title: What's the nature of sdA stars?

abstract:
  White dwarfs with log g lower than 7.0 are called Extremely Low Mass white
dwarfs (ELMs). They were first found as companions to pulsars, then to other
white dwarfs and main sequence stars (The ELM Survey: 2010 to 2016), and can
only be formed in interacting binaries in the age of the Universe. In our SDSS
DR12 white dwarf catalog (Kepler et al. 2016), we found a few thousand stars in
the effective temperature and surface gravity ranges attributed to ELMs. We
have called these objects sdAs, alluding to their narrow hydrogen line spectra
showing sub-main sequence log g. One possible explanation for the sdAs is that
they are ELMs. Increasing the ELMs sample would help constrain the number of
close binaries in the Galaxy. Interestingly, if they turn out to be A stars
with an overestimated log g, the distance modulus would put these young stars
in the Galaxy's halo.


title:
Weighted Positive Binary Decision Diagrams for Exact Probabilistic
  Inference

abstract:
  Recent work on weighted model counting has been very successfully applied to
the problem of probabilistic inference in Bayesian networks. The probability
distribution is encoded into a Boolean normal form and compiled to a target
language, in order to represent local structure expressed among conditional
probabilities more efficiently. We show that further improvements are possible,
by exploiting the knowledge that is lost during the encoding phase and
incorporating it into a compiler inspired by Satisfiability Modulo Theories.
Constraints among variables are used as a background theory, which allows us to
optimize the Shannon decomposition. We propose a new language, called Weighted
Positive Binary Decision Diagrams, that reduces the cost of probabilistic
inference by using this decomposition variant to induce an arithmetic circuit
of reduced size.


title: The Density-Potential Mapping in Quantum Dynamics

abstract:
  This work studies in detail the possibility of defining a one-to-one mapping
from charge densities as obtained by the time-dependent Schr\"odinger equation
to external potentials. Such a mapping is provided by the Runge-Gross theorem
and lies at the very core of time-dependent density functional theory. After
introducing the necessary mathematical concepts, the usual mapping "there" -
from potentials to wave functions as solutions to the Schr\"odinger equation -
is revisited paying special attention to Sobolev regularity. This is
scrutinised further when the question of functional differentiability of the
solution with respect to the potential arises, a concept related to linear
response theory. Finally, after a brief introduction to general density
functional theory, the mapping "back again" - from densities to potentials
thereby inverting the Schr\"odinger equation for a fixed initial state - is
defined. Apart from utilising the original Runge-Gross proof this is achieved
through a fixed-point procedure. Both approaches give rise to mathematical
issues, previously unresolved, which however could be dealt with to some extent
within the framework at hand.


title:
Criteria of convergence of a non ordinary random continued fractions on
  a symmetric cone

abstract:
  In this paper, we use a notion of ratio based on a division algorithm, to
extend to a symmetric cone the definition of a continued fraction in its more
general form. We then give a criteria of convergence of a non ordinary random
continued fraction that has arisen in the study of some probability
distributions related to the beta distribution on the cone of positive definite
symmetric matrices or on any symmetric cone.


title: The pre-penumbral magnetic canopy in the solar atmosphere

abstract:
  Penumbrae are the manifestation of magnetoconvection in highly inclined (to
the vertical direction) magnetic field. The penumbra of a sunspot tends to
form, initially, along the arc of the umbra antipodal to the main region of
flux emergence. The question of how highly inclined magnetic field can
concentrate along the antipodal curves of umbrae, at least initially, remains
to be answered. Previous observational studies have suggested the existence of
some form of overlying magnetic canopy which acts as the progenitor for
penumbrae. We propose that such overlying magnetic canopies are a consequence
of how the magnetic field emerges into the atmosphere and are, therefore, part
of the emerging region. We show, through simulations of twisted flux tube
emergence, that canopies of highly inclined magnetic field form preferentially
at the required locations above the photosphere.


title:
Online Contrastive Divergence with Generative Replay: Experience Replay
  without Storing Data

abstract:
  Conceived in the early 1990s, Experience Replay (ER) has been shown to be a
successful mechanism to allow online learning algorithms to reuse past
experiences. Traditionally, ER can be applied to all machine learning paradigms
(i.e., unsupervised, supervised, and reinforcement learning). Recently, ER has
contributed to improving the performance of deep reinforcement learning. Yet,
its application to many practical settings is still limited by the memory
requirements of ER, necessary to explicitly store previous observations. To
remedy this issue, we explore a novel approach, Online Contrastive Divergence
with Generative Replay (OCD_GR), which uses the generative capability of
Restricted Boltzmann Machines (RBMs) instead of recorded past experiences. The
RBM is trained online, and does not require the system to store any of the
observed data points. We compare OCD_GR to ER on 9 real-world datasets,
considering a worst-case scenario (data points arriving in sorted order) as
well as a more realistic one (sequential random-order data points). Our results
show that in 64.28% of the cases OCD_GR outperforms ER and in the remaining
35.72% it has an almost equal performance, while having a considerably reduced
space complexity (i.e., memory usage) at a comparable time complexity.


title: Identifiability and Transportability in Dynamic Causal Networks

abstract:
  In this paper we propose a causal analog to the purely observational Dynamic
Bayesian Networks, which we call Dynamic Causal Networks. We provide a sound
and complete algorithm for identification of Dynamic Causal Net- works, namely,
for computing the effect of an intervention or experiment, based on passive
observations only, whenever possible. We note the existence of two types of
confounder variables that affect in substantially different ways the iden-
tification procedures, a distinction with no analog in either Dynamic Bayesian
Networks or standard causal graphs. We further propose a procedure for the
transportability of causal effects in Dynamic Causal Network settings, where
the re- sult of causal experiments in a source domain may be used for the
identification of causal effects in a target domain.


title: Coherent Population Oscillation-Based Light Storage

abstract:
  We theoretically study the propagation and storage of a classical field in a
$\Lambda$-type atomic medium using coherent population oscillations (CPOs). We
show that the propagation eigenmodes strongly relate to the different CPO modes
of the system. Light storage in such modes is discussed by introducing a
"populariton" quantity, a mixture of populations and field, by analogy to the
dark state polariton used in the context of electromagnetically induced
transparency light storage protocol. As experimentally shown, this memory
relies on populations and is then - by contrast with usual Raman coherence
optical storage protocols - robust to dephasing effects.


title:
A short FE implementation for a 2d homogeneous Dirichlet problem of a
  Fractional Laplacian

abstract:
  In \cite{AcostaBorthagaray}, a complete $n$-dimensional finite element
analysis of the homogeneous Dirichlet problem associated to a fractional
Laplacian was presented. Here we provide a comprehensive and simple 2D {\it
MATLAB}\textsuperscript{\textregistered} finite element code for such a
problem. The code is accompanied with a basic discussion of the theory relevant
in the context. The main program is written in about 80 lines and can be easily
modified to deal with other kernels as well as with time dependent problems.
The present work fills a gap by providing an input for a large number of
mathematicians and scientists interested in numerical approximations of
solutions of a large variety of problems involving nonlocal phenomena in
two-dimensional space.


title:
On the Hyperprior Choice for the Global Shrinkage Parameter in the
  Horseshoe Prior

abstract:
  The horseshoe prior has proven to be a noteworthy alternative for sparse
Bayesian estimation, but as shown in this paper, the results can be sensitive
to the prior choice for the global shrinkage hyperparameter. We argue that the
previous default choices are dubious due to their tendency to favor solutions
with more unshrunk coefficients than we typically expect a priori. This can
lead to bad results if this parameter is not strongly identified by data. We
derive the relationship between the global parameter and the effective number
of nonzeros in the coefficient vector, and show an easy and intuitive way of
setting up the prior for the global parameter based on our prior beliefs about
the number of nonzero coefficients in the model. The results on real world data
show that one can benefit greatly -- in terms of improved parameter estimates,
prediction accuracy, and reduced computation time -- from transforming even a
crude guess for the number of nonzero coefficients into the prior for the
global parameter using our framework.


title: A remarkable 20-crossing tangle

abstract:
  For any positive integer r, we exhibit a knot Kr with (20 $\times$ 2 r--1 +
1) crossings whose Jones polynomial V (Kr) is equal to 1 mod-ulo 2 r. Our
construction rests on a certain 20-crossing tangle T 20 which is undetectable
by the Kauffman bracket polynomial pair mod 2.


title: Adaptive stimulus design for dynamic recurrent neural network models

abstract:
  We present a theoretical application of an optimal experiment design (OED)
methodology to the development of mathematical models to describe the
stimulus-response relationship of sensory neurons. Although there are a few
related studies in the computational neuroscience literature on this topic,
most of them are either involving non-linear static maps or simple linear
filters cascaded to a static non-linearity. Although the linear filters might
be appropriate to demonstrate some aspects of neural processes, the high level
of non-linearity in the nature of the stimulus-response data may render them
inadequate. In addition, modelling by a static non-linear input - output map
may mask important dynamical (time-dependent) features in the response data.
Due to all those facts a non-linear continuous time dynamic recurrent neural
network that models the excitatory and inhibitory membrane potential dynamics
is preferred. The main goal of this research is to estimate the parametric
details of this model from the available stimulus-response data. In order to
design an efficient estimator an optimal experiment design scheme is proposed
which computes a pre-shaped stimulus to maximize a certain measure of Fisher
Information Matrix. This measure depends on the estimated values of the
parameters in the current step and the optimal stimuli are used in a maximum
likelihood estimation procedure to find an estimate of the network parameters.
This process works as a loop until a reasonable convergence occurs. The
response data is discontinuous as it is composed of the neural spiking instants
which is assumed to obey the Poisson statistical distribution. Thus the
likelihood functions depend on the Poisson statistics. In order to validate the
approach and evaluate its performance, a comparison with another approach on
estimation based on randomly generated stimuli is also presented.


title: Do Price Ranges Increase Click-throughs?

abstract:
  An important goal of online comparison shopping services is to "convert" a
viewer from general product category pages (for example product groups such as
"smartphones" or "air-conditioners") to detailed product pages and ultimately
to order pages. Comparison shopping websites provide a familiar web interface
as well as a chance for consumers to purchase items at competitive prices. In
return for providing access to a large market of potential consumers, the
comparison shopping service usually receives financial compensation for product
clicks and orders. This study looked at 2.5 million product listing visits at
price.com.hk to determine whether a modification in the way prices are
displayed on general category pages resulted in more "conversions" to product
detail pages. We found a statistically significant improvement over-all as a
result of the new price display resulting in 3.6% more product clicks over all
categories. Additional analysis showed that the effect is heterogeneous among
different categories, and in a few cases there may be some categories
negatively affected by the display modification.


title: Entropy-based link prediction in weighted networks

abstract:
  Information entropy has been proved to be an effective tool to quantify the
structural importance of complex networks. In the previous work (Xu et al, 2016
\cite{xu2016}), we measure the contribution of a path in link prediction with
information entropy. In this paper, we further quantify the contribution of a
path with both path entropy and path weight, and propose a weighted prediction
index based on the contributions of paths, namely Weighted Path Entropy (WPE),
to improve the prediction accuracy in weighted networks. Empirical experiments
on six weighted real-world networks show that WPE achieves higher prediction
accuracy than three typical weighted indices.


title: Active inference, eye movements and oculomotor delays

abstract:
  This paper considers the problem of sensorimotor delays in the optimal
control of (smooth) eye movements under uncertainty. Specifically, we consider
delays in the visuo-oculomotor loop and their implications for active
inference. Active inference uses a generalisation of Kalman filtering to
provide Bayes optimal estimates of hidden states and action in generalized
coordinates of motion. Representing hidden states in generalized coordinates
provides a simple way of compensating for both sensory and oculomotor delays.
The efficacy of this scheme is illustrated using neuronal simulations of
pursuit initiation responses, with and without compensation. We then consider
an extension of the gener-ative model to simulate smooth pursuit eye movements
- in which the visuo-oculomotor system believes both the target and its centre
of gaze are attracted to a (hidden) point moving in the visual field. Finally,
the generative model is equipped with a hierarchical structure, so that it can
recognise and remember unseen (occluded) trajectories and emit anticipatory
responses. These simulations speak to a straightforward and neurobiologically
plausible solution to the generic problem of integrating information from
different sources with different temporal delays and the particular
difficulties encountered when a system - like the oculomotor system - tries to
control its environment with delayed signals.


title:
Stabilised dG-FEM for incompressible natural convection flows with
  boundary and moving interior layers on non-adapted meshes

abstract:
  This paper presents heavily grad-div and pressure jump stabilised, equal- and
mixed-order discontinuous Galerkin finite element methods for non-isothermal
incompressible flows based on the Oberbeck-Boussinesq approximation. In this
framework, the enthalpy-porosity model for multiphase flow in melting and
solidification problems can be employed. By considering the differentially
heated cavity and the melting of pure gallium in a rectangular enclosure, it is
shown that both boundary layers and sharp moving interior layers can be handled
naturally by the proposed class of non-conforming methods. Due to the
stabilising effect of the grad-div term and the robustness of discontinuous
Galerkin methods, it is possible to solve the underlying problems accurately on
coarse, non-adapted meshes. The interaction of heavy grad-div stabilisation and
discontinuous Galerkin methods significantly improves the mass conservation
properties and the overall accuracy of the numerical scheme which is observed
for the first time. Hence, it is inferred that stabilised discontinuous
Galerkin methods are highly robust as well as computationally efficient
numerical methods to deal with natural convection problems arising in
incompressible computational thermo-fluid dynamics.

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


title: Edge Based Grid Super-Imposition for Crowd Emotion Recognition

abstract:
  Numerous automatic continuous emotion detection system studies have examined
mostly use of videos and images containing individual person expressing
emotions. This study examines the detection of spontaneous emotions in a group
and crowd settings. Edge detection was used with a grid of lines
superimposition to extract the features. The feature movement in terms of
movement from the reference point was used to track across sequences of images
from the color channel. Additionally the video data capturing was done on
spontaneous emotions invoked by watching sports events from group of
participants. The method was view and occlusion independent and the results
were not affected by presence of multiple people chaotically expressing various
emotions. The edge thresholds of 0.2 and grid thresholds of 20 showed the best
accuracy results. The overall accuracy of the group emotion classifier was
70.9%.


title: Master's Thesis : Deep Learning for Visual Recognition

abstract:
  The goal of our research is to develop methods advancing automatic visual
recognition. In order to predict the unique or multiple labels associated to an
image, we study different kind of Deep Neural Networks architectures and
methods for supervised features learning. We first draw up a state-of-the-art
review of the Convolutional Neural Networks aiming to understand the history
behind this family of statistical models, the limit of modern architectures and
the novel techniques currently used to train deep CNNs. The originality of our
work lies in our approach focusing on tasks with a low amount of data. We
introduce different models and techniques to achieve the best accuracy on
several kind of datasets, such as a medium dataset of food recipes (100k
images) for building a web API, or a small dataset of satellite images (6,000)
for the DSG online challenge that we've won. We also draw up the
state-of-the-art in Weakly Supervised Learning, introducing different kind of
CNNs able to localize regions of interest. Our last contribution is a
framework, build on top of Torch7, for training and testing deep models on any
visual recognition tasks and on datasets of any scale.


title: Quadric bundles and their moduli spaces

abstract:
  Quadric bundles on a compact Riemann surface X generalise orthogonal bundles
and arise naturally in the study of the moduli space of representations of
$\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of
quadric bundles over X of arbitrary rank and then survey deeper results in the
rank 2 case.


title:
Transverse momentum and multiplicity fluctuations in Ar+Sc collisions at
  the CERN SPS from NA61/SHINE

abstract:
  The NA61/SHINE experiment aims to discover the critical point of strongly
interacting matter and study the properties of the onset of deconfinement. For
these goals a scan of the two dimensional phase diagram ($T$-$\mu_{B}$) is
being performed at the SPS by measurements of hadron production in
proton-proton, proton-nucleus and nucleus-nucleus interactions as a function of
collision energy and system size. In this contribution preliminary results on
transverse momentum and multiplicity fluctuations expressed in terms of
strongly intensive quantities from the Ar+Sc energy scan will be presented.
These fluctuations are expected to be sensitive to the existence of a critical
point. The results are compared with results from the p+p and Be+Be energy scan
as well as with NA49 measurements.


title: Index of projective elliptic operators

abstract:
  Mathai, Melrose, and Singer introduced the notion of projective elliptic
operators on manifolds equipped with an Azumaya bundle. In this note we compute
the equivariant index of transversally elliptic operators that are the pullback
of projective elliptic operators on the trivialization of the Azumaya bundle.
It encompasses the fractional index formula of projective elliptic operator by
Mathai-Melrose-Singer.


title:
Circuit Quantum Electrodynamics Architecture for Gate-Defined Quantum
  Dots in Silicon

abstract:
  We demonstrate a hybrid device architecture where the charge states in a
double quantum dot (DQD) formed in a Si/SiGe heterostructure are read out using
an on-chip superconducting microwave cavity. A quality factor Q = 5,400 is
achieved by selectively etching away regions of the quantum well and by
reducing photon losses through low-pass filtering of the gate bias lines.
Homodyne measurements of the cavity transmission reveal DQD charge stability
diagrams and a charge-cavity coupling rate g_c/2pi = 23 MHz. These measurements
indicate that electrons trapped in a Si DQD can be effectively coupled to
microwave photons, potentially enabling coherent electron-photon interactions
in silicon.


title:
Study of filamentation instability on the divergence of ultraintense
  laser-driven electrons

abstract:
  Generation of relativistic electron (RE) beams during ultraintense laser
pulse interaction with plasma targets is studied by collisional
particle-in-cell (PIC) simulations. Strong magnetic field with transverse scale
length of several local plasma skin depths, associated with RE currents
propagation in the target, is generated by filamentation instability (FI) in
collisional plasmas, inducing a great enhancement of the divergence of REs
compared to that of collisionless cases. Such effect is increased with laser
intensity and target charge state, suggesting that the RE divergence might be
improved by using low-Z materials under appropriate laser intensities in future
fast ignition experiments and in other applications of laser-driven electron
beams.


title:
Inferring the core-collapse supernova explosion mechanism with
  gravitational waves

abstract:
  A detection of a core-collapse supernova (CCSN) gravitational-wave (GW)
signal with an Advanced LIGO and Virgo detector network may allow us to measure
astrophysical parameters of the dying massive star. GWs are emitted from deep
inside the core and, as such, they are direct probes of the CCSN explosion
mechanism. In this study we show how we can determine the CCSN explosion
mechanism from a GW supernova detection using a combination of principal
component analysis and Bayesian model selection. We use simulations of GW
signals from CCSN exploding via neutrino-driven convection and rapidly-rotating
core collapse. Previous studies have shown that the explosion mechanism can be
determined using one LIGO detector and simulated Gaussian noise. As real GW
detector noise is both non-stationary and non-Gaussian we use real detector
noise from a network of detectors with a sensitivity altered to match the
advanced detectors design sensitivity. For the first time we carry out a
careful selection of the number of principal components to enhance our model
selection capabilities. We show that with an advanced detector network we can
determine if the CCSN explosion mechanism is neutrino-driven convection for
sources in our Galaxy and rapidly-rotating core collapse for sources out to the
Large Magellanic Cloud.


title: Engineering Curvature Induced Anisotropy in Thin Ferromagnetic Films

abstract:
  The large curvature effects on micromagnetic energy of a thin ferromagnetic
film with nonlocal dipolar energy are considered. We predict that the dipolar
interaction and surface curvature can produce perpendicular anisotropy which
can be controlled by engineering a special type of periodic surface shape
structure. Similar effects can be achieved by a significant surface roughness
in the film. We show that in general the anisotropy can point in an arbitrary
direction depending on the surface curvature. We provide simple examples of
these periodic surface structures to demonstrate how to engineer particular
anisotropies in the film.


title:
Dichotomy between in-plane magnetic susceptibility and resistivity
  anisotropies in extremely strained $BaFe_{2}As_{2}$

abstract:
  The in-plane resistivity and uniform magnetic susceptibility anisotropies of
$BaFe_{2}As_{2}$ are obtained with a new method, in which a large
symmetry-breaking uniaxial strain is applied using a substrate with a very
anisotropic thermal expansion. The resistivity anisotropy and its corresponding
elastoresistivity exhibit very similar diverging behavior as those obtained
from piezo-stack experiments. This suggests that the resistivity anisotropy is
more a direct measure of magnetism than of nematicity, since the nematic
transition is no longer well-defined under a large strain. In strong contrast
to the large resistivity anisotropy above $T_{N}$, the anisotropy of the
in-plane magnetic susceptibility develops largely below $T_{N}$. Using an
itinerant model, we show that the observed anisotropy ($\chi_{b}>\chi_{a}$) is
determined by spin-orbit coupling and the orientation of the magnetic moments
in the antiferromagnetic phase, and that the anisotropy is dominated by
intra-orbital ($yz,yz$) contributions of the Umklapp susceptibility.


title:
Information processing using three-qubit and qubit-qutrit encodings of
  noncomposite quantum systems

abstract:
  We study quantum information properties of a seven-level system realized by a
particle in an one-dimensional square-well trap. Features of encodings of
seven-level systems in a form of three-qubit or qubit-qutrit systems are
discussed. We use the three-qubit encoding of the system in order to
investigate subadditivity and strong subadditivity conditions for the thermal
state of the particle. The qubit-qutrit encoding is employed to suggest a
single qudit algorithm for calculation of parity of a bit string. Obtained
results indicate on the potential resource of multilevel systems for
realization of quantum information processing.


title: The constant of recognizability is computable for primitive morphisms

abstract:
  Moss\'e proved that primitive morphisms are recognizable. In this paper we
give a computable upper bound for the constant of recognizability of such a
morphism. This bound can be expressed only using the cardinality of the
alphabet and the length of the longest image under the morphism of a letter.


title:
A possible mechanism for over luminous type Ia supernovae explosions
  inspired by dark matter

abstract:
  Dark matter is believed to be a major component of our universe. In this
paper we propose a new mechanism based on dark matter inspired
super-Chandrasekhar mass white dwarf to explain the recent observation of super
luminous type Ia supernovae explosions. Our calculation shows when a white
dwarf accretes enough dark matter, due to the Pauli exclusive principle between
fermionic dark matter particles, the mass of corresponding dark white dwarf
(which means the white dwarf mixed with dark matters) can significantly exceeds
the Chandrasekhar limit. Moreover, we investigate some physical observable
quantities, such as the redshift and moment of inertia of the dark white dwarf
and found that these quantities are sensitive to the dark matter particle's
distributions and thus can be potentially used to probe the relevant
information of dark matter particles in the future.


title: A Scalable Multi-Stage Packet-Switch for Data Center Networks

abstract:
  The growing trends of data centers over last decades including social
networking, cloud-based applications and storage technologies enabled many
advances to take place in the networking area. Recent changes imply continuous
demand for bandwidth to manage the large amount of packetized traffic. Cluster
switches and routers make the switching fabric in a Data Center Network (DCN)
environment and provide interconnectivity between elements of the same DC and
inter DCs. To handle the constantly variable loads, switches need deliver
outstanding throughput along with resiliency and scalability for DCN
requirements. Conventional DCN switches adopt crossbars or/and blocks of
memories mounted in a multistage fashion (commonly 2-Tiers or 3-Tiers).
However, current multistage switches, with their space-memory variants, are
either too complex to implement, have poor performance, or not cost effective.
We propose a novel and highly scalable multistage switch based on
Networks-on-Chip (NoC) fabrics for DCNs. In particular, we describe a
three-stage Clos packet-switch with a Round Robin packets dispatching scheme
where each central stage module is based on a Unidirectional NoC (UDN), instead
of the conventional single-hop crossbar. The design, referred to as Clos-UDN,
overcomes shortcomings of traditional multistage architectures as it (i)
Obviates the need for a complex and costly input modules, by means of few, yet
simple, input FIFO queues. (ii) Avoids the need for a complex and synchronized
scheduling process over a high number of input-output modules and/or port
pairs. (iii) Provides speedup, load balancing and path-diversity thanks to a
dynamic dispatching scheme as well as the NoC based fabric nature. Simulations
show that the Clos-UDN outperforms some common multistage switches under a
range of input traffics, making it highly appealing for ultra-high capacity DC
networks.


title: Optimal Energy Harvesting from Vortex-Induced Vibrations of Cables

abstract:
  Vortex-induced vibrations (VIV) of flexible cables are an example of
flow-induced vibrations that can act as energy harvesting systems by converting
energy associated with the spontaneous cable motion into electricity. This work
investigates the optimal positioning of the harvesting devices along the cable,
using numerical simulations with a wake oscillator model to describe the
unsteady flow forcing. Using classical gradient-based optimization, the optimal
harvesting strategy is determined for the generic configuration of a flexible
cable fixed at both ends, including the effect of flow forces and gravity on
the cable's geometry. The optimal strategy is found to consist systematically
in a concentration of the harvesting devices at one of the cable's ends,
relying on deformation waves along the cable to carry the energy toward this
harvesting site. Furthermore, we show that the performance of systems based on
VIV of flexible cables is significantly more robust to flow velocity
variations, in comparison with a rigid cylinder device. This results from two
passive control mechanisms inherent to the cable geometry : (i) the
adaptability to the flow velocity of the fundamental frequencies of cables
through the flow-induced tension and (ii) the selection of successive vibration
modes by the flow velocity for cables with gravity-induced tension.


title:
$2$- capability and $2$- nilpotent multiplier of finite dimensional
  nilpotent Lie algebras

abstract:
  In the present context, we investigate to obtain some more results about
$2$-nilpotent multiplier $\mathcal{M}^{(2)}(L)$ of a finite dimensional
nilpotent Lie algebra $L$. For instance, we characterize the structure of
$\mathcal{M}^{(2)}(H)$ when $H$ is a Heisenberg Lie algebra. Moreover, we give
some inequalities on $ \mathrm{dim}~ \mathcal{M}^{(2)}(L)$ to reduce a well
known upper bound on $2$-nilpotent multiplier as much as possible. Finally, we
show that $H(m)$ is 2-capable if and only if m=1.


title:
Momentum distribution and non-Fermi liquid behaviour in low-doped
  two-orbital model: finite-size cluster quantum Monte Carlo approach

abstract:
  The two-dimensional two-orbital Hubbard model is studied with the use of
finite-size cluster worldline quantum Monte Carlo algorithm. This model is
widely used for simulation of the band structure of FeAs clusters, which are
structure elements of Fe-based high-temperature superconductors. The choice of
a special basis set of hyper-sites allowed to take into account four-fermion
operator terms and to overcome partly the sign problem. Spectral functions and
the density of states for various parameters of the model are obtained in the
undoped and low-doped regimes. The correlated distortion of the spectral
density with the change of doping is observed, and the applicability of the
"hard-band" approximation in the doped regime is demonstrated. Profiles of the
momentum distribution are obtained for the first Brillouin zone; they have
pronounced jump near the Fermi level, which decreases with the growth of the
strength of the interaction. The invariance of the Fermi surface with respect
to the strength of the interaction is testified. Nesting is found in the case
of electron and hole doping. Fermi-liquid parameters of the model are derived.
Z-factor grows sharply with the increasing the level of doping, and
monotonously decreases with the growth of the strength of the interaction.
Moreover, electron-hole doping asymmetry of the Z-factor is revealed. The
non-Fermi liquid behaviour and the deviation from Luttinger theorem are
observed.


title: Price Dynamics Via Expectations, and the Role of Money Therein

abstract:
  Beyond its obvious macro-economic relevance, fiat money has important
micro-economic implications. They matter for addressing No. 8 in Smale's
"Mathematical Problems for the Next Century": extend the mathematical model of
general equilibrium theory to include price adjustments. In the canonical
Arrow-Debreu framework, equilibrium prices are set by a fictitious auctioneer.
Removing that fiction raises the question of how prices are set and adjusted by
decentralised actors with incomplete information. We investigate this question
through a very basic model where a unique factor of production, labour,
produces a single consumption good, called jelly for brevity. The point of the
model is to study a price dynamics based on the firm's expectations about jelly
demand and labour supply. The system tends towards economic equilibrium,
however, depending on the initial conditions it might not get there. In
different model versions, different kinds of money are introduced. Compared to
the case of no money, the introduction of money as a store of value facilitates
the system reaching economic equilibrium. If money is introduced as a third
commodity, i.e. there is also a demand for money, the system dynamics in
general becomes more complex.


title: Branes and integrable lattice models

abstract:
  This is a brief review of my work on the correspondence between
four-dimensional $\mathcal{N} = 1$ supersymmetric field theories realized by
brane tilings and two-dimensional integrable lattice models. I explain how to
construct integrable lattice models from extended operators in partially
topological quantum field theories, and elucidate the correspondence as an
application of this construction.


title:
Effect of entropy on the nucleation of cavitation bubbles in water under
  tension

abstract:
  Water can exist in a metastable liquid state under tension for long times
before the system relaxes into the vapor via cavitation, i.e., bubble
nucleation. Microscopic information on the cavitation process can be extracted
from experimental data by use of the nucleation theorem, which relates measured
cavitation rates to the size of the critical bubble. To apply the nucleation
theorem to experiments performed along an isochoric path, for instance, in
cavitation experiments in mineral inclusions, knowledge of the bubble entropy
is required. Using computer simulations, we compute the entropy of bubbles in
water as a function of their volume over a wide range of tensions from free
energy calculations. We find that the bubble entropy is an important
contribution to the free energy which significantly lowers the barrier to
bubble nucleation, thereby facilitating cavitation. Furthermore, the bubble
entropy per surface area depends on the curvature of the liquid--vapor
interface, decreasing approximately linearly with its mean curvature over the
studied range of bubble volumes. At room temperature, the entropy of a flat
liquid--vapor interface at ambient pressure is very similar to that of critical
bubbles over a wide range of tensions, which justifies the use of the former as
an approximation when interpreting data from experiments. Based on our
simulation results, we obtain an estimate for the volume of the critical bubble
from experimentally measured cavitation rates.


title: Deep Identity-aware Transfer of Facial Attributes

abstract:
  This paper presents a Deep convolutional network model for Identity-Aware
Transfer (DIAT) of facial attributes. Given the source input image and the
reference attribute, DIAT aims to generate a facial image that owns the
reference attribute as well as keeps the same or similar identity to the input
image. In general, our model consists of a mask network and an attribute
transform network which work in synergy to generate a photo-realistic facial
image with the reference attribute. Considering that the reference attribute
may be only related to some parts of the image, the mask network is introduced
to avoid the incorrect editing on attribute irrelevant region. Then the
estimated mask is adopted to combine the input and transformed image for
producing the transfer result. For joint training of transform network and mask
network, we incorporate the adversarial attribute loss, identity-aware adaptive
perceptual loss, and VGG-FACE based identity loss. Furthermore, a denoising
network is presented to serve for perceptual regularization to suppress the
artifacts in transfer result, while an attribute ratio regularization is
introduced to constrain the size of attribute relevant region. Our DIAT can
provide a unified solution for several representative facial attribute transfer
tasks, e.g., expression transfer, accessory removal, age progression, and
gender transfer, and can be extended for other face enhancement tasks such as
face hallucination. The experimental results validate the effectiveness of the
proposed method. Even for the identity-related attribute (e.g., gender), our
DIAT can obtain visually impressive results by changing the attribute while
retaining most identity-aware features.


title:
Auxiliary Beam Pair Enabled AoD and AoA Estimation in Closed-Loop
  Large-Scale mmWave MIMO Systems

abstract:
  Channel estimation is of critical importance in millimeter-wave (mmWave)
multiple-input multiple-output (MIMO) systems. Due to the use of large antenna
arrays, low-complexity mmWave specific channel estimation algorithms are
required. In this paper, an auxiliary beam pair design is proposed to provide
high-resolution estimates of the channel's angle-of-departure (AoD) and
angle-of-arrival (AoA) for mmWave MIMO systems. By performing an amplitude
comparison with respect to each auxiliary beam pair, a set of ratio measures
that characterize the channel's AoD and AoA are obtained by the receiver.
Either the best ratio measure or the estimated AoD is quantized and fed back to
the transmitter via a feedback channel. The proposed technique can be
incorporated into control channel design to minimize initial access delay.
Though the design principles are derived assuming a high-power regime,
evaluation under more realistic assumption shows that by employing the proposed
method, good angle estimation performance is achieved under various
signal-to-noise ratio levels and channel conditions.


title: On the values of Dedekind sums

abstract:
  Let $S(a,b)=12s(a,b)$, where $s(a,b)$ denotes the classical Dedekind sum. For
a given denominator $q\in \mathbb N$, we study the numerators $k\in\mathbb Z$
of the values $k/q$, $(k,q)=1$, of Dedekind sums $S(a,b)$. Our main result says
that if $k$ is such a numerator, then the whole residue class of $k$ modulo
$(q^2-1)q$ consists of numerators of this kind. This fact reduces the task of
finding all possible numerators $k$ to that of finding representatives for
finitely many residue classes modulo $(q^2-1)q$. By means of the proof of this
result we have determined all possible numerators $k$ for $2\le q\le 50$, the
case $q=1$ being trivial. The result of this search suggests a conjecture about
all possible values $k/q$, $(k,q)=1$, of Dedekind sums $S(a,b)$ for an
arbitrary $q\in\mathbb N$.


title:
Salem-Zygmund Inequality for locally sub-Gaussian random variables,
  random trigonometric polynomials, and random circulant matrices

abstract:
  In this manuscript we give an extension of the classic Salem--Zygmund
inequality for locally sub-Gaussian random variables. As an application, the
concentration of the roots of a Kac polynomial is studied, which is the main
contribution of this manuscript. More precisely, we assume the existence of the
moment generating function for the iid random coefficients for the Kac
polynomial and prove that there exists an annulus of width \[O(n^{-2}(\log
n)^{-1/2-\gamma}), \quad \gamma>1/2\] around the unit circle that does not
contain roots with high probability. As an another application, we show that
the smallest singular value of a random circulant matrix is at least
$n^{-\rho}$, $\rho\in(0,1/4)$ with probability $1-O(n^{-2\rho})$.


title: Three Lectures on Probability and Statistics

abstract:
  Notes for a Course on Probability and Statistics: L1: Elements of
Probability; L2: Bayesian Inference; L3: Monte Carlo Methods


title: On the History of Dibaryons and their Final Observation

abstract:
  A review is given about the long-standing search for dibaryons, i.e.
six-quark objects, from the early days until present, when the first dibaryon
resonance has been established, which has the potential of constituting a
compact six-quark object.


title: Conserved quantities on multisymplectic manifolds

abstract:
  Given a vector field on a manifold M, we define a globally conserved quantity
to be a differential form whose Lie derivative is exact. Integrals of conserved
quantities over suitable submanifolds are constant under time evolution, the
Kelvin circulation theorem being a well-known special case. More generally,
conserved quantities are well-behaved under transgression to spaces of maps
into M.
  We focus on the case of multisymplectic manifolds and Hamiltonian vector
fields. We show that in the presence of a Lie group of symmetries admitting a
homotopy co-momentum map, one obtains a whole family of globally conserved
quantities. This extends a classical result in symplectic geometry. We carry
this out in a general setting, considering several variants of the notion of
globally conserved quantity.


title:
Understanding and maintaining tactics graphically OR how we are learning
  that a diagram can be worth more than 10K LoC

abstract:
  The use of a functional language to implement proof strategies as proof
tactics in interactive theorem provers, often provides short, concise and
elegant implementations. Whilst being elegant, the use of higher order features
and combinator languages often results in a very procedural view of a strategy,
which may deviate significantly from the high-level ideas behind it. This can
make a tactic hard to understand and hence difficult to to debug and maintain
for experts and non-experts alike: one often has to tear apart complex
combinations of lower level tactics manually in order to analyse a failure in
the overall strategy. In an industrial technology transfer project, we have
been working on porting a very large and complex proof tactic into PSGraph, a
graphical language for representing proof strategies, supported by the Tinker
tool. The goal of this work is to improve understandability and maintainability
of tactics. Motivated by some initial successes with this, we here extend
PSGraph with additional features for development and debugging. Through the
re-implementation and refactoring of several existing tactics, we demonstrates
the advantages of PSGraph compared with a typical linear (term-based) tactic
language with respect to debugging, readability and maintenance. In order to
act as guidance for others, we give a fairly detailed comparison of the user
experience with the two approaches. The paper is supported by a web page
providing further details about the implementation as well as interactive
illustrations of the examples.


title:
Energetic analysis of disorder effects in an artificial spin ice with
  dipolar interactions

abstract:
  We study the effect of quenched disorder in square artificial spin ice by
means of numerical simulations. We introduce disorder in the length of magnetic
islands using two kinds of distributions: Gaussian and uniform. As the system
behavior depends on its geometrical parameters, we focus on studying it in the
proximity of the ice regime which is quite difficult to thermalize both in
experiments and simulations. We show how length disorder affect the
antiferromagnetic and (locally) ferromagnetic ordering, by inducing the system,
in the case of weak disorder, to intermediate or mix states. Moreover, in the
case of strong disorder, ferromagnetic plaquettes prevail regardless of whether
the mean length of the islands corresponds to an antiferromagnetic ordering.


title:
Femtosecond probing of light-speed plasma wakefields by using a
  relativistic electron bunch

abstract:
  Relativistic wakes produced by intense laser or particle beams propagating
through plasmas are being considered as accelerators for next generation of
colliders and coherent light sources. Such wakes have been shown to accelerate
electrons and positrons to several gigaelectronvolts (GeV), with a few percent
energy spread and a high wake-to-beam energy transfer efficiency. However,
complete mapping of electric field structure of the wakes has proven elusive.
Here we show that a high-energy electron bunch can be used to probe the fields
of such light-speed wakes with femtosecond resolution. The highly transient,
microscopic wakefield is reconstructed from the density modulated ultra-short
probe bunch after it has traversed the wake. This technique enables
visualization of linear wakefields in low-density plasmas that can accelerate
electrons and positrons beams. It also allows characterization of wakes in
plasma density ramps critical for maintaining the beam emittance, improving the
energy transfer efficiency and producing high brightness beams from plasma
accelerators.


title: Clumpy molecular structures revolving the B[e] supergiant MWC 137

abstract:
  The peculiar emission-line star MWC 137 with its extended optical nebula was
recently classified as B[e] supergiant. To study the spatial distribution of
its circumstellar molecular gas on small and large scales, we obtained
near-infrared and radio observations using SINFONI and APEX, respectively. We
find that the hot CO gas is arranged in moving clumpy ring and shell structures
close to the star, while a cold CO envelope is encircling the borders of the
optical nebula from the south to the west.


title: Involutions on algebraic surfaces and zero cycles

abstract:
  In this note we are going to consider a smooth projective surface equipped
with an involution and study the action of the involution at the level of Chow
group of zero cycles.


title: An SMDP Approach to Optimal PHY Configuration in Wireless Networks

abstract:
  In this work, we study the optimal configuration of the physical layer in
wireless networks by means of Semi-Markov Decision Process (SMDP) modeling. In
particular, assume the physical layer is characterized by a set of potential
operating points, with each point corresponding to a rate and reliability pair;
for example, these pairs might be obtained through a now-standard
diversity-vs-multiplexing tradeoff characterization. Given the current network
state (e.g., buffer occupancies), a Decision Maker (DM) needs to dynamically
decide which operating point to use. The SMDP problem formulation allows us to
choose from these pairs an optimal selection, which is expressed by a decision
rule as a function of the number of awaiting packets in the source's finite
queue, channel state, size of the packet to be transmitted. We derive a general
solution which covers various model configurations, including packet size
distributions and varying channels. For the specific case of exponential
transmission time, we analytically prove the optimal policy has a threshold
structure. Numerical results validate this finding, as well as depict
muti-threshold policies for time varying channels such as the Gilber-Elliott
channel.


title:
Fermionic vacuum polarization by a magnetic tube in the cosmic string
  spacetime

abstract:
  In this paper, we consider a charged massive fermionic quantum field in the
idealized cosmic string spacetime and in the presence of a magnetic field
confined in a cylindrical tube of finite radius. Three distinct configurations
for the magnetic fields are taken into account: (i) a cylindrical shell of
radius $a$, (ii) a magnetic field proportional to $1/r$ and (iii) a constant
magnetic field. In these three cases, the axis of the infinitely long tube of
radius $a$ coincides with the cosmic string. Our main objectives in this paper
are to analyze the fermionic condensat (FC) e and the vacuum expectation value
(VEV) of the fermionic energy-momentum tensor. In order to do that, we
explicitly construct the complete set of normalized wave-functions for each
configuration of magnetic field. We show that in the region outside the tube,
the FC and the VEV of the energy-momentum tensor are decomposed into two parts:
the first ones correspond to the zero-thickness magnetic flux contributions,
and the seconds are induced by the non-trivial structure of the magnetic field,
named core-induced contributions. The latter present specific forms depending
on the magnetic field configuration considered. We also show that the VEV of
the energy-momentum tensor is diagonal, obeys the conservation condition and
its trace is expressed in terms of the fermionic condensate. The zero-thickness
contributions to the FC and VEV of the energy-momentum tensor, depend only on
the fractional part of the ration of the magnetic flux inside the tube by the
quantum one. As to the core-induced contributions they depend on the total
magnetic flux inside the tube, and consequently, in general, are not a periodic
function of the magnetic flux.


title: On Artin L-functions and Gassmann Equivalence for Global Function Fields

abstract:
  In this paper we present an approach to study arithmetical properties of
global function fields by working with Artin L-functions. In particular we
recall and then extend a criteria of two function fields to be arithmetically
equivalent in terms of Artin L-functions of representations associated to the
common normal closure of those fields. We provide few examples of such
non-isomorphic fields and also discuss an algorithm to construct many such
examples by using torsion points on elliptic curves. Finally, we will show how
to apply our results in order to distinguish two global fields by a finite list
of Artin L-functions.


title:
High-performance K-means Implementation based on a Simplified Map-Reduce
  Architecture

abstract:
  The k-means algorithm is one of the most common clustering algorithms and
widely used in data mining and pattern recognition. The increasing
computational requirement of big data applications makes hardware acceleration
for the k-means algorithm necessary. In this paper, a simplified Map-Reduce
architecture is proposed to implement the k-means algorithm on an FPGA.
Algorithmic segmentation, data path elaboration and automatic control are
applied to optimize the architecture for high performance. In addition, high
level synthesis technique is utilized to reduce development cycles and
complexity. For a single iteration in the k-means algorithm, a throughput of
28.74 Gbps is achieved. The performance shows at least 3.93x speedup compared
with four representative existing FPGA-based implementations and can satisfy
the demand of big data applications.


title:
Capturing relativistic wake eld structures in plasmas using ultrashort
  high-energy electrons as a probe

abstract:
  A new method capable of capturing coherent electric field structures
propagating at nearly the speed of light in plasma with a time resolution as
small as a few femtoseconds is proposed. This method uses a few femtoseconds
long relativistic electron bunch to probe the wake produced in a plasma by an
intense laser pulse or an ultra-short relativistic charged particle beam. As
the probe bunch traverses the wake, its momentum is modulated by the electric
field of the wake, leading to a density variation of the probe after free-space
propagation. This variation of probe density produces a snapshot of the wake
that can directly give many useful information of the wake structure and its
evolution. Furthermore, this snapshot allows detailed mapping of the
longitudinal and transverse components of the wakefield. We develop a
theoretical model for field reconstruction and verify it using 3-dimensional
particle-in-cell (PIC) simulations. This model can accurately reconstruct the
wakefield structure in the linear regime, and it can also qualitatively map the
major features of nonlinear wakes. The capturing of the injection in a
nonlinear wake is demonstrated through 3D PIC simulations as an example of the
applications of this new method.


title: Compositional Synthesis of Leakage Resilient Programs

abstract:
  A promising approach to defend against side channel attacks is to build
programs that are leakage resilient, in a formal sense. One such formal notion
of leakage resilience is the n-threshold-probing model proposed in the seminal
work by Ishai et al. In a recent work, Eldib and Wang have proposed a method
for automatically synthesizing programs that are leakage resilient according to
this model, for the case n=1. In this paper, we show that the
n-threshold-probing model of leakage resilience enjoys a certain
compositionality property that can be exploited for synthesis. We use the
property to design a synthesis method that efficiently synthesizes
leakage-resilient programs in a compositional manner, for the general case of n
> 1. We have implemented a prototype of the synthesis algorithm, and we
demonstrate its effectiveness by synthesizing leakage-resilient versions of
benchmarks taken from the literature.


title: Dynamic Assortment Personalization in High Dimensions

abstract:
  We study the problem of dynamic assortment personalization with large,
heterogeneous populations and wide arrays of products, and demonstrate the
importance of structural priors for effective, efficient large-scale
personalization. Assortment personalization is the problem of choosing, for
each individual (type), a best assortment of products, ads, or other offerings
(items) so as to maximize revenue. This problem is central to revenue
management in e-commerce and online advertising where both items and types can
number in the millions.
  We formulate the dynamic assortment personalization problem as a
discrete-contextual bandit with $m$ contexts (types) and exponentially many
arms (assortments of the $n$ items). We assume that each type's preferences
follow a simple parametric model with $n$ parameters. In all, there are $mn$
parameters, and existing literature suggests that order optimal regret scales
as $mn$. However, the data required to estimate so many parameters is orders of
magnitude larger than the data available in most revenue management
applications; and the optimal regret under these models is unacceptably high.
  In this paper, we impose a natural structure on the problem -- a small latent
dimension, or low rank. In the static setting, we show that this model can be
efficiently learned from surprisingly few interactions, using a time- and
memory-efficient optimization algorithm that converges globally whenever the
model is learnable. In the dynamic setting, we show that structure-aware
dynamic assortment personalization can have regret that is an order of
magnitude smaller than structure-ignorant approaches. We validate our
theoretical results empirically.


title:
Relativistic Heat Equation via L\'{e}vy stable distributions: Exact
  Solutions

abstract:
  We introduce and study an extension of the heat equation relevant to
relativistic energy formula involving square root of differential operators. We
furnish exact solutions of corresponding Cauchy (initial) problem using the
operator formalism invoking one-sided L\'{e}vy stable distributions. We note a
natural appearance of Bessel polynomials which allow one the obtention of
closed form solutions for a number of initial conditions. The resulting
relativistic diffusion is slower than the non-relativistic one, although it
still can be termed a normal one. Its detailed statistical characterization is
presented in terms of exact evaluation of arbitrary moments and is compared
with the non-relativistic case.


title: Overcoming the Bradyon-Tachyon Barrier

abstract:
  In this study, the problem of overcoming the infinite energy barrier
separating the bradyonic and tachyonic realms is investigated. Making use of
the Majorana equation for particles with arbitrary spin and the Heisenberg
uncertainty principle, it is proved that, under certain conditions of spatial
confinement, quantum fluctuations allow particles with very small mass and
velocity close to the speed of light to pass in the tachyonic realm, avoiding
the problem of the infinite barrier. This theoretical approach allows an
avoidance of the difficulties encountered in quantum field theory when it is
extended to particles with imaginary rest mass.


title: The $\mathrm{L}_3(4)$ near octagon

abstract:
  In recent work we constructed two new near octagons, one related to the
finite simple group $\mathrm{G}_2(4)$ and another one as a sub-near-octagon of
the former. In the present paper, we give a direct construction of this
sub-near-octagon using a split extension of the group $\mathrm{L}_3(4)$. We
derive several geometric properties of this $\mathrm{L}_3(4)$ near octagon, and
determine its full automorphism group. We also prove that the $\mathrm{L}_3(4)$
near octagon is closely related to the second subconstituent of the
distance-regular graph on 486 vertices discovered by Soicher in 1993.


title: On a Microscopic Representation of Space-Time V

abstract:
  In order to extend our approach based on SU$*$(4), we were led to (real)
projective and (line) Complex geometry. So here we start from quadratic
Complexe which yield naturally the 'light cone'
$x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-x_{0}^{2}=0$ when being related to (homogeneous)
point coordinates $x_{\alpha}^{2}$ and infinitesimal dynamics by tetrahedral
Complexe (or line elements). This introduces naturally projective
transformations by preserving anharmonic ratios. Referring to old work of
Pl{\"u}cker relating quadratic Complexe to optics, we discuss (linear)
symplectic symmetry and line coordinates, the main purpose and thread within
this paper, however, is the identification and discussion of special relativity
as direct invariance properties of line/Complex coordinates as well as their
relation to 'quantum field theory' by complexification of point coordinates or
Complexe. This can be established by the Lie mapping which relates
lines/Complexe to sphere geometry so that SU(2), SU(2)$\times$U(1),
SU(2)$\times$SU(2) and the Dirac spinor description emerge without additional
assumptions. We give a short outlook in that quadratic Complexe are related to
dynamics e.g.~power expressions in terms of six-vector products of Complexe,
and action principles may be applied. (Quadratic) products like
$F^{\mu\nu}F_{\mu\nu}$ or $F^{a\,\mu\nu}F^{a}_{\mu\nu}$, $1\leq a\leq 3$ are
natural quadratic Complex expressions ('invariants') which may be extended by
line constraints $\lambda k\cdot\epsilon=0$ with respect to an 'action
principle' so that we identify 'quantum field theory' with projective or
line/Complex geometry having applied the Lie mapping.


title: New Aspects of Photon Propagation in Expanding Universes

abstract:
  According to present cosmological views the energy density of CMB (Cosmic
Microwave Background) photons, freely propagating through the expanding cosmos,
varies proportional to 1/S^4 with S being the scale factor of the universe.
This behavior is expected, because General Theory of Relativity, in application
to FLRW- (Friedmann-Lemaitre-Robertson-Walker) cosmological universes, leads to
the conclusion that the photon wavelengths increase during their free passage
through the spacetime metrics of the universe by the same factor as does the
scale factor S. This appears to be a reasonable explanation for the presently
observed Planckian CMB spectrum with its actual temperature of about 2.7 K,
while at the time of its origin after the last scattering during the
recombination phase its temperature should have been about 3000 K, at an epoch
of about 380 ky after the Big Bang, when the scale of the universe S_r was
smaller by roughly a factor of S/S_r = 1+z_r = 1100 compared to the present
scale S = S_0 of the universe. In this paper we start from putting the question
whether the scale-behavior of the CMB energy density that enters the
energy-momentum tensor of the field equations describing the expanding universe
is really falling off like 1/S^4 and, if in fact a deviation from a behavior
according to 1/S^4 would occur, why do we nevertheless presently observe a CMB
energy density which appears to be in accordance with such a 1/S^4-scaling?
This question arises from another basic and fundamental question, namely: Can
we really assume that the wavelength of the freely propagating photon during
its travel all the way along its light geodetic is permanently affected by the
expansion of the universe, i.e continuously recognizes the expansion of the
cosmic scale S? With other words: Do freely propagating photons ........


title: Dynamics of Particles around Time Conformal Schwarzschild Black Hole

abstract:
  In this work, we present the new technique for discussing the dynamical
motion of neutral as well as charged particles in the absence/presence of
magnetic field around the time conformal Schwarzschild black hole. Initially,
we find the numerical solutions of geodesics of Schwarzschild black hole and
the time conformal Schwarzschild black hole. We observe that the Schwarzschild
spacetime admits the time conformal factor $e^{\epsilon f(t)}$, where $f(t)$ is
an arbitrary function and $\epsilon$ is very small which causes the
perturbation in the spacetimes. This technique also re-scale the energy content
of spacetime. We also investigate the thermal stability, horizons and energy
conditions corresponding time conformal Schwarzschild spacetime. Also, we
examine the dynamics of neutral and charged particle around time conformal
Schwarzschild black hole. We investigate the circumstances under which the
particle can escape from vicinity of black hole after collision with another
particle. We analyze the effective potential and effective force of particle in
the presence of magnetic field with angular momentum graphically.


title: Planck-Einstein-de Broglie type relations for the acoustic waves

abstract:
  In this paper we prove, by expressing the energy as a function of the wave
propagation speed, it is highlighted the existence of an equivalent mass of the
wave, as well as of an Einstein type relations between the energy and this
mass. Also, we establish a relation between angular frequency and energy
similar to that of the Planck relation. For the propagating wave, there is a de
Broglie type relationship between the linear momentum and the action variable
(the angular momentum), i.e. the wave linear momentum is proportional to the
wave number, the proportionality coefficient being the action.


title:
Census Signal Temporal Logic Inference for Multi-Agent Group Behavior
  Analysis

abstract:
  In this paper, we define a novel census signal temporal logic (CensusSTL)
that focuses on the number of agents in different subsets of a group that
complete a certain task specified by the signal temporal logic (STL). CensusSTL
consists of an "inner logic" STL formula and an "outer logic" STL formula. We
present a new inference algorithm to infer CensusSTL formulae from the
trajectory data of a group of agents. We first identify the "inner logic" STL
formula and then infer the subgroups based on whether the agents' behaviors
satisfy the "inner logic" formula at each time point. We use two different
approaches to infer the subgroups based on similarity and complementarity,
respectively. The "outer logic" CensusSTL formula is inferred from the census
trajectories of different subgroups. We apply the algorithm in analyzing data
from a soccer match by inferring the CensusSTL formula for different subgroups
of a soccer team.


title:
From Traditional to Modern : Domain Adaptation for Action Classification
  in Short Social Video Clips

abstract:
  Short internet video clips like vines present a significantly wild
distribution compared to traditional video datasets. In this paper, we focus on
the problem of unsupervised action classification in wild vines using
traditional labeled datasets. To this end, we use a data augmentation based
simple domain adaptation strategy. We utilise semantic word2vec space as a
common subspace to embed video features from both, labeled source domain and
unlablled target domain. Our method incrementally augments the labeled source
with target samples and iteratively modifies the embedding function to bring
the source and target distributions together. Additionally, we utilise a
multi-modal representation that incorporates noisy semantic information
available in form of hash-tags. We show the effectiveness of this simple
adaptation technique on a test set of vines and achieve notable improvements in
performance.


title: Quantum Authentication and Encryption with Key Recycling

abstract:
  We propose an information-theoretically secure encryption scheme for
classical messages with quantum ciphertexts that offers detection of
eavesdropping attacks, and re-usability of the key in case no eavesdropping
took place: the entire key can be securely re-used for encrypting new messages
as long as no attack is detected. This is known to be impossible for fully
classical schemes, where there is no way to detect plain eavesdropping attacks.
This particular application of quantum techniques to cryptography was
originally proposed by Bennett, Brassard and Breidbart in 1982, even before
proposing quantum-key-distribution, and a simple candidate scheme was suggested
but no rigorous security analysis was given. The idea was picked up again in
2005, when Damgard, Pedersen and Salvail suggested a new scheme for the same
task, but now with a rigorous security analysis. However, their scheme is much
more demanding in terms of quantum capabilities: it requires the users to have
a quantum computer. In contrast, and like the original scheme by Bennett et
al., our new scheme merely requires to prepare and measure single BB84 qubits.
As such, we not only show a provably-secure scheme that is within reach of
current technology, but we also confirm Bennett et al.'s original intuition
that a scheme in the spirit of their original construction is indeed secure.


title: Electric control of antiferromagnets

abstract:
  In the past five years, most of the paradigmatic concepts employed in
spintronics have been replicated substituting ferromagnets by antiferromagnets
in critical parts of the devices. The numerous research efforts directed to
manipulate and probe the magnetic moments in antiferromagnets have been
gradually established a new and independent field known as antiferromagnetic
spintronics. In this paper, we focus on the electrical control and detection of
antiferromagnetic moments at a constant temperature. We address separately the
experimental results concerning insulating and metallic thin films as they
correspond to voltage and electrical current controlled devices, respectively.
First, we present results on the voltage control of antiferromagnetic order in
insulating thin films. The experiments show that voltage pulses can switch the
chirality of a modulated antiferromagnetic structure. Second, we describe the
recent advances in metallic antiferromagnetic systems. We present results
obtained with the first USB-operated portable device able to perform the
non-volatile electrical current-induced switching of an antiferromagnet
combined with magnetoresistive readout at room temperature. We discuss on
potential applications that can be realized using antiferromagnetic memory
cells.


title: 3-Rainbow index and forbidden subgraphs

abstract:
  A tree in an edge-colored connected graph $G$ is called \emph{a rainbow tree}
if no two edges of it are assigned the same color. For a vertex subset
$S\subseteq V(G)$, a tree is called an \emph{$S$-tree} if it connects $S$ in
$G$. A \emph{$k$-rainbow coloring} of $G$ is an edge-coloring of $G$ having the
property that for every set $S$ of $k$ vertices of $G$, there exists a rainbow
$S$-tree in $G$. The minimum number of colors that are needed in a $k$-rainbow
coloring of $G$ is the \emph{$k$-rainbow index} of $G$, denoted by $rx_k(G)$.
The \emph{Steiner distance $d(S)$} of a set $S$ of vertices of $G$ is the
minimum size of an $S$-tree $T$. The \emph{$k$-Steiner diameter $sdiam_k(G)$}
of $G$ is defined as the maximum Steiner distance of $S$ among all sets $S$
with $k$ vertices of $G$. In this paper, we focus on the 3-rainbow index of
graphs and find all finite families $\mathcal{F}$ of connected graphs, for
which there is a constant $C_\mathcal{F}$ such that, for every connected
$\mathcal{F}$-free graph $G$, $rx_3(G)\leq sdiam_3(G)+C_\mathcal{F}$.


title:
A Tractable Framework for the Analysis of Dense Heterogeneous Cellular
  Networks

abstract:
  This paper investigates the downlink performance of K-tier heteregeneous
cellular networks (HCNs) under general settings. First, Gaussian approximation
bounds for the standardized aggregate wireless interference (AWI) in dense
K-tier HCNs are obtained for when base stations (BSs) in each tier are
distributed over the plane according to a spatial and general Poisson point
process. The Kolmogorov-Smirnov (KS) distance is used to measure deviations of
the distribution of the standardized AWI from the standard normal distribution.
An explicit and analytical expression bounding the KS distance between these
two distributions is obtained as a function of a broad range of network
parameters such as per-tier transmission power levels, per-tier BS intensity,
BS locations, general fading statistics, and general bounded path-loss models.
Bounds achieve a good statistical match between the standardized AWI
distribution and its normal approximation even for moderately dense HCNs.
Second, various spatial performance metrics of interest such as outage
capacity, ergodic capacity and area spectral efficiency in the downlink of
K-tier HCNs for general signal propogation models are investigated by making
use of the derived distribution approximation results. Considering two specific
BS association policies, it is shown that the derived performance bounds track
the actual performance metrics reasonably well for a wide range of BS
intensities, with the gap among them becoming negligibly small for denser HCN
deployments.


title: Gauge momenta as Casimir functions of nonholonomic systems

abstract:
  We consider nonholonomic systems with symmetry possessing a certain type of
first integrals that are linear in the velocities. We develop a systematic
method for modifying the standard nonholonomic almost Poisson structure that
describes the dynamics so that these integrals become Casimir functions after
reduction. This explains a number of recent results on Hamiltonization of
nonholonomic systems, and has consequences for the study of relative equilibria
in such systems.


title:
On the universal late X-ray emission of binary-driven hypernovae and its
  possible collimation

abstract:
  It has previously been discovered that there is a universal power law
behavior exhibited by the late X-ray emission (LXRE) of a "golden sample" (GS)
of six long energetic GRBs, when observed in the rest-frame of the source. This
remarkable feature, independent of the different isotropic energy (E_iso) of
each GRB, has been used to estimate the cosmological redshift of some long
GRBs. This analysis is extended here to a new class of 161 long GRBs, all with
E_iso > 10^52 erg. These GRBs are indicated as binary-driven hypernovae (BdHNe)
in view of their progenitors: a tight binary system composed of a carbon-oxygen
core (CO_core) and a neutron star undergoing an induced gravitational collapse
(IGC) to a black hole triggered by the CO_core explosion as a supernova (SN).
We confirm the universal behavior of the LXRE for the "enlarged sample" (ES) of
161 BdHNe observed up to the end of 2015, assuming a double-cone emitting
region. We obtain a distribution of half-opening angles peaking at 17.62
degrees, with a mean value of 30.05 degrees, and a standard deviation of 19.65
degrees. This, in turn, leads to the possible establishment of a new
cosmological candle. Within the IGC model, such universal LXRE behavior is only
indirectly related to the GRB and originates from the SN ejecta, of a standard
constant mass, being shocked by the GRB emission. The fulfillment of the
universal relation in the LXRE and its independence of the prompt emission,
further confirmed in this article, establishes a crucial test for any viable
GRB model.


title:
Collinear triples and quadruples for Cartesian products in
  $\mathbb{F}_p^2$

abstract:
  In this ote, which has been absorbed by arXiv1702.01003, we combine a recent
point-line incidence bound of Stevens and de Zeeuw with an older lemma of
Bourgain, Katz and Tao to bound the number of collinear triples and quadruples
in a Cartesian product in $\mathbb{F}_p^2$.


title:
FEM for time-fractional diffusion equations, novel optimal error
  analyses

abstract:
  A semidiscrete Galerkin finite element method applied to time-fractional
diffusion equations with time-space dependent diffusivity on bounded convex
spatial domains will be studied. The main focus is on achieving optimal error
results with respect to both the convergence order of the approximate solution
and the regularity of the initial data. By using novel energy arguments, for
each fixed time $t$, optimal error bounds in the spatial $L^2$- and $H^1$-norms
are derived for both cases: smooth and nonsmooth initial data.


title: Preparing and correcting extracted BRITE observations

abstract:
  Extracted BRITE lightcurves must be carefully prepared and corrected for
instrumental effects before a scientific analysis can be performed. Therefore,
we have created a suite of Python routines to prepare and correct the
lightcurves, which is publicly available. In this paper we describe the method
and successive steps performed by these routines.


title: Topology of the Electroweak Vacua

abstract:
  In the Standard Model, the electroweak symmetry is broken by a complex,
$SU(2)$-doublet Higgs field and the vacuum manifold $SU(2)\times U(1)/U(1)$ has
the topology of a 3-sphere. We remark that there exist theoretical alternatives
that are locally isomorphic, but in which the vacuum manifold is homeomorphic
to an arbitrary non-trivial principal $U(1)$-bundle over a 2-sphere. These
alternatives have non-trivial fundamental group and thus feature
topologically-stable electroweak strings. An alternative based on the manifold
$\mathbb{R}P^3$ (with fundamental group $\mathbb{Z}/2$) allows custodial
protection of gauge boson masses and their couplings to fermions, but, in
common with all alternatives to $S^3$, has a problem with fermion masses.


title: Monte Carlo Implementation of Polarized Hadronization

abstract:
  We study the polarized quark hadronization in a Monte Carlo (MC) framework
based on the recent extension of the quark-jet framework, where a
self-consistent treatment of the quark polarization transfer in a sequential
hadronization picture has been presented. Here, we first adopt this approach
for MC simulations of hadronization process with finite number of produced
hadrons, expressing the relevant probabilities in terms of the eight leading
twist quark-to-quark transverse momentum dependent (TMD) splitting functions
(SFs) for elementary $q \to q'+h$ transition. We present explicit expressions
for the unpolarized and Collins fragmentation functions (FFs) of unpolarized
hadrons emitted at rank two. Further, we demonstrate that all the current
spectator-type model calculations of the leading twist quark-to-quark TMD SFs
violate the positivity constraints, and propose quark model based ansatz for
these input functions that circumvents the problem. We validate our MC
framework by explicitly proving the absence of unphysical azimuthal modulations
of the computed polarized FFs, and by precisely reproducing the earlier derived
explicit results for rank two pions. Finally, we present the full results for
pion unpolarized and Collins FFs, as well as the corresponding analyzing powers
from high statistics MC simulations with a large number of produced hadrons for
two different model input elementary SFs. The results for both sets of input
functions exhibit the same general features of opposite signed Collins function
for favored and unfavored channels at large $z$, and at the same time
demonstrate the flexibility of the quark-jet framework by producing
significantly different dependences of the results at mid- to low-$z$ for the
two model inputs.


title: Understanding the photometric variability of {\zeta} Ori Aa

abstract:
  We studied the variability of the magnetic O-type supergiant $\zeta$ Ori Aa
using multi-colour BRITE photometry. We confirmed the known rotation frequency
$f_{\rm rot} = 0.15 \pm 0.02$ c/d, and detected some of its higher harmonics,
of which $4f_{\rm rot}$ is compatible with the known DAC recurrence timescale.
Thanks to simultaneous high-resolution CHIRON spectroscopy, we could identify
another frequency $f_{\rm env} = 0.10 \pm 0.02$ c/d, caused by the
circumstellar environment. Variations in the circumstellar environment are
believed to cause the observed difference between the BRITE lightcurves.


title:
Supercloseness analysis and polynomial preserving recovery for a class
  of weak Galerkin method

abstract:
  In this paper, we analyze convergence and supercloseness properties of a
class of weak Galerkin (WG) finite element methods for solving second-order
elliptic problems. It is shown that the WG solution is superclose to the
Lagrange type interpolation using Lobatto points. This supercloseness behavior
is obtained through some newly designed stabilization terms. A post-processing
technique using the polynomial preserving recovery (PPR) is introduced for WG
approximation. Superconvergence analysis is carried out for the PPR
approximation. Numerical examples are provided to verify our theoretical
results.


title:
Robust Wasserstein Profile Inference and Applications to Machine
  Learning

abstract:
  We show that several machine learning estimators, including square-root LASSO
(Least Absolute Shrinkage and Selection) and regularized logistic regression
can be represented as solutions to distributionally robust optimization (DRO)
problems. The associated uncertainty regions are based on suitably defined
Wasserstein distances. Hence, our representations allow us to view
regularization as a result of introducing an artificial adversary that perturbs
the empirical distribution to account for out-of-sample effects in loss
estimation. In addition, we introduce RWPI (Robust Wasserstein Profile
Inference), a novel inference methodology which extends the use of methods
inspired by Empirical Likelihood to the setting of optimal transport costs (of
which Wasserstein distances are a particular case). We use RWPI to show how to
optimally select the size of uncertainty regions, and as a consequence, we are
able to choose regularization parameters for these machine learning estimators
without the use of cross validation. Numerical experiments are also given to
validate our theoretical findings.


title: Killing vector fields and a homogeneous isotropic universe

abstract:
  Some basic theorems on Killing vector fields are reviewed. In particular, the
topic of a constant-curvature space is examined. A detailed proof is given for
a theorem describing the most general form of the metric of a homogeneous
isotropic space-time. Although this theorem can be considered to be commonly
known, its complete proof is difficult to find in the literature. An example
metric is presented such that all its spatial cross sections correspond to
constant-curvature spaces, but it is not homogeneous and isotropic as a whole.
An equivalent definition of a homogeneous and isotropic space-time in terms of
embedded manifolds is also given.


title:
Explosion Dynamics of Parametrized Spherically Symmetric Core-Collapse
  Supernova Simulations

abstract:
  We report on a method, PUSH, for triggering core-collapse supernova (CCSN)
explosions of massive stars in spherical symmetry. This method provides a
framework to study many important aspects of core collapse supernovae: the
effects of the shock passage through the star, explosive supernova
nucleosynthesis and the progenitor-remnant connection. Here we give an overview
of the method, compare the results to multi-dimensional simulations and
investigate the effects of the progenitor and the equation of state on black
hole formation.


title:
On the characterization of abelian varieties for log pairs in zero and
  positive characteristic

abstract:
  Let $(X,\Delta)$ be a pair. We study how the condition $\kappa(K_X +
\Delta)=0$ causes surjectivity or birationality of the Albanese map and the
Albanese morphism of $X$ in both characteristic $0$ and characteristic $p > 0$.
In particular in characteristic $0$ we generalize Kawamata's result to the
cases of log canonial pairs, and in characteristic $p>0$ we generalize a result
of Hacon-Patakfalvi to the cases of log pairs. Moreover we show that if $X$ is
a normal projective threefold in characteristic $p>0$, the coefficients of the
components of $\Delta$ are $\le 1$ and $-(K_X+\Delta)$ is semiample, then the
Albanese morphism of $X$ is surjective under reasonable assumptions on $p$ and
the singularities of the general fibers of the Albanese morphism. This is a
positive characteristic analog in dimension 3 of a result of Zhang on a
conjecture of Demailly-Peternell-Schneider.


title:
Preparation, structure and giant magnetoresistance of electrodeposited
  Fe Co/Cu multilayers

abstract:
  No systematic studies have been carried out on the giant magnetoresistance
(GMR) of electrodeposited (ED) Fe-Co/Cu multilayers since the elaboration of a
method for the optimization of the Cu layer deposition potential. In this
paper, we present results on the electrochemical optimization of the Cu layer
deposition potential which was found to depend on the relative iron
concentration in the bath. An X-ray diffraction study of ED Fe5Co95(1.5
nm)/Cu(dCu) multilayers with dCu ranging from 0.8 nm to 10 nm revealed an fcc
structure. For most of the multilayers, a weak superlattice satellite
reflection could be identified. The room-temperature magnetoresistance was
studied in detail as a function of the individual layer thicknesses.
Multilayers with Cu layer thicknesses above about 1.5 nm were found to exhibit
a GMR behavior with a maximum GMR of about 5 % and a typical saturation field
of 1 kOe. The GMR magnitude decreased with increasing Fe-content in the
magnetic layer. The spacer layer thickness evolution of the MR data was
established in detail after separating the ferromagnetic and superparamagnetic
GMR contributions and no oscillatory GMR was found. A comparison with
literature data on both physically deposited and ED Fe-Co/Cu multilayers is
also made.


title:
Competing magnetic ground states and their coupling to the crystal
  lattice in CuFe2Ge2

abstract:
  Identifying and characterizing systems with coupled and competing
interactions is central to the development of physical models that can
accurately describe and predict emergent behavior in condensed matter systems.
This work demonstrates that the metallic compound CuFe$_2$Ge$_2$ has competing
magnetic ground states, which are shown to be strongly coupled to the lattice
and easily manipulated using temperature and applied magnetic fields.
Temperature-dependent magnetization $M$ measurements reveal a
ferromagnetic-like onset at 228(1)\,K and a broad maximum in $M$ near 180\,K.
Powder neutron diffraction confirms antiferromagnetic ordering below
$T_{\textrm{N}}\approx$175\,K, and an incommensurate spin density wave is
observed below $\approx$125\,K. Coupled with the small refined moments
(0.5-1\,$\mu_B$/Fe), this provides a picture of itinerant magnetism in
CuFe$_2$Ge$_2$. The neutron diffraction data also reveal a coexistence of two
magnetic phases that further highlights the near-degeneracy of various magnetic
states. These results demonstrate that the ground state in CuFe$_2$Ge$_2$ can
be easily manipulated by external forces, making it of particular interest for
doping, pressure, and further theoretical studies.


title:
Astrophysical Prior Information and Gravitational-wave Parameter
  Estimation

abstract:
  The detection of electromagnetic counterparts to gravitational waves has
great promise for the investigation of many scientific questions. It has long
been hoped that in addition to providing extra, non-gravitational information
about the sources of these signals, the detection of an electromagnetic signal
in conjunction with a gravitational wave could aid in the analysis of the
gravitational signal itself. That is, knowledge of the sky location,
inclination, and redshift of a binary could break degeneracies between these
extrinsic, coordinate-dependent parameters and the physical parameters, such as
mass and spin, that are intrinsic to the binary. In this paper, we investigate
this issue by assuming a perfect knowledge of extrinsic parameters, and
assessing the maximal impact of this knowledge on our ability to extract
intrinsic parameters. However, we find only modest improvements in a few
parameters --- namely the primary component's spin --- and conclude that, even
in the best case, the use of additional information from electromagnetic
observations does not improve the measurement of the intrinsic parameters
significantly.


title: Low Temperature Thermoelectric Properties of Co- and Cr- doped CuAgSe

abstract:
  High mobility phonon-glass semimetal $CuAgSe$ has shown promise in recent
years as a potential low-temperature thermoelectric material. It exhibits
reasonably strong thermoelectric performance as well as an extremely high
carrier mobility, both of which are enhanced when the material is doped with Ni
at the Cu sites. The exact mechanism by which these enhancements result;
however, is unclear. In order to further investigate the effects of chemical
substitution on the material's thermoelectric properties, we have prepared and
performed various measurements on $CuAgSe$ samples doped with Co and Cr
according to the following compositional formulas: $Cu_{1-x}Co_{x}AgSe$
$(x=0.02, 0.05, 0.10)$ and $Cu_{1-x}Cr_{x}AgSe$ $(x=0.02, 0.05)$. Measurements
of temperature and magnetic field dependent thermal conductivity, electrical
resistivity, and Seebeck coefficient will be discussed. Our results reveal a
remarkable sensitivity of $CuAgSe$'s thermoelectric properties to chemical
doping in general as well as a particular sensitivity to specific dopants. This
demonstrated tunability of $CuAgSe$'s various properties furthers the case that
high mobility phonon glass-semimetals are strong candidates for potential low
temperature thermoelectric applications.


title: Exact Initial Data for Black Hole Universes with a Cosmological Constant

abstract:
  We construct exact initial data for closed cosmological models filled with
regularly arranged black holes in the presence of $\Lambda$. The intrinsic
geometry of the 3-dimensional space described by this data is a sum of simple
closed-form expressions, while the extrinsic curvature is just proportional to
$\Lambda$. We determine the mass of each of the black holes in this space by
performing a limiting procedure around the location of each of the black holes,
and then compare the result to an appropriate slice through the
Schwarzschild-de Sitter spacetime. The consequences of the inhomogeneity of
this model for the large-scale expansion of space are then found by comparing
the lengths of curves in the cosmological region to similar curves in a
suitably chosen Friedmann-Lemaitre-Robertson-Walker (FLRW) solution. Finally,
we locate the positions of the apparent horizons of the black holes, and
determine the extremal values of their mass, for every possible regular
arrangement of masses. We find that as the number of black holes is increased,
the large-scale expansion of space approaches that of an FLRW model filled with
dust and $\Lambda$, and that the extremal values of the black hole masses
approaches that of the Schwarzschild-de Sitter solution.


title:
On the probability of hitting the boundary for Brownian motions on the
  SABR plane

abstract:
  Starting from the hyperbolic Brownian motion as a time-changed Brownian
motion, we explore a set of probabilistic models--related to the SABR model in
mathematical finance--which can be obtained by geometry-preserving
transformations, and show how to translate the properties of the hyperbolic
Brownian motion (density, probability mass, drift) to each particular model.
Our main result is an explicit expression for the probability of any of these
models hitting the boundary of their domains, the proof of which relies on the
properties of the aforementioned transformations as well as time-change
methods.


title:
Blow-up solutions to the semilinear wave equation with a stylized
  pyramid as a blow-up surface

abstract:
  We consider the semilinear wave equation with subconformal power nonlinearity
in two space dimensions. We construct a finite-time blow-up solution with an
isolated characteristic blow-up point at the origin, and a blow-up surface
which is centered at the origin and has the shape of a stylized pyramid, whose
edges follow the bisectrices of the axes in $R^2$. The blow-up surface is
differentiable outside the bisecrtices. As for the asymptotic behavior in
similariy variables, the solution converges to the classical one-dimensional
soliton outside the bisectrices. On the bisectrices outside the origin, it
converges (up to a subsequence) to a genuinely two-dimensional stationary
solution, whose existence is a by-product of the proof.
  At the origin, it behaves like the sum of 4 solitons localized on the two
axes, with opposite signs for neighbors. This is the first example of a blow-up
solution with a characteristic point in higher dimensions, showing a really
two-dimensional behavior.
  Moreover, the points of the bisectrices outside the origin give us the first
example of non-characteristic points where the blow-up surface is
non-differentiable.


title:
Banados and SUSY: On Supersymmetry and Minimal Surfaces of Locally AdS3
  Geometries

abstract:
  We extend the classification of supersymmetric locally AdS$_3$ geometries,
beyond BTZ black holes, to the Banados geometries, noting that supersymmetries
are in one-to-one correspondence with solutions to the Hill differential
condition. We show that the number of global supersymmetries is an orbit
invariant quantity and identify geometries with zero, one, two, three and four
global supersymmetries. As an application of our classification, we exploit
supersymmetry, which is preserved locally in the bulk, to determine space-like
co-dimension two surfaces in AdS$_3$. In the process, we by-pass geodesics or
mappings of AdS$_3$, neither of which have an analogue in higher dimensions, to
recover known Hubeny-Rangamani-Takayanagi surfaces. Our findings suggest
supersymmetry can be exploited to find extremal surfaces in holographic
entanglement entropy.


title: Gauge engineering and propagators

abstract:
  Beyond perturbation theory gauge-fixing becomes more involved due to the
Gribov-Singer ambiguity: The appearance of additional gauge copies requires to
define a procedure how to handle them. For the case of Landau gauge the
structure and properties of these additional gauge copies will be investigated.
Based on these properties gauge conditions are constructed to account for these
gauge copies.
  The dependence of the propagators on the choice of these complete
gauge-fixings will then be investigated using lattice gauge theory for
Yang-Mills theory. It is found that the implications for the infrared, and to
some extent mid-momentum behavior, can be substantial. In going beyond the
Yang-Mills case it turns out that the influence of matter can generally not be
neglected. This will be briefly discussed for various types of matter.


title: Special Relativity: Scientific or Philosophical Theory?

abstract:
  In this article, we argue that the theory of special relativity, as
formulated by Einstein, is a philosophical rather than a scientific theory.
What is scientific and experimentally supported is the formalism of the
relativistic mechanics embedded in the Lorentz transformations and their direct
mathematical, experimental and observational consequences. This is in parallel
with the quantum mechanics where the scientific content and experimental
support of this branch of physics is embedded in the formalism of quantum
mechanics and not in its philosophical interpretations such as the Copenhagen
school or the parallel worlds explanations. Einstein theory of special
relativity gets unduly credit from the success of the relativistic mechanics of
Lorentz transformations. Hence, all the postulates and consequences of Einstein
interpretation which have no direct experimental or observational support
should be reexamined and the relativistic mechanics of Lorentz transformations
should be treated in education, academia and research in a similar fashion to
that of quantum mechanics.


title: A revised moving cluster distance to the Pleiades open cluster

abstract:
  Aims: We provide a new distance estimate for the Pleiades based on the moving
cluster method, which will be useful to further discuss the so-called Pleiades
distance controversy and compare it with the very precise parallaxes from the
Gaia space mission.
  Methods: We apply a refurbished implementation of the convergent point search
method to an updated census of Pleiades stars to calculate the convergent point
position of the cluster from stellar proper motions. Then, we derive individual
parallaxes for 64 cluster members using radial velocities compiled from the
literature, and approximate parallaxes for another 1146 stars based on the
spatial velocity of the cluster. This represents the largest sample of Pleiades
stars with individual distances to date.
  Results: The parallaxes derived in this work are in good agreement with
previous results obtained in different studies (excluding Hipparcos) for
individual stars in the cluster. We report a mean parallax of $7.44\pm
0.08$~mas and distance of $134.4^{+2.9}_{-2.8}$pc that is consistent with the
weighted mean of $135.0\pm 0.6$pc obtained from the non-Hipparcos results in
the literature.
  Conclusions: Our result for the distance to the Pleiades open cluster is not
consistent with the Hipparcos catalog, but favors the recent and more precise
distance determination of $136.2\pm 1.2$pc obtained from Very Long Baseline
Interferometry observations. It is also in good agreement with the mean
distance of $133\pm 5$pc obtained from the first trigonometric parallaxes
delivered by the Gaia satellite for the brightest cluster members in common
with our sample.


title: Weak Compactness and Fixed Point Property for Affine Bi-Lipschitz Maps

abstract:
  In this paper we show that if $(y_n)$ is a seminormalized sequence in a
Banach space which does not have any weakly convergent subsequence, then it
contains a wide-$(s)$ subsequence $(x_n)$ which admits an equivalent convex
basic sequence. This fact is used to characterize weak-compactness of bounded,
closed convex sets in terms of the generic fixed point property
($\mathcal{G}$-$FPP$) for the class of affine bi-Lipschitz maps. This result
generalizes a theorem by Benavides, Jap\'on Pineda and Prus previously proved
for the class of continuous maps. We also introduce a relaxation of this notion
($\mathcal{WG}$-$FPP$) and observe that a closed convex bounded subset of a
Banach space is weakly compact iff it has the $\mathcal{WG}$-$FPP$ for affine
$1$-Lipschitz maps. Related results are also proved. For example, a complete
convex bounded subset $C$ of a Hlcs $X$ is weakly compact iff it has the
$\mathcal{G}$-$FPP$ for the class of affine continuous maps $f\colon C\to X$
with weak-approximate fixed point nets.