$xy$ of $G$, the graph $G-x-y$ is $(n-2)$-chromatic. In 1966, Erd\H os and
Lov\'asz conjectured that the only double-critical $n$-chromatic graph is
$K_n$. This conjecture remains unresolved for $n \ge 6.$ In this short note, we
verify this conjecture for claw-free graphs $G$ of chromatic number $6$.


title: Chained Gaussian Processes

abstract:
  Gaussian process models are flexible, Bayesian non-parametric approaches to
regression. Properties of multivariate Gaussians mean that they can be combined
linearly in the manner of additive models and via a link function (like in
generalized linear models) to handle non-Gaussian data. However, the link
function formalism is restrictive, link functions are always invertible and
must convert a parameter of interest to a linear combination of the underlying
processes. There are many likelihoods and models where a non-linear combination
is more appropriate. We term these more general models Chained Gaussian
Processes: the transformation of the GPs to the likelihood parameters will not
generally be invertible, and that implies that linearisation would only be
possible with multiple (localized) links, i.e. a chain. We develop an
approximate inference procedure for Chained GPs that is scalable and applicable
to any factorized likelihood. We demonstrate the approximation on a range of
likelihood functions.


title: Complexity Dichotomies for Unweighted Scoring Rules

abstract:
  Scoring systems are an extremely important class of election systems. We
study the complexity of manipulation, constructive control by deleting voters
(CCDV), and bribery for scoring systems.
  For manipulation, we show that for all scoring rules with a constant number
of different coefficients, manipulation is in P. And we conjecture that there
is no dichotomy theorem.
  On the other hand, we obtain dichotomy theorems for CCDV and bribery problem.
More precisely, we show that both of these problems are easy for 1-approval,
2-approval, 1-veto, 2-veto, 3-veto, generalized 2-veto, and (2,1,...,1,0), and
hard in all other cases. These results are the "dual" of the dichotomy theorem
for the constructive control by adding voters (CCAV) problem from
(Hemaspaandra, Hemaspaandra, Schnoor, AAAI 2014), but do not at all follow from
that result. In particular, proving hardness for CCDV is harder than for CCAV
since we do not have control over what the controller can delete, and proving
easiness for bribery tends to be harder than for control, since bribery can be
viewed as control followed by manipulation.


title: Monte Carlo simulation study of diblock copolymer self assembly

abstract:
  A technique is presented which maps the parameters of a bead spring model,
using the Flory Huggins theory, to a specific experimental system. By keeping
only necessary details, for the description of these systems, the mapping
procedure turns into an estimation of a few characteristic parameters. An asset
of this technique is that it is simple to apply and captures the behavior of
block copolymer phase separation. In our study this mapping technique is
utilized in conjunction with a Monte Carlo (MC) algorithm to perform
simulations on block copolymer systems. The microphase separation is
investigated in the bulk and under confinement, on unpatterned and patterned
surfaces.


title:
Finding Common Characteristics Among NBA Playoff and Championship Teams:
  A Machine Learning Approach

abstract:
  In this paper, we employ machine learning techniques to analyze seventeen
seasons (1999-2000 to 2015-2016) of NBA regular season data from every team to
determine the common characteristics among NBA playoff teams. Each team was
characterized by 26 predictor variables and one binary response variable taking
on a value of "TRUE" if a team had made the playoffs, and value of "FALSE" if a
team had missed the playoffs. After fitting an initial classification tree to
this problem, this tree was then pruned which decreased the test error rate.
Further to this, a random forest of classification trees was grown which
provided a very accurate model from which a variable importance plot was
generated to determine which predictor variables had the greatest influence on
the response variable. The result of this work was the conclusion that the most
important factors in characterizing a team's playoff eligibility are a team's
opponent number of assists per game, a team's opponent number of made two point
shots per game, and a team's number of steals per game. This seems to suggest
that defensive factors as opposed to offensive factors are the most important
characteristics shared among NBA playoff teams. We then use neural networks to
classify championship teams based on regular season data. From this, we show
that the most important factor in a team not winning a championship is that
team's opponent number of made three-point shots per game. This once again
implies that defensive characteristics are of great importance in not only
determining a team's playoff eligibility, but certainly, one can conclude that
a lack of perimeter defense negatively impacts a team's championship chances in
a given season. Further, it is shown that made two-point shots and defensive
rebounding are by far the most important factor in a team's chances at winning
a championship in a given season.


title: Stieltjes functions of finite order and hyperbolic monotonicity

abstract:
  A class of Stieltjes functions of finite type is introduced. These satisfy
Widder's conditions on the successive derivatives up to some finite order, and
are not necessarily smooth. We show that such functions have a unique integral
representation, along some generic kernel which is a truncated Laurent series
approximating the standard Stieltjes kernel. We then obtain a two-to-one
correspondence, via the logarithmic derivative, between these functions and a
subclass of hyperbolically monotone functions of finite type. This
correspondence generalizes a representation of HCM functions in terms of two
Stieltjes transforms earlier obtained by the first author.


title:
A partial Fourier transform method for a class of hypoelliptic
  Kolmogorov equations

abstract:
  We consider hypoelliptic Kolmogorov equations in $n+1$ spatial dimensions,
with $n\geq 1$, where the differential operator in the first $n$ spatial
variables featuring in the equation is second-order elliptic, and with respect
to the $(n+1)$st spatial variable the equation contains a pure transport term
only and is therefore first-order hyperbolic. If the two differential
operators, in the first $n$ and in the $(n+1)$st co-ordinate directions, do not
commute, we benefit from hypoelliptic regularization in time, and the solution
for $t>0$ is smooth even for a Dirac initial datum prescribed at $t=0$. We
study specifically the case where the coefficients depend only on the first $n$
variables. In that case, a Fourier transform in the last variable and standard
central finite difference approximation in the other variables can be applied
for the numerical solution. We prove second-order convergence in the spatial
mesh size for the model hypoelliptic equation $\frac{\partial u}{\partial t} +
x \frac{\partial u}{\partial y} = \frac{\partial^2 u}{\partial x^2}$ subject to
the initial condition $u(x,y,0) = \delta (x) \delta (y)$, with $(x,y) \in
\mathbb{R} \times\mathbb{R}$ and $t>0$, proposed by Kolmogorov, and for an
extension with $n=2$. We also demonstrate exponential convergence of an
approximation of the inverse Fourier transform based on the trapezium rule.
Lastly, we apply the method to a PDE arising in mathematical finance, which
models the distribution of the hedging error under a mis-specified derivative
pricing model.