title:
The distribution of maximal prime gaps in Cramer's probabilistic model
  of primes

abstract:
  In the framework of Cramer's probabilistic model of primes, we explore the
exact and asymptotic distributions of maximal prime gaps. We show that the
Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal
gaps between Cramer's random primes. The result can be derived from a general
theorem about intervals between discrete random events occurring with slowly
varying probability monotonically decreasing to zero. A straightforward
generalization extends the Gumbel limit law to maximal gaps between prime
constellations in Cramer's model.


title: Formation of subhorizon black holes from preheating

abstract:
  We study the production of primordial black holes (PBHs) during the
preheating stage that follows a chaotic inflationary phase. The scalar fields
present in the process are evolved numerically using a modified version of the
HLATTICE code. From the output of the numerical simulation, we compute the
probability distribution of curvature fluctuations, paying particular attention
to sub-horizon scales. We find that in some specific models these modes grow to
large amplitudes developing highly non-Gaussian probability distributions. We
then calculate PBH abundances using the standard Press-Schechter criterion and
find that overproduction of PBHs is likely in some regions of the chaotic
preheating parameter space.


title: An N-Body Solution to the Problem of Fock Exchange

abstract:
  We report an N-Body approach to computing the Fock exchange matrix with and
without permutational symmetry. The method achieves an O(N lg N) computational
complexity through an embedded metric-query, allowing hierarchical application
of direct SCF criteria. The advantages of permutational symmetry are found to
be 4-fold for small systems, but decreasing with increasing system size and/or
more permissive neglect criteria. This work sets the stage for: (1) the
introduction of range queries in multi-level multipole schemes for rank
reduction, and (2) recursive task parallelism.


title:
Compressive Classification of a Mixture of Gaussians: Analysis, Designs
  and Geometrical Interpretation

abstract:
  This paper derives fundamental limits on the performance of compressive
classification when the source is a mixture of Gaussians. It provides an
asymptotic analysis of a Bhattacharya based upper bound on the
misclassification probability for the optimal Maximum-A-Posteriori (MAP)
classifier that depends on quantities that are dual to the concepts of
diversity-order and coding gain in multi-antenna communications. The
diversity-order of the measurement system determines the rate at which the
probability of misclassification decays with signal-to-noise ratio (SNR) in the
low-noise regime. The counterpart of coding gain is the measurement gain which
determines the power offset of the probability of misclassification in the
low-noise regime. These two quantities make it possible to quantify differences
in misclassification probability between random measurement and
(diversity-order) optimized measurement. Results are presented for two-class
classification problems first with zero-mean Gaussians then with nonzero-mean
Gaussians, and finally for multiple-class Gaussian classification problems. The
behavior of misclassification probability is revealed to be intimately related
to certain fundamental geometric quantities determined by the measurement
system, the source and their interplay. Numerical results, representative of
compressive classification of a mixture of Gaussians, demonstrate alignment of
the actual misclassification probability with the Bhattacharya based upper
bound. The connection between the misclassification performance and the
alignment between source and measurement geometry may be used to guide the
design of dictionaries for compressive classification.


title: Optimal Spread in Network Consensus Models

abstract:
  In a model of network communication based on a random walk in an undirected
graph, what subset of nodes (subject to constraints on the set size), enable
the fastest spread of information? The dynamics of spread is described by a
process dual to the movement from informed to uninformed nodes. In this
setting, an optimal set $A$ minimizes the sum of the expected first hitting
times $F(A)$, of random walks that start at nodes outside the set.
  In this paper,the problem is reformulated so that the search for solutions is
restricted to a class of optimal and "near" optimal subsets of the graph. We
introduce a submodular, non-decreasing rank function $\rho$, that permits some
comparison between the solution obtained by the classical greedy algorithm and
one obtained by our methods. The supermodularity and non-increasing properties
of $F$ are used to show that the rank of our solution is at least
$(1-\frac{1}{e})$ times the rank of the optimal set. When the solution has a
higher rank than the greedy solution this constant can be improved to
$(1-\frac{1}{e})(1+\chi)$ where $\chi >0$ is determined a posteriori. The
method requires the evaluation of $F$ for sets of some fixed cardinality $m$,
where $m$ is much smaller than the cardinality of the optimal set. When $F$ has
forward elemental curvature $\kappa$, we can provide a rough description of the
trade-off between solution quality and computational effort $m$ in terms of
$\kappa$.


title:
Co-Evolution of Friendship and Publishing in Online Blogging Social
  Networks

abstract:
  In the past decade, blogging web sites have become more sophisticated and
influential than ever. Much of this sophistication and influence follows from
their network organization. Blogging social networks (BSNs) allow individual
bloggers to form contact lists, subscribe to other blogs, comment on blog
posts, declare interests, and participate in collective blogs. Thus, a BSN is a
bimodal venue, where users can engage in publishing (post) as well as in social
(make friends) activities. In this paper, we study the co-evolution of both
activities. We observed a significant positive correlation between blogging and
socializing. In addition, we identified a number of user archetypes that
correspond to "mainly bloggers," "mainly socializers," etc. We analyzed a BSN
at the level of individual posts and changes in contact lists and at the level
of trajectories in the friendship-publishing space. Both approaches produced
consistent results: the majority of BSN users are passive readers; publishing
is the dominant active behavior in a BSN; and social activities complement
blogging, rather than compete with it.


title:
The long-term post-outburst spin down and flux relaxation of magnetar
  Swift J1822.3$-$1606

abstract:
  The magnetar Swift J1822.3$-$1606 entered an outburst phase in 2011 July.
Previous X-ray studies of its post-outburst rotational evolution yielded
inconsistent measurements of the spin-inferred magnetic field. Here we present
the timing behavior and flux relaxation from over two years of Swift, XTE, and
Chandra observations following the outburst. We find that the ambiguity in
previous timing solutions was due to enhanced spin down that resembles an
exponential recovery following a glitch at the outburst onset. After fitting
out the effects of the recovery, we measure a long-term spin-down rate of
$\dot\nu=(-3.0\pm0.3)\times10^{-8}$ s$^{-2}$ which implies a dipolar magnetic
field of $1.35\times10^{13}$ G, lower than all previous estimates for this
source. We also consider the post-outburst flux evolution, and fit it with both
empirical and crustal cooling models. We discuss the flux relaxation in the
context of both crustal cooling and magnetospheric relaxation models.


title:
3D particle-in-cell simulation of electron acceleration by Langmuir
  waves in an inhomogeneous plasma

abstract:
  A possible solution to the unexplained high intensity hard x-ray (HXR)
emission observable during solar flares was investigated via 3D fully
relativistic, electromagnetic particle-in-cell (PIC) simulations with realistic
ion to electron mass ratio. A beam of accelerated electrons was injected into a
magnetised, Maxwellian, homogeneous and inhomogeneous background plasma. The
electron distribution function was unstable to the beam-plasma instability and
was shown to generate Langmuir waves, while relaxing to plateau formation. In
order to estimate the role of the background density gradient on an unbound
(infinite spatial extent) beam, three different scenarios were investigated: a)
a uniform density background; b) a weak density gradient, n_R/n_L=3; c) a
strong gradient case, n_R/n_L=10, where n_R and n_L denote background electron
densities on the left and right edges of the simulation box respectively. The
strong gradient case produced the largest fraction of electrons beyond 15 v_th.
Further, two cases (uniform and strong gradient background) with spatially
localized beam injections were performed aiming to show drifts of the generated
Langmuir wave wavenumbers, as suggested in previous studies. For the strong
gradient case, the Langmuir wave power is shown to drift to smaller
wavenumbers, as found in previous quasi-linear simulations.


title: How much weigh a pound in gravitational field

abstract:
  The force in the equation of motion of a particle should be in accordance
with energy conservation in a constant gravitational field. It turns out that
this is possible only if the force is given by the change of momentum per unit
of coordinate (not proper) time. We discuss the consequences of this fact. In
particular it turns out that the spring balance, which keeps the body at rest
in (strong) gravitation field, shows the finite value even at infinitely close
approach to horizons of black holes, if they exist in Nature.


title: Fixed-rank Rayleigh Quotient Maximization by an $M$PSK Sequence

abstract:
  Certain optimization problems in communication systems, such as
limited-feedback constant-envelope beamforming or noncoherent $M$-ary
phase-shift keying ($M$PSK) sequence detection, result in the maximization of a
fixed-rank positive semidefinite quadratic form over the $M$PSK alphabet. This
form is a special case of the Rayleigh quotient of a matrix and, in general,
its maximization by an $M$PSK sequence is $\mathcal{NP}$-hard. However, if the
rank of the matrix is not a function of its size, then the optimal solution can
be computed with polynomial complexity in the matrix size. In this work, we
develop a new technique to efficiently solve this problem by utilizing
auxiliary continuous-valued angles and partitioning the resulting continuous
space of solutions into a polynomial-size set of regions, each of which
corresponds to a distinct $M$PSK sequence. The sequence that maximizes the
Rayleigh quotient is shown to belong to this polynomial-size set of sequences,
thus efficiently reducing the size of the feasible set from exponential to
polynomial. Based on this analysis, we also develop an algorithm that
constructs this set in polynomial time and show that it is fully
parallelizable, memory efficient, and rank scalable. The proposed algorithm
compares favorably with other solvers for this problem that have appeared
recently in the literature.


title:
Room-temperature vibrational properties of multiferroic MnWO4 under
  quasi-hydrostatic compression up to 39 GPa

abstract:
  The multiferroic manganese tungstate (MnWO4) has been studied by
high-pressure Raman spectroscopy at room temperature under quasi-hydrostatic
conditions up to 39.3 GPa. The low-pressure wolframite phase undergoes a phase
transition at 25.7 GPa, a pressure around 8 GPa higher than that found in
previous works which used less hydrostatic pressure-transmitting media. The
pressure dependence of the Raman active modes of both the low- and
high-pressure phases are reported and discussed comparing with the results
available in the literature for MnWO4 and related wolframites. A gradual
pressure-induced phase transition from the low- to the high- pressure phase is
suggested on the basis of the linear intensity decrease of the Raman mode with
the lowest frequency up to the end of the phase transition.


title:
Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of
  strings

abstract:
  The Lagrangian description of mechanical systems and the Legendre
Transformation (considered as a passage from the Lagrangian to the Hamiltonian
formulation of the dynamics) for point-like objects, for which the
infinitesimal configuration space is TM, is based on the existence of canonical
symplectic isomorphisms of double vector bundles T*TM, T*TM, and TT*M. We show
that there exist an analogous picture in the dynamics of objects for which the
configuration space is the vector bundle of n-vectors, if we make use of
certain graded bundle structures of degree n, i.e. objects generalizing vector
bundles (for which n=1). For instance, the role of TT*M is played in our
approach by the vector bundle of n-vectors on the bundle of n-covectors, which
is canonically a graded bundle of degree n over the bundle of n-vectors.
Dynamics of strings and the Plateau problem in statics are particular cases of
this framework.


title:
Performance Analysis of Spin Transfer Torque Random Access Memory with
  cross shaped free layer using Heusler Alloys by using micromagnetic studies

abstract:
  We investigated the performance of spin transfer torque random access memory
(STT-RAM) cell with cross shaped Heusler compound based free layer using
micromagnetic simulations. We designed the free layer using Cobalt based
Heusler compounds. Here in this paper, simulation results predict that
switching time from one state to other state is reduced. Also it is examined
that critical switching current density to switch the magnetization of free
layer of STT RAM cell is reduced.


title: Holographic Chiral Electric Separation Effect

abstract:
  We investigate the chiral electric separation effect, where an axial current
is induced by an electric field in the presence of both vector and axial
chemical potentials, in a strongly coupled plasma via the Sakai-Sugimoto model
with an $U(1)_R\times U(1)_L$ symmetry. By introducing different chemical
potentials in $U(1)_R$ and $U(1)_L$ sectors, we compute the axial direct
current (DC) conductivity stemming from the chiral current and the normal DC
conductivity. We find that the axial conductivity is approximately proportional
to the product of the axial and vector chemical potentials for arbitrary
magnitudes of the chemical potentials. We also evaluate the axial alternating
current (AC) conductivity induced by a frequency-dependent electric field,
where the oscillatory behavior with respect to the frequency is observed.


title:
On the non-locality of tripartite non-signaling boxes emerging from
  wirings

abstract:
  It has been recently shown, that some of the tripartite boxes admitting
bilocal decomposition, lead to non-locality under wiring operation applied to
two of the subsystems [R. Gallego et al. Physical Review Letters 109, 070401
(2012)]. In the following, we study this phenomenon quantitatively. Basing on
the known classes of boxes closed under wirings, we introduced multipartite
monotones which are counterparts of bipartite ones - the non-locality cost and
robustness of non-locality. We then provide analytical lower bounds on both the
monotones in terms of the Maximal Non-locality which can be obtained by Wirings
(MWN). We prove also upper bounds for the MWN of a given box, based on the
weight of boxes signaling in a particular direction, that appear in its bilocal
decomposition. We study different classes of partially local boxes and find MWN
for each class, using Linear Programming. We identify also the wirings which
lead to MWN and exhibit that some of them can serve as a witness of certain
classes. We conclude with example of partially local boxes being analogue of
quantum states that allow to distribute entanglement in separable manner.


title:
Fermions in a Reissner-Nordstr\"{o}m-anti-de Sitter Black Hole
  Background and $N=4$ Supersymmetry with non-trivial Topological Charges

abstract:
  We demonstrate that the fermions in Reissner-Nordstr\"{o}m-anti-de Sitter
black hole background in the chiral limit $m=0$, are related to an $N=4$
extended one dimensional supersymmetry with non-trivial topological charges. We
also show that the $N=4$ extended supersymmetry is unbroken and we extend the
two $N=2$ one dimensional supersymmetries that the system also possess, to have
a trivial central charge. The implications of the trivial central charge on the
Witten index are also discussed.


title: A decoding algorithm for CSS codes using the X/Z correlations

abstract:
  We propose a simple decoding algorithm for CSS codes taking into account the
correlations between the X part and the Z part of the error. Applying this idea
to surface codes, we derive an improved version of the perfect matching
decoding algorithm which uses these X/Z correlations.


title: Blowup solutions of Jang's equation near a spacetime singularity

abstract:
  We study Jang's equation on a one-parameter family of asymptotically flat,
spherically symmetric Cauchy hypersurfaces in the maximally extended
Schwarzschild spacetime. The hypersurfaces contain apparent horizons and are
parametrized by their proximity to the singularity at $r = 0$. We show that on
those hypersurfaces sufficiently close to the singularity, every radial
solution to Jang's equation blows up. The proof depends only on the geometry in
an arbitrarily small neighborhood of the singularity, suggesting that Jang's
equation is in fact detecting the singularity. We comment on possible
applications to the weak cosmic censorship conjecture.


title: Electron screening effects on crustal torsional oscillations

abstract:
  We systematically examine the crustal torsional oscillations as varying the
stellar mass and radius, where we take into account the effect of electron
screening due to the inhomogeneity of electron distribution. In the
examinations, we adopt two different equations of state (EOSs) for the inner
crust region of neutron stars. As a result, we find that the frequencies depend
obviously on the EOS, even if the neutron star models are almost independent of
the EOS. That is, one could solve the degeneracy of the stellar models with
different EOS via the observations of shear oscillations frequencies.
Additionally, we find that the fundamental frequencies of the $l$-th order
torsional oscillations can reduce 6% due to the effect of electron screening,
which is independent of the adopted EOS and stellar models. This reduction of
frequencies can be crucial to make a constraints on the density dependence of
the nuclear symmetry energy, $L$, i.e., the constraint on $L$ can reduce ~15%
by the electron screening effect.


title: Sparsistency and agnostic inference in sparse PCA

abstract:
  The presence of a sparse "truth" has been a constant assumption in the
theoretical analysis of sparse PCA and is often implicit in its methodological
development. This naturally raises questions about the properties of sparse PCA
methods and how they depend on the assumption of sparsity. Under what
conditions can the relevant variables be selected consistently if the truth is
assumed to be sparse? What can be said about the results of sparse PCA without
assuming a sparse and unique truth? We answer these questions by investigating
the properties of the recently proposed Fantope projection and selection (FPS)
method in the high-dimensional setting. Our results provide general sufficient
conditions for sparsistency of the FPS estimator. These conditions are weak and
can hold in situations where other estimators are known to fail. On the other
hand, without assuming sparsity or identifiability, we show that FPS provides a
sparse, linear dimension-reducing transformation that is close to the best
possible in terms of maximizing the predictive covariance.


title:
Correlation Functions of the Schur Process Through Macdonald Difference
  Operators

abstract:
  Introduced by Okounkov and Reshetikhin, the Schur process is known to be a
determinantal point process, meaning that its correlation functions are minors
of a single correlation kernel matrix. Previously, this was derived using
determinantal expressions for the skew-Schur polynomials. In this paper we
obtain this result in a different way, using the fact that the Schur
polynomials are eigenfunctions of Macdonald difference operators.


title:
Gaussian decay for a difference of traces of the Schr\"odinger semigroup
  associated to the isotropic harmonic oscillator

abstract:
  This paper deals with the derivation of a sharp estimate on the difference of
traces of the one-parameter Schr\"odinger semigroup associated to the quantum
isotropic harmonic oscillator. Denoting by $H_{\infty,\kappa}$ the self-adjoint
realization in $L^{2}(\mathbb{R}^{d})$, $d \in \{1,2,3\}$ of the Schr\"odinger
operator $-\frac{1}{2} \Delta + \frac{1}{2} \kappa^{2}\vert \bold{x}\vert^{2}$,
$\kappa>0$ and by $H_{L,\kappa}$, $L>0$ the Dirichlet realization in
$L^{2}(\Lambda_{L}^{d})$ where $\Lambda_{L}^{d}:=\{\bold{x} \in
\mathbb{R}^{d}:- \frac{L}{2} < x_{l} < \frac{L}{2},\,l=1,\ldots,d\}$, we prove
that the difference of traces $\mathrm{Tr}_{L^{2}(\mathbb{R}^{d})}
\mathrm{e}^{-t H_{\infty,\kappa}} -
\mathrm{Tr}_{L^{2}(\Lambda_{L}^{d})}\mathrm{e}^{-t H_{L,\kappa}}$, $t>0$ has
for $L$ sufficiently large a Gaussian decay in $L$. Furthermore, the estimate
that we derive is sharp in the two following senses: its behavior when $t
\downarrow 0$ is similar to the one given by
$\mathrm{Tr}_{L^{2}(\mathbb{R}^{d})}\ mathrm{e}^{-t H_{\infty,\kappa}} =
(2\sinh( \frac{\kappa}{2}t))^{-d}$ and the exponential decay in $t$ arising
from $\mathrm{Tr}_{L^{2}(\mathbb{R}^{d})}\mathrm{e}^{-t H_{\infty,\kappa}}$
when $t\uparrow \infty$ is preserved. For illustrative purposes, we give a
simple application within the framework of quantum statistical mechanics.


title: Scalable Online Betweenness Centrality in Evolving Graphs

abstract:
  Betweenness centrality is a classic measure that quantifies the importance of
a graph element (vertex or edge) according to the fraction of shortest paths
passing through it. This measure is notoriously expensive to compute, and the
best known algorithm runs in O(nm) time. The problems of efficiency and
scalability are exacerbated in a dynamic setting, where the input is an
evolving graph seen edge by edge, and the goal is to keep the betweenness
centrality up to date. In this paper we propose the first truly scalable
algorithm for online computation of betweenness centrality of both vertices and
edges in an evolving graph where new edges are added and existing edges are
removed. Our algorithm is carefully engineered with out-of-core techniques and
tailored for modern parallel stream processing engines that run on clusters of
shared-nothing commodity hardware. Hence, it is amenable to real-world
deployment. We experiment on graphs that are two orders of magnitude larger
than previous studies. Our method is able to keep the betweenness centrality
measures up to date online, i.e., the time to update the measures is smaller
than the inter-arrival time between two consecutive updates.


title: Damage detection via shortest path network sampling

abstract:
  Large networked systems are constantly exposed to local damages and failures
that can alter their functionality. The knowledge of the structure of these
systems is however often derived through sampling strategies whose
effectiveness at damage detection has not been thoroughly investigated so far.
Here we study the performance of shortest path sampling for damage detection in
large scale networks. We define appropriate metrics to characterize the
sampling process before and after the damage, providing statistical estimates
for the status of nodes (damaged, not-damaged). The proposed methodology is
flexible and allows tuning the trade-off between the accuracy of the damage
detection and the number of probes used to sample the network. We test and
measure the efficiency of our approach considering both synthetic and real
networks data. Remarkably, in all the systems studied the number of correctly
identified damaged nodes exceeds the number false positives allowing to uncover
precisely the damage.


title: A Model Structure for Enriched Coloured Operads

abstract:
  We prove that, under certain conditions, the model structure on a monoidal
model category $\mathcal{V}$ can be transferred to a model structure on the
category of $\mathcal{V}$-enriched coloured (symmetric) operads. As a
particular case we recover the known model structure on simplicial operads.


title: Kaldi+PDNN: Building DNN-based ASR Systems with Kaldi and PDNN

abstract:
  The Kaldi toolkit is becoming popular for constructing automated speech
recognition (ASR) systems. Meanwhile, in recent years, deep neural networks
(DNNs) have shown state-of-the-art performance on various ASR tasks. This
document describes our open-source recipes to implement fully-fledged DNN
acoustic modeling using Kaldi and PDNN. PDNN is a lightweight deep learning
toolkit developed under the Theano environment. Using these recipes, we can
build up multiple systems including DNN hybrid systems, convolutional neural
network (CNN) systems and bottleneck feature systems. These recipes are
directly based on the Kaldi Switchboard 110-hour setup. However, adapting them
to new datasets is easy to achieve.


title:
Regular Bulk Solutions and Black Strings from Dynamical Braneworlds with
  Variable Tension

abstract:
  Regular black strings solutions associated to a dynamical
Friedmann-Robertson-Walker braneworld are obtained as a particular case of a
regular bulk metric, in the context of a variable brane tension. By analyzing
the 5D Kretschmann invariants, we show that the variable brane tension is
capable to remove bulk singularities, along some eras of the evolution of the
Universe. In particular, the black string time-dependent profile in the bulk is
analyzed in the context of the McVittie metric on an E\"otv\"os fluid
braneworld, wherein the fluid dynamical brane tension depends on the brane
temperature. The whole bulk is shown to be regular for a Universe dominated by
non-relativistic matter or by relativistic matter/radiation, as the
cosmological time elapses. In a particular case the associated black strings
are shown to have finite extension along the extra dimension, what prominently
modify the higher-dimensional physical singularities. For a Universe dominated
by matter or radiation, we show that the brane singularities are removed along
the extra dimension, as an effect of the variable brane tension, corresponding
also to the vanishing of the black string horizon. In this case there is a
regular solution in the bulk. We show further that no additional physical
singularity is introduced in the bulk when the Universe is dominated by a
cosmological constant.


title:
First results from the CALYPSO IRAM-PdBI survey. I. Kinematics of the
  inner envelope of NGC1333-IRAS2A

abstract:
  The structure and kinematics of Class 0 protostars on scales of a few hundred
AU is poorly known. Recent observations have revealed the presence of Keplerian
disks with a diameter of 150-180 AU in L1527-IRS and VLA1623A, but it is not
clear if such disks are common in Class 0 protostars. Here we present
high-angular-resolution observations of two methanol lines in NGC1333-IRAS2A.
We argue that these lines probe the inner envelope, and we use them to study
the kinematics of this region. Our observations suggest the presence of a
marginal velocity gradient normal to the direction of the outflow. However, the
position velocity diagrams along the gradient direction appear inconsistent
with a Keplerian disk. Instead, we suggest that the emission originates from
the infalling and perhaps slowly rotating envelope, around a central protostar
of 0.1-0.2 M$_\odot$. If a disk is present, it is smaller than the disk of
L1527-IRS, perhaps suggesting that NGC1333-IRAS2A is younger.


title:
Energy Spectrum of Cosmic Protons and Helium Nuclei by a Hybrid
  Measurement at 4300 m a.s.l

abstract:
  The energy spectrum of cosmic Hydrogen and Helium nuclei has been measured,
below the so-called "knee", by using a hybrid experiment with a wide
field-of-view Cherenkov telescope and the Resistive Plate Chamber (RPC) array
of the ARGO-YBJ experiment at 4300 m above sea level. The Hydrogen and Helium
nuclei have been well separated from other cosmic ray components by using a
multi-parameter technique. A highly uniform energy resolution of about 25% is
achieved throughout the whole energy range (100 TeV - 700 TeV). The observed
energy spectrum is compatible with a single power law with index
gamma=-2.63+/-0.06.


title: Criptografia com Curvas El\'ipticas

abstract:
  This paper presents an overview of the use of elliptic curves in
cryptography. The security of this cryptosystem is based on the discrete
logarithm problem, which appears to be much harder compared to the discrete
logarithm problem in other cryptosystems. An overview of common cryptosystems
is given, such as Diffie-Hellman and RSA, and an elliptic curve cryptography
scheme is discussed.
  --------
  Este trabalho apresenta o uso das curvas el\'ipticas em criptografia. Sua
seguran\c{c}a est\'a baseada no problema do logaritmo discreto. Este problema
aparentemente \'e significativamente mais dif\'icil de resolver, comparado com
o problema do logaritmo discreto usado por outros sistemas de criptografia. \'E
dada uma vis\~ao geral de sistemas de criptografia comuns, como Diffie-Hellman
e RSA, e discute-se um esquema de criptografia usando curvas el\'ipticas.


title: Torsion homology growth and cycle complexity of arithmetic manifolds

abstract:
  Let M be an arithmetic hyperbolic 3-manifold, such as a Bianchi manifold. We
conjecture that there is a basis for the second homology of M, where each basis
element is represented by a surface of `low' genus, and give evidence for this.
We explain the relationship between this conjecture and the study of torsion
homology growth.


title: Ultra low noise YBCO nanoSQUIDs implementing nanowires

abstract:
  We present results on ultra low noise YBa$_2$Cu$_3$O$_{7-\delta}$ nano
Superconducting QUantum Interference Devices (nanoSQUIDs). To realize such
devices, we implemented high quality YBCO nanowires, working as weak links
between two electrodes. We observe critical current modulation as a function of
an externally applied magnetic field in the full temperature range below the
transition temperature $T_C$. The white flux noise below 1 $\mu
\Phi_0/\sqrt{\mathrm{Hz}}$ at T = 8 K makes our nanoSQUIDs very attractive for
the detection of small spin systems.


title:
Lie group analysis of a generalized Krichever-Novikov
  differential-difference equation

abstract:
  The symmetry algebra of the differential--difference equation $$\dot u_n =
[P(u_n)u_{n+1}u_{n-1} + Q(u_n)(u_{n+1}+u_{n-1})+ R(u_n)]/(u_{n+1}-u_{n-1}),$$
where $P$, $Q$ and $R$ are arbitrary analytic functions is shown to have the
dimension $1 \le \mbox{dim}L \le 5$. When $P$, $Q$ and $R$ are specific second
order polynomials in $u_n$ (depending on 6 constants) this is the integrable
discretization of the Krichever--Novikov equation. We find 3 cases when the
arbitrary functions are not polynomials and the symmetry algebra satisfies
$\mbox{dim}L=2$. These cases are shown not to be integrable. The symmetry
algebras are used to reduce the equations to purely difference ones. The
symmetry group is also used to impose periodicity $u_{n+N}=u_n$ and thus to
reduce the differential--difference equation to a system of $N$ coupled
ordinary three points difference equations.


title:
Size of dot product sets determined by pairs of subsets of vector spaces
  over finite fields

abstract:
  In this paper we study the cardinality of the dot product set generated by
two subsets of vector spaces over finite fields. We notice that the results on
the dot product problems for one set can be simply extended to two sets. Let E
and F be subsets of the d-dimensional vector space F_q^d over a finite field
F_q with q elements. As a new result, we prove that if E and F are subsets of
the paraboloid and |E||F|\geq C q^d for some large C>1, then |\Pi(E,F)|\geq c q
for some 0<c<1. In particular, we find a connection between the size of the dot
product set and the number of lines through both the origin and a nonzero point
in the given set E. As an application of this observation, we obtain more
sharpened results on the generalized dot product set problems. The discrete
Fourier analysis and geometrical observation play a crucial role in proving our
results.


title:
Relativistic quasiparticle self-consistent electronic structure of
  hybrid halide perovskite photovoltaic absorbers

abstract:
  Solar cells based on a light absorbing layer of the organometal halide
perovskite CH$_3$NH$_3$PbI$_3$ have recently reached 15% conversion efficiency,
though how these materials work remains largely unknown. We analyse the
electronic structure and optical properties within the quasiparticle
self-consistent GW approximation. While this compound bears some similarity to
conventional sp semiconductors, it also displays unique features. Quasiparticle
self-consistency is essential for an accurate description of the band
structure: bandgaps are much larger than what is predicted by the local density
approximation (LDA) or GW based on the LDA. Valence band dispersions are
modified in a very unusual manner. In addition, spin orbit coupling strongly
modifies the band structure and gives rise to unconventional dispersion
relations and a Dresselhaus splitting at the band edges. The average hole mass
is small, which accounts for the long diffusion lengths recently observed. The
surface ionisation potential (workfunction) is calculated to be 5.7 eV with
respect to the vacuum level, explaining efficient carrier transfer to TiO$_2$
and Au electrical contacts.


title:
$L^2$-error estimates for finite element approximations of boundary
  fluxes

abstract:
  We prove quasi-optimal a priori error estimates for finite element
approximations of boundary normal fluxes in the $L^2$-norm. Our results are
valid for a variety of different schemes for weakly enforcing Dirichlet
boundary conditions including Nitsche's method, and Lagrange multiplier
methods. The proof is based on an error representation formula that is derived
by using a discrete dual problem with $L^2$-Dirichlet boundary data and
combines a weighted discrete stability estimate for the dual problem with
anisotropic interpolation estimates in the boundary zone.


title: What is needed to accept the new explanation of DAMA results

abstract:
  The DAMA experiment clearly observes a small oscillatory signal. The observed
yearly modulation is in phase with the Earth's motion around the Sun. Recent
reference [Vavra, 2014] suggested that the DAMA experiment observes a WIMP of
much smaller mass than what Xenon 10, Xenon 100, LUX and CDMS experiments can
possibly reach. Scattering would occur on proton or oxygen target present in
the NaI(Tl) crystal as OH-contamination at a few ppm level. This paper
elaborates further on the idea that the OH-molecule could act as a very
sensitive detection mechanism for neutrons or WIMPs, and suggests a calibration
procedure to prove this idea. We also propose a new detector concept to detect
a low mass WIMP.


title: Two Lectures On The Jones Polynomial And Khovanov Homology

abstract:
  In the first of these two lectures, I describe a gauge theory approach to
understanding quantum knot invariants as Laurent polynomials in a complex
variable q. The two main steps are to reinterpret three-dimensional
Chern-Simons gauge theory in four dimensional terms and then to apply
electric-magnetic duality. The variable q is associated to instanton number in
the dual description in four dimensions. In the second lecture, I describe how
Khovanov homology can emerge upon adding a fifth dimension. (Based on lectures
presented at the Clay Research Conference at Oxford University, and also at the
Galileo Galilei Institute in Florence, the University of Milan, Harvard
University, and the University of Pennsylvania.)


title:
Weak version of restriction estimates for spheres and paraboloids in
  finite fields

abstract:
  We study L^p-L^r restriction estimates for algebraic varieties in
d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if
the dimension $d$ is even, then it is conjectured that the L^{(2d+2)/(d+3)}-L^2
Stein-Tomas restriction result can be improved to the L^{(2d+4)/(d+4)}-L^2
estimate for both spheres and paraboloids in finite fields. In this paper we
show that the conjectured L^p-L^2 restriction estimate holds in the specific
case when test functions under consideration are restricted to d-coordinate
functions or homogeneous functions of degree zero. To deduce our result, we use
the connection between the restriction phenomena for our varieties in $d$
dimensions and those for homogeneous varieties in (d+1)dimensions.


title:
First results from the CALYPSO IRAM-PdBI survey. II. Resolving the hot
  corino in the Class 0 protostar NGC 1333-IRAS2A

abstract:
  We investigate the origin of complex organic molecules (COMs) in the gas
phase around the low-mass Class~0 protostar NGC1333-IRAS2A, to determine if the
COM emission lines trace an embedded disk, shocks from the protostellar jet, or
the warm inner parts of the protostellar envelope. In the framework of the
CALYPSO (Continuum And Lines in Young ProtoStellar Objects) IRAM Plateau de
Bure survey, we obtained large bandwidth spectra at sub-arcsecond resolution
towards NGC 1333-IRAS2A. We identify the emission lines towards the central
protostar and perform Gaussian fits to constrain the size of the emitting
region for each of these lines, tracing various physical conditions and scales.
The emission of numerous COMs such as methanol, ethylene glycol, and methyl
formate is spatially resolved by our observations. This allows us to measure,
for the first time, the size of the COM emission inside the protostellar
envelope, finding that it originates from a region of radius 40-100 AU,
centered on the NGC 1333-IRAS2A protostellar object. Our analysis shows no
preferential elongation of the COM emission along the jet axis, and therefore
does not support the hypothesis that COM emission arises from shocked envelope
material at the base of the jet. Down to similar sizes, the dust continuum
emission is well reproduced with a single envelope model, and therefore does
not favor the hypothesis that COM emission arises from the thermal sublimation
of grains embedded in a circumstellar disk. Finally, the typical scale $\sim$60
AU observed for COM emission is consistent with the size of the inner envelope
where $T_{\rm{dust}} > 100$ K is expected. Our data therefore strongly suggest
that the COM emission traces the hot corino in IRAS2A, i.e., the warm inner
envelope material where the icy mantles of dust grains evaporate because they
are passively heated by the central protostellar object.


title:
Synchronization of two coupled multimode oscillators with time-delayed
  feedback

abstract:
  Effects of synchronization in a system of two coupled oscillators with
time-delayed feedback are investigated. Phase space of a system with time delay
is infinite-dimensional. Thus, the picture of synchronization in such systems
acquires many new features not inherent to finite-dimensional ones. A picture
of oscillation modes in cases of identical and non-identical coupled
oscillators is studied in detail. Periodical structure of amplitude death and
"broadband synchronization" zones is investigated. Such a behavior occurs due
to the resonances between different modes of the infinite-dimensional system
with time delay.


title: Uniqueness of Eigenforms on Fractals-II

abstract:
  I give an explicitly verifiable necessary and sufficient condition for the
uniqueness of the eigenform on finitely ramified fractals, once an eigenform is
known. This improves the results of my previous paper [14], where I gave some
necessary and some sufficient conditions, and with a relatively mild additional
requirement on the known eigenform. The result of this paper can be interpreted
as a uniqueness result for self-similar energies on the fractal.


title:
A modified $\chi^2$-test for uplift models with applications in
  marketing performance measurement

abstract:
  Uplift, essentially being the difference between two probabilities, is a
central number in marketing performance measurement. A frequent question in
applications is whether the uplifts of two campaigns are significantly
different. In this article we present a new $\chi^2$-statistic which allows to
answer this question by performing a statistical test. We show that this
statistic is asymptotically $\chi^2$-distributed and demonstrate its
application in a real life example. By running simulations with this new and
alternative approaches, we find our suggested test to exhibit a better decisive
power.


title:
Fast and energy-efficient technique for jammed region mapping in
  wireless sensor networks

abstract:
  Wireless sensor networks (WSNs) have great practical importance for
surveillance systems to perform monitoring by acquiring and sending information
on any intrusion in a secured area. Requirement of very little human
intervention is one of the most desirable features of WSNs, thus making it a
cheaper and safer alternative for securing large areas such as international
borders. Jamming attacks in WSNs can be applied to disrupt communications among
the sensor nodes in the network. Since it is difficult to prevent jamming
attacks, detection and mapping out the jammed regions is critical to overcome
this problem. In a security monitoring scenario, the network operators will be
able to take proper measures against jamming once the jammed regions in the
network are known to them. It is also desirable to keep the interactions of the
sensor nodes in the network minimal, as they are low powered devices and need
to conserve their resources. In this paper we propose a light-weight technique
for faster mapping of the jammed regions. We minimize the load on the sensors
by removing the actual responsibility of mapping from the network to the
central base station (BS). After a few nodes report to the BS, it carries out
the task of mapping of the jammed regions in the network. We use our simulation
results to compare our proposed system with the existing techniques and also to
measure the performance of our system. Our results show that the jammed regions
in a network can be mapped from fewer nodes reporting to the base station.


title:
Detection of l=4 and l=5 modes in 12 years of solar VIRGO-SPM data ---
  Tests on Kepler observations of 16 Cyg A and B

abstract:
  We present the detection of l=4 and l=5 modes in power spectra of the Sun,
constructed from 12 yr full-disk VIRGO-SPM data sets. A method for enhancing
the detectability of these modes in asteroseismic targets is presented and
applied to Kepler data of the two solar analogues 16 Cyg A and B. For these
targets we see indications of a signal from l=4 modes, while nothing is yet
seen for l=5 modes. We further simulate the power spectra of these stars and
from this we estimate that it should indeed be possible to see such indications
of l=4 modes at the present length of the data sets. In the simulation process
we briefly look into the apparent misfit between observed and calculated mode
visibilities. We predict that firm detections of at least l=4 should be
possible in any case at the end of the Kepler mission. For l=5 we do not
predict any firm detections from Kepler data.


title:
Cosmological perturbations in the presence of a solid with positive
  pressure

abstract:
  Evolution of scalar perturbations in a universe containing solid matter with
positive pressure is studied. Solution for pure solid is found and matched with
solution for ideal fluid, including the case when the pressure to energy
density ratio $w$ has a jump. Two classes of solutions are explored in detail,
solutions with radiation-like solid ($w = 1/3$) and solutions with stiff solid
($w > 1/3$) appearing in a universe filled with radiation. For radiation-like
solid, an almost flat spectrum of large-scale perturbations is obtained only if
the shear stress to energy density ratio $\xi$ is close to zero, $|\xi|
\lesssim 10^{-5}$. For a solid with stiff equation of state, large-scale
perturbations are enhanced for $\xi$ negative and suppressed for $\xi$
positive. If the solid dominated the dynamics of the universe long enough,
perturbations could end up suppressed as much as by several orders of
magnitude, and in order that the inclination of the large-scale spectrum is
consistent with observations, radiation must have prevailed over the solid long
enough before recombination. In Newtonian gauge, corrections to metric and
energy density are typically much greater than 1 in the first period after the
shear stress appears, but the linearized theory is still applicable because the
corrections stay small when one uses the proper-time comoving gauge.


title:
Supporting document to the paper "Logical limit laws for minor-closed
  classes of graphs"

abstract:
  We provide a hand-checkable proof for Lemma 4.9 in the paper "Logical limit
laws for minor-closed classes of graphs" by Heinig, Muller, Noy and Taraz.


title: Polar Codes for Some Multi-terminal Communications Problems

abstract:
  It is shown that polar coding schemes achieve the known achievable rate
regions for several multi-terminal communications problems including lossy
distributed source coding, multiple access channels and multiple descriptions
coding. The results are valid for arbitrary alphabet sizes (binary or
nonbinary) and arbitrary distributions (symmetric or asymmetric).


title:
A Weighted Ostrowski Type inequality for L$_{1}\left[ a,b\right] $ and
  applications

abstract:
  The aim of this paper is to obtain some generalized weighted Ostrowski
inequalities for differentiable mappings. Some well known inequalities can be
derived as special cases of the inequalities obtained here. In addition,
perturbed mid-point inequality and perturbed trapezoid inequality are also
obtained. The inequalities obtained here have direct applications in Numerical
Integration, Probability Theory, Information Theory and Integral Operator
Theory. Some of these applications are discussed.


title: Lagrangian formulation of Newtonian cosmology

abstract:
  In this paper, we use the Lagrangian formalism of classical mechanics and
some assumptions to obtain cosmological differential equations analogous to
Friedmann and Einstein equations, obtained from the theory of general
relativity. This method can be used to a universe constituted of incoherent
matter, that is, the cosmologic substratum is comprised of dust.


title: GHZ transform (I): Bell transform and quantum teleportation

abstract:
  It is well-known that maximally entangled states such as the
Greenberger-Horne-Zeilinger (GHZ) states, with the Bell states as the simplest
examples, are widely exploited in quantum information and computation. We study
the application of such maximally entangled states from the viewpoint of the
GHZ transform, which is a unitary basis transformation from the product states
to the GHZ states. The algebraic structure of the GHZ transform is made clear
and representative examples for it are verified as multi-qubit Clifford gates.
In this paper, we focus on the Bell transform as the simplest example of the
GHZ transform and apply it to the reformulation of quantum circuit model of
teleportation and the reformulation of the fault-tolerant construction of
single-qubit gates and two-qubit gates in teleportation-based quantum
computation. We clearly show that there exists a natural algebraic structure
called the teleportation operator in terms of the Bell transform to catch
essential points of quantum teleportation, and hence we expect that there would
also exist interesting algebraic structures in terms of the GHZ transform to
play important roles in quantum information and computation.


title: Bondi-Hoyle Accretion in an Isothermal Magnetized Plasma

abstract:
  In regions of star formation, protostars and newborn stars accrete mass from
their natal clouds. These clouds are threaded by magnetic fields with a
strength characterized by the plasma beta---the ratio of thermal and magnetic
pressures. Observations show molecular clouds have beta <= 1, so magnetic
fields can play a significant role in the accretion process. We have carried
out a numerical study of the effect of large-scale magnetic fields on the rate
of accretion onto a uniformly moving point particle from a uniform,
non-self-gravitating, isothermal gas. We consider gas moving with sonic Mach
numbers of up M ~ 45, magnetic fields that are either parallel, perpendicular,
or oriented 45 degrees to the flow, and beta as low as 0.01. Our simulations
utilize AMR to obtain high spatial resolution where needed; this also allows
the simulation boundaries to be far from the accreting object. Additionally, we
show our results are independent of our exact prescription for accreting mass
in the sink particle. We give simple expressions for the steady-state accretion
rate as a function of beta, M, and field orientation. Using typical molecular
clouds values of M ~ 5 and beta ~ 0.04 from the literature, our fits suggest a
0.4 M_Sun star accretes ~ 4*10^{-9} M_Sun/year, almost a factor of two less
than accretion rates predicted by hydrodynamic models. This disparity grows to
orders of magnitude for stronger fields and lower Mach numbers. We discuss the
applicability of these accretion rates versus accretion rates expected from
gravitational collapse, and when a steady state is possible. This reduction in
Mdot increases the time required to form stars in competitive accretion models,
making such models less efficient. In numerical codes, our results should
enable accurate subgrid models of sink particles accreting from magnetized
media.


title:
Effective field theory, three-loop perturbative expansion, and their
  experimental implications in graphene many-body effects

abstract:
  Many-body electron-electron interaction effects are theoretically considered
in monolayer graphene from a continuum effective field-theoretic perspective by
going beyond the standard leading-order perturbative renormalization group (RG)
analysis. Given that the bare fine structure constant in graphene is of order
unity, which is neither small to justify a perturbative expansion nor large
enough for strong-coupling theories to be applicable, the problem is a
difficult one, with some similarity to 2+1-dimensional strong-coupling quantum
electrodynamics (QED). In this work, we take a systematic and comprehensive
analytical approach, working primarily at the Dirac point (intrinsic graphene),
by going up to three loops in the diagrammatic expansion to both ascertain the
validity of perturbation theory and to estimate quantitatively higher-order
renormalization effects. While no direct signatures for non-Fermi liquid
behavior at the Dirac point have yet been observed experimentally, there is
ample evidence for the interaction-induced renormalization of the graphene
velocity as the carrier density approaches zero. We provide a critical
comparison between theory and experiment, using both bare- and
screened-interaction (RPA) calculations. We find that while the one-loop RG
analysis gives reasonable agreement with the experimental data, especially when
screening and finite-density effects are included through the RPA, the two-loop
analysis reveals a strong-coupling critical point in suspended graphene,
signifying either a quantum phase transition or a breakdown of the
weak-coupling RG approach. We show that the latter is more likely by adapting
Dyson's argument for the breakdown of perturbative QED to the case of graphene.
We propose future experiments and theoretical directions to make further
progress on this important and difficult problem.


title:
Transport near the Ising-nematic quantum critical point of metals in two
  dimensions

abstract:
  We consider two-dimensional metals near a Pomeranchuk instability which
breaks 90$^\circ$ lattice rotation symmetry. Such metals realize
strongly-coupled non-Fermi liquids with critical fluctuations of an
Ising-nematic order. At low temperatures, impurity scattering provides the
dominant source of momentum relaxation, and hence a non-zero electrical
resistivity. We use the memory matrix method to compute the resistivity of this
non-Fermi liquid to second order in the impurity potential, without assuming
the existence of quasiparticles. Impurity scattering in the $d$-wave channel
acts as a random "field" on the Ising-nematic order. We find contributions to
the resistivity with a nearly linear temperature dependence, along with more
singular terms; the most singular is the random-field contribution which
diverges in the limit of zero temperature.


title:
Supernovae with Two Peaks in the Optical Light Curve and the Signature
  of Progenitors with Low-mass Extended Envelopes

abstract:
  Early observations of supernova light curves are powerful tools for shedding
light on the pre-explosion structures of their progenitors and their mass-loss
histories just prior to explosion. Some core-collapse supernovae that are
detected during the first days after the explosion prominently show two peaks
in the optical bands, including the $R$ and $I$ bands, where the first peak
appears to be powered by the cooling of shocked surface material and the second
peak is clearly powered by radioactive decay. Such light curves have been
explored in detail theoretically for SN 1993J and 2011dh, where it was found
that they may be explained by progenitors with extended, low-mass envelopes.
Here we generalize these results. We explore, first, whether any double-peaked
light curve of this type can be generated by a progenitor with a "standard"
density profile, such as a red supergiant or a Wolf-Rayet star. We show that a
standard progenitor (1) cannot produce a double-peaked light curve in the $R$
and $I$ bands, and (2) cannot exhibit a fast drop in the bolometric luminosity
as is seen after the first peak. We then explore the signature of a progenitor
with a compact core surrounded by extended, low-mass material. This may be a
hydrostatic low-mass envelope or material ejected just prior to the explosion.
We show that it naturally produces both of these features. We use this result
to provide simple formulae to estimate (1) the mass of the extended material
from the time of the first peak, (2) the extended material radius from the
luminosity of the first peak, and (3) an upper limit on the core radius from
the luminosity minimum between the two peaks.


title: Mass Renormalization in String Theory: General States

abstract:
  In a previous paper we described a procedure for computing the renormalized
masses and S-matrix elements in bosonic string theory for a special class of
massive states which do not mix with unphysical states under renormalization.
In this paper we extend this result to general states in bosonic string theory,
and argue that only the squares of renormalized physical masses appear as the
locations of the poles of the S-matrix of other physical states. We also
discuss generalizations to Neveu-Schwarz sector states in heterotic and
superstring theories.


title: Time-Dependent Warping and Non-Singular Bouncing Cosmologies

abstract:
  In this note, we construct a family of non-singular time-dependent solutions
of a six-dimensional gravitational theory that are warped products of a four
dimensional bouncing cosmological solution and a two dimensional internal
manifold. The warp factor is time-dependent and breaks translation invariance
along one of the internal directions. When the warp factor is periodic in time,
the non-compact part of the geometry bounces periodically. The six dimensional
geometry is supported by matter that does not violate the null energy
condition. We show that this 6D geometry does not admit a closed trapped
surface and hence the Hawking-Penrose singularity theorems do not apply to
these solutions. We also present examples of singular solutions where the
topology of the internal manifold changes dynamically.


title: Partition Functions in Even Dimensional AdS via Quasinormal Mode Methods

abstract:
  In this note, we calculate the one-loop determinant for a massive scalar
(with conformal dimension $\Delta$) in even-dimensional AdS$_{d+1}$ space,
using the quasinormal mode method developed in arXiv:0908.2657 by Denef,
Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean
hyperbolic plane $H_2$, we find a series of zero modes for negative real values
of $\Delta$ whose presence indicates a series of poles in the one-loop
partition function $Z(\Delta)$ in the $\Delta$ complex plane; these poles
contribute temperature-independent terms to the thermal AdS partition function
computed in arXiv:0908.2657. Our results match those in a series of papers by
Camporesi and Higuchi, as well as Gopakumar et al. in arXiv:1103.3627 and
Banerjee et al. in arXiv:1005.3044. We additionally examine the meaning of
these zero modes, finding that they Wick-rotate to quasinormal modes of the
AdS$_2$ black hole. They are also interpretable as matrix elements of the
discrete series representations of $SO(2,1)$ in the space of smooth functions
on $S^1$. We generalize our results to general even dimensional AdS$_{2n}$,
again finding a series of zero modes which are related to discrete series
representations of $SO(2n,1)$, the motion group of $H_{2n}$.


title:
Calcium-rich Gap Transients: Solving the Calcium Conundrum in the
  Intracluster Medium

abstract:
  X-ray measurements suggest the abundance of Calcium in the intracluster
medium is higher than can be explained using favored models for core-collapse
and Type Ia supernovae alone. We investigate whether the Calcium conundrum in
the intracluster medium can be alleviated by including a contribution from the
recently discovered subclass of supernovae known as Calcium-rich gap
transients. Although the Calcium-rich gap transients make up only a small
fraction of all supernovae events, we find that their high Calcium yields are
sufficient to reproduce the X-ray measurements found for nearby rich clusters.
We find the $\chi^{2}$ goodness-of-fit metric improves from 84 to 2 by
including this new class. Moreover, Calcium-rich supernovae preferentially
occur in the outskirts of galaxies making it easier for the nucleosynthesis
products of these events to be incorporated in the intracluster medium via
ram-pressure stripping. The discovery of a Calcium-rich gap transients in
clusters and groups far from any individual galaxy suggests supernovae
associated with intracluster stars may play an important role in enriching the
intracluster medium. Calcium-rich gap transients may also help explain
anomalous Calcium abundances in many other astrophysical systems including
individual stars in the Milky Way, the halos of nearby galaxies and the
circumgalactic medium. Our work highlights the importance of considering the
diversity of supernovae types and corresponding yields when modeling the
abundance of the intracluster medium and other gas reservoirs.


title: Locality and Nonlinear Quantum Mechanics

abstract:
  Nonlinear modifications of quantum mechanics generically lead to nonlocal
effects which violate relativistic causality. We study these effects using the
functional Schrodinger equation for quantum fields and identify a type of
nonlocality which causes nearly instantaneous entanglement of spacelike
separated systems. We describe a simple example involving widely separated
wave-packet (coherent) states, showing that nonlinearity in the Schrodinger
evolution causes spacelike entanglement, even in free field theory.


title: Dips in the Diffuse Supernova Neutrino Background

abstract:
  Scalar (fermion) dark matter with mass in the MeV range coupled to ordinary
neutrinos and another fermion (scalar) is motivated by scenarios that establish
a link between radiatively generated neutrino masses and the dark matter relic
density. With such a coupling, cosmic supernova neutrinos, on their way to us,
could resonantly interact with the background dark matter particles, giving
rise to a dip in their redshift-integrated spectra. Current and future neutrino
detectors, such as Super-Kamiokande, LENA and Hyper-Kamiokande, could be able
to detect this distortion.


title: A Stochastic Quasi-Newton Method for Large-Scale Optimization

abstract:
  The question of how to incorporate curvature information in stochastic
approximation methods is challenging. The direct application of classical
quasi- Newton updating techniques for deterministic optimization leads to noisy
curvature estimates that have harmful effects on the robustness of the
iteration. In this paper, we propose a stochastic quasi-Newton method that is
efficient, robust and scalable. It employs the classical BFGS update formula in
its limited memory form, and is based on the observation that it is beneficial
to collect curvature information pointwise, and at regular intervals, through
(sub-sampled) Hessian-vector products. This technique differs from the
classical approach that would compute differences of gradients, and where
controlling the quality of the curvature estimates can be difficult. We present
numerical results on problems arising in machine learning that suggest that the
proposed method shows much promise.


title: Logical limit laws for minor-closed classes of graphs

abstract:
  Let $\mathcal G$ be an addable, minor-closed class of graphs. We prove that
the zero-one law holds in monadic second-order logic (MSO) for the random graph
drawn uniformly at random from all {\em connected} graphs in $\mathcal G$ on
$n$ vertices, and the convergence law in MSO holds if we draw uniformly at
random from all graphs in $\mathcal G$ on $n$ vertices. We also prove analogues
of these results for the class of graphs embeddable on a fixed surface,
provided we restrict attention to first order logic (FO). Moreover, the
limiting probability that a given FO sentence is satisfied is independent of
the surface $S$. We also prove that the closure of the set of limiting
probabilities is always the finite union of at least two disjoint intervals,
and that it is the same for FO and MSO. For the classes of forests and planar
graphs we are able to determine the closure of the set of limiting
probabilities precisely. For planar graphs it consists of exactly 108
intervals, each of length $\approx 5\cdot 10^{-6}$. Finally, we analyse
examples of non-addable classes where the behaviour is quite different. For
instance, the zero-one law does not hold for the random caterpillar on $n$
vertices, even in FO.


title: Inflationary Freedom and Cosmological Neutrino Constraints

abstract:
  The most stringent bounds on the absolute neutrino mass scale come from
cosmological data. These bounds are made possible because massive relic
neutrinos affect the expansion history of the universe and lead to a
suppression of matter clustering on scales smaller than the associated free
streaming length. However, the resulting effect on cosmological perturbations
is relative to the primordial power spectrum of density perturbations from
inflation, so freedom in the primordial power spectrum affects neutrino mass
constraints. Using measurements of the cosmic microwave background, the galaxy
power spectrum and the Hubble constant, we constrain neutrino mass and number
of species for a model independent primordial power spectrum. Describing the
primordial power spectrum by a 20-node spline, we find that the neutrino mass
upper limit is a factor three weaker than when a power law form is imposed, if
only CMB data are used. The primordial power spectrum itself is constrained to
better than 10 % in the wave vector range $k \approx 0.01 - 0.25$ Mpc$^{-1}$.
Galaxy clustering data and a determination of the Hubble constant play a key
role in reining in the effects of inflationary freedom on neutrino constraints.
The inclusion of both eliminates the inflationary freedom degradation of the
neutrino mass bound, giving for the sum of neutrino masses $\Sigma m_\nu <
0.18$ eV (at 95 % confidence level, Planck+BOSS+$H_0$), approximately
independent of the assumed primordial power spectrum model. When allowing for a
free effective number of species, $N_{eff}$, the joint constraints on $\Sigma
m_\nu$ and $N_{eff}$ are loosened by a factor 1.7 when the power law form of
the primordial power spectrum is abandoned in favor of the spline
parametrization.


title: Severi degrees on toric surfaces

abstract:
  Ardila and Block used tropical results of Brugalle and Mikhalkin to count
nodal curves on a certain family of toric surfaces. Building on a linearity
result of the first author, we revisit their work in the context of the
Goettsche-Yau-Zaslow formula for counting nodal curves on arbitrary smooth
surfaces, addressing several questions they raised by proving stronger versions
of their main theorems. In the process, we give new combinatorial formulas for
the coefficients arising in the Goettsche-Yau-Zaslow formulas, and give
correction terms arising from rational double points in the relevant family of
toric surfaces.


title:
Scale Factor Dependencies in Quantum Dipole Coupled Lee-Goldburg
  Cross-Polarization Experiments

abstract:
  Lee-Goldburg cross polarization is used in many NMR experiments to determine
internuclear distances. Distances calculated from frequency peaks in the
dipolar coupled dimension are subject to scale factors. Experimentally
determined scale factors can differ significantly from the theoreticalyy useful
value described in the literature. In this work, simulations using
SPINEVOLUTION explore effects of varying experimental parameters of frequency
offset and cross polarization powers on $^{15}$N-H systems. Experimental data
is used to corroborate the simulation. The scale factor is shown not only to
depend on the offset frequency but also the cross polarization powers of the
observed nucleus. Scale factors greater than one are shown to be possible in
simulated data, though such factors obscure the determination of internuclear
distances.


title:
Homogenization of a pore scale model for precipitation and dissolution
  in porous media

abstract:
  In this paper we employ homogenization techniques to provide a rigorous
derivation of the Darcy scale model for precipitation and dissolution in porous
media proposed in [19]. The starting point is the pore scale model in [12],
which is a coupled system of evolution equations, involving a parabolic
equation and an ordinary differential equation. The former models ion transport
and is defined in a periodically perforated medium. It is further coupled
through the boundary conditions to the latter, defined on the boundaries of the
perforations and modelling the dissolution and precipitation of the
precipitate.
  The main challenge is in dealing with the dissolution and precipitation
rates, which involve a monotone but multi-valued mapping. Due to this, the
micro-scale solution lacks regularity. With $\ep$ being the scale parameter
(the ratio between the micro scale and the macro scale length), we adopt the
2-scale framework to achieve the convergence of the homogenization procedure as
$\ep$ approaches zero.


title: BMS supertranslations and Weinberg's soft graviton theorem

abstract:
  Recently it was conjectured that a certain infinite-dimensional "diagonal"
subgroup of BMS supertranslations acting on past and future null infinity
(${\mathscr I}^-$ and ${\mathscr I}^+$) is an exact symmetry of the quantum
gravity ${\cal S}$-matrix, and an associated Ward identity was derived. In this
paper we show that this supertranslation Ward identity is precisely equivalent
to Weinberg's soft graviton theorem. Along the way we construct the canonical
generators of supertranslations at ${\mathscr I}^\pm$, including the relevant
soft graviton contributions. Boundary conditions at the past and future of
${\mathscr I}^\pm$ and a correspondingly modified Dirac bracket are required.
The soft gravitons enter as boundary modes and are manifestly the Goldstone
bosons of spontaneously broken supertranslation invariance.


title: Intermediate \beta-shifts of finite type

abstract:
  An aim of this article is to highlight dynamical differences between the
greedy, and hence the lazy, $\beta$-shift (transformation) and an intermediate
$\beta$-shift (transformation), for a fixed $\beta \in (1, 2)$. Specifically, a
classification in terms of the kneading invariants of the linear maps
$T_{\beta,\alpha} \colon x \mapsto \beta x + \alpha \bmod 1$ for which the
corresponding intermediate $\beta$-shift is of finite type is given. This
characterisation is then employed to construct a class of pairs
$(\beta,\alpha)$ such that the intermediate $\beta$-shift associated with
$T_{\beta, \alpha}$ is a subshift of finite type. It is also proved that these
maps $T_{\beta,\alpha}$ are not transitive. This is in contrast to the
situation for the corresponding greedy and lazy $\beta$-shifts and
$\beta$-transformations, for which both of the two properties do not hold.


title:
Preliminary Analysis of SOHO/STEREO Observations of Sungrazing Comet
  ISON (C/2012 S1) Around Perihelion

abstract:
  We present photometric and morphological analysis of the behavior of
sungrazing comet C/2012 S1 ISON in SOHO and STEREO images around its perihelion
on 2013 November 28.779 UT. ISON brightened gradually November 20-26 with a
superimposed outburst on November 21.3-23.5. The slope of brightening changed
about November 26.7 and was significantly steeper in SOHO's orange and clear
filter images until November 27.9 when it began to flatten out, reaching a peak
about November 28.1 ($r_H{\sim}17 R_\odot$), then fading before brightening
again from November 28.6 ($r_H{\sim}5 R_\odot$) until disappearing behind the
occulting disc. ISON brightened continuously as it approached perihelion while
visible in all other telescopes/filters. The central condensation disappeared
about November 28.5 and the leading edge became progressively more elongated
until perihelion. These photometric and morphological behaviors are reminiscent
of the tens of meter sized Kreutz comets regularly observed by SOHO and STEREO
and strongly suggest that the nucleus of ISON was destroyed prior to
perihelion. This is much too small to support published gas production rates
and implies significant mass loss and/or disruption in the days and weeks
leading up to perihelion. No central condensation was seen post-perihelion. The
post-perihelion lightcurve was nearly identical in all telescopes/filters and
fell slightly steeper than $r_H^{-2}$. This implies that the brightness was
dominated by reflected solar continuum off of remnant dust in the coma/tail and
that any remaining active nucleus was <10 m in radius.


title: Iterative Universal Rigidity

abstract:
  A bar framework determined by a finite graph $G$ and configuration $\bf p$ in
$d$ space is universally rigid if it is rigid in any ${\mathbb R}^D \supset
{\mathbb R}^d$. We provide a characterization of universally rigidity for any
graph $G$ and any configuration ${\bf p}$ in terms of a sequence of affine
subsets of the space of configurations. This corresponds to a facial reduction
process for closed finite dimensional convex cones.


title: Characterizing Wolf-Rayet Stars in the Near and Mid Infrared

abstract:
  We present refined color-color selection criteria for identifying Wolf-Rayet
(WR) stars using available mid infrared (MIR) photometry from WISE in
combination with near infrared (NIR) photometry from 2MASS. Using a sample of
spectrally classified objects, we find that WR stars are well distinguished
from the field stellar population in the (W1-W2) vs. (J-Ks) color-color
diagram, and further distinguished from other emission line objects such as
Planetary Nebulae, Be, and Cataclysmic variable stars using a combination of
NIR and MIR color constraints. As proof of concept we applied the color
constraints to a photometric sample in the Galactic plane, located WR star
candidates, and present five new spectrally confirmed and classified WC (1) and
WN (4) stars. Analysis of the 0.8-5.0 micron spectral data for a subset of
known, bright WC and WN stars shows that emission lines (primarily He I) extend
into the 3.0 - 5.0 micron spectral region, although their strength is greatly
diminished compared to the 0.8-2.5 micron region. The WR population stands out
relative to background field stars at NIR and MIR colors due to an excess
continuum contribution, likely caused by free-free scattering in dense winds.
Mean photometric properties of known WRs are presented and imply that reddened
late-type WN and WC sources are easier to detect than earlier-type sources at
larger Galactic radii. WISE W3 and W4 images of 10 Wolf Rayet stars show
evidence of circumstellar shells linked to mass ejections from strong stellar
winds.


title: Probing Quintessence Potential with Future Cosmological Surveys

abstract:
  Quintessence, a scalar field model, has been proposed to account for the
acceleration of the Universe at present. We discuss how accurately quintessence
models are discriminated by future cosmological surveys, which include
experiments of CMB, galaxy clustering, weak lensing, and the type Ia SNe
surveys, by making use of the conventional parameterized dark energy models. We
can see clear differences between the thawing and the freezing quintessence
models at more than $1\sigma$ ($2\sigma$) confidence level as long as the
present equation of state for quintessence is away from $-1$ as $w_X \gtrsim
-0.95 (-0.90)$. However, it is found to be difficult to probe the effective
mass squared for the potential in thawing models, whose signs are different
between the quadratic and the cosine-type potentials. This fact may require us
to invent a new estimator to distinguish quintessence models beyond the thawing
and the freezing ones.


title:
Operator algebras and subproduct systems arising from stochastic
  matrices

abstract:
  We study subproduct systems in the sense of Shalit and Solel arising from
stochastic matrices on countable state spaces, and their associated operator
algebras. We focus on the non-self-adjoint tensor algebra, and Viselter's
generalization of the Cuntz-Pimsner C*-algebra to the context of subproduct
systems. Suppose that $X$ and $Y$ are Arveson-Stinespring subproduct systems
associated to two stochastic matrices over a countable set $\Omega$, and let
$\mathcal{T}_+(X)$ and $\mathcal{T}_+(Y)$ be their tensor algebras. We show
that every algebraic isomorphism from $\mathcal{T}_+(X)$ onto
$\mathcal{T}_+(Y)$ is automatically bounded. Furthermore, $\mathcal{T}_+(X)$
and $\mathcal{T}_+(Y)$ are isometrically isomorphic if and only if $X$ and $Y$
are unitarily isomorphic up to a *-automorphism of $\ell^\infty(\Omega)$. When
$\Omega$ is finite, we prove that $\mathcal{T}_+(X)$ and $\mathcal{T}_+(Y)$ are
algebraically isomorphic if and only if there exists a similarity between $X$
and $Y$ up to a *-automorphism of $\ell^\infty(\Omega)$. Moreover, we provide
an explicit description of the Cuntz-Pimsner algebra $\mathcal{O}(X)$ in the
case where $\Omega$ is finite and the stochastic matrix is essential.


title:
The study of time series of monthly averaged values of F10.7 from 1950
  to 2010

abstract:
  Prior to 1947, the activity of the Sun was assessed by the relative numbers
of sunspots (W). The 10.7 cm radio emission (frequency of 2.8 GHz) for
observations of the variability of radiation of chromosphere and the lower
corona (F10.7) became used from 1947. For the F10,7 are available more detailed
observational archive data, so this activity index more often than the other
indices is used in the prediction and monitoring of the solar activity. We have
made the analysis of time series of F10.7 with the use of different mother
wavelets: Daubechies 10, Symlet 8, Meyer, Gauss 8 and Morlet. Wavelet spectrum
allows us not only to identify cycles, but analyze their change in time. Each
wavelet has its own characteristic features, so sometimes with the help of
different wavelets it can be better identify and highlight the different
properties of the analyzed signal. We intended to choose the mother wavelet,
which is more fully gives information about the analyzed index F10.7. We have
received, that all these wavelets show similar values to the maximums of the
cyclic activity. However, we can see the difference when using different
wavelets. There are also a number of periods, which, perhaps, are the harmonics
of main period. The mean value of 11-year cycle is about 10.2 years. All the
above examples show that the best results we get when using wavelets Morley,
Gauss (real-valued) and multiparameter family of wavelets Morley and Gauss
(complex-valued).


title:
TARVOS - an Event-Based Simulator for Performance Analysis, Supporting
  MPLS, RSVP-TE, and Fast Recovery

abstract:
  This paper presents a new discrete event-based network simulator named TARVOS
- Computer Networks Simulator, being designed as part of the first Author's
Masters research and will provide support to simulating MPLS architecture,
several RSVP-TE protocol functionalities and fast recovery in case of link
failure. The tool is used in a case study, where the impact of a link failure
on a VoIP application, within an MPLS domain network, is analyzed. The paper
displays a preliminary research of six already available simulators and reasons
why they were not adopted as tools for the Masters research. Then, it follows
to describe the basics of TARVOS implementation and exhibits the case study
simulated by this new tool.


title: Bottom Quark Mass from $\Upsilon$ Sum Rules to ${\cal O}(\alpha_s^3)$

abstract:
  We use the ${\cal O}(\alpha_s^3)$ approximation of the heavy-quark vacuum
polarization function in the threshold region to determine the bottom quark
mass from nonrelativistic $\Upsilon$ sum rules. We find very good stability and
convergence of the perturbative series for the bottom quark mass in
$\rm\overline{MS}$ renormalization scheme. Our final result is
$\overline{m}_b(\overline{m}_b)=4.169\pm 0.008_{th}\pm 0.002_{\alpha_s}\pm
0.002_{exp}$.


title: Active phase and amplitude fluctuations of flagellar beating

abstract:
  The eukaryotic flagellum beats periodically, driven by the oscillatory
dynamics of molecular motors, to propel cells and pump fluids. Small, but
perceivable fluctuations in the beat of individual flagella have physiological
implications for synchronization in collections of flagella as well as for
hydrodynamic interactions between flagellated swimmers. Here, we characterize
phase and amplitude fluctuations of flagellar bending waves using shape mode
analysis and limit cycle reconstruction. We report a quality factor of
flagellar oscillations, $Q=38.0\pm 16.7$ (mean$\pm$s.e.). Our analysis shows
that flagellar fluctuations are dominantly of active origin. Using a minimal
model of collective motor oscillations, we demonstrate how the stochastic
dynamics of individual motors can give rise to active small-number fluctuations
in motor-cytoskeleton systems.


title: A Note on the Relationship between Sunspot Numbers and Active Days

abstract:
  We have studied the relationship between three different versions of the
sunspot number (Group, International and American sunspot number) and the
number of active days (i.e., the number of days with spots on the solar disk).
We have detected an approximately linear relationship for low solar activity
conditions. However, this relationship for the International sunspot number is
very different to the ones obtained with the other versions of the sunspot
number. The discordant values correspond to older observations.


title:
A sparse representation of gravitational waves from precessing compact
  binaries

abstract:
  Many relevant applications in gravitational wave physics share a significant
common problem: the seven-dimensional parameter space of gravitational
waveforms from precessing compact binary inspirals and coalescences is large
enough to prohibit covering the space of waveforms with sufficient density. We
find that by using the reduced basis method together with a parametrization of
waveforms based on their phase and precession, we can construct ultra-compact
yet high-accuracy representations of this large space. As a demonstration, we
show that less than $100$ judiciously chosen precessing inspiral waveforms are
needed for $200$ cycles, mass ratios from $1$ to $10$ and spin magnitudes $\le
0.9$. In fact, using only the first $10$ reduced basis waveforms yields a
maximum mismatch of $0.016$ over the whole range of considered parameters. We
test whether the parameters selected from the inspiral regime result in an
accurate reduced basis when including merger and ringdown; we find that this is
indeed the case in the context of a non-precessing effective-one-body model.
This evidence suggests that as few as $\sim 100$ numerical simulations of
binary black hole coalescences may accurately represent the seven-dimensional
parameter space of precession waveforms for the considered ranges.


title: A proposal for sympathetically cooling neutral molecules using cold ions

abstract:
  We describe a method for cooling neutral molecules that have magnetic and
electric dipole moments using collisions with cold ions. An external magnetic
field is used to split the ground rovibrational energy levels of the molecule.
The highest energy state within the ground rovibrational manifold increases in
energy as the distance to the ion decreases leading to a repelling potential.
At low energy, inelastic collisions are strongly suppressed due to the large
distance of closest approach. Thus, a collision between a neutral molecule and
a cold ion will lead to a decrease in the molecule's kinetic energy with no
change in internal energy. We present results for the specific case of OH
molecules cooled by Be$^+$, Mg$^+$, or Ca$^+$ ions.


title: Matroids representable over fields with a common subfield

abstract:
  A matroid is $\text{GF}(q)$-regular if it is representable over all proper
superfields of the field $\text{GF}(q)$. We show that, for highly connected
matroids having a large projective geometry over $\text{GF}(q)$ as a minor, the
property of $\text{GF}(q)$-regularity is equivalent to representability over
both $\text{GF}(q^2)$ and $\text{GF}(q^t)$ for some odd integer $t \geq 3$. We
do this by means of an exact structural description of all such matroids.


title:
Information Path from Randomness and Uncertainty to Information,
  Thermodynamics, and Intelligence of Observer

abstract:
  Finding observing path creating its observer is important problem in physics
and information science. In observing processes, each observation is act
changing the observing process that generates interactive observation. Each
interaction is discrete Yes-No impulse modeling Bit. Recurring inter-actions
independent of physical nature is phenomenon of information. Multiple
interactions generate random Markov chains covering multiple Bits. Impulse No
action cuts maximum entropy-uncertainty, Yes action transfers cut minimum to
next impulse creating maximin principle decreasing uncertainty. The cutoff
entropies reveal hidden information naturally observing interactive impulse as
elementary observer. Conversion impulse entropies to information integrates
path functional. The maxmin variation principle formalizes interactive
information equations. Merging Yes-No actions generate microprocess within
bordered impulses running superposition of conjugated entropies entangling
during time interval within forming space intervals. Interaction curves impulse
geometry creating asymmetry which logically erases entangled entropy removing
causal probabilistic entropy with symmetrical reversible logic and bringing
asymmetrical information logic. Entropy-information topological gap connects
asymmetrical logic with physical Markov diffusion whose energy memorizes
logical Bit. Moving Bits selfform unit of information macroprocess attracting
new UP through free Information. Multiple UP triples adjoin hierarchical
network (IN) whose free information produces new UP at higher level node and
encodes triple code logic. Each UP unique position in IN hierarchy defines
location of each code logical structure. The IN node hierarchical level
classifies quality of assembled Information. Ending IN node enfolds all IN
levels. Multiple INs enclose Observer cognition and intelligence with
consciousness.


title: How to Walk Your Dog in the Mountains with No Magic Leash

abstract:
  We describe a $O(\log n )$-approximation algorithm for computing the
homotopic \Frechet distance between two polygonal curves that lie on the
boundary of a triangulated topological disk. Prior to this work, algorithms
were known only for curves on the Euclidean plane with polygonal obstacles.
  A key technical ingredient in our analysis is a $O(\log n)$-approximation
algorithm for computing the minimum height of a homotopy between two curves. No
algorithms were previously known for approximating this parameter.
Surprisingly, it is not even known if computing either the homotopic \Frechet
distance, or the minimum height of a homotopy, is in NP.


title:
Randomized Minmax Regret for Combinatorial Optimization Under
  Uncertainty

abstract:
  The minmax regret problem for combinatorial optimization under uncertainty
can be viewed as a zero-sum game played between an optimizing player and an
adversary, where the optimizing player selects a solution and the adversary
selects costs with the intention of maximizing the regret of the player. The
existing minmax regret model considers only deterministic solutions/strategies,
and minmax regret versions of most polynomial solvable problems are NP-hard. In
this paper, we consider a randomized model where the optimizing player selects
a probability distribution (corresponding to a mixed strategy) over solutions
and the adversary selects costs with knowledge of the player's distribution,
but not its realization. We show that under this randomized model, the minmax
regret version of any polynomial solvable combinatorial problem becomes
polynomial solvable. This holds true for both the interval and discrete
scenario representations of uncertainty. Using the randomized model, we show
new proofs of existing approximation algorithms for the deterministic model
based on primal-dual approaches. Finally, we prove that minmax regret problems
are NP-hard under general convex uncertainty.


title:
Lattice equations arising from discrete Painlev\'e systems (I):
  $(A_2+A_1)^{(1)}$ and $(A_1+A_1')^{(1)}$ cases

abstract:
  We introduce the concept of $\omega$-lattice, constructed from $\tau$
functions of Painlev\'e systems, on which quad-equations of ABS type appear. In
particular, we consider the $A_5^{(1)}$- and $A_6^{(1)}$-surface $q$-Painlev\'e
systems corresponding affine Weyl group symmetries are of $(A_2+A_1)^{(1)}$-
and $(A_1+A_1)^{(1)}$-types, respectively.


title: Foundational aspects of singular integrals

abstract:
  We investigate integration of classes of real-valued continuous functions on
(0,1]. Of course difficulties arise if there is a non-$L^1$ element in the
class, and the Hadamard finite part integral ({\em p.f.}) does not apply. Such
singular integrals arise naturally in many contexts including PDEs and singular
ODEs.
  The Lebesgue integral as well as $p.f.$, starting at zero, obey two
fundamental conditions: (i) they act as antiderivatives and, (ii) if $f =g$ on
$(0,a)$, then their integrals from $0$ to $x$ coincide for any $x\in (0,a)$.
  We find that integrals from zero with the essential properties of $p.f.$,
plus positivity, exist by virtue of the Axiom of Choice (AC) on all functions
on $(0,1]$ which are $L^1((\epsilon,1])$ for all $\epsilon>0$. However, this
existence proof does not provide a satisfactory construction. Without some
regularity at $0$, the existence of general antiderivatives which satisfy only
(i) and (ii) above on classes with a non-$L^1$ element is independent of ZF
(the usual ZFC axioms for mathematics without AC), and even of ZFDC (ZF with
the Axiom of Dependent Choice). Moreover we show that there is no mathematical
description that can be proved (within ZFC or even extensions of ZFC with large
cardinal hypotheses) to uniquely define such an antiderivative operator.
  Such results are precisely formulated for a variety of sets of functions, and
proved using methods from mathematical logic, descriptive set theory and
analysis. We also analyze $p.f.$ on analytic functions in the punctured unit
disk, and make the connection to singular initial value problems.


title: Coarsening modes of clusters of aggregating particles

abstract:
  There are two modes by which clusters of aggregating particles can coalesce:
The clusters can merge either (i) by the Ostwald ripening process in which
particles diffuse from one cluster to the other whilst the cluster centres
remain stationary, or (ii) by means of a cluster translation mode, in which the
clusters move towards each other and join. To understand in detail the
interplay between these different modes, we study a model system of hard
particles with an additional attraction between them. The particles diffuse
along narrow channels with smooth or periodically corrugated walls, so that the
system may be treated as one-dimensional. When the attraction between the
particles is strong enough, they aggregate to form clusters. The channel
potential influences whether clusters can move easily or not through the system
and can prevent cluster motion. We use Dynamical Density Functional theory to
study the dynamics of the aggregation process, focusing in particular on the
coalescence of two equal size clusters. As long as the particle hard-core
diameter is non-zero, we find that the coalescence process can be halted by a
sufficiently strong corrugation potential. The period of the potential
determines the size of the final stable clusters. For the case of smooth
channel walls, we demonstrate that there is a cross-over in the dominance of
the two different coarsening modes, that depends on the strength of the
attraction between particles, the cluster sizes and the separation distance
between clusters.


title:
Toward compressed DMD: spectral analysis of fluid flows using
  sub-Nyquist-rate PIV data

abstract:
  Dynamic mode decomposition (DMD) is a powerful and increasingly popular tool
for performing spectral analysis of fluid flows. However, it requires data that
satisfy the Nyquist-Shannon sampling criterion. In many fluid flow experiments,
such data are impossible to capture. We propose a new approach that combines
ideas from DMD and compressed sensing. Given a vector-valued signal, we take
measurements randomly in time (at a sub-Nyquist rate) and project the data onto
a low-dimensional subspace. We then use compressed sensing to identify the
dominant frequencies in the signal and their corresponding modes. We
demonstrate this method using two examples, analyzing both an artificially
constructed test dataset and particle image velocimetry data collected from the
flow past a cylinder. In each case, our method correctly identifies the
characteristic frequencies and oscillatory modes dominating the signal, proving
the proposed method to be a capable tool for spectral analysis using
sub-Nyquist-rate sampling.


title:
Helical order in one-dimensional magnetic atom chains and possible
  emergence of Majorana bound states

abstract:
  We theoretically obtain the phase diagram of localized magnetic impurity
spins arranged in a one-dimensional chain on top of a one- or two-dimensional
electron gas with Rashba spin-orbit coupling. The interactions between the
spins are mediated by the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism
through the electron gas. Recent work predicts that such a system may
intrinsically support topological superconductivity when a helical spin-density
wave is formed in the spins, and superconductivity is induced in the electron
gas. We analyze, using both analytical and numerical techniques, the conditions
under which such a helical spin state is stable in a realistic situation in the
presence of disorder. We show that it becomes unstable towards the formation of
(anti) ferromagnetic domains if the disorder in the impurity spin positions
$\delta R$ becomes comparable with the Fermi wave length. We also examine the
stability of the helical state against Gaussian potential disorder in the
electronic system using a diagrammatic approach. Our results suggest that in
order to stabilize the helical spin state, and thus the emergent topological
superconductivity, a sufficiently strong Rashba spin-orbit coupling, giving
rise to Dzyaloshinskii-Moriya interactions, is required.


title: Virtual Domination of $3$-manifolds

abstract:
  For any closed oriented hyperbolic $3$-manifold $M$, and any closed oriented
$3$-manifold $N$, we will show that $M$ admits a finite cover $M'$, such that
there exists a degree-$2$ map $f:M'\rightarrow N$, i.e. $M$ virtually
$2$-dominates $N$.


title:
Dark Matter in Minimal Universal Extra Dimensions with a Stable Vacuum
  and the "Right" Higgs

abstract:
  The recent discovery of a Higgs boson with mass of about 125 GeV, along with
its striking similarity to the prediction from the Standard Model, informs and
constrains many models of new physics. The Higgs mass exhausts one out of three
input parameters of the minimal, five-dimensional version of universal extra
dimension models, the other two parameters being the Kaluza-Klein (KK) scale
and the cut-off scale of the theory. The presence of KK fermions with large
coupling to the Higgs implies a short-lived electro-weak vacuum, unless the
cut-off scale is at most a few times higher than the KK mass scale, providing
an additional tight constraint to the theory parameter space. Here, we focus on
the lightest KK particle as a dark matter candidate, and investigate the
regions of parameter space where such particle has a thermal relic density in
accord with the cosmological dark matter density. We find the paradoxical
result that, for low enough cutoff scales consistent with vacuum stability,
larger than previously thought KK mass scales become preferred to explain the
dark matter abundance in the universe. We explain this phenomenon by
pinpointing the additional particles which, at such low cutoffs, become close
enough in mass to the dark matter candidate to coannihilate with it. We make
predictions for both collider and direct dark matter searches that might soon
close in on all viable theory parameter space.


title:
Cross-correlation between cosmic microwave background lensing and galaxy
  intrinsic alignment as a contaminant to gravitational lensing
  cross-correlated probes of the universe

abstract:
  We introduce here a cross-correlation term between CMB lensing and galaxy
intrinsic alignment, noted hereby as $\phi I$. This effect acts as a
contaminant to the cross-correlation between CMB lensing and galaxy lensing.
The latter cross-correlation has recently been detected for the first time, and
measurements will greatly improve as the area of overlap between galaxy and CMB
surveys increases and measurements of the CMB polarization become more
significant. This will constitute a powerful probe for studying the structure
and evolution of the universe. The magnitude of the $\phi I$ term is found to
be about 15% of the pure CMB lensing-galaxy lensing component and acts to
reduce the magnitude of its measured spectrum. This offset in the spectrum will
strongly impact its use for precision cosmological study if left unmitigated.
We also propose here a method to calibrate this $\phi I$ contamination through
use of a scaling relation that allows one to reduce the impact of $\phi I$ by a
factor of 20 or more in all redshift bins, which would reduce its magnitude
down to detection limits in almost all cases. This will allow the full use of
this probe for precision cosmology.


title:
The semigroup of metric measure spaces and its infinitely divisible
  probability measures

abstract:
  A metric measure space is a complete separable metric space equipped with
probability measure that has full support. Two such spaces are equivalent if
they are isometric as metric spaces via an isometry that maps the probability
measure on the first space to the probability measure on the second. The
resulting set of equivalence classes can be metrized with the Gromov-Prohorov
metric of Greven, Pfaffelhuber and Winter.
  We consider the natural binary operation $\boxplus$ on this space that takes
two metric measure spaces and forms their Cartesian product equipped with the
sum of the two metrics and the product of the two probability measures. We show
that the metric measure spaces equipped with this operation form a
cancellative, commutative, Polish semigroup with a translation invariant metric
and that each element has a unique factorization into prime elements.
  We investigate the interaction between the semigroup structure and the
natural action of the positive real numbers on this space that arises from
scaling the metric. For example, we show that for any given positive real
numbers $a,b,c$ the trivial space is the only space $\mathcal{X}$ that
satisfies $a \mathcal{X} \boxplus b \mathcal{X} = c \mathcal{X}$.
  We establish that there is no analogue of the law of large numbers: if
$\mathbf{X}_1, \mathbf{X}_2$..., is an identically distributed independent
sequence of random spaces, then no subsequence of $\frac{1}{n} \boxplus_{k=1}^n
\mathbf{X}_k$ converges in distribution unless each $\mathbf{X}_k$ is almost
surely equal to the trivial space.
  We characterize the infinitely divisible probability measures and the L\'evy
processes on this semigroup, characterize the stable probability measures and
establish a counterpart of the LePage representation for the latter class.


title:
The corona theorem and Bass stable rank for $M(D(\sum_{i=1}^k a_i
  \delta_{\zeta_i}))$

abstract:
  In this paper, we prove the corona theorem for $M(D(\mu_k))$ in two different
ways, where $\mu_k = \sum_{i=1}^k a_i \delta_{\zeta_i}$. Then we prove that the
Bass stable rank of $M(D(\mu_k))$ is one.


title: Review of Recent Measurements of Meson and Hyperon Form Factors

abstract:
  A review of recent precision measurements of the electromagnetic form factors
of the mesons, pion and kaon, and the hyperons, $\Lambda^0$, $\Sigma^0$,
$\Sigma^+$, $\Xi^-$, $\Xi^0$, $\Omega^-$, at large timelike momentum transfers
is presented. Evidence is found for diquark correlations in $\Lambda^0$,
$\Sigma^0$ hyperons.