title:
Confining and repulsive potentials from effective non-Abelian gauge
  fields in graphene bilayers

abstract:
  We investigate the effect of shear and strain in graphene bilayers, under
conditions where the distortion of the lattice gives rise to a smooth
one-dimensional modulation in the stacking sequence of the bilayer. We show
that strain and shear produce characteristic Moir\'e patterns which can have
the same visual appearance on a large scale, but representing graphene bilayers
with quite different electronic properties. The different features in the
low-energy electronic bands can be ascribed to the effect of a fictitious
non-Abelian gauge field mimicking the smooth modulation of the stacking order.
Strained and sheared bilayers show a complementary behavior, which can be
understood from the fact that the non-Abelian gauge field acts as a repulsive
interaction in the former, expelling the electron density away from the
stacking domain walls, while behaving as a confining interaction leading to
localization of the electronic states in the sheared bilayers. In this latter
case, the presence of the effective gauge field explains the development of
almost flat low-energy bands, resembling the form of the zeroth Landau level
characteristic of a Dirac fermion field. The estimate of the gauge field
strength in those systems gives a magnitude of the order of several tens of
Tesla, implying a robust phenomenology that should be susceptible of being
observed in suitably distorted bilayer samples.


title: Some comments on the electrostatic forces between circular electrodes

abstract:
  We study the force between two circular electrodes in different
configurations. A formula analogous to Kelvin's formula for the spheres is
given in the case of equal disks held at the same potential and when one plate
is earthed. An expression for the force at short distance between two
arbitrarily charged disks is found: the generic case shows a logarithmic
repulsive force, also for disks carrying charges of opposite sign. Some
numerical computations support the results. A classification for the possible
behaviors of the force is proposed on the basis of a decomposition of the
capacitance matrix. It is shown that the forces depend strongly on the
dimensionality of the contact zone between the conductors. The analysis is
supported by a numerical computation carried for the case of two disks of
different radii.


title: The Asteroid Belt as a Relic From a Chaotic Early Solar System

abstract:
  The orbital structure of the asteroid belt holds a record of the Solar
System's dynamical history. The current belt only contains ${\rm \sim 10^{-3}}$
Earth masses yet the asteroids' orbits are dynamically excited, with a large
spread in eccentricity and inclination. In the context of models of terrestrial
planet formation, the belt may have been excited by Jupiter's orbital
migration. The terrestrial planets can also be reproduced without invoking a
migrating Jupiter; however, as it requires a severe mass deficit beyond Earth's
orbit, this model systematically under-excites the asteroid belt. Here we show
that the orbits of the asteroids may have been excited to their current state
if Jupiter and Saturn's early orbits were chaotic. Stochastic variations in the
gas giants' orbits cause resonances to continually jump across the main belt
and excite the asteroids' orbits on a timescale of tens of millions of years.
While hydrodynamical simulations show that the gas giants were likely in mean
motion resonance at the end of the gaseous disk phase, small perturbations
could have driven them into a chaotic but stable state. The gas giants' current
orbits were achieved later, during an instability in the outer Solar System.
Although it is well known that the present-day Solar System exhibits chaotic
behavior, our results suggest that the early Solar System may also have been
chaotic.


title:
Adhesion and non-linear rheology of adhesives with supramolecular
  crosslinking points

abstract:
  Soft supramolecular materials are promising for the design of innovative and
highly tunable adhesives. These materials are composed of polymer chains
functionalized by strongly interacting moieties, sometimes called "stickers".
In order to systematically investigate the effect of the presence of
associative groups on the debonding properties of a supramolecular adhesive, a
series of supramolecular model systems has been characterized by probe-tack
tests. These model materials, composed of linear and low dispersity
poly(butylacrylate) chains functionalized in the middle by a single tri-urea
sticker, are able to self-associate by six hydrogen bonds and range in
molecular weight (M n) between 5 and 85 kg/mol. The linear rheology and the
nanostructure of the same materials (called "PnBA3U") was the object of a
previous study 1,2. At room temperature, the association of polymers via
hydrogen bonds induces the formation of rod-like aggregates structured into
bundles for M n \textless{} 40kg/mol and the behavior of a soft elastic
material was observed (G'\textgreater{}\textgreater{}G "and G'~$\omega$ 0). For
higher M n , the filaments were randomly oriented and polymers displayed a
crossover towards viscous behavior although terminal relaxation was not reached
in the experimental frequency window. All these materials show however similar
adhesive properties characterized by a cohesive mode of failure and low
debonding energies (W adh \textless{}40J/m 2 for a debonding speed of
100$\mu$m/s). The debonding mechanisms observed during the adhesion tests have
been investigated in detail with an Image tools analysis developed by our group
3. The measure of the projected area covered by cavities growing in the
adhesive layer during debonding can be used to estimate the true stress in the
walls of the cavities and thus, to characterize the in-situ large strain
deformation of the thin layer during the adhesion test itself. This analysis
revealed in particular that the PnBA3U materials with M n \textless{} 40 kg/mol
soften very markedly at large deformation like yield stress fluids, explaining
the low adhesion energies measured for these viscoelastic gels. 2


title:
Designing nanostructures for interfacial phonon transport via Bayesian
  optimization

abstract:
  We demonstrate optimization of thermal conductance across nanostructures by
developing a method combining atomistic Green's function and Bayesian
optimization. With an aim to minimize and maximize the interfacial thermal
conductance (ITC) across Si-Si and Si-Ge interfaces by means of Si/Ge composite
interfacial structure, the method identifies the optimal structures from
calculations of only a few percent of the entire candidates (over 60,000
structures). The obtained optimal interfacial structures are non-intuitive and
impacting: the minimum-ITC structure is an aperiodic superlattice that realizes
50% reduction from the best periodic superlattice. The physical mechanism of
the minimum ITC can be understood in terms of crossover of the two effects on
phonon transport: as the layer thickness in superlattice increases, the impact
of Fabry-P\'erot interference increases, and the rate of reflection at the
layer-interfaces decreases. Aperiodic superlattice with spatial variation in
the layer thickness has a degree of freedom to realize optimal balance between
the above two competing mechanism. Furthermore, aperiodicity breaks the
constructive phonon interference between the interfaces inhibiting the coherent
phonon transport. The present work shows the effectiveness and advantage of
material informatics in designing nanostructures to control heat conduction,
which can be extended to other interfacial structures.


title:
Generalized Plasma Skimming Model for Cells and Drug Carriers in the
  Microvasculature

abstract:
  In microvascular transport, where both blood and drug carriers are involved,
plasma skimming has a key role on changing hematocrit level and drug carrier
concentration in capillary beds after continuous vessel bifurcation in the
microvasculature. While there have been numerous studies on modeling the plasma
skimming of blood, previous works lacked in consideration of its interaction
with drug carriers. In this paper, a generalized plasma skimming model is
suggested to predict the redistributions of both the cells and drug carriers at
each bifurcation. In order to examine its applicability, this new model was
applied on a single bifurcation system to predict the redistribution of red
blood cells and drug carriers. Furthermore, this model was tested at
microvascular network level under different plasma skimming conditions for
predicting the concentration of drug carriers. Based on these results, the
applicability of this generalized plasma skimming model is fully discussed and
future works along with the model's limitations are summarized.


title: On the tenth-order mock theta functions

abstract:
  Using properties of Appell-Lerch functions, we give insightful proofs for six
of Ramanujan's identities for the tenth-order mock theta functions.


title: Asymptotics of Symmetry in Matroids

abstract:
  We prove that asymptotically almost all matroids have a trivial automorphism
group, or an automorphism group generated by a single transposition.
Additionally, we show that asymptotically almost all sparse paving matroids
have a trivial automorphism group.


title: Interface Engineering in La0.67Sr0.33MnO3-SrTiO3 Heterostructures

abstract:
  Interface engineering is an extremely useful tool for systematically
investigating materials and the various ways materials interact with each
other. We describe different interface engineering strategies designed to
reveal the origin of the electric and magnetic dead-layer at La0.67Sr0.33MnO3
interfaces. La0.67Sr0.33MnO3 is a key example of a strongly correlated
peroskite oxide material in which a subtle balance of competing interactions
gives rise to a ferromagnetic metallic groundstate. This balance, however, is
easily disrupted at interfaces. We systematically vary the dopant profile, the
disorder and the oxygen octahedra rotations at the interface to investigate
which mechanism is responsible for the dead layer. We find that the magnetic
dead layer can be completely eliminated by compositional interface engineering
such that the polar discontinuity at the interface is removed. This, however,
leaves the electrical dead-layer largely intact. We find that deformations in
the oxygen octahedra network at the interface are the dominant cause for the
electrical dead layer.


title: Linear-quadratic optimal control under non-Markovian switching

abstract:
  We study a finite-dimensional continuous-time optimal control problem on
finite horizon for a controlled diffusion driven by Brownian motion, in the
linear-quadratic case. We admit stochastic coefficients, possibly depending on
an underlying independent marked point process, so that our model is general
enough to include controlled switching systems where the switching mechanism is
not required to be Markovian. The problem is solved by means of a Riccati
equation, which a backward stochastic differential equation driven by the
Bronwian motion and by the random measure associated to the marked point
process.


title:
Unconventional topological phase transition in two-dimensional systems
  with space-time inversion symmetry

abstract:
  We study a topological phase transition between a normal insulator and a
quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal
and two-fold rotation symmetries. Contrary to the case of ordinary
time-reversal invariant systems where a direct transition between two
insulators is generally predicted, we find that the topological phase
transition in systems with an additional two-fold rotation symmetry is mediated
by an emergent stable two-dimensional Weyl semimetal phase between two
insulators. Here the central role is played by the so-called space-time
inversion symmetry, the combination of time-reversal and two-fold rotation
symmetries, which guarantees the quantization of the Berry phase around a 2D
Weyl point even in the presence of strong spin-orbit coupling.
Pair-creation/pair-annihilation of Weyl points accompanying partner exchange
between different pairs induces a jump of a 2D $Z_{2}$ topological invariant
leading to a topological phase transition. According to our theory, the
topological phase transition in HgTe/CdTe quantum well structure is mediated by
a stable 2D Weyl semimetal phase since the quantum well, lacking inversion
symmetry intrinsically, has two-fold rotation about the growth direction.
Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior
within a small but finite interval in the thickness of HgTe layers between a
normal insulator and a quantum spin Hall insulator. We also propose that
few-layer black phosphorus under perpendicular electric field is another
candidate system to observe the unconventional topological phase transition
mechanism accompanied by emerging 2D Weyl semimetal phase protected by
space-time inversion symmetry.


title: On Effective Degrees of Freedom in the Early Universe

abstract:
  We explore the effective degrees of freedom in the early universe, from
before the electroweak scale at a few femtoseconds after the Big Bang, until
the last positrons disappeared a few minutes later. We first look at the
established concepts of effective degrees of freedom for energy density,
pressure and entropy density, and introduce effective degrees of freedom for
number density as well. We discuss what happens with particle species as their
temperature cools down from relativistic to semi- and non-relativistic
temperatures, and then annihilates completely. This will affect the pressure as
well as the entropy per particle. We also look at the transition from a
quark-gluon plasma to a hadron gas. Using a list of known hadrons, we use a
"cross-over" temperature of 214 MeV where the effective degrees of freedom for
a quark-gluon plasma equals that of a hadron gas.


title:
Equilibrium configurations of director in a planar nematic cell with one
  spatially modulated surface

abstract:
  We study two-dimensional equilibrium configurations of nematic liquid crystal
(NLC) director in a cell confined between two parallel surfaces: a planar
surface and a spatially modulated one. The relief of the modulated surface is
described by a smooth periodic sine-like function. The director easy axis
orientation is homeotropic at one of the bounding surfaces and is planar at the
other one. Strong NLC anchoring with both surfaces is assumed. We consider the
case where disclination lines occur in the bulk of NLC strictly above local
extrema of the modulated surface. These disclination lines run along the crests
and troughs of the relief waves. In the approximation of planar director
deformations we obtain analytical expressions describing a director
distribution in the bulk of the cell. Equilibrium distances from disclination
lines to the modulated surface are calculated and their dependences on the cell
thickness and the period and depth of the surface relief are studied. It is
shown that the distances from disclination lines to the modulated surface
decrease as the depth of the relief increases.


title:
All-sky search for time-integrated neutrino emission from astrophysical
  sources with 7 years of IceCube data

abstract:
  Since the recent detection of an astrophysical flux of high energy neutrinos,
the question of its origin has not yet fully been answered. Much of what is
known about this flux comes from a small event sample of high neutrino purity,
good energy resolution, but large angular uncertainties. In searches for
point-like sources, on the other hand, the best performance is given by using
large statistics and good angular reconstructions. Track-like muon events
produced in neutrino interactions satisfy these requirements. We present here
the results of searches for point-like sources with neutrinos using data
acquired by the IceCube detector over seven years from 2008--2015. The
discovery potential of the analysis in the northern sky is now significantly
below $E_\nu^2d\phi/dE_\nu=10^{-12}\:\mathrm{TeV\,cm^{-2}\,s^{-1}}$, on average
$38\%$ lower than the sensitivity of the previously published analysis of four
years exposure. No significant clustering of neutrinos above background
expectation was observed, and implications for prominent neutrino source
candidates are discussed.


title:
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem.
  V. Software for the continuous and discontinuous 1-row case

abstract:
  We present software for investigations with cut-generating functions in the
Gomory--Johnson model and extensions, implemented in the computer algebra
system SageMath.


title: Phase diagram of a graphene bilayer in the zero-energy Landau level

abstract:
  Bilayer graphene under a magnetic field has an octet of quasidegenerate
levels due to spin, valley, and orbital degeneracies. This zero-energy Landau
level is resolved into several incompressible states whose nature is still
elusive. We use a Hartree-Fock treatment of a realistic tight-binding four-band
model to understand the quantum ferromagnetism phenomena expected for integer
fillings of the octet levels. We include the exchange interaction with filled
Landau levels below the octet states. This Lamb-shift-like effect contributes
to the orbital splitting of the octet. We give phase diagrams as a function of
applied bias and magnetic field. Some of our findings are in agreement with
experiments. We discuss the possible appearance of phases with orbital
coherence.


title:
Radiation induced oscillating gap states of nonequilibrium
  two-dimensional superconductors

abstract:
  We study effects of infrared radiations on a two-dimensional BCS
superconductor coupled with a normal metal substrate through a tunneling
barrier. The phase transition conditions are analyzed by inspecting stability
of the system against perturbations of pairing potentials. We find an
oscillating gap phase with a frequency not directly related to the radiation
frequency but resulting from the asymmetry of electron density of states of the
system as well as the tunneling amplitude. When such a superconductor is in
contact with another superconductor, it will give rise to an unusual
alternating Josephson current.


title: A Differentiable Alternative to the Lasso Penalty

abstract:
  Regularized regression has become very popular nowadays, particularly on
high-dimensional problems where the addition of a penalty term to the
log-likelihood allows inference where traditional methods fail. A number of
penalties have been proposed in the literature, such as lasso, SCAD, ridge and
elastic net to name a few. Despite their advantages and remarkable performance
in rather extreme settings, where $p \gg n$, all these penalties, with the
exception of ridge, are non-differentiable at zero. This can be a limitation in
certain cases, such as computational efficiency of parameter estimation in
non-linear models or derivation of estimators of the degrees of freedom for
model selection criteria. With this paper, we provide the scientific community
with a differentiable penalty, which can be used in any situation, but
particularly where differentiability plays a key role. We show some desirable
features of this function and prove theoretical properties of the resulting
estimators within a regularized regression context. A simulation study and the
analysis of a real dataset show overall a good performance under different
scenarios. The method is implemented in the R package DLASSO freely available
from CRAN.


title: Hypercyclicity Properties of Commutator Maps

abstract:
  We investigate the hypercyclic properties of commutator maps acting on
separable ideals of operators. As the main result we prove the commutator map
induced by scalar multiples of the backward shift operator fails to be
hypercyclic on the space of compact operators on $\ell^2$. We also establish
some necessary conditions which identify large classes of operators that do not
induce hypercyclic commutator maps.


title: Triangular decomposition of skein algebras

abstract:
  By introducing a finer version of the Kauffman bracket skein algebra, we show
how to decompose the Kauffman bracket skein algebra of a surface into
elementary blocks corresponding to the triangles in an ideal triangulation of
the surface. The new skein algebra of an ideal triangle has a simple
presentation. This gives an easy proof of the existence of the quantum trace
map of Bonahon and Wong. We also explain the relation between our skein algebra
and the one defined by Muller, and use it to show that the quantum trace map
can be extended to the Muller skein algebra.


title:
A robust conservative mixed finite element method for compressible flow
  on pipe networks

abstract:
  We consider the numerical approximation of compressible flow in a pipe
network. Appropriate coupling conditions are formulated that allow us to derive
a variational characterization of solutions and to prove global balance laws
for the conservation of mass and energy on the whole network. This variational
principle, which is the basis of our further investigations, is amenable to a
conforming Galerkin approximation by mixed finite elements. The resulting
semi-discrete problems are well-posed and automatically inherit the global
conservation laws for mass and energy from the continuous level. We also
consider the subsequent discretization in time by a problem adapted implicit
time stepping scheme which leads to conservation of mass and a slight
dissipation of energy of the full discretization. The well-posedness of the
fully discrete scheme is established and a fixed-point iteration is proposed
for the solution of the nonlinear systems arising in every single time step.
Some computational results are presented for illustration of our theoretical
findings and for demonstration of the robustness and accuracy of the new
method.


title: Radiative heat transfer as a Landauer-B\"{u}ttiker problem

abstract:
  We study the radiative heat transfer between two semi-infinite half-spaces,
bounded by conductive surfaces in contact with vacuum. This setup is
interpreted as a four-terminal mesoscopic transport problem. The slabs and
interfaces are viewed as bosonic reservoirs, coupled perfectly to a scattering
center consisting of the two interfaces and vacuum. Using Rytov's fluctuational
electrodynamics and assuming Kirchhoff's circuital law, we calculate the heat
flow in each bath. This allows for explicit evaluation of a conductance matrix,
from which one readily verifies B\"{u}ttiker symmetry. Thus, radiative heat
transfer in layered media with conductive interfaces becomes a
Landauer-B\"{u}ttiker transport problem.


title:
The large-$m$ limit, and spin liquid correlations in kagome-like spin
  models

abstract:
  It is noted that the pair correlation matrix $\hat{\chi}$ of the nearest
neighbor Ising model on periodic three-dimensional ($d=3$) kagome-like lattices
of corner-sharing triangles can be calculated partially exactly. Specifically,
a macroscopic number $1/3 \, N+1$ out of $N$ eigenvalues of $\hat{\chi}$ are
degenerate at all temperatures $T$, and correspond to an eigenspace
$\mathbb{L}_{-}$ of $\hat{\chi}$, independent of $T$. Degeneracy of the
eigenvalues, and $\mathbb{L}_{-}$ are an exact result for a complex $d=3$
statistical physical model. It is further noted that the eigenvalue degeneracy
describing the same $\mathbb{L}_{-}$ is exact at all $T$ in an infinite spin
dimensionality $m$ limit of the isotropic $m$-vector approximation to the Ising
models. A peculiar match of the opposite $m=1$ and $m\rightarrow \infty$ limits
can be interpreted that the $m\rightarrow\infty$ considerations are exact for
$m=1$. It is not clear whether the match is coincidental. It is then speculated
that the exact eigenvalues degeneracy in $\mathbb{L}_{-}$ in the opposite
limits of $m$ can imply their quasi-degeneracy for intermediate $1 \leqslant m
< \infty$. For an anti-ferromagnetic nearest neighbor coupling, that renders
kagome-like models highly geometrically frustrated, these are spin states
largely from $\mathbb{L}_{-}$ that for $m\geqslant 2$ contribute to
$\hat{\chi}$ at low $T$. The $m\rightarrow\infty$ formulae can be thus
quantitatively correct in description of $\hat{\chi}$ and clarifying the role
of perturbations in kagome-like systems deep in the collective paramagnetic
regime. An exception may be an interval of $T$, where the order-by-disorder
mechanisms select sub-manifolds of $\mathbb{L}_{-}$.


title: Duality of ODE-determined norms

abstract:
  Recently a new approach to varying exponent $L^{p(\cdot)}$ space norms
employing weak solutions to first order ordinary differential equations was
initiated by the author. The duality of these ODE-determined $L^{p(\cdot)}$
spaces is analyzed here. The superreflexivity of these spaces is characterized
under the anticipated conditions. A universal space construction is also given
for these spaces.


title: Fermionic condensate and the Casimir effect in cosmic string spacetime

abstract:
  We investigate combined effects of nontrivial topology, induced by a cosmic
string, and boundaries on the fermionic condensate and the vacuum expectation
value (VEV) of the energy-momentum tensor for a massive fermionic field. As
geometry of boundaries we consider two plates perpendicular to the string axis
on which the field is constrained by the MIT bag boundary condition. By using
the Abel-Plana type summation formula, the VEVs in the region between the
plates are decomposed into the boundary-free and boundary-induced contributions
for general case of the planar angle deficit. The boundary-induced parts in
both the fermionic condensate and the energy-momentum tensor vanish on the
cosmic string. Fermionic condensate is positive near the string and negative al
large distances, whereas the vacuum energy density is negative everywhere. The
radial stress is equal to the energy density. For a massless field, the
boundary-induced contribution in the VEV of the energy-momentum tensor is
different from zero in the region between the plates only and it does not
depend on the coordinate along the string axis. In the region between the
plates and at large distances from the string, the decay of the topological
part is exponential for both massive and massless fields. This behavior is in
contrast to that for the VEV of the energy-momentum tensor in the boundary-free
geometry with the power law decay for a massless field. The vacuum pressure on
the plates is inhomogeneous and vanishes at the location of the string. The
corresponding Casimir forces are attractive.


title: SSPALS: a tool for studying positronium

abstract:
  Single-shot positron annihilation lifetime spectroscopy (SSPALS) is an
extremely useful tool for experiments involving the positronium atom (Ps). I
examine some of the methods that are typically employed to analyze lifetime
spectra, and use a Monte-Carlo simulation to explore the advantages and
limitations these have in laser spectroscopy experiments, such as
resonance-enhanced multiphoton ionization (REMPI) or the production of Rydberg
Ps.


title: Exploration Potential

abstract:
  We introduce exploration potential, a quantity that measures how much a
reinforcement learning agent has explored its environment class. In contrast to
information gain, exploration potential takes the problem's reward structure
into account. This leads to an exploration criterion that is both necessary and
sufficient for asymptotic optimality (learning to act optimally across the
entire environment class). Our experiments in multi-armed bandits use
exploration potential to illustrate how different algorithms make the tradeoff
between exploration and exploitation.


title:
An Analytical Study on the Synchronization of Strange Non-Chaotic
  Attractors

abstract:
  In this paper we present an analytical study on the synchronization dynamics
observed in unidirectionally-coupled quasiperiodically-forced systems that
exhibit Strange Non-chaotic Attractors (SNA) in their dynamics. The SNA
dynamics observed in the uncoupled system is studied analytically through phase
portraits and poincare maps. A difference system is obtained by coupling the
state equations of similar piecewise linear regions of the drive and response
systems. The mechanism of synchronization of the coupled system is realized
through the bifurcation of the eigenvalues in one of the piecewise linear
regions of the difference system. The analytical solutions obtained for the
normalized state equations in each piecewise linear region of the difference
system has been used to explain the synchronization dynamics though phase
portraits and timeseries analysis. The stability of the synchronized state is
confirmed through the Master Stability Function. An explicit analytical
solution explaining the synchronization of SNAs is reported in the literature
for the first time.


title:
Refined Structure of Metastable Ice XVII from Neutron Diffraction
  Measurements

abstract:
  The structure of the recently identified metastable ice XVII, obtained by
release of hydrogen from the C$_0$ D$_2$O-H$_2$ compound (filled ice), has been
accurately measured by neutron powder diffraction. The diffraction pattern is
indexed with a hexagonal cell and can be refined with space group $P6_122$ so
to obtain accurate values of the oxygen and deuterium positions. The values of
the lattice constants at three temperatures between 25 to 100 K are reported,
and their behavior is compared with that of ice Ih. Ice XVII is a porous solid
that, if exposed to H$_2$ gas, may adsorb a substantial amount of it.
Monitoring this effect at a constant temperature of 50 K, we have observed that
the two lattice constants show opposite behavior, $a$ increases and $c$
decreases, with the volume showing a linear increase. At temperatures higher
than 130 K the metastability of this form of porous ice is lost and the sample
transforms into ice Ih.


title:
Cavity-induced back-action in Purcell-enhanced photoemission of a single
  ion in an ultraviolet fiber-cavity

abstract:
  We study the behavior of a single laser-driven trapped ion inside a
microscopic optical Fabry-Perot cavity. In particular, we demonstrate a fiber
Fabry-Perot cavity operating on the principal $S_{1/2}\to P_{1/2}$ electric
dipole transition of an Yb$^+$ ion at $369\,$nm with an atom-ion coupling
strength of $g=2\pi\times 67(1)\,$MHz. We employ the cavity to study the
generation of single photons and observe cavity-induced back-action in the
Purcell-enhanced emission of photons. Tuning of the amplitude and phase of the
back-action allows us to enhance or suppress the total rate of photoemission
from the ion-cavity system.


title: Predicting the neutralino relic density in the MSSM more precisely

abstract:
  The dark matter relic density being a powerful observable to constrain models
of new physics, the recent experimental progress calls for more precise
theoretical predictions. On the particle physics side, improvements are to be
made in the calculation of the (co)annihilation cross-section of the dark
matter particle. We present the project DM@NLO which aims at calculating the
neutralino (co)annihilation cross-section in the MSSM including radiative
corrections in QCD. In the present document, we briefly review selected results
for different (co)annihilation processes. We then discuss the estimation of the
associated theory uncertainty obtained by varying the renormalization scale.
Finally, perspectives are discussed.


title:
Thermal Stability and Anisotropic Sublimation of Two-Dimensional
  Colloidal Bi2Te3 and Bi2Se3 Nanocrystals

abstract:
  The structural and compositional stabilities of two dimensional 2D Bi2Te3 and
Bi2Se3 nanocrystals, produced by both colloidal synthesis and by liquid phase
exfoliation, were studied by in situ transmission electron microscopy TEM
during annealing at temperatures between 350 and 500 C. The sublimation process
induced by annealing is structurally and chemically anisotropic and takes place
through the preferential dismantling of the prismatic 011-0 type planes, and
through the preferential sublimation of Te or Se.


title: Sturm's operator for scalar weight in arbitrary genus

abstract:
  In contrast to the wellknown cases of large weights, Sturm's operator does
not realize the holomorphic projection operator for lower weights. We prove its
failure for arbitrary Siegel genus $m\geq 2$ and scalar weight $\kappa=m+1$.
This generalizes a result for genus two in [4].


title: Stamp processing with examplar features

abstract:
  Document digitization is becoming increasingly crucial. In this work, we
propose a shape based approach for automatic stamp verification/detection in
document images using an unsupervised feature learning. Given a small set of
training images, our algorithm learns an appropriate shape representation using
an unsupervised clustering. Experimental results demonstrate the effectiveness
of our framework in challenging scenarios.


title: State access patterns in embarrassingly parallel computations

abstract:
  We introduce a set of state access patterns suitable for managing state in
embarrassingly parallel computations on streams. The state access patterns are
useful to model typical stream parallel applications. We present a
classification of the patterns according to the extent and way in which the
state is modified. We define precisely the state access patterns and discuss
possible implementation schemas, performances and possibilities to manage
adaptivity (parallelism degree) in the patterns. We present experimental
results relative to an implementations on top of the structured parallel
programming framework FastFlow that demonstrate the feasibility and efficiency
of the proposed access patterns.


title:
Explaining the emergence of echo chambers on social media: the role of
  ideology and extremism

abstract:
  The emergence of politically driven divisions in online discussion networks
has attracted a wealth of literature, but also one which has thus far been
largely limited to single country studies. Hence whilst there is good evidence
that these networks do divide and fragment into what are often described as
"echo chambers", we know little about the factors which might explain this
division or make networks more or less fragmented, as studies have been limited
to a small number of political groupings with limited possibilities for
systematic comparison.
  This paper seeks to remedy this deficit, by providing a systematic large
scale study of fragmentation on Twitter which considers discussion networks
surrounding 90 different political parties in 23 different countries. It shows
that political party groupings which are further apart in ideological terms
interact less, and that individuals and parties which sit at the extreme ends
of the ideological scale are particularly likely to form echo chambers. Indeed,
exchanges between centrist parties who sit on different sides of the left-right
divide are more likely than communication between centrist and extremist
parties who are, notionally, from the same ideological wing. In light of the
results, theory about exposure to different ideological viewpoints online is
discussed and enhanced.


title:
Tracer diffusion in a sea of polymers with binding zones: mobile vs
  frozen traps

abstract:
  We use molecular dynamics simulations to investigate the tracer diffusion in
a sea of polymers with specific binding zones for the tracer. These binding
zones act as traps. Our simulations show that the tracer can undergo normal yet
non-Gaussian diffusion under certain circumstances, e.g, when the polymers with
traps are frozen in space and the volume fraction and the binding strength of
the traps are moderate. In this case, as the tracer moves, it experiences a
heterogeneous environment and exhibits confined continuous time random walk
(CTRW) like motion resulting a non-Gaussian behavior. Also the long time
dynamics becomes subdiffusive as the number or the binding strength of the
traps increases. However, if the polymers are mobile then the tracer dynamics
is Gaussian but could be normal or subdiffusive depending on the number and the
binding strength of the traps. In addition, with increasing binding strength
and the number of the polymer traps, the probability of the tracer being
trapped increases. On the other hand, removing the binding zones does not
result trapping, even at comparatively high crowding. Our simulations also show
that the trapping probability increases with the increasing size of the tracer
and for a bigger tracer with the frozen polymer background the dynamics is only
weakly non-Gaussian but highly subdiffusive. Our observations are in the same
spirit as found in many recent experiments on tracer diffusion in polymeric
materials and questions the validity of Gaussian theory to describe diffusion
in crowded environment in general.


title: Homology of the three flag Hilbert scheme

abstract:
  We prove the existence of an affine paving for the three-step flag Hilbert
scheme $$ \text{Hilb}^{n, n+1, n+2}(0) := \left\{\mathbb{C}[[x,y]]\supset
I_n\supset I_{n+1}\supset I_{n+2}: I_i \,\,\text{ ideals with }
\text{dim}_{\mathbb{C}} {\mathbb{C}[x,y]}/{I_i} = i \right\} $$ of
0-dimensional subschemes that are supported at the origin of $\mathbb{C}^2$.
This is done by showing that the space stratifies in smooth subvarieties, the
Hilbert-Samuel's strata, each of which has an affine paving with cells of known
dimension, indexed by marked Young diagrams. The affine pavings of the
Hilbert-Samuel's strata allow us to prove that the Poincar\'{e} polynomials for
$\text{Hilb}^{n,n+1, n+2}(0)$ satisfy:$$ \sum_{n\geq 0}
P_q\left(\text{Hilb}^{n,n+1, n+2}(0)\right) z^n =
\frac{q+1}{(1-zq)(1-z^2q^2)}\,\, \prod_{k\geq 1} \frac{1}{1-z^kq^{k-1}}. $$ In
the process of proving this formula we relate combinatorially the homology of
our spaces with that of known subspaces of $\text{Hilb}^{n+1, n+3}(0)$. As a
corollary we find an affine paving and a formula for the generating function of
the Poincar\'{e} polynomials of $\text{Hilb}^{n, n+2}(0)$ for all $n\in
\mathbb{N}$.


title: Fabry-P\'erot interference in a triple-gated quantum point contact

abstract:
  We demonstrated that a triple-gated GaAs quantum point contact, which has an
additional surface gate between a pair of split gates to strengthen the lateral
confinement, produces the well-defined quantized conductance and
Fabry-P\'erot-type (FP-type) oscillations on it even using a relatively low
mobility wafer. A one-dimensional phenomenological model potential was
developed to explain the oscillatory behavior. By combining the model
calculations and dc bias spectroscopy, we obtained detailed information about
the energy scales of the oscillatory structures. The relationships between the
FP-type oscillations and the anomaly below the first plateau will be addressed.


title:
Quantum De Moivre-Laplace theorem for noninteracting indistinguishable
  particles

abstract:
  The asymptotic form of the average probability to count $N$ indistinguishable
identical particles in a small number $r \ll N$ of binned-together output ports
of a $M$-port Haar-random unitary network, proposed recently in
\textit{Scientific Reports} \textbf{7}, 31 (2017) in a heuristic manner with
some numerical confirmation, is presented with the mathematical rigor and
generalized to an arbitrary (mixed) input state of $N$ indistinguishable
particles. It is shown that, both in the classical (distinguishable particles)
and quantum (indistinguishable particles) cases, the average counting
probability into $r$ output bins factorizes into a product of $r-1$ counting
probabilities into two bins. This fact relates the asymptotic Gaussian law to
the de Moivre-Laplace theorem in the classical case and similarly in the
quantum case where an analogous theorem can be stated. The results have
applications to the setups where randomness plays a key role, such as the
multiphoton propagation in disordered media and the scattershot Boson Sampling.

categories: quant-ph cond-mat.other math-ph math.MP physics.atom-ph


title: Optimising self-assembly through time-dependent interactions

abstract:
  We demonstrate a simple method by which time-dependent interactions can be
exploited to improve self-assembly in colloidal systems. We apply this method
to two systems: a model colloid with short-ranged attractive potentials that
undergoes crystallisation, and a schematic model of cluster growth. The method
is based on initially strong bonds between particles, to accelerate nucleation,
followed by a stage with weaker bonds, to promote growth of high-quality
assembled structures. We track the growth of clusters during assembly, which
reveals insight into effects of multiple nucleation events, and of competition
between the growth of clusters with different properties.


title:
Optimal Channel Shortener Design for Reduced-State Soft-Output Viterbi
  Equalizer in Single-Carrier Systems

abstract:
  We consider optimal channel shortener design for reduced-state soft-output
Viterbi equalizer (RS-SOVE) in single-carrier (SC) systems. To use RS-SOVE,
three receiver filters need to be designed: a prefilter, a target response and
a feedback filter. The collection of these three filters are commonly referred
to as the \lq\lq{}channel shortener\rq\rq{}. Conventionally, the channel
shortener is designed to transform an intersymbol interference (ISI) channel
into an equivalent minimum-phase equivalent form. In this paper, we design the
channel shortener to maximize a mutual information lower bound (MILB) based on
a mismatched detection model. By taking the decision-feedback quality in the
RS-SOVE into consideration, the prefilter and feedback filter are found in
closed forms, while the target response is optimized via a gradient-ascending
approach with the gradient explicitly derived. The information theoretical
properties of the proposed channel shortener are analyzed. Moreover, we show
through numerical results that, the proposed channel shortener design achieves
superior detection performance compared to previous channel shortener designs
at medium and high code-rates.


title:
Decoration of exfoliated black phosphorus with nickel nanoparticles and
  application in catalysis

abstract:
  Nickel nanoparticles were dispersed on the surface of exfoliated black
phosphorus and the resulting nanohybrid Ni/2DBP showed an improved stability
respect to pristine 2D BP when kept in ambient conditions in the darkness.
Ni/2DBP was applied as catalyst in the semihydrogenation of phenylacetylene and
exhibited high conversion and selectivity towards styrene. These features were
preserved after recycling tests revealing the high stability of the nanohybrid.


title: Convex separation from convex optimization for large-scale problems

abstract:
  We present a scheme, based on Gilbert's algorithm for quadratic minimization
[SIAM J. Contrl., vol. 4, pp. 61-80, 1966], to prove separation between a point
and an arbitrary convex set $S\subset\mathbb{R}^{n}$ via calls to an oracle
able to perform linear optimizations over $S$. Compared to other methods, our
scheme has almost negligible memory requirements and the number of calls to the
optimization oracle does not depend on the dimensionality $n$ of the underlying
space. We study the speed of convergence of the scheme under different promises
on the shape of the set $S$ and/or the location of the point, validating the
accuracy of our theoretical bounds with numerical examples. Finally, we present
some applications of the scheme in quantum information theory. There we find
that our algorithm out-performs existing linear programming methods for certain
large scale problems, allowing us to certify nonlocality in bipartite scenarios
with upto $42$ measurement settings. We apply the algorithm to upper bound the
visibility of two-qubit Werner states, hence improving known lower bounds on
Grothendieck's constant $K_G(3)$. Similarly, we compute new upper bounds on the
visibility of GHZ states and on the steerability limit of Werner states for a
fixed number of measurement settings.


title: Spatial Patterns of Wind Speed Distributions in Switzerland

abstract:
  This paper presents an initial exploration of high frequency records of
extreme wind speed in two steps. The first consists in finding the suitable
extreme distribution for $120$ measuring stations in Switzerland, by comparing
three known distributions: Weibull, Gamma, and Generalized extreme value. This
comparison serves as a basis for the second step which applies a spatial
modelling by using Extreme Learning Machine. The aim is to model distribution
parameters by employing a high dimensional input space of topographical
information. The knowledge of probability distribution gives a comprehensive
information and a global overview of wind phenomena. Through this study, a
flexible and a simple modelling approach is presented, which can be generalized
to almost extreme environmental data for risk assessment and to model renewable
energy.


title: The bounded cohomology of SL_2 over local fields and S-integers

abstract:
  It is proved that the continuous bounded cohomology of SL_2(k) vanishes in
all positive degrees whenever k is a non-Archimedean local field. This holds
more generally for boundary-transitive groups of tree automorphisms and implies
low degree vanishing for SL_2 over S-integers.


title:
Optimal phase synchronization in networks of phase-coherent chaotic
  oscillators

abstract:
  We investigate the existence of an optimal interplay between the natural
frequencies of a group chaotic oscillators and the topological properties of
the network they are embedded in. We identify the conditions for achieving
phase synchronization in the most effective way, i.e., with the lowest possible
coupling strength. Specifically, we show by means of numerical and experimental
results that it is possible to define a synchrony alignment function linking
the natural frequencies of a set of non-identical phase-coherent chaotic
oscillators with the topology of the Laplacian matrix $L$, the latter
accounting for the specific organization of the network of interactions between
oscillators. We use the classical R\"ossler system to show that the synchrony
alignment function obtained for phase oscillators can be extended to
phase-coherent chaotic systems. Finally, we carry out a series of experiments
with nonlinear electronic circuits to show the robustness of the theoretical
predictions despite the intrinsic noise and parameter mismatch of the
electronic components.


title: The full Keller-Segel model is well-posed on nonsmooth domains

abstract:
  In this paper we prove that the full Keller-Segel system, a quasilinear
strongly coupled reaction-crossdiffusion system of four parabolic equations, is
well-posed in space dimensions 2 and 3 in the sense that it always admits an
unique local-in-time solution in an adequate function space, provided that the
initial values are suitably regular. The proof is done via an abstract solution
theorem for nonlocal quasilinear equations by Amann and is carried out for
general source terms. It is fundamentally based on recent nontrivial elliptic
and parabolic regularity results which hold true even on rather general
nonsmooth spatial domains. This enables us to work in a nonsmooth setting which
is not available in classical parabolic systems theory. Apparently, there
exists no comparable existence result for the full Keller-Segel system up to
now. Due to the large class of possibly nonsmooth domains admitted, we also
obtain new results for the "standard" Keller-Segel system consisting of only
two equations as a special case.


title: Stability of multiplanet systems in binaries

abstract:
  When exploring the stability of multiplanet systems in binaries, two
parameters are normally exploited: the critical semimajor axis ac computed by
Holman and Wiegert (1999) within which planets are stable against the binary
perturbations, and the Hill stability limit Delta determining the minimum
separation beyond which two planets will avoid mutual close encounters. Our aim
is to test whether these two parameters can be safely applied in multiplanet
systems in binaries or if their predictions fail for particular binary orbital
configurations. We have used the frequency map analysis (FMA) to measure the
diffusion of orbits in the phase space as an indicator of chaotic behaviour.
First we revisited the reliability of the empirical formula computing ac in the
case of single planets in binaries and we find that, in some cases, it
underestimates by 10-20% the real outer limit of stability. For two planet
systems, the value of Delta is close to that computed for planets around single
stars, but the level of chaoticity close to it substantially increases for
smaller semimajor axes and higher eccentricities of the binary orbit. In these
configurations ac also begins to be unreliable and non linear secular
resonances with the stellar companion lead to chaotic behaviour well within ac,
even for single planet systems. For two planet systems, the superposition of
mean motion resonances, either mutual or with the binary companion, and non
linear secular resonances may lead to chaotic behaviour in all cases. We have
developed a parametric semiempirical formula determining the minimum value of
the binary semimajor axis, for a given eccentricity of the binary orbit, below
which stable two planet systems cannot exist.


title: Constrained Triangulations, Volumes of Polytopes, and Unit Equations

abstract:
  Given a polytope $\mathcal{P}$ in $\mathbb{R}^d$ and a subset $U$ of its
vertices, is there a triangulation of $\mathcal{P}$ using $d$-simplices that
all contain $U$? We answer this question by proving an equivalent and
easy-to-check combinatorial criterion for the facets of $\mathcal{P}$. Our
proof relates triangulations of $\mathcal{P}$ to triangulations of its
"shadow", a projection to a lower-dimensional space determined by $U$. In
particular, we obtain a formula relating the volume of $\mathcal{P}$ with the
volume of its shadow. This leads to an exact formula for the volume of a
polytope arising in the theory of unit equations.


title:
Intermediate Field Representation for Positive Matrix and Tensor
  Interactions

abstract:
  In this paper we introduce an intermediate field representation for random
matrices and random tensors with positive (stable) interactions of degree
higher than 4. This representation respects the symmetry axis responsible for
positivity. It is non-perturbative and allows to prove that such models are
Borel-Le Roy summable of the appropriate order in their coupling constant.
However we have not been able yet to associate a convergent Loop Vertex
Expansion to this representation, hence our Borel summability result is not of
the optimal expected form when the size N of the matrix or of the tensor tends
to infinity.


title:
Generation of Spectral Clusters in a Mixture of Noble and Raman-Active
  Gases

abstract:
  We report a novel scheme for the generation of dense clusters of Raman
sidebands. The scheme uses a broadband-guiding hollow-core photonic crystal
fiber (HC-PCF) filled with a mixture of H2, D2, and Xe for efficient
interaction between the gas mixture and a green laser pump pulse (532 nm, 1 ns)
of only 5 uJ energy. This results in the generation from noise of more than 135
ro-vibrational Raman sidebands covering the visible spectral region with an
average spacing of only 2 THz. Such a spectrally dense and compact fiber-based
source is ideal for applications where closely spaced narrow-band laser lines
with high spectral power density are required, such as in spectroscopy and
sensing. When the HC-PCF is filled with a H2-D2 mixture the Raman comb spans
the spectral region from the deep UV (280 nm) to the near infrared (1000 nm).


title: A Formal Algebra for OLAP

abstract:
  Online Analytical Processing (OLAP) comprises tools and algorithms that allow
querying multidimensional databases. It is based on the multidimensional model,
where data can be seen as a cube, where each cell contains one or more measures
can be aggregated along dimensions. Despite the extensive corpus of work in the
field, a standard language for OLAP is still needed, since there is no
well-defined, accepted semantics, for many of the usual OLAP operations. In
this paper, we address this problem, and present a set of operations for
manipulating a data cube. We clearly define the semantics of these operations,
and prove that they can be composed, yielding a language powerful enough to
express complex OLAP queries. We express these operations as a sequence of
atomic transformations over a fixed multidimensional matrix, whose cells
contain a sequence of measures. Each atomic transformation produces a new
measure. When a sequence of transformations defines an OLAP operation, a flag
is produced indicating which cells must be considered as input for the next
operation. In this way, an elegant algebra is defined. Our main contribution,
with respect to other similar efforts in the field is that, for the first time,
a formal proof of the correctness of the operations is given, thus providing a
clear semantics for them. We believe the present work will serve as a basis to
build more solid practical tools for data analysis.


title:
Changes in nuclear structure along the Mn isotopic chain studied via
  charge radii

abstract:
  The hyperfine spectra of $^{51,53-64}$Mn were measured in two experimental
runs using collinear laser spectroscopy at ISOLDE, CERN. Laser spectroscopy was
performed on the atomic $3d^5\ 4s^2\ ^{6}\text{S}_{5/2}\rightarrow 3d^5\ 4s4p\
^{6}\text{P}_{3/2}$ and ionic $3d^5\ 4s\ ^{5}\text{S}_2 \rightarrow 3d^5\ 4p\
^{5}\text{P}_3$ transitions, yielding two sets of isotope shifts. The mass and
field shift factors for both transitions have been calculated in the
multiconfiguration Dirac-Fock framework and were combined with a King plot
analysis in order to obtain a consistent set of mean-square charge radii which,
together with earlier work on neutron-deficient Mn, allow the study of nuclear
structure changes from $N=25$ across $N=28$ up to $N=39$. A clear development
of deformation is observed towards $N=40$, confirming the conclusions of the
nuclear moments studies. From a Monte Carlo Shell Model study of the shape in
the Mn isotopic chain, it is suggested that the observed development of
deformation is not only due to an increase in static prolate deformation but
also due to shape fluctuations and triaxiality. The changes in mean-square
charge radii are well reproduced using the Duflo-Zuker formula except in the
case of large deformation.


title:
A double copy for ${\cal N}=2$ supergravity: a linearised tale told
  on-shell

abstract:
  We construct the on-shell double copy for linearised four-dimensional ${\cal
N}=2$ supergravity coupled to one vector multiplet with a quadratic
prepotential. We apply this dictionary to the weak-field approximation of
dyonic BPS black holes in this theory.


title: Finite time St\"uckelberg interferometry with nanomechanical modes

abstract:
  St\"uckelberg interferometry describes the interference of two strongly
coupled modes during a double passage through an avoided energy level crossing.
In this work, we experimentally investigate finite time effects in
St\"uckelberg interference and provide an exact analytical solution of the
St\"uckelberg problem. Approximating this solution in distinct limits reveals
uncharted parameter regimes of St\"uckelberg interferometry. Experimentally, we
study these regimes using a purely classical, strongly coupled nanomechanical
two-mode system of high quality factor. The classical two-mode system consists
of the in-plane and out-of-plane fundamental flexural mode of a high stress
silicon nitride string resonator, coupled via electric gradient fields. The
dielectric control and microwave cavity enhanced universal transduction of the
nanoelectromechanical system allows for the experimental access to all
theoretically predicted St\"uckelberg parameter regimes. We exploit our
experimental and theoretical findings by studying the onset of St\"uckelberg
interference in dependence of the characteristic system control parameters and
obtain characteristic excitation oscillations between the two modes even
without the explicit need of traversing the avoided crossing. The presented
theory is not limited to classical mechanical two-mode systems but can be
applied to every strongly coupled (quantum) two-level system, for example a
spin-1/2 system or superconducting qubit.


title:
On a cross-diffusion model for multiple species with nonlocal
  interaction and size exclusion

abstract:
  The aim of this paper is to study a PDE model for two diffusing species
interacting by local size exclusion and global attraction. This leads to a
nonlinear degenerate cross-diffusion system, for which we provide a global
existence result. The analysis is motivated by the formulation of the system as
a formal gradient flow for an appropriate energy functional consisting of
entropic terms as well as quadratic nonlocal terms. Key ingredients are entropy
dissipation methods as well as the recently developed boundedness by entropy
principle. Moreover, we investigate phase separation effects inherent in the
cross-diffusion model by an analytical and numerical study of minimizers of the
energy functional and their asymptotics to a previously studied case as the
diffusivity tends to zero. Finally we briefly discuss coarsening dynamics in
the system, which can be observed in numerical results and is motivated by
rewriting the PDEs as a system of nonlocal Cahn-Hilliard equations.


title: Equivariant Rho-Invariants and Instanton Homology of Torus Knots

abstract:
  The equivariant rho-invariants studied in this paper are a version of the
classical rho-invariants of Atiyah, Patodi, and Singer in the presence of an
isometric involution. We compute these rho-invariants for all involutions on
the 3-dimensional lens spaces with 1-dimensional fixed point sets, as well as
for some involutions on Brieskorn homology spheres. As an application, we
compute the generators and Floer gradings in the singular instanton chain
complex of (p,q)-torus knots with odd p and q.


title:
Extreme dissipation event due to plume collision in a turbulent
  convection cell

abstract:
  An extreme dissipation event in the bulk of a closed three-dimensional
turbulent convection cell is found to be correlated with a strong reduction of
the large-scale circulation flow in the system that happens at the same time as
a plume emission event from the bottom plate. The reduction in the large-scale
circulation opens the possibility for a nearly frontal collision of down- and
upwelling plumes and the generation of a high-amplitude thermal dissipation
layer in the bulk. This collision is locally connected to a subsequent
high-amplitude energy dissipation event in the form of a strong shear layer.
Our analysis illustrates the impact of transitions in the large-scale
structures on extreme events at the smallest scales of the turbulence, a direct
link that is observed in a flow with boundary layers. We also show that
detection of extreme dissipation events which determine the far-tail statistics
of the dissipation fields in the bulk requires long-time integrations of the
equations of motion over at least hundred convective time units.


title:
Kinetics of fragmentation and dissociation of two-strand protein
  filaments: Coarse-grained simulations and experiments

abstract:
  While a significant body of investigations have been focused on the process
of protein self-assembly, much less is understood about the reverse process of
a filament breaking due to thermal motion into smaller fragments, or
depolymerization of subunits from the filament ends. Indirect evidence for
actin and amyloid filament fragmentation has been reported, although the
phenomenon has never been directly observed either experimentally or in
simulations. Here we report the direct observation of filament depolymerization
and breakup in a minimal, calibrated model of coarse-grained molecular
simulation. We quantify the orders of magnitude by which the depolymerization
rate from the filament ends $k_\mathrm{off}$ is larger than fragmentation rate
$k_{-}$ and establish the law $k_\mathrm{off}/k_- = \exp [( \varepsilon_\| -
\varepsilon_\bot) / k_\mathrm{B}T ] = \exp [0.5 \varepsilon / k_\mathrm{B}T ]$,
which accounts for the topology and energy of bonds holding the filament
together. This mechanism and the order-of-magnitude predictions are well
supported by direct experimental measurements of depolymerization of insulin
amyloid filaments.


title: Primordial Lepton Oscillations and Baryogenesis

abstract:
  The baryon asymmetry of the Universe should have been produced after the
inflation era. We consider the possibility that the asymmetry is generated by
the flavor oscillations in the reheating process after inflation, so that the
baryon asymmetry is realized already at the beginning of the radiation
dominated era. In the seesaw model, we show that the propagators of the
left-handed leptons generically have flavor mixings in the thermal background,
that can generate flavor-dependent lepton asymmetry through the $CP$ violation
in the oscillation phenomena. The flavor dependent rates for the wash-out
process can leave the net asymmetry today.


title: Phenomenology of minimal Z' models: from the LHC to the GUT scale

abstract:
  We consider a class of minimal abelian extensions of the Standard Model with
an extra neutral gauge boson $Z'$ at the TeV scale. In these scenarios an
extended scalar sector and heavy right-handed neutrinos are naturally
envisaged. We present some of their striking signatures at the Large Hadron
Collider, the most interesting arising from a $Z'$ decaying to heavy neutrino
pairs as well as a heavy scalar decaying to two Standard Model Higgses. Using
renormalisation group methods, we characterise the high energy behaviours of
these extensions and exploit the constraints imposed by the embedding into a
wider GUT scenario.


title:
Cyclotron resonant scattering feature simulations. I. Thermally averaged
  cyclotron scattering cross sections, mean free photon-path tables, and
  electron momentum sampling

abstract:
  Electron cyclotron resonant scattering features (CRSFs) are observed as
absorption-like lines in the spectra of X-ray pulsars. A significant fraction
of the computing time for Monte Carlo simulations of these quantum mechanical
features is spent on the calculation of the mean free path for each individual
photon before scattering, since it involves a complex numerical integration
over the scattering cross section and the (thermal) velocity distribution of
the scattering electrons.
  We aim to numerically calculate interpolation tables which can be used in
CRSF simulations to sample the mean free path of the scattering photon and the
momentum of the scattering electron. The tables also contain all the
information required for sampling the scattering electron's final spin.
  The tables were calculated using an adaptive Simpson integration scheme. The
energy and angle grids were refined until a prescribed accuracy is reached. The
tables are used by our simulation code to produce artificial CRSF spectra. The
electron momenta sampled during these simulations were analyzed and justified
using theoretically determined boundaries.
  We present a complete set of tables suited for mean free path calculations of
Monte Carlo simulations of the cyclotron scattering process for conditions
expected in typical X-ray pulsar accretion columns (0.01<B/B_{crit}<=0.12,
where B_{crit}=4.413x10^{13} G and 3keV<=kT<15keV). The sampling of the tables
is chosen such that the results have an estimated relative error of at most
1/15 for all points in the grid. The tables are available online at
http://www.sternwarte.uni-erlangen.de/research/cyclo.


title:
Heat and momentum transfer for magnetoconvection in a vertical external
  magnetic field

abstract:
  The scaling theory of Grossmann and Lohse (J. Fluid Mech. 407, 27 (2000)) for
the turbulent heat and momentum transfer is extended to the magnetoconvection
case in the presence of a (strong) vertical magnetic field. The comparison with
existing laboratory experiments and direct numerical simulations in the
quasistatic limit allows to restrict the parameter space to very low Prandtl
and magnetic Prandtl numbers and thus to reduce the number of unknown
parameters in the model. Also included is the Chandrasekhar limit for which the
outer magnetic induction field B is large enough such that convective motion is
suppressed and heat is transported by diffusion. Our theory identifies four
distinct regimes of magnetoconvection which are distinguished by the strength
of the outer magnetic field and the level of turbulence in the flow,
respectively.


title: Measurement of second-order response without perturbation

abstract:
  We study the second order response functions of a colloidal particle being
subjected to an anharmonic potential. Contrary to typical response measurements
which require an external perturbation, here we experimentally confirm a
recently developed approach where the system's susceptibilities up to second
order are obtained from the particle's equilibrium trajectory [PCCP
$\mathrm{{\bf 17}}$, 6653 (2015)]. The measured susceptibilities are in
quantitative agreement with those obtained from the response to an external
perturbation.


title: Quantification of multidimensional entanglement stored in a crystal

abstract:
  The use of multidimensional entanglement opens new perspectives for quantum
information processing. However, an important challenge in practice is to
certify and characterize multidimensional entanglement from measurement data
that are typically limited. Here, we report the certification and
quantification of two-photon multidimensional energy-time entanglement between
many temporal modes, after one photon has been stored in a crystal. We develop
a method for entanglement quantification which makes use of only sparse data
obtained with limited resources. This allows us to efficiently certify an
entanglement of formation of 1.18 ebits after performing quantum storage. The
theoretical methods we develop can be readily extended to a wide range of
experimental platforms, while our experimental results demonstrate the
suitability of energy-time multidimensional entanglement for a quantum repeater
architecture.


title: What You Will Gain By Rounding: Theory and Algorithms for Rounding Rank

abstract:
  When factorizing binary matrices, we often have to make a choice between
using expensive combinatorial methods that retain the discrete nature of the
data and using continuous methods that can be more efficient but destroy the
discrete structure. Alternatively, we can first compute a continuous
factorization and subsequently apply a rounding procedure to obtain a discrete
representation. But what will we gain by rounding? Will this yield lower
reconstruction errors? Is it easy to find a low-rank matrix that rounds to a
given binary matrix? Does it matter which threshold we use for rounding? Does
it matter if we allow for only non-negative factorizations? In this paper, we
approach these and further questions by presenting and studying the concept of
rounding rank. We show that rounding rank is related to linear classification,
dimensionality reduction, and nested matrices. We also report on an extensive
experimental study that compares different algorithms for finding good
factorizations under the rounding rank model.


title:
A fast and effective method for a Poisson denoising model with total
  variation

abstract:
  In this paper, we present a fast and effective method for solving the
Poisson-modified total variation model proposed in [9]. The existence and
uniqueness of the model are again proved using different method. A
semi-implicit difference scheme is designed to discretize the derived gradient
descent flow with a large time step and can guarantee the restored image to be
strictly positive in the image domain. Experimental results show the efficiency
and effectiveness of our method.


title:
Spatialized Evolutionary prisoner's dilemma: Homogenization and
  propagation of chaos

abstract:
  Epstein introduced an agent-based model called Demographic Prisoner's
dilemma. He shows, via simulations, that cooperation in this spatial
evolutionary repeated game can be sustained. In order to do proves, we put on
this model a particle system framework in order to prove the convergence of the
spatial model to a random matching model, using homogenization techniques. Then
we prove the convergence of the random matching model to a mean field model,
using propagation of chaos techniques.


title: Hyperfine phononic frequency comb

abstract:
  Optical frequency combs [1-8] have resulted in significant advances in
optical frequency metrology and found wide application to precise physical
measurements [1-4, 9] and molecular fingerprinting [8]. A direct analogue of
frequency combs in the phononic or acoustic domain has not been reported to
date. In this letter, we report the first clear experimental evidence for a
phononic frequency comb. In contrast to the Kerr nonlinearity [10] in optical
frequency comb formation, the phononic frequency comb is generated through the
intrinsic coupling of a driven phonon mode with an auto-parametrically excited
sub-harmonic mode [16]. Through systematic experiments at different drive
frequencies and amplitudes, we portray the well-connected process of phononic
frequency comb formation and define attributes to control the features [17-18]
associated with comb formation in such a system. Further, the interplay between
these nonlinear resonances and the well-known Duffing phenomenon [12-14] is
also observed. The presented pathway for phononic frequency comb formation
finds general relevance to other nonlinear systems in both classical and
quantum domains.


title: Numerous approximations of Riemann-Stieltjes double integrals

abstract:
  The concept of Riemann-Stieltjes integral $\int_a^b {f\left( t
\right)du\left( t \right)}$; where $f$ is called the integrand, $u$ is called
the integrator, plays an important role in Mathematics. The approximation
problem of the Riemann-Stieltjes integral $\int_a^b {f\left( t \right)du\left(
t \right)}$ in terms of the Riemann-Stieltjes sums have been considered
recently by many authors. However, a small attention and a few works have been
considered for mappings of two variables; i.e., The approximation problem of
the Riemann-Stieltjes double integral $\int_a^b {\int_c^d {f\left( {t,s}
\right)d_s d_t u\left( {t,s} \right)} }$ in terms of the Riemann-Stieltjes
double sums. This study is devoted to obtain several bounds for $\int_a^b
{\int_c^d {f\left( {t,s} \right)d_s d_t u\left( {t,s} \right)} }$ under various
assumptions on the integrand $f$ and the integrator $u$. Mainly, the concepts
of bounded variation and bi-variation are used at large in the thesis. Several
proposed cubature formula are introduced to approximate such double integrals.
For mappings of two variables several inequalities of Trapezoid, Gr\"{u}ss and
Ostrowski type for mappings of bounded variation, bounded bi-variation,
Lipschitzian and monotonic are introduced and discussed. Namely, Trapezoid-type
rules for $\mathcal{RS}$-Double integrals are proved, and therefore the
classical Hermite-Hadamard inequality for mappings of two variables is
established. A Korkine type identity is used to obtain several Gr\"{u}ss type
inequalities for integrable functions. Finally, approximating real functions of
two variables which possess $n$-th partial derivatives of bounded bi-variation,
Lipschitzian and absolutely continuous are established and investigated.


title:
Supersymmetric AdS$_{5}$ solutions of type IIB supergravity without D3
  branes

abstract:
  We analyse the most general bosonic supersymmetric solutions of type IIB
supergravity whose metrics are warped products of five-dimensional anti-de
Sitter space (AdS$_5$) with a five-dimensional Riemannian manifold $M_{5}$,
where the five-form flux vanishes, while all remaining fluxes are allowed to be
non-vanishing consistent with SO(4,2) symmetry. This completes the program of
classifying all supersymmetric solutions of ten and eleven-dimensional
supergravity with an AdS$_5$ factor. We investigate the supersymmetry
conditions in some special cases, and demonstrate how these are satisfied by a
solution originally found in arXiv:1410.2650[hep-th], utilising the method of
non-Abelian T-duality.


title:
The upper critical magnetic field of holographic superconductor with
  conformally invariant power-Maxwell electrodynamics

abstract:
  The properties of $(d-1)$-dimensional $s$-wave holographic superconductor in
the presence of power-Maxwell field is explored. We study the probe limit in
which the scalar and gauge fields do not backreact on the background geometry.
Our study is based on the matching of solutions on the boundary and on the
horizon at some intermediate point. At first, the case without external
magnetic field is considered, and the critical temperature is obtained in terms
of the charge density, the dimensionality, and the power-Maxwell exponent.
Then, a magnetic field is turned on in the $d$-dimensional bulk which can
influence the $(d-1)$-dimensional holographic superconductor at the boundary.
The phase behavior of the corresponding holographic superconductor is obtained
by computing the upper critical magnetic field in the presence of power-Maxwell
electrodynamics, characterized by the power exponent $q$. Interestingly, it is
observed that in the presence of magnetic field, the physically acceptable
phase behavior of the holographic superconductor is obtained for $q={d}/{4}$,
which guaranties the conformal invariance of the power-Maxwell Lagrangian. The
case of physical interest in five spacetime dimensions ($d=5$, and $q=5/4$) is
considered in detail, and compared with the results obtained for the usual
Maxwell electrodynamics $q=1$ in the same dimensions.


title: On conservation laws in quantum mechanics

abstract:
  We raise fundamental questions about the very meaning of conservation laws in
quantum mechanics and we argue that the standard way of defining conservation
laws, while perfectly valid as far as it goes, misses essential features of
nature and has to be revisited and extended.


title: An Analytic Method for $S$-Expansion involving Resonance and Reduction

abstract:
  In this paper we describe an analytic method able to give the multiplication
table(s) of the set(s) involved in an $S$-expansion process (with either
resonance or $0_S$-resonant-reduction) for reaching a target Lie (super)algebra
from a starting one, after having properly chosen the partitions over subspaces
of the considered (super)algebras. This analytic method gives us a simple set
of expressions to find the partitions over the set(s) involved in the process.
Then, we use the information coming from both the initial (super)algebra and
the target one for reaching the multiplication table(s) of the mentioned
set(s). Finally, we check associativity with an auxiliary computational
algorithm, in order to understand whether the obtained set(s) can describe
semigroup(s) or just abelian set(s) connecting two (super)algebras. We also
give some interesting examples of application, which check and corroborate our
analytic procedure and also generalize some result already presented in the
literature.


title: Linear representations of convolutional codes over rings

abstract:
  In this paper we extend the relation between convolutional codes and linear
systems over finite fields to certain commutative rings through first order
representations . We introduce the definition of rings with representations as
those for which these representations always exist, and we show that finite
products of finite fields belong to this class. We develop the
input/state/output representations for convolutional codes over these rings,
and we show how to use them to construct observable convolutional codes as in
the classical case.


title: On Gehring-Martin-Tan groups with an elliptic generator

abstract:
  The Gehring-Martin-Tan inequality for 2-generator subgroups of PSL(2,C) is
one of the best known discreteness conditions. A Kleinian group $G$ is called a
Gehring-Martin-Tan group if the equality holds for the group $G$. We give a
method for constructing Gehring-Martin-Tan groups with a generator of order
four and present some examples. These groups arise as groups of finite volume
hyperbolic 3-orbifolds.


title:
The Spatial Distribution of Complex Organic Molecules in the L1544
  Pre-stellar Core

abstract:
  The detection of complex organic molecules (COMs) toward cold sources such as
pre-stellar cores (with T<10 K), has challenged our understanding of the
formation processes of COMs in the interstellar medium. Recent modelling on COM
chemistry at low temperatures has provided new insight into these processes
predicting that COM formation depends strongly on parameters such as visual
extinction and the level of CO freeze out. We report deep observations of COMs
toward two positions in the L1544 pre-stellar core: the dense,
highly-extinguished continuum peak with Av>=30 mag within the inner 2700 au;
and a low-density shell with average Av~7.5-8 mag located at 4000 au from the
core's center and bright in CH3OH. Our observations show that CH3O, CH3OCH3 and
CH3CHO are more abundant (by factors ~2-10) toward the low-density shell than
toward the continuum peak. Other COMs such as CH3OCHO, c-C3H2O, HCCCHO, CH2CHCN
and HCCNC show slight enhancements (by factors <=3) but the associated
uncertainties are large. This suggests that COMs are actively formed and
already present in the low-density shells of pre-stellar cores. The modelling
of the chemistry of O-bearing COMs in L1544 indicates that these species are
enhanced in this shell because i) CO starts freezing out onto dust grains
driving an active surface chemistry; ii) the visual extinction is sufficiently
high to prevent the UV photo-dissociation of COMs by the external interstellar
radiation field; and iii) the density is still moderate to prevent severe
depletion of COMs onto grains.


title: A new interpretation of quantum mechanics

abstract:
  The present paper is based upon equations obtained in an earlier paper by the
author devoted to a new formulation of quantum electrodynamics. The equations
describe the structure of the electron as well as its motion in external
fields, interaction with a measuring apparatus inclusive, in a deterministic
manner without any jumps. Quantum mechanics is an approximate theory because
its equations follow from the above equations upon neglecting the self-field of
the electron itself. Just this leads to paradoxes, seeming contradictions and
jumps in quantum mechanics. The quantum mechanical wavefunction has a dual
interpretation. In some problems the square of its modulus represents a real
distribution of the electronic density while in others the same square
determines the probability distribution of coordinates. It is shown why, given
the different interpretations of the wavefunction, it satisfies one and the
same Dirac or Schr\"odinger equation. Description of many-electron systems is
also considered in the starting approach as well as in quantum mechanics.
Neutrinos are discussed in brief.


title:
Switching of a large anomalous Hall effect between metamagnetic phases
  of a non-collinear antiferromagnet

abstract:
  The anomalous Hall effect (AHE), which in long-range ordered ferromagnets
appears as a voltage transverse to the current and usually is proportional to
the magnetization, often is believed to be of negligible size in
antiferromagnets due to their low uniform magnetization. However, recent
experiments and theory have demonstrated that certain antiferromagnets with a
non-collinear arrangement of magnetic moments exhibit a sizeable spontaneous
AHE at zero field due to a non-vanishing Berry curvature arising from the
quantum mechanical phase of the electron's wave functions. Here we show that
antiferromagnetic Mn5Si3 single crystals exibit a large AHE which is strongly
anisotropic and shows multiple transitions with sign changes at different
magnetic fields due to field-induced rearrangements of the magnetic structure
despite only tiny variations of the total magnetization. The presence of
multiple non-collinear magnetic phases offers the unique possiblity to explore
the details of the AHE and the sensitivity of the Hall effect on the details of
the magnetic texture.


title:
Comprehensive Wide-Band Magnitudes and Albedos for the Planets, With
  Applications to Exo-Planets and Planet Nine

abstract:
  Complete sets of reference magnitudes in all 7 Johnson-Cousins bands (U, B,
V, R, I, Rc and Ic) and the 5 principal Sloan bands (u', g', r', i', and z')
are presented for the 8 planets. These data are accompanied by illumination
phase functions and other formulas which characterize the instantaneous
brightness of the planets. The main source of Johnson-Cousins magnitudes is a
series of individualized photometric studies reported in recent years. Gaps in
that dataset were filled with magnitudes synthesized in this study from
published spectrophotometry. The planetary Sloan magnitudes, which are
established here for the first time, are an average of newly recorded Sloan
filter photometry, synthetic magnitudes and values transformed from the
Johnson-Cousins system. Geometric albedos derived from these two sets of
magnitudes are consistent within each photometric system and between the
systems for all planets and in all bands. This consistency validates the
albedos themselves as well as the magnitudes from which they were derived. In
addition, a quantity termed the delta stellar magnitude is introduced to
indicate the difference between the magnitude of a planet and that of its
parent star. A table of these delta values for exo-planets possessing a range
of physical characteristics is presented. The delta magnitudes are for phase
angle 90 degrees where a planet is near the greatest apparent separation from
its star. This quantity may be useful in exo-planet detection and observation
strategies when an estimate of the signal-to-noise ratio is needed. Likewise,
the phase curves presented in this paper can be used for characterizing
exo-planets. Finally, magnitudes for the proposed Planet Nine are estimated,
and we note that P9 may be especially faint at red and near-IR wavelengths.


title:
Regularization of an Ill-posed Cauchy Problem for the Wave Equation
  (Fourier Method)

abstract:
  An ill-posed Cauchy problem for the wave equation is considered: the solution
is to be determined by the Cauchy data on some part of the time-space boundary.
By means of Fourier method we obtain a regularization algorithm for this
problem, which is given by rather explicit formula.


title:
Isospin breaking in the decay constants of heavy mesons from QCD sum
  rules

abstract:
  We present a study of the strong isospin-breaking (IB) effect, due in QCD to
the difference between $u$- and $d$-quark masses, in the leptonic decay
constants of charmed and beauty pseudoscalar and vector mesons using the method
of QCD sum rules. We apply the sum-rule analysis to the decay constants of
mesons containing one heavy quark and one light quark with the light mass in
the range from the average $u/d$ quark mass to the strange-quark mass. We then
analyse the dependence of the decay constants on the light quark mass and
extract with good accuracy the IB ratios of decay constants at leading order in
the mass difference $(m_d - m_u)$, obtaining: $(f_{D^+} - f_{D^0}) / f_{D} =
0.0047 (6)$, $(f_{D^{*+}} - f_{D^{*0}}) / f_{D^*} = 0.0068 (9)$, $(f_{B^0} -
f_{B^+}) / f_{B} = 0.0047 (6)$, and $(f_{B^{*0}} - f_{B^{*+}}) / f_{B^*} =
0.0045 (5)$, which yield: $f_{D^+} - f_{D^0} = 0.97 \pm 0.13$ MeV, $f_{D^{*+}}
- f_{D^{*0}} = 1.73 \pm 0.27$ MeV, $f_{B^0} - f_{B^+} = 0.90 \pm 0.13$ MeV,
$f_{B^{*0}} - f_{B^{*+}} = 0.81 \pm 0.11$ MeV. In the case of the $D$-meson our
finding is consistent with recent lattice QCD results, whereas it is much lower
in the case of the $B$-meson showing a tension of $\approx 3$ standard
deviations.


title:
A Fractional Differential Transformation Solution Method for the
  Assessment, Monitoring, Control, and Evaluation of HIV/AIDS Confirmed Status
  with Vertical Transmission in Nigeria

abstract:
  HIV is a deadly virus transmitted either through having of unprotected sex,
mother to child transmission, sharing of unsterilized objects that is capable
of making cut or wounds on the body, through blood or bodily fluid
transmission. AIDS has no permanent cure but remedies that help in suppressing
the power effect of the virus are available. Previous studies has shown that
the epidemic claimed more lives via vertical transmission, mother-to-child
transmission, blood transfusion, sexual intercourse and injection drug users.
The associated models were derived using diagnosis and treatments records of
confirmed status of HIV/AIDS clients. A new model analysis were proposed that
could handle cases of HIV/AIDS routes of transmission and treatments via
vertical, mother-to-child, blood transfusion, sexual intercourse, injection
drug users that were not considered in previous studies. The new model was
solved using Fractional Differential Transformation by Caputo sense algorithm.
The new model is a major contribution for optimal assessment, monitoring,
evaluation, control and management of HIV/AIDS, with 75% accuracy.


title: Uncertainty of current understanding regarding OBT formation in plants

abstract:
  Radiological impact models are important tools that support nuclear safety.
For tritium, a special radionuclide that readily enters the life cycle, the
processes involved in its transport into the environment are complex and
inadequately understood. For example, tritiated water (HTO) enters plants by
leaf and root uptake and is converted to organically bound tritium (OBT) in
exchangeable and non-exchangeable forms; however, the observed OBT/HTO ratios
in crops exhibit large variability and contradict the current models for
routine releases. Non-routine or spike releases of tritium further complicate
the prediction of OBT formation. The experimental data for a short and intense
atmospheric contamination of wheat are presented together with various models
predictions. The experimental data on wheat demonstrate that the OBT formation
is a long process, it is dependent on receptor location and stack dynamics,
there are differences between night and day releases, and the HTO dynamics in
leaf and ear is a very important contributor to OBT formation.


title:
First limits on the occurrence rate of short-period planets orbiting
  brown dwarfs

abstract:
  Planet formation theories predict a large but still undetected population of
short-period terrestrial planets orbiting brown dwarfs. Should specimens of
this population be discovered transiting relatively bright and nearby brown
dwarfs, the Jupiter-size and the low luminosity of their hosts would make them
exquisite targets for detailed atmospheric characterisation with JWST and
future ground-based facilities. The eventual discovery and detailed study of a
significant sample of transiting terrestrial planets orbiting nearby brown
dwarfs could prove to be useful not only for comparative exoplanetology but
also for astrobiology, by bringing us key information on the physical
requirements and timescale for the emergence of life.
  In this context, we present a search for transit-signals in archival
time-series photometry acquired by the Spitzer Space Telescope for a sample of
44 nearby brown dwarfs. While these 44 targets were not particularly selected
for their brightness, the high precision of their Spitzer light curves allows
us to reach sensitivities below Earth-sized planets for 75% of the sample and
down to Europa-sized planets on the brighter targets. We could not identify any
unambiguous planetary signal. Instead, we could compute the first limits on the
presence of planets on close-in orbits. We find that within a 1.28 day orbit,
the occurrence rate of planets with a radius between 0.75 and 3.25 R$_\oplus$
is {\eta} < 67 $\pm$ 1%. For planets with radii between 0.75 and 1.25
R$_\oplus$, we place a 95% confident upper limit of {\eta} < 87 $\pm$ 3%. If we
assume an occurrence rate of {\eta} = 27% for these planets with radii between
0.75 and 1.25 R$_\oplus$, as the discoveries of the Kepler-42b and TRAPPIST-1b
systems would suggest, we estimate that 175 brown dwarfs need to be monitored
in order to guarantee (95%) at least one detection.


title: Least Square Estimation-Based SDP Cuts for SOCP Relaxation of AC OPF

abstract:
  This paper presents a method that generates affine inequalities to strengthen
the second-order conic programming (SOCP) relaxation of an alternating current
optimal power flow (AC OPF) problem. The affine inequalities serve as cuts to
get rid of points outside of the feasible region of AC OPF with semi-definite
programming (SDP) relaxation. Hence, the affine inequalities are names as SDP
cuts. While AC OPF with SDP relaxation has a high computational complexity, AC
OPF with SOCP has a much lower computational complexity. Recent research has
found that the feasible region of SDP relaxation is contained inside the
feasible region of the SOCP relaxation. Therefore, the integration of SDP cuts
into SOCP relaxation provides better scalability compared to the SDP relaxation
and a tighter gap compared to the SOCP relaxation. The SDP cuts are generated
by solving least square estimation (LSE) problems at cycle basis and further
exploring the geometric characteristic of LSE. General feasibility cuts
generating method is also employed for analysis. We found that the SDP cuts
generated by LSE method are indeed feasibility cuts. The SDP cuts effectively
reduce the search space. Case studies of systems with several buses to hundreds
of buses have demonstrated the method is very effective in reducing the gaps.


title: A Simple Model of Credit Expansion

abstract:
  The proposed model is aimed to reveal important patterns in the behavior of a
simplified financial system. The patterns could be detected as regular cycles
consisting of debt bubbles and crises. Financial cycles have a well defined
structure and form periodic sequences along the axis of credit expansion while
retaining stochastic nature in terms of time.


title: Copula-Based Univariate Time Series Structural Shift Identification Test

abstract:
  An approach is proposed to determine structural shift in time-series assuming
non-linear dependence of lagged values of dependent variable. Copulas are used
to model non-linear dependence of time series components.


title: Unbiased Sparse Subspace Clustering By Selective Pursuit

abstract:
  Sparse subspace clustering (SSC) is an elegant approach for unsupervised
segmentation if the data points of each cluster are located in linear
subspaces. This model applies, for instance, in motion segmentation if some
restrictions on the camera model hold. SSC requires that problems based on the
$l_1$-norm are solved to infer which points belong to the same subspace. If
these unknown subspaces are well-separated this algorithm is guaranteed to
succeed. The algorithm rests upon the assumption that points on the same
subspace are well spread. The question what happens if this condition is
violated has not yet been investigated. In this work, the effect of particular
distributions on the same subspace will be analyzed. It will be shown that SSC
fails to infer correct labels if points on the same subspace fall into more
than one cluster.


title: A Formal Solution to the Grain of Truth Problem

abstract:
  A Bayesian agent acting in a multi-agent environment learns to predict the
other agents' policies if its prior assigns positive probability to them (in
other words, its prior contains a \emph{grain of truth}). Finding a reasonably
large class of policies that contains the Bayes-optimal policies with respect
to this class is known as the \emph{grain of truth problem}. Only small classes
are known to have a grain of truth and the literature contains several related
impossibility results. In this paper we present a formal and general solution
to the full grain of truth problem: we construct a class of policies that
contains all computable policies as well as Bayes-optimal policies for every
lower semicomputable prior over the class. When the environment is unknown,
Bayes-optimal agents may fail to act optimally even asymptotically. However,
agents based on Thompson sampling converge to play {\epsilon}-Nash equilibria
in arbitrary unknown computable multi-agent environments. While these results
are purely theoretical, we show that they can be computationally approximated
arbitrarily closely.


title: Decomposing planar cubic graphs

abstract:
  The 3-Decomposition Conjecture states that every connected cubic graph can be
decomposed into a spanning tree, a 2-regular subgraph and a matching. We show
that this conjecture holds for the class of connected plane cubic graphs.


title: On symmetric decompositions of positive operators

abstract:
  Inspired by some problems in Quantum Information Theory, we present some
results concerning decompositions of positive operators acting on finite
dimensional Hilbert spaces. We focus on decompositions by families having
geometrical symmetry with respect to the Euclidean scalar product and we
characterize all such decompositions, comparing our results with the case of
SIC--POVMs from Quantum Information Theory. We also generalize some Welch--type
inequalities from the literature.


title:
Knowledge-based machine learning methods for macromolecular 3D structure
  prediction

abstract:
  Predicting the 3D structure of a macromolecule, such as a protein or an RNA
molecule, is ranked top among the most difficult and attractive problems in
bioinformatics and computational biology. Its importance comes from the
relationship between the 3D structure and the function of a given protein or
RNA. 3D structures also help to find the ligands of the protein, which are
usually small molecules, a key step in drug design. Unfortunately, there is no
shortcut to accurately obtain the 3D structure of a macromolecule. Many
physical measurements of macromolecular 3D structures cannot scale up, due to
their large labor costs and the requirements for lab conditions.
  In recent years, computational methods have made huge progress due to advance
in computation speed and machine learning methods. These methods only need the
sequence information to predict 3D structures by employing various mathematical
models and machine learning methods. The success of computational methods is
highly dependent on a large database of the proteins and RNA with known
structures.
  However, the performance of computational methods are always expected to be
improved. There are several reasons for this. First, we are facing, and will
continue to face sparseness of data.Secondly, the 3D structure space is too
large for our computational capability.
  The two obstacles can be removed by knowledge-based methods, which combine
knowledge learned from the known structures and biologists' knowledge of the
folding process of protein or RNA. In the dissertation, I will present my
results in building a knowledge-based method by using machine learning methods
to tackle this problem. My methods include the knowledge constraints on
intermediate states, which can highly reduce the solution space of a protein or
RNA, in turn increasing the efficiency of the structure folding method and
improving its accuracy.


title: Five-dimensional Nernst branes from special geometry

abstract:
  We construct Nernst brane solutions, that is black branes with zero entropy
density in the extremal limit, of FI-gauged minimal five-dimensional
supergravity coupled to an arbitrary number of vector multiplets. While the
scalars take specific constant values and dynamically determine the value of
the cosmological constant in terms of the FI-parameters, the metric takes the
form of a boosted AdS Schwarzschild black brane. This metric can be brought to
the Carter-Novotny-Horsky form that has previously been observed to occur in
certain limits of boosted D3-branes. By dimensional reduction to four
dimensions we recover the four-dimensional Nernst branes of arXiv:1501.07863
and show how the five-dimensional lift resolves all their UV singularities. The
dynamics of the compactification circle, which expands both in the UV and in
the IR, plays a crucial role. At asymptotic infinity, the curvature singularity
of the four-dimensional metric and the run-away behaviour of the
four-dimensional scalar combine in such a way that the lifted solution becomes
asymptotic to AdS5. Moreover, the existence of a finite chemical potential in
four dimensions is related to fact that the compactification circle has a
finite minimal value. While it is not clear immediately how to embed our
solutions into string theory, we argue that the same type of dictionary as
proposed for boosted D3-branes should apply, although with a lower amount of
supersymmetry.


title:
Travel the World: Analyzing and Predicting Booking Behavior using E-mail
  Travel Receipts

abstract:
  Tourism industry has grown tremendously in the previous several decades.
Despite its global impact, there still remain a number of open questions
related to better understanding of tourists and their habits. In this work we
analyze the largest data set of travel receipts considered thus far, and focus
on exploring and modeling booking behavior of online customers. We extract
useful, actionable insights into the booking behavior, and tackle the task of
predicting the booking time. The presented results can be directly used to
improve booking experience of customers and optimize targeting campaigns of
travel operators.