title:
Entropy production from chaoticity in Yang-Mills field theory with use
  of the Husimi function

abstract:
  We investigate possible entropy production in Yang-Mills (YM) field theory by
using a quantum distribution function called Husimi function $f_{\rm H}(A, E,
t)$ for YM field, which is given by a coarse graining of Wigner function and
non-negative. We calculate the Husimi-Wehrl (HW) entropy $S_{\rm HW}(t)=-{\rm
Tr}f_H \log f_H$ defined as an integral over the phase-space, for which two
adaptations of the test-particle method are used combined with Monte-Carlo
method. We utilize the semiclassical approximation to obtain the time evolution
of the distribution functions of the YM field, which is known to show a chaotic
behavior in the classical limit. We also make a simplification of the
multi-dimensional phase-space integrals by making a product ansatz for the
Husimi function, which is found to give a 10-20 per cent over estimate of the
HW entropy for a quantum system with a few degrees of freedom. We show that the
quantum YM theory does exhibit the entropy production, and that the entropy
production rate agrees with the sum of positive Lyapunov exponents or the
Kolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YM
field causes the entropy production in the quantum YM theory.


title: Nonlinear Spinor Fields in Bianchi type-III spacetime

abstract:
  Within the scope of Bianchi type-III spacetime we study the role of spinor
field on the evolution of the Universe as well as the influence of gravity on
the spinor field. In doing so we have considered a polynomial type of
nonlinearity. In this case the spacetime remains locally rotationally symmetric
and anisotropic all the time. It is found that depending on the sign of
nonlinearity the models allows both accelerated and oscillatory modes of
expansion. The non-diagonal components of energy-momentum tensor though impose
some restrictions on metric functions and components of spinor field, unlike
Bianchi type I, V and $VI_0$ cases, they do not lead to vanishing mass and
nonlinear terms of the spinor field.


title:
Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides
  XP$_2$ (X = Mo, W)

abstract:
  The recently discovered type-II Weyl points appear at the boundary between
electron and hole pockets. Type-II Weyl semimetals that host such points are
predicted to exhibit a new type of chiral anomaly and possess thermodynamic
properties very different from their type-I counterparts. In this Letter, we
describe the prediction of a type-II Weyl semimetal phase in the transition
metal diphosphides MoP$_2$ and WP$_2$. These materials are characterized by
relatively simple band structures with four pairs of type-II Weyl points.
Neighboring Weyl points have the same chirality, which makes the predicted
topological phase robust with respect to small perturbations of the crystalline
lattice. In addition, this peculiar arrangement of the Weyl points results in
long topological Fermi arcs, thus making them readily accessible in
angle-resolved photoemission spectroscopy.


title:
Observation of Collective Coulomb Blockade in a Gate-controlled Linear
  Quantum-dot Array

abstract:
  The quantum transport of electrons in an artificial atom, such as a quantum
dot (QD), is governed by the Coulomb blockade (CB) effects, revealing the
ground-state charge configuration of the electronic system under interplays of
the on-site strong Coulomb interactions. In a coherently-coupled QD array, i.e.
artificial molecules, the phenomenon of collective CB (CCB) was predicted by
theoretical studies circa two decades ago but its evidence remains
controversial. Here, we present direct evidence for the observation of CCB in a
six-quantum-dot array (QDA) under high magnetic fields at 20 mK. The coherent
inter-dot coupling is enhanced and mediated via the Quantum Hall edge states of
the GaAs sample substrate. Two continuously fine-tuned gate voltages enable the
quantum dot conductance spectrum to undergo a localization to delocalization
transition process which manifests as an emergence and a collapse of CCB. The
transition between these two distinct quantum phases is analogous to the
Mott-Hubbard metal-insulator transition. The gate-voltage-dependent conductance
map thus obtained makes it possible to utilize QDA as an on-chip laboratory for
studying CCB and Mott physics. Our QDA device provides a platform for
developing engineered QD materials, qubit systems and artificial molecular
devices in the future.


title:
TAPER: query-aware, partition-enhancement for large, heterogenous,
  graphs

abstract:
  Graph partitioning has long been seen as a viable approach to address Graph
DBMS scalability. A partitioning, however, may introduce extra query processing
latency unless it is sensitive to a specific query workload, and optimised to
minimise inter-partition traversals for that workload. Additionally, it should
also be possible to incrementally adjust the partitioning in reaction to
changes in the graph topology, the query workload, or both. Because of their
complexity, current partitioning algorithms fall short of one or both of these
requirements, as they are designed for offline use and as one-off operations.
The TAPER system aims to address both requirements, whilst leveraging existing
partitioning algorithms. TAPER takes any given initial partitioning as a
starting point, and iteratively adjusts it by swapping chosen vertices across
partitions, heuristically reducing the probability of inter-partition
traversals for a given pattern matching queries workload. Iterations are
inexpensive thanks to time and space optimisations in the underlying support
data structures. We evaluate TAPER on two different large test graphs and over
realistic query workloads. Our results indicate that, given a hash-based
partitioning, TAPER reduces the number of inter-partition traversals by around
80%; given an unweighted METIS partitioning, by around 30%. These reductions
are achieved within 8 iterations and with the additional advantage of being
workload-aware and usable online.


title:
Modified Micropipline Architecture for Synthesizable Asynchronous FIR
  Filter Design

abstract:
  The use of asynchronous design approaches to construct digital signal
processing (DSP) systems is a rapidly growing research area driven by a wide
range of emerging energy constrained applications such as wireless sensor
network, portable medical devices and brain implants. The asynchronous design
techniques allow the construction of systems which are samples driven, which
means they only dissipate dynamic energy when there processing data and idle
otherwise. This inherent advantage of asynchronous design over conventional
synchronous circuits allows them to be energy efficient. However the
implementation flow of asynchronous systems is still difficult due to its lack
of compatibility with industry-standard synchronous design tools and modelling
languages. This paper devises a novel asynchronous design for a finite impulse
response (FIR) filter, an essential building block of DSP systems, which is
synthesizable and suitable for implementation using conventional synchronous
systems design flow and tools. The proposed design is based on a modified
version of the micropipline architecture and it is constructed using four phase
bundled data protocol. A hardware prototype of the proposed filter has been
developed on an FPGA, and systematically verified. The results prove correct
functionality of the novel design and a superior performance compared to a
synchronous FIR implementation. The findings of this work will allow a wider
adoption of asynchronous circuits by DSP designers to harness their energy and
performance benefits.


title:
Accelerating a hybrid continuum-atomistic fluidic model with on-the-fly
  machine learning

abstract:
  We present a hybrid continuum-atomistic scheme which combines molecular
dynamics (MD) simulations with on-the-fly machine learning techniques for the
accurate and efficient prediction of multiscale fluidic systems. By using a
Gaussian process as a surrogate model for the computationally expensive MD
simulations, we use Bayesian inference to predict the system behaviour at the
atomistic scale, purely by consideration of the macroscopic inputs and outputs.
Whenever the uncertainty of this prediction is greater than a predetermined
acceptable threshold, a new MD simulation is performed to continually augment
the database, which is never required to be complete. This provides a
substantial enhancement to the current generation of hybrid methods, which
often require many similar atomistic simulations to be performed, discarding
information after it is used once.
  We apply our hybrid scheme to nano-confined unsteady flow through a
high-aspect-ratio converging-diverging channel, and make comparisons between
the new scheme and full MD simulations for a range of uncertainty thresholds
and initial databases. For low thresholds, our hybrid solution is highly
accurate\,---\,within the thermal noise of a full MD simulation. As the
uncertainty threshold is raised, the accuracy of our scheme decreases and the
computational speed-up increases (relative to a full MD simulation), enabling
the compromise between precision and efficiency to be tuned. The speed-up of
our hybrid solution ranges from an order of magnitude, with no initial
database, to cases where an extensive initial database ensures no new MD
simulations are required.


title: Group actions, non-K\"ahler complex manifolds and SKT structures

abstract:
  We give a construction of integrable complex structures on the total space of
a smooth principal bundle over a complex manifold, with an even dimensional
compact Lie group as structure group, under certain conditions. This
generalizes the constructions of complex structure on compact Lie groups by
Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others.
It also yields large classes of new examples of non-K\"ahler compact complex
manifolds. Moreover, under suitable restrictions on the base manifold, the
structure group, and characteristic classes, the total space of the principal
bundle admits SKT metrics. This generalizes recent results of Grantcharov et
al. We study the Picard group and the algebraic dimension of the total space in
some cases. We also use a slightly generalized version of the construction to
obtain (non-K\"ahler) complex structures on tangential frame bundles of complex
orbifolds.


title:
Adiabatic elimination for open quantum systems with effective Lindblad
  master equations

abstract:
  We consider an open quantum system described by a Lindblad-type master
equation with two times-scales. The fast time-scale is strongly dissipative and
drives the system towards a low-dimensional decoherence-free space. To perform
the adiabatic elimination of this fast relaxation, we propose a geometric
asymptotic expansion based on the small positive parameter describing the
time-scale separation. This expansion exploits geometric singular perturbation
theory and center-manifold techniques. We conjecture that, at any order, it
provides an effective slow Lindblad master equation and a completely positive
parameterization of the slow invariant sub-manifold associated to the
low-dimensional decoherence-free space. By preserving complete positivity and
trace, two important structural properties attached to open quantum dynamics,
we obtain a reduced-order model that directly conveys a physical interpretation
since it relies on effective Lindbladian descriptions of the slow evolution. At
the first order, we derive simple formulae for the effective Lindblad master
equation. For a specific type of fast dissipation, we show how any Hamiltonian
perturbation yields Lindbladian second-order corrections to the first-order
slow evolution governed by the Zeno-Hamiltonian. These results are illustrated
on a composite system made of a strongly dissipative harmonic oscillator, the
ancilla, weakly coupled to another quantum system.


title: Radiative Seesaw Model with Degenerate Majorana Dark Matter

abstract:
  We study a three loop induced neutrino mass model with exotic vector-like
isospin doublet leptons which contain a dark matter candidate. Then we explore
lepton flavor violations, and dark matter physics in co-annihilation system. In
this paper the nearly degenerate Majorana fermion dark matter can naturally be
achieved at the two loop level, while the mass splitting can be larger than
${\cal O}$(200) keV which is required from the constraint of the direct
detection search with spin independent inelastic scattering through $Z$ boson
portal. As a result a monochromatic photon excess, its threshold energy is
greater than ${\cal O}$(200) keV, is predicted in our model that could be
measured through indirect detection experiments such as INTEGRAL.


title: Beyond representing orthology relations by trees

abstract:
  Reconstructing the evolutionary past of a family of genes is an important
aspect of many genomic studies. To help with this, simple operations on a set
of sequences called orthology relations may be employed. In addition to being
interesting from a practical point of view they are also attractive from a
theoretical perspective in that e. g. a characterization is known for when such
a relation is representable by a certain type of phylogenetic tree. For an
orthology relation inferred from real biological data it is however generally
too much to hope for that it satisfies that characterization. Rather than
trying to correct the data in some way or another which has its own drawbacks,
as an alternative, we propose to represent an orthology relation $\delta$ in
terms of a structure more general than a phylogenetic tree called a
phylogenetic network. To compute such a network in the form of a level-1
representation for $\delta$, we introduce the novel {\sc Network-Popping}
algorithm which has several attractive properties. In addition, we characterize
orthology relations $\delta$ on some set $X$ that have a level-1 representation
in terms of eight natural properties for $\delta$ as well as in terms for
level-1 representations of orthology relations on certain subsets of $X$.


title: Microswimming with inertia

abstract:
  Microswimmers, especially in theoretical treatments, are generally taken to
be completely inertia-free, since inertial effects on their motion are
typically small and assuming their absence simplifies the problem considerably.
Yet in nature there is no discrete break between swimmers for which inertia is
negligibly small and for which it is detectable. Here we study a microswimming
model for which the effect of inertia is calculated explicitly in the regime of
transition between the Stokesian and the non-Stokesian flow limits, which we
term the intermediate regime. The model in the inertialess limit is the
bead-spring swimmer. We first show that in the intermediate regime a mechanical
microswimmer exhibits damped inertial coasting like an underdamped harmonic
oscillator. We then calculate analytically the swimmer's velocity by including
a mass-acceleration term in the equations of motion which are otherwise based
on the Stokes flow. We show that this hybrid treatment combining aspects of
underdamped and overdamped dynamics provides an accurate description of the
motion in the intermediate regime, as verified here by comparison to
simulations using the lattice Boltzmann method, and is a significant
improvement over the results from the inertialess theory when either the mass
of the swimmer or the forces driving its motion is/are large enough.


title:
Conditions for describing triplet states in reduced density matrix
  functional theory

abstract:
  We consider necessary conditions for the one-body-reduced density matrix
(1RDM) to correspond to a triplet wave-function of a two electron system. The
conditions concern the occupation numbers and are different for the high spin
projections, $S_z=\pm 1$, and the $S_z=0$ projection. Hence, they can be used
to test if an approximate 1RDM functional yields the same energies for both
projections. We employ these conditions in reduced density matrix functional
theory calculations for the triplet excitations of two-electron systems. In
addition, we propose that these conditions can be used in the calculation of
triplet states of systems with more than two electrons by restricting the
active space. We assess this procedure in calculations for a few atomic and
molecular systems. We show that the quality of the optimal 1RDMs improves by
applying the conditions in all the cases we studied.


title:
A Universal Approach Towards Computational Characterization of
  Dislocation Microstructure

abstract:
  Dislocations - linear defects within the crystal lattice of, e.g., metals -
already have been directly observed and analyzed for nearly a century. While
experimental characterization methods can nowadays reconstruct
three-dimensional pictures of complex dislocation networks, simulation methods
are at the same time more and more able to predict the evolution of such
systems in great detail. Concise methods for analyzing and comparing
dislocation microstructure, however, are still lagging behind. We introduce a
universal microstructure "language" which could be used for direct comparisons
and detailed analysis of very different experimental and simulation methods.


title:
A nonlinear dynamical system approach for the yielding behaviour of a
  viscoplastic fluid

abstract:
  A nonlinear dynamical system model that approximates a microscopic Gibbs
field model for the yielding of a viscoplastic material subjected to varying
external stress recently reported in [1] is presented. The predictions of the
model are in a fair agreement with the microscopic simulations and in a very
good agreement with the microstructural semi-empirical model reported in [2].
With only two internal parameters, the nonlinear dynamical system model
captures several key features of the solid-fluid transition observed in
experiments: the effect of the interactions between microscopic constituents on
the yield point, the abruptness of solid-fluid transition and the emergence of
a hysteresis of the micro-structural states upon increasing/decreasing external
forcing.The scaling behaviour of the magnitude of the hysteresis with the
degree of the steadiness of the flow is consistent with previous experimental
observations.


title: On the Randomization of Frolov's Algorithm for Multivariate Integration

abstract:
  We are concerned with the numerical integration of functions from the Sobolev
space $H^{r,\text{mix}}([0,1]^d)$ of dominating mixed smoothness
$r\in\mathbb{N}$ over the $d$-dimensional unit cube.
  In 1976, K. K. Frolov introduced a deterministic quadrature rule whose worst
case error has the order $n^{-r} \, (\log n)^{(d-1)/2}$ with respect to the
number $n$ of function evaluations. This is known to be optimal. 39 years
later, Erich Novak and me introduced a randomized version of this algorithm
using $d$ random dilations. We showed that its error is bounded above by a
constant multiple of $n^{-r-1/2} \, (\log n)^{(d-1)/2}$ in expectation and by
$n^{-r} \, (\log n)^{(d-1)/2}$ almost surely. The main term $n^{-r-1/2}$ is
again optimal and it turns out that the very same algorithm is also optimal for
the isotropic Sobolev space $H^s([0,1]^d)$ of smoothness $s>d/2$. We also added
a random shift to this algorithm to make it unbiased. Just recently, Mario
Ullrich proved that the expected error of the resulting algorithm on
$H^{r,\text{mix}}([0,1]^d)$ is even bounded above by $n^{-r-1/2}$. This thesis
is a review of the mentioned upper bounds and their proofs.


title: Instability of Non-uniform Toroidal Magnetic Fields in Accretion Disks

abstract:
  A new type of instability that is expected to drive magnetohydrodynamic (MHD)
turbulence from a purely toroidal magnetic field in an accretion disk is
presented. It is already known that in a differentially rotating system, the
uniform toroidal magnetic field is unstable due to a magnetorotational
instability (MRI) under a non-axisymmetric and vertical perturbation, while it
is stable under a purely vertical perturbation. Contrary to the previous study,
this paper proposes an unstable mode completely confined to the equatorial
plane, driven by the expansive nature of the magnetic pressure gradient force
under a non-uniform toroidal field. The basic nature of this growing eigenmode,
to which we give a name "magneto-gradient driven instability", is studied using
linear analysis, and the corresponding nonlinear evolution is then investigated
using two-dimensional ideal MHD simulations. Although a single localized
magnetic field channel alone cannot provide sufficient Maxwell stress to
contribute significantly to the angular momentum transport, we find that the
mode coupling between neighboring toroidal fields under multiple localized
magnetic field channels drastically generates a highly turbulent state and
leads to the enhanced transport of angular momentum, comparable to the
efficiency seen in previous studies on MRIs. This horizontally confined mode
may play an important role in the saturation of an MRI through complementray
growth with the toroidal MHDs and coupling with magnetic reconnection.


title: Properties of minimal charts and their applications IV: Loops

abstract:
  We investigate minimal charts with loops, a simple closed curve consisting of
edges of label $m$ containing exactly one white vertex. We shall show that
there does not exist any loop in a minimal chart with exactly seven white
vertices in this paper.


title: Gamma-ray bursts and Population III stars

abstract:
  Gamma-ray bursts (GRBs) are ideal probes of the epoch of the first stars and
galaxies. We review the recent theoretical understanding of the formation and
evolution of the first (so-called Population III) stars, in light of their
viability of providing GRB progenitors. We proceed to discuss possible unique
observational signatures of such bursts, based on the current formation
scenario of long GRBs. These include signatures related to the prompt emission
mechanism, as well as to the afterglow radiation, where the surrounding
intergalactic medium might imprint a telltale absorption spectrum. We emphasize
important remaining uncertainties in our emerging theoretical framework.


title: Compositional game theory

abstract:
  We introduce open games as a compositional foundation of economic game
theory. A compositional approach potentially allows methods of game theory and
theoretical computer science to be applied to large-scale economic models for
which standard economic tools are not practical. An open game represents a game
played relative to an arbitrary environment and to this end we introduce the
concept of coutility, which is the utility generated by an open game and
returned to its environment. Open games are the morphisms of a symmetric
monoidal category and can therefore be composed by categorical composition into
sequential move games and by monoidal products into simultaneous move games.
Open games can be represented by string diagrams which provide an intuitive but
formal visualisation of the information flows. We show that a variety of games
can be faithfully represented as open games in the sense of having the same
Nash equilibria and off-equilibrium best responses.


title:
Heavy quark-antiquark free energy and thermodynamics of string-hadron
  avoided crossings

abstract:
  The correlation function between two Polyakov loops encodes the free-energy
shift due to a pair of separated colour conjugated sources in the hot QCD
medium. This is analyzed in terms of a novel K\"all\'en-Lehmann spectral
representation for the separating distance, implying an increasing and concave
free-energy at all temperatures. We express the heavy $\bar{Q} Q$ free-energy
shift below the phase transition in QCD in terms of colour neutral purely
hadronic states with no explicit reference to quarks and gluons. Good agreement
with lattice data is achieved when considering the avoided crossing mechanism
underlying string breaking and with standard quenched values of the string
tension known from charmonium and bottomonium phenomenology. We also address
the role of the corresponding entropy shift and its renormalization group
properties.


title:
Generalized threshold-based epidemics in random graphs: the power of
  extreme values

abstract:
  Bootstrap percolation is a well-known activation process in a graph, in which
a node becomes active when it has at least $r$ active neighbors. Such process,
originally studied on regular structures, has been recently investigated also
in the context of random graphs, where it can serve as a simple model for a
wide variety of cascades, such as the spreading of ideas, trends, viral
contents, etc. over large social networks. In particular, it has been shown
that in $G(n,p)$ the final active set can exhibit a phase transition for a
sub-linear number of seeds. In this paper, we propose a unique framework to
study similar sub-linear phase transitions for a much broader class of graph
models and epidemic processes. Specifically, we consider i) a generalized
version of bootstrap percolation in $G(n,p)$ with random activation thresholds
and random node-to-node influences; ii) different random graph models,
including graphs with given degree sequence and graphs with community structure
(block model). The common thread of our work is to show the surprising
sensitivity of the critical seed set size to extreme values of distributions,
which makes some systems dramatically vulnerable to large-scale outbreaks. We
validate our results running simulation on both synthetic and real graphs.


title: Lipid membrane-mediated attractions between curvature inducing objects

abstract:
  The interplay of membrane proteins is vital for many biological processes,
such as cellular transport, cell division, and signal transduction between
nerve cells. Theoretical considerations have led to the idea that the membrane
itself mediates protein self-organization in these processes through
minimization of membrane curvature energy. Here, we present a combined
experimental and numerical study in which we quantify these interactions
directly for the first time. In our experimental model system we control the
deformation of a lipid membrane by adhering colloidal particles. Using confocal
microscopy, we establish that these membrane deformations cause an attractive
interaction force leading to reversible binding. The attraction extends over
2.5 times the particle diameter and has a strength of three times the thermal
energy (-3.3 kT). Coarse-grained Monte-Carlo simulations of the system are in
excellent agreement with the experimental results and prove that the measured
interaction is independent of length scale. Our combined experimental and
numerical results reveal membrane curvature as a common physical origin for
interactions between any membrane-deforming objects, from nanometre-sized
proteins to micrometre-sized particles.


title: Active region filaments might harbor weak magnetic fields

abstract:
  Recent spectropolarimetric observations of active region filaments have
revealed polarization profiles with signatures typical of the strong field
Zeeman regime. The conspicuous absence in those observations of scattering
polarization and Hanle effect signatures was then pointed out by some authors.
This was interpreted either as a signature of mixed "turbulent" field
components or as a result of optical thickness. In this article, we present a
natural scenario to explain these Zeeman-only spectro-polarimetric observations
of active region filaments. We propose a two-component model, one on top of the
other. Both components have horizontal fields, the azimuth difference between
them being close to 90 degrees. The component that lies lower in the atmosphere
is permeated by a strong field of the order of 600 G, while the upper component
has much weaker fields, of the order of 10 G. The ensuing scattering
polarization signatures of the individual components have opposite signs, so
that its combination along the line of sight reduces --and even can cancel
out-- the Hanle signatures, giving rise to an apparent only-Zeeman profile.
This model is also applicable to other chromospheric structures seen in
absorption above active regions.


title:
Optimum orientation versus orientation averaging description of cluster
  radioactivity

abstract:
  Background: The deformation of the nuclei involved in the cluster decay of
heavy nuclei affect seriously their half-lives against the decay. Purpose: We
investigate the description of the different decay stages in both the optimum
orientation and the orientation-averaged pictures of the cluster decay process.
Method: We consider the decays of 232,233,234U and 236,238Pu isotopes. The
quantum mechanical knocking frequency and penetration probability based on the
Wentzel-Kramers-Brillouin approximation are used to find the decay width.
Results: We found that the orientation-averaged decay width is one or two
orders of magnitude less than its value along the non-compact optimum
orientation. The difference between the two values increases with decreasing
the mass number of the emitted cluster. Correspondingly, the extracted
preformation probability based on the averaged decay width increases with the
same orders of magnitude compared to its value obtained considering the optimum
orientation. The cluster preformation probabilities (Sc) obtained in the two
considered schemes give more or less comparable agreement with the
Blendowske-Walliser (BW) formula based on the preformation probability of
Sa(ave.) obtained from the orientation-averaging scheme. All the obtained
results, including those obtained in the optimum-orientation scheme, deviate
substantially from the BW law based on Sa(opt.) obtained using the
optimum-orientation scheme. Conclusion: In order to account for deformations of
the participating nuclei, it is more relevant to calculate the decay width by
averaging over the different possible orientations of the participating
deformed nucleus, rather than considering the corresponding non-compact optimum
orientation.


title: Computational temporal ghost imaging

abstract:
  Ghost imaging is a fascinating process, where light interacting with an
object is recorded without resolution, but the shape of the object is
nevertheless retrieved, thanks to quantum or classical correlations of this
interacting light with either a computed or detected random signal. Recently,
ghost imaging has been extended to a time object, by using several thousands
copies of this periodic object. Here, we present a very simple device, inspired
by computational ghost imaging, that allows the retrieval of a single
non-reproducible, periodic or non-periodic, temporal signal. The reconstruction
is performed by a single shot, spatially multiplexed, measurement of the
spatial intensity correlations between computer-generated random images and the
images, modulated by a temporal signal, recorded and summed on a chip CMOS
camera used with no temporal resolution. Our device allows the reconstruction
of either a single temporal signal with monochrome images or
wavelength-multiplexed signals with color images.


title:
Understanding the Dynamics of Glass-forming Liquids with Random Pinning
  within the Random First Order Transition Theory

abstract:
  Extensive computer simulations are performed for a few model glass-forming
liquids in both two and three dimensions to study their dynamics when a
randomly chosen fraction of particles are frozen in their equilibrium
positions. For all the studied systems, we find that the temperature-dependence
of the $\alpha$ relaxation time extracted from an overlap function related to
the self part of the density autocorrelation function can be explained within
the framework of the Random First Order Transition (RFOT) theory of the glass
transition. We propose a scaling description to rationalize the simulation
results and show that our data for the $\alpha$ relaxation time for all
temperatures and pin concentrations are consistent with this description. We
find that the fragility parameter obtained from fits of the temperature
dependence of the $\alpha$ relaxation time to the Vogel-Fulcher-Tammann (VFT)
form decreases by almost an order of magnitude as the pin concentration is
increased from zero. Our scaling description relates the fragility parameter to
the static length scale of RFOT and thus provides a physical understanding of
fragility within the framework of the RFOT theory. Implications of these
findings for the values of the exponents appearing in the RFOT theory are
discussed.


title: Vortex ground states for Klein-Gordon-Maxwell-Proca type systems

abstract:
  We look for three dimensional vortex-solutions, which have finite energy and
are stationary solutions, of Klein-Gordon-Maxwell-Proca type systems of
equations. We prove the existence of three dimensional cylindrically symmetric
vortex-solutions having a least possible energy among all symmetric solutions.
Moreover we show that, if the Proca mass disappears, then the solutions tends
to a solution of the Klein-Gordon-Maxwell system.


title: On Lagrangian algebras in group-theoretical braided fusion categories

abstract:
  We describe Lagrangian algebras in twisted Drinfeld centres for finite
groups.
  Using the full centre construction, we establish a 1-1 correspondence between
Lagrangian algebras and module categories over pointed fusion categories.


title:
Effective Landau-Zener transitions in circuit dynamical Casimir effect
  with time-varying modulation frequency

abstract:
  We consider the dissipative single-qubit circuit QED architecture in which
the atomic transition frequency undergoes a weak external time-modulation. For
sinusoidal modulation with linearly varying frequency we derive effective
Hamiltonians that resemble the Landau-Zener problem of finite duration
associated to a two- or multi-level systems. The corresponding off-diagonal
coupling coefficients originate either from the rotating or the
counter-rotating terms in the Rabi Hamiltonian, depending on the values of the
modulation frequency. It is demonstrated that in the dissipation less case one
can accomplish almost complete transitions between the eigenstates of the bare
Rabi Hamiltonian even for relatively short duration of the frequency sweep. To
assess the experimental feasibility of our scheme we solved numerically the
phenomenological and the microscopic quantum master equations in the Markovian
regime at zero temperature. Both models exhibit qualitatively similar behavior
and indicate that photon generation from vacuum via effective Landau-Zener
transitions could be implemented with the current technology on the timescales
of a few microseconds. Moreover, unlike the harmonic dynamical Casimir effect
implementations, our proposal does not require the precise knowledge of the
resonant modulation frequency to accomplish meaningful photon generation.


title:
Roulettes: A weak lensing formalism for strong lensing - II. Derivation
  and analysis

abstract:
  We present a new extension of the weak lensing formalism capable of
describing strongly lensed images. This paper accompanies Paper I,
arXiv:1603.04698 where we provided a condensed overview of the approach and
illustrated how it works. Here we give all the necessary details, together with
some more explicit examples. We solve the non-linear geodesic deviation
equation order-by-order, keeping the leading derivatives of the optical tidal
matrix, giving rise to a series of maps from which a complete strongly lensed
image is formed. The family of maps are decomposed by separating the trace and
trace-free parts of each map. Each trace-free tensor represents an independent
spin mode, which distort circles into a variety of roulettes in the
screen-space. It is shown how summing this series expansion allows us to create
large strongly lensed images in regions where convergence, shear and flexion
are not sufficient. This paper is a detailed exposition of Paper I which
presents the key elements of the subject matter in a wider context.


title:
FEM-analysis on graded meshes for turning point problems exhibiting an
  interior layer

abstract:
  We consider singularly perturbed boundary value problems with a simple
interior turning point whose solutions exhibit an interior layer. These
problems are discretised using higher order finite elements on layer-adapted
graded meshes proposed by Liseikin. We prove $\epsilon$-uniform error estimates
in the energy norm. Furthermore, for linear elements we are able to prove
optimal order $\epsilon$-uniform convergence in the $L^2$-norm on these graded
meshes.


title: "K-theoretic" analog of Postnikov-Shapiro algebra distinguishes graphs

abstract:
  In this paper we study a filtered "K-theoretical" analog of a graded algebra
associated to any loopless graph G which was introduced in \cite{PS}. We show
that two such filtered algebras are isomorphic if and only if their graphs are
isomorphic. We also study a large family of filtered generalizations of the
latter graded algebra which includes the above "K-theoretical" analog.


title:
Designing Electron Spin Textures and Spin Interferometers by Shape
  Deformations

abstract:
  We demonstrate that the spin orientation of an electron propagating in a
one-dimensional nanostructure with Rashba spin-orbit (SO) coupling can be
manipulated on demand by changing the geometry of the nanosystem. Shape
deformations that result in a non-uniform curvature give rise to complex
three-dimensional spin textures in space. We employ the paradigmatic example of
an elliptically deformed quantum ring to unveil the way to get an
all-geometrical and all-electrical control of the spin orientation. The
resulting spin textures exhibit a tunable topological character with windings
around the radial and the out-of-plane directions. We show that these
topologically non trivial spin patterns affect the spin interference effect in
the deformed ring, thereby resulting in different geometry-driven ballistic
electronic transport behaviors. Our results establish a deep connection between
electronic spin textures, spin transport and the nanoscale shape of the system.


title: Stellar Tidal Streams in External Galaxies

abstract:
  To place the highly substructured stellar halos of the Milky Way and M31 in a
larger context of hierarchical galaxy formation, it is necessary to understand
the prevalence and properties of tidal substructure around external galaxies.
This chapter details the current state of our observational knowledge of
streams in galaxies in and beyond the Local Group, which are studied both in
resolved stellar populations and in integrated light. Modeling of individual
streams in extragalactic systems is hampered by our inability to obtain
resolved stellar kinematics in the streams, though many streams contain
alternate luminous kinematic tracers, such as globular clusters or planetary
nebulae. We compare the observed structures to the predictions of models of
galactic halo formation, which provide insight in the number and properties of
streams expected around Milky Way like galaxies. More specifically, we discuss
the inferences that can be made about stream progenitors based only on observed
morphologies. We expand our discussion to consider hierarchical accretion at
lower mass scales, in particular the observational evidence that substructure
exists on smaller mass scales and the effects accretion events may have on the
evolution of dwarf galaxies (satellite or isolated). Lastly, we discuss
potential correlations between the presence of substructure in the halo and the
structural properties of the disk. While many exciting discoveries have been
made of tidal substructures around external galaxies, the "global" questions of
galaxy formation and evolution via hierarchical accretion await a more complete
census of the low surface brightness outskirts of galaxies in and beyond the
Local Group.


title:
Weighted estimates for vector-valued intrinsic square functions and
  commutators in the Morrey type spaces

abstract:
  In this paper, the boundedness properties of vector-valued intrinsic square
functions and their vector-valued commutators with $BMO(\mathbb R^n)$ functions
are discussed. We first show the weighted strong type and weak type estimates
of vector-valued intrinsic square functions in the Morrey type spaces. Then we
obtain weighted strong type estimates of vector-valued analogues of commutators
in Morrey type spaces. In the endpoint case, we establish the weighted weak
$L\log L$-type estimates for these vector-valued commutators in the setting of
weighted Lebesgue spaces. Furthermore, we prove weighted endpoint estimates of
these commutator operators in Morrey type spaces. In particular, we can obtain
strong type and endpoint estimates of vector-valued intrinsic square functions
and their commutators in the weighted Morrey spaces and the generalized Morrey
spaces.


title:
Weighted inequalities for fractional integral operators and linear
  commutators in the Morrey type spaces

abstract:
  In this paper, we first introduce some new Morrey type spaces containing
generalized Morrey space and weighted Morrey space with two weights as special
cases. Then we give the weighted strong type and weak type estimates for
fractional integral operators $I_\alpha$ in these new Morrey type spaces.
Furthermore, the weighted strong type estimate and endpoint estimate of linear
commutators $[b,I_{\alpha}]$ formed by $b$ and $I_{\alpha}$ are established.
Also we study related problems about two-weight, weak type inequalities for
$I_{\alpha}$ and $[b,I_{\alpha}]$ in the Morrey type spaces and give partial
results.


title:
The Small Contribution of Molecular Bremsstrahlung Radiation to the
  Air-Fluorescence Yield of Cosmic Ray Shower Particles

abstract:
  A small contribution of molecular Bremsstrahlung radiation to the
air-fluorescence yield in the UV range is estimated based on an approach
previously developed in the framework of the radio-detection of showers in the
gigahertz frequency range. First, this approach is shown to provide an estimate
of the main contribution of the fluorescence yield due to the de-excitation of
the C $^3\Pi_{\mathrm{u}}$ electronic level of nitrogen molecules to the B
$^3\Pi_{\mathrm{g}}$ one amounting to $Y_{[337]}=(6.05\pm 1.50)~$ MeV$^{-1}$ at
800 hPa pressure and 293 K temperature conditions, which compares well to
previous dedicated works and to experimental results. Then, under the same
pressure and temperature conditions, the fluorescence yield induced by
molecular Bremsstrahlung radiation is found to be
$Y_{[330-400]}^{\mathrm{MBR}}=0.10~$ MeV$^{-1}$ in the wavelength range of
interest for the air-fluorescence detectors used to detect extensive air
showers induced in the atmosphere by ultra-high energy cosmic rays. This means
that out of $\simeq 175~$ photons with wavelength between 330 and 400 nm
detected by fluorescence detectors, one of them has been produced by molecular
Bremsstrahlung radiation. Although small, this contribution is not negligible
in regards to the total budget of systematic uncertainties when considering the
absolute energy scale of fluorescence detectors.


title: Energy Costs for Traffic Offloading by Cache-enabled D2D Communications

abstract:
  Device-to-Device (D2D) communications can offload the traffic and boost the
throughput of cellular networks. By caching files at users, content delivery
traffic can be offloaded via D2D links, if a helper user are willing to send
the cached file to the user who requests the file. Yet it is unclear how much
energy needs to be consumed at a helper user to support the traffic offloading.
In this paper, we strive to find the minimal energy consumption required at a
helper user to maximize the amount of offloaded traffic. To this end, we
introduce a user-centric proactive caching policy that can control the energy
cost for a helper user to convey a file, and then optimize the caching policy
to maximize the offloaded traffic. To reduce the energy during transmission, we
optimize the transmit power to minimize the energy consumed by a helper to send
a file. We analyze the relationship between traffic offloading and energy cost
with the optimized caching policy and transmit power by numerical and
simulation results, which demonstrate that a significant amount of traffic can
be offloaded with affordable energy costs.


title:
Normal approximation and almost sure central limit theorem for
  non-symmetric Rademacher functionals

abstract:
  In this work, we study the normal approximation and almost sure central limit
theorems for some functionals of an independent sequence of Rademacher random
variables. In particular, we provide a new chain rule that improves the one
derived by Nourdin, Peccati and Reinert(2010) and then we deduce the bound on
Wasserstein distance for normal approximation using the (discrete)
Malliavin-Stein approach. Besides, we are able to give the almost sure central
limit theorem for a sequence of random variables inside a fixed Rademacher
chaos using the Ibragimov-Lifshits criterion.


title:
Insights on finite size effects in Ab-initio study of CO adsorption and
  dissociation on Fe 110 surface

abstract:
  Adsorption and dissociation of hydrocarbons on metallic surfaces represent
crucial steps to carburization of metal. Here, we use density functional theory
total energy calculations with the climbing-image nudged elastic band method to
estimate the adsorption energies and dissociation barriers for different CO
coverages with surface supercells of different sizes. For the absorption of CO,
the contribution from van der Waals interaction in the computation of
adsorption parameters is found important in small systems with high
CO-coverages. The dissociation process involves carbon insertion into the Fe
surface causing a lattice deformation that requires a larger surface system for
unrestricted relaxation. We show that, in larger surface systems associated
with dilute CO-coverages, the dissociation barrier is significantly decreased.
The elastic deformation of the surface is generic and can potentially
applicable for all similar metal-hydrocarbon reactions and therefore a dilute
coverage is necessary for the simulation of these reactions as isolated
processes.


title:
Comparative Multi Fractal De-trended Fluctuation Analysis of heavy ion
  interactions at a few GeV to a few hundred GeV

abstract:
  We have studied the multifractality of pion emission process in 16O-AgBr
interactions at 2.1AGeV & 60AGeV, 12CAgBr &24Mg-AgBr interactions at 4.5AGeV
and 32S-AgBr interactions at 200AGeV using Multifractal Detrended Fluctuation
Analysis (MFDFA) method which is capable of extracting the actual multifractal
property filtering out the average trend of fluctuation. The analysis revels
that the pseudo rapidity distribution of the shower particles is multifractal
in nature for all the interactions i.e. pion production mechanism has in built
multi-scale self-similarity property. We have employed MFDFA method for
randomly generated events for 32S-AgBr interactions at 200 AGeV. Comparison of
expt. results with those obtained from randomly generated data set reveals that
the source of multifractality in our data is the presence of long range
correlation. Comparing the results obtained from different interactions, it may
be concluded that strength of multifractality decreases with projectile mass
for same projectile energy and for a particular projectile it increases with
energy. The values of ordinary Hurst exponent suggest that there is long range
correlation present in our data for all the interactions.


title: Cooperative Device-to-Device Communications With Caching

abstract:
  Device-to-Device (D2D) communications can increase the throughput of cellular
networks significantly, where the interference among D2D links should be
properly managed. In this paper, we propose an opportunistic cooperative D2D
transmission strategy by exploiting the caching capability at the users to deal
with the interference among D2D links. To increase the cooperative opportunity
and improve spatial reuse gain, we divide the D2D users into clusters and cache
different popular files at the users within a cluster, and then find the
optimal cluster size. To maximize the network throughput, we assign different
frequency bands to cooperative and non-cooperative D2D links and optimize the
bandwidth partition. Simulation results demonstrate that the proposed strategy
can provide 500%-600% throughput gain over existing cache-enabled D2D
communications when the popularity distribution is skewed, and can provide
40%-80% gain even when the popularity distribution is uniform.


title:
Angular momentum content of the $\rho(1450)$ from chiral lattice
  fermions

abstract:
  We identify the chiral and angular momentum content of the leading
quark-antiquark Fock component for the $\rho(770)$ and $\rho(1450)$ mesons
using a two-flavor lattice simulation with dynamical Overlap Dirac fermions. We
extract this information from the overlap factors of two interpolating fields
with different chiral structure and from the unitary transformation between
chiral and angular momentum basis. For the chiral content of the mesons we find
that the $\rho(770)$ slightly favors the $(1,0)\oplus(0,1)$ chiral
representation and the $\rho(1450)$ slightly favors the $(1/2,1/2)_b$ chiral
representation. In the angular momentum basis the $\rho(770)$ is then a $^3S_1$
state, in accordance with the quark model. The $\rho(1450)$ is a $^3D_1$ state,
showing that the quark model wrongly assumes the $\rho(1450)$ to be a radial
excitation of the $\rho(770)$.


title:
Band Structure of EuO/Si Spin Contact: Justification for Silicon
  Spintronics

abstract:
  Silicon spintronics requires injection of spin-polarized carriers into Si. An
emerging approach is direct electrical injection from a ferromagnetic
semiconductor - EuO being the prime choice. Functionality of the EuO/Si spin
contact is determined by the interface band alignment. In particular, the band
offset should fall within the 0.5-2 eV range. We employ soft-X-ray ARPES to
probe the electronic structure of the buried EuO/Si interface with momentum
resolution and chemical specificity. The band structure reveals a conduction
band offset of 1.0 eV attesting the technological potential of the EuO/Si
system.


title: Stationary Graph Processes and Spectral Estimation

abstract:
  Stationarity is a cornerstone property that facilitates the analysis and
processing of random signals in the time domain. Although time-varying signals
are abundant in nature, in many practical scenarios the information of interest
resides in more irregular graph domains. This lack of regularity hampers the
generalization of the classical notion of stationarity to graph signals. The
contribution in this paper is twofold. Firstly, we propose a definition of weak
stationarity for random graph signals that takes into account the structure of
the graph where the random process takes place, while inheriting many of the
meaningful properties of the classical definition in the time domain. Our
definition requires that stationary graph processes can be modeled as the
output of a linear graph filter applied to a white input. We will show that
this is equivalent to requiring the correlation matrix to be diagonalized by
the graph Fourier transform. Secondly, we analyze the properties of the power
spectral density and propose a number of methods to estimate it. We start with
nonparametric approaches, including periodograms, window-based average
periodograms, and filter banks. We then shift the focus to parametric
approaches, discussing the estimation of moving-average (MA), autoregressive
(AR) and ARMA processes. Finally, we illustrate the power spectral density
estimation in synthetic and real-world graphs.


title: Off-shell higher spin N=2 supermultiplets in three dimensions

abstract:
  Off-shell higher spin N=2 supermultiplets in three spacetime dimensions (3D)
are presented in this paper. We propose gauge prepotentials for higher spin
superconformal gravity and construct the corresponding gauge-invariant field
strengths, which are proved to be conformal primary superfields. These field
strengths are higher spin generalisations of the (linearised) N=2 super-Cotton
tensor, which controls the superspace geometry of conformal supergravity. We
also construct the higher spin extensions of the linearised N=2 conformal
supergravity action. We provide two dually equivalent off-shell formulations
for massless higher spin N=2 supermultiplets. They involve one and the same
superconformal prepotential but differ in the compensators used. For the lowest
superspin value 3/2, these higher spin series terminate at the linearised
actions for the (1,1) minimal and w=-1 non-minimal N=2 Poincar\'e supergravity
theories constructed in arXiv:1109.0496. Similar to the pure 3D supergravity
actions, their higher spin counterparts propagate no degrees of freedom.
However, the massless higher spin supermultiplets are used to construct
off-shell massive N=2 supermultiplets by combining the massless actions with
those describing higher spin extensions of the linearised N=2 conformal
supergravity. We also demonstrate that every higher spin super-Cotton tensor
can be represented as a linear superposition of the equations of motion for the
corresponding massless higher spin supermultiplet,with the coefficients being
higher-derivative linear operators.


title:
Modeling Dropwise Condensation underneath Unidirectional Wettability
  Graded Surfaces

abstract:
  The dropwise condensation underneath a horizontal super-hydrophobic surface
having unidirectional wettability gradient is modeled with implication to
enhance the rate of condensation. The mathematical model includes nucleation,
growth by vapor condensation and coalescence, and drop instability arising from
force imbalances at the three-phase contact line. The wettability graded
surfaces, formed by a variable surface energy coating, allow the micro-drop of
condensate to slide from the hydrophobic to the hydrophilic region without the
aid of gravity. The resulting decrease in the drop sliding size shifts the drop
size distribution to smaller radii. Furthermore, this decrease in sliding size
enhances the heat transfer rate during dropwise condensation. Simulation data
has been compared with condensation patterns for a horizontal surface and
inclined surface, both with zero wettability gradients. Results obtained show
that a wettability graded surface can effectively control the condensation
process by decreasing the cycle time of nucleation, growth and removal.


title: Fleming-Viot processes : two explicit examples

abstract:
  The purpose of this paper is to extend the investigation of the Fleming-Viot
process in discrete space started in a previous work to two specific examples.
The first one corresponds to a random walk on the complete graph. Due to its
geometry, we establish several explicit and optimal formulas for the
Fleming-Viot process (invariant distribution, correlations, spectral gap). The
second example corresponds to a Markov chain in a two state space. In this
case, the study of the Fleming-Viot particle system is reduced to the study of
birth and death process with quadratic rates.


title: Active galaxies can make axionic dark energy

abstract:
  AGN jets carry helical magnetic fields, which can affect dark matter if the
latter is axionic. This preliminary study shows that, in the presence of strong
helical magnetic fields, the nature of the axionic condensate may change and
become dark energy. Such dark energy may affect galaxy formation and galactic
dynamics, so this possibility should not be ignored when considering axionic
dark matter.


title:
Disentangling the hadronic molecule nature of the $P_c(4380)$
  pentaquark-like structure

abstract:
  We demonstrate that the relative ratio of the decays of hidden charm
pentaquark-like structure $P^+_c(4380)$ to $\bar{D}^* \Lambda_c^+$ and $J/\psi
p$ are very different for $P^+_c$ being $\bar{D} \Sigma_c^*(2520)$ or
$\bar{D}^* \Sigma_c(2455)$ molecule states. While the partial width of the
$\bar{D} \Sigma_c^*(2520)$ molecule to the $\bar{D}^* \Lambda_c^+$ is much
larger, by one order of magnitude, than that to the $J/\psi p$, the $\bar{D}^*
\Sigma_c(2455)$ molecule shows a different pattern. Our analysis shows that the
$\bar{D} \Sigma_c^*$ bound state ansatz is more reasonable than the $\bar{D}^*
\Sigma_c$ one to explain the broad $P_c(4380)$ structure. We suggest to search
for the $P_c(4380)$ in the $\bar{D}^* \Lambda_c^+$ system, which can be used to
disentangle the nature of the $P^+_c(4380)$ structure.


title:
Magnetic activity cycles in solar-like stars: The cross-correlation
  technique of p-mode frequency shifts

abstract:
  Aims. We aim studying the use of cross-correlation techniques to infer the
frequency shifts induced by changing magnetic fields in the p-mode frequencies
and provide precise estimation of the error bars. Methods. This technique and
the calculation of the associated errors is first tested and validated on the
Sun where the p-mode magnetic behaviour is very well known. These validation
tests are performed on 6000-day time series of Sun-as-a-star observations
delivered by the SoHO spacecraft. Errors of the frequency shifts are quantified
through Monte Carlo simulations. The same methodology is then applied to three
solar-like oscillating stars: HD 49933, observed by CoRoT, as well as KIC
3733735 and KIC 7940546 observed by Kepler. Results. We first demonstrate the
reliability of the error bars computed with the Monte Carlo simulations using
the Sun. From the three analyzed stars we confirm the presence of a magnetic
activity cycle with this methodology in HD 49933 and we unveil seismic
signature of on going magnetic variations in KIC 3733735. Finally, the third
star, KIC 7940546, seems to be in a quiet regime.


title: How Does Metallicity Affect the Gas and Dust Properties of Galaxies?

abstract:
  Comparison of the ISM properties of a wide range of metal-poor galaxies with
normal metal-rich galaxies reveals striking differences. We find that the
combination of the low dust abundance and the active star formation results in
a very porous ISM filled with hard photons, heating the dust in dwarf galaxies
to overall higher temperatures than their metal-rich counterparts. This results
in photodissociation of molecular clouds to greater depths, leaving relatively
large PDR envelopes and difficult-to-detect CO cores. From detailed modeling of
the low-metallicity ISM, we find significant fractions of CO-dark H2 - a
reservoir of molecular gas not traced by CO, but present in the [CII] and
[CI]-emitting envelopes. Self-consistent analyses of the neutral and ionized
gas diagnostics along with the dust SED is the necessary way forward in
uncovering the multiphase structure of galaxies


title:
Interplay of Quantum Size Effect, Anisotropy and Surface Stress Shapes
  the Instability of Thin Metal Films

abstract:
  Morphological instability of a planar surface ([111], [011], or [001]) of an
ultra-thin metal film is studied in a parameter space formed by three major
effects (the quantum size effect, the surface energy anisotropy and the surface
stress) that influence a film dewetting. The analysis is based on the extended
Mullins equation, where the effects are cast as functions of the film
thickness. The formulation of the quantum size effect (Z. Zhang et al., PRL 80,
5381 (1998)) includes the oscillation of the surface energy with thickness
caused by electrons confinement. By systematically comparing the effects, their
contributions into the overall stability (or instability) is highlighted.

categories: cond-mat.mtrl-sci cond-mat.mes-hall math.AP nlin.PS


title: Emergence of linear elasticity from the atomistic description of matter

abstract:
  We investigate the emergence of the continuum elastic limit from the
atomistic description of matter at zero temperature considering how locally
defined elastic quantities depend on the coarse graining length scale. Results
obtained numerically investigating different model systems are rationalized in
a unifying picture according to which the continuum elastic limit emerges
through a process determined by two system properties, the degree of disorder,
and a length scale associated to the transverse low-frequency vibrational
modes. The degree of disorder controls the emergence of long-range local shear
stress and shear strain correlations, while the transverse length scale
influences the amplitude of the fluctuations of the local elastic constants.


title:
Quasiparticle band structure of the almost-gapless
  transition-metal-based Heusler semiconductors

abstract:
  Transition-metal-based Heusler semiconductors are promising materials for a
variety of applications ranging from spintronics to thermoelectricity.
Employing the $GW$ approximation within the framework of the FLAPW method, we
study the quasi-particle band structure of a number of such compounds being
almost gapless semiconductors. We find that in contrast to the
\textit{sp}-electron based semiconductors such as Si and GaAs, in these systems
the many-body corrections have a minimal effect on the electronic band
structure and the energy band gap increases by less than 0.2~eV, which makes
the starting point density functional theory (DFT) a good approximation for the
description of electronic and optical properties of these materials.
Furthermore, the band gap can be tuned either by the variation of the lattice
parameter or by the substitution of the \emph{sp}-chemical element.


title: The $C^*$-algebras of quantum lens and weighted projective spaces

abstract:
  It is shown that the algebra of continuous functions on the quantum
$2n+1$-dimensional lens space $C(L^{2n+1}_q(N; m_0,\ldots, m_n))$ is a graph
$C^*$-algebra, for arbitrary positive weights $ m_0,\ldots, m_n$. The form of
the corresponding graph is determined from the skew product of the graph which
defines the algebra of continuous functions on the quantum sphere $S_q^{2n+1}$
and the cyclic group $\mathbb{Z}_N$, with the labelling induced by the weights.
Based on this description, the K-groups of specific examples are computed.
Furthermore, the K-groups of the algebras of continuous functions on quantum
weighted projective spaces $C(\mathbb{WP}_q^n(m_0,\ldots, m_n))$, interpreted
as fixed points under the circle action on $C(S_q^{2n+1})$, are computed under
a mild assumption on the weights.


title:
Photon bremsstrahlung from quark jet via transverse and longitudinal
  scatterings: single versus multiple scatterings

abstract:
  We study the production of jet-bremsstrahlung photons through the scattering
with the constituents of a dense nuclear matter within the framework of
deep-inelastic scattering off a large nucleus. Applying a gradient expansion up
to the second order for the exchanged three-dimensional momentum between jet
and medium, we derive the single photon bremsstrahlung spectrum with the
inclusion of the contributions from the transverse broadening as well as the
longitudinal drag and diffusion of the hard parton's momentum. We also compare
the medium-induced photon radiation spectra for single scattering and from the
resummation of multiple scatterings. It is found that the coupling between
different scatterings can give additional contribution to medium-induced photon
radiation, while for small momentum exchange, the leading contribution from the
drag and diffusions to the photon emission spectra remain the same for single
and multiple scatterings.


title: Global solutions to the shallow-water system

abstract:
  The classical system of shallow-water (Saint--Venant) equations describes
long surface waves in an inviscid incompressible fluid of a variable depth.
Although shock waves are expected in this quasilinear hyperbolic system for a
wide class of initial data, we find a sufficient condition on the initial data
that guarantees existence of a global classical solution continued from a local
solution. The sufficient conditions can be easily satisfied for the fluid flow
propagating in one direction with two characteristic velocities of the same
sign and two monotonically increasing Riemann invariants. We prove that these
properties persist in the time evolution of the classical solutions to the
shallow-water equations and provide no shock wave singularities formed in a
finite time over a half-line or an infinite line. On a technical side, we
develop a novel method of an additional argument, which allows to obtain local
and global solutions to the quasilinear hyperbolic systems in physical rather
than characteristic variables.


title:
The derived category of complex periodic K-theory localized at an odd
  prime

abstract:
  We prove that for an odd prime $p$, the derived category
$\mathcal{D}(KU_{(p)})$ of the $p$-local complex periodic $K$-theory spectrum
$KU_{(p)}$ is triangulated equivalent to the derived category of its homotopy
ring $\pi_*KU_{(p)}$. This implies that if $p$ is an odd prime, the
triangulated category $\mathcal{D}(KU_{(p)})$ is algebraic.


title:
Dynamic Analysis of Bet-Hedging Strategies as a Protection Mechanism
  against Environmental Fluctuations

abstract:
  In order to increase their robustness against environmental fluctuations,
many biological populations have developed bet-hedging mechanisms in which the
population `bets' against the presence of prolonged favorable environmental
conditions by having a few individual behaving as if they sensed a threatening
or stressful environment. As a result, the population (as a whole) increases
its chances of surviving environmental fluctuations in the long term, while
sacrificing short-term performance. In this paper, we propose a theoretical
framework, based on Markov jump linear systems, to model and evaluate the
performance of bet-hedging strategies in the presence of stochastic
fluctuations. We illustrate our results using numerical simulations.


title: Kullback-Leibler Divergence Approach to Partitioned Update Kalman Filter

abstract:
  Kalman filtering is a widely used framework for Bayesian estimation. The
partitioned update Kalman filter applies a Kalman filter update in parts so
that the most linear parts of measurements are applied first. In this paper, we
generalize partitioned update Kalman filter, which requires the use oft the
second order extended Kalman filter, so that it can be used with any Kalman
filter extension. To do so, we use a Kullback-Leibler divergence approach to
measure the nonlinearity of the measurement, which is theoretically more sound
than the nonlinearity measure used in the original partitioned update Kalman
filter. Results show that the use of the proposed partitioned update filter
improves the estimation accuracy.


title: Double supergeometry

abstract:
  A geometry of superspace corresponding to double field theory is developed,
with type II supergravity in D=10 as the main example. The formalism is based
on an orthosymplectic extension OSp(d,d|2s) of the continuous T-duality group.
Covariance under generalised super-diffeomorphisms is manifest. Ordinary
superspace is obtained as a solution of the orthosymplectic section condition.
A systematic study of curved superspace Bianchi identities is performed, and a
relation to a double pure spinor superfield cohomology is established. A
Ramond-Ramond superfield is constructed as an infinite-dimensional
orthosymplectic spinor. Such objects in minimal orbits under the OSp supergroup
("pure spinors") define super-sections.


title:
Idempotent and p-potent quadratic functions: Distribution of
  nonlinearity and co-dimension

abstract:
  The Walsh transform $\widehat{Q}$ of a quadratic function
$Q:F_{p^n}\rightarrow F_p$ satisfies $|\widehat{Q}(b)| \in
\{0,p^{\frac{n+s}{2}}\}$ for all $b\in F_{p^n}$, where $0\le s\le n-1$ is an
integer depending on $Q$. In this article, we study the following three classes
of quadratic functions of wide interest. The class $\mathcal{C}_1$ is defined
for arbitrary $n$ as $\mathcal{C}_1 = \{Q(x) = Tr(\sum_{i=1}^{\lfloor
(n-1)/2\rfloor}a_ix^{2^i+1})\;:\; a_i \in F_2\}$, and the larger class
$\mathcal{C}_2$ is defined for even $n$ as $\mathcal{C}_2 = \{Q(x) =
Tr(\sum_{i=1}^{(n/2)-1}a_ix^{2^i+1}) + {\rm Tr_{n/2}}(a_{n/2}x^{2^{n/2}+1})
\;:\; a_i \in F_2\}$. For an odd prime $p$, the subclass $\mathcal{D}$ of all
$p$-ary quadratic functions is defined as $\mathcal{D} = \{Q(x) =
Tr(\sum_{i=0}^{\lfloor n/2\rfloor}a_ix^{p^i+1})\;:\; a_i \in F_p\}$. We
determine the distribution of the parameter $s$ for $\mathcal{C}_1,
\mathcal{C}_2$ and $\mathcal{D}$. As a consequence we obtain the distribution
of the nonlinearity for the rotation symmetric quadratic Boolean functions, and
in the case $p > 2$, our results yield the distribution of the co-dimensions
for the rotation symmetric quadratic $p$-ary functions, which have been
attracting considerable attention recently. We also present the complete weight
distribution of the subcodes of the second order Reed-Muller codes
corresponding to $\mathcal{C}_1$ and $\mathcal{C}_2$.


title:
Circuit Quantum Electrodynamics Simulator of Flat Band Physics in Lieb
  lattice

abstract:
  The concept of flat band plays an important role in strongly-correlated
many-body physics. However, the demonstration of the flat band physics is
highly nontrivial due to intrinsic limitations in conventional condensed matter
materials. Here we propose a circuit quantum electrodynamics simulator of the
2D Lieb lattice exhibiting a flat middle band. By exploiting the simple
parametric conversion method, we design a photonic Lieb lattice with \textit{in
situ} tunable hopping strengths in a 2D array of coupled superconducting
transmissionline resonators. Moreover, the flexibility of our proposal enables
the immediate incorporation of both the artificial gauge field and the strong
photon-photon interaction in a time- and site-resolved manner. To unambiguously
demonstrate the synthesized flat band, we further investigate the observation
of the flat band localization of microwave photons through the pumping and the
steady-state measurements of only few sites on the lattice. Requiring only
current level of technique and being robust against imperfections in realistic
circuits, our scheme can be readily tested in experiments and may pave a new
way towards the future realization of exotic photonic quantum Hall fluids
including anomalous quantum Hall effect and bosonic fractional quantum Hall
states without magnetic fields.


title: Recurrent Network Models Of Sequence Generation And Memory

abstract:
  Sequential activation of neurons is a common feature of network activity
during a variety of behaviors, including working memory and decision making.
Previous network models for sequences and memory emphasized specialized
architectures in which a principled mechanism is pre-wired into their
connectivity. Here we demonstrate that, starting from random connectivity and
modifying a small fraction of connections, a largely disordered recur- rent
network can produce sequences and implement working memory efficiently. We use
this process, called Partial In-Network Training (PINning), to model and match
cellular resolution imaging data from the posterior parietal cortex during a
virtual memory- guided two-alternative forced-choice task. Analysis of the
connectivity reveals that sequences propagate by the cooperation between
recurrent synaptic interactions and external inputs, rather than through
feedforward or asymmetric connections. Together our results suggest that neural
sequences may emerge through learning from largely unstructured network
architectures.


title: Classical integrable defects as quasi B\"acklund transformations

abstract:
  We consider the algebraic setting of classical defects in discrete and
continuous integrable theories. We derive the "equations of motion" on the
defect point via the space-like and time-like description. We then exploit the
structural similarity of these equations with the discrete and continuous
Backlund transformations. And although these equations are similar they are not
exactly the same to the Backlund transformations. We also consider specific
examples of integrable models to demonstrate our construction, i.e. the Toda
chain and the sine-Gordon model. The equations of the time (space) evolution of
the defect (discontinuity) degrees of freedom for these models are explicitly
derived.


title: The Quench Action

abstract:
  We give a pedagogical introduction to the methodology of the Quench Action,
which is an effective representation for the calculation of time-dependent
expectation values of physical operators following a generic out-of-equilibrium
state preparation protocol (for example a quantum quench). The representation,
originally introduced in [Caux and Essler, Phys. Rev. Lett. 110, 257203
(2013)], is founded on a mixture of exact data for overlaps together with
variational reasonings. It is argued to be quite generally valid and
thermodynamically exact for arbitrary times after the quench (from short times
all the way up to the steady state), and applicable to a wide class of
physically relevant observables. Here, we introduce the method and its
language, give an overview of some recent results, suggest a roadmap and offer
some perspectives on possible future research directions.


title:
A 2.542-Approximation for Precedence Constrained Single Machine
  Scheduling with Release Dates and Total Weighted Completion Time Objective

abstract:
  We present a $\sqrt{e}/(\sqrt{e}-1)$-approximation algorithm for the
nonpreemptive scheduling problem to minimize the total weighted completion time
of jobs on a single machine subject to release dates and precedence
constraints. The previously best known approximation algorithm dates back to
1997; its performance guarantee can be made arbitrarily close to the Euler
constant $e$.


title:
Parity of the Langlands parameters of conjugate self-dual
  representations of GL(n) and the local Jacquet-Langlands correspondence

abstract:
  We determine the parity of the Langlands parameter of a conjugate self-dual
supercuspidal representation of GL(n) over a non-archimedean local field by
means of the local Jacquet-Langlands correspondence. It gives a partial
generalization of a previous result on the self-dual case by Prasad and
Ramakrishnan.


title: Irreducible admissible mod-p representations of metaplectic groups

abstract:
  Let $p$ be an odd prime number, and $F$ a nonarchimedean local field of
residual characteristic $p$. We classify the smooth, irreducible, admissible
genuine mod-$p$ representations of the twofold metaplectic cover
$\widetilde{\textrm{Sp}}_{2n}(F)$ of $\textrm{Sp}_{2n}(F)$ in terms of genuine
supercuspidal (equivalently, supersingular) representations of Levi subgroups.
To do so, we use results of Henniart--Vign\'{e}ras as well as new technical
results to adapt Herzig's method to the metaplectic setting. As consequences,
we obtain an irreducibility criterion for principal series representations
generalizing the complete irreducibility of principal series representations in
the rank 1 case, as well as the fact that irreducibility is preserved by
parabolic induction from the cover of the Siegel Levi subgroup.


title:
Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal
  representations II: wild case

abstract:
  We construct a family of affinoids in the Lubin-Tate perfectoid space and
their formal models such that the middle cohomology of their reductions
realizes the local Langlands correspondence and the local Jacquet-Langlands
correspondence for the simple supercuspidal representations. The reductions of
the formal models are isomorphic to the perfections of some Artin-Schreier
varieties, whose cohomology realizes primitive Galois representations. We show
also the Tate conjecture for Artin-Schreier varieties associated to quadratic
forms.


title: Zeros of Ramanujan Type Entire Functions

abstract:
  In this work we establish some polynomials and entire functions have only
real zeros. These polynomials generalize q-Laguerre polynomials
$L_{n}^{(\alpha)}(x;q)$, while the entire functions are generalizations of
Ramanujan's entire function $A_{q}(z)$, q-Bessel functions
$J_{\nu}^{(2)}(z;q)$, $J_{\nu}^{(3)}(z;q)$ and confluent basic hypergeometric
series.


title: Estructuras de grupo topol\'ogico en (Z,+)

abstract:
  In this work we have considered the complexity of the different structures as
topological group on Z. We collect some new results, as well as some known
results on the group of the integers in order to present: -A family of
$2^\cont$ precompact Hausdorff. -A wide family of metrizable non-precompact,
non-complete group topologies. -A wide family of complete non-metrizable
topologies. We leave some open questions - for instance the problem of the
cardinality of the families above.


title: Weak lensing study of 16 DAFT/FADA clusters: substructures and filaments

abstract:
  While our current cosmological model places galaxy clusters at the nodes of a
filament network (the cosmic web), we still struggle to detect these filaments
at high redshifts. We perform a weak lensing study for a sample of 16 massive,
medium-high redshift (0.4<z<0.9) galaxy clusters from the DAFT/FADA survey,
that are imaged in at least three optical bands with Subaru/Suprime-Cam or
CFHT/MegaCam. We estimate the cluster masses using an NFW fit to the shear
profile measured in a KSB-like method, adding our contribution to the
calibration of the observable-mass relation required for cluster abundance
cosmological studies. We compute convergence maps and select structures within,
securing their detection with noise re-sampling techniques. Taking advantage of
the large field of view of our data, we study cluster environment, adding
information from galaxy density maps at the cluster redshift and from X-ray
images when available. We find that clusters show a large variety of weak
lensing maps at large scales and that they may all be embedded in filamentary
structures at megaparsec scale. We classify them in three categories according
to the smoothness of their weak lensing contours and to the amount of
substructures: relaxed (~7%), past mergers (~21.5%), recent or present mergers
(~71.5%). The fraction of clusters undergoing merging events observationally
supports the hierarchical scenario of cluster growth, and implies that massive
clusters are strongly evolving at the studied redshifts. Finally, we report the
detection of unusually elongated structures in CLJ0152, MACSJ0454, MACSJ0717,
A851, BMW1226, MACSJ1621, and MS1621.


title:
Electroweak and Majorana Sector Higgs Bosons and Pseudo-Nambu-Goldstone
  Bosons

abstract:
  We propose a Clifford algebra based model, which treats both gravity and
Yang-Mills interactions as gauge fields. There are two sectors of boson fields
as electroweak and Majorana bosons. The electroweak boson sector induces
fermion masses via spontaneous symmetry breaking. It is composed of scalar
Higgs, pseudoscalar Higgs, and antisymmetric tensor components. The Majorana
boson sector contributes to flavor mixing and Majorana masses of right-handed
neutrinos. It is comprised of neutrino Higgs and pseudo-Nambu-Goldstone bosons.
The LHC 750 GeV diphoton resonance might possibly be identified as a Majorana
sector pseudo-Nambu-Goldstone boson, which results from spontaneous symmetry
breaking of a flavor-related global U(1) symmetry involving four-fermion
condensation of right-handed leptons and quarks. The diphoton decay is loop
induced, since tree-level decay is suppressed by large Majorana mass of the
right-handed neutrino. There is also a potential dark matter candidate, which
is the four-lepton condensation of muon, muon-neutrino, tau, and tau-neutrino.


title: Roulettes: A weak lensing formalism for strong lensing - I. Overview

abstract:
  We present a new perspective on gravitational lensing. We describe a new
extension of the weak lensing formalism capable of describing strongly lensed
images. By integrating the non-linear geodesic deviation equation, the
amplification matrix of weak lensing is generalised to a sum over independent
amplification tensors of increasing rank. We show how an image distorted by a
generic lens may be constructed as a sum over `roulettes', which are the
natural curves associated with the independent spin modes of the amplification
tensors. Highly distorted images can be constructed even for large sources
observed near or within the Einstein radius of a lens where the shear and
convergence are large. The amplitude of each roulette is formed from a sum over
appropriate derivatives of the lensing potential. Consequently, measuring these
individual roulettes for images around a lens gives a new way to reconstruct a
strong lens mass distribution without requiring a lens model. This formalism
generalises the convergence, shear and flexion of weak lensing to arbitrary
order, and provides a unified bridge between the strong and weak lensing
regimes.
  This overview paper is accompanied by a much more detailed Paper II,
arXiv:1603.04652


title: Sideband Rabi spectroscopy of finite-temperature trapped Bose gases

abstract:
  We use Rabi spectroscopy to explore the low-energy excitation spectrum of a
finite-temperature Bose gas of rubidium atoms across the phase transition to a
Bose-Einstein condensate (BEC). To record this spectrum, we coherently drive
the atomic population between two spin states. A small relative displacement of
the spin-specific trapping potentials enables sideband transitions between
different motional states. The intrinsic non-linearity of the motional
spectrum, mainly originating from two-body interactions, makes it possible to
resolve and address individual excitation lines. Together with sensitive
atom-counting, this constitutes a feasible technique to count single excited
atoms of a BEC and to determine the temperature of nearly pure condensates. As
an example, we show that for a nearly pure BEC of N = 800 atoms the first
excited state has a population of less than 5 atoms, corresponding to an upper
bound on the temperature of 30 nK.


title:
Topologically protected edge gap solitons of interacting Bosons in
  one-dimensional superlattices

abstract:
  We comprehensively investigate the nontrivial states of interacting Bose
system in one-dimensional optical superlattices under the open boundary
condition. Our results show that there exists a kind of stable localized
states: edge gap solitons. We argue that the states originate from the
eigenstates of independent edge parabolas. In particular, the edge gap solitons
exhibit a nonzero topological invariant. The topological nature is due to the
connection of the present model to the quantized adiabatic particle transport
problem. In addition, the composition relations between the gap solitons and
the extend states under the open boundary condition are discussed.


title:
Many-Body-Localization Transition : strong multifractality spectrum for
  matrix elements of local operators

abstract:
  For short-ranged disordered quantum models in one dimension, the
Many-Body-Localization is analyzed via the adaptation to the Many-Body context
[M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless
point of view on the Anderson transition : the question is whether a local
interaction between two long chains is able to reshuffle completely the
eigenstates (Delocalized phase with a volume-law entanglement) or whether the
hybridization between tensor states remains limited (Many-Body-Localized Phase
with an area-law entanglement). The central object is thus the level of
Hybridization induced by the matrix elements of local operators, as compared
with the difference of diagonal energies. The multifractal analysis of these
matrix elements of local operators is used to analyze the corresponding
statistics of resonances. Our main conclusion is that the critical point is
characterized by the Strong-Multifractality Spectrum $f(0 \leq \alpha \leq
2)=\frac{\alpha}{2}$, well known in the context of Anderson Localization in
spaces of effective infinite dimensionality, where the size of the Hilbert
space grows exponentially with the volume. Finally, the possibility of a
delocalized non-ergodic phase near criticality is discussed.


title: Numerical study of a recent black hole lasing experiment

abstract:
  We theoretically analyse a recent experiment reporting the observation of a
self-amplifying Hawking radiation in a flowing atomic condensate [J.Steinhauer,
Nature Physics, vol.10, pp.864, Nov 2014]. We are able to accurately reproduce
the experimental observations using a theoretical model based on the numerical
solution of a mean-field Gross-Pitaevskii equation that does not include
quantum fluctuations of the matter field. In addition to confirming the black
hole lasing mechanism, our results show that the underlying dynamical
instability has a classical hydrodynamic origin and is triggered by a seed of
deterministic nature, linked to the non-stationary of the process, rather than
by thermal or zero-point fluctuations.


title:
Scaling limit and convergence of smoothed covariance for gradient models
  with non-convex potential

abstract:
  A discrete gradient model for interfaces is studied. The interaction
potential is a non-convex perturbation of the quadratic gradient potential.
Based on a representation for the finite volume Gibbs measure obtained via a
renormalization group analysis by Adams, Koteck\'{y} and M\"uller in [AKM] it
is proven that the scaling limit is a continuum massless Gaussian free field.
From probabilistic point of view, this is a Central Limit Theorem for strongly
dependent random fields. Additionally, the convergence of covariances, smoothed
on a scale smaller than the system size, is proven.


title: Statistical steady state in turbulent droplet condensation

abstract:
  Motivated by systems in which droplets grow and shrink in a turbulence-driven
supersaturation field, we investigate the problem of turbulent condensation in
a general manner. Using direct numerical simulations we show that the turbulent
fluctuations of the supersaturation field offer different conditions for the
growth of droplets which evolve in time due to turbulent transport and mixing.
Based on that, we propose a Lagrangian stochastic model for condensation and
evaporation of small droplets in turbulent flows. It consists of a set of
stochastic integro-differential equations for the joint evolution of the
squared radius and the supersaturation along the droplet trajectories. The
model has two parameters fixed by the total amount of water and the
thermodynamic properties, as well as the Lagrangian integral timescale of the
turbulent supersaturation. The model reproduces very well the droplet size
distributions obtained from direct numerical simulations and their time
evolution. A noticeable result is that, after a stage where the squared radius
simply diffuses, the system converges exponentially fast to a statistical
steady state independent of the initial conditions. The main mechanism involved
in this convergence is a loss of memory induced by a significant number of
droplets undergoing a complete evaporation before growing again. The
statistical steady state is characterised by an exponential tail in the droplet
mass distribution. These results reconcile those of earlier numerical studies,
once these various regimes are considered.


title: Embeddings of spherical homogeneous spaces in characteristic p

abstract:
  Let G be a reductive group over an algebraically closed field of
characteristic p>0. We study properties of embeddings of spherical homogeneous
G-spaces. We look at Frobenius splittings, canonical or by a (p-1)-th power,
compatible with certain subvarieties. We also look at cohomology vanishing and
show the existence of rational G-equivariant resolutions by toroidal
embeddings. We show that the class of homogeneous spaces for which our results
hold contains the symmetric homogeneous spaces in characteristic not 2 and is
closed under parabolic induction.


title: Shifted Domino tableaux

abstract:
  We introduce new combinatorial objects called the shifted domino tableaux. We
prove that these objects are in bijection with pairs of shifted Young tableaux.
This bijection shows that shifted domino tableaux can be seen as elements of
the super shifted plactic monoid, which is the shifted analog of the super
plactic monoid. We also show that the sum over all shifted domino tableaux of a
fixed shape describe a product of two Q-Schur functions, and by taking a
different kind of shifted domino tableaux we describe a product of two P-Schur
functions.


title:
Estimating the Probability of Wind Ramping Events: A Data-driven
  Approach

abstract:
  This letter proposes a data-driven method for estimating the probability of
wind ramping events without exploiting the exact probability distribution
function (PDF) of wind power. Actual wind data validates the proposed method.


title:
First results on applying a non-linear effect formalism to alliances
  between political parties and buy and sell dynamics

abstract:
  We discuss a non linear extension of a model of alliances in politics,
recently proposed by one of us. The model is constructed in terms of operators,
describing the \emph{interest} of three parties to form, or not, some political
alliance with the other parties. The time evolution of what we call \emph{the
decision functions} is deduced by introducing a suitable hamiltonian, which
describes the main effects of the interactions of the parties amongst
themselves and with their \emph{environments}, {which are }generated by their
electors and by people who still have no clear {idea }for which party to vote
(or even if to vote). The hamiltonian contains some non-linear effects, which
takes into account the role of a party in the decision process of the other two
parties. Moreover, we show how the same hamiltonian can also be used to
construct a formal structure which can describe the dynamics of buying and
selling financial assets (without however implying a specific price setting
mechanism).


title:
Understanding the geometry of transport: diffusion maps for Lagrangian
  trajectory data unravel coherent sets

abstract:
  Dynamical systems often exhibit the emergence of long-lived coherent sets,
which are regions in state space that keep their geometric integrity to a high
extent and thus play an important role in transport. In this article, we
provide a method for extracting coherent sets from possibly sparse Lagrangian
trajectory data. Our method can be seen as an extension of diffusion maps to
trajectory space, and it allows us to construct "dynamical coordinates" which
reveal the intrinsic low-dimensional organization of the data. The only a
priori knowledge about the dynamics that we require is a locally valid notion
of distance, which renders our method highly suitable for automated data
analysis. We show convergence of our method to the analytic transfer operator
framework of coherence in the infinite data limit, and illustrate its potential
on several two- and three-dimensional examples as well as real world data.


title:
Global Attractivity for Fractional Differential Equations in Weighted
  Spaces

abstract:
  We investigate fractional Cauchy type problem. By using Schauder fixed point
theorem we obtain sufficient conditions for the global attractivity of
solutions for nonlinear fractional differential equations in weighted spaces.


title: Hot and Turbulent Gas in Clusters

abstract:
  The gas in galaxy clusters is heated by shock compression through accretion
(outer shocks) and mergers (inner shocks). These processes additionally produce
turbulence. To analyse the relation between the thermal and turbulent energies
of the gas under the influence of non-adiabatic processes, we performed
numerical simulations of cosmic structure formation in a box of 152 Mpc
comoving size with radiative cooling, UV background, and a subgrid scale model
for numerically unresolved turbulence. By smoothing the gas velocities with an
adaptive Kalman filter, we are able to estimate bulk flows toward cluster
cores. This enables us to infer the velocity dispersion associated with the
turbulent fluctuation relative to the bulk flow. For halos with masses above
$10^{13}\,M_\odot$, we find that the turbulent velocity dispersions averaged
over the warm-hot intergalactic medium (WHIM) and the intracluster medium (ICM)
are approximately given by powers of the mean gas temperatures with exponents
around 0.5, corresponding to a roughly linear relation between turbulent and
thermal energies and transonic Mach numbers. However, turbulence is only weakly
correlated with the halo mass. Since the power-law relation is stiffer for the
WHIM, the turbulent Mach number tends to increase with the mean temperature of
the WHIM. This can be attributed to enhanced turbulence production relative to
dissipation in particularly hot and turbulent clusters.


title: Ax-Schanuel for Linear Differential Equations

abstract:
  We generalise the exponential Ax-Schanuel theorem to arbitrary linear
differential equations with constant coefficients. Using the analysis of the
exponential differential equation by J. Kirby and C. Crampin we give a complete
axiomatisation of the first order theories of linear differential equations and
show that the generalised Ax-Schanuel inequalities are adequate for them.


title: Modeling Time Series Similarity with Siamese Recurrent Networks

abstract:
  Traditional techniques for measuring similarities between time series are
based on handcrafted similarity measures, whereas more recent learning-based
approaches cannot exploit external supervision. We combine ideas from
time-series modeling and metric learning, and study siamese recurrent networks
(SRNs) that minimize a classification loss to learn a good similarity measure
between time series. Specifically, our approach learns a vectorial
representation for each time series in such a way that similar time series are
modeled by similar representations, and dissimilar time series by dissimilar
representations. Because it is a similarity prediction models, SRNs are
particularly well-suited to challenging scenarios such as signature
recognition, in which each person is a separate class and very few examples per
class are available. We demonstrate the potential merits of SRNs in
within-domain and out-of-domain classification experiments and in one-shot
learning experiments on tasks such as signature, voice, and sign language
recognition.


title:
Asymptotic reductions and solitons of nonlocal nonlinear Schr\"{o}dinger
  equations

abstract:
  Asymptotic reductions of a defocusing nonlocal nonlinear Schr\"{o}dinger
model in $(3+1)$-dimensions, in both Cartesian and cylindrical geometry, are
presented. First, at an intermediate stage, a Boussinesq equation is derived,
and then its far-field, in the form of a variety of Kadomtsev-Petviashvilli
(KP) equations for right- and left-going waves, is found. KP models include
versions of the KP-I and KP-II equations, in Cartesian and cylindrical
geometry. Solitary waves solutions, planar or ring-shaped, and of dark or
anti-dark type, are also predicted to occur. Their nature and stability is
determined by a parameter defined by the physical parameters of the original
nonlocal system. It is thus found that (dark) anti-dark solitary waves are only
supported by a weak (strong) nonlocality, and are unstable (stable) in
higher-dimensions. Our analytical predictions are corroborated by direct
numerical simulations.


title:
The local boundedness of gradients of weak solutions to elliptic and
  parabolic phi-Laplacian systems

abstract:
  In this thesis, a unified approach to prove the boundedness of gradients of
solutions to degenerate and singular elliptic and parabolic phi-Laplacian
systems is presented. At first, a Cacciopoli-type energy inequality with an
additional function f which can be chosen freely is proven. Then, Di Giorgi's
method is applied using level sets which will lead to L-infinity-estimates on
the gradient of the weak solution.


title:
Lower bound on concurrence for arbitrary-dimensional tripartite quantum
  systems

abstract:
  In this paper, we study the concurrence of arbitrary dimensional tripartite
quantum systems. An explicit operational lower bound of concurrence is obtained
in terms of the concurrence of sub-states. A given example show that our lower
bound may improve the well known existing lower bounds of concurrence. The
significance of our result is to get a lower bound when we study the
concurrence of arbitrary dimensional multipartite quantum systems.


title:
Generation of finite simple groups by an involution and an element of
  prime order

abstract:
  We prove that every non-abelian finite simple group is generated by an
involution and an element of prime order.


title: Higgs decay to two muons at ILC

abstract:
  The coupling of the Higgs to second generation particles can be studied by
measuring the decay of the Higgs boson to two muons. In this analysis we
considered the process at a centre of mass energy of 1 TeV, where the WW-fusion
process is dominant and the Higgsstrahlung can be neglected. We assumed an
integrated luminosity of 500 fb-1 and a beam polarization of (Pe- Pe+) =
(-0.8,+0.2). We estimated the sensitivity of the Higgs coupling to muons using
full simulation of the ILD detector described in the DBD. We developed a new
selection for the two muons based on the latest available particle ID tools.
This improved the sensitivity by more than 10%. A further 10% gains was
achieved by exploiting multi variate techniques. Combining the two improvements
we reached a sensitivity of 2.7, a significant improvement with respect to the
previous estimate.


title:
Dimensionality and irreversibility of field-induced transitions in
  SrDy2O4

abstract:
  Low temperature ultrasound velocity measurements are presented on the
frustrated spin system SrDy2O4 that allow us to define high resolution phase
diagrams with the magnetic field applied along all three principal axes. For
H||b, a region of field-induced long range order is delimited by a dome of
first-order phase transitions. An unusual magnetization process is observed
with significant irreversibility at very low temperatures when passing between
the low-field spin liquid phase and the long range ordered phase which we
attribute to large energy barriers. For H||c, the system appears to remain
effectively one-dimensional, exhibiting two transitions as a function of
magnetic field, but no finite-temperature long range order.