title:
A new gene co-expression network analysis based on Core Structure
  Detection (CSD)

abstract:
  We propose a novel method to cluster gene networks. Based on a dissimilarity
built using correlation structures, we consider networks that connect all the
genes based on the strength of their dissimilarity. The large number of genes
require the use of the threshold to find sparse structures in the graph. in
this work, using the notion of graph coreness, we identify clusters of genes
which are central in the network. Then we estimate a network that has these
genes as main hubs. We use this new representation to identify biologically
meaningful clusters, and to highlight the importance of the nodes that compose
the core structures based on biological interpretations.


title: Envy-Free Cake-Cutting among Families

abstract:
  This paper extends the classic cake-cutting problem to a situation in which
the "cake" is divided among families. Each piece of cake is owned and used
simultaneously by all members of the family. A typical example of such a cake
is land. We examine three ways to assess the fairness of such a division, based
on the classic no-envy criterion: (a) Average envy-freeness means that for each
family, the average value of its share (averaged over all family members) is
weakly larger than the average value of any other share; (b) Unanimous
envy-freeness means that in each family, each member values the family's share
weakly more than any other share; (c) Democratic envy-freeness means that in
each family, at least half the members value the family's share weakly more
than any other share. We study each of these definitions from both an
existential and a computational perspective.


title:
Formation of dilute adhesion domains driven by weak elasticity-mediated
  interactions

abstract:
  Cell-cell adhesion is established by specific binding of receptor and ligand
proteins. The adhesion bonds attract each other and often aggregate into large
clusters that are central to many biological processes. One possible origin of
attractive interactions between adhesion bonds is the elastic response of the
membranes to their deformation by the bonds. Here, we analyze these
elasticity-mediated interactions using a novel mean-field approach. Analysis of
systems at different densities of bonds, $\phi$, reveals that the phase diagram
exhibits a nearly-universal behavior when the temperature $T$ is plotted vs.
the scaled density $x=\phi \xi^2$, where $\xi$ is the linear size of the
membrane's region affected by a single bond. The critical point $(\phi_c,T_c)$
is located at very low densities and slightly below $T_c$ we identify phase
coexistence between two low-density phases. Dense domains are observed only
when the height by which the bonds deform the membranes, $h_0$, is much larger
than their thermal roughness, $\Delta$, which occurs at very low temperatures
$T\ll T_c$. We conclude that the elasticity-mediated interactions are weak and
cannot be regarded as responsible for the formation of dense adhesion domains.
The weakness of the elasticity-mediated effect and its relevance to dilute
systems only can be attributed to the fact that the membrane's elastic energy
saturates in the semi-dilute regime, when the typical spacing between the bonds
$r\gtrsim \xi$, i.e., for $x\lesssim 1$. Therefore, at higher densities, only
the mixing entropy of the bonds (which favors uniform distributions) is
thermodynamically relevant. We discuss the implications of our results to the
question of immunological synapse formation, and demonstrate the
elasticity-mediated interactions may be involved in the aggregation of these
semi-dilute membrane domains.


abstract:
  We introduce a new class of processes for the evaluation of multivariate
equity derivatives. The proposed setting is well suited for the application of
the standard copula function theory to processes, rather than variables, and
easily enables to enforce the martingale pricing requirement. The martingale
condition is imposed in a general multidimensional Markov setting to which we
only add the restriction of no-Granger-causality of the increments
(Granger-independent increments). We call this class of processes GIMP (Granger
Independent Martingale Processes). The approach can also be extended to the
application of time change, under which the martingale restriction continues to
hold. Moreover, we show that the class of GIMP processes is closed under time
changing: if a Granger independent process is used as a multivariate stochastic
clock for the change of time of a GIMP process, the new process is also GIMP.


title:
Relaxation of strongly coupled electron and phonon fields after
  photoemission and high-energy part of ARPES spectra of cuprates

abstract:
  We consider photoemission from cuprate high-temperature superconductors
taking into account joint relaxation of strongly coupled fields: a field of
correlated electrons and phonon field. Such relaxation occurs in systems with
predominantly long-range electron-phonon interaction at sufficiently high
carrier concentration due to coexistence of autolocalized and delocalized
carriers. A simple method to calculate analytically a high-energy part of the
ARPES spectrum arising is proposed. The approach suggested yields all the
high-energy spectral features like broad bands of Gaussian shape and vertical
dispersion patterns being in good quantitative agreement with the experiments
at any doping with both types of carriers. Demonstrated coexistence of
autolocalized and delocalized carriers in cuprate superconductors is important
for understanding their transport and magnetic properties. Presence of
large-radius autolocalized carriers shown may be helpful in explanation of
charge ordering in doped cuprates.


title:
On the wave function renormalization for Wilson actions and their 1PI
  actions

abstract:
  We clarify the relation between the wave function renormalization for Wilson
actions and that for the 1PI actions in the exact renormalization group
formalism. Our study depends crucially on the use of two independent cutoff
functions for the Wilson actions. We relate our results to those obtained
previously by Bervillier, Rosten, and Osborn & Twigg.


title:
Polarization of radiation of electrons in highly turbulent magnetic
  fields

abstract:
  We study the polarization properties of the jitter and synchrotron radiation
produced by electrons in highly turbulent anisotropic magnetic fields. The net
polarization is provided by the geometry of the magnetic field the directions
of which are parallel to a certain plane. Such conditions may appear in the
relativistic shocks during the amplification of the magnetic field through the
so-called Weibel instability. While the polarization properties of the jitter
radiation allows extraction of direct information on the turbulence spectrum as
well as the geometry of magnetic field, the polarization of the synchrotron
radiation reflects the distribution of the magnetic field over its strength.
For the isotropic distribution of monoenergetic electrons, we found that the
degree of polarization of the synchrotron radiation is larger than the
polarization of the jitter radiation. For the power-law energy distribution of
electrons the relation between the degree of polarization of synchrotron and
jitter radiation depends on the spectral index of the distribution.


title: Robust spin transfer torque in antiferromagnetic tunnel junctions

abstract:
  We theoretically study the current-induced spin torque in antiferromagnetic
tunnel junctions, composed of two semi-infinite antiferromagnetic layers
separated by a tunnel barrier, in both clean and disordered regimes. We find
that the torque enabling the electrical manipulation of the N\'eel
antiferromagnetic order parameter is out of plane $\sim {\bf n}\times{\bf p}$,
while the torque competing with the antiferromagnetic exchange is in-plane
$\sim {\bf n}\times({\bf p}\times{\bf n})$. Here, ${\bf { p}}$ and ${\bf { n}}$
are the N\'eel order parameter direction of the reference and free layers,
respectively. Their bias dependence shows similar behavior as in ferromagnetic
tunnel junctions, the in-plane torque being mostly linear in bias while the
out-of-plane torque is quadratic. Most importantly, we find that the spin
transfer torque in antiferromagnetic tunnel junctions is much more robust
against disorder than in antiferromagnetic metallic spin-valves due to the
tunneling nature of spin transport.


title: The delamination of a growing elastic sheet with adhesion

abstract:
  We study the onset of delamination blisters in a growing elastic sheet
adhered to a flat stiff substrate. When the ends of the sheet are kept fixed,
its growth arouses residual stresses that lead to delamination. This
instability can be viewed as a discontinuous buckling between the complete
adhered solution and the buckled solution. We provide an analytic expression
for the critical deformation at which the instability occurs. We show that the
critical threshold scales with a single dimensionless parameter that comprises
information from the geometry of the sheet, the mechanical parameters of
material and the adhesive features of the substrate.


title: Discrete Balayage and Boundary Sandpile

abstract:
  We introduce a new lattice growth model, which we call boundary sandpile. The
model amounts to potential-theoretic redistribution of a given initial mass on
$\mathbb{Z}^d$ ($d\geq 2$) onto the boundary of an (a priori) unknown domain.
The latter evolves through sandpile dynamics, and has the property that the
mass on the boundary is forced to stay below a prescribed threshold. Since
finding the domain is part of the problem, the redistribution process is a
discrete model of a free boundary problem, whose continuum limit is yet to be
understood.
  We prove general results concerning our model. These include canonical
representation of the model in terms of the smallest super-solution among a
certain class of functions, uniform Lipschitz regularity of the scaled odometer
function, and hence the convergence of a subsequence of the odometer and the
visited sites, discrete symmetry properties, as well as directional
monotonicity of the odometer function. The latter (in part) implies the
Lipschitz regularity of the free boundary of the sandpile.
  As a direct application of some of the methods developed in this paper,
combined with earlier results on classical Abelian sandpile, we show that the
boundary of the scaling limit of Abelian sandpile is locally a Lipschitz graph.


title:
Globular clusters as tracers of the host galaxy mass distribution: the
  Fornax dSph test case

abstract:
  The Fornax dwarf spheroidal galaxy is the most massive satellites of the
Milky Way, claimed to be embedded in a huge dark matter halo, and the only
among the Milky Way satellites hosting five globular clusters. Interestingly,
their estimated masses, ages and positions seem hardly compatible with the
presence of a significant dark matter component, as expected in the $\Lambda$
CDM scheme. Indeed, if Fornax would have a CDM halo with a standard density
profile, all its globular clusters should have sunk to the galactic centre many
Gyr ago due to dynamical friction. Due to this, some authors proposed that the
most massive clusters may have formed out of Fornax and later tidally captured.
In this paper we investigate the past evolution of the Fornax GC system by
using both a recently developed, semi-analytical treatment of dynamical
friction and direct $N$-body simulations of the orbital evolution of the
globular clusters within Fornax and of Fornax galaxy around the Milky Way. Our
results suggest that an "in-situ" origin for all the clusters is likely if
their observed positions are close to their spatial ones and their orbits are
almost circular. Moreover, the Milky Way seems to accelerate the GC decay
reducing the decay time of $15\%$. Nevertheless, our results indicate that the
GCs survival probability exceeds $50\%$, even in the case of cuspy density
profiles. We conclude that more detailed data are required to shed light on the
Fornax dark matter content, to distinguish between a cuspy or a cored profile.


title:
Geometric control condition for the wave equation with a time-dependent
  observation domain

abstract:
  We characterize the observability property (and, by duality, the
controllability and the stabilization) of the wave equation on a Riemannian
manifold $\Omega,$ with or without boundary, where the observation (or control)
domain is time-varying. We provide a condition ensuring observability, in terms
of propagating bicharacteristics. This condition extends the well-known
geometric control condition established for fixed observation domains. As one
of the consequences, we prove that it is always possible to find a
time-dependent observation domain of arbitrarily small measure for which the
observability property holds. From a practical point of view, this means that
it is possible to reconstruct the solutions of the wave equation with only few
sensors (in the Lebesgue measure sense), at the price of moving the sensors in
the domain in an adequate way.We provide several illustrating examples, in
which the observationdomain is the rigid displacement in $\Omega$ of a fixed
domain, withspeed $v,$ showing that the observability property depends both on
$v$and on the wave speed. Despite the apparent simplicity of some of
ourexamples, the observability property can depend on nontrivial
arithmeticconsiderations.


title: New quantum number for the many-electron Dirac-Coulomb Hamiltonian

abstract:
  By breaking the spin symmetry in the relativistic domain, a powerful tool in
physical sciences was lost. In this work, we examine an alternative of spin
symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian.
We show that the square of many-electron operator $\mathcal{K}_+$, defined as a
sum of individual single-electron time-reversal (TR) operators, is a linear
Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a
finite Fock subspace. In contrast to the square of a standard unitary
many-electron TR operator $\mathcal{K}$, the $\mathcal{K}^2_+$ has a rich
eigenspectrum having potential to substitute spin symmetry in the relativistic
domain. We demonstrate that $\mathcal{K}_+$ is connected to $\mathcal{K}$
through an exponential mapping, in the same way as spin operators are mapped to
the spin rotational group. Consequently, we call $\mathcal{K}_+$ the generator
of the many-electron TR symmetry. By diagonalizing the operator
$\mathcal{K}^2_+$ in the basis of Kramers-restricted Slater determinants, we
introduce the relativistic variant of configuration state functions (CSF),
denoted as Kramers CSF. A new quantum number associated with $\mathcal{K}^2_+$
has potential to be used in many areas, for instance, (a) to design effective
spin Hamiltonians for electron spin resonance spectroscopy of heavy-element
containing systems; (b) to increase efficiency of methods for the solution of
many-electron problems in relativistic computational chemistry and physics; (c)
to define Kramers contamination in unrestricted density functional and
Hartree--Fock theory as a relativistic analog of the spin contamination in the
nonrelativistic domain.


title:
Quantitative assessment of drivers of recent climate variability: An
  information theoretic approach

abstract:
  Identification and quantification of possible drivers of recent climate
variability remain a challenging task. This important issue is addressed
adopting a non-parametric information theory technique, the Transfer Entropy
and its normalized variant. It distinctly quantifies actual information
exchanged along with the directional flow of information between any two
variables with no bearing on their common history or inputs, unlike
correlation, mutual information etc. Measurements of greenhouse gases, CO2,
CH4, and N2O; volcanic aerosols; solar activity: UV radiation, total solar
irradiance (TSI ) and cosmic ray flux (CR); El Nino Southern Oscillation (ENSO)
and Global Mean Temperature Anomaly (GMTA) made during 1984-2005 are utilized
to distinguish driving and responding climate signals. Estimates of their
relative contributions reveal that CO 2 (~24%), CH 4 (~19%) and volcanic
aerosols (~23%) are the primary contributors to the observed variations in
GMTA. While, UV (~9%) and ENSO (~12%) act as secondary drivers of variations in
the GMTA, the remaining play a marginal role in the observed recent climate
variability. Interestingly, ENSO and GMTA mutually drive each other at varied
time lags. This study assists future modelling efforts in climate science.


title: Markoff Surfaces and Strong Approximation: 1

abstract:
  We prove results pertaining to strong approximation for Markoff triples in
the case of prime moduli.


title: Thermal response of nonequilibrium RC-circuits

abstract:
  We analyze experimental data obtained from an electrical circuit having
components at different temperatures, showing how to predict its response to
temperature variations. This illustrates in detail how to utilize a recent
linear response theory for nonequilibrium overdamped stochastic systems. To
validate these results, we introduce a reweighting procedure that mimics the
actual realization of the perturbation and allows extracting the susceptibility
of the system from steady state data. This procedure is closely related to
other fluctuation-response relations based on the knowledge of the steady state
probability distribution. As an example, we show that the nonequilibrium heat
capacity in general does not correspond to the correlation between the energy
of the system and the heat flowing into it. Rather, also non-dissipative
aspects are relevant in the nonequilbrium fluctuation response relations.


title: NLO QCD corrections to off-shell ttj production at the LHC

abstract:
  A short summary of results for top-quark pair production in association with
a jet with NLO QCD off-shell effects at the LHC is given. The calculation is
based on the matrix element for the $pp \to e^+ \nu_e \mu^-\bar{\nu}_\mu
b\bar{b} j$ process. All quantum effects are properly accounted for, which
amounts to including all Feynman diagrams that result in this final state with
interference effects as well as non-zero top-quark width effects. Results for
total cross sections and a few differential distributions at the LHC Run1
energy of $\sqrt{s}=8$ TeV are presented. In addition, the size of top-quark
off-shell effects is quantified for the total cross section in presence of
rather inclusive cuts on all final states. Numerical results shown in this
proceedings have been obtained with the HELAC-NLO Monte Carlo program.


title:
Message Importance Measure and Its Application to Minority Subset
  Detection in Big Data

abstract:
  Message importance measure (MIM) is an important index to describe the
message importance in the scenario of big data. Similar to the Shannon Entropy
and Renyi Entropy, MIM is required to characterize the uncertainty of a random
process and some related statistical characteristics. Moreover, MIM also need
to highlight the importance of those events with relatively small occurring
probabilities, thereby is especially applicable to big data. In this paper, we
first define a parametric MIM measure from the viewpoint of information theory
and then investigate its properties. We also present a parameter selection
principle that provides answers to the minority subsets detection problem in
the statistical processing of big data.


title: Geometric transition in Non-perturbative Topological string

abstract:
  We study a geometric transition in non-perturbative topological string. We
consider two cases. One is the geometric transition from the closed topological
string on the local $\mathcal{B}_{3}$ to the closed topological string on the
resolved conifold. The other is the geometric transition from the closed
topological string on the local $\mathcal{B}_{3}$ to the open topological
string on the resolved conifold with a toric A-brane. We find that, in both
cases, the geometric transition can be applied for the non-perturbative
topological string. We also find the corrections of the value of K\"ahler
parameters at which the geometric transition occurs.


title:
Observability properties of the homogeneous wave equation on a closed
  manifold

abstract:
  We consider the wave equation on a closed Riemannian manifold. We observe the
restriction of the solutions to a measurable subset $\omega$ along a time
interval $[0, T]$ with $T>0$. It is well known that, if $\omega$ is open and if
the pair $(\omega,T)$ satisfies the Geometric Control Condition then an
observability inequality is satisfied, comparing the total energy of solutions
to their energy localized in $\omega \times (0, T)$. The observability constant
$C\_T({\omega})$ is then defined as the infimum over the set of all nontrivial
solutions of the wave equation of the ratio of localized energy of solutions
over their total energy. In this paper, we provide estimates of the
observability constant based on a low/high frequency splitting procedure
allowing us to derive general geometric conditions guaranteeing that the wave
equation is observable on a measurable subset $\omega$. We also establish that,
as $T\rightarrow+\infty$, the ratio $C\_T({\omega})/T$ converges to the minimum
of two quantities: the first one is of a spectral nature and involves the
Laplacian eigenfunctions, the second one is of a geometric nature and involves
the average time spent in $\omega$ by Riemannian geodesics.


title: On SL(3,$\mathbb C$)-representations of the Whitehead link group

abstract:
  We describe a family of representations in SL(3,$\mathbb C$) of the
fundamental group $\pi$ of the Whitehead link complement. These representations
are obtained by considering pairs of regular order three elements in
SL(3,$\mathbb C$) and can be seen as factorising through a quotient of $\pi$
defined by a certain exceptional Dehn surgery on the Whitehead link. Our main
result is that these representations form an algebraic component of the
SL(3,$\mathbb C$)-character variety of $\pi$.


title: Optimal Locally Repairable Systematic Codes Based on Packings

abstract:
  Locally repairable codes are desirable for distributed storage systems to
improve the repair efficiency. In this paper, we first build a bridge between
locally repairable code and packing. As an application of this bridge, some
optimal locally repairable codes can be obtained by packings, which gives
optimal locally repairable codes with flexible parameters.


title: Definition of Power Converters

abstract:
  The paper is intended to introduce power conversion principles and to define
common terms in the domain. The concepts of sources and switches are defined
and classified. From the basic laws of source interconnections, a generic
method of power converter synthesis is presented. Some examples illustrate this
systematic method. Finally, the commutation cell and soft commutation are
introduced and discussed.


title: Translating Scala Programs to Isabelle/HOL

abstract:
  We present a trustworthy connection between the Leon verification system and
the Isabelle proof assistant. Leon is a system for verifying functional Scala
programs. It uses a variety of automated theorem provers (ATPs) to check
verification conditions (VCs) stemming from the input program. Isabelle, on the
other hand, is an interactive theorem prover used to verify mathematical
specifications using its own input language Isabelle/Isar. Users specify
(inductive) definitions and write proofs about them manually, albeit with the
help of semi-automated tactics. The integration of these two systems allows us
to exploit Isabelle's rich standard library and give greater confidence
guarantees in the correctness of analysed programs.


title: Metallized Film Capacitor Lifetime Evaluation and Failure Mode Analysis

abstract:
  One of the main concerns for power electronic engineers regarding capacitors
is to predict their remaining lifetime in order to anticipate costly failures
or system unavailability. This may be achieved using a Weibull statistical law
combined with acceleration factors for the temperature, the voltage, and the
humidity. This paper discusses the different capacitor failure modes and their
effects and consequences.


title: Quantum duality under the theta-exact Seiberg-Witten map

abstract:
  We show that in the perturbative regime defined by the coupling constant, the
theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with
or without Supersymmetry-- gives an ordinary gauge theory which is, at the
quantum level, dual to the former. We do so by using the on-shell DeWitt
effective action and dimensional regularization. We explicitly compute the
one-loop two-point function contribution to the on-shell DeWitt effective
action of the ordinary U(1) theory furnished by the theta-exact Seiberg-Witten
map. We find that the non-local UV divergences found in the propagator in the
Feynman gauge all but disappear, so that they are not physically relevant. We
also show that the quadratic noncommutative IR divergences are gauge-fixing
independent and go away in the Supersymmetric version of the U(1) theory.


title:
On transformation formulae for Srivastava-Daoust type $q$-hypergeometric
  series

abstract:
  We present here the $q$-analogues of certain transformations or reduction
formulae for Srivastava-Daoust type double hypergeometric series. These
reduction formulae are derived by utilizing the extended Bailey's Transform
developed and studied by Joshi and Vyas [Int. J. Math. Sci., (12), 2005,
1909-1927]. A number of well-known $q$-hypergeometric transformations are also
obtained as special cases of our results.


title: A corrugated termination shock in pulsar wind nebulae?

abstract:
  Successful phenomenological models of pulsar wind nebulae assume efficient
dissipation of the Poynting flux of the magnetized electron-positron wind as
well as efficient acceleration of the pairs in the vicinity of the termination
shock, but how this is realized is not yet well understood. The present paper
suggests that the corrugation of the termination shock, at the onset of
non-linearity, may lead towards the desired phenomenology. Non-linear
corrugation of the termination shock would convert a fraction of order unity of
the incoming ordered magnetic field into downstream turbulence, slowing down
the flow to sub-relativistic velocities. The dissipation of turbulence would
further preheat the pair population on short length scales, close to
equipartition with the magnetic field, thereby reducing the initial high
magnetization to values of order unity. Furthermore, it is speculated that the
turbulence generated by the corrugation pattern may sustain a relativistic
Fermi process, accelerating particles close to the radiation reaction limit, as
observed in the Crab nebula. The required corrugation could be induced by the
fast magnetosonic modes of downstream nebular turbulence; but it could also be
produced by upstream turbulence, either carried by the wind or seeded in the
precursor by the accelerated particles themselves.


title:
Trail-Needs pseudopotentials in quantum Monte Carlo calculations with
  plane-wave/blip basis sets

abstract:
  We report a systematic analysis of the performance of a widely used set of
Dirac-Fock pseudopotentials for quantum Monte Carlo (QMC) calculations. We
study each atom in the periodic table from hydrogen (Z=1) to mercury (Z=80),
with the exception of the 4f elements (57 <= Z <= 70). We demonstrate that
ghost states are a potentially serious problem when plane-wave basis sets are
used in density functional theory (DFT) orbital-generation calculations, but
that this problem can be almost entirely eliminated by choosing the s channel
to be local in the DFT calculation; the d channel can then be chosen to be
local in subsequent QMC calculations, which generally leads to more accurate
results. We investigate the achievable energy variance per electron with
different levels of trial wave function and we determine appropriate plane-wave
cutoff energies for DFT calculations for each pseudopotential. We demonstrate
that the so-called "T-move" scheme in diffusion Monte Carlo is essential for
many elements. We investigate the optimal choice of spherical integration rule
for pseudopotential projectors in QMC calculations. The information reported
here will prove crucial in the planning and execution of QMC projects involving
beyond-first-row elements.


title: Computation of numerical semigroups by means of seeds

abstract:
  For the elements of a numerical semigroup which are larger than the Frobenius
number, we introduce the definition of, seed, by broadening the notion of
generator. This new concept allows us to explore the semigroup tree in an
alternative efficient way, since the seeds of each descendant can be easily
obtained from the seeds of its parent. The paper is devoted to presenting the
results which are related to this approach, leading to a new algorithm for
computing and counting the semigroups of a given genus.


title: Photon propagation in slowly varying electromagnetic fields

abstract:
  We study the effective theory of soft photons in slowly varying
electromagnetic background fields at one-loop order in QED. This is of
relevance for the study of all-optical signatures of quantum vacuum
nonlinearity in realistic electromagnetic background fields as provided by
high-intensity lasers. The central result derived in this article is a new
analytical expression for the photon polarization tensor in two linearly
polarized counter-propagating pulsed Gaussian laser beams. As we treat the peak
field strengths of both laser beams as free parameters this field configuration
can be considered as interpolating between the limiting cases of a purely
right- or left-moving laser beam (if one of the peak field strengths is set to
zero) and the standing-wave type scenario with two counter-propagating beams of
equal strength.


title:
Dynamic off-equilibrium transition in systems slowly driven across
  thermal first-order phase transitions

abstract:
  We study the off-equilibrium behavior of systems with short-range
interactions driven across a thermal first-order transition, where the dynamics
is exponentially slow. We consider a dynamics that starts in the high-T phase
at time t = t_i<0 and ends in in the low-T phase at t=t_f>0, with a
time-dependent temperature T(t)/T_c \approx 1 - t/t_s, where t_s is the
protocol time scale. A general off-equilibrium scaling (OS) behavior emerges in
the limit of large t_s. We check it at the first-order transition of the
two-dimensional q-state Potts model with q=10 and 20. The numerical results
show evidence of a dynamic transition, where the OS functions show a
spinodal-like singularity. Therefore, the general mean-field picture valid for
systems with long-range interactions is qualitatively recovered, provided the
time dependence is appropriately (logarithmically) rescaled.


title: Deleting digits

abstract:
  In 2000, J. Shallit introduced a special partial ordering of a subset of
positive integers and proposed the problem of finding the set of minimal
elements with respect to this ordering. Shallit himself solved this problem for
the set of primes and also for the set of composite numbers. In this
recreational mathematics note, we compute the minimal sets of a few other
arithmetically interesting sets and discuss questions on size and shape of
minimal sets in general.


title:
Desarguesian spreads and field reduction for elements of the semilinear
  group

abstract:
  The goal of this note is to create a sound framework for the interplay
between field reduction for finite projective spaces, the general semilinear
groups acting on the defining vector spaces and the projective semilinear
groups. This approach makes it possible to reprove a result of Dye on the
stabiliser in PGL of a Desarguesian spread in a more elementary way, and extend
it to P{\Gamma}L(n, q). Moreover a result of Drudge [5] relating Singer cycles
with Desarguesian spreads, as well as a result on subspreads (by Sheekey,
Rottey and Van de Voorde [19]) are reproven in a similar elementary way.
Finally, we try to use this approach to shed a light on Condition (A) of
Csajbok and Zanella, introduced in the study of linear sets [4].


title: Gamma-ray burst cosmology: Hubble diagram and star formation history

abstract:
  We briefly introduce the disadvantages for Type Ia supernovae (SNe Ia) as
standard candles to measure the Universe, and suggest Gamma-ray bursts (GRBs)
can serve as a powerful tool for probing the properties of high redshift
Universe. We use GRBs as distance indicators in constructing the Hubble diagram
at redshifts beyond the current reach of SNe Ia observations. Since the
progenitors of long GRBs are confirmed to be massive stars, they are deemed as
an effective approach to study the cosmic star formation rate (SFR). A detailed
representation of how to measure high-$z$ SFR using GRBs is presented.
Moreover, first stars can form only in structures that are suitably dense,
which can be parameterized by defining the minimum dark matter halo mass
$M_{\rm min}$. $M_{\rm min}$ must play a crucial role in star formation. The
association of long GRBs with the collapses of massive stars also indicates
that the GRB data can be applied to constrain the minimum halo mass $M_{\rm
min}$ and to investigate star formation in dark matter halos.


title:
On Sampling and Greedy MAP Inference of Constrained Determinantal Point
  Processes

abstract:
  Subset selection problems ask for a small, diverse yet representative subset
of the given data. When pairwise similarities are captured by a kernel, the
determinants of submatrices provide a measure of diversity or independence of
items within a subset. Matroid theory gives another notion of independence,
thus giving rise to optimization and sampling questions about Determinantal
Point Processes (DPPs) under matroid constraints. Partition constraints, as a
special case, arise naturally when incorporating additional labeling or
clustering information, besides the kernel, in DPPs. Finding the maximum
determinant submatrix under matroid constraints on its row/column indices has
been previously studied. However, the corresponding question of sampling from
DPPs under matroid constraints has been unresolved, beyond the simple
cardinality constrained k-DPPs. We give the first polynomial time algorithm to
sample exactly from DPPs under partition constraints, for any constant number
of partitions. We complement this by a complexity theoretic barrier that rules
out such a result under general matroid constraints. Our experiments indicate
that partition-constrained DPPs offer more flexibility and more diversity than
k-DPPs and their naive extensions, while being reasonably efficient in running
time. We also show that a simple greedy initialization followed by local search
gives improved approximation guarantees for the problem of MAP inference from
k- DPPs on well-conditioned kernels. Our experiments show that this improvement
is significant for larger values of k, supporting our theoretical result.


title: Spectrum of area in the Faddeev formulation of gravity

abstract:
  Faddeev formulation of general relativity (GR) is considered where the metric
is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use
of the field equations, this theory results in the usual GR. Earlier we have
proposed first-order representation of the minisuperspace model for the Faddeev
formulation where the tetrad fields are piecewise constant on the polytopes
like 4-simplices or, say, cuboids into which ${\rm R}^4$ can be decomposed, an
analogue of the Cartan-Weyl connection-type form of the Hilbert-Einstein action
in the usual continuum GR. In the Hamiltonian formalism, the tetrad bilinears
are canonically conjugate to the orthogonal connection matrices. We evaluate
the spectrum of the elementary areas, functions of the tetrad bilinears. The
spectrum is discrete and proportional to the Faddeev analog $\gamma_{\rm F}$ of
the Barbero-Immirzi parameter $\gamma$. The possibility of the tetrad and
metric discontinuities in the Faddeev gravity allows to consider any surface as
consisting of a set of virtually independent elementary areas and its spectrum
being the sum of the elementary spectra. Requiring consistency of the black
hole entropy calculations known in the literature we are able to estimate
$\gamma_{\rm F}$.


title: X-ray diagnostics of massive star winds

abstract:
  Nearly all types of massive stars with radiatively driven stellar winds are
X-ray sources that can be observed by the presently operating powerful X-ray
telescopes. In this review I briefly address recent advances in our
understanding of stellar winds obtained from X-ray observations. The winds of
OB dwarfs with subtypes later than O9V may be predominantly in a hot phase, and
X-ray observations offer the best window for their studies. The X-ray
properties of OB supergiants are largely determined by the effects of radiative
transfer in their clumped stellar winds. The recently suggested method to
directly measure mass-loss rates of O stars by fitting the shapes of X-ray
emission lines is considered but its validity cannot be confirmed. To obtain
robust quantitative information on stellar wind parameters from X-ray
spectroscopy, a multiwavelength analysis by means of stellar atmosphere models
is required. Independent groups are now performing such analyses with
encouraging results. Joint analyses of optical, UV, and X-ray spectra of OB
supergiants yield consistent mass-loss rates. Depending on the adopted clumping
parameters, the empirically derived mass-loss rates are comparable (within a
factor of a few) to those predicted by standard recipes (Vink et al. 2001). All
sufficiently studied O stars display variable X-ray emission that might be
related to corotating interaction regions in their winds. In the latest stages
of stellar evolution, single red supergiants and luminous blue variable stars
do not emit observable amounts of X-rays. On the other hand, nearly all types
of Wolf-Rayet (WR) stars are X-ray sources. X-ray spectroscopy allows a
sensitive probe of WR wind abundances and opacities.


title: Analysis of nulling phase functions suitable to image plane coronagraphy

abstract:
  Coronagraphy is a very efficient technique for identifying and characterizing
extra-solar planets orbiting in the habitable zone of their parent star,
especially when used in a space environment. An important family of
coronagraphs is based on phase plates located at an intermediate image plane of
the optical system, that spread the starlight outside the "Lyot" exit pupil
plane of the instrument. In this communication we present a set of candidate
phase functions generating a central null at the Lyot plane, and study how it
propagates to the image plane of the coronagraph. These functions include
linear azimuthal phase ramps (the well-known optical vortex), azimuthally
cosine-modulated phase profiles, and circular phase gratings. Numerical
simulations of the expected null depth, inner working angle, sensitivity to
pointing errors, effect of central obscuration located at the pupil or image
planes, and effective throughput including image mask and Lyot stop
transmissions are presented and discussed. The preliminary conclusion is that
azimuthal cosine functions appear as an interesting alternative to the
classical optical vortex of integer topological charge.


title:
Square selenene and tellurene: novel group VI elemental 2D semi-Dirac
  materials and topological insulators

abstract:
  With first principles calculations, we predict a novel stable 2D layered
structure for group VI elements Se and Te that we call square selenene and
square tellurene, respectively. They have chair-like buckled structures similar
to other layered materials such as silicene and germanene but with a square
unit cell rather than hexagonal. This special structure gives rise to
anisotropic band dispersions near the Fermi level that can be described by a
generalized semi-Dirac Hamiltonian. We show that the considerably large band
gap ($\sim$0.1 eV) opened by spin-orbit coupling makes square selenene and
tellurene topological insulators, hosting non-trivial edge states. Therefore,
square selenene and tellurene are promising materials for novel electronic and
spintronic applications. Finally, we show that this new type of 2D elemental
material can potentially be grown on proper substrates, such as a Au(100)
surface.


title: Power Converters and Power Quality

abstract:
  This paper discusses the subject of power quality for power converters. The
first part gives an overview of most of the common disturbances and power
quality issues in electrical networks for particle accelerators, and explains
their consequences for accelerator operation. The propagation of asymmetrical
network disturbances into a network is analysed. Quantitative parameters for
network disturbances in a typical network are presented, and immunity levels
for users' electrical equipment are proposed. The second part of this paper
discusses the technologies and strategies used in particle accelerator networks
for power quality improvement. Particular focus is given to networks supplying
loads with cycling active and reactive power.


title: Squarefree smooth numbers and Euclidean prime generators

abstract:
  We show that for each prime p > 7, every residue mod p can be represented by
a squarefree number with largest prime factor at most p. We give two
applications to recursive prime generators akin to the one Euclid used to prove
the infinitude of primes.


title: Introduction of spin-orbit interaction into graphene with hydrogenation

abstract:
  Introduction of spin-orbit interaction (SOI) into graphene with weak
hydrogenation ($\sim$0.1\%) by dissociation of hydrogen silsesquioxane resist
has been confirmed through the appearance of inverse spin Hall effect. The spin
current was produced by spin injection from permalloy electrodes excluding
non-spin relating experimental artifact.


title: Electromagnetic Compatibility of Power Converters

abstract:
  This paper describes the main challenges related to power converters in a
scientific environment. It proposes some methods of EMC analysis, design,
measurement, and EMC troubleshooting.


title:
Experimental demonstration of a crossed cubes nuller for coronagraphy
  and interferometry

abstract:
  In this communication we present the first experimental results obtained on
the Crossed-cubes nuller (CCN), that is a new type of Achromatic phase shifter
(APS) based on a pair of crossed beamsplitter cubes. We review the general
principle of the CCN, now restricted to two interferometric outputs for
achieving better performance, and describe the experimental apparatus developed
in our laboratory. It is cheap, compact, and easy to align. The results
demonstrate a high extinction rate in monochromatic light and confirm that the
device is insensitive to its polarization state. Finally, the first lessons
from the experiment are summarized and discussed in view of future space
missions searching for extra-solar planets located in the habitable zone,
either based on a coronagraphic telescope or a sparse-aperture nulling
interferometer


title: Rational curves on fibered Calabi-Yau manifolds

abstract:
  We show that a smooth projective complex manifold of dimension greater than
two endowed with an elliptic fiber space structure and with finite fundamental
group always contains a rational curve, provided its canonical bundle is
relatively trivial. As an application of this result, we prove that any
Calabi-Yau manifold that admits a fibration onto a curve whose general fibers
are abelian varieties always contains a rational curve.


title:
Modelling the thermal X-ray emission around the Galactic Centre from
  colliding Wolf-Rayet winds

abstract:
  The Galactic Centre is a hotbed of astrophysical activity, with the injection
of wind material from $\sim$30 massive Wolf-Rayet (WR) stars orbiting within 12
arcsec of the supermassive black hole (SMBH) playing an important role.
Hydrodynamic simulations of such colliding and accreting winds produce a
complex density and temperature structure of cold wind material shocking with
the ambient medium, creating a large reservoir of hot, X-ray-emitting gas. This
work aims to confront the 3 Ms of Chandra X-ray Visionary Program observations
of this diffuse emission by computing the X-ray emission from these
hydrodynamic simulations of the colliding WR winds, amid exploring a variety of
SMBH feedback mechanisms. The major success of the model is that it reproduces
the spectral shape from the 2-5 arcsec ring around the SMBH, where most of the
stellar wind material that is ultimately captured by Sgr A* is shock-heated and
thermalised. This naturally explains that the hot gas comes from colliding WR
winds, and that the wind speeds of these stars are, in general, well
constrained. The flux level of these spectra, as well as 12 $\times$
12-arcsec$^2$ images of 4-9 keV, shows that the X-ray flux is tied to the SMBH
feedback strength; stronger feedback clears out more hot gas, thereby
decreasing the thermal X-ray emission. The model in which Sgr A* produced an
intermediate-strength outflow during the last few centuries best matches the
observations to within about 10 per cent, showing that SMBH feedback is
required to interpret the X-ray emission in this region.


title: Moduli spaces of oriented Type A manifolds of dimension at least 3

abstract:
  We examine the moduli space of oriented locally homogeneous manifolds of Type
A which have non-degenerate symmetric Ricci tensor both in the setting of
manifolds with torsion and also in the torsion free setting where the dimension
is at least 3. These exhibit phenomena that is very different than in the case
of surfaces. In dimension 3, we determine all the possible symmetry groups in
the torsion free setting.


title: Chaotic provinces in the kingdom of the Red Queen

abstract:
  The interplay between parasites and their hosts is found in all kinds of
species and plays an important role in understanding the principles of
evolution and coevolution. Usually, the different genotypes of hosts and
parasites oscillate in their abundances. The well-established theory of
oscillatory Red Queen dynamics proposes an ongoing change in frequencies of the
different types within each species. So far, it is unclear in which way Red
Queen dynamics persists with more than two types of hosts and parasites. In our
analysis, an arbitrary number of types within two species are examined in a
deterministic framework with constant or changing population size. This general
framework allows for analytical solutions for internal fixed points and their
stability. For more than two species, apparently chaotic dynamics has been
reported. Here we show that even for two species, once more than two types are
considered per species, irregular dynamics in their frequencies can be observed
in the long run. The nature of the dynamics depends strongly on the initial
configuration of the system; the usual regular Red Queen oscillations are only
observed in some parts of the parameter region.


title: Switched Mode Four-Quadrant Power Converters

abstract:
  This paper was originally presented at CAS-2004, and was slightly modified
for CAS-2014. It presents a review of the key parameters that impact the design
choices for a true four-quadrant power converter, in the range 1-10 kW, mainly
based on switching mode converter topology. This paper will first describe the
state-of-the-art for this power converter family, giving the drawbacks and
advantages of different possible solutions. It will also present practical
results obtained from the CERN-designed converter. It will finally give some
important tips regarding critical phases like test one, when conducting a
project dealing with this type of power converter.


title: The bundle Laplacian on discrete tori

abstract:
  We prove an asymptotic formula for the determinant of the bundle Laplacian on
discrete $d$-dimensional tori as the number of vertices tends to infinity. This
determinant has a combinatorial interpretation in terms of cycle-rooted
spanning forests. We also establish a relation (in the limit) between the
spectral zeta function of a line bundle over a discrete torus, the spectral
zeta function of the infinite graph $\mathbb{Z}^d$ and the Epstein-Hurwitz zeta
function. The latter can be viewed as the spectral zeta function of the twisted
continuous torus which is the limit of the sequence of discrete tori.


title:
Reinterpreting the magnetoelectric coupling of polarizability tensors of
  infinite cylinders using symmetry: a simple TM/TE view

abstract:
  Recently, Strickland et al retrieved dynamic polarizabilities of infinitely
long wires at oblique incidence, reporting non-zero magnetoelectric coupling,
seemingly defying existing theorems which forbid this in centrosymmetric
scatterers. We reconcile this finding with existing symmetry restrictions on
microscopic polarizabilities using a property of line dipoles. This motivates a
reformulation of cylinder polarizability, yielding diagonal tensors that
decompose the response into TM and TE contributions, simplifying subsequent
treatment by homogenization theories. A transformation is derived between
Strickland et al.'s formulation and our reformulation, allowing magnetoelectric
coupling to be identified as the contrast between TM and TE responses, and
enabling simple geometric insights into all its scaling and symmetry
properties.


title:
Fault-tolerant verifiable blind quantum computing with logical state
  remote preparation

abstract:
  Verifiable blind quantum computing allows a client with poor quantum devices
to delegate universal quantum computing to a remote quantum server in such a
way that the client's privacy is protected and the honesty of the server is
verified. In existing protocols, the client has to send single-qubit states to
the server. These states might be decohered by the channel noise. Furthermore,
the client hides some "trap" qubits in the server's register so that the client
can detect the server's deviation. In reality, however, these trap qubits are
disturbed by imperfect operations by the server, which reduces the probability
that the client accepts the honest server. To solve these problems, we propose
a new gadget that allows the client to remotely prepare encoded logical
single-qubit states in the server's place. Importantly, in our fault-tolerant
verifiable blind quantum computing protocol, the client needs only the ability
of physical single-qubit measurements in $X$ and $Z$ bases.


title: Nash Social Welfare Approximation for Strategic Agents

abstract:
  The fair division of resources is an important age-old problem that has led
to a rich body of literature. At the center of this literature lies the
question of whether there exist fair mechanisms despite strategic behavior of
the agents. A fundamental objective function used for measuring fair outcomes
is the Nash social welfare, defined as the geometric mean of the agent
utilities. This objective function is maximized by widely known solution
concepts such as Nash bargaining and the competitive equilibrium with equal
incomes. In this work we focus on the question of (approximately) implementing
the Nash social welfare. The starting point of our analysis is the Fisher
market, a fundamental model of an economy, whose benchmark is precisely the
(weighted) Nash social welfare. We begin by studying two extreme classes of
valuations functions, namely perfect substitutes and perfect complements, and
find that for perfect substitutes, the Fisher market mechanism has a constant
approximation: at most 2 and at least e1e. However, for perfect complements,
the Fisher market does not work well, its bound degrading linearly with the
number of players.
  Strikingly, the Trading Post mechanism---an indirect market mechanism also
known as the Shapley-Shubik game---has significantly better performance than
the Fisher market on its own benchmark. Not only does Trading Post achieve an
approximation of 2 for perfect substitutes, but this bound holds for all
concave utilities and becomes arbitrarily close to optimal for Leontief
utilities (perfect complements), where it reaches $(1+\epsilon)$ for every
$\epsilon > 0$. Moreover, all the Nash equilibria of the Trading Post mechanism
are pure for all concave utilities and satisfy an important notion of fairness
known as proportionality.


title: Radio Frequency Solid State Amplifiers

abstract:
  Solid state amplifiers are being increasingly used instead of electronic
vacuum tubes to feed accelerating cavities with radio frequency power in the
100 kW range. Power is obtained from the combination of hundreds of transistor
amplifier modules. This paper summarizes a one hour lecture on solid state
amplifiers for accelerator applications.


title: The kite integral to all orders in terms of elliptic polylogarithms

abstract:
  We show that the Laurent series of the two-loop kite integral in
$D=4-2\varepsilon$ space-time dimensions can be expressed in each order of the
series expansion in terms of elliptic generalisations of (multiple)
polylogarithms. Using differential equations we present an iterative method to
compute any desired order. As an example, we give the first three orders
explicitly.


title: Long Pulse Modulators

abstract:
  Long pulse modulators are used to produce high-voltage, high-power pulses
with durations of several hundred microseconds up to some milliseconds. The
loads are one or more klystrons for producing RF power to accelerate the
particle beam in superconducting cavities. After years of development and
improvements in different institutes a variety of topologies exist, and are
presented. The basics of modulators, pulse requirements and klystrons are
explained. Additionally, the charging of internal energy storage will be
addressed. The outlook for future developments is given.


title: Radiation Risks and Mitigation in Electronic Systems

abstract:
  Electrical and electronic systems can be disturbed by radiation-induced
effects. In some cases, radiation-induced effects are of a low probability and
can be ignored; however, radiation effects must be considered when designing
systems that have a high mean time to failure requirement, an impact on
protection, and/or higher exposure to radiation. High-energy physics power
systems suffer from a combination of these effects: a high mean time to failure
is required, failure can impact on protection, and the proximity of systems to
accelerators increases the likelihood of radiation-induced events. This paper
presents the principal radiation-induced effects, and radiation environments
typical to high-energy physics. It outlines a procedure for designing and
validating radiation-tolerant systems using commercial off-the-shelf
components. The paper ends with a worked example of radiation-tolerant power
converter controls that are being developed for the Large Hadron Collider and
High Luminosity-Large Hadron Collider at CERN.


title: Risk and Machine Protection for Stored Magnetic and Beam Energies

abstract:
  Risk is a fundamental consideration when designing electronic systems. For
most systems a view of risk can assist in setting design objectives, whereas
both a qualitative and quantitative understanding of risk is mandatory when
considering protection systems. This paper gives an overview of the risks due
to stored magnetic and beam energies in high-energy physics, and shows how a
risk-based approach can be used to design new systems mitigating these risks,
using a lifecycle inspired by IEC 61508. Designing new systems in high-energy
physics can be challenging as new and novel techniques are difficult to
quantify and predict. This paper shows how the same lifecycle approach can be
used in reverse to analyse existing systems, following their operation and
first experiences.


title: On the steady-state behavior of a nonlinear power system model

abstract:
  In this article, we consider a dynamic model of a three-phase power system
including nonlinear generator dynamics, transmission line dynamics, and static
nonlinear loads. We define a synchronous steady-state behavior which
corresponds to the desired nominal operating point of a power system and obtain
necessary and sufficient conditions on the control inputs, load model, and
transmission network, under which the power system admits this steady-state
behavior. We arrive at a separation between the steady-state conditions of the
transmission network and generators, which allows us to recover the
steady-state of the entire power system solely from a prescribed operating
point of the transmission network. Moreover, we constructively obtain necessary
and sufficient steady-state conditions based on network balance equations
typically encountered in power flow analysis. Our analysis results in several
necessary conditions that any power system control strategy needs to satisfy.


title: Irreducibility of coherent states

abstract:
  We suggest an optical method which tests a nonclassical feature with a
coherent state input. The test is designed with a multiplexer of on/off
detectors and post-selection, adopting sub-binomiality as a nonclassical
feature, replacing Mandel's $Q$-factor. The sub-binomiality is shown negative
even for coherent states when the post-selection is made. However, we show that
it can be reproduced also by a classical model assuming a stochastic on/off
detectors. In the sense, the sub-binomiality is unlikely to identify the
genuine nonclassicality. On the other hand, we propose a coincident probability
of first two branches of the multiplexer and show that the classical model
fails to reproduce the quantum coincident probability. The failure of the
classical model results from the classical description of light, i.e. the
divisibility of intensity into parts no matter how small it is. Then our
optical test identifies a nonclassical feature of coherent states against the
classical divisibility of light, which we call irreducibility.


title: CUNet: A Compact Unsupervised Network for Image Classification

abstract:
  In this paper, we propose a compact network called CUNet (compact
unsupervised network) to counter the image classification challenge. Different
from the traditional convolutional neural networks learning filters by the
time-consuming stochastic gradient descent, CUNet learns the filter bank from
diverse image patches with the simple K-means, which significantly avoids the
requirement of scarce labeled training images, reduces the training
consumption, and maintains the high discriminative ability. Besides, we propose
a new pooling method named weighted pooling considering the different weight
values of adjacent neurons, which helps to improve the robustness to small
image distortions. In the output layer, CUNet integrates the feature maps
gained in the last hidden layer, and straightforwardly computes histograms in
non-overlapped blocks. To reduce feature redundancy, we implement the
max-pooling operation on adjacent blocks to select the most competitive
features. Comprehensive experiments are conducted to demonstrate the
state-of-the-art classification performances with CUNet on CIFAR-10, STL-10,
MNIST and Caltech101 benchmark datasets.


title: Thermal Design of Power Electronic Circuits

abstract:
  The heart of every switched mode converter consists of several switching
semiconductor elements. Due to their non-ideal behaviour there are ON state and
switching losses heating up the silicon chip. That heat must effectively be
transferred to the environment in order to prevent overheating or even
destruction of the element. For a cost-effective design, the semiconductors
should be operated close to their thermal limits. Unfortunately the chip
temperature cannot be measured directly. Therefore a detailed understanding of
how losses arise, including their quantitative estimation, is required.
Furthermore, the heat paths to the environment must be understood in detail.
This paper describes the main issues of loss generation and its transfer to the
environment and how it can be estimated by the help of datasheets and/or
experiments.


title:
Generalization of the Sherman-Morrison-Woodbury formula involving the
  Schur complement

abstract:
  Let $X\in\mathbb{C}^{m\times m}$ and $Y\in\mathbb{C}^{n\times n}$ be
nonsingular matrices, and let $N\in\mathbb{C}^{m\times n}$. Explicit
expressions for the Moore-Penrose inverses of $M=XNY$ and a two-by-two block
matrix, under appropriate conditions, have been established by
Castro-Gonz\'{a}lez et al. [Linear Algebra Appl. 471 (2015) 353-368]. Based on
these results, we derive a novel expression for the Moore-Penrose inverse of
$A+UV^{\ast}$ under suitable conditions, where $A\in \mathbb{C}^{m\times n}$,
$U\in \mathbb{C}^{m\times r}$, and $V\in \mathbb{C}^{n\times r}$. In
particular, if both $A$ and $I+V^{\ast}A^{-1}U$ are nonsingular matrices, our
expression reduces to the celebrated Sherman-Morrison-Woodbury formula.
Moreover, we extend our results to the bounded linear operators case.


title:
Construction of an invariant for integral homology 3-spheres via
  completed Kauffman bracket skein algebras

abstract:
  We construct an invariant $z (M) =1+a_1(A^4-1)+ a_2(A^4-1)^2+a_3(A^4-1)^3 +
\cdots \in \mathbb{Q} [[A^4-1]]= \mathbb{Q} [[A+1]]$ for an integral homology
$3$-sphere $M$ using a completed skein algebra and a Heegaard splitting. The
invariant $z(M)\mathrm{mod} ((A+1)^{n+1}) $ is a finite type invariant of order
$n$. In particular, $-a_1/6$ equals the Casson invariant. If $M$ is the
Poincar\'{e} homology 3-sphere, $(z(M))_{|A^4 =q} \mod (q+1)^{14} $ is the
Ohtsuki series for $M$.


title: Regulation Theory

abstract:
  This paper reviews the design of regulation loops for power converters. Power
converter control being a vast domain, it does not aim to be exhaustive. The
objective is to give a rapid overview of the main synthesis methods in both
continuous- and discrete-time domains.


title:
Bagged Boosted Trees for Classification of Ecological Momentary
  Assessment Data

abstract:
  Ecological Momentary Assessment (EMA) data is organized in multiple levels
(per-subject, per-day, etc.) and this particular structure should be taken into
account in machine learning algorithms used in EMA like decision trees and its
variants. We propose a new algorithm called BBT (standing for Bagged Boosted
Trees) that is enhanced by a over/under sampling method and can provide better
estimates for the conditional class probability function. Experimental results
on a real-world dataset show that BBT can benefit EMA data classification and
performance.


title:
Existence and Multiplicity of Nontrivial Weak Solutions for
  Kirchhoff-type Fractional $p$-Laplacian Equation

abstract:
  We discuss the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the
left and right fractional derivative operators. By using the mountain pass
theorem and the genus properties in critical point theory, we get some new
results on the existence and multiplicity of nontrivial weak solutions for such
Dirichlet problem.


title: High Precision Current Measurement for Power Converters

abstract:
  The accurate measurement of power converter currents is essential to
controlling and delivering stable and repeatable currents to magnets in
particle accelerators. This paper reviews the most commonly used devices for
the measurement of power converter currents and discusses test and calibration
methods.


title:
Solar Energetic Particle Event Associated with the 2012 July 23 Extreme
  Solar Storm

abstract:
  We study the solar energetic particle (SEP) event associated with the 2012
July 23 extreme solar storm, for which STEREO and the spacecraft at L1 provide
multi-point remote sensing and in situ observations. The extreme solar storm,
with a superfast shock and extremely enhanced ejecta magnetic fields observed
near 1 AU at STEREO A, was caused by the combination of successive coronal mass
ejections (CMEs). Meanwhile, energetic particles were observed by STEREO and
near-Earth spacecraft such as ACE and SOHO, suggestive of a wide longitudinal
spread of the particles at 1 AU. Combining the SEP observations with in situ
plasma and magnetic field measurements we investigate the longitudinal
distribution of the SEP event in connection with the associated shock and CMEs.
Our results underscore the complex magnetic configuration of the inner
heliosphere formed by solar eruptions. The examinations of particle
intensities, proton anisotropy distributions, element abundance ratios,
magnetic connectivity and spectra also give important clues for the particle
acceleration, transport and distribution.


title:
Ground State Solutions of Kirchhoff-type Fractional Dirichlet Problem
  with $p$-Laplacian

abstract:
  We consider the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the
left and right fractional derivative operators. By using the Nehari method in
critical point theory, we obtain the existence theorem of ground state
solutions for such Dirichlet problem.


title: Linear stability analysis of magnetized jets: the rotating case

abstract:
  We perform a linear stability analysis of magnetized rotating cylindrical jet
flows in the approximation of zero thermal pressure. We focus our analysis on
the effect of rotation on the current driven mode and on the unstable modes
introduced by rotation. We find that rotation has a stabilizing effect on the
current driven mode only for rotation velocities of the order of the Alfv\'en
velocity. Rotation introduces also a new unstable centrifugal buoyancy mode and
the "cold" magnetorotational instability. The first mode is analogous to the
Parker instability with the centrifugal force playing the role of effective
gravity. The magnetorotational instability can be present, but only in a very
limited region of the parameter space and is never dominant. The current driven
mode is characterized by large wavelenghts and is dominant at small values of
the rotational velocity, while the buoyancy mode becomes dominant as rotation
is increased and is characterized by small wavelenghts.


title: Diophantine equations in moderately many variables

abstract:
  We give upper bounds for the number of integral solutions of bounded height
to a system of equations $f_i(x_1,\ldots,x_n) = 0$, $1 \leq i \leq r$, where
the $f_i$ are polynomials with integer coefficients. The estimates are obtained
by generalising an approach due to Heath-Brown, using a certain $q$-analogue of
van der Corput's method, to the case of systems of polynomials of differing
degree. Our results apply for a wider range of $n$, in terms of the degrees of
the polynomials $f_i$, than bounds obtained with the circle method.


title:
Analogue to Digital and Digital to Analogue Converters (ADCs and DACs):
  A Review Update

abstract:
  This is a review paper updated from that presented for CAS 2004. Essentially,
since then, commercial components have continued to extend their performance
boundaries but the basic building blocks and the techniques for choosing the
best device and implementing it in a design have not changed. Analogue to
digital and digital to analogue converters are crucial components in the
continued drive to replace analogue circuitry with more controllable and less
costly digital processing. This paper discusses the technologies available to
perform in the likely measurement and control applications that arise within
accelerators. It covers much of the terminology and 'specmanship' together with
an application-oriented analysis of the realisable performance of the various
types. Finally, some hints and warnings on system integration problems are
given.


title: Indexing dif/2

abstract:
  Many Prolog programs are unnecessarily impure because of inadequate means to
express syntactic inequality. While the frequently provided built-in `dif/2` is
able to correctly describe expected answers, its direct use in programs often
leads to overly complex and inefficient definitions --- mainly due to the lack
of adequate indexing mechanisms. We propose to overcome these problems by using
a new predicate that subsumes both equality and inequality via reification.
Code complexity is reduced with a monotonic, higher-order if-then-else
construct based on `call/N`. For comparable correct uses of impure definitions,
our approach is as determinate and similarly efficient as its impure
counterparts.


title: Ordering states of Tsallis relative $\alpha$-entropies of coherence

abstract:
  In this paper, we study the ordering states with Tsallis relative
$\alpha$-entropies of coherence and $l_{1}$ norm of coherence for single-qubit
states. We show that any Tsallis relative $\alpha$-entropies of coherence and
$l_{1}$ norm of coherence give the same ordering for single-qubit pure states.
However, they don't generate the same ordering for some high dimensional pure
states, even though these states are pure. We also consider three special
Tsallis relative $\alpha$-entropies of coherence, such as $C_{1}$ ,$C_{2}$ and
$C_{\frac{1}{2}}$, and show any one of these three measures and $C_{l_{1}}$
will not generate the same ordering for single-qubit mixed states. Furthermore,
we find that any two of these three special measures generate different
ordering for single-qubit mixed states.


title:
Global existence for a 3D non-stationary Stokes flow with Coulomb's type
  friction boundary conditions

abstract:
  In this paper we study non stationary viscous incompressible fluid flows with
nonlinear boundary slip conditions given by a subdifferential property of
friction type. More precisely we assume that the tangential velocity vanishes
as long as the shear stress remains below a threshold, that may depend on the
time and the position variables but also on the stress tensor, allowing to
consider Coulomb's type friction laws. An existence and uniqueness theorem is
obtained first when the shear stress threshold is a data and sharp estimates
are derived for the velocity and pressure fields as well as for the stress
tensor. Then an existence result is proved for the non-local Coulomb's friction
case by using a successive approximation technique with respect to the shear
stress threshold.


title:
A covariant nonlocal Lagrangian for the description of the scalar kaonic
  sector

abstract:
  Mesons are extended objects, hence their interaction can be described by
utilizing form factors. At the Lagrangian level, one can use nonlocal
interaction terms. Here we describe two possible nonlocal Lagrangians leading
to a 3D form factor: the first one is simple but does not fulfill covariance
(if one insists on a 3D cutoff), the second extension is more involved but
guarantees covariance. Such form factors are useful when calculating mesonic
loops. As an important example, we discuss the scalar kaonic sector,
$I(J^{P})=\frac{1}{2}(0^{+})$. The Lagrangian contains a single scalar kaon
(the well-establish state $K_{0}^{\ast}(1430)$), but through loops
$K_{0}^{\ast}(800)$ emerges as a dynamically generated companion pole (which
disappears in the large-$N_{c}$ limit).


title: Controls and Interfaces

abstract:
  Reliable powering of accelerator magnets requires reliable power converters
and controls, able to meet the powering specifications in the long term. In
this paper, some of the issues that will challenge a power converter controls
engineer are discussed.


title: Power Converters for Accelerators

abstract:
  Particle accelerators use a great variety of power converters for energizing
their sub-systems; while the total number of power converters usually depends
on the size of the accelerator or combination of accelerators (including the
experimental setup), the characteristics of power converters depend on their
loads and on the particle physics requirements: this paper aims to provide an
overview of the magnet power converters in use in several facilities worldwide.


title: Putting it into Practice

abstract:
  This paper presents the latest trends in the powering of particle
accelerators. A series of solutions is proposed for responding to the
challenges of high performance machines. This paper covers the domains of
magnetic field uncertainty, power converter control, and energy saving. This
list is not exhaustive, but it does correspond to the latest innovations in the
field of powering particle accelerators.


title: Requirements for Power Converters

abstract:
  This paper introduces the requirements for power converters needed for
particle accelerators. It describes the role of power converters and the
challenges and constraints when powering magnets. The different circuit layouts
are presented as well as the operating cycles. The power converter control and
high precision definition are also introduced. This paper lists the key circuit
parameters to be taken into consideration to properly specify a power converter
that can be compiled in a functional specification.


title:
Multipair Two-way Half-Duplex Relaying with Massive Arrays and Imperfect
  CSI

abstract:
  We consider a two-way half-duplex relaying system where multiple pairs of
single antenna users exchange information assisted by a multi-antenna relay.
Taking into account the practical constraint of imperfect channel estimation,
we study the achievable sum spectral efficiency of the amplify-and-forward (AF)
and decode-and-forward (DF) protocols, assuming that the relay employs simple
maximum ratio processing. We derive an exact closed-form expression for the sum
spectral efficiency of the AF protocol and a large-scale approximation for the
sum spectral efficiency of the DF protocol when the number of relay antennas,
$M$, becomes sufficiently large. In addition, we study how the transmit power
scales with $M$ to maintain a desired quality-of-service. In particular, our
results show that by using a large number of relay antennas, the transmit
powers of the user, relay, and pilot symbol can be scaled down proportionally
to $1/M^\alpha$, $1/M^\beta$, and $1/M^\gamma$ for certain $\alpha$, $\beta$,
and $\gamma$, respectively. This elegant power scaling law reveals a
fundamental tradeoff between the transmit powers of the user/relay and pilot
symbol. Finally, capitalizing on the new expressions for the sum spectral
efficiency, novel power allocation schemes are designed to further improve the
sum spectral efficiency.


title: A Tverberg type theorem for matroids

abstract:
  Let b(M) denote the maximal number of disjoint bases in a matroid M. It is
shown that if M is a matroid of rank d+1, then for any continuous map f from
the matroidal complex M into the d-dimensional Euclidean space there exist t
\geq \sqrt{b(M)}/4 disjoint independent sets \sigma_1,\ldots,\sigma_t \in M
such that \bigcap_{i=1}^t f(\sigma_i) \neq \emptyset.


title:
Coupling rotational and translational motion via a continuous
  measurement in an optomechanical sphere

abstract:
  We consider a measurement of the position of a spot painted on the surface of
a trapped nano-optomechanical sphere. The measurement extracts information
about the position of the spot and in doing so measures a combination of the
orientation and position of the sphere. The quantum back-action of the
measurement entangles and correlates these two degrees of freedom. Such a
measurement is not available for atoms or ions, and provides a mechanism to
probe the quantum mechanical properties of trapped optomechanical spheres. In
performing simulations of this measurement process we also test a numerical
method introduced recently by Rouchon and collaborators for solving stochastic
master equations. This method guarantees the positivity of the density matrix
when the Lindblad operators for all simultaneous continuous measurements are
mutually commuting. We show that it is both simpler and far more efficient than
previous methods.


title:
Constraining High-Energy Cosmic Neutrino Sources: Implications and
  Prospects

abstract:
  We consider limits on the local ($z=0$) density ($n_0$) of extragalactic
neutrino sources set by the nondetection of steady high-energy neutrino sources
producing $\gtrsim50$ TeV muon multiplets in the present IceCube data, taking
into account the redshift evolution, luminosity function and neutrino spectrum
of the sources. We show that the lower limit depends moderately on source
spectra and strongly on redshift evolution. We find
$n_0\gtrsim{10}^{-8}-{10}^{-7}~{\rm Mpc}^{-3}$ for standard candle sources
evolving rapidly, $n_s\propto{(1+z)}^3$, and
$n_0\gtrsim{10}^{-6}-{10}^{-5}~{\rm Mpc}^{-3}$ for nonevolving sources. The
corresponding upper limits on their neutrino luminosity are $L_{{\nu_\mu}}^{\rm
eff}\lesssim10^{42}-10^{43}~{\rm erg}~{\rm s}^{-1}$ and $L_{{\nu_\mu}}^{\rm
eff}\lesssim10^{41}-10^{42}~{\rm erg}~{\rm s}^{-1}$, respectively. Applying
these results to a wide range of classes of potential sources, we show that
powerful blazar jets associated with active galactic nuclei are unlikely to be
the dominant sources. For almost all other steady candidate source classes
(including starbursts, radio galaxies, and galaxy clusters and groups), an
order of magnitude increase in the detector sensitivity at $\sim0.1-1$ PeV will
enable a detection (as point sources) of the few brightest objects. Such an
increase, which may be provided by next-generation detectors like IceCube-Gen2
and an upgraded KM3NET, can improve the limit on $n_0$ by more than two orders
of magnitude. Future gamma-ray observations (by Fermi, HAWC and CTA) will play
a key role in confirming the association of the neutrinos with their sources.


title:
Detecting fixed points of nonexpansive maps by illuminating the unit
  ball

abstract:
  We give necessary and sufficient conditions for a nonexpansive map on a
finite dimensional normed space to have a nonempty, bounded set of fixed
points. Among other results we show that if $f : V \rightarrow V$ is a
nonexpansive map on a finite dimensional normed space $V$, then the fixed point
set of $f$ is nonempty and bounded if and only if there exist $w_1, \ldots ,
w_m$ in $V$ such that $\{f(w_i) - w_i : i = 1, \ldots, m \}$ illuminates the
unit ball. This yields a numerical procedure for detecting fixed points of
nonexpansive maps on finite dimensional spaces. We also discuss applications of
this procedure to certain nonlinear eigenvalue problems arising in game theory
and mathematical biology.


title: Bifurcations in the elementary Desboves family

abstract:
  We give an example of a family of endomorphisms of $\mathbb P^2 (\mathbb C)$
whose Julia set depends continuously on the parameter and whose bifurcation
locus has non empty interior.


title: L\'evy Transport in Slab Geometry of Inhomogeneous Media

abstract:
  We present a physical example, where a fractional (both in space and time)
Schr\"odinger equation appears only as a formal effective description of
diffusive wave transport in complex inhomogeneous media. This description is a
result of the parabolic equation approximation that corresponds to the paraxial
small angle approximation of the fractional Helmholtz equation. The obtained
effective quantum dynamics is fractional in both space and time. As an example,
L\'evy flights in an infinite potential well are considered numerically. An
analytical expression for the effective wave function of the quantum dynamics
is obtained as well.


title: The chromatic number of the square of the 8-cube

abstract:
  A cube-like graph is a Cayley graph for the elementary abelian group of order
$2^n$. In studies of the chromatic number of cube-like graphs, the $k$th power
of the $n$-dimensional hypercube, $Q_n^k$, is frequently considered. This
coloring problem can be considered in the framework of coding theory, as the
graph $Q_n^k$ can be constructed with one vertex for each binary word of length
$n$ and edges between vertices exactly when the Hamming distance between the
corresponding words is at most $k$. Consequently, a proper coloring of $Q_n^k$
corresponds to a partition of the $n$-dimensional binary Hamming space into
codes with minimum distance at least $k+1$. The smallest open case, the
chromatic number of $Q_8^2$, is here settled by finding a 13-coloring. Such
13-colorings with specific symmetries are further classified.


title:
The deformation of symplectic critical surfaces in a K\"ahler
  surface-II---Compactness

abstract:
  In this paper we consider the compactness of $\beta$-symplectic critical
surfaces in a K\"ahler surface. Let $M$ be a compact K\"ahler surface and
$\Sigma_i\subset M$ be a sequence of closed $\beta_i$-symplectic critical
surfaces with $\beta_i\to\beta_0\in (0,\infty)$. Suppose the quantity
$\int_{\Sigma_i}\frac{1}{\cos^q\alpha_i}d\mu_i$ (for some $q>4$) and the genus
of $\Sigma_{i}$ are bounded, then there exists a finite set of points
${\mathcal S}\subset M$ and a subsequence $\Sigma_{i'}$ that converges
uniformly in the $C^l$ topology (for any $l<\infty$) on compact subsets of
$M\backslash {\mathcal S}$ to a $\beta_0$-symplectic critical surface
$\Sigma\subset M$, each connected component of $\Sigma\setminus {\mathcal S}$
can be extended smoothly across ${\mathcal S}$.


title:
Simultaneous band gap narrowing and carrier lifetime prolongation of
  organic-inorganic trihalide perovskites

abstract:
  The organic-inorganic hybrid lead trihalide perovskites have been emerging as
the most attractive photovoltaic material. As regulated by Shockley-Queisser
theory, a formidable materials science challenge for the next level improvement
requires further band gap narrowing for broader absorption in solar spectrum,
while retaining or even synergistically prolonging the carrier lifetime, a
critical factor responsible for attaining the near-band gap photovoltage.
Herein, by applying controllable hydrostatic pressure we have achieved
unprecedented simultaneous enhancement in both band gap narrowing and carrier
lifetime prolongation (up to 70~100% increase) under mild pressures at ~0.3
GPa. The pressure-induced modulation on pure hybrid perovskites without
introducing any adverse chemical or thermal effect clearly demonstrates the
importance of band edges on the photon-electron interaction and maps a
pioneering route towards a further boost in their photovoltaic performance.


title:
Dynamics of Hydrogen Bonds Coupling on the Specific DNA-Protein
  Interactions

abstract:
  We propose a dynamical model depicting the interactions between DNA and a
specific binding protein involving long range transmissions. The dynamics rely
on the coupling between Hydrogen bonds formed between DNA and protein and
between the base pairs because they account for site specificity of the
binding. We adopt the Morse potential with coupling terms to construct the
Hamiltonian. This model gives rise to a breather excitation, corresponding to
the DNA bubble formation, which propagates as the carrier of genetic
information. We examine the various kind of possible coupling dynamics and
suggest the model feasibility in depicting the renaturation or hybridization
processes.


title:
Unexpected superconductivity at nanoscale junctions made on the
  topological crystalline insulator Pb$_{0.6}$Sn$_{0.4}$Te

abstract:
  Discovery of exotic phases of matter from the topologically non-trivial
systems not only makes the research on topological materials more interesting
but also enriches our understanding of the fascinating physics of such
materials. Pb$_{0.6}$Sn$_{0.4}$Te was recently shown to be a topological
crystalline insulator. Here we show that by forming a mesoscopic point-contact
using a normal non-superconducting elemental metal on the surface of
Pb$_{0.6}$Sn$_{0.4}$Te a novel superconducting phase is created locally in a
confined region under the point-contact. This happens while the bulk of the
sample remains to be non-superconducting and the superconducting phase emerges
as a nano-droplet under the point-contact. The superconducting phase shows a
high transition temperature $T_c$ that varies for different point-contacts and
falls in a range between 3.7 K and 6.5 K. Therefore, this Letter presents the
discovery of a new superconducting phase on the surface of a topological
crystalline insulator and the discovery is expected to shed light on the
mechanism of induced superconductivity in topologically non-trivial systems in
general.


title:
Equation of state and hybrid star properties with the weakly interacting
  light U-boson in relativistic models

abstract:
  It has been a puzzle whether quarks may exist in the interior of massive
neutron stars, since the hadron-quark phase transition softens the equation of
state (EOS) and reduce the neutron star (NS) maximum mass very significantly.
In this work, we consider the light U-boson that increases the NS maximum mass
appreciably through its weak coupling to fermions. The inclusion of the U-boson
may thus allow the existence of the quark degrees of freedom in the interior of
large mass neutron stars. Unlike the consequence of the U-boson in hadronic
matter, the stiffening role of the U-boson in the hybrid EOS is not sensitive
to the choice of the hadron phase models. In addition, we have also
investigated the effect of the effective QCD correction on the hybrid EOS. This
correction may reduce the coupling strength of the U-boson that is needed to
satisfy NS maximum mass constraint. While the inclusion of the U-boson also
increases the NS radius significantly, we find that appropriate in-medium
effects of the U-boson may reduce the NS radii significantly, satisfying both
the NS radius and mass constraints well.


title:
Superconductivity in KCa$_2$Fe$_4$As$_4$F$_2$ with Separate Double
  Fe$_2$As$_2$ Layers

abstract:
  We report synthesis, crystal structure and physical properties of a quinary
iron-arsenide fluoride KCa$_2$Fe$_4$As$_4$F$_2$. The new compound crystallizes
in a body-centered tetragonal lattice (with space group $I4/mmm$, $a$ =
3.8684(2) {\AA}, c = 31.007(1) {\AA}, and $Z$ = 2), which contains double
Fe$_2$As$_2$ conducting layers separated by insulating Ca$_2$F$_2$ layers. Our
measurements of electrical resistivity, dc magnetic susceptibility and heat
capacity demonstrate bulk superconductivity at 33 K in
KCa$_2$Fe$_4$As$_4$F$_2$.


title: Fractional Order Optimal Control Model For Malaria Infection

abstract:
  We propose and study an optimal control model for malaria infection described
by system of fractional differential equations. The model is formulated in
terms of the left and right Caputo fractional derivatives. We determine the
necessary conditions for the optimality of the controlled dynamical system.The
forward-backward sweep method with generalized euler scheme is applied to
numerically compute the solutions of the optimality system.


title: Propagation of Electromagnetic Waves in Extremely Dense Media

abstract:
  We study the propagation of electromagnetic (EM) waves in extremely dense
exotic systems with very unique properties. These EM waves develop a
longitudinal component due to interactions with the medium. Renormalization
scheme of QED is used to understand the propagation of EM waves in both
longitudinal and transverse directions. The propagation of EM waves in a
quantum statistically treatable medium affects the properties of the medium
itself. The electric permittivity and the magnetic permeability of the medium
are modified and influence the related behavior of the medium. All the
electromagnetic properties of a medium become a function of temperature and
chemical potential of the medium. We study in detail the modifications of
electric permittivity and magnetic permeability and other related properties of
a medium in the superdense stellar objects.


title: High-Fidelity Hot Gates for Generic Spin-Resonator Systems

abstract:
  We propose and analyze a high-fidelity hot gate for generic spin-resonator
systems which allows for coherent spin-spin coupling, in the presence of a
thermally populated resonator mode. Our scheme is non-perturbative, applies to
a broad class of physical systems, including for example spins coupled to
circuit-QED and surface acoustic wave resonators as well as nanomechanical
oscillators, and can be implemented readily with state-of-the-art experimental
setups. We provide and numerically verify simple expressions for the fidelity
of creating maximally entangled states under realistic conditions.


title:
Uniqueness and stability of time and space-dependent conductivity in a
  hyperbolic cylindrical domain

abstract:
  This paper is devoted to the reconstruction of the time and space-dependent
coefficient in an infinite cylindrical hyperbolic domain. Using a local
Carleman estimate we prove the uniqueness and a H\"older stability in the
determining of the conductivity by a single measurement on the lateral
boundary. Our numerical examples show good reconstruction of the location and
contrast of the conductivity function in three dimensions.


title: Probing the hue of the stochastic magnetization dynamics

abstract:
  The Fokker--Planck equation describes the evolution of a probability
distribution towards equilibrium--the flow parameter is the equilibration time.
Assuming the distribution remains normalizable for all times, it is equivalent
to an open hierarchy of equations for the moments. Ways of closing this
hierarchy have been proposed; ways of explicitly solving the hierarchy
equations have received much less attention. In this paper we show that much
insight can be gained by mapping the Fokker--Planck equation to a Schr\"odinger
equation, where Planck's constant is identified with the diffusion coefficient.

categories: cond-mat.stat-mech math-ph math.MP physics.comp-ph


title:
High-redshift supernova rates measured with the gravitational telescope
  A1689

abstract:
  We present a ground-based near-infrared search for lensed supernovae behind
the massive cluster Abell 1689 at z=0.18, one of the most powerful
gravitational telescopes that nature provides. Our survey was based on
multi-epoch $J$-band observations with the HAWK-I instrument on VLT, with
supporting optical data from the Nordic Optical Telescope. Our search resulted
in the discovery of five high-redshift, $0.671<z<1.703$, photometrically
classified core-collapse supernovae with magnifications in the range $\Delta m$
= $-0.31$ to $-1.58$ mag, as calculated from lensing models in the literature.
Thanks to the power of the lensing cluster, the survey had the sensitivity to
detect supernovae up to very high-redshifts, $z$$\sim$$3$, albeit for a limited
region of space. We present a study of the core-collapse supernova rates for
$0.4\leq z< 2.9$, and find good agreement with both previous estimates, and the
predictions from the star formation history. During our survey, we also
discovered 2 type Ia supernovae in A1689 cluster members, which allowed us to
determine the cluster Ia rate to be $0.14^{+0.19}_{-0.09}\pm0.01$
$\rm{SNuB}$$\,h^2$ (SNuB$\equiv 10^{-12} \,\rm{SNe} \, L^{-1}_{\odot,B}
yr^{-1}$). The cluster rate normalized by the stellar mass is
$0.10^{+0.13}_{-0.06}\pm0.02$ in $\rm SNuM$$\,h^2$ (SNuM$\equiv 10^{-12}
\,\rm{SNe} \, M^{-1}_{\odot} yr^{-1}$). Furthermore, we explore the optimal
future survey for improving the core-collapse supernova rate measurements at
$z\gtrsim2$ using gravitational telescopes, as well as for the detections with
multiply lensed images, and find that the planned WFIRST space mission has
excellent prospects. Massive clusters can be used as gravitational telescopes
to significantly expand the survey range of supernova searches, with important
implications for the study of the high-$z$ transient universe.


title:
The spin-charge-family theory offers understanding of the triangle
  anomalies cancellation in the standard model

abstract:
  The standard model has for massless quarks and leptons "miraculously" no
triangle anomalies due to the fact that the sum of all possible traces $Tr
[\tau^{Ai}$$ \tau^{Bj}$$ \tau^{Ck}]$ --- where $\tau^{Ai}, \tau^{Bi}$ and
$\tau^{Ck}$ are the generators of one, of two or of three of the groups $SU(3),
SU(2)$ and $U(1)$ --- over the representations of one family of the left handed
fermions and anti-fermions (and separately of the right handed fermions and
anti-fermions), contributing to the triangle currents, is equal to zero. It is
demonstrated in this paper that this cancellation of the standard model
triangle anomaly follows straightforwardly if the $SO(3,1), SU(2), U(1)$ and $
SU(3)$ are the subgroups of the orthogonal group $SO(13,1)$, as it is in the
spin-charge-family theory. We comment on the $SO(10)$ anomaly cancellation,
which works if handedness and charges are related "by hand".


title: Swaption Prices in HJM model. Nonparametric fit

abstract:
  Closed form formulas for swaption prices in HJM model are derived. These
formulas are used for nonparametric fit of deterministic forward volatility. It
is demonstrated that this formula and non-parametric fit works very well and
can be used to identify arbitrage opportunities


title: L\'evy processes on a generalized fractal comb

abstract:
  Comb geometry, constituted of a backbone and fingers, is one of the most
simple paradigm of a two dimensional structure, where anomalous diffusion can
be realized in the framework of Markov processes. However, the intrinsic
properties of the structure can destroy this Markovian transport. These effects
can be described by the memory and spatial kernels. In particular, the fractal
structure of the fingers, which is controlled by the spatial kernel in both the
real and the Fourier spaces, leads to the L\'evy processes (L\'evy flights) and
superdiffusion. This generalization of the fractional diffusion is described by
the Riesz space fractional derivative. In the framework of this generalized
fractal comb model, L\'evy processes are considered, and exact solutions for
the probability distribution functions are obtained in terms of the Fox
$H$-function for a variety of the memory kernels, and the rate of the
superdiffusive spreading is studied by calculating the fractional moments. For
a special form of the memory kernels, we also observed a competition between
long rests and long jumps. Finally, we considered the fractional structure of
the fingers controlled by a Weierstrass function, which leads to the power-law
kernel in the Fourier space. It is a special case, when the second moment
exists for superdiffusion in this competition between long rests and long
jumps.


title: On the Jacobian conjecture in characteristic zero

abstract:
  We study the Jacobian conjecture for Keller maps
$f:X_0:=\mathbf{A}^n\rightarrow Y_0:=\mathbf{A}^n$ in characteristic $0$ and
attempt to prove it. We are quite aware of the fact that many people have tried
to prove the Jacobian conjecture before us and hence we stress that this
manuscripts is only an attempt. Our approach is to study the finiteness variety
$V_f \subset Y_0$ of $f$, the set of points of $Y_0$ over which $f$ fails to be
proper. We study a general component $V \subset V_f$ of this set by introducing
a suitable representation of $X_0$ which we call the $u-\gamma$ representation.
This view of $X_0$ has the advantage that it allows us to explicitly write down
the Jacobian matrix of $f$. We then turn our attention to the condition that
$|J(f)| = 1$, which we interpret as a partial differential equation in one
unknown function. We study the characteristics of this equation and prove that
the dynamics of this is strongly related to the ramification $K$ above $V$. We
then study the action of a certain cyclic Galois group induced by the
$u-\gamma$ action on these differential equations and prove that the growth of
the functions are bounded. Alternatively we prove the same result via a vector
field argument where we deduce that if $K > 0$ then the function $u^{-K}$ is in
fact an analytic function around $v \in V \subset Y_0$. This leads to $K = 1$
and as $\pi_1(Y_0 - S) \simeq \pi_1(Y_0)$ if $S$ is of codimension at least
two, the Jacobian conjecture follows immediately.


title:
Inferring hidden states in Langevin dynamics on large networks: Average
  case performance

abstract:
  We present average performance results for dynamical inference problems in
large networks, where a set of nodes is hidden while the time trajectories of
the others are observed. Examples of this scenario can occur in signal
transduction and gene regulation networks. We focus on the linear stochastic
dynamics of continuous variables interacting via random Gaussian couplings of
generic symmetry. We analyze the inference error, given by the variance of the
posterior distribution over hidden paths, in the thermodynamic limit and as a
function of the system parameters and the ratio {\alpha} between the number of
hidden and observed nodes. By applying Kalman filter recursions we find that
the posterior dynamics is governed by an "effective" drift that incorporates
the effect of the observations. We present two approaches for characterizing
the posterior variance that allow us to tackle, respectively, equilibrium and
nonequilibrium dynamics. The first appeals to Random Matrix Theory and reveals
average spectral properties of the inference error and typical posterior
relaxation times, the second is based on dynamical functionals and yields the
inference error as the solution of an algebraic equation.


title:
Magnetic-field-induced spin crossover of Y-doped
  Pr$_{0.7}$Ca$_{0.3}$CoO$_{3}$

abstract:
  The family of hole-doped Pr-based perovskite cobaltites,
Pr$_{0.5}$Ca$_{0.5}$CoO$_{3}$ and
(Pr$_{1-y}$RE$_{y}$)$_{0.3}$Ca$_{0.7}$CoO$_{3}$ (where RE is rare earth) has
recently been found to exhibit simultaneous metal-insulator, spin-state, and
valence transitions. We have investigated magnetic-field-induced phase
transitions of (Pr$_{1-y}$Y$_{y}$)$_{0.7}$Ca$_{0.3}$CoO$_{3}$ by means of
magnetization measurements at 4.2$-$100 K up to an ultrahigh magnetic field of
140 T with the chemical pressure varied by $y$ = 0.0625, 0.075, 0.1. The
observed magnetic-field-induced transitions were found to occur simultaneously
with the metal-insulator transitions up to 100 T. The obtained magnetic
field-temperature ($B$-$T$) phase diagram and magnetization curves are well
analyzed by a spin-crossover model of a single ion with interion interactions.
On the other hand, the chemical pressure dependence of the experimentally
obtained magnetization change during the phase transition disagrees with the
single ion model when approaching low temperatures. The significant $y$
dependence of the magnetization change at low temperatures may arise from the
itinerant magnetism of Co$^{3+}$ in the paramagnetic metallic phase, where the
chemical pressure enhances the exchange splitting by promoting the
double-exchange interaction. The observed $B$-$T$ phase diagrams of
(Pr$_{1-y}$Y$_{y}$)$_{0.7}$Ca$_{0.3}$CoO$_{3}$ are quite contrary to that of
LaCoO$_{3}$, indicating that in (Pr$_{1-y}$Y$_{y}$)$_{0.7}$Ca$_{0.3}$CoO$_{3}$
the high-field phase possesses higher entropy than the low-field phase, whereas
it is the other way around in LaCoO$_{3}$.