title: Drawing and Recognizing Chinese Characters with Recurrent Neural Network

abstract:
  Recent deep learning based approaches have achieved great success on
handwriting recognition. Chinese characters are among the most widely adopted
writing systems in the world. Previous research has mainly focused on
recognizing handwritten Chinese characters. However, recognition is only one
aspect for understanding a language, another challenging and interesting task
is to teach a machine to automatically write (pictographic) Chinese characters.
In this paper, we propose a framework by using the recurrent neural network
(RNN) as both a discriminative model for recognizing Chinese characters and a
generative model for drawing (generating) Chinese characters. To recognize
Chinese characters, previous methods usually adopt the convolutional neural
network (CNN) models which require transforming the online handwriting
trajectory into image-like representations. Instead, our RNN based approach is
an end-to-end system which directly deals with the sequential structure and
does not require any domain-specific knowledge. With the RNN system (combining
an LSTM and GRU), state-of-the-art performance can be achieved on the
ICDAR-2013 competition database. Furthermore, under the RNN framework, a
conditional generative model with character embedding is proposed for
automatically drawing recognizable Chinese characters. The generated characters
(in vector format) are human-readable and also can be recognized by the
discriminative RNN model with high accuracy. Experimental results verify the
effectiveness of using RNNs as both generative and discriminative models for
the tasks of drawing and recognizing Chinese characters.


title: Synthetic differential geometry within homotopy type theory I

abstract:
  This paper gives a first step towards developing synthetic differential
geometry within homotopy type theory. Its model theory will be discussed in a
subsequent paper.


title:
An adaptive moving mesh finite element solution of the Regularized Long
  Wave equation

abstract:
  An adaptive moving mesh finite element method is proposed for the numerical
solution of the regularized long wave (RLW) equation. A moving mesh strategy
based on the so-called moving mesh PDE is used to adaptively move the mesh to
improve computational accuracy and efficiency. The RLW equation represents a
class of partial differential equations containing spatial-time mixed
derivatives. For the numerical solution of those equations, a $C^0$ finite
element method cannot apply directly on a moving mesh since the mixed
derivatives of the finite element approximation may not be defined. To avoid
this difficulty, a new variable is introduced and the RLW equation is rewritten
into a system of two coupled equations. The system is then discretized using
linear finite elements in space and the fifth-order Radau IIA scheme in time. A
range of numerical examples in one and two dimensions, including the RLW
equation with one or two solitary waves and special initial conditions that
lead to the undular bore and solitary train solutions, are presented. Numerical
results demonstrate that the method has a second order convergence and is able
to move and adapt the mesh to the evolving features in the solution.


title: Flavor-dependent eigenvolume interactions in a hadron resonance gas

abstract:
  Eigenvolume effects in the hadron resonance gas (HRG) model are studied for
experimental hadronic yields in nucleus-nucleus collisions. If particle
eigenvolumes are different for different hadron species, the excluded volume
HRG (EV-HRG) improves fits to multiplicity data. In particular, using different
mass~-~volume relations for strange and non-strange hadrons we observe a
remarkable improvement in the quality of the fits. This effect appears to be
rather insensitive to other details in the schemes employed in the EV-HRG. We
show that the parameters found from fitting the data of the ALICE Collaboration
in central Pb+Pb collisions at the collision energy $\sqrt{s_{\rm NN}} =
2.76$~TeV entail the same improvement for all centralities at the same
collision energy, and for the RHIC and SPS data at lower collision energies.
Our findings are put in the context of recent fits of lattice QCD results.


title:
An Uncertainty-Aware Approach to Optimal Configuration of Stream
  Processing Systems

abstract:
  Finding optimal configurations for Stream Processing Systems (SPS) is a
challenging problem due to the large number of parameters that can influence
their performance and the lack of analytical models to anticipate the effect of
a change. To tackle this issue, we consider tuning methods where an
experimenter is given a limited budget of experiments and needs to carefully
allocate this budget to find optimal configurations. We propose in this setting
Bayesian Optimization for Configuration Optimization (BO4CO), an auto-tuning
algorithm that leverages Gaussian Processes (GPs) to iteratively capture
posterior distributions of the configuration spaces and sequentially drive the
experimentation. Validation based on Apache Storm demonstrates that our
approach locates optimal configurations within a limited experimental budget,
with an improvement of SPS performance typically of at least an order of
magnitude compared to existing configuration algorithms.


title: Pre-explosion dynamo in the cores of massive stars

abstract:
  We propose a speculative scenario where dynamo amplification of magnetic
fields in the core convective shells of massive stars, tens of years to hours
before they explode, leads to envelope expansion and enhanced mass loss rate,
resulting in pre-explosion outbursts (PEOs). The convective luminosity in the
burning shells of carbon, neon, oxygen, and then silicon, are very high. Based
on the behavior of active main sequence stars we speculate that the convective
shells can trigger magnetic activity with a power of about 0.001 times the
convective luminosity. Magnetic flux tubes might buoy outward, and deposit
their energy in the outer parts of the envelope. This in turn might lead to the
expansion of the envelope and to an enhanced mass loss rate. If a close binary
companion is present, mass transfer might take place and lead to an energetic
outburst. The magnetic activity requires minimum core rotation and that the
stochastic magnetic activity be on its high phase. Only in rare cases these
conditions are met, accounting for that only the minority of core collapse
supernovae (CCSNe) experience PEO. Such a pre-explosion magnetic activity might
have implications for the explosion mechanism itself.


title:
Geodesic Motion in the Spacetime Of a SU(2)-Colored (A)dS Black Hole in
  Conformal Gravity

abstract:
  In this paper, we study the geodesic motion in the spacetime of a
SU(2)-colored (A)dS black hole in conformal gravity, and also we investigate
spacetime features, such as light spheres and horizons. Moreover, we derive the
analytical solutions for the equation of motion of test particles and light
rays using Weierstrass elliptic and Kleinian sigma functions. Depending on the
particle energy levels and angular momentums, we classify the solutions of the
geodesic equations. Furthermore, several examples of possible types of orbits
illustrate the results


title:
Cavity ring-up spectroscopy for dissipative and dispersive sensing in a
  whispering gallery mode resonator

abstract:
  In whispering gallery mode resonator sensing applications, the conventional
way to detect a change in the parameter to be measured is by observing the
steady state transmission spectrum through the coupling waveguide.
Alternatively, cavity ring-up spectroscopy (CRUS) sensing can be achieved
transiently. In this work, we investigate CRUS using coupled mode equations and
find analytical solutions with a large spectral broadening approximation of the
input pulse. The relationships between the frequency detuning, coupling gap and
ring-up peak height are determined and experimentally verified using an
ultrahigh \textit{Q}-factor silica microsphere. This work shows that
distinctive dispersive and dissipative transient sensing can be realised by
simply measuring the peak height of the CRUS signal, which might improve the
data collection rate.


title: Distance proper connection of graphs

abstract:
  Let $G$ be an edge-colored connected graph. A path $P$ in $G$ is called a
distance $\ell$-proper path if no two edges of the same color appear with fewer
than $\ell$ edges in between on $P$. The graph $G$ is called $(k,\ell)$-proper
connected if every pair of distinct vertices of $G$ are connected by $k$
pairwise internally vertex-disjoint distance $\ell$-proper paths in $G$. For a
$k$-connected graph $G$, the minimum number of colors needed to make $G$
$(k,\ell)$-proper connected is called the $(k,\ell)$-proper connection number
of $G$ and denoted by $pc_{k,\ell}(G)$. In this paper, we prove that
$pc_{1,2}(G)\leq 5$ for any $2$-connected graph $G$. Considering graph
operations, we find that $3$ is a sharp upper bound for the $(1,2)$-proper
connection number of the join and the Cartesian product of almost all graphs.
In addition, we find some basic properties of the $(k,\ell)$-proper connection
number and determine the values of $pc_{1,\ell}(G)$ where $G$ is a traceable
graph, a tree, a complete bipartite graph, a complete multipartite graph, a
wheel, a cube or a permutation graph of a nontrivial traceable graph.


title: A local-global principle for symplectic $\mathrm K_2$

abstract:
  We prove that an element of the symplectic Steinberg group is trivial if and
only if its image under any maximal localisation homomorphism is trivial.


title:
Quantum statistical effects in multi-channel wave packet scattering of
  non-interacting identical particles

abstract:
  For a number of non-interacting identical particles entering a multi-channel
scatterer in various wave packet states, we construct a generating function for
the probabilities of various scattering outcomes. This is used to evaluate the
mean numbers of particles $\overline{n}_m$ scattered into a given ($m$-th)
channel, single-channel statistics, and inter-channel correlations. We show
that for initially uncorrelated particles, indistinguishability changes single
channel statistics without altering the the value of $\overline{n}_m$. For
uncorrelated bosons and fermions, bunching and anti-bunching behaviour can be
detected in the extreme-case probabilities, to have all particles scattered
into the same channel, or none of particles scattered into a channel, or
channels. As an example, we consider a cavity with a single long-lived
resonance accessible to the particles, which allows them to "pile up" inside
the scatterer.


title:
Collectivity in diffusion of colloidal particles: from effective
  interactions to spatially correlated noise

abstract:
  The collectivity in the simultaneous diffusion of many particles, i.e. the
interdependence of stochastic forces affecting different particles in the same
solution, is a largely overlooked phenomenon with no well-established theory.
Recently, we have proposed a novel type of thermodynamically consistent
Langevin dynamics driven by the Spatially Correlated Noise (SCN) that can
contribute to the understanding of this problem. This model draws a link
between the theory of effective interactions in binary colloidal mixtures and
the properties of SCN. In the current article we review this model from the
perspective of collective diffusion and generalize it to the case of multiple
($N>2$) particles. Since our theory of SCN-driven Langevin dynamics has certain
issues that could not be resolved within its framework, in this article we also
provide another approach to the problem of collectivity. We discuss the
multi-particle Mori-Zwanzig model, which is fully microscopically consistent.
Indeed, we show that this model supplies many information, complementary to the
SCN-based approach, e.g. it predicts the deterministic dynamics of the relative
distance between the particles, it provides the approximation for
non-equilibrium effective interactions and predicts the collective subdiffusion
of tracers in group. These results provide the short-range, inertial limit of
the earlier model and agree with its predictions under some general conditions.
In this article we also review the origin of SCN and its consequences for the
variety of physical systems, with emphasis on the colloids.


title: Recollements and homological dimensions

abstract:
  We investigate the behavior of the homological dimensions under recollements
of derived categories of algebras. In particular, we establish a series of new
bounds among the selfinjective dimension or $\phi$-dimension of the algebras
linked by recollements of derived module categories.


title:
Strain tensor selection and the elastic theory of incompatible thin
  sheets

abstract:
  The existing theory of incompatible elastic sheets uses the deviation of the
surface metric from a reference metric to define the strain tensor [Efrati et
al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple
axisymmetric problems we examine an alternative formulation, defining the
strain based on deviations of distances (rather than distances squared) from
their rest values. While the two formulations converge in the limit of small
slopes and in the limit of an incompressible sheet, for other cases they are
found not to be equivalent. The alternative formulation offers several features
which are absent in the existing theory. (a) In the case of planar deformations
of flat incompatible sheets, it yields linear, exactly solvable, equations of
equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it
coincides with the theory of extensible elastica; in particular, for a
uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It
gives a simple criterion determining whether an isometric immersion of an
incompatible sheet is at mechanical equilibrium with respect to normal forces.
For a reference metric of constant positive Gaussian curvature, a spherical cap
is found to satisfy this criterion except in an arbitrarily narrow boundary
layer.


title: Equilateral triangle skew condition for quasiconformality

abstract:
  We characterize quasiconformal mappings in terms of the distortion of the
vertices of equilateral triangles.


title: Classical weight one forms in Hida families: Hilbert modular case

abstract:
  The purpose of this paper is to investigate the number of classical weight
one specializations of a non-CM ordinary Hida family of parallel weight Hilbert
cusp forms. It is known that a specialization of a primitive ordinary Hida
family at any arithmetic points of weight at least two is a classical
holomorphic Hilbert cusp form. However, this is not always the case for weight
one specializations. Balasubramanyam, Ghate and Vatsal proved that such a Hida
family admits infinitely many classical weight one specializations if and only
if it is of CM type. We give an explicit upper bound on the number of classical
weight one specializations of a non-CM primitive ordinary Hida family.


title: A stochastic model of supercoiling-dependent transcription

abstract:
  We propose a stochastic model for gene transcription coupled to DNA
supercoiling, where we incorporate the experimental observation that
polymerases create supercoiling as they unwind the DNA helix, and that these
enzymes bind more favourably to regions where the genome is unwound. Within
this model, we show that when the transcriptionally induced flux of
supercoiling increases, there is a sharp crossover from a regime where
torsional stresses relax quickly and gene transcription is random, to one where
gene expression is highly correlated and tightly regulated by supercoiling. In
the latter regime, the model displays transcriptional bursts, waves of
supercoiling, and up-regulation of divergent or bidirectional genes. It also
predicts that topological enzymes which relax twist and writhe should provide a
pathway to down-regulate transcription. This article has been published in
Physical Review Letters, May 2016.


title:
Uncertainty quantification of inflow boundary condition and proximal
  arterial stiffness coupled effect on pulse wave propagation in a vascular
  network

abstract:
  SUMMARY This work aims at quantifying the effect of inherent uncertainties
from cardiac output on the sensitivity of a human compliant arterial network
response based on stochastic simulations of a reduced-order pulse wave
propagation model. A simple pulsatile output form is utilized to reproduce the
most relevant cardiac features with a minimum number of parameters associated
with left ventricle dynamics. Another source of critical uncertainty is the
spatial heterogeneity of the aortic compliance which plays a key role in the
propagation and damping of pulse waves generated at each cardiac cycle. A
continuous representation of the aortic stiffness in the form of a generic
random field of prescribed spatial correlation is then considered. Resorting to
a stochastic sparse pseudospectral method, we investigate the spatial
sensitivity of the pulse pressure and waves reflection magnitude with respect
to the different model uncertainties. Results indicate that uncertainties
related to the shape and magnitude of the prescribed inlet flow in the proximal
aorta can lead to potent variation of both the mean value and standard
deviation of blood flow velocity and pressure dynamics due to the interaction
of different wave propagation and reflection features. These results have
potential physiological and pathological implications. They will provide some
guidance in clinical data acquisition and future coupling of arterial pulse
wave propagation reduced-order model with more complex beating heart models.


title: Order Invariance on Decomposable Structures

abstract:
  Order-invariant formulas access an ordering on a structure's universe, but
the model relation is independent of the used ordering. Order invariance is
frequently used for logic-based approaches in computer science. Order-invariant
formulas capture unordered problems of complexity classes and they model the
independence of the answer to a database query from low-level aspects of
databases. We study the expressive power of order-invariant monadic
second-order (MSO) and first-order (FO) logic on restricted classes of
structures that admit certain forms of tree decompositions (not necessarily of
bounded width).
  While order-invariant MSO is more expressive than MSO and, even, CMSO (MSO
with modulo-counting predicates), we show that order-invariant MSO and CMSO are
equally expressive on graphs of bounded tree width and on planar graphs. This
extends an earlier result for trees due to Courcelle. Moreover, we show that
all properties definable in order-invariant FO are also definable in MSO on
these classes. These results are applications of a theorem that shows how to
lift up definability results for order-invariant logics from the bags of a
graph's tree decomposition to the graph itself.


title:
Study of the geodesic equations of a spherical symmetric spacetime in
  conformal gravity

abstract:
  Set of analytic solutions of the geodesic equation in a spherical conformal
spacetime is presented. Solutions of this geodesics can be expressed in terms
of the Weierstrass {\wp} function and the Kleinian {\sigma} function. Using
conserved energy and angular momentum we can characterize the different orbits.
Also, considering parametric diagrams and effective potentials, we plot some
possible orbits. Moreover, with the help of analytical solutions, we
investigate the light deflection for such an escape orbit.


title:
Speciation in the Derrida-Higgs model with finite genomes and spatial
  populations

abstract:
  The speciation model proposed by Derrida and Higgs demonstrated that a
sexually reproducing population can split into different species in the absence
of natural selection or any type of geographic isolation, provided that mating
is assortative and the number of genes involved in the process is infinite.
Here we revisit this model and simulate it for finite genomes, focusing on the
question of how many genes it actually takes to trigger neutral sympatric
speciation. We find that, for typical parameters used in the original model, it
takes of the order of $10^5$ genes. We compare the results with a similar
spatially explicit model where about 100 genes suffice for speciation. We show
that when the number of genes is small the species that emerge are strongly
segregated in space. For larger number of genes, on the other hand, the spatial
structure of the population is less important and the species distribution
overlap considerably.


title:
Convergence Error Estimates of the Crank-Nicolson Scheme for Solving
  Decoupled FBSDEs

abstract:
  The Crank-Nicolson (short for C-N) scheme for solving {\it backward
stochastic differential equation} (BSDE), driven by Brownian motions, was first
developed by the authors W. Zhao, L. Chen and S. Peng [SIAM J. Sci. Comput., 28
(2006), 1563--1581], and numerical experiments showed that the accuracy of this
C-N scheme was of second order for solving BSDE. This C-N scheme was extended
to solve decoupled {\it forward-backward stochastic differential equations}
(FBSDEs) by W. Zhao, Y. Li and Y. Fu [Sci. China. Math., 57 (2014), 665--686],
and it was numerically shown that the accuracy of the extended C-N scheme was
also of second order.
  To our best knowledge, among all one-step (two-time level) numerical schemes
with second-order accuracy for solving BSDE or FBSDEs, such as the ones in the
above two papers and the one developed by the authors D. Crisan and K.
Manolarakis [Ann. Appl. Probab., 24, 2 (2014), 652--678], the C-N scheme is the
simplest one in applications. The theoretical proofs of second-order error
estimates reported in the literature for these schemes for solving decoupled
FBSDEs did not include the C-N scheme.
  The purpose of this work is to theoretically analyze the error estimate of
the C-N scheme for solving decoupled FBSDEs. Based on the Taylor and
It\^o-Taylor expansions, the Malliavin calculus theory (e.g., the multiple
Malliavin integration-by-parts formula), and our new truncation error
cancelation techniques, we rigorously prove that the strong convergence rate of
the C-N scheme is of second order for solving decoupled FBSDEs, which fills the
gap between the second-order numerical and theoretical analysis of the C-N
scheme.


title:
Coherent 3j-symbol representation for the loop quantum gravity
  intertwiner space

abstract:
  We introduce a new technique for dealing with the matrix elements of the
Hamiltonian operator in loop quantum gravity, based on the use of intertwiners
projected on coherent states of angular momentum. We give explicit expressions
for the projections of intertwiners on the spin coherent states in terms of
complex numbers describing the unit vectors which label the coherent states.
Operators such as the Hamiltonian can then be reformulated as differential
operators acting on polynomials of these complex numbers. This makes it
possible to describe the action of the Hamiltonian geometrically, in terms of
the unit vectors originating from the angular momentum coherent states, and
opens up a way towards investigating the semiclassical limit of the dynamics
via asymptotic approximation methods.


title: Logistic push: a regression framework for partial AUC optimization

abstract:
  The area under the receiver operating characteristic curve (AUC) is often
used to evaluate the performance of clinical prediction models. Recently, a
more refined strategy has been proposed to examine a partial area under the
curve (pAUC), which can account for differing costs associated with false
negative versus false positive results. Such consideration can substantially
increase the clinical utility of prediction models depending on the clinical
question. Properties of the pAUC estimator create significant challenges for
pAUC-optimal marker selection and model building. As such, current approaches
towards these aims can be complex and computationally intensive. We present a
simpler method based on weighted logistic regressions. We refer to our strategy
as logistic push, due to shared heuristics with the ranking algorithm P-norm
push. Logistic push is particularly useful in the high-dimensional setting,
where fast and broadly available algorithms for fitting penalized regressions
can be used for both marker selection and model fitting.


title: Active micromachines: Microfluidics powered by mesoscale turbulence

abstract:
  Dense active matter, from bacterial suspensions and microtubule bundles
driven by motor proteins to cellular monolayers and synthetic Janus particles,
is characterised by mesoscale turbulence, the emergence of chaotic flow
structures. By immersing an ordered array of symmetric rotors in an active
fluid, we introduce a microfluidic system that exploits spontaneous symmetry
breaking in mesoscale turbulence to generate work. The lattice of rotors
self-organises into a spin-state where neighbouring discs continuously rotate
in permanent alternating directions due to combined hydrodynamic and elastic
effects. Our virtual prototype demonstrates a new research direction for the
design of micromachines powered by the nematohydrodynamic properties of active
turbulence.


title:
An artificial neural network to find correlation patterns in an
  arbitrary number of variables

abstract:
  Methods to find correlation among variables are of interest to many
disciplines, including statistics, machine learning, (big) data mining and
neurosciences. Parameters that measure correlation between two variables are of
limited utility when used with multiple variables. In this work, I propose a
simple criterion to measure correlation among an arbitrary number of variables,
based on a data set. The central idea is to i) design a function of the
variables that can take different forms depending on a set of parameters, ii)
calculate the difference between a statistics associated to the function
computed on the data set and the same statistics computed on a randomised
version of the data set, called "scrambled" data set, and iii) optimise the
parameters to maximise this difference. Many such functions can be organised in
layers, which can in turn be stacked one on top of the other, forming a neural
network. The function parameters are searched with an enhanced genetic
algortihm called POET and the resulting method is tested on a cancer gene data
set. The method may have potential implications for some issues that affect the
field of neural networks, such as overfitting, the need to process huge amounts
of data for training and the presence of "adversarial examples".


title: Concrete Problems in AI Safety

abstract:
  Rapid progress in machine learning and artificial intelligence (AI) has
brought increasing attention to the potential impacts of AI technologies on
society. In this paper we discuss one such potential impact: the problem of
accidents in machine learning systems, defined as unintended and harmful
behavior that may emerge from poor design of real-world AI systems. We present
a list of five practical research problems related to accident risk,
categorized according to whether the problem originates from having the wrong
objective function ("avoiding side effects" and "avoiding reward hacking"), an
objective function that is too expensive to evaluate frequently ("scalable
supervision"), or undesirable behavior during the learning process ("safe
exploration" and "distributional shift"). We review previous work in these
areas as well as suggesting research directions with a focus on relevance to
cutting-edge AI systems. Finally, we consider the high-level question of how to
think most productively about the safety of forward-looking applications of AI.


title: Faster Computation of Path-Width

abstract:
  Tree-width and path-width are widely successful concepts. Many NP-hard
problems have efficient solutions when restricted to graphs of bounded
tree-width. Many efficient algorithms are based on a tree decomposition.
Sometimes the more restricted path decomposition is required. The bottleneck
for such algorithms is often the computation of the width and a corresponding
tree or path decomposition. For graphs with $n$ vertices and tree-width or
path-width $k$, the standard linear time algorithm to compute these
decompositions dates back to 1996. Its running time is linear in $n$ and
exponential in $k^3$ and not usable in practice. Here we present a more
efficient algorithm to compute the path-width and provide a path decomposition.
Its running time is $2^{O(k^2)} n$. In the classical algorithm of Bodlaender
and Kloks, the path decomposition is computed from a tree decomposition. Here,
an optimal path decomposition is computed from a path decomposition of about
twice the width. The latter is computed from a constant factor smaller graph.


title:
Using infrared/X-ray flare statistics to probe the emission regions near
  the event horizon of Sgr A*

abstract:
  The supermassive black hole at the centre of the Galaxy flares at least daily
in the infrared (IR) and X-ray bands, yet the process driving these flares is
still unknown. So far detailed analysis has only been performed on a few bright
flares. In particular, the broadband spectral modelling suffers from a strong
lack of simultaneous data. However, new monitoring campaigns now provide data
on thousands of flaring events, allowing a statistical analysis of the flare
properties. In this paper, we investigate the X-ray and IR flux distributions
of the flare events. Using a self-consistent calculation of the particle
distribution, we model the statistical properties of the flares. Based on a
previous work on single flares, we consider two families of models: pure
synchrotron models and synchrotron self-Compton (SSC) models. We investigate
the effect of fluctuations in some relevant parameters (e.g. acceleration
properties, density, magnetic field) on the flux distributions. The
distribution of these parameters is readily derived from the flux distributions
observed at different wavelengths. In both scenarios, we find that fluctuations
of the power injected in accelerated particles plays a major role. This must be
distributed as a power-law (with different indices in each model). In the
synchrotron dominated scenario, we derive the most extreme values of the
acceleration power required to reproduce the brightest flares. In that model,
the distribution of the acceleration slope fluctuations is constrained and in
the SSC scenario we constrain the distributions of the correlated magnetic
field and flow density variations.


title:
Growth of supermassive black holes, galaxy mergers and supermassive
  binary black holes

abstract:
  The study of galaxy mergers and supermassive binary black holes (SMBBHs) is
central to our understanding of the galaxy and black hole assembly and
(co-)evolution at the epoch of structure formation and throughout cosmic
history. Galaxy mergers are the sites of major accretion episodes, they power
quasars, grow supermassive black holes (SMBHs), and drive SMBH-host scaling
relations. The coalescing SMBBHs at their centers are the loudest sources of
gravitational waves (GWs) in the universe, and the subsequent GW recoil has a
variety of potential astrophysical implications which are still under
exploration. Future GW astronomy will open a completely new window on structure
formation and galaxy mergers, including the direct detection of coalescing
SMBBHs, high-precision measurements of their masses and spins, and constraints
on BH formation and evolution in the high-redshift universe.


title:
Gradient Estimates of Mean Curvature Equation with Neumann Boundary
  Condition in $ M^n\times \mathbb{R}$

abstract:
  In this note, we study the prescribed mean curvature equation with
  Neumann boundary conditions on Riemannian product manifold $ M^n\times
\mathbb{R}$. The main goal is to establish the boundary gradient estimates for
solutions by the maximum principle.
  As a consequence, we obtain an existence result.


title: Metastability-Containing Circuits

abstract:
  In digital circuits, metastability can cause deteriorated signals that
neither are logical 0 or logical 1, breaking the abstraction of Boolean logic.
Unfortunately, any way of reading a signal from an unsynchronized clock domain
or performing an analog-to-digital conversion incurs the risk of a metastable
upset; no digital circuit can deterministically avoid, resolve, or detect
metastability (Marino, 1981). Synchronizers, the only traditional
countermeasure, exponentially decrease the odds of maintained metastability
over time. Trading synchronization delay for an increased probability to
resolve metastability to logical 0 or 1, they do not guarantee success.
  We propose a fundamentally different approach: It is possible to contain
metastability by fine-grained logical masking so that it cannot infect the
entire circuit. This technique guarantees a limited degree of metastability
in---and uncertainty about---the output.
  At the heart of our approach lies a time- and value-discrete model for
metastability in synchronous clocked digital circuits. Metastability is
propagated in a worst-case fashion, allowing to derive deterministic
guarantees, without and unlike synchronizers. The proposed model permits
positive results and passes the test of reproducing Marino's impossibility
results. We fully classify which functions can be computed by circuits with
standard registers. Regarding masking registers, we show that they become
computationally strictly more powerful with each clock cycle, resulting in a
non-trivial hierarchy of computable functions.


title: A negative group delay model for feedback-delayed manual tracking

abstract:
  We propose that feedback-delayed manual tracking performance is limited by
fundamental constraints imposed by the physics of negative group delay. To test
this hypothesis, the results of an experiment in which subjects demonstrate
both reactive and predictive dynamics are modeled by a linear system with
delay-induced negative group delay. Although one of the simplest real-time
predictors conceivable, this model explains key components of experimental
observations. Most notably, it explains the observation that prediction time
linearly increases with feedback delay, up to a certain point when tracking
performance deteriorates. It also explains the transition from reactive to
predictive behavior with increasing feedback delay. The model contains only one
free parameter, the feedback gain, which has been fixed by comparison with one
set of experimental observations for the reactive case. Our model provides
quantitative predictions that can be tested in further experiments.


title: On the Davenport-Mahler bound

abstract:
  We prove that the Davenport-Mahler bound holds for arbitrary graphs with
vertices on the set of roots of a given univariate polynomial with complex
coefficients.


title:
Cosmological singularities in Eddington-inspired-Born-Infeld theory and
  its possible extension

abstract:
  The Eddington-inspired-Born-Infeld (EiBI) gravity, which is formulated within
the Palatini formalism, is characterized by its ability to cure the big bang
singularity in the very beginning of the Universe. We further analyze the EiBI
phantom model, and investigate the possible avoidance or alleviation of other
dark energy related singularities. We find that except for the big rip
singularity and little rip event, most of the cosmological singularities of
interest can be partially alleviated in this model. Furthermore, we generalize
the EiBI theory by adding a pure trace term to the determinant of the action.
This amendment is the most general rank-two tensor composed of up to first
order of the Riemann curvature. We find that this model allows the occurrence
of primitive bounces and some smoother singularities than that of big bang.
Most interestingly, for certain parameter space, the big bang singularity can
be followed naturally by an inflationary stage in a radiation dominated
universe.


title:
Effects of nickel doping on the preferred orientation and oxidation
  potential of Ti/Sb-SnO2 anodes prepared by spray pyrolysis

abstract:
  Nickel and antimony co-doped Ti/SnO2 (Ti/Ni-Sb-SnO2) anodes were prepared by
spray pyrolysis. Effects of nickel concentration on the structure and onset
potential for oxygen evolution of Ti/Ni-Sb-SnO2 anodes have been systematically
investigated. XRD analyses suggest that SnO2 thin films grow in preferential
orientation along (101) plane as the nickel concentration increases. The
enhanced onset potential of oxygen is above 2.4 V vs NHE due to the
introduction of nickel doping, and increases slightly with the nickel
concentration. The calculated results show that work function of Ni/Sb co-doped
SnO2 also increases with the Ni doping level, which contributes to the
enhancement of onset potential for oxygen evolution.


title:
Order Reconstruction for Nematics on Squares and Regular Polygons: A
  Landau-de Gennes Study

abstract:
  We construct an order reconstruction (OR)-type Landau-de Gennes critical
point on a square domain of edge length $\lambda$, motivated by the well order
reconstruction solution numerically reported by Kralj and Majumdar. The OR
critical point is distinguished by an uniaxial cross with negative scalar order
parameter along the square diagonals. The OR critical point is defined in terms
of a saddle-type critical point of an associated scalar variational problem.
The OR-type critical point is globally stable for small $\lambda$ and undergoes
a supercritical pitchfork bifurcation in the associated scalar variational
setting. We consider generalizations of the OR-type critical point to a regular
hexagon, accompanied by numerical estimates of stability criteria of such
critical points on both a square and a hexagon in terms of material-dependent
constants.


title:
Lower Bounds on Parameter Modulation-Estimation Under Bandwidth
  Constraints

abstract:
  We consider the problem of modulating the value of a parameter onto a
band-limited signal to be transmitted over a continuous-time, additive white
Gaussian noise (AWGN) channel, and estimating this parameter at the receiver.
The performance is measured by the mean power-$\alpha$ error (MP$\alpha$E),
which is defined as the worst-case $\alpha$-th order moment of the absolute
estimation error. The optimal exponential decay rate of the MP$\alpha$E as a
function of the transmission time, is investigated. Two upper (converse) bounds
on the MP$\alpha$E exponent are derived, on the basis of known bounds for the
AWGN channel of inputs with unlimited bandwidth. The bounds are computed for
typical values of the error moment and the signal-to-noise ratio (SNR), and the
SNR asymptotics of the different bounds are analyzed. The new bounds are
compared to known converse and achievability bounds, which were derived from
channel coding considerations.


title: On almost hypohamiltonian graphs

abstract:
  A graph $G$ is almost hypohamiltonian (a.h.) if $G$ is non-hamiltonian, there
exists a vertex $w$ in $G$ such that $G - w$ is non-hamiltonian, and $G - v$ is
hamiltonian for every vertex $v \ne w$ in $G$. The second author asked in [J.
Graph Theory 79 (2015) 63--81] for all orders for which a.h. graphs exist. Here
we solve this problem. To this end, we present a specialised algorithm which
generates complete sets of a.h. graphs for various orders. Furthermore, we show
that the smallest cubic a.h. graphs have order 26. We provide a lower bound for
the order of the smallest planar a.h. graph and improve the upper bound for the
order of the smallest planar a.h. graph containing a cubic vertex. We also
determine the smallest planar a.h. graphs of girth 5, both in the general and
cubic case. Finally, we extend a result of Steffen on snarks and improve two
bounds on longest paths and longest cycles in polyhedral graphs due to
Jooyandeh, McKay, {\"O}sterg{\aa}rd, Pettersson, and the second author.


title:
Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk
  to Excess Variance

abstract:
  Growth-optimal portfolios are guaranteed to accumulate higher wealth than any
other investment strategy in the long run. However, they tend to be risky in
the short term. For serially uncorrelated markets, similar portfolios with more
robust guarantees have been recently proposed. This paper extends these robust
portfolios by accommodating non-zero autocorrelations that may reflect
investors' beliefs about market movements. Moreover, we prove that the risk
incurred by such autocorrelations can be absorbed by modifying the covariance
matrix of asset returns.


title:
Multiwavelength campaign on Mrk 509 XV. A global modeling of the broad
  emission lines in the Optical, UV and X-ray bands

abstract:
  We model the broad emission lines present in the optical, UV and X-ray
spectra of Mrk 509, a bright type 1 Seyfert galaxy. The broad lines were
simultaneously observed during a large multiwavelength campaign, using the
XMM-Newton-OM for the optical lines, HST-COS for the UV lines and
XMM-Newton-RGS and Epic for the X-ray lines respectively. We also used FUSE
archival data for the broad lines observed in the far-ultra-violet. The goal is
to find a physical connection among the lines measured at different wavelengths
and determine the size and the distance from the central source of the emitting
gas components. We used the "Locally optimally emission Cloud" (LOC) model
which interprets the emissivity of the broad line region (BLR) as regulated by
powerlaw distributions of both gas density and distances from the central
source. We find that one LOC component cannot model all the lines
simultaneously. In particular, we find that the X-ray and UV lines likely may
originate in the more internal part of the AGN, at radii in the range
~5x10^{14}-3x10^{17} cm, while the optical lines and part of the UV lines may
likely be originating further out, at radii ~3x10^{17}-3x^{18} cm. These two
gas components are parametrized by a radial distribution of the luminosities
with a slope gamma of ~1.15 and ~1.10, respectively, both of them covering at
least 60% of the source. This simple parameterization points to a structured
broad line region, with the higher ionized emission coming from closer in,
while the emission of the low-ionization lines is more concentrated in the
outskirts of the broad line region.


title: Strategic Contention Resolution with Limited Feedback

abstract:
  In this paper, we study contention resolution protocols from a game-theoretic
perspective. We focus on \emph{acknowledgment-based} protocols, where a user
gets feedback from the channel only when she attempts transmission. In this
case she will learn whether her transmission was successful or not. Users that
do not transmit will not receive any feedback. We are interested in equilibrium
protocols, where no player has an incentive to deviate.
  The limited feedback makes the design of equilibrium protocols a hard task as
best response policies usually have to be modeled as Partially Observable
Markov Decision Processes, which are hard to analyze. Nevertheless, we show how
to circumvent this for the case of two players and present an equilibrium
protocol. For many players, we give impossibility results for a large class of
acknowledgment-based protocols, namely \emph{age-based} and \emph{backoff}
protocols with finite expected finishing time. Finally, we provide an age-based
equilibrium protocol, which has infinite expected finishing time, but every
player finishes in linear time with high probability.


title: Fine-grained dichotomies for the Tutte plane and Boolean #CSP

abstract:
  Jaeger, Vertigan, and Welsh [15] proved a dichotomy for the complexity of
evaluating the Tutte polynomial at fixed points: The evaluation is #P-hard
almost everywhere, and the remaining points admit polynomial-time algorithms.
Dell, Husfeldt, and Wahl\'en [9] and Husfeldt and Taslaman [12], in combination
with Curticapean [7], extended the #P-hardness results to tight lower bounds
under the counting exponential time hypothesis #ETH, with the exception of the
line $y=1$, which was left open. We complete the dichotomy theorem for the
Tutte polynomial under #ETH by proving that the number of all acyclic subgraphs
of a given $n$-vertex graph cannot be determined in time $exp(o(n))$ unless
#ETH fails.
  Another dichotomy theorem we strengthen is the one of Creignou and Hermann
[6] for counting the number of satisfying assignments to a constraint
satisfaction problem instance over the Boolean domain. We prove that all
#P-hard cases are also hard under #ETH. The main ingredient is to prove that
the number of independent sets in bipartite graphs with $n$ vertices cannot be
computed in time $exp(o(n))$ unless #ETH fails. In order to prove our results,
we use the block interpolation idea by Curticapean [7] and transfer it to
systems of linear equations that might not directly correspond to
interpolation.


title:
Augmenting Supervised Neural Networks with Unsupervised Objectives for
  Large-scale Image Classification

abstract:
  Unsupervised learning and supervised learning are key research topics in deep
learning. However, as high-capacity supervised neural networks trained with a
large amount of labels have achieved remarkable success in many computer vision
tasks, the availability of large-scale labeled images reduced the significance
of unsupervised learning. Inspired by the recent trend toward revisiting the
importance of unsupervised learning, we investigate joint supervised and
unsupervised learning in a large-scale setting by augmenting existing neural
networks with decoding pathways for reconstruction. First, we demonstrate that
the intermediate activations of pretrained large-scale classification networks
preserve almost all the information of input images except a portion of local
spatial details. Then, by end-to-end training of the entire augmented
architecture with the reconstructive objective, we show improvement of the
network performance for supervised tasks. We evaluate several variants of
autoencoders, including the recently proposed "what-where" autoencoder that
uses the encoder pooling switches, to study the importance of the architecture
design. Taking the 16-layer VGGNet trained under the ImageNet ILSVRC 2012
protocol as a strong baseline for image classification, our methods improve the
validation-set accuracy by a noticeable margin.


title: Domain formation in membranes near the onset of instability

abstract:
  The formation of microdomains, also called rafts, in biomembranes can be
attributed to the surface tension of the membrane. In order to model this
phenomenon, a model involving a coupling between the local composition and the
local curvature was proposed by Seul and Andelman in 1995. In addition to the
familiar Cahn-Hilliard/Modica-Mortola energy, there are additional `forces'
that prevent large domains of homogeneous concentration. This is taken into
account by the bending energy of the membrane, which is coupled to the value of
the order parameter, and reflects the notion that surface tension associated
with a slightly curved membrane influences the localization of phases as the
geometry of the lipids has an effect on the preferred placement on the
membrane.
  The main result of the paper is the study of the $\Gamma$-convergence of this
family of energy functionals, involving nonlocal as well as negative terms.
Since the minimizers of the limiting energy have minimal interfaces, the
physical interpretation is that, within a sufficiently strong interspecies
surface tension and a large enough sample size, raft microdomains are not
formed.


title:
The boundedness of operators in Muckenhoupt weighted Morrey spaces via
  extrapolation techniques and duality

abstract:
  The bidual of the closure of smooth functions with respect to the Morrey norm
coincides with the Morrey space. This assertion is generalized to some
Muckenhoupt weighted Morrey spaces. We combine this fact with basic
extrapolation techniques due to Rubio de Francia adapted to weighted Morrey
spaces. This leads to new results on the boundedness of operators even for the
unweighted case.


title: Vapour-Liquid Coexistence of an Active Lennard-Jones fluid

abstract:
  We study a three-dimensional system of self-propelled Lennard-Jones particles
using Brownian Dynamics simulations. Using recent theoretical results for
active matter, we calculate the pressure and report equations of state for the
system. Additionally, we chart the vapour-liquid coexistence and show that the
coexistence densities can be well described using simple power laws. Lastly, we
demonstrate that our out-of-equilibrium system shows deviations from both the
law of rectilinear diameters and the law of corresponding states.


title: On the stability of Brunn-Minkowski type inequalities

abstract:
  Log-Brunn-Minkowski inequality was conjectured by Bor\"oczky, Lutwak, Yang
and Zhang \cite{BLYZ}, and it states that a certain strengthening of the
classical Brunn-Minkowski inequality is admissible in the case of symmetric
convex sets. It was recently shown by Nayar, Zvavitch, the second and the third
authors \cite{LMNZ}, that Log-Brunn-Minkowski inequality implies a certain
dimensional Brunn-Minkowski inequality for log-concave measures, which in the
case of Gaussian measure was conjectured by Gardner and Zvavitch \cite{GZ}.
  In this note, we obtain stability results for both Log-Brunn-Minkowski and
dimensional Brunn-Minkowski inequalities for rotation invariant log-conave
measures near a ball. Remarkably, the assumption of symmetry is only necessary
for Log-Brunn-Minkowski stability, which emphasizes an important difference
between the two conjectured inequalities.
  Also, we determine the infinitesimal version of the log-Brunn-Minkowski
inequality. As a consequence, we obtain a strong Poincar\'{e}-type inequality
in the case of unconditional convex sets, as well as for symmetric convex sets
on the plane.
  Additionally, we derive an infinitesimal equivalent version of the
B-conjecture for an arbitrary measure.


title: 2MASS photometry and kinematical studies of open cluster NGC 188

abstract:
  In this paper, we present our results for the photometric and kinematical
studies of old open cluster NGC 188. We determined various astrophysical
parameters like limited radius, core and tidal radii, distance, luminosity and
mass functions, total mass, relaxation time etc. for the cluster using 2MASS
catalog. We obtained the cluster's distance from the Sun as 1721+/-41 pc and
log (age)= 9.85+/-0.05 at Solar metallicity. The relaxation time of the cluster
is smaller than the estimated cluster age which suggests that the cluster is
dynamically relaxed. Our results agree with the values mentioned in the
literature. We also determined the cluster's apex coordinates as (281.88 deg,
-44.76 deg) using AD-diagram method. Other kinematical parameters like space
velocity components, cluster center and elements of Solar motion etc. have also
been computed.


title: ML-based tactile sensor calibration: A universal approach

abstract:
  We study the responses of two tactile sensors, the fingertip sensor from the
iCub and the BioTac under different external stimuli. The question of interest
is to which degree both sensors i) allow the estimation of force exerted on the
sensor and ii) enable the recognition of differing degrees of curvature. Making
use of a force controlled linear motor affecting the tactile sensors we acquire
several high-quality data sets allowing the study of both sensors under exactly
the same conditions. We also examined the structure of the representation of
tactile stimuli in the recorded tactile sensor data using t-SNE embeddings. The
experiments show that both the iCub and the BioTac excel in different settings.


title:
Thermodynamic analysis of the static spherically symmetric field
  equations in Rastall theory

abstract:
  The restrictions on the Rastall theory due to apply the Newtonian limit to
the theory are derived. In addition, we use the zero-zero component of the
Rastall field equations as well as the unified first law of thermodynamics to
find the Misner-Sharp mass content confined to the event horizon of the
spherically symmetric static spacetimes in the Rastall framework. The obtained
relation is calculated for the Schwarzschild and de-Sitter back holes as two
examples. Bearing the obtained relation for the Misner-Sharp mass in mind
together with recasting the one-one component of the Rastall field equations
into the form of the first law of thermodynamics, we obtain expressions for the
horizon entropy and the work term. Finally, we also compare the thermodynamic
quantities of system, including energy, entropy and work, with their
counterparts in the Einstein framework to have a better view about the role of
the Rastall hypothesis on the thermodynamics of system.


title:
On a phenomenology of the accelerated expansion with a varying ghost
  dark energy

abstract:
  Subject of our study it is the accelerated expansion of the large scale
universe, where a varying ghost dark energy can take the role of the dark
energy. The model of the varying ghost dark energy considered in this work it
is a phenomenological modification of the ghost dark energy. Recently, three
other phenomenological models of the varying ghost dark energy have been
suggested and the model considered in this work will complete the logical chain
of considered modifications. The best fit of theoretical results to the
luminosity distance, has been used to obtain preliminary constraints on the
parameters of the models. This does help us to reduce amount of discussion. On
the other hand, detailed comparison of theoretical results with observational
data has been left as a subject of another discussion elsewhere. Moreover, a
look to considered models via $Om$ and statefinder hierarchy analysis is
presented and discussed for different forms of interaction between the varying
ghost dark energy and cold dark matter.


title: Tests for Comparing Weighted Histograms. Review and Improvements

abstract:
  Histograms with weighted entries are used to estimate probability density
functions. Computer simulation is the main application of this type of
histograms. A review on chi-square tests for comparing weighted histograms is
presented in this paper. Improvements to these tests that have a size closer to
its nominal value are proposed. Numerical examples are presented for evaluation
and demonstration of various applications of the tests.

categories: physics.data-an astro-ph.IM hep-ex nucl-ex stat.AP


title: On some factorial properties of subrings

abstract:
  We discuss various factorial properties of subrings as well as properties
involving irreducible and square-free elements, in particular ones connected
with Jacobian conditions.


title: A Distributed Newton Method for Large Scale Consensus Optimization

abstract:
  In this paper, we propose a distributed Newton method for consensus
optimization. Our approach outperforms state-of-the-art methods, including
ADMM. The key idea is to exploit the sparsity of the dual Hessian and recast
the computation of the Newton step as one of efficiently solving symmetric
diagonally dominant linear equations. We validate our algorithm both
theoretically and empirically. On the theory side, we demonstrate that our
algorithm exhibits superlinear convergence within a neighborhood of optimality.
Empirically, we show the superiority of this new method on a variety of machine
learning problems. The proposed approach is scalable to very large problems and
has a low communication overhead.


title:
Comment on Mente, O'Donnell, Rangarajan, et al. "Associations of urinary
  sodium excretion with cardiovascular events in individuals with an without
  hypertension: a pooled analysis of data from four studies"

abstract:
  Mente, O'Donnell, Rangarajan, et al. ignore a possible source of bias that
may invalidate their finding of an anticorrelation between sodium intake and
cardiovascular events


title:
Development and characterization of a 2.2 W narrow-linewidth 318.6 nm
  ultraviolet laser

abstract:
  We demonstrate a high-power narrow-linewidth ultraviolet (UV) laser system at
318.6 nm for direct 6S1/2-nP (n = 70 to 100) Rydberg excitation of cesium
atoms. Based on commercial fiber lasers and efficient nonlinear frequency
conversion technology, 2.26 W of tunable UV laser power is obtained from
cavity-enhanced second harmonic generation following sum-frequency generation
of two infrared lasers at 1560.5 nm and 1076.9 nm to 637.2 nm. The maximum
doubling efficiency is 57.3%. The typical UV laser power root-mean-square
fluctuation is less than 0.87% over 30 minutes, and the continuously tunable
range of the UV laser frequency is more than 6 GHz. Its beam quality factors M2
X and M2 Y are 1.16 and 1.48, respectively. This high-performance UV laser has
significant potential use in quantum optics and cold atom physics.


title:
Different Prospects of the Universe Depending on Dark Energy and/or a
  New Kind of Extra Dimension

abstract:
  Generally making the cosmological scale factor $R$ be a function of the
coordinate of the extra dimension $\sigma $ that is also a function of time
$t$, we achieve a new kind of cosmic acceleration mechanism depending on extra
dimension. We give the constraints on $\sigma $ under four different prospects
of the universe, and indicate that dark energy is not required for both the
small extra dimension and the accelerating expansion of our universe. This
results in this paper show that the accelerating expansion of our universe may
come from both dark energy and the achieved new mechanism here, or the latter
alone.


title:
Modularity of elliptic curves over abelian totally real fields
  unramified at 3, 5, and 7

abstract:
  This version improves the old version entitled "On the modularity of elliptic
curves with a residually irreducible representation".
  Let $E$ be an elliptic curve over an abelian totally real field $K$
unramified at 3,5, and 7. We prove that $E$ is modular.


title:
Integrable motion of two interacting curves, spin systems and the
  Manakov system

abstract:
  Integrable spin systems are an important subclass of integrable (soliton)
nonlinear equations. They play important role in physics and mathematics. At
present, many integrable spin systems were found and studied. They are related
with the motion of 3-dimensional curves. In this paper, we consider a model of
two moving interacting curves. Next, we find its integrable reduction related
with some integrable coupled spin system. Then we show that this integrable
coupled spin system is equivalent to the famous Manakov system.


title: Elastic Moduli and Vibrational Modes in Jammed Particulate Packings

abstract:
  When we elastically impose a homogeneous, affine deformation on amorphous
solids, they also undergo an inhomogeneous, non-affine deformation, which can
have a crucial impact on the overall elastic response. To correctly understand
the elastic modulus $M$, it is therefore necessary to take into account not
only the affine modulus $M_A$, but also the non-affine modulus $M_N$ that
arises from the non-affine deformation. In the present work, we study the bulk
($M=K$) and shear ($M=G$) moduli in static jammed particulate packings over a
range of packing fractions $\varphi$. One novelty of this work is to elucidate
the contribution of each vibrational mode to the non-affine $M_N$ through a
modal decomposition of the displacement and force fields. In the vicinity of
the (un)jamming transition, $\varphi_{c}$, the vibrational density of states,
$g(\omega)$, shows a plateau in the intermediate frequency regime above a
characteristic frequency $\omega^\ast$. We illustrate that this unusual feature
apparent in $g(\omega)$ is reflected in the behavior of $M_N$: As $\varphi
\rightarrow \varphi_c$, where $\omega^\ast \rightarrow 0$, those modes for
$\omega < \omega^\ast$ contribute less and less, while contributions from those
for $\omega > \omega^\ast$ approach a constant value which results in $M_N$ to
approach a critical value $M_{Nc}$, as $M_N-M_{Nc} \sim \omega^\ast$. At
$\varphi_c$ itself, the bulk modulus attains a finite value $K_c=K_{Ac}-K_{Nc}
> 0$, such that $K_{Nc}$ has a value that remains below $K_{Ac}$. In contrast,
for the critical shear modulus $G_c$, $G_{Nc}$ and $G_{Ac}$ approach the same
value so that the total value becomes exactly zero, $G_c = G_{Ac}-G_{Nc} =0$.
We explore what features of the configurational and vibrational properties
cause such the distinction between $K$ and $G$, allowing us to validate
analytical expressions for their critical values.


title:
Near-Infrared-Assisted Charge Control and Spin Readout of the
  Nitrogen-Vacancy Center in Diamond

abstract:
  We utilize nonlinear absorption to design all-optical protocols that improve
both charge state initialization and spin readout for the nitrogen-vacancy (NV)
center in diamond. Non-monotonic variations in the equilibrium charge state as
a function of visible and near-infrared (NIR) optical power are attributed to
competing multiphoton absorption processes. In certain regimes, multicolor
illumination enhances the steady-state population of the NV's negative charge
state above 90%. At higher NIR intensities, selective ionization of the singlet
manifold facilitates a protocol for spin-to-charge conversion that dramatically
enhances the spin readout fidelity. We demonstrate a 6-fold increase in the
signal-to-noise ratio for single-shot spin measurements and predict an
orders-of-magnitude experimental speedup over traditional methods for emerging
applications in magnetometry and quantum information science using NV spins.


title:
A local and renormalizable framework for the gauge-invariant operator
  $A^2_{\min}$ in Euclidean Yang-Mills theories in linear covariant gauges

abstract:
  We address the issue of the renormalizability of the gauge-invariant
non-local dimension-two operator $A^2_{\rm min}$, whose minimization is defined
along the gauge orbit. Despite its non-local character, we show that the
operator $A^2_{\rm min}$ can be cast in local form through the introduction of
an auxiliary Stueckelberg field. The localization procedure gives rise to an
unconventional kind of Stueckelberg-type action which turns out to be
renormalizable to all orders of perturbation theory. In particular, as a
consequence of its gauge invariance, the anomalous dimension of the operator
$A^2_{\rm min}$ turns out to be independent from the gauge parameter $\alpha$
entering the gauge-fixing condition, being thus given by the anomalous
dimension of the operator $A^2$ in the Landau gauge.


title: Kardar-Parisi-Zhang Universality

abstract:
  This is the article by the same name which was published in the March 2016
issue of the AMS Notices. Due to space constraints, some references contained
here were not provided in the published version were not provided. The figures
in this article were made collaboratively with William Casselman.


title:
Theoretical and Experimental Investigation on Structural, Electronic and
  Magnetic Properties of layered Mn5O8

abstract:
  We have investigated the crystal, electronic, and magnetic structure of Mn5O8
by means of state of-the-art density functional theory calculations and neutron
powder diffraction (NPD) measurements. This compound stabilizes in the
monoclinic structure with space group C2/m where the Mn ions are in the
distorted octahedral and trigonal prismatic coordination with oxygen atoms. The
calculated structural parameters based on total energy calculations are found
to be in excellent agreement with low temperature NPD measurements when we
accounted correct magnetic structure and Coulomb correlation effect into the
computation. Bond strength analysis based on crystal orbital Hamiltonian
population between constituents indicating strong anisotropy in the bonding
behavior which results in layered nature of its crystal structure. Using fully
relativistic generalized-gradient approximation with Hubbard U (GGA+U) we found
that the magnetic ordering in Mn5O8 is A-type antiferromagnetic and the
direction of easy axis is [1 0 0] in agreement with susceptibility and NPD
measurements. However, the calculation without the inclusion of HubbardU leads
to ferrimagnetic half metal as ground state contradictory to experimental
findings, indicating the presence of strong Coulomb correlation effect in this
material. The GGA calculations without Coulomb correction effect itself is
sufficient to reproduce our experimentally observed magnetic moments in various
Mn sites.


title:
Stochastic Runge-Kutta Software Package for Stochastic Differential
  Equations

abstract:
  As a result of the application of a technique of multistep processes
stochastic models construction the range of models, implemented as a
self-consistent differential equations, was obtained. These are partial
differential equations (master equation, the Fokker--Planck equation) and
stochastic differential equations (Langevin equation). However, analytical
methods do not always allow to research these equations adequately. It is
proposed to use the combined analytical and numerical approach studying these
equations. For this purpose the numerical part is realized within the framework
of symbolic computation. It is recommended to apply stochastic Runge--Kutta
methods for numerical study of stochastic differential equations in the form of
the Langevin. Under this approach, a program complex on the basis of analytical
calculations metasystem Sage is developed. For model verification logarithmic
walks and Black--Scholes two-dimensional model are used. To illustrate the
stochastic "predator--prey" type model is used. The utility of the combined
numerical-analytical approach is demonstrated.


title:
Thermodynamic equilibrium in relativity: four-temperature, Killing
  vectors and Lie derivatives

abstract:
  The main concepts of general relativistic thermodynamics and general
relativistic statistical mechanics are reviewed. The main building block of the
proper relativistic extension of the classical thermodynamics laws is the
four-temperature vector \beta, which plays a major role in the quantum
framework and defines a very convenient hydrodynamic frame. The general
relativistic thermodynamic equilibrium condition demands \beta to be a Killing
vector field. We show that a remarkable consequence is that all Lie derivatives
of all physical observables along the four-temperature flow must then vanish.


title: Instability of insulators near quantum phase transitions

abstract:
  Thin films of Amorphous indium oxide undergo a magnetic field driven
superconducting to insulator quantum phase transition. In the insulating phase,
the current-voltage characteristics show large current discontinuities due to
overheating of electrons. We show that the onset voltage for the
discontinuities vanishes as we approach the quantum critical point.
  As a result the insulating phase becomes unstable with respect to any applied
voltage making it, at least experimentally, immeasurable.
  We emphasize that unlike previous reports of the absence of linear response
near quantum phase transitions, in our system, the departure from equilibrium
is discontinuous. Because the conditions for these discontinuities are
satisfied in most insulators at low temperatures, and due to the decay of all
characteristic energy scales near quantum phase transitions, we believe that
this instability is general and should occur in various systems while
approaching their quantum critical point. Accounting for this instability is
crucial for determining the critical behavior of systems near the transition.


title: Haar null and Haar meager sets: a survey and new results

abstract:
  We survey results about Haar null subsets of (not necessarily locally
compact) Polish groups. The aim of this paper is to collect the fundamental
properties of the various possible definitions of Haar null sets, and also to
review the techniques that may enable the reader to prove results in this area.
We also present several recently introduced ideas, including the notion of Haar
meager sets, which are closely analogous to Haar null sets. We prove some
results in a more general setting than that of the papers where they were
originally proved and prove some results for Haar meager sets which were
already known for Haar null sets.


title: Engineering dissipation with phononic spectral hole burning

abstract:
  Optomechanics, nano-electromechanics, and integrated photonics have brought
about a renaissance in phononic device physics and technology. Central to this
advance are devices and materials that support ultra long-lived photonic and
phononic excitations, providing access to novel regimes of classical and
quantum dynamics based on tailorable photon-phonon coupling. Silica-based
devices have been at the forefront of such innovations for their ability to
support optical excitations persisting for nearly 1 billion cycles, and for
their low optical nonlinearity. Remarkably, acoustic phonon modes can persist
for a comparable number of cycles in crystalline solids at cryogenic
temperatures, permitting radical enhancement of photon-phonon coupling.
However, it has not been possible to achieve similar phononic coherence times
in silica, as silica becomes acoustically opaque at low temperatures. In this
paper, we demonstrate that intrinsic forms of phonon dissipation are greatly
reduced (by > 90%) using nonlinear saturation with continuous driving fields of
disparate frequencies. We demonstrate steady-state phononic spectral hole
burning for the first time, and show that this technique for controlling
dissipation in glass produces a wide-band transparency window. These studies
were carried out in a micro-scale fiber waveguide where the acoustic
intensities necessary to manipulate phonon dissipation can be achieved with
optically generated phonon fields of modest (nW) powers. We developed a simple
model that explains both dissipative and dispersive changes produced by
phononic saturation. In showing how the dissipative and dispersive properties
of glasses can be manipulated using external fields, we open the door to
dynamical phononic switching and the use of glasses as low loss phononic media
which may enable new forms of controllable laser dynamics, information
processing, and precision metrology.


title: Chern-Simons Theory on Supermanifolds

abstract:
  We consider quantum field theories on supermanifolds using integral forms.
The latter are used to define a geometric theory of integration and they are
essential for a consistent action principle. The construction relies on Picture
Changing Operators, analogous to the one introduced in String Theory. As an
application, we construct a geometric action principle for N=1 D=3
super-Chern-Simons theory.


title: Torsion Effects and LLG Equation

abstract:
  Based on the non-relativistic regime of the Dirac equation coupled to a
torsion pseudo-vector, we study the dynamics of magnetization and how it is
affected by the presence of torsion. We consider that torsion interacting terms
in Dirac equation appear in two ways one of these is thhrough the covariant
derivative considering the spin connection and gauge magnetic field and the
other is through a non-minimal spin torsion coupling. We show within this
framework, that it is possible to obtain the most general Landau, Lifshitz and
Gilbert (LLG) equation including the torsion effects, where we refer to torsion
as a geometric field playing an important role in the spin coupling process. We
show that the torsion terms can give us two important landscapes in the
magnetization dynamics: one of them related with damping and the other related
with the screw dislocation that give us a global effect like a helix damping
sharped. These terms are responsible for changes in the magnetization
precession dynamics.


title:
Divide and Conquer: An Incremental Sparsity Promoting Compressive
  Sampling Approach for Polynomial Chaos Expansions

abstract:
  This paper introduces an efficient sparse recovery approach for Polynomial
Chaos (PC) expansions, which promotes the sparsity by breaking the
dimensionality of the problem. The proposed algorithm incrementally explores
sub-dimensional expansions for a sparser recovery, and shows success when
removal of uninfluential parameters that results in a lower coherence for
measurement matrix, allows for a higher order and/or sparser expansion to be
recovered. The incremental algorithm effectively searches for the sparsest PC
approximation, and not only can it decrease the prediction error, it can also
reduce the dimensionality of PCE model. Four numerical examples are provided to
demonstrate the validity of the proposed approach. The results from these
examples show that the incremental algorithm substantially outperforms
conventional compressive sampling approaches for PCE, in terms of both solution
sparsity and prediction error.


title:
The spin structure of the proton at low $x$ and low $Q^2$ in
  two-dimensional bins from COMPASS

abstract:
  The longitudinal double spin asymmetries $A_1^p$ and the spin dependent
structure function of the proton $g_1^p$ were extracted from COMPASS data in
the region of low Bjorken scaling variable $x$ and low photon virtuality $Q^2$.
The data were taken in 2007 and 2011 from scattering of polarised muons off
polarised protons, resulting in a sample that is 150 times larger than the one
from the previous experiment SMC that pioneered studies in this kinematic
region.
  For the first time, $A_1^p$ and $g_1^p$ were evaluated in this region in
two-dimensional bins of kinematic variables: $(x,Q^2)$, $(\nu ,Q^2)$, $(x,\nu)$
and $(Q^2,x)$. The following kinematic region was investigated: $4\times
10^{-5}<x<4\times 10^{-2}$, $0.001$~(GeV/$c$)$^2<Q^2<1$~(GeV/$c$)$^2$ and
$14$~GeV$<\nu <194$~GeV. The obtained results were confronted with theoretical
models.


title:
Application of quasi-Monte Carlo methods to elliptic PDEs with random
  diffusion coefficients - a survey of analysis and implementation

abstract:
  This article provides a survey of recent research efforts on the application
of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations
(PDEs) with random diffusion coefficients. It considers, and contrasts, the
uniform case versus the lognormal case, single-level algorithms versus
multi-level algorithms, first order QMC rules versus higher order QMC rules,
and deterministic QMC methods versus randomized QMC methods. It gives a summary
of the error analysis and proof techniques in a unified view, and provides a
practical guide to the software for constructing and generating QMC points
tailored to the PDE problems. The analysis for the uniform case can be
generalized to cover a range of affine parametric operator equations.


title:
Global Structure Search for Molecules on Surfaces: Efficient Sampling
  with Curvilinear Coordinates

abstract:
  Efficient structure search is a major challenge in computational materials
science. We present a modification of the basin hopping global geometry
optimization approach that uses a curvilinear coordinate system to describe
global trial moves. This approach has recently been shown to be efficient in
structure determination of clusters [Nano Letters 15, 8044-8048 (2015)] and is
here extended for its application to covalent, complex molecules and large
adsorbates on surfaces. The employed, automatically constructed delocalized
internal coordinates are similar to molecular vibrations, which enhances the
generation of chemically meaningful trial structures. By introducing flexible
constraints and local translation and rotation of independent geometrical
subunits we enable the use of this method for molecules adsorbed on surfaces
and interfaces. For two test systems, trans-$\beta$-ionylideneacetic acid
adsorbed on a Au(111) surface and methane adsorbed on a Ag(111) surface, we
obtain superior performance of the method compared to standard optimization
moves based on Cartesian coordinates.


title:
On the Milnor monodromy of the exceptional reflection arrangement of
  type $G_{31}$

abstract:
  Combining recent results by A. Macinic, S. Papadima and R. Popescu with a
spectral sequence and computer aided computations, we determine the monodromy
action on $H^1(F,\mathbb{C})$, where $F$ denotes the Milnor fiber of the
hyperplane arrangement associated to the exceptional irreducible complex
reflection group $G_{31}$. This completes the description given by the first
author of such monodromy operators for all the other irreducible complex
reflection groups.


title: Double Beta Decays into Excited States in $^{110}$Pd and $^{102}$Pd

abstract:
  A search for double beta decays of $^{110}$Pd and $^{102}$Pd into excited
states of the daughter nuclides has been performed using three ultra-low
background gamma-spectrometry measurements in the Felsenkeller laboratory,
Germany, the HADES laboratory, Belgium and at the LNGS, Italy. The combined
Bayesian analysis of the three measurements sets improved half-life limits for
the $2\nu\beta\beta$ and $0\nu\beta\beta$ decay modes of the $2^+_1$, $0^+_1$
and $2^+_2$ transitions in $^{110}$Pd to $2.9\cdot10^{20}$ yr,
$4.0\cdot10^{20}$ yr and $3.0\cdot10^{20}$ yr respectively and in $^{102}$Pd to
$7.6\cdot10^{18}$ yr, $8.8\cdot10^{18}$ yr and $1.4\cdot10^{19}$ yr
respectively with 90% credibility.


title: A Self-Index on Block Trees

abstract:
  The Block Tree is a recently proposed data structure that reaches compression
close to Lempel-Ziv while supporting efficient direct access to text
substrings. In this paper we show how a self-index can be built on top of a
Block Tree so that it provides efficient pattern searches while using space
proportional to that of the original data structure. More precisely, if a
Lempel-Ziv parse cuts a text of length $n$ into $z$ non-overlapping phrases,
then our index uses $O(z\log(n/z))$ words and finds the $occ$ occurrences of a
pattern of length $m$ in time $O(m\log n+occ\log^\epsilon n)$ for any constant
$\epsilon>0$.


title: Stein's method, many interacting worlds and quantum mechanics

abstract:
  Hall, Deckert and Wiseman (2014) recently proposed that quantum theory can be
understood as the continuum limit of a deterministic theory in which there is a
large, but finite, number of classical "worlds." A resulting Gaussian limit
theorem for particle positions in the ground state, agreeing with quantum
theory, was conjectured in Hall, Deckert and Wiseman (2014) and proven by
McKeague and Levin (2016) using Stein's method. In this article we propose new
connections between Stein's method and Many Interacting Worlds (MIW) theory. In
particular, we show that quantum position probability densities for higher
energy levels beyond the ground state arise as distributional fixed points in a
new generalization of Stein's method. These are then used to obtain a rate of
distributional convergence for conjectured particle positions in the first
energy level above the ground state to the (two-sided) Maxwell distribution;
new techniques must be developed for this setting where the usual "density
approach" Stein solution (see Chatterjee and Shao (2011)) has a singularity.


title:
Dispersion and lineshape of plasmon satellites in one, two and three
  dimensions

abstract:
  Using state-of-the-art many-body Green's function calculations based on the
"GW plus cumulant" approach, we analyze the properties of plasmon satellites in
the electron spectral function resulting from electron-plasmon interactions in
one-, two- and three-dimensional systems. Specifically, we show how their
dispersion relation, lineshape and linewidth are related to the properties of
the constituent electrons and plasmons. To gain insight into the many-body
processes giving rise to the formation of plasmon satellites, we connect the
"GW plus cumulant" approach to a many-body wavefunction picture of
electron-plasmon interactions and introduce the coupling-strength weighted
electron-plasmon joint-density states as a powerful concept for understanding
plasmon satellites.


title: Equiangular Lines and Spherical Codes in Euclidean Space

abstract:
  A family of lines through the origin in Euclidean space is called equiangular
if any pair of lines defines the same angle. The problem of estimating the
maximum cardinality of such a family in $\mathbb{R}^n$ was extensively studied
for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973,
in this paper we prove that for every fixed angle $\theta$ and sufficiently
large $n$ there are at most $2n-2$ lines in $\mathbb{R}^n$ with common angle
$\theta$. Moreover, this is achievable only for $\theta = \arccos(1/3)$. We
also show that for any set of $k$ fixed angles, one can find at most $O(n^k)$
lines in $\mathbb{R}^n$ having these angles. This bound, conjectured by Bukh,
substantially improves the estimate of Delsarte, Goethals and Seidel from 1975.
Various extensions of these results to the more general setting of spherical
codes will be discussed as well.


title: Entanglement Classification with Algebraic Geometry

abstract:
  We approach multipartite entanglement classification in the symmetric
subspace in terms of algebraic geometry, its natural language. We show that the
class of symmetric separable states has the structure of a Veronese variety and
that its $k$-secant varieties are SLOCC invariants. Thus SLOCC classes gather
naturally into families. This classification presents useful properties such as
a linear growth of the number of families with the number of particles, and
nesting, i.e. upward consistency of the classification. We attach physical
meaning to this classification through the required interaction length of
parent Hamiltonians. We show that the states $W_N$ and GHZ$_N$ are in the same
secant family and that, effectively, the former can be obtained in a limit from
the latter. This limit is understood in terms of tangents, leading to a
refinement of the previous families. We compute explicitly the classification
of symmetric states with $N\leq 4$ qubits in terms of both secant families and
its refinement using tangents. This paves the way to further use of projective
varieties in algebraic geometry to solve open problems in entanglement theory.


title:
Question Relevance in VQA: Identifying Non-Visual And False-Premise
  Questions

abstract:
  Visual Question Answering (VQA) is the task of answering natural-language
questions about images. We introduce the novel problem of determining the
relevance of questions to images in VQA. Current VQA models do not reason about
whether a question is even related to the given image (e.g. What is the capital
of Argentina?) or if it requires information from external resources to answer
correctly. This can break the continuity of a dialogue in human-machine
interaction. Our approaches for determining relevance are composed of two
stages. Given an image and a question, (1) we first determine whether the
question is visual or not, (2) if visual, we determine whether the question is
relevant to the given image or not. Our approaches, based on LSTM-RNNs, VQA
model uncertainty, and caption-question similarity, are able to outperform
strong baselines on both relevance tasks. We also present human studies showing
that VQA models augmented with such question relevance reasoning are perceived
as more intelligent, reasonable, and human-like.


title:
An empirical study on large scale text classification with skip-gram
  embeddings

abstract:
  We investigate the integration of word embeddings as classification features
in the setting of large scale text classification. Such representations have
been used in a plethora of tasks, however their application in classification
scenarios with thousands of classes has not been extensively researched,
partially due to hardware limitations. In this work, we examine efficient
composition functions to obtain document-level from word-level embeddings and
we subsequently investigate their combination with the traditional
one-hot-encoding representations. By presenting empirical evidence on large,
multi-class, multi-label classification problems, we demonstrate the efficiency
and the performance benefits of this combination.


title: Schr\"oder partitions, Schr\"oder tableaux and weak poset patterns

abstract:
  We introduce the notions of Schr\"oder shape and of Schr\"oder tableau, which
provide some kind of analogs of the classical notions of Young shape and Young
tableau. We investigate some properties of the partial order given by
containment of Schr\"oder shapes. Then we propose an algorithm which is the
natural analog of the well known RS correspondence for Young tableaux, and we
characterize those permutations whose insertion tableaux have some special
shapes. The last part of the article relates the notion of Schr\"oder tableau
with those of interval order and of weak containment (and strong avoidance) of
posets. We end our paper with several suggestions for possible further work.


title: Tensor-based dynamic mode decomposition

abstract:
  Dynamic mode decomposition (DMD) is a recently developed tool for the
analysis of the behavior of complex dynamical systems. In this paper, we will
propose an extension of DMD that exploits low-rank tensor decompositions of
potentially high-dimensional data sets to compute the corresponding DMD modes
and eigenvalues. The goal is to reduce the computational complexity and also
the amount of memory required to store the data in order to mitigate the curse
of dimensionality. The efficiency of these tensor-based methods will be
illustrated with the aid of several different fluid dynamics problems such as
the von K\'arm\'an vortex street and the simulation of two merging vortices.


title: Effects of temporal correlations in social multiplex networks

abstract:
  Multi-layered networks represent a major advance in the description of
natural complex systems, and their study has shed light on new physical
phenomena. Despite its importance, however, the role of the temporal dimension
in their structure and function has not been investigated in much detail so
far. Here we study the temporal correlations between layers exhibited by real
social multiplex networks. At a basic level, the presence of such correlations
implies a certain degree of predictability in the contact pattern, as we
quantify by an extension of the entropy and mutual information analyses
proposed for the single-layer case. At a different level, we demonstrate that
temporal correlations are a signature of a 'multitasking' behavior of network
agents, characterized by a higher level of switching between different social
activities than expected in a uncorrelated pattern. Moreover, temporal
correlations significantly affect the dynamics of coupled epidemic processes
unfolding on the network. Our work opens the way for the systematic study of
temporal multiplex networks and we anticipate it will be of interest to
researchers in a broad array of fields.


title: Relativistic Stars in Beyond Horndeski Theories

abstract:
  This work studies relativistic stars in beyond Horndeski scalar-tensor
theories that exhibit a breaking of the Vainshtein mechanism inside matter,
focusing on a model based on the quartic beyond Horndeski Lagrangian. We
self-consistently derive the scalar field profile for static spherically
symmetric objects in asymptotically de Sitter space-time and show that the
Vainshtein breaking branch of the solutions is the physical branch thereby
resolving several ambiguities with non-relativistic frameworks. The geometry
outside the star is shown to be exactly Schwarzschild-de Sitter and therefore
the PPN parameter $\beta_{\rm PPN}=1$, confirming that the external screening
works at the post-Newtonian level. The Tolman-Oppenheimer-Volkoff (TOV)
equations are derived and a new lower bound on the Vainshtein breaking
parameter $\Upsilon_1>-4/9$ is found by requiring the existence of static
spherically symmetric stars. Focusing on the unconstrained case where
$\Upsilon_1<0$, we numerically solve the TOV equations for polytropic and
realistic equations of state and find stars with larger radii at fixed mass.
Furthermore, the maximum mass can increase dramatically and stars with masses
in excess of $3M_\odot$ can be found for relatively small values of the
Vainshtein breaking parameter. We re-examine white dwarf stars and show that
post-Newtonian corrections are important in beyond Horndeski theories and
therefore the bounds coming from previous analyses should be revisited.


title: Smooth varieties with torus actions

abstract:
  In this paper we provide a characterization of smooth algebraic varieties
endowed with a faithful algebraic torus action in terms of a combinatorial
description given by Altmann and Hausen. Our main result is that such a variety
X is smooth if and only if it is locally isomorphic in the \'etale topology to
the affine space endowed with a linear torus action. Furthermore, this is the
case if and only if the combinatorial data describing X is locally isomorphic
in the \'etale topology to the combinatorial data describing affine space
endowed with a linear torus action. Finally, we provide an effective method to
check the smoothness of a Gm-threefold in terms of the combinatorial data.


title: Parallel Galton Watson Process

abstract:
  In this paper, we study a parallel version of Galton-Watson processes for the
random generation of tree-shaped structures. Random trees are useful in many
situations (testing, binary search, simulation of physics phenomena,...) as
attests more than 49000 citations on Google scholar. Using standard analytic
combinatorics, we first give a theoretical, average-case study of the random
process in order to evaluate how parallelism can be extracted from this
process, and we deduce a parallel generation algorithm. Then we present how it
can be implemented in a task-based parallel paradigm for shared memory (here,
Intel Cilk). This implementation faces several challenges, among which
efficient, thread-safe random bit generation, memory management and algorithmic
modifications for small-grain parallelism. Finally, we evaluate the performance
of our implementation and the impact of different choices and parameters. We
obtain a significant efficiency improvement for the generation of big trees. We
also conduct empirical and theoretical studies of the average behaviour of our
algorithm.


title: On Multiplicative Integration with Recurrent Neural Networks

abstract:
  We introduce a general and simple structural design called Multiplicative
Integration (MI) to improve recurrent neural networks (RNNs). MI changes the
way in which information from difference sources flows and is integrated in the
computational building block of an RNN, while introducing almost no extra
parameters. The new structure can be easily embedded into many popular RNN
models, including LSTMs and GRUs. We empirically analyze its learning behaviour
and conduct evaluations on several tasks using different RNN models. Our
experimental results demonstrate that Multiplicative Integration can provide a
substantial performance boost over many of the existing RNN models.


title:
Classification of excited-state quantum phase transitions for arbitrary
  number of degrees of freedom

abstract:
  Classical stationary points of an analytic Hamiltonian induce singularities
of the density of quantum energy levels and their flow with a control parameter
in the system's infinite-size limit. We show that for a system with $f$ degrees
of freedom, a non-degenerate stationary point with index $r$ causes a
discontinuity (for $r$ even) or divergence ($r$ odd) of the $(f-1)$ th
derivative of both density and flow of the spectrum. An increase of flatness
for a degenerate stationary point shifts the singularity to lower derivatives.
The findings are verified in an $f=3$ toy model.


title:
String Theory in Polar Coordinates and the Vanishing of the One-Loop
  Rindler Entropy

abstract:
  We analyze the string spectrum of flat space in polar coordinates, following
the small curvature limit of the $SL(2,\mathbb{R})/U(1)$ cigar CFT. We first
analyze the partition function of the cigar itself, making some clarifications
of the structure of the spectrum that have escaped attention up to this point.
The superstring spectrum (type 0 and type II) is shown to exhibit an involution
symmetry, that survives the small curvature limit. We classify all marginal
states in polar coordinates for type II superstrings, with emphasis on their
links and their superconformal structure. This classification is confirmed by
an explicit large $\tau_2$ analysis of the partition function. Next we compare
three approaches towards the type II genus one entropy in Rindler space: using
a sum-over-fields strategy, using a Melvin model approach and finally using a
saddle point method on the cigar partition function. In each case we highlight
possible obstructions and motivate that the correct procedures yield a
vanishing result: $S=0$. We finally discuss how the QFT UV divergences of the
fields in the spectrum disappear when computing the free energy and entropy
using Euclidean techniques.


title:
Multi-scale detection of variance changes in renewal processes in the
  presence of rate change points

abstract:
  Non-stationarity of the rate or variance of events is a well-known problem in
the description and analysis of time series of events, such as neuronal spike
trains. A multiple filter test (MFT) for rate homogeneity has been proposed
earlier that detects change points on multiple time scales simultaneously. It
is based on a filtered derivative approach, and the rejection threshold derives
from a Gaussian limit process $L$ which is independent of the point process
parameters.
  Here we extend the MFT to variance homogeneity of life times. When the rate
is constant, the MFT extends directly to the null hypothesis of constant
variance. In the presence of rate change points, we propose to incorporate
estimates of these in the test for variance homogeneity, using an adaptation of
the test statistic. The resulting limit process shows slight deviations from
$L$ that depend on unknown process parameters. However, these deviations are
small and do not considerably change the properties of the statistical test.
This allows practical application, e.g.~to neuronal spike trains, which
indicates various profiles of rate and variance change points.


title: Rhythmic behavior in a two-population mean field Ising model

abstract:
  Many real systems comprised of a large number of interacting components, as
for instance neural networks , may exhibit collective periodic behavior even
though single components have no natural tendency to behave periodically.
Macroscopic oscillations are indeed one of the most common self-organized
behavior observed in living systems. In the present paper we study some
dynamical features of a two-population generalization of the mean field Ising
model with the scope of investigating simple mechanisms capable to generate
rhythm in large groups of interacting individuals. We show that the system may
undergo a transition from a disordered phase, where the magnetization of each
population fluctuates closely around zero, to a phase in which they both
display a macroscopic regular rhythm. In particular, there exists a region in
the parameter space where having two groups of spins with inter- and
intra-population interactions of different strengths suffices for the emergence
of a robust periodic behavior.

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


title: Simple regular black hole with logarithmic entropy correction

abstract:
  A simple regular black hole solution satisfying the weak energy condition is
obtained within Einstein--non--linear electrodynamics theory. We have computed
the thermodynamic properties of this black hole by a careful analysis of the
horizons and we have found that the usual Bekenstein--Hawking entropy gets
corrected by a logarithmic term. Therefore, in this sense our model realizes
some quantum gravity predictions which add this kind of correction to the black
hole entropy. In particular, we have established some similitudes between our
model and a quadratic generalized uncertainty principle. This similitude has
been confirmed by the existence of a remnant, which prevents complete
evaporation, in agreement with the quadratic generalized uncertainty principle
case.


title:
Intriguingly Simple and Efficient Time-Dependent Routing in Road
  Networks

abstract:
  We study the earliest arrival problem in road networks with static
time-dependent functions as arc weights. We propose and evaluate the following
simple algorithm: (1) average the travel time in k time windows, (2) compute a
shortest time-independent path within each window and mark the edges in these
paths, and (3) compute a shortest time-dependent path in the original graph
restricted to the marked edges. Our experimental evaluation shows that this
simple algorithm yields near optimal results on well-established benchmark
instances. We additionally demonstrate that the error can be further reduced by
additionally considering alternative routes at the expense of more marked
edges. Finally, we show that the achieved subgraphs are small enough to be able
to efficiently implement profile queries using a simple sampling-based
approach. A highlight of our introduced algorithms is that they do not rely on
linking and merging profile functions.


title: A solvable double well

abstract:
  We study the quantum behaviour of a particle moving in a one-dimensional
double well potential. This double well is obtained by gluing together, at the
origin, two shifted harmonic oscillator potentials. The Schr\"odinger equation
is exactly solvable. The requirement that discontinuities, in the wavefunction
and its first derivative, are absent at the origin, leads to the quantisation
of the energy eigenvalues. We also show that oscillations in time take place
between two nearby single harmonic oscillator ground states. Finally, the
double well potential is augmented by a Dirac delta-function potentials at the
origin and the corresponding Schr\"odinger equation is solved.