title: Metamorphoses of functional shapes in Sobolev spaces

abstract:
  In this paper, we describe in detail a model of geometric-functional
variability between fshapes. These objects were introduced for the first time
by the authors in [Charlier et al. 2015] and are basically the combination of
classical deformable manifolds with additional scalar signal map. Building on
the aforementioned work, this paper's contributions are several. We first
extend the original $L^2$ model in order to represent signals of higher
regularity on their geometrical support with more regular Hilbert norms
(typically Sobolev). We describe the bundle structure of such fshape spaces
with their adequate geodesic distances, encompassing in one common framework
usual shape comparison and image metamorphoses. We then propose a formulation
of matching between any two fshapes from the optimal control perspective, study
existence of optimal controls and derive Hamiltonian equations and conservation
laws describing the dynamics of geodesics. Secondly, we tackle the discrete
counterpart of these problems and equations through appropriate finite elements
interpolation schemes on triangular meshes. At last, we show a few results of
metamorphosis matchings on synthetic and several real data examples in order to
highlight the key specificities of the approach.


title: Graphons and cut metric on sigma-finite measure spaces

abstract:
  Borgs, Chayes, Cohn and Holden (2016+) recently extended the definition of
graphons from probability spaces to arbitrary $\sigma$-finite measure spaces,
in order to study limits of sparse graphs. They also extended the definition of
the cut metric, and proved various results on the resulting metric space.
  We continue this line of research and give various further results on
graphons and the cut metric in this general setting, extending known results
for the standard case of graphons on probability spaces. In particular, we
characterize pairs of equivalent graphons, and we give new results on
completeness and compactness.


title: FORM, Diagrams and Topologies

abstract:
  We discuss a number of FORM features that are essential in the automatic
processing of very large numbers of diagrams as used in the Forcer program for
4-loop massless propagator diagrams. Most of these features are new.


title: Stable-Unstable Semantics: Beyond NP with Normal Logic Programs

abstract:
  Standard answer set programming (ASP) targets at solving search problems from
the first level of the polynomial time hierarchy (PH). Tackling search problems
beyond NP using ASP is less straightforward. The class of disjunctive logic
programs offers the most prominent way of reaching the second level of the PH,
but encoding respective hard problems as disjunctive programs typically
requires sophisticated techniques such as saturation or meta-interpretation.
The application of such techniques easily leads to encodings that are
inaccessible to non-experts. Furthermore, while disjunctive ASP solvers often
rely on calls to a (co-)NP oracle, it may be difficult to detect from the input
program where the oracle is being accessed. In other formalisms, such as
Quantified Boolean Formulas (QBFs), the interface to the underlying oracle is
more transparent as it is explicitly recorded in the quantifier prefix of a
formula. On the other hand, ASP has advantages over QBFs from the modeling
perspective. The rich high-level languages such as ASP-Core-2 offer a wide
variety of primitives that enable concise and natural encodings of search
problems. In this paper, we present a novel logic programming--based modeling
paradigm that combines the best features of ASP and QBFs. We develop so-called
combined logic programs in which oracles are directly cast as (normal) logic
programs themselves. Recursive incarnations of this construction enable logic
programming on arbitrarily high levels of the PH. We develop a proof-of-concept
implementation for our new paradigm.
  This paper is under consideration for acceptance in TPLP.


title: Random Lax--Oleinik semigroups for Hamilton--Jacobi systems

abstract:
  Following the random approach of Mitake, Siconolfi,Tran and Yamada, we define
a Lax--Oleinik formula adapted to evolutive weakly coupled systems of
Hamilton--Jacobi equations. It is reminiscent of the corresponding scalar
formula, with the relevant difference that it has a stochastic character since
it involves, loosely speaking, random switchings between the various associated
Lagrangians. We prove that the related value functions are viscosity solutions
to the system, and establish existence of minimal random curves under fairly
general hypotheses. Adding Tonelli like assumptions on the Hamiltonians, we
show differentiability properties of such minimizers, and existence of adjoint
random curves. Minimizers and adjoint curves are trajectories of a twisted
generalized Hamiltonian dynamics.


title: Pathlengths of open channels in multiple scattering media

abstract:
  We report optical measurements of the spectral width of open transmission
channels in a three-dimensional diffusive medium. The light transmission
through a sample is enhanced by efficiently coupling to open transmission
channels using repeated digital optical phase conjugation. The spectral
properties are investigated by enhancing the transmission, fixing the incident
wavefront and scanning the wavelength of the laser. We measure the transmitted
field to extract the field correlation function and the enhancement of the
total transmission. We find that optimizing the total transmission leads to a
significant increase in the frequency width of the field correlation function.
Additionally we find that the enhanced transmission persists over an even
larger frequency bandwidth. This result shows open channels in the diffusive
regime are spectrally much wider than previous measurements in the localized
regime suggest.


title:
Inference from the small scales of cosmic shear with current and future
  Dark Energy Survey data

abstract:
  Cosmic shear is sensitive to fluctuations in the cosmological matter density
field, including on small physical scales, where matter clustering is affected
by baryonic physics in galaxies and galaxy clusters, such as star formation,
supernovae feedback and AGN feedback. While muddying any cosmological
information that is contained in small scale cosmic shear measurements, this
does mean that cosmic shear has the potential to constrain baryonic physics and
galaxy formation. We perform an analysis of the Dark Energy Survey (DES)
Science Verification (SV) cosmic shear measurements, now extended to smaller
scales, and using the Mead et al. 2015 halo model to account for baryonic
feedback. While the SV data has limited statistical power, we demonstrate using
a simulated likelihood analysis that the final DES data will have the
statistical power to differentiate among baryonic feedback scenarios. We also
explore some of the difficulties in interpreting the small scales in cosmic
shear measurements, presenting estimates of the size of several other
systematic effects that make inference from small scales difficult, including
uncertainty in the modelling of intrinsic alignment on nonlinear scales,
`lensing bias', and shape measurement selection effects. For the latter two, we
make use of novel image simulations. While future cosmic shear datasets have
the statistical power to constrain baryonic feedback scenarios, there are
several systematic effects that require improved treatments, in order to make
robust conclusions about baryonic feedback.


title:
Pulsar observations with European telescopes for testing gravity and
  detecting gravitational waves

abstract:
  A background of nanohertz gravitational waves from supermassive black hole
binaries could soon be detected by pulsar timing arrays, which measure the
times-of-arrival of radio pulses from millisecond pulsars with very high
precision. The European Pulsar Timing Array uses five large European radio
telescopes to monitor high-precision millisecond pulsars, imposing in this way
strong constraints on a gravitational wave background. To achieve the necessary
precision needed to detect gravitational waves, the Large European Array for
Pulsars (LEAP) performs simultaneous observations of pulsars with all five
telescopes, which allows us to coherently add the radio pulses, maximize the
signal-to-noise of pulsar signals and increase the precision of
times-of-arrival. We report on the progress made and results obtained by the
LEAP collaboration, and in particular on the addition of the Sardinia Radio
Telescope to the LEAP observations during its scientific validation phase. In
addition, we discuss how LEAP can be used to monitor strong-gravity systems
such as double neutron star systems and impose strong constraints on
post-keplerian parameters.


title: Direct bulk sensitive probe of 5f symmetry in URu2Si2

abstract:
  The second-order phase transition into a hidden order phase in URu$_2$Si$_2$
goes along with an order parameter which is still a mystery, despite 30 years
of research. However, it is understood that the symmetry of the order parameter
must be related to the symmetry of the low lying local electronic $f$-states.
Here we present results of a novel spectroscopy, namely core-level non-resonant
inelastic x-ray scattering (NIXS). This method allows for the measurement of
local high-multipole excitations and it is bulk sensitive. The observed
anisotropy of the scattering function unambiguously shows that the 5$f$ ground
state wave function is composed mainly, but essentially not purely, of the
$\Gamma_1$ with majority $J_z$ =$|4\rangle$ + $|-4\rangle$ and/or $\Gamma_2$
singlet states.


title: Split ring resonator resonance assisted terahertz antennas

abstract:
  We report on the computational development of novel architectures of low
impedance broadband antennas, for efficient detection of Terahertz (THz)
frequency beams. The conceived Split Ring Resonator Resonance Assisted (SRR RA)
antennas are based on both a capacitive and inductive scheme, exploiting a 200
Ohm and 400 Ohm impedance, respectively. Moreover, the impedance is tunable by
varying the coupling parameters in the exploited geometry, allowing for better
matching with the detector circuit for maximum power extraction. Our simulation
results have been obtained by assuming a 1.5 THz operation frequency.


title:
Absence makes the heart grow fonder: social compensation when failure to
  interact risks weakening a relationship

abstract:
  Social networks require active relationship maintenance if they are to be
kept at a constant level of emotional closeness. For primates, including
humans, failure to interact leads inexorably to a decline in relationship
quality, and a consequent loss of the benefits that derive from individual
relationships. As a result, many social species compensate for weakened
relationships by investing more heavily in them. Here we study how humans
behave in similar situations, using data from mobile call detail records from a
European country. For the less frequent contacts between pairs of communicating
individuals we observe a logarithmic dependence of the duration of the
succeeding call on the time gap with the previous call. We find that such
behaviour is likely when the individuals in these dyadic pairs have the same
gender and are in the same age bracket as well as being geographically distant.
Our results indicate that these pairs deliberately invest more time in
communication so as to reinforce their social bonding and prevent their
relationships decaying when these are threatened by lack of interaction.


title:
Ghostbusters in higher derivative supersymmetric theories: who is afraid
  of propagating auxiliary fields?

abstract:
  We present for the first time a ghost-free higher-derivative chiral model
with a propagating auxiliary F-term field (highest component of the chiral
multiplet). We obtain this model by removing a ghost in a higher derivative
chiral model, with Higgsing it in terms of an auxiliary vector superfield.
Depending on the sign of the quadratic derivative term of the chiral
superfield, the model contains two ghost free branches of the parameter
regions. We find that supersymmetry is spontaneously broken in one branch while
it is preserved in the other branch. As a consequence of dynamical F-term
field, a conserved U(1) charge corresponding to the number density of $F$
appears, which can be regarded as a generalization of the R-symmetry.


title: L\'evy NMF for robust nonnegative source separation

abstract:
  Source separation, which consists in decomposing data into meaningful
structured components, is an active research topic in many areas, such as music
and image signal processing, applied physics and text mining. In this paper, we
introduce the Positive $\alpha$-stable (P$\alpha$S) distributions to model the
latent sources, which are a subclass of the stable distributions family. They
notably permit us to model random variables that are both nonnegative and
impulsive. Considering the L\'evy distribution, the only P$\alpha$S
distribution whose density is tractable, we propose a mixture model called
L\'evy Nonnegative Matrix Factorization (L\'evy NMF). This model accounts for
low-rank structures in nonnegative data that possibly has high variability or
is corrupted by very adverse noise. The model parameters are estimated in a
maximum-likelihood sense. We also derive an estimator of the sources given the
parameters, which extends the validity of the generalized Wiener filtering to
the P$\alpha$S case. Experiments on synthetic data show that L\'evy NMF
compares favorably with state-of-the art techniques in terms of robustness to
impulsive noise. The analysis of two types of realistic signals is also
considered: musical spectrograms and fluorescence spectra of chemical species.
The results highlight the potential of the L\'evy NMF model for decomposing
nonnegative data.


title: Maximal hyperbolic towers and weight in the theory of free groups

abstract:
  We show that in general for a given group the structure of a maximal
hyperbolic tower over a free group is not canonical: We construct examples of
groups having hyperbolic tower structures over free subgroups which have
arbitrarily large ratios between their ranks. These groups have the same first
order theory as non-abelian free groups and we use them to study the weight of
types in this theory.


title:
A Small-Scale Prototype to Study the Take-Off of Tethered Rigid
  Aircrafts for Airborne Wind Energy

abstract:
  The design of a prototype to carry out take-off and flight tests with
tethered aircrafts is presented. The system features a ground station equipped
with a winch and a linear motion system. The motion of these two components is
regulated by an automatic control system, whose goal is to accelerate a
tethered aircraft to take-off speed using the linear motion system, while
reeling-out the tether from the winch with low pulling force and avoiding
entanglement. The mechanical, electrical, measurement and control aspects of
the prototype are described in detail. Experimental results with a
manually-piloted aircraft are presented, showing a good matching with previous
theoretical findings.


title:
High energy density spots and production of kink-antikink pairs in
  particle collisions

abstract:
  The maximal energy density that can be achieved in the collisions of the
particle-like wave trains in the $\phi^4$ model has been investigated
numerically for different wave train parameters. From these results the
prediction is made on how many kink-antikink pairs can be produced in wave
train collisions taking into account that in collision of $N$ kinks maximal
energy density is equal to $N^2/2$ for even $N$. Our numerical results are in a
reasonably good agreement with the predicted maximal number of kink-antikink
pairs formed in wave train collisions.


title:
Accumulate and Jam: Towards Secure Communication via A Wireless-Powered
  Full-Duplex Jammer

abstract:
  This paper develops a new cooperative jamming protocol, termed
accumulate-and-jam (AnJ), to improve physical layer security in wireless
communications. Specifically, a full-duplex (FD) friendly jammer is deployed to
secure the direct communication between source and destination in the presence
of a passive eavesdropper. We consider the friendly jammer as an
energy-constrained node without embedded power supply but with an energy
harvesting unit and rechargeable energy storage; it can thus harvest energy
from the radio frequency (RF) signals transmitted by the source, accumulate the
energy in its battery, and then use this energy to perform cooperative jamming.
In the proposed AnJ protocol, based on the energy status of the jammer and the
channel state of source-destination link, the system operates in either
dedicated energy harvesting (DEH) or opportunistic energy harvesting (OEH)
mode. Thanks to the FD capability, the jammer also harvests energy from the
information-bearing signal that it overhears from the source. We study the
complex energy accumulation and consumption procedure at the jammer by
considering a practical finite-capacity energy storage, of which the long-term
stationary distribution is characterized through applying a discrete-state
Markov Chain. An alternative energy storage with infinite capacity is also
studied to serve as an upper bound. We further derive closed-form expressions
for two secrecy metrics, i.e., secrecy outage probability and probability of
positive secrecy capacity. In addition, the impact of imperfect channel state
information on the performance of our proposed protocol is also investigated.
Numerical results validate all theoretical analyses and reveal the merits of
the proposed AnJ protocol over its half-duplex counterpart.


title:
The effect of a disc on the population of cuspy and cored dark matter
  substructures in Milky Way-like galaxies

abstract:
  We use high-resolution $N$-body simulations to study the effect of a galactic
disc on the dynamical evolution of dark matter substructures with orbits and
structural parameters extracted from the Aquarius A-2 merger tree (Springel et
al. 2008). Satellites are modelled as equilibrium $N$-body realizations of
generalized Hernquist profiles with $2\times10^6$ particles and injected in the
analytical evolving host potential at $z_\mathrm{infall}$, defined by the peak
of their mass evolution. We select all substructures with
$M_{200}(z_\mathrm{infall})\geq 10^8\,\mathrm{M_\odot}$ and first pericentric
distances $r_p<r_{200}$. Motivated by observations of Milky Way dwarf
spheroidal galaxies, we also explore satellite models with cored dark matter
profiles with a fixed core size $r_c=0.8\,a_s$ where $a_s$ is the Hernquist
scale radius. We find that models with cuspy satellites have twice as many
surviving substructures at $z=0$ than their cored counterparts, and four times
as many if we only consider those on orbits with $r_p\lesssim0.1\,r_{200}$. For
a given profile, adding an evolving disc potential reduces the number of
surviving substructures further by a factor of $\lesssim2$ for satellites on
orbits that penetrate the disc ($r_p\lesssim 20\,\mathrm{kpc}$). For large
$r_p$, where tidal forces and the effect of the disc become negligible, the
number of satellites per pericentre bin converges to similar values for all
four models.


title: On the equivalence of GPD representations

abstract:
  Phenomenological representations of generalized parton distributions (GPDs)
implementing the non-trivial field theoretical requirements are employed in the
present day strategies for extracting of hadron structure information encoded
in GPDs from the observables of hard exclusive reactions. Showing out the
equivalence of various GPD representations can help to get more insight into
GPD properties and allow to build up flexible GPD models capable of
satisfactory description of the whole set of available experimental data. We
review the mathematical aspects of establishing equivalence between the the
double partial wave expansion of GPDs in the conformal partial waves and in the
$t$-channel ${\rm SO}(3)$ partial waves and the double distribution
representation of GPDs.


title:
Functional Erd\"os-R\'enyi law of large numbers for nonconventional sums
  under weak dependence

abstract:
  We obtain a functional Erd\H os-R\' enyi law of large numbers for
"nonconventional" sums of the form $\Sig_n=\sum_{m=1}^nF(X_m,X_{2m},...,X_{\ell
m})$ where $X_1,X_2,...$ is a sequence of exponentially fast $\psi$-mixing
random vectors and $F$ is a Borel vector function extendin in several
directions our previous result concerning i.i.d. random variables
$X_1,X_2,...$.


title: K-Stability of Fano spherical varieties

abstract:
  We prove a criterion for K-stability of a $\mathbb{Q}$-Fano spherical variety
with respect to equivariant special test configurations, in terms of its moment
polytope and some combinatorial data associated to the open orbit. Combined
with the equivariant version of the Yau-Tian-Donaldson conjecture for Fano
manifolds proved by Datar and Sz\'ekelyhidi, it yields a criterion for the
existence of a K\"ahler-Einstein metric on a spherical Fano manifold. The
results hold also for modified K-stability and existence of K\"ahler-Ricci
solitons.


title: Martingale-coboundary decomposition for families of dynamical systems

abstract:
  We prove statistical limit laws for sequences of Birkhoff sums of the type
$\sum_{j=0}^{n-1}v_n\circ T_n^j$ where $T_n$ is a family of nonuniformly
hyperbolic transformations. The key ingredient is a new martingale-coboundary
decomposition for nonuniformly hyperbolic transformations which is useful
already in the case when the family $T_n$ is replaced by a fixed transformation
$T$, and which is particularly effective in the case when $T_n$ varies with
$n$. In addition to uniformly expanding/hyperbolic dynamical systems, our
results include cases where the family $T_n$ consists of intermittent maps,
unimodal maps (along the Collet-Eckmann parameters), Viana maps, and externally
forced dispersing billiards. As an application, we prove a homogenization
result for discrete fast-slow systems where the fast dynamics is generated by a
family of nonuniformly hyperbolic transformations.


title:
Sub-cycle optical control of current in a semiconductor: from the
  multiphoton to the tunneling regime

abstract:
  Nonlinear interactions between ultrashort optical waveforms and solids can be
used to induce and steer electric current on a femtosecond (fs) timescale,
holding promise for electronic signal processing at PHz frequencies [Nature
493, 70 (2013)]. So far, this approach has been limited to insulators,
requiring extremely strong peak electric fields and intensities. Here, we show
all-optical generation and control of directly measurable electric current in a
semiconductor relevant for high-speed and high-power (opto)electronics, gallium
nitride (GaN), within an optical cycle and on a timescale shorter than 2 fs, at
intensities at least an order of magnitude lower than those required for
dielectrics. Our approach opens the door to PHz electronics and metrology,
applicable to low-power (non-amplified) laser pulses, and may lead to future
applications in semiconductor and photonic integrated circuit technologies.


title:
Disentangling planetary and stellar activity features in the CoRoT-2
  light curve

abstract:
  [Abridged] Context. Stellar activity is an important source of systematic
errors and uncertainties in the characterization of exoplanets. Most of the
techniques used to correct for this activity focus on an ad hoc data reduction.
Aims. We have developed a software for the combined fit of transits and stellar
activity features in high-precision long-duration photometry. Our aim is to
take advantage of the modelling to derive correct stellar and planetary
parameters, even in the case of strong stellar activity. Methods. We use an
analytic approach to model the light curve. The code KSint, modified by adding
the evolution of active regions, is implemented into our Bayesian modelling
package PASTIS. The code is then applied to the light curve of CoRoT-2. The
light curve is divided in segments to reduce the number of free parameters
needed by the fit. We perform a Markov chain Monte Carlo analysis in two ways.
In the first, we perform a global and independent modelling of each segment of
the light curve, transits are not normalized and are fitted together with the
activity features, and occulted features are taken into account during the
transit fit. In the second, we normalize the transits with a model of the
non-occulted activity features, and then we apply a standard transit fit, which
does not take the occulted features into account. Results. Our model recovers
the activity features coverage of the stellar surface and different rotation
periods for different features. We find variations in the transit parameters of
different segments and show that they are likely due to the division applied to
the light curve. Neglecting stellar activity or even only bright spots while
normalizing the transits yields a $\sim 1.2\sigma$ larger and $2.3\sigma$
smaller transit depth, respectively. The stellar density also presents up to
$2.5\sigma$ differences depending on the normalization technique...


title: The Power of Non-Ground Rules in Answer Set Programming

abstract:
  Answer set programming (ASP) is a well-established logic programming language
that offers an intuitive, declarative syntax for problem solving. In its
traditional application, a fixed ASP program for a given problem is designed
and the actual instance of the problem is fed into the program as a set of
facts. This approach typically results in programs with comparably short and
simple rules. However, as is known from complexity analysis, such an approach
limits the expressive power of ASP; in fact, an entire NP-check can be encoded
into a single large rule body of bounded arity that performs both a guess and a
check within the same rule.
  Here, we propose a novel paradigm for encoding hard problems in ASP by making
explicit use of large rules which depend on the actual instance of the problem.
We illustrate how this new encoding paradigm can be used, providing examples of
problems from the first, second, and even third level of the polynomial
hierarchy. As state-of-the-art solvers are tuned towards short rules, rule
decomposition is a key technique in the practical realization of our approach.
We also provide some preliminary benchmarks which indicate that giving up the
convenient way of specifying a fixed program can lead to a significant
speed-up.
  This paper is under consideration for acceptance into TPLP.


title:
Study of hard double-parton scattering in four-jet events in $pp$
  collisions at $\sqrt{s} = 7$ TeV with the ATLAS experiment

abstract:
  Inclusive four-jet events produced in proton-proton collisions at a
centre-of-mass energy of $\sqrt{s} = 7$ TeV are analysed for the presence of
hard double-parton scattering using data corresponding to an integrated
luminosity of 37.3 pb$^{-1}$, collected with the ATLAS detector at the LHC. The
contribution of hard double-parton scattering to the production of four-jet
events is extracted using an artificial neural network, assuming that hard
double-parton scattering can be approximated by an uncorrelated overlaying of
dijet events. For events containing at least four jets with transverse momentum
$p_{\mathrm{T}} \geq 20$ GeV and pseudorapidity $\eta \leq 4.4$, and at least
one having $p_{\mathrm{T}} \geq 42.5$ GeV, the contribution of hard
double-parton scattering is estimated to be $f_{\mathrm{DPS}} = 0.092
^{+0.005}_{-0.011} (\mathrm{stat.}) ^{+0.033}_{-0.037} (\mathrm{syst.})$. After
combining this measurement with those of the inclusive dijet and four-jet
cross-sections in the appropriate phase space regions, the effective overlap
area between the interacting protons, $\sigma_{\mathrm{eff}}$, was determined
to be $\sigma_{\mathrm{eff}} = 14.9 ^{+1.2}_{-1.0} (\mathrm{stat.})
^{+5.1}_{-3.8} (\mathrm{syst.})$ mb. This result is consistent within the
quoted uncertainties with previous measurements of $\sigma_{\mathrm{eff}}$,
performed at centre-of-mass energies between 63 GeV and 8 TeV using various
final states, and it corresponds to $21^{+7}_{-6}$% of the total inelastic
cross-section measured at $\sqrt{s} = 7$ TeV. The distributions of the
observables sensitive to the contribution of hard double-parton scattering,
corrected for detector effects, are also provided.


title: Erd\"os-R\'enyi law of large numbers in the averaging setup

abstract:
  We extend the Erd\H os-R\' enyi law of large numbers to the averaging setup
both in discrete and continuous time cases. We consider both stochastic
processes and dynamical systems as fast motions whenever they are fast mixing
and satisfy large deviations estimates. In the continuous time case we consider
flows with large deviations estimates which allow a suspension representation
and it turns out that fast mixing of corresponding base transformation suffices
for our results.


title:
Wireless-Powered Two-Way Relaying with Power Splitting-based Energy
  Accumulation

abstract:
  This paper investigates a wireless-powered two-way relay network (WP-TWRN),
in which two sources exchange information with the aid of one
amplify-and-forward (AF) relay. Contrary to the conventional two-way relay
networks, we consider the scenario that the AF relay has no embedded energy
supply, and it is equipped with an energy harvesting unit and rechargeable
battery. As such, it can accumulate the energy harvested from both sources'
signals before helping forwarding their information. In this paper, we develop
a power splitting-based energy accumulation (PS-EA) scheme for the considered
WP-TWRN. To determine whether the relay has accumulated sufficient energy, we
set a predefined energy threshold for the relay. When the accumulated energy
reaches the threshold, relay splits the received signal power into two parts,
one for energy harvesting and the other for information forwarding. If the
stored energy at the relay is below the threshold, all the received signal
power will be accumulated at the relay's battery. By modeling the
finite-capacity battery of relay as a finite-state Markov Chain (MC), we derive
a closed-form expression for the system throughput of the proposed PS-EA scheme
over Nakagami-m fading channels. Numerical results validate our theoretical
analysis and show that the proposed PS-EA scheme outperforms the conventional
time switching-based energy accumulation (TS-EA) scheme and the existing power
splitting schemes without energy accumulation.


title: $A_4$ and CP symmetry and a model with maximal CP violation

abstract:
  We study a second CP symmetry compatible with the $A_4$ flavor group, which
interchanges the representations $\mathbf{1}'$ and $\mathbf{1}"$. We analyze
the lepton mixing patterns arising from the $A_4$ and CP symmetry broken to
residual subgroups $Z_3$ and $Z_2\times CP$ in the charged lepton and neutrino
sectors respectively. One phenomenologically viable mixing pattern is found,
and it predicts maximal atmospheric mixing angle as well as maximal Dirac CP
phase, trivial Majorana phase and the correlation
$\sin^2\theta_{12}\cos^2\theta_{13}=1/3$. We construct a concrete model based
on the $A_4$ and CP symmetry, the above interesting mixing pattern is achieved,
the observed charged lepton mass hierarchy is reproduced, and the reactor
mixing angle $\theta_{13}$ is of the correct order.


title:
Imaging of the umbrella motion and tunneling in the ammonia molecule by
  strong-field ionization

abstract:
  The geometry-dependent ionization behavior of the ammonia molecule is
investigated. Different theoretical approaches for obtaining the ionization
yield are compared, all of them showing a strong dependence of the ionization
yield on the inversion coordinate at long wavelengths ($\geq$ 800 nm). It is
shown how this effect can be exploited to create and probe nuclear wave packets
in neutral ammonia using Lochfra{\ss}. Furthermore, imaging of a wave packet
tunneling through the barrier of a double-well potential in real time is
discussed.


title: Lifting the Franck-Condon blockade in driven quantum dots

abstract:
  Electron-vibron coupling in quantum dots can lead to a strong suppression of
the average current in the sequential tunneling regime. This effect is known as
Franck-Condon blockade and can be traced back to an overlap integral between
vibron states with different electron numbers which becomes exponentially small
for large electron-vibron coupling strength. Here, we investigate the effect of
a time-dependent drive on this phenomenon, in particular the effect of an
oscillatory gate voltage acting on the electronic dot level. We employ two
different approaches: perturbation theory based on nonequilibrium Keldysh
Green's functions and a master equation in Born-Markov approximation. In both
cases, we find that the drive can lift the blockade by exciting vibrons. As a
consequence, the relative change in average current grows exponentially with
the drive strength.


title: Backward step control for Hilbert space problems

abstract:
  We analyze backward step control globalization for finding zeros of
G\^ateaux-differentiable functions that map from a Banach space to a Hilbert
space. The results include global convergence to a distinctive solution
characterized by propagating the initial guess by a generalized Newton flow
with guaranteed bounds on the discrete nonlinear residual norm decrease and an
(also numerically) easily controllable asymptotic linear residual convergence
rate. The convergence theory can be exploited to construct efficient numerical
methods, which we demonstrate for the case of a Krylov-Newton method and an
approximation-by-discretization multilevel framework. Both approaches optimize
the asymptotic linear residual convergence rate, either over the Krylov
subspace or through adaptive discretization, which in turn yields practical and
efficient stopping criteria and refinement strategies that balance the
nonlinear residuals with the relative residuals of the linear systems. We apply
these methods to the class of nonlinear elliptic boundary value problems and
present numerical results for the Carrier equation and the minimum surface
equation.


title:
On the convergence of fixed point iterations for the moving geometry in
  a fluid-structure interaction problem

abstract:
  In this paper a fluid-structure interaction problem for the incompressible
Newtonian fluid is studied. We prove the convergence of an iterative process
with respect to the computational domain geometry. In our previous works on
numerical approximation of similar problems we refer this approach as the
global iterative method. This iterative approach can be understood as a
linearization of the so-called geometric nonlinearity of the underlying model.
The proof of the convergence is based on the Banach fixed point argument, where
the contractivity of the corresponding mapping is shown due to the continuous
dependence of the weak solution on the given domain deformation. This estimate
is obtained by remapping the problem onto a fixed domain and using appropriate
divergence-free test functions involving the difference of two solutions.


title: Superconformal Vertex Algebras and Jacobi Forms

abstract:
  We discuss the appearance of Jacobi automorphic forms in the theory of
superconformal vertex algebras, explaining it by way of supercurves and formal
geometry. We touch on related topics such as Ramanujan's differential equations
for Eisenstein series.


title:
Fusing Deep Convolutional Networks for Large Scale Visual Concept
  Classification

abstract:
  Deep learning architectures are showing great promise in various computer
vision domains including image classification, object detection, event
detection and action recognition. In this study, we investigate various aspects
of convolutional neural networks (CNNs) from the big data perspective. We
analyze recent studies and different network architectures both in terms of
running time and accuracy. We present extensive empirical information along
with best practices for big data practitioners. Using these best practices we
propose efficient fusion mechanisms both for single and multiple network
models. We present state-of-the art results on benchmark datasets while keeping
computational costs at a lower level. Another contribution of our paper is that
these state-of-the-art results can be reached without using extensive data
augmentation techniques.


title: Dwyer-Kan Homotopy Theory of Algebras over Operadic Collections

abstract:
  Over suitable monoidal model categories, we construct a Dwyer-Kan model
category structure on the category of algebras over an augmented operadic
collection. As examples we obtain Dwyer-Kan model category structure on the
categories of enriched wheeled props, wheeled properads, and wheeled operads,
among others. This result extends known model category structure on the
categories of operads, properads, and props enriched in simplicial sets and
other monoidal model categories. We also show that our Dwyer-Kan model category
structure is well behaved with respect to simultaneous changes of the
underlying monoidal model category and the augmented operadic collection.


title:
Increased Mobility in Presence of Multiple Contacts - Identifying
  Contact Configurations that Enable Arbitrary Acceleration of CoM

abstract:
  Planning of any motion starts by planning the trajectory of the CoM. It is of
the highest importance to ensure that the robot will be able to perform planned
trajectory. With increasing capabilities of the humanoid robots, the case when
contacts are spatially distributed should be considered. In this paper, it is
shown that there are some contact configurations in which any acceleration of
the center of mass (CoM) is feasible. The procedure for identifying such a
configurations is presented, as well as its physical meaning. On the other
hand, for the configurations in which the constraint on CoM movement exists, it
will be shown how to find that linear constraint, which defines the space of
feasible motion. The proposed algorithm has a low complexity and to speed up
the procedure even further, it will be shown that the whole procedure needs to
be run only once when contact configuration changes. As the CoM moves, the new
constraints can be calculated from the initial one, thus yielding significant
computation speedup. The methods are illustrated in two simulated scenarios.


title: Surjectivity of Mean Value Operators on Noncompact Symmetric Spaces

abstract:
  Let $X=G/K$ be a symmetric space of the non-compact type. We prove that the
mean value operator over translated $K$-orbits of a fixed point is surjective
on the space of smooth functions on $X$ if $X$ is either complex or of rank
one. For higher rank spaces it is shown that the same statement is true for
points in an appropriate Weyl subchamber.


title:
Who Wants to Self-Track Anyway? Measuring the Relation between
  Self-Tracking Behavior and Personality Traits

abstract:
  We describe an empirical study of the usage of a mobility self-tracking app,
SensibleJournal 2014, which provides personal mobility information to N=796
participants as part of a large mobile sensing study. Specifically, we report
on the app design, as well as deployment, uptake and usage of the app. The
latter analysis is based on logging of user interactions as well as answers
gathered from a questionnaire provided to the participants. During the study
enrollment process, participants were asked to fill out a questionnaire
including a Big Five inventory and Narcissism NAR-Q personality tests. A
comparison of personality traits was conducted to understand potential
differences among the users and non-users of the app. We found a relation
between self-tracking and conscientiousness, but contrary to the view in
popular media, we found no relation between self-tracking behavior and
narcissism.


title: Mechanical dissipation in MoRe superconducting metal drums

abstract:
  We experimentally investigate dissipation in mechanical resonators made of a
disordered superconducting thin film of Molybdenum-Rhenium(MoRe) alloy. By
electrostatically driving the drum with a resonant AC voltage, we detect its
motion using a superconducting microwave cavity. From the temperature
dependence of mechanical resonance frequencies and quality factors, we find
evidence for non-resonant, mechanically active two-level systems (TLSs)
limiting its quality factor at low temperature. In addition, we observe a
strong suppression of mechanical dissipation at large mechanical driving
amplitudes, suggesting an unconventional saturation of the non-resonant TLSs.
These new observations shed light on the mechanism of mechanical damping in
superconducting drums and routes towards understanding dissipation in such
mechanical systems.


title:
Synchronization of Active Atomic Clocks via Quantum and Classical
  Channels

abstract:
  Superradiant lasers based on atomic ensembles exhibiting ultra-narrow optical
transitions can emit light of unprecedented spectral purity and may serve as
active atomic clocks. We consider two frequency-detuned active atomic clocks,
which are coupled in a cascaded setup, i.e. as master & slave lasers, and study
the synchronization of the slave to the master clock. In a setup where both
atomic ensembles are coupled to a common cavity mode such synchronization
phenomena have been predicted by Xu et al. [Phys. Rev. Lett. 113, 154101
(2014)] and experimentally observed by Weiner et al. [arXiv:1503.06464 (2015)].
Here we demonstrate that synchronization still occurs in cascaded setups but
exhibits distinctly different phase diagrams. We study the characteristics of
synchronization in comparison to the case of coupling through a common cavity.
We also consider synchronization through a classical channel where light of the
master laser is measured phase sensitively and the slave laser is injection
locked by feedback and compare to the results achievable by coupling through
quantum channels.


title: On chromatic numbers of some distance graphs

abstract:
  In this paper we find chromatic numbers of distance graphs $G(n,3,2)$ for
infinitely many n. Also we improve upper bound for $\chi(G(n,r,s))$ in large
part of cases.


title: Forward Stagewise Additive Model for Collaborative Multiview Boosting

abstract:
  Multiview assisted learning has gained significant attention in recent years
in supervised learning genre. Availability of high performance computing
devices enables learning algorithms to search simultaneously over multiple
views or feature spaces to obtain an optimum classification performance. The
paper is a pioneering attempt of formulating a mathematical foundation for
realizing a multiview aided collaborative boosting architecture for multiclass
classification. Most of the present algorithms apply multiview learning
heuristically without exploring the fundamental mathematical changes imposed on
traditional boosting. Also, most of the algorithms are restricted to two class
or view setting. Our proposed mathematical framework enables collaborative
boosting across any finite dimensional view spaces for multiclass learning. The
boosting framework is based on forward stagewise additive model which minimizes
a novel exponential loss function. We show that the exponential loss function
essentially captures difficulty of a training sample space instead of the
traditional `1/0' loss. The new algorithm restricts a weak view from over
learning and thereby preventing overfitting. The model is inspired by our
earlier attempt on collaborative boosting which was devoid of mathematical
justification. The proposed algorithm is shown to converge much nearer to
global minimum in the exponential loss space and thus supersedes our previous
algorithm. The paper also presents analytical and numerical analysis of
convergence and margin bounds for multiview boosting algorithms and we show
that our proposed ensemble learning manifests lower error bound and higher
margin compared to our previous model. Also, the proposed model is compared
with traditional boosting and recent multiview boosting algorithms.


title: Sample Complexity for Non-Truthful Mechanisms

abstract:
  This paper considers the design of non-truthful mechanisms from samples. We
identify a parameterized family of mechanisms with strategically simple
winner-pays-bid, all-pay, and truthful payment formats. In general (not
necessarily downward-closed) single-parameter feasibility environments we prove
that the family has low representation and generalization error. Specifically,
polynomially many bid samples suffice to identify and run a mechanism that is
$\epsilon$-close in Bayes-Nash equilibrium revenue or welfare to that of the
optimal truthful mechanism with high probability.


title:
Chiral optical Tamm states at the boundary of the medium with helical
  symmetry of the dielectric tensor [In Russian]

abstract:
  A new optical state is described both analytically and numerically at the
boundary of a chiral medium with continuous helical symmetry of the dielectric
tensor. The tangential wave number is assumed to be zero. The state appears to
be localized near the boundary. It does not transfer energy along this boundary
and falls off exponentially with the distance from the boundary. The field
penetration into chiral medium is blocked at wavelengths close to the helical
pitch and corresponding to the photonic band gap. The polarization of light
near the boundary has the same sign of chirality as the helical medium. It is
shown that the homogeneous environment, or the substrate must exhibit the
anisotropic metallic reflection. Spectral manifestation of the state is
determined by the angle between the optical axes at the interface. A realistic
example is considered at the boundary of a cholesteric liquid crystal and a
metal-dielectric anisotropic nanocomposite.


title: Thermoelectric properties of graphyne from first-principles calculations

abstract:
  The two-dimensional graphene-like carbon allotrope, graphyne, has been
recently fabricated and exhibits many interesting electronic properties. In
this work, we investigate the thermoelectric properties of {\gamma}-graphyne by
performing first-principles calculations combined with Boltzmann transport
theory for both electron and phonon. The carrier relaxation time is accurately
evaluated from the ultra-dense electron-phonon coupling matrix elements
calculated by adopting the density functional perturbation theory and Wannier
interpolation, rather than the generally used deformation potential theory
which only considers the electron-acoustic phonon scattering. It is found that
the thermoelectric performance of {\gamma}-graphyne exhibits a strong
dependence on the temperature and carrier type. At an intermediate temperature
of 600 K, a maximum ZT value of 1.5 and 1.0 can be achieved for the p- and
n-type systems, respectively.


title:
Symmetry, reductions and exact solutions of the difference equation
  $u_{n+2}=au_n/(1+bu_nu_{n+1})$

abstract:
  We investigate the solutions of the second-order difference equation
$u_{n+2}=(au_n)/(1+bu_nu_{n+1})$ using a group of transformations (Lie
symmetries) that leaves the solutions invariant.


title:
On the analysis of inexact augmented Lagrangian schemes for misspecified
  conic convex programs

abstract:
  We consider the misspecified optimization problem of minimizing a convex
function $f(x;\theta^*)$ in $x$ over a conic constraint set represented by
$h(x;\theta^*) \in \mathcal{K}$, where $\theta^*$ is an unknown (or
misspecified) vector of parameters, $\mathcal{K}$ is a closed convex cone and
$h$ is affine in $x$. Suppose $\theta^*$ is unavailable but may be learnt by a
separate process that generates a sequence of estimators $\theta_k$, each of
which is an increasingly accurate approximation of $\theta^*$. We develop a
first-order inexact augmented Lagrangian (AL) scheme for computing an optimal
solution $x^*$ corresponding to $\theta^*$ while simultaneously learning
$\theta^*$. In particular, we derive rate statements for such schemes when the
penalty parameter sequence is either constant or increasing, and derive bounds
on the overall complexity in terms of proximal-gradient steps when AL
subproblems are inexactly solved via an accelerated proximal-gradient scheme.
Numerical results for a portfolio optimization problem with a misspecified
covariance matrix suggest that these schemes perform well in practice while
naive sequential schemes may perform poorly in comparison.


title:
Precise prediction for the light MSSM Higgs boson mass combining
  effective field theory and fixed-order calculations

abstract:
  In the Minimal Supersymmetric Standard Model heavy superparticles introduce
large logarithms in the calculation of the lightest $\mathcal{CP}$-even Higgs
boson mass. These logarithmic contributions can be resummed using effective
field theory techniques. For light superparticles, however, fixed-order
calculations are expected to be more accurate. To gain a precise prediction
also for intermediate mass scales, both approaches have to be combined. Here,
we report on an improvement of this method in various steps: the inclusion of
electroweak contributions, of separate electroweakino and gluino thresholds, as
well as resummation at the NNLL level. These improvements can lead to
significant numerical effects. In most cases, the lightest $\mathcal{CP}$-even
Higgs boson mass is shifted downwards by about 1 GeV. This is mainly caused by
higher order corrections to the $\bar{\text{MS}}$ top-quark mass. We also
describe the implementation of the new contributions in the code {\tt
FeynHiggs}.


title:
Combination of CDF and D0 results on the mass of the top quark using up
  $9.7\:{\rm fb}^{-1}$ at the Tevatron

abstract:
  We summarize the current top quark mass ($m_t$) measurements from the CDF and
D0 experiments at Fermilab. We combine published results from Run I
(1992--1996) with the most precise published and preliminary Run II
(2001--2011) measurements based on $p\bar{p}$ data corresponding to up to
$9.7\:{\rm fb}^{-1}$ of $p\bar{p}$ collisions. Taking correlations of
uncertainties into account, and combining the statistical and systematic
contributions in quadrature, the preliminary Tevatron average mass value for
the top quark is $m_t = 174.30 \ \pm 0.65\:\mathrm{GeV}/c^{2}$, corresponding
to a relative precision of $0.37\%$


title: A sharp bound for the Chebyshev functional

abstract:
  In this work a sharp bound of the \v{C}eby\v{s}ev functional for absolutely
continuous functions $f,g$ whose derivatives $f'\in L_{\infty}[a,b]$ and $g'\in
L_{1}[a,b]$ is obtained.


title: Phonon anharmonicity and negative thermal expansion in SnSe

abstract:
  The anharmonic phonon properties of SnSe in the Pnma phase were investigated
with a combination of experiments and first-principles simulations. Using
inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray
scattering (NRIXS), we have measured the phonon dispersions and density of
states (DOS) and their temperature dependence, which revealed a strong,
inhomogeneous shift and broadening of the spectrum on warming. First-principles
simulations were performed to rationalize these measurements, and to explain
the previously reported anisotropic thermal expansion, in particular the
negative thermal expansion within the Sn-Se bilayers. Including the anisotropic
strain dependence of the phonon free energy, in addition to the electronic
ground state energy, is essential to reproduce the negative thermal expansion.
From the phonon DOS obtained with INS and additional calorimetry measurements,
we quantify the harmonic, dilational, and anharmonic components of the phonon
entropy, heat capacity, and free energy. The origin of the anharmonic phonon
thermodynamics is linked to the electronic structure.


title: Winograd Schemas and Machine Translation

abstract:
  A Winograd schema is a pair of sentences that differ in a single word and
that contain an ambiguous pronoun whose referent is different in the two
sentences and requires the use of commonsense knowledge or world knowledge to
disambiguate. This paper discusses how Winograd schemas and other sentence
pairs could be used as challenges for machine translation using distinctions
between pronouns, such as gender, that appear in the target language but not in
the source.


title:
Density functional theory calculations of the stress of oxidised (110)
  silicon surfaces

abstract:
  The measurement of the lattice-parameter of silicon by x-ray interferometry
assumes the use of strain-free crystals. This might not be the case because
surface relaxation, reconstruction, and oxidation cause strains without the
application of any external force. In a previous work, this intrinsic strain
was estimated by a finite element analysis, where the surface stress was
modeled by an elastic membrane having a 1 N/m tensile strength. The present
paper quantities the surface stress by a density functional theory calculation.
We found a value exceeding the nominal value used, which potentially affects
the measurement accuracy.


title: Fat tailed distributions for deaths in conflicts and disasters

abstract:
  We study the statistics of human deaths from wars, conflicts, similar
man-made conflicts as well as natural disasters. The probability distribution
of number of people killed in natural disasters as well as man made situations
show power law decay for the largest sizes, with similar exponent values.
Comparisons with natural disasters, when event sizes are measured in terms of
physical quantities (e.g., energy released in earthquake, volume of rainfall,
land area affected in forest fires, etc.) also show striking resemblances. The
universal patterns in their statistics suggest that some subtle similarities in
their mechanisms and dynamics might be responsible.


title:
Superresolution through the topological shaping of sound with an
  acoustic vortex wave antenna

abstract:
  In this paper, we demonstrate far-field acoustic superresolution using shaped
acoustic vortices. Compared with previously proposed near-field methods of
acoustic superresolution, in this work we describe how far-field
superresolution can be obtained using an acoustic vortex wave antenna. This is
accomplished by leveraging the recent advances in optical vortices in
conjunction with the topological diversity of a leaky wave antenna design. In
particular, the use of an acoustic vortex wave antenna eliminates the need for
a complicated phased array consisting of multiple active elements, and enables
a superresolving aperture to be achieved with a single simple acoustic source
and total aperture size less than a wavelength in diameter. A theoretical
formulation is presented for the design of an acoustic vortex wave antenna with
arbitrary planar arrangement, and explicit expressions are developed for the
radiated acoustic pressure field. This geometric versatility enables
variously-shaped acoustic vortex patterns to be achieved, which propagate from
the near-field into the far-field through an arrangement of stable integer mode
vortices. Two examples are presented and discussed in detail, illustrating the
generation and transmission of an "X" and "Y" shape into the far-field. Despite
the total aperture size being less than a wavelength in diameter, the proposed
acoustic vortex wave antenna is shown to achieve far-field superresolution with
feature sizes 4-9 times smaller than the resolution limit.


title:
Comparison of Tsallis statistics with the Tsallis-factorized statistics
  in the ultrarelativistic $pp$ collisions

abstract:
  The Tsallis statistics was applied to describe the experimental data on the
transverse momentum distributions of hadrons. We considered the energy
dependence of the parameters of the Tsallis-factorized statistics, which is now
widely used for the description of the experimental transverse momentum
distributions of hadrons, and the Tsallis statistics for the charged pions
produced in $pp$ collisions at high energies. We found that the results of the
Tsallis-factorized statistics deviate from the results of the Tsallis
statistics only at low NA61/SHINE energies when the value of the entropic
parameter is close to unity. At higher energies, when the value of the entropic
parameter deviates essentially from unity, the Tsallis-factorized statistics
satisfactorily recovers the results of the Tsallis statistics.


title:
Autonomous Take-Off and Flight of a Tethered Aircraft for Airborne Wind
  Energy

abstract:
  A control design approach to achieve fully autonomous take-off and flight
maneuvers with a tethered aircraft is presented and demonstrated in real-world
flight tests with a small-scale prototype. A ground station equipped with a
controlled winch and a linear motion system accelerates the aircraft to
take-off speed and controls the tether reeling in order to limit the pulling
force. This setup corresponds to airborne wind energy systems with ground-based
energy generation and rigid aircrafts. A simple model of the aircraft's
dynamics is introduced and its parameters are identified from experimental
data. A model-based, hierarchical feedback controller is then designed, whose
aim is to manipulate the elevator, aileron and propeller inputs in order to
stabilize the aircraft during the take-off and to achieve figure-of-eight
flight patterns parallel to the ground. The controller operates in a fully
decoupled mode with respect to the ground station. Parameter tuning and
stability/robustness aspect are discussed, too. The experimental results
indicate that the controller is able to achieve satisfactory performance and
robustness, notwithstanding its simplicity, and confirm that the considered
take-off approach is technically viable and solves the issue of launching this
kind of airborne wind energy systems in a compact space and at low additional
cost.


title: Metamaterial bricks and quantization of meta-surfaces

abstract:
  Controlling acoustic fields is crucial in diverse applications such as
loudspeaker design, ultrasound imaging and therapy, or acoustic particle
manipulation. The current approaches use fixed lenses or expensive phased
arrays. Here, using a process of analogue-to-digital conversion and wavelet
decomposition, we develop the notion of quantal meta-surfaces. The quanta here
are small, pre-manufactured three-dimensional units - which we call
metamaterial bricks - each encoding a specific phase delay. These bricks can be
assembled into meta-surfaces to generate any diffraction-limited acoustic
field. We apply this methodology to show experimental examples of acoustic
focusing, steering and, after stacking single meta-surfaces into layers, the
more complex field of an acoustic tractor beam. We demonstrate experimentally
single-sided air-borne acoustic levitation using meta-layers at various
bit-rates: from a 4-bit uniform to 3-bit non-uniform quantization in phase.
This powerful methodology dramatically simplifies the design of acoustic
devices and provides a key-step towards realising spatial sound modulators.


title: Toward Development of a New Health Economic Evaluation Definition

abstract:
  Economic evaluation is a dynamically advancing knowledge area of health
economics. It has been conceived to provide evidence for allocating scarce
resources to gain the best value for money. The problem of efficiency of
investments becomes even more crucial with advances in modern medicine and
public health which bring about both improved patient outcomes and higher
costs. Despite the abundance of literature on the economic evaluation concepts,
some key notions including the definition of the health economic evaluation
remain open for discussion. Academic literature offers a large number and
growing variety of economic evaluation definitions. It testifies to the fact
that existing definitions do not meet requirements of economists. The aim of
this study was to examine existing definitions and reveal their common
features.


title:
Borophene as an extremely high capacity electrode material for Li-ion
  and Na-ion batteries

abstract:
  Two-dimensional (2D) materials as electrodes is believed to be the trend for
future Li-ion and Na-ion batteries technologies. Here, by using
first-principles methods, we predict that the recently reported borophene (2D
born sheet) can serve as an ideal electrode material with high electrochemical
performance for both Li-ion and Na-ion batteries. The calculations are
performed on the two experimentally stable borophene structures, namely
\b{eta}12 and \c{hi}3 structures. The optimized Li and Na adsorption sites are
identified, and the host materials are found to maintain good electric
conductivity before and after adsorption. Besides advantages including small
diffusion barriers and low average open-circuit voltages, most remarkably, the
storage capacity can be as high as 1984 mA h g-1 in \b{eta}12 borophene and
1240 mA h g-1 in \c{hi}3 borophene for both Li and Na, which is several times
higher than the commercial graphite electrode and is the highest among all the
2D materials discovered to date. Our results highly support that borophenes can
be appealing anode materials for both Li-ion and Na-ion batteries with
extremely high power density.


title:
Homogenization of viscous and non-viscous HJ equations: a remark and an
  application

abstract:
  It was pointed out in [P.L. Lions, G. Papanicolaou, S. Varadhan,
Homogenization of Hamilton-Jacobi equation, unpublished preprint (1987)] that,
for first order Hamilton-Jacobi (HJ) equations, homogenization starting with
affine initial data implies homogenization for general uniformly continuous
initial data. The argument makes use of some properties of the HJ semi-group,
in particular, the finite speed of propagation. The last property is lost for
viscous HJ equations. In this paper we prove the above mentioned implication in
both viscous and non-viscous cases. Our proof relies on a variant of Evans's
perturbed test function method. As an application, we show homogenization in
the stationary ergodic setting for viscous and non-viscous HJ equations in one
space dimension with non-convex Hamiltonians of specific form. The results are
new in the viscous case.


title: A New Approach to Inverse Local Times

abstract:
  In 1981 F. Knight published an article with a partial solution to a problem
proposed by Ito-McKean see [Ito,[p.217]]. In this paper Knight, see [Knight],
characterized the Levy measures of gap diffusions also known as
quasi-diffusions. The proof is very elegant but it uses quite a lot functional
analysis, more specifically spectral Krein Theory. We present a new proof of
Knight's Theorem, defined at the beginning of the Introduction as well as the
new proof of the same theorem referred as Theorem 2.6 in Section 2.


title:
Semiparametric inference on the fractal index of Gaussian and
  conditionally Gaussian time series data

abstract:
  We study a well-known estimator of the fractal index of a stochastic process.
Our framework is very general and encompasses many models of interest; we show
how to extend the theory of the estimator to a large class of non-Gaussian
processes. Particular focus is on clarity and ease of implementation of the
estimator and the associated asymptotic results, making it easy for
practitioners to apply the methods. We additionally show how measurement noise
in the observations will bias the estimator, potentially resulting in the
practitioner erroneously finding evidence of fractal characteristics in a time
series. We propose a new estimator which is robust to such noise and construct
a formal hypothesis test for the presence of noise in the observations.
Finally, the methods are illustrated on two empirical data sets; one of
turbulent velocity flows and one of financial prices.


title: Blind Deconvolution of PET Images using Anatomical Priors

abstract:
  Images from positron emission tomography (PET) provide metabolic information
about the human body. They present, however, a spatial resolution that is
limited by physical and instrumental factors often modeled by a blurring
function. Since this function is typically unknown, blind deconvolution (BD)
techniques are needed in order to produce a useful restored PET image. In this
work, we propose a general BD technique that restores a low resolution blurry
image using information from data acquired with a high resolution modality
(e.g., CT-based delineation of regions with uniform activity in PET images).
The proposed BD method is validated on synthetic and actual phantoms.


title:
Second Law Considerations in Fourier Heat Conduction of a Lattice Chain
  in Relation to Intermolecular Potentials

abstract:
  Two aspects of conductive heat are focused here (i) the nature of conductive
heat, defined as that form of energy that is transferred as a result of a
temperature difference and (ii) the nature of the intermolecular potentials
that induces both thermal energy flow and the temperature profile at the steady
state for a 1-D lattice chain. It is found that the standard presuppositions of
people like Benofy and Quay (BQ) following Joseph Fourier do not obtain for at
least a certain specified regime of intermolecular potential parameters related
to harmonic (quadratic) potentials for nearest neighbor interactions. For these
harmonic potentials, it appears from the simulation results that steady state
solutions exist utilizing non-synthetic thermostats that couple not just the
two particles at the extreme ends of the lattice chain, but to a control volume
of $N$ particles located at either ends of the chain that does not accord with
the unique analytical solutions that obtains for single particle thermostatting
at the ends of the lattice with a different thermostatting algorithm that
utilizes coupling coefficients. If the method used here is considered a more
"realistic" or feasible model of the physical reality, then a re-evaluation of
some aspects of the standard theoretical methodology is warranted since the
standard model solution profile does not accord with the simulation temperature
profile determined here for this related model. We also note that the
sinusoidal temperature profile generated suggests that thermal integrated
circuits with several thermal P-N junctions may be constructed, opening a way
to create more complex thermal transistor circuits. A stationary principle is
proposed for regions that violate the Fourier principle $\mathbf{J_q.}\nabla T
\le 0 $, where $\mathbf{J_q}$ is the heat current vector and $T$ the
temperature.


title:
Bifurcation equations for periodic orbits of implicit discrete dynamical
  systems

abstract:
  Bifurcation equations, non-degeneracy and transversality conditions are
obtained for the fold, transcritical, pitchfork and flip bifurcations for
periodic points of one dimensional implicitly defined discrete dynamical
systems. The backward Euler method and the trapezoid method for numeric
solutions of ordinary differential equations fall in the category of implicit
dynamical systems. Examples of bifurcations are given for some implicit
dynamical systems including bifurcations for the backward Euler method when the
step size is changed.


title: Guess the Larger Number

abstract:
  We discuss variations of the zero-sum game where Bob selects two distinct
numbers, and Alice learns one of them to make a guess which of the numbers is
the larger.


title: Serendipity and strategy in rapid innovation

abstract:
  Innovation is to organizations what evolution is to organisms: it is how
organisations adapt to changes in the environment and improve. Governments,
institutions and firms that innovate are more likely to prosper and stand the
test of time; those that fail to do so fall behind their competitors and
succumb to market and environmental change. Yet despite steady advances in our
understanding of evolution, what drives innovation remains elusive. On the one
hand, organizations invest heavily in systematic strategies to drive
innovation. On the other, historical analysis and individual experience suggest
that serendipity plays a significant role in the discovery process. To unify
these two perspectives, we analyzed the mathematics of innovation as a search
process for viable designs across a universe of building blocks. We then tested
our insights using historical data from language, gastronomy and technology. By
measuring the number of makeable designs as we acquire more components, we
observed that the relative usefulness of different components is not fixed, but
cross each other over time. When these crossovers are unanticipated, they
appear to be the result of serendipity. But when we can predict crossovers
ahead of time, they offer an opportunity to strategically increase the growth
of our product space. Thus we find that the serendipitous and strategic visions
of innovation can be viewed as different manifestations of the same thing: the
changing importance of component building blocks over time.


title: A New, Low Braking Index For the LMC Pulsar B0540-69

abstract:
  We report the results of a 16-month monitoring campaign using the Swift
satellite of PSR B0540-69, a young pulsar in the Large Magellanic Cloud. Phase
connection was maintained throughout the campaign so that a reliable ephemeris
could be determined, and the length of the campaign is adequate to accurately
determine the spin frequency and its first and second derivatives. The braking
index is 0.031 +/- 0.013 (90% confidence), a value much lower than previously
reported for B0540-69 and almost all other young pulsars. We use data from the
extensive monitoring campaign with RXTE to show that timing noise is unlikely
to significantly affect the measurement. This is the first measurement of the
braking index in the pulsar's recently discovered high spin-down state. We
discuss possible mechanisms for producing the low braking index.


title:
Scattering amplitudes over finite fields and multivariate functional
  reconstruction

abstract:
  Several problems in computer algebra can be efficiently solved by reducing
them to calculations over finite fields. In this paper, we describe an
algorithm for the reconstruction of multivariate polynomials and rational
functions from their evaluation over finite fields. Calculations over finite
fields can in turn be efficiently performed using machine-size integers in
statically-typed languages. We then discuss the application of the algorithm to
several techniques related to the computation of scattering amplitudes, such as
the four- and six-dimensional spinor-helicity formalism, tree-level recursion
relations, and multi-loop integrand reduction via generalized unitarity. The
method has good efficiency and scales well with the number of variables and the
complexity of the problem. As an example combining these techniques, we present
the calculation of full analytic expressions for the two-loop five-point
on-shell integrands of the maximal cuts of the planar penta-box and the
non-planar double-pentagon topologies in Yang-Mills theory, for a complete set
of independent helicity configurations.


title:
Weak convergence of a pseudo maximum likelihood estimator for the
  extremal index

abstract:
  The extremes of a stationary time series typically occur in clusters. A
primary measure for this phenomenon is the extremal index, representing the
reciprocal of the expected cluster size. Both a disjoint and a sliding blocks
estimator for the extremal index are analyzed in detail. In contrast to many
competitors, the estimators only depend on the choice of one parameter
sequence. We derive an asymptotic expansion, prove asymptotic normality and
show consistency of an estimator for the asymptotic variance. Explicit
calculations in certain models and a finite-sample Monte Carlo simulation study
reveal that the sliding blocks estimator outperforms other blocks estimators,
and that it is competitive to runs- and inter-exceedance estimators in various
models. The methods are applied to a variety of financial time series.


title: Parity Symmetry Breaking and Topological Phases in a Superfluid Ring

abstract:
  We study analytically the superfluid flow of a Bose-Einstein condensate in a
ring geometry in presence of a rotating barrier. We show that a phase
transition breaking a parity symmetry among two topological phases occurs at a
critical value of the height of the barrier. Furthermore, a discontinuous
(accompanied by hysteresis) phase transition is observed in the ordered phase
when changing the angular velocity of the barrier. At the critical point where
the hysteresis area vanishes, chemical potential of the ground state develops a
cusp (a discontinuity in the first derivative). Along this path, the jump
between the two corresponding states having a different winding number shows
strict analogies with a topological phase transition. We finally study the
current-phase relation of the system and compare some of our calculations with
published experimental results.


title:
Conformally Euclidean metrics on $\mathbb{R}^n$ with arbitrary total
  $Q$-curvature

abstract:
  We study the existence of solution to the problem $$(-\Delta)^\frac
n2u=Qe^{nu}\quad\text{in }\mathbb{R}^{n},\quad
\kappa:=\int_{\mathbb{R}^{n}}Qe^{nu}dx<\infty,$$ where $Q\geq 0$, $\kappa\in
(0,\infty)$ and $n\geq 3$. Using ODE techniques Martinazzi for $n=6$ and
Huang-Ye for $n=4m+2$ proved the existence of solution to the above problem
with $Q\equiv const>0$ and for every $\kappa\in (0,\infty)$. We extend these
results in every dimension $n\geq 5$, thus completely answering the problem
opened by Martinazzi. Our approach also extends to the case in which $Q$ is
non-constant, and under some decay assumptions on $Q$ we can also treat the
cases $n=3$ and $4$.


title:
Evaluation of the Finite Element Lattice Boltzmann Method for Binary
  Fluid Flows

abstract:
  In contrast to the commonly used lattice Boltzmann method, off-lattice
Boltzmann methods decouple the velocity discretization from the underlying
spatial grid, thus allowing for more efficient geometric representations of
complex boundaries. The current work combines characteristic-based integration
of the streaming step with the free-energy based multiphase model by Lee et.
al. [Journal of Computational Physics, 206 (1), 2005 ]. This allows for
simulation time steps more than an order of magnitude larger than the
relaxation time. Unlike previous work by Wardle et. al. [Computers and
Mathematics with Applications, 65 (2), 2013 ] that integrated intermolecular
forcing terms in the advection term, the current scheme applies collision and
forcing terms locally for a simpler finite element formulation. A series of
thorough benchmark studies reveal that this does not compromise stability and
that the scheme is able to accurately simulate flows at large density and
viscosity contrasts.


title:
Dynamical Tides in General Relativity: Effective Action and
  Effective-One-Body Hamiltonian

abstract:
  Tidal effects have an important impact on the late inspiral of compact binary
systems containing neutron stars. Most current models of tidal deformations of
neutron stars assume that the tidal bulge is directly related to the tidal
field generated by the companion, with a constant response coefficient.
However, if the orbital motion approaches a resonance with one of the internal
modes of the neutron star, this adiabatic description of tidal effects starts
to break down, and the tides become dynamical. In this paper, we consider
dynamical tides in general relativity due to the quadrupolar fundamental
oscillation mode of a neutron star. We devise a description of the effects of
the neutron star's finite size on the orbital dynamics based on an effective
point-particle action augmented by dynamical quadrupolar degrees of freedom. We
analyze the post-Newtonian and test-particle approximations of this model and
incorporate the results into an effective-one-body Hamiltonian. This enables us
to extend the description of dynamical tides over the entire inspiral. We
demonstrate that dynamical tides give a significant enhancement of matter
effects compared to adiabatic tides, at least for neutron stars with large
radii and for low mass-ratio systems, and should therefore be included in
accurate models for gravitational-wave data analysis.


title: Separability of three qubit Greenberger-Horne-Zeilinger diagonal states

abstract:
  We characterize the separability of three qubit GHZ diagonal states in terms
of entries. This enables us to check separability of GHZ diagonal states
without decomposition into the sum of pure product states. In the course of
discussion, we show that the necessary criterion of G\"uhne for (full)
separability of three qubit GHZ diagonal states is sufficient with a simpler
formula. The main tool is to use entanglement witnesses which are tri-partite
Choi matrices of positive bi-linear maps.


title: Perfectly Secure Message Transmission in Two Rounds

abstract:
  In the model that has become known as "Perfectly Secure Message
Transmission"(PSMT), a sender Alice is connected to a receiver Bob through n
parallel two-way channels. A computationally unbounded adversary Eve controls t
of these channels, meaning she can acquire and alter any data that is
transmitted over these channels. The sender Alice wishes to communicate a
secret message to Bob privately and reliably, i.e. in such a way that Eve will
not get any information about the message while Bob will be able to recover it
completely.
  In this paper, we focus on protocols that work in two transmission rounds for
n= 2t+1. We break from previous work by following a conceptually simpler
blueprint for achieving a PSMT protocol. We reduce the previously best-known
communication complexity, i.e. the number of transmitted bits necessary to
communicate a 1-bit secret, from O(n^3 log n) to O(n^2 log n). Our protocol
also answers a question raised by Kurosawa and Suzuki and hitherto left open:
their protocol reaches optimal transmission rate for a secret of size O(n^2 log
n) bits, and the authors raised the problem of lowering this threshold. The
present solution does this for a secret of O(n log n) bits. Additionally, we
show how our protocol can be adapted to a Network Coding context.


title:
Resolving Out-of-Vocabulary Words with Bilingual Embeddings in Machine
  Translation

abstract:
  Out-of-vocabulary words account for a large proportion of errors in machine
translation systems, especially when the system is used on a different domain
than the one where it was trained. In order to alleviate the problem, we
propose to use a log-bilinear softmax-based model for vocabulary expansion,
such that given an out-of-vocabulary source word, the model generates a
probabilistic list of possible translations in the target language. Our model
uses only word embeddings trained on significantly large unlabelled monolingual
corpora and trains over a fairly small, word-to-word bilingual dictionary. We
input this probabilistic list into a standard phrase-based statistical machine
translation system and obtain consistent improvements in translation quality on
the English-Spanish language pair. Especially, we get an improvement of 3.9
BLEU points when tested over an out-of-domain test set.


title: The Many Faces of Graph Dynamics

abstract:
  The topological structure of complex networks has fascinated researchers for
several decades, resulting in the discovery of many universal properties and
reoccurring characteristics of different kinds of networks. However, much less
is known today about the network dynamics: indeed, complex networks in reality
are not static, but rather dynamically evolve over time.
  Our paper is motivated by the empirical observation that network evolution
patterns seem far from random, but exhibit structure. Moreover, the specific
patterns appear to depend on the network type, contradicting the existence of a
"one fits it all" model. However, we still lack observables to quantify these
intuitions, as well as metrics to compare graph evolutions. Such observables
and metrics are needed for extrapolating or predicting evolutions, as well as
for interpolating graph evolutions.
  To explore the many faces of graph dynamics and to quantify temporal changes,
this paper suggests to build upon the concept of centrality, a measure of node
importance in a network. In particular, we introduce the notion of centrality
distance, a natural similarity measure for two graphs which depends on a given
centrality, characterizing the graph type. Intuitively, centrality distances
reflect the extent to which (non-anonymous) node roles are different or, in
case of dynamic graphs, have changed over time, between two graphs.
  We evaluate the centrality distance approach for five evolutionary models and
seven real-world social and physical networks. Our results empirically show the
usefulness of centrality distances for characterizing graph dynamics compared
to a null-model of random evolution, and highlight the differences between the
considered scenarios. Interestingly, our approach allows us to compare the
dynamics of very different networks, in terms of scale and evolution speed.


title:
DNA like$-$charge attraction and overcharging by divalent counterions in
  the presence of divalent co$-$ions

abstract:
  Strongly correlated electrostatics of DNA systems has drawn the interest of
many groups, especially the condensation and overcharging of DNA by multivalent
counterions. By adding counterions of different valencies and shapes, one can
enhance or reduce DNA overcharging. In this papers, we focus on the effect of
multivalent co-ions, specifically divalent co-ions such as SO$_4^{2-}$. A
computational experiment of DNA condensation using Monte$-$Carlo simulation in
grand canonical ensemble is carried out where DNA system is in equilibrium with
a bulk solution containing a mixture of salt of different valency of co-ions.
Compared to system with purely monovalent co-ions, the influence of divalent
co-ions shows up in multiple aspects. Divalent co-ions lead to an increase of
monovalent salt in the DNA condensate. Because monovalent salts mostly
participate in linear screening of electrostatic interactions in the system,
more monovalent salt molecules enter the condensate leads to screening out of
short-range DNA$-$DNA like charge attraction and weaker DNA condensation free
energy. The overcharging of DNA by multivalent counterions is also reduced in
the presence of divalent co$-$ions. Strong repulsions between DNA and divalent
co-ions and among divalent co-ions themselves leads to a {\em depletion} of
negative ions near DNA surface as compared to the case without divalent
co-ions. At large distance, the DNA$-$DNA repulsive interaction is stronger in
the presence of divalent co$-$ions, suggesting that divalent co$-$ions role is
not only that of simple stronger linear screening.


title: Data reduction for the MATISSE instrument

abstract:
  We present in this paper the general formalism and data processing steps used
in the MATISSE data reduction software, as it has been developed by the MATISSE
consortium. The MATISSE instrument is the mid-infrared new generation
interferometric instrument of the Very Large Telescope Interferometer (VLTI).
It is a 2-in-1 instrument with 2 cryostats and 2 detectors: one 2k x 2k
Rockwell Hawaii 2RG detector for L\&M-bands, and one 1k x 1k Raytheon Aquarius
detector for N-band, both read at high framerates, up to 30 frames per second.
MATISSE is undergoing its first tests in laboratory today.


title: Out-of-Time-Order Correlation for Many-Body Localization

abstract:
  In this paper we first compute the out-of-time-order correlators (OTOC) for
both a phenomenological model and a random-field XXZ model in the many-body
localized phase. We show that the OTOC decreases in power law in a many-body
localized system at the scrambling time. We also find that the OTOC can also be
used to distinguish a many-body localized phase from an Anderson localized
phase, while a normal correlator cannot. Furthermore, we prove an exact theorem
that relates the growth of the second R\'enyi entropy in the quench dynamics to
the decay of the OTOC in equilibrium. This theorem works for a generic quantum
system. We discuss various implications of this theorem.

categories: cond-mat.quant-gas cond-mat.dis-nn cond-mat.stat-mech cond-mat.str-el


title: Heat flow and quantitative differentiation

abstract:
  For every Banach space $(Y,\|\cdot\|_Y)$ that admits an equivalent uniformly
convex norm we prove that there exists $c=c(Y)\in (0,\infty)$ with the
following property. Suppose that $n\in \mathbb{N}$ and that $X$ is an
$n$-dimensional normed space with unit ball $B_X$. Then for every $1$-Lipschitz
function $f:B_X\to Y$ and for every $\varepsilon\in (0,1/2]$ there exists a
radius $r\ge\exp(-1/\varepsilon^{cn})$, a point $x\in B_X$ with $x+rB_X\subset
B_X$, and an affine mapping $\Lambda:X\to Y$ such that
$\|f(y)-\Lambda(y)\|_Y\le \varepsilon r$ for every $y\in x+rB_X$.


title:
Conductance fluctuations and disorder induced $\nu=0$ quantum Hall
  plateau in topological insulator nanowires

abstract:
  Clean topological insulators exposed to a magnetic field develop Landau
levels accompanied by a nonzero Hall conductivity for the infinite slab
geometry. In this work we consider the case of disordered topological insulator
nanowires and find, in contrast, that a zero Hall plateau emerges within a
broad energy window close to the Dirac point. We numerically calculate the
conductance and its distribution for a statistical ensemble of disordered
nanowires, and use the conductance fluctuations to study the dependence of the
insulating phase on system parameters, such as the nanowire length, disorder
strength and the magnetic field.


title: Nonparaxial Near-nondiffracting Accelerating Optical Beams

abstract:
  We show that new families of accelerating and almost nondiffracting beams
(solutions) for Maxwell's equations can be constructed. These are complex
geometrical optics (CGO) solutions to Maxwell's equations with nonlinear
limiting Carleman weights. They have the form of wave packets that propagate
along circular trajectories while almost preserving a transverse intensity
profile. We also show similar waves constructed using the approach combining
CGO solutions and the Kelvin transform.


title:
Models of spherical shells as sources of Majumdar-Papapetrou type
  spacetimes

abstract:
  By starting with a seed Newtonian potential-density pair we construct
relativistic thick spherical shell models for a Majumdar-Papapetrou type
conformastatic spacetime. As a simple example, we consider a family of
Plummer-Hernquist type relativistic spherical shells. As a second application,
these structures are then used to model a system composite by a dust disk and a
halo of matter. We study the equatorial circular motion of test particles
around such configurations. Also the stability of the orbits is analyzed for
radial perturbation using an extension of the Rayleigh criterion. The models
considered satisfying all the energy conditions.


title:
Differentiability of non-archimedean volumes and non-archimedean
  Monge-Amp\`ere equations (with an appendix by Robert Lazarsfeld)

abstract:
  Let $X$ be a normal projective variety over a complete discretely valued
field and $L$ a line bundle on $X$. We denote by $X^\textrm{an}$ the
analytification of $X$ in the sense of Berkovich and equip the analytification
$L^\textrm{an}$ of $L$ with a continuous metric $\| \ \|$. We study
non-archimedean volumes, a tool which allows us to control the asymptotic
growth of small sections of big powers of $L$. We prove that the
non-archimedean volume is differentiable at a continuous semipositive metric
and that the derivative is given by integration with respect to a
Monge-Amp\`ere measure. Such a differentiability formula had been proposed by
M. Kontsevich and Y. Tschinkel. In residue characteristic zero, it implies an
orthogonality property for non-archimedean plurisubharmonic functions which
allows us to drop an algebraicity assumption in a theorem of S. Boucksom, C.
Favre and M. Jonsson about the solution to the non-archimedean Monge-Amp\`{e}re
equation. The appendix by R. Lazarsfeld establishes the holomorphic Morse
inequalities in arbitrary characteristic.


title: Why should we care about quantum discord?

abstract:
  Entanglement is a central feature of quantum theory. Mathematical properties
and physical applications of pure state entanglement make it a template to
study quantum correlations. However, an extension of entanglement measures to
mixed states in terms of separability does not always correspond to all the
operational aspects. Quantum discord measures allow an alternative way to
extend the idea of quantum correlations to mixed states. In many cases these
extensions are motivated by physical scenarios and quantum information
protocols. In this chapter we discuss several settings involving correlated
quantum systems, ranging from distributed gates to detectors testing quantum
fields. In each setting we show how entanglement fails to capture the relevant
features of the correlated system, and discuss the role of discord as a
possible alternative.


title:
The Rainbow at the End of the Line --- A PPAD Formulation of the
  Colorful Carath\'eodory Theorem with Applications

abstract:
  Let $C_1,...,C_{d+1}$ be $d+1$ point sets in $\mathbb{R}^d$, each containing
the origin in its convex hull. A subset $C$ of $\bigcup_{i=1}^{d+1} C_i$ is
called a colorful choice (or rainbow) for $C_1, \dots, C_{d+1}$, if it contains
exactly one point from each set $C_i$. The colorful Carath\'eodory theorem
states that there always exists a colorful choice for $C_1,\dots,C_{d+1}$ that
has the origin in its convex hull. This theorem is very general and can be used
to prove several other existence theorems in high-dimensional discrete
geometry, such as the centerpoint theorem or Tverberg's theorem. The colorful
Carath\'eodory problem (CCP) is the computational problem of finding such a
colorful choice. Despite several efforts in the past, the computational
complexity of CCP in arbitrary dimension is still open.
  We show that CCP lies in the intersection of the complexity classes PPAD and
PLS. This makes it one of the few geometric problems in PPAD and PLS that are
not known to be solvable in polynomial time. Moreover, it implies that the
problem of computing centerpoints, computing Tverberg partitions, and computing
points with large simplicial depth is contained in $\text{PPAD} \cap
\text{PLS}$. This is the first nontrivial upper bound on the complexity of
these problems. Finally, we show that our PPAD formulation leads to a
polynomial-time algorithm for a special case of CCP in which we have only two
color classes $C_1$ and $C_2$ in $d$ dimensions, each with the origin in its
convex hull, and we would like to find a set with half the points from each
color class that contains the origin in its convex hull.


title: Hidden Phases Revealed at the Surface of Double-Layered Sr3(Ru1-xMnx)2O7

abstract:
  Double-layered Sr3Ru2O7 has received phenomenal consideration because it
exhibits a plethora of exotic phases when perturbed. New phases emerge with the
application of pressure, magnetic field, or doping. Here we show that creating
a surface is an alternative and effective way to reveal hidden phases that are
different from those seen in the bulk by investigating the surface properties
of Sr3(Ru1-xMnx)2O7. Driven by the tilt distortion of RuO6 octahedra, the
surface of Sr3Ru2O7 is less metallic than the bulk. In contrast, because of the
vanishing of tilt and enhanced rotation with Mn-doping, the surface of
Sr3(Ru0.84Mn0.16)2O7 is metallic while the bulk is insulating. Our result
demonstrates that the electronic and structural properties at the surface are
intimately coupled and consistent with quasi two-dimensional character.


title: Variabilities of Gamma-ray Bursts from Black Hole Hyper-accretion Disks

abstract:
  The emission from black hole binaries (BHBs) and active galactic nuclei
(AGNs) displays significant aperiodic variabilities. The most promising
explanation for these variabilities is the propagating fluctuations in the
accretion flow. It is natural to expect that the mechanism driving
variabilities in BHBs and AGNs may operate in a black hole hyper-accretion
disk, which is believed to power gamma-ray bursts (GRBs). We study the
variabilities of jet power in GRBs based on the model of propagating
fluctuations. It is found that the variabilities of jet power and the temporal
profile of erratic spikes in this scenario are similar to those in observed
light curves of prompt gamma-ray emission of GRBs. Our results show that the
mechanism driving X-ray variabilities in BHBs and AGNs may operate in the
central engine to drive the variabilities of GRBs.


title: On the origin of the HLX-1 outbursts

abstract:
  HLX-1, currently the best intermediate-mass black hole candidate, has
undergone seven violent outbursts, each with a peak X-ray luminosity of
$L_{\mathrm{peak},\mathrm{X}}\sim 10^{42}\ \rm{erg\ s^{-1}}$. Interestingly,
the properties of the HLX-1 outbursts evolve with time. In this work, we aim to
constrain the physical parameters of the central engine of the HLX-1 outbursts
in the framework of the black hole accretion. We find that the physical
properties of the HLX-1 outbursts are consistent with being driven by the
radiation pressure instability. This scenario can explain the evolution of the
recurrent timescales of the HLX-1 outbursts as a function of the durations.


title: On spectral properties of the Bloch-Torrey operator in two dimensions

abstract:
  We investigate a two-dimensional Schr\"odinger operator, $-h^2 \Delta
+iV(x)$, with a purely complex potential $iV(x)$. A rigorous definition of this
non-selfadjoint operator is provided for bounded and unbounded domains with
common boundary conditions (Dirichlet, Neumann, Robin and transmission). We
propose a general perturbative approach to construct its quasimodes in the
semi-classical limit. An alternative WKB construction is also discussed. These
approaches are local and thus valid for both bounded and unbounded domains,
allowing one to compute the approximate eigenvalues to any order in the small
$h$ limit. The general results are further illustrated on the particular case
of the Bloch-Torrey operator, $-h^2\Delta + ix_1$, for which a four-term
asymptotics is explicitly computed. Its high accuracy is confirmed by a
numerical computation of the eigenvalues and eigenfunctions of this operator
for a disk and circular annuli. The localization of eigenfunctions near the
specific boundary points is revealed. Some applications in the field of
diffusion nuclear magnetic resonance are discussed.


title: Landau-Zener Tunneling of Solitons

abstract:
  A simple mechanical analog describing Landau-Zener tunneling effect is
proposed using two weakly coupled chains of nonlinear oscillators with
gradually decreasing (first chain) and increasing (second chain) masses. The
model allows to investigate nonlinear generalization of Landau-Zener tunneling
effect considering soliton propagation and tunneling between the chains. It is
shown that soliton tunneling characteristics become drastically dependent on
its amplitude in nonlinear regime. The validity of the developed tunneling
theory is justified via comparison with direct numerical simulations on
oscillator ladder system.


title:
Correlated Non-Gaussian phase fluctuations in LaAlO$_3$/SrTiO$_3$
  heterointerface

abstract:
  We probe the existence of large correlated non-Gaussian phase fluctuations in
the vicinity of the superconducting phase transition in the conducting layer
residing at the interface of LaAlO$_3$/SrTiO$_3$ heterostructures. The
non-Gaussian fluctuations appear between the Berezinskii-Kosterlitz-Thouless
transition temperature $T_{BKT}$ and the mean field transition temperature
$T_C$. Subsequent theoretical analysis reveals that non-Gaussianity arises
predominantly due to the percolative transition of a Josephson coupled network
of superconductors. Our results confirm that the superconductivity in this
system is confined to two-dimensions. Our study of the non-Gaussian resistance
fluctuation spectrum provides a novel means to explore the BKT-transition in
two-dimensional inhomogeneous superconductors.


title: Scalar Fields in Particle Physics

abstract:
  Extending the scalar sector helps in studying the Higgs mechanism and some
Standard Model problems. We implement the correspondence between the
gauge-dependent elementary states and the non-perturbative non-abelian
gauge-invariant asymptotic states, necessary to study the non-perturbative
phenomenology of two-Higgs-doublet models. The Flavour and CP violation in
experimental data follows a hierarchical pattern, accounted by the Standard
Model. We define the Minimal Flavour Violation condition with six spurions in
effective field theories, implying Flavour and CP violation entirely dependent
on the fermion mixing matrices but independent of the fermion masses hierarchy;
it is renormalization-group invariant. We study the phenomenology of
renormalizable two-Higgs-doublet models which verify the defined condition as
consequence of a symmetry; new light physical scalars, mediating Flavour
Changing Neutral Currents, are allowed by flavour data without flavour
coefficients beyond the Standard Model; we tested the models with C++ libraries
linked by the symbolic skills of the GiNaC library and we propose more
libraries supporting a systematic search for Flavour Changing Neutral Currents.
We also map the complex to the real Poincare group representations, derive the
free Dirac equation requiring covariant localizability of the representations
and study Localization and gauge symmetries in Quantum Field Theory.


title: A conjectured bound on the spanning tree number of bipartite graphs

abstract:
  The Ferrers bound conjecture is a natural graph-theoretic extension of the
enumeration of spanning trees for Ferrers graphs. We document the current
status of the conjecture and provide a further conjecture which implies it.