title: Attenuation map reconstruction from TOF PET data

abstract:
  To reconstruct a radioactive tracer distribution with positron emission
tomography (PET), the background attenuation correction is needed to eliminate
image artifacts. Recent research shows that time-of-flight (TOF) PET data
determine the attenuation sinogram up to a constant, and its gradient can be
computed using an analytic algorithm. In this paper, we study a direct
estimation of the sinogram only from TOF PET data. First, the gradient of the
attenuation sinogram is estimated using the aforementioned algorithm. Then, a
relationship is established to link the differential attenuation sinogram and
the underlying attenuation background. Finally, an iterative algorithm is
designed to determine the attenuation sinogram accurately and stably. A 2D
numerical simulation study is conducted to verify the correctness of our
proposed approach.


title:
A Quadratically Convergent Algorithm for Structured Low-Rank
  Approximation

abstract:
  Structured Low-Rank Approximation is a problem arising in a wide range of
applications in Numerical Analysis and Engineering Sciences. Given an input
matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear
or affine subspace $E$ of matrices (usually encoding a specific structure) such
that the Frobenius distance $\lVert M-M'\rVert$ is small. We propose a
Newton-like iteration for solving this problem, whose main feature is that it
converges locally quadratically to such a matrix under mild transversality
assumptions between the manifold of matrices of rank $r$ and the linear/affine
subspace $E$. We also show that the distance between the limit of the iteration
and the optimal solution of the problem is quadratic in the distance between
the input matrix and the manifold of rank $r$ matrices in $E$. To illustrate
the applicability of this algorithm, we propose a Maple implementation and give
experimental results for several applicative problems that can be modeled by
Structured Low-Rank Approximation: univariate approximate GCDs (Sylvester
matrices), low-rank Matrix completion (coordinate spaces) and denoising
procedures (Hankel matrices). Experimental results give evidence that this
all-purpose algorithm is competitive with state-of-the-art numerical methods
dedicated to these problems.


title: The rational homology of spaces of long links

abstract:
  We provide a complete understanding of the rational homology of the space of
long links of m strands in the euclidean space of dimension d > 3. First, we
construct explicitly a cosimplicial chain complex whose totalization is
quasi-isomorphic to the singular chain complex of the space of long links. Next
we show (using the fact that the Bousfield-Kan spectral sequence associated to
this cosimplcial chain complex collapses at the page 2) that the homology
Bousfield-Kan spectral sequence associated to the Munson-Volic cosimplicial
model for the space of long links collapses at the page 2 rationally, and this
solves a conjecture of Munson-Volic. Our method enables us also to determine
the rational homology of the high dimensional analogues of spaces of long
links. The last result of this paper states that the radius of convergence of
the Poincar\'e series for the space of long links (modulo immersions) tends to
zero as m goes to the infinity.


title:
Low-energy eta-nuclear scattering parametres vs. binding properties in
  light nuclei

abstract:
  The connection of the binding energy and width of possible bound eta-mesic
states is given to the complex scattering length for s-states in the hope that,
with knowledge of the final state interaction this could be useful in searches
of these states. In spite of the strong direct potential dependence of both
observables this connection is seen to be very model independent even for
various nuclei once the influence of also the effective range is considered.
The importance of this term is pointed also for data analyses. Although the
nucleus considered here is 12C, extension to other nuclei is implied in the
background work.


title:
Spectral formation in a radiative shock: application to anomalous X-ray
  pulsars and soft gamma-ray repeaters

abstract:
  In the fallback disk model for the persistent emission of Anomalous X-ray
pulsars (AXPs) and soft gamma-ray repeaters (SGRs), the hard X-ray emission
arises from bulk- and thermal Comptonization of bremsstrahlung photons, which
are generated in the accretion column. The relatively low X-ray luminosity of
these sources implies a moderate transverse optical depth to electron
scattering, with photons executing a small number of shock crossings before
escaping sideways. We explore the range of spectral shapes that can be obtained
with this model and characterize the most important parameter dependencies. We
use a Monte Carlo code to study the crisscrossing of photons in a radiative
shock in an accretion column and compute the resulting spectrum. As expected,
high-energy power-law X-ray spectra are produced in radiative shocks with
photon-number spectral index larger than or about 0.5. We find that the
required transverse optical depth is between 1 and 7. Such spectra are observed
in low-luminosity X-ray pulsars. We demonstrate here with a simple model that
Compton upscattering in the radiative shock in the accretion column can produce
hard X-ray spectra similar to those seen in the persistent and transient
emission of AXPs and SGRs. In particular, one can obtain a high-energy
power-law spectrum, with photon-number spectral index ~ 1 and a cutoff at 100 -
200 keV, with a transverse Thomson optical depth of ~ 5, which is shown to be
typical in AXPs/SGRs.


title: Learning to Fold Proteins Using Energy Landscape Theory

abstract:
  This review is a tutorial for scientists interested in the problem of protein
structure prediction, particularly those interested in using coarse-grained
molecular dynamics models that are optimized using lessons learned from the
energy landscape theory of protein folding. We also present a review of the
results of the AMH/AMC/AMW/AWSEM family of coarse-grained molecular dynamics
protein folding models to illustrate the points covered in the first part of
the article. Accurate coarse-grained structure prediction models can be used to
investigate a wide range of conceptual and mechanistic issues outside of
protein structure prediction; specifically, the paper concludes by reviewing
how AWSEM has in recent years been able to elucidate questions related to the
unusual kinetic behavior of artificially designed proteins, multidomain protein
misfolding, and the initial stages of protein aggregation.

categories: q-bio.BM cond-mat.soft cond-mat.stat-mech physics.bio-ph


title: A New Term Rewriting Characterisation of ETIME functions

abstract:
  Adopting former term rewriting characterisations of polytime and
exponential-time computable functions, we introduce a new reduction order, the
Path Order for ETIME (POE* for short), that is sound and complete for ETIME
computable functions. The proposed reduction order for ETIME makes contrasts to
those related complexity classes clear.


abstract:
  We define and study Sobolev spaces associated with Jacobi expansions. We
prove that these Sobolev spaces are isomorphic to Jacobi potential spaces. As a
technical tool, we also show some approximation properties of Poisson-Jacobi
integrals.


title: Kondo conductance across the smallest spin 1/2 radical molecule

abstract:
  Molecular contacts are generally poorly conducting because their energy
levels tend to lie far from the Fermi energy of the metal contact,
necessitating undesirably large gate and bias voltages in molecular electronics
applications. Molecular radicals are an exception because their partly filled
orbitals undergo Kondo screening, opening the way to electron passage even at
zero bias. While that phenomenon has been experimentally demonstrated for
several complex organic radicals, quantitative theoretical predictions have not
been attempted so far. It is therefore an open question whether and to what
extent an ab initio-based theory is able to make accurate predictions for Kondo
temperatures and conductance lineshapes. Choosing nitric oxide NO as a simple
and exemplary spin 1/2 molecular radical, we present calculations based on a
combination of density functional theory and numerical renormalization group
(DFT+NRG) predicting a zero bias spectral anomaly with a Kondo temperature of
15 K for NO/Au(111). A scanning tunneling spectroscopy study is subsequently
carried out to verify the prediction, and a striking zero bias Kondo anomaly is
confirmed, still quite visible at liquid nitrogen temperatures. Comparison
shows that the experimental Kondo temperature of about 43 K is larger than the
theoretical one, while the inverted Fano lineshape implies a strong source of
interference not included in the model. These discrepancies are not a surprise,
providing in fact an instructive measure of the approximations used in the
modeling, which supports and qualifies the viability of the DFT+NRG approach to
the prediction of conductance anomalies in larger molecular radicals.


title: Monogamy of entanglement of formation

abstract:
  It is well known that a particle cannot freely share entanglement with two or
more particles. This restriction is generally called monogamy. However the
formal quantification of such restriction is only known for some measures of
entanglement and for two-level systems. The first and broadly known monogamy
relation was established by Coffman, Kundu, and Wootters for the square of the
concurrence. Since then, it is usually said that the entanglement of formation
is not monogamous, as it does not obey the same relation. We show here that
despite that, the entanglement of formation cannot be freely shared and
therefore should be said to be monogamous. Furthermore, the square of the
entanglement of formation does obey the same relation of the squared
concurrence, a fact recently noted for three particles and extended here for N
particles. Therefore the entanglement of formation is as monogamous as the
concurrence. We also numerically study how the entanglement is distributed in
pure states of three qubits and the relation between the sum of the bipartite
entanglement and the classical correlation.


title: The Science of al-Biruni

abstract:
  Al-Biruni (973-1048) was one of the greatest scientists of all times. He was
an astronomer, mathematician and philosopher, and studied physics and natural
sciences. In this paper, we will discuss some of his experimental methods and
some instruments he used.


title: Graph theory and Pfaffian representations of Ising partition function

abstract:
  A well known theorem due to Kasteleyn states that the partition function of
an Ising model on an arbitrary planar graph can be represented as the Pfaffian
of a skew-symmetric matrix associated to the graph. This results both embodies
the free fermionic nature of any planar Ising model and eventually gives an
effective way of computing its partition functions in closed form. An extension
of this result to non planar models expresses the partition function as a sum
of Pfaffians which number is related to the genus of the oriented surface on
which the graph can be embedded. In graph theory, McLane's theorem (1937) gives
a characterization of planarity as a property of the cycle space of a graph,
and recently, Diestel et al. (2009) extended this approach to embeddings in
arbitrary surfaces. Here we show that McLane's approach naturally leads to
Kasteleyn's results: McLane characterization of planar graphs is just what is
needed to turn an Ising partition function into a Pfaffian. Using this
approach, we prove that the Ising partition function on an arbitrary non planar
graph can be written as \emph{the real part}of the Pfaffian of a single matrix
with coefficients taken in a multicomplex algebra $\C_{\tilde g}$, where
$\tilde g$ is the non-orientable genus, or crosscap number, of the embedding
surface. Known representations as sums of Pfaffians follow from this result. In
particular, Kasteleyn's result which involves $4^g$ matrices with real
coefficients, $g$ orientable genus, is also recovered through some algebraic
reduction.

categories: math-ph cond-mat.stat-mech math.CO math.MP


title: A second binding model to study diffusion of $Cr$ diluted in BCC $Fe$

abstract:
  A classical molecular static technique (CMST) and DFT calculations using
SIESTA, are employed here to characterize the self diffusion and the tracer
solute diffusion in the bulk of BCC diluted $FeCr$ alloy driven by both vacancy
and interstitial migration. For the first time in the literature, a
six-frequency model (developed by Okamura and Allnatt) involved in a second
nearest neighbor binding approach is adapted for calculations in a real system.
We obtain microscopic parameters, namely: i) the free energy of vacancy
formation and the vacancy-solute binding energy, ii) the involved jump
frequencies, and iii) the tracer correlation factor. The present approximation
describes much better the experimental data of self and solute atoms than
recent calculations using a first binding approach. Also, we confirm that a
vacancy drag mechanism is unlikely to occur in $FeCr$ diluted alloys. Our
results also show that the diffusion processes is mainly mediated by vacancies,
while diffusion by intertitial mechanism is several orders of magnitudes
slower.


title: Enabling a linear model for the IMGC-02 absolute gravimeter

abstract:
  Measurement procedures of most rise-and-fall absolute gravimeters has to
resolve singularity at the apex of the trajectory caused by the discrete fringe
counting in the Michelson-type interferometers. Traditionally the singularity
is addressed by implementing non-linear models of the trajectory, but they
introduce problems of their own, such as biasness, non-uniqueness, and
instability of the gravity estimates. Using IMGC-02 gravimeter as example, we
show that the measurement procedure of the rise-and-fall gravimeters can be
based on the linear models which successfully resolve the singularity and
provide rigorous estimates of the gravity value. The linear models also
facilitate further enhancements of the instrument, such as accounting for new
types of disturbances and active compensation for the vibrations.


title:
Two Timescale Convergent Q-learning for Sleep--Scheduling in Wireless
  Sensor Networks

abstract:
  In this paper, we consider an intrusion detection application for Wireless
Sensor Networks (WSNs). We study the problem of scheduling the sleep times of
the individual sensors to maximize the network lifetime while keeping the
tracking error to a minimum. We formulate this problem as a
partially-observable Markov decision process (POMDP) with continuous
state-action spaces, in a manner similar to (Fuemmeler and Veeravalli [2008]).
However, unlike their formulation, we consider infinite horizon discounted and
average cost objectives as performance criteria. For each criterion, we propose
a convergent on-policy Q-learning algorithm that operates on two timescales,
while employing function approximation to handle the curse of dimensionality
associated with the underlying POMDP. Our proposed algorithm incorporates a
policy gradient update using a one-simulation simultaneous perturbation
stochastic approximation (SPSA) estimate on the faster timescale, while the
Q-value parameter (arising from a linear function approximation for the
Q-values) is updated in an on-policy temporal difference (TD) algorithm-like
fashion on the slower timescale. The feature selection scheme employed in each
of our algorithms manages the energy and tracking components in a manner that
assists the search for the optimal sleep-scheduling policy. For the sake of
comparison, in both discounted and average settings, we also develop a function
approximation analogue of the Q-learning algorithm. This algorithm, unlike the
two-timescale variant, does not possess theoretical convergence guarantees.
Finally, we also adapt our algorithms to include a stochastic iterative
estimation scheme for the intruder's mobility model. Our simulation results on
a 2-dimensional network setting suggest that our algorithms result in better
tracking accuracy at the cost of only a few additional sensors, in comparison
to a recent prior work.


title:
Asymptotic eigenvalue estimates for a Robin problem with a large
  parameter

abstract:
  Robin problem for the Laplacian in a bounded planar domain with a smooth
boundary and a large parameter in the boundary condition is considered. We
prove a two-sided three-term asymptotic estimate for the negative eigenvalues.
Furthermore, improving the upper bound we get a two term asymptotics in terms
of the coupling constant and the maximum of the boundary curvature.


title: Linear groups with Borel's property

abstract:
  When does Borel's theorem on free subgroups of semisimple groups generalize
to other groups? We initiate a systematic study of this question and find
positive and negative answers for it. In particular, we fully classify
fundamental groups of surfaces and von Dyck groups that satisfy Borel's
theorem. Further, as a byproduct of this theory, we make headway on a question
of Breuillard, Green, Guralnick, and Tao concerning double word maps.


title:
An asymptotic formula for Goldbach's conjecture with monic polynomials
  in $\mathbb{Z}[\theta][x]$

abstract:
  In this paper, we consider $D=\mathbb{Z}[\theta]$, where
  $$\theta= \sqrt{-k} \,\,\,\, \mbox{if}\;\;\;-k\not\equiv 1
\;(\mbox{mod}\;4)\,\,\,\,\mbox{or}\,\,\,\, \theta=\frac{\sqrt{-k}+1}{2}
\,\,\,\, \mbox{if}\;\;\;-k\equiv 1 \;(\mbox{mod}\;4),$$
  $k\geq 2$ is a squarefree integer, and we proved that the number $R(y)$ of
representations of a monic polynomial $f(x)\in \mathbb{Z}[\theta][x]$, of
degree $d\geq 1$, as a sum of two monic irreducible polynomials $g(x)$ and
$h(x)$ in $\mathbb{Z}[\theta][x]$, with the coefficients of $g(x)$ and $h(x)$
bounded in complex modulus by $y$, is asymptotic to $(4y)^{2d-2}$.


title: Online Steiner Tree with Deletions

abstract:
  In the online Steiner tree problem, the input is a set of vertices that
appear one-by-one, and we have to maintain a Steiner tree on the current set of
vertices. The cost of the tree is the total length of edges in the tree, and we
want this cost to be close to the cost of the optimal Steiner tree at all
points in time. If we are allowed to only add edges, a tight bound of
$\Theta(\log n)$ on the competitiveness is known. Recently it was shown that if
we can add one new edge and make one edge swap upon every vertex arrival, we
can maintain a constant-competitive tree online.
  But what if the set of vertices sees both additions and deletions? Again, we
would like to obtain a low-cost Steiner tree with as few edge changes as
possible. The original paper of Imase and Waxman had also considered this
model, and it gave a greedy algorithm that maintained a constant-competitive
tree online, and made at most $O(n^{3/2})$ edge changes for the first $n$
requests. In this paper give the following two results.
  Our first result is an online algorithm that maintains a Steiner tree only
under deletions: we start off with a set of vertices, and at each time one of
the vertices is removed from this set: our Steiner tree no longer has to span
this vertex. We give an algorithm that changes only a constant number of edges
upon each request, and maintains a constant-competitive tree at all times. Our
algorithm uses the primal-dual framework and a global charging argument to
carefully make these constant number of changes.
  We then study the natural greedy algorithm proposed by Imase and Waxman that
maintains a constant-competitive Steiner tree in the fully-dynamic model (where
each request either adds or deletes a vertex). Our second result shows that
this algorithm makes only a constant number of changes per request in an
amortized sense.


title:
New Method to Measure Proper Motions of Microlensed Sources: Application
  to Candidate Free-Floating-Planet Event MOA-2011-BLG-262

abstract:
  We develop a new method to measure source proper motions in microlensing
events, which can partially overcome problems due to blending. It takes
advantage of the fact that the source position is known precisely from the
microlensing event itself. We apply this method to the event MOA-2011-BLG-262,
which has a short timescale t_E=3.8 day, a companion mass ratio q=0.0047 and a
very high or high lens-source relative proper motion mu_rel=20 mas/yr or 12
mas/yr (for two possible models). These three characteristics imply that the
lens could be a brown dwarf or a massive planet with a roughly Earth-mass
"moon". The probability of such an interpretation would be greatly increased if
it could be shown that the high lens-source relative proper motion was
primarily due to the lens rather than the source. Based on the long-term
monitoring data of the Galactic bulge from the Optical Gravitational Lensing
Experiment (OGLE), we measure the source proper motion that is small, mu_s =
(-2.3, -0.9) +- (2.8,2.6) mas/yr in a (North, East) Galactic coordinate frame.
These values are then important input into a Bayesian analysis of the event
presented in a companion paper by Bennett et al.


title:
Ground-state magnetic phase diagram of bow-tie graphene nanoflakes in
  external magnetic field

abstract:
  The magnetic phase diagram of a ground state is studied theoretically for
graphene nanoflakes of bow-tie shape and various size in external in-plane
magnetic field. The tight-binding Hamiltonian supplemented with Hubbard term is
used to model the electronic structure of the systems in question. The
existence of the antiferromagnetic phase with magnetic moments localized at the
sides of the bow-tie is found for low field and a field-induced spin-flip
transition to ferromagnetic state is predicted to occur in charge-undoped
structures. For small nanoflake doped with a single charge carrier the
low-field phase is ferrimagnetic and a metamagnetic transition to ferromagnetic
ordering can be forced by the field. The critical field is found to decrease
with increasing size of the nanoflake. The influence of diagonal and
off-diagonal disorder on the mentioned magnetic properties is studied. The
effect of off-diagonal disorder is found to be more important than this of
diagonal disorder, leading to significantly widened distribution of critical
fields for disordered population of nanoflakes.


title:
Bifurcation of common levels of first integrals of the Kovalevskaya
  problem

abstract:
  The structure of integral manifolds in the Kovalevskaya problem of the motion
of a heavy rigid body about a fixed point is considered. An analytic
description of a bifurcation set is obtained, and bifurcation diagrams are
constructed. The number of two-dimensional tori is indicated for each connected
component of the supplement to the bifurcation set in the space of the first
integrals constants. The main topological bifurcations of the regular tori are
described.


title:
Space charge dynamics in solid electrolytes with steric effect and
  Vegard stresses: resistive switching and ferroelectric-like hysteresis of
  electromechanical response

abstract:
  We performed self-consistent modelling of electrotransport and
electromechanical response of solid electrolyte thin films allowing for steric
effects of mobile charged defects (ions, protons or vacancies), electron
degeneration and Vegard stresses. We establish correlations between the
features of the space-charge dynamics, current-voltage and bending-voltage
curves in the wide frequency range of applied electric voltage. The pronounced
ferroelectric-like hysteresis of bending-voltage loops and current maxima on
double hysteresis current-voltage loops appear for the electron-open
electrodes. The double hysteresis loop with pronounced humps indicates the
resistance switching of memristor-type. The switching occurs due to the strong
coupling between electronic and ionic subsystem. The sharp meta-stable maximum
of the electron density appears near one open electrode and moves to another
one during the periodic change of applied voltage. Our results can explain the
nature and correlation of electrical and mechanical memory effects in thin
films of solid electrolytes. The analytical expression proving that the
electrically induced bending of solid electrolyte films can be detected by
interferometric methods is derived.


title:
Central role of domain wall depinning for perpendicular magnetization
  switching driven by spin torque from the spin Hall effect

abstract:
  We study deterministic magnetic reversal of a perpendicularly magnetized Co
layer in a Co/MgO/Ta nano-square driven by spin Hall torque from an in-plane
current flowing in an underlying Pt layer. The rate-limiting step of the
switching process is domain-wall (DW) depinning by spin Hall torque via a
thermally-assisted mechanism that eventually produces full reversal by domain
expansion. An in-plane applied magnetic field collinear with the current is
required, with the necessary field scale set by the need to overcome DW
chirality imposed by the Dzyaloshinskii-Moriya interaction. Once Joule heating
is taken into account the switching current density is quantitatively
consistent with a spin Hall angle {\theta}$_{SH}$ ${\approx}$ 0.07 for 4 nm of
Pt.


title: Learning Human Pose Estimation Features with Convolutional Networks

abstract:
  This paper introduces a new architecture for human pose estimation using a
multi- layer convolutional network architecture and a modified learning
technique that learns low-level features and higher-level weak spatial models.
Unconstrained human pose estimation is one of the hardest problems in computer
vision, and our new architecture and learning schema shows significant
improvement over the current state-of-the-art results. The main contribution of
this paper is showing, for the first time, that a specific variation of deep
learning is able to outperform all existing traditional architectures on this
task. The paper also discusses several lessons learned while researching
alternatives, most notably, that it is possible to learn strong low-level
feature detectors on features that might even just cover a few pixels in the
image. Higher-level spatial models improve somewhat the overall result, but to
a much lesser extent then expected. Many researchers previously argued that the
kinematic structure and top-down information is crucial for this domain, but
with our purely bottom up, and weak spatial model, we could improve other more
complicated architectures that currently produce the best results. This mirrors
what many other researchers, like those in the speech recognition, object
recognition, and other domains have experienced.


title:
Spin Transfer Torque and Electric Current in Helical Edge States in
  Quantum Spin Hall Devices

abstract:
  We study the dynamics of a quantum spin Hall edge coupled to a magnet with
its own dynamics. Using spin transfer torque principles, we analyze the
interplay between spin currents in the edge state and dynamics of the axis of
the magnet, and draw parallels with circuit analogies. As a highlighting
feature, we show that while coupling to a magnet typically renders the edge
state insulating by opening a gap, in the presence of a small potential bias,
spin-transfer torque can restore perfect conductance by transferring angular
momentum to the magnet. In the presence of interactions within the edge state,
we employ a Luttinger liquid treatment to show that the edge, when subject to a
small voltage bias, tends to form a unique dynamic rotating spin wave state
that naturally couples into the dynamics of the magnet. We briefly discuss
realistic physical parameters and constraints for observing this interplay
between quantum spin Hall and spin-transfer torque physics.


title:
Gamma rays and neutrinos from a cosmic ray source in the Galactic Center
  region

abstract:
  The center of the our Galaxy is a region where very energetic phenomena take
place. In particular powerful cosmic ray sources can be located in that region.
The cosmic rays accelerated in these sources may interact with ambient protons
and/or low energy photons producing gamma rays and neutrinos. The observation
of these two types of secondary particles can be very useful for the
identification of the cosmic ray sources and for the understanding of the
physical processes occurring during acceleration.
  Motivated by the excess in the neutrino spectrum recently reported by the
IceCube Collaboration, we study in detail the shape of the gamma ray and
neutrino spectra originated from the interaction of cosmic ray protons with
ambient protons for sources located in the Galactic Center region. We consider
different models for proton acceleration and study the impact on the gamma ray
and neutrino spectra. We also discuss the possibility to constrain and even
identify a particular neutrino source by using the information given by the
gamma ray spectrum taking advantage of the modification of the spectral shape,
caused by the interaction of the gamma rays with the photons of the radiation
field present in the interstellar medium, which strongly depends on the source
distance.


title: Probabilistic Computability and Choice

abstract:
  We study the computational power of randomized computations on infinite
objects, such as real numbers. In particular, we introduce the concept of a Las
Vegas computable multi-valued function, which is a function that can be
computed on a probabilistic Turing machine that receives a random binary
sequence as auxiliary input. The machine can take advantage of this random
sequence, but it always has to produce a correct result or to stop the
computation after finite time if the random advice is not successful. With
positive probability the random advice has to be successful. We characterize
the class of Las Vegas computable functions in the Weihrauch lattice with the
help of probabilistic choice principles and Weak Weak K\H{o}nig's Lemma. Among
other things we prove an Independent Choice Theorem that implies that Las Vegas
computable functions are closed under composition. In a case study we show that
Nash equilibria are Las Vegas computable, while zeros of continuous functions
with sign changes cannot be computed on Las Vegas machines. However, we show
that the latter problem admits randomized algorithms with weaker failure
recognition mechanisms. The last mentioned results can be interpreted such that
the Intermediate Value Theorem is reducible to the jump of Weak Weak
K\H{o}nig's Lemma, but not to Weak Weak K\H{o}nig's Lemma itself. These
examples also demonstrate that Las Vegas computable functions form a proper
superclass of the class of computable functions and a proper subclass of the
class of non-deterministically computable functions. We also study the impact
of specific lower bounds on the success probabilities, which leads to a strict
hierarchy of classes. In particular, the classical technique of probability
amplification fails for computations on infinite objects. We also investigate
the dependency on the underlying probability space.


title:
Algorithmic Perspectives of Network Transitive Reduction Problems and
  their Applications to Synthesis and Analysis of Biological Networks

abstract:
  In this survey paper, we will present a number of core algorithmic questions
concerning several transitive reduction problems on network that have
applications in network synthesis and analysis involving cellular processes.
Our starting point will be the so-called minimum equivalent digraph problem, a
classic computational problem in combinatorial algorithms. We will subsequently
consider a few non-trivial extensions or generalizations of this problem
motivated by applications in systems biology. We will then discuss the
applications of these algorithmic methodologies in the context of three major
biological research questions: synthesizing and simplifying signal transduction
networks, analyzing disease networks, and measuring redundancy of biological
networks.


title: Density and isospin asymmetry dependence of high-momentum components

abstract:
  We study the one-body momentum distribution at different densities in nuclear
matter, with special emphasis on its components at high momentum. Explicit
calculations for finite neutron-proton asymmetry, based on the ladder
self-consistent Green's function approach, allow us to access the isospin
dependence of momentum distributions and elucidate their role in neutron-rich
systems. Comparisons with the deuteron momentum distribution indicate that a
substantial proportion of high-momentum components are dominated by tensor
correlations. We identify the density dependence of these tensor correlations
in the momentum distributions. Further, we find that high-momentum components
are determined by the density of each sub-species and we provide a new isospin
asymmetry scaling of these components. We use different realistic
nucleon-nucleon interactions to quantify the model dependence of our results.


title: lil' UCB : An Optimal Exploration Algorithm for Multi-Armed Bandits

abstract:
  The paper proposes a novel upper confidence bound (UCB) procedure for
identifying the arm with the largest mean in a multi-armed bandit game in the
fixed confidence setting using a small number of total samples. The procedure
cannot be improved in the sense that the number of samples required to identify
the best arm is within a constant factor of a lower bound based on the law of
the iterated logarithm (LIL). Inspired by the LIL, we construct our confidence
bounds to explicitly account for the infinite time horizon of the algorithm. In
addition, by using a novel stopping time for the algorithm we avoid a union
bound over the arms that has been observed in other UCB-type algorithms. We
prove that the algorithm is optimal up to constants and also show through
simulations that it provides superior performance with respect to the
state-of-the-art.


title: Neutrino mass hierarchy and matter effects

abstract:
  Matter effects modify the mixing and the effective masses of neutrinos in a
way which depends on the neutrino mass hierarchy. Consequently, for normal and
inverted hierarchies the oscillations and flavor conversion results are
different. Sensitivity to the mass hierarchy appears whenever the matter
effects on the 1-3 mixing and mass splitting become substantial. This happens
in supernovae in wide energy range and in the matter of the Earth. The Earth
density profile is a multi-layer medium where the resonance and parametric
enhancements of oscillations occur. The enhancement is realized in neutrino
(antineutrino) channels for the normal (inverted) mass hierarchy. Multi-megaton
scale under ice (water) atmospheric neutrino detectors with low energy
threshold can establish mass hierarchy with $(3 - 10) \sigma$ confidence level
in few years. The main challenges of these experiments are discussed and
various ways to improve sensitivity are outlined. In particular, inelasticity
measurements will allow to increase significance of the hierarchy
identification by $20 - 50 \%$ .


title: The perturbative structure of spin glass field theory

abstract:
  Cubic replicated field theory is used to study the glassy phase of the
short-range Ising spin glass just below the transition temperature, and for
systems above, at, and slightly below the upper critical dimension six. The
order parameter function is computed up to two-loop order. There are two,
well-separated bands in the mass spectrum, just as in mean field theory. The
small mass band acts as an infrared cutoff, whereas contributions from the
large mass region can be computed perturbatively (d>6), or interpreted by the
epsilon-expansion around the critical fixed point (d=6-epsilon). The one-loop
calculation of the (momentum-dependent) longitudinal mass, and the whole
replicon sector is also presented. The innocuous behavior of the replicon
masses while crossing the upper critical dimension shows that the ultrametric
replica symmetry broken phase remains stable below six dimensions.

categories: cond-mat.dis-nn cond-mat.stat-mech math-ph math.MP


title: Cosmological viable f(R,T) dark energy model: dynamics and stability

abstract:
  In this paper we undertake the modified theory of gravity f(R,T) where R and
T are the Ricci scalar and the trace of the energy momentum tensor,
respectively. Imposing the conservation of the energy momentum tensor, we
obtain a model about what dynamics and stability are studied. The stability is
developed using the de Sitter and power-law solutions. The results show that
the model presents stability for both the de Sitter and power-law solutions.
Regarding the dynamics, cosmological solutions are obtained by integrating the
background equations for both the low-redshift and High-redshift regimes and
are consistent with the observational data.


title: Metha-Ramanathan for {\epsilon} and k-semistable Decorated Sheaves

abstract:
  This paper is devoted to generalizing the Mehta-Ramanathan restriction
theorem to the case of {\epsilon}-semistable and k-semistable decorated
sheaves. After recalling the definition of decorated sheaves and their usual
semistability we define the {\epsilon} and k-(semi)stablility. We first prove
the existence of a (unique) {\epsilon}-maximal destabilizing subsheaf for
decorated sheaves (Section 3.1). After some others preliminar results (such as
the opennes condition for families of {\epsilon}-semistable decorated sheaves)
we finally prove, in Section 3.7, a restriction theorem for slope
{\epsilon}-semistable decorated sheaves. In Section 4 we reach the same results
in the k-semistability case that we did in the {\epsilon}-semistability, but
only for decorated sheaves of rank less or equal than 3.


title: Modularity, Calabi-Yau geometry and 2d CFTs

abstract:
  We give a short overview over recent work on finding constraints on partition
functions of 2d CFTs from modular invariance. We summarize the constraints on
the spectrum and their connection to Calabi-Yau compactifications.


title:
Measurements of Fission Products from the Fukushima Daiichi Incident in
  San Francisco Bay Area Air Filters, Automobile Filters, Rainwater, and Food

abstract:
  A variety of environmental media were analyzed for fallout radionuclides
resulting from the Fukushima nuclear accident by the Low Background Facility
(LBF) at the Lawrence Berkeley National Laboratory (LBNL) in Berkeley, CA.
Monitoring activities in air and rainwater began soon after the onset of the
March 11, 2011 tsunami and are reported here through the end of 2012. Observed
fallout isotopes include $^{131}$I, $^{132}$I,$^{132}$Te,$^{134}$Cs,
$^{136}$Cs, and $^{137}$Cs. Isotopes were measured on environmental air
filters, automobile filters, and in rainwater. An additional analysis of
rainwater in search of $^{90}$Sr is also presented. Last, a series of food
measurements conducted in September of 2013 are included due to extended media
concerns of $^{134, 137}$Cs in fish. Similar measurements of fallout from the
Chernobyl disaster at LBNL, previously unpublished publicly, are also presented
here as a comparison with the Fukushima incident. All measurements presented
also include natural radionuclides found in the environment to provide a basis
for comparison.


title: One-dimensional transport of bosons between weakly linked reservoirs

abstract:
  We study a flow of ultracold bosonic atoms through a one-dimensional channel
that connects two macroscopic three-dimensional reservoirs of Bose-condensed
atoms via weak links implemented as potential barriers between each of the
reservoirs and the channel. We consider reservoirs at equal chemical potentials
so that a superflow of the quasi-condensate through the channel is driven
purely by a phase difference, $2\Phi$, imprinted between the reservoirs. We
find that the superflow never has the standard Josephson form $\sim \sin 2\Phi
$. Instead, the superflow discontinuously flips direction at $2\Phi =\pm\pi$
and has metastable branches. We show that these features are robust and not
smeared by fluctuations or phase slips. We describe a possible experimental
setup for observing these phenomena.


title: On the relative dual of an $S^1$-gerbe over an orbifold

abstract:
  We construct a new effective orbifold $\widehat{\Y}$ with an $S^1$-gerbe $c$
to study an $S^1$-gerbe $\mathfrak{t}$ on a $G$-gerbe $\Y$ over an orbifold
$\B$. We view the former as the relative dual, relative to $\B$, of the latter.
We show that the two pairs $(\Y, \mathfrak{t})$ and $(\widehat{\Y}, c)$ have
isomorphic categories of sheaves, and also the associated twisted groupoid
algebras are Morita equivalent. As a corollary, the K-theory and cohomology
groups of $(\Y, \mathfrak{t})$ and $(\widehat{\Y}, c)$ are isomorphic.


title:
Spin echo dynamics under an applied drift field in graphene nanoribbon
  superlattices

abstract:
  We investigate the evolution of spin dynamics in graphene nanoribbon
superlattices (GNSLs) with armchair and zigzag edges in the presence of a drift
field. We determine the exact evolution operator and show that it exhibits spin
echo phenomena due to rapid oscillations of the quantum states along the
ribbon. The evolution of the spin polarization is accompanied by strong beating
patterns. We also provide detailed analysis of the band structure of GNSLs with
armchair and zigzag edges.


title:
On automorphisms with natural tangent actions on homogeneous parabolic
  geometries

abstract:
  We consider automorphisms of homogeneous parabolic geometries with a fixed
point. Parabolic geometries carry the distinguished distributions and we study
those automorphisms which enjoy natural actions on the distributions at the
fixed points. We describe the sets of such automorphisms on homogeneous
parabolic geometries in detail and classify, whether there are non--flat
homogeneous parabolic geometries carrying such automorphisms. We present two
general constructions of such geometries and we provide complete
classifications for the types (G,P) of the parabolic geometries that have G
simple and the automorphisms are of order 2.


title: Van-der-Waals stabilized Rydberg aggregates

abstract:
  Assemblies of Rydberg atoms subject to resonant dipole-dipole interactions
form Frenkel excitons. We show that van-der-Waals shifts can significantly
modify the exciton wave function, whenever atoms approach each other closely.
As a result, attractive excitons and repulsive van-der-Waals interactions can
be combined to form stable one-dimensional atom chains, akin to bound
aggregates. Here the van-der-Waals shifts ensure a stronger homogeneous
delocalisation of a single excitation over the whole chain, enabling it to bind
up to six atoms. When brought into unstable configurations, such Rydberg
aggregates allow the direct monitoring of their dissociation dynamics.


title: A proof of Grothendieck's base change theorem

abstract:
  We give an elementary short proof of Grothendieck's base change theorem for
the cohomology of flat coherent sheaves.


title: Detecting Wave Function Collapse Without Prior Knowledge

abstract:
  We are concerned with the problem of detecting with high probability whether
a wave function has collapsed or not, in the following framework: A quantum
system with a $d$-dimensional Hilbert space is initially in state $\psi$; with
probability $0<p<1$, the state collapses relative to the orthonormal basis
$b_1,...,b_d$. That is, the final state $\psi'$ is random; it is $\psi$ with
probability $1-p$ and $b_k$ (up to a phase) with $p$ times Born's probability
$|\langle b_k|\psi \rangle|^2$. Now an experiment on the system in state
$\psi'$ is desired that provides information about whether or not a collapse
has occurred. Elsewhere, we identify and discuss the optimal experiment in case
that $\psi$ is either known or random with a known probability distribution.
Here we present results about the case that no a priori information about
$\psi$ is available, while we regard $p$ and $b_1,...,b_d$ as known. For
certain values of $p$, we show that the set of $\psi$s for which any experiment
E is more reliable than blind guessing is at most half the unit sphere; thus,
in this regime, any experiment is of questionable use, if any at all.
Remarkably, however, there are other values of $p$ and experiments E such that
the set of $\psi$s for which E is more reliable than blind guessing has measure
greater than half the sphere, though with a conjectured maximum of 64% of the
sphere.


title:
Representing Quantum Superpositions: Powers, Potentia and Potential
  Effectuations

abstract:
  In this paper we attempt to provide a physical representation of quantum
superpositions. For this purpose we discuss the constraints of the quantum
formalism to the notion of possibility and the necessity to consider a
potential realm independent of actuality. Taking these insights into account
and from the basic principles of quantum mechanics itself we advance towards
the definition of the notions of power and potentia. Assuming these notions as
a standpoint we analyze the meaning of 'observation' and 'interaction'. As a
conclusion we provide a set of axioms which comprise our interpretation of
quantum mechanics and argue in favor of a redefinition of the orthodox problems
discussed in the literature.


title: Norm Convergence of Realistic Projection and Reflection Methods

abstract:
  We provide sufficient conditions for norm convergence of various projection
and reflection methods, as well as giving limiting examples regarding
convergence rates.


title: Chain recurrent sets of generic mappings on compact spaces

abstract:
  Let 0-CR denote the class of all metric compacta X such that the set of maps
$f:X\to X$ with 0-dimensional sets CR(f) of chain recurrent points is a dense
$G_\delta$-subset of the mapping space C(X,X) (with the uniform convergence).
We prove, among others, that countable products of polyhedra or locally
connected curves belong to 0-CR. Compacta that admit, for each $\epsilon >0$,
an $\epsilon$-retraction onto a subspace from 0-CR belong to 0-CR themselves.
Perfect ANR-compacta or n-dimensional $LC^{n-1}$-compacta have perfect CR(f)
for a generic self-map f. In the cases of polyhedra, compact Hilbert cube
manifolds, local dendrites and their finite products, a generic f has CR(f)
being a Cantor set and the set of periodic points of f of arbitrarily large
periods is dense in CR(f). The results extend some known facts about CR(f) of
generic self-maps f on PL-manifolds.


title:
Spatial correlation functions and dynamical exponents in very large
  samples of 4D spin glasses

abstract:
  The study of the low temperature phase of spin glass models by means of Monte
Carlo simulations is a challenging task, because of the very slow dynamics and
the severe finite size effects they show. By exploiting at the best the
capabilities of standard modern CPUs (especially the SSE instructions), we have
been able to simulate the four-dimensional (4D) Edwards-Anderson model with
Gaussian couplings up to sizes $L=70$ and for times long enough to accurately
measure the asymptotic behavior. By quenching systems of different sizes to the
the critical temperature and to temperatures in the whole low temperature
phase, we have been able to identify the regime where finite size effects are
negligible: $\xi(t) \lesssim L/7$. Our estimates for the dynamical exponent ($z
\simeq 1/T$) and for the replicon exponent ($\alpha \simeq 1.0$ and
$T$-independent), that controls the decay of the spatial correlation in the
zero-overlap sector, are consistent with the RSB theory, but the latter differs
from the theoretically conjectured value.


title:
Replica Exchange using q-Gaussian Swarm Quantum Particle Intelligence
  Method

abstract:
  We present a newly developed Replica Exchange algorithm using q -Gaussian
Swarm Quantum Particle Optimization (REX@q-GSQPO) method for solving the
problem of finding the global optimum. The basis of the algorithm is to run
multiple copies of independent swarms at different values of q parameter. Based
on an energy criterion, chosen to satisfy the detailed balance, we are swapping
the particle coordinates of neighboring swarms at regular iteration intervals.
The swarm replicas with high q values are characterized by high diversity of
particles allowing escaping local minima faster, while the low q replicas,
characterized by low diversity of particles, are used to sample more
efficiently the local basins. We compare the new algorithm with the standard
Gaussian Swarm Quantum Particle Optimization (GSQPO) and q-Gaussian Swarm
Quantum Particle Optimization (q-GSQPO) algorithms, and we found that the new
algorithm is more robust in terms of the number of fitness function calls, and
more efficient in terms ability convergence to the global minimum. In
additional, we also provide a method of optimally allocating the swarm replicas
among different q values. Our algorithm is tested for three benchmark
functions, which are known to be multimodal problems, at different
dimensionalities. In addition, we considered a polyalanine peptide of 12
residues modeled using a G\=o coarse-graining potential energy function.


title: Analytic cohomology groups of infinite dimensional complex manifolds

abstract:
  Given a cohesive sheaf $\Cal S$ over a complex Banach manifold $M$, we endow
the cohomology groups $H^q(M,\Cal S)$ of $M$ and $H^q(\frak U,\Cal S)$ of open
covers $\frak U$ of $M$ with a locally convex topology. Under certain
assumptions we prove that the canonical map $H^q(\frak U,\Cal S)\to H^q(M,\Cal
S)$ is an isomorphism of topological vector spaces.


title: A family of density expansions for L\'evy-type processes

abstract:
  We consider a defaultable asset whose risk-neutral pricing dynamics are
described by an exponential Levy-type martingale subject to default. This class
of models allows for local volatility, local default intensity, and a locally
dependent Levy measure. Generalizing and extending the novel adjoint expansion
technique of Pagliarani, Pascucci, and Riga (2013), we derive a family of
asymptotic expansions for the transition density of the underlying as well as
for European-style option prices and defaultable bond prices. For the density
expansion, we also provide error bounds for the truncated asymptotic series.
Our method is numerically efficient; approximate transition densities and
European option prices are computed via Fourier transforms; approximate bond
prices are computed as finite series. Additionally, as in Pagliarani et al.
(2013), for models with Gaussian-type jumps, approximate option prices can be
computed in closed form. Sample Mathematica code is provided.


title: A note on symplectic topology of $b$-manifolds

abstract:
  A Poisson manifold $(M^{2n},\p)$ is $b$-symplectic if $\bigwedge^n\p$ is
transverse to the zero section. In this paper we apply techniques native to
Symplectic Topology to address questions pertaining to $b$-symplectic
manifolds. We provide constructions of $b$-symplectic structures on open
manifolds by Gromov's $h$-principle, and of $b$-symplectic manifolds with a
prescribed singular locus, by means of surgeries.


title:
The Venus ground-based image Active Archive: a database of amateur
  observations of Venus in ultraviolet and infrared light

abstract:
  The Venus ground-based image Active Archive is an online database designed to
collect ground-based images of Venus in such a way that they are optimally
useful for science. The Archive was built to support ESA's Venus Amateur
Observing Project, which utilises the capabilities of advanced amateur
astronomers to collect filtered images of Venus in ultraviolet, visible and
near-infrared light. These images complement the observations of the Venus
Express spacecraft, which cannot continuously monitor the northern hemisphere
of the planet due to its elliptical orbit with apocentre above the south pole.
We present the first set of observations available in the Archive and assess
the usability of the dataset for scientific purposes.


title:
Trans-generational effect of trained aversive and appetitive experiences
  in Drosophila

abstract:
  Associative learning allows animals to rapidly adapt to changes in the
environment. Whether and what aspects of such acquired traits may be
transmittable across generations remains unclear. Using prolonged olfactory
training and subsequent two-forced choice testing in Drosophila melanogaster,
it is observed that certain aspects of learned behavior were transmitted from
parents to offspring. Offspring of parents exposed to distinct odors during
both aversive and appetitive conditioning displayed a heightened sensitivity to
those same odors. The conditioned responses associated with those odors,
however, were not transmitted to the offspring as they displayed a constitutive
preference to the parent-exposed stimuli irrespective of whether they were
associated with aversive or appetitive training. Moreover, the degree to which
the offspring preferred the conditioned stimuli markedly varied from
odor-to-odor. These findings suggest that heightened sensitivities to certain
salient stimuli in the environment, but not their associated conditioned
behaviors, may be transmittable from parents to offspring. Such
trans-generational adaptations may influence animal traits over short
evolutionary time-scales.


title: The proof of the removable pair conjecture for fractional dimension

abstract:
  In 1971 Trotter conjectured that every finite poset on at least $3$ points
has a pair whose removal does not decrease the dimension by more than $1$. In
1992 Brightwell and Scheinerman introduced fractional dimension of posets, and
they made a similar conjecture for fractional dimension. This paper settles
this latter conjecture.


title:
The average number of elements in the 4-Selmer groups of elliptic curves
  is 7

abstract:
  We prove that when all elliptic curves over $\mathbb{Q}$ are ordered by
height, the average size of their 4-Selmer groups is equal to 7. As a
consequence, we show that a positive proportion (in fact, at least one fifth)
of all 2-Selmer elements of elliptic curves, when ordered by height, do not
lift to 4-Selmer elements, and thus correspond to nontrivial 2-torsion elements
in the associated Tate--Shafarevich groups.


title:
Coisotropic Hofer-Zehnder capacities and non-squeezing for relative
  embeddings

abstract:
  We introduce the notion of a symplectic capacity relative to a coisotropic
submanifold of a symplectic manifold, and we construct two examples of such
capacities through modifications of the Hofer-Zehnder capacity. As a
consequence, we obtain a non-squeezing theorem for symplectic embeddings
relative to coisotropic constraints and existence results for leafwise chords
on energy surfaces.


title: Correlation-based construction of neighborhood and edge features

abstract:
  Motivated by an abstract notion of low-level edge detector filters, we
propose a simple method of unsupervised feature construction based on pairwise
statistics of features. In the first step, we construct neighborhoods of
features by regrouping features that correlate. Then we use these subsets as
filters to produce new neighborhood features. Next, we connect neighborhood
features that correlate, and construct edge features by subtracting the
correlated neighborhood features of each other. To validate the usefulness of
the constructed features, we ran AdaBoost.MH on four multi-class classification
problems. Our most significant result is a test error of 0.94% on MNIST with an
algorithm which is essentially free of any image-specific priors. On CIFAR-10
our method is suboptimal compared to today's best deep learning techniques,
nevertheless, we show that the proposed method outperforms not only boosting on
the raw pixels, but also boosting on Haar filters.


title: The signature of initial conditions on magnetohydrodynamic turbulence

abstract:
  We demonstrate that special correlations in the initial conditions of freely
evolving, homogeneous magnetohydrodynamic (MHD) turbulence can lead to the
formation of enormous current sheets. These coherent structures are observed at
the peak of the energy dissipation rate and are the carriers of long-range
correlations despite all the non-linear interactions during the formation of
turbulence. Even though the largest scale separation has been achieved at this
point, these structures are coherent with a size that spans our computational
domain dominating the scaling of the energy spectrum, which follows a $E
\propto k^{-2}$ power law. As Reynolds number increases curling of the current
sheets, due to Kelvin-Helmhotlz type instabilities and reconnection, modifies
the scaling of the energy spectrum from $k^{-2}$ towards $k^{-5/3}$. This
transition occurs at the highest Reynolds numbers of direct numerical
simulations with resolutions up to $2048^3$ grid points. Finite Reynolds number
behaviour is observed due to the initial correlations without reaching a finite
asymptote for the energy dissipation rate and with an unexpected scaling
between the Taylor and the integral scale Reynolds numbers, i.e. $Re_\lambda
\propto Re^{2/3}$. Our results, therefore, demonstrate that even
state-of-the-art numerical simulations of the highest resolution can be
influenced by the choice of initial conditions and consequently they are
inadequate to deduce unequivocally the fate of universality in MHD turbulence.


title: Minimizing Metastatic Risk in Radiotherapy Fractionation Schedules

abstract:
  Metastasis is the process by which cells from a primary tumor disperse and
form new tumors at distant anatomical locations. The treatment and prevention
of metastatic cancer remains an extremely challenging problem. This work
introduces a novel biologically motivated objective function to the radiation
optimization community that takes into account metastatic risk instead of the
status of the primary tumor. In this work, we consider the problem of
developing fractionated irradiation schedules that minimize production of
metastatic cancer cells while keeping normal tissue damage below an acceptable
level. A dynamic programming framework is utilized to determine the optimal
fractionation scheme. We evaluated our approach on a breast cancer case using
the heart and the lung as organs-at-risk (OAR). For small tumor $\alpha/\beta$
values, hypo-fractionated schedules were optimal, which is consistent with
standard models. However, for relatively larger $\alpha/\beta$ values, we found
the type of schedule depended on various parameters such as the time when
metastatic risk was evaluated, the $\alpha/\beta$ values of the OARs, and the
normal tissue sparing factors. Interestingly, in contrast to standard models,
hypo-fractionated and semi-hypo-fractionated schedules (large initial doses
with doses tapering off with time) were suggested even with large tumor
$\alpha$/$\beta$ values. Numerical results indicate potential for significant
reduction in metastatic risk.


title: On solvability of an indefinite Riccati equation

abstract:
  This note concerns a class of matrix Riccati equations associated with
stochastic linear-quadratic optimal control problems with indefinite state and
control weighting costs. A novel sufficient condition of solvability of such
equations is derived, based on a monotonicity property of a newly defined set.
Such a set is used to describe a family of solvable equations.


title:
On the number of integral binary $n$-ic forms having bounded Julia
  invariant

abstract:
  In 1848, Hermite introduced a reduction theory for binary forms of degree $n$
which was developed more fully in the seminal 1917 treatise of Julia. This
canonical method of reduction made use of a new, fundamental, but irrational
$\mathrm{SL}_2$-invariant of binary $n$-ic forms defined over $\mathbb{R}$,
which is now known as the Julia invariant. In this paper, for each $n$ and $k$
with $n+k\geq 3$, we determine the asymptotic behavior of the number of
$\mathrm{SL}_2(\mathbb{Z})$-equivalence classes of binary $n$-ic forms, with
$k$ pairs of complex roots, having bounded Julia invariant. Specializing to
$(n,k)=(2,1)$ and $(3,0)$, respectively, recovers the asymptotic results of
Gauss and Davenport on positive definite binary quadratic forms and positive
discriminant binary cubic forms, respectively.


title: Quantum Fluctuations in Cosmology and How They Lead to a Multiverse

abstract:
  This article discusses density perturbations in inflationary models, offering
a pedagogical description of how these perturbations are generated by quantum
fluctuations in the early universe. A key feature of inflation is that that
rapid expansion can stretch microscopic fluctuations to cosmological
proportions. I discuss also another important conseqence of quantum
fluctuations: the fact that almost all inflationary models become eternal, so
that once inflation starts, it never stops.


title: Functions preserving slowly oscillating double sequences

abstract:
  A double sequence $\textbf{x}=\{x_{k,l}\}$ of points in $\textbf{R}$ is
slowly oscillating if for any given $\varepsilon>0$, there exist
$\alpha=\alpha(\varepsilon)>0$, $\delta=\delta (\varepsilon) >0$, and
$N=N(\varepsilon)$ such that $|x_{k,l}-x_{s,t}|<\varepsilon$ whenever $k,l\geq
N(\varepsilon)$ and $k\leq s \leq (1+\alpha)k$, $l\leq t \leq (1+\delta)l$. We
study continuity type properties of factorable double functions defined on a
double subset $A\times A$ of $\textbf{R}^{2}$ into $\textbf{R}$, and obtain
interesting results related to uniform continuity, sequential continuity, and a
newly introduced type of continuity of factorable double functions defined on a
double subset $A\times A$ of $\textbf{R}^{2}$ into $\textbf{R}$.


title: Optimal Prediction of the Last-Passage Time of a Transient Diffusion

abstract:
  We identify the integrable stopping time $\tau_*$ with minimal $L^1$-distance
to the last-passage time $\gamma_z$ to a given level $z>0$, for an arbitrary
non-negative time-homogeneous transient diffusion $X$. We demonstrate that
$\tau_*$ is in fact the first time that $X$ assumes a value outside a half-open
interval $[0,r_*)$. The upper boundary $r_*>z$ of this interval is
characterised either as the solution for a one-dimensional optimisation
problem, or as part of the solution for a free-boundary problem. A number of
concrete examples illustrate the result.


title:
Efficiency analysis of diffusion on T-fractals in the sense of random
  walks

abstract:
  Efficiently controlling the diffusion process is crucial in the study of
diffusion problem in complex systems. In the sense of random walks with a
single trap, mean trapping time(MTT) and mean diffusing time(MDT) are good
measures of trapping efficiency and diffusion efficiency respectively. They
both vary with the location of the node. In this paper, we study random walks
on T-fractal and provided general methods to calculate the MTT for any target
node and the MDT for any source node. Using the MTT and the MDT as the measure
of trapping efficiency and diffusion efficiency respectively, we compare the
trapping efficiency and diffusion efficiency among all nodes of T-fractal and
find the best (or worst) trapping sites and the best (or worst) diffusing
sites. Our results show that: the hub node of T-fractal is the best trapping
site, but it is also the worst diffusing site, the three boundary nodes are the
worst trapping sites, but they are also the best diffusing sites. Comparing the
minimum and maximum of MTT and MDT, we found that the maximum of MTT is almost
$6$ times of the minimum for MTT and the maximum of MDT is almost equal to the
minimum for MDT. These results show that the location of target node has big
effect on the trapping efficiency, but the location of source node almost has
no effect on diffusion efficiency. We also conducted numerical simulation to
test the results we have derived, the results we derived are consistent with
those obtained by numerical simulation.


title:
Effects of node position on diffusion and trapping efficiency for random
  walks on fractal scale-free trees

abstract:
  We study unbiased discrete random walks on the FSFT based on the its
self-similar structure and the relations between random walks and electrical
networks. First, we provide new methods to derive analytic solutions of the
MFPT for any pair of nodes, the MTT for any target node and MDT for any
starting node. And then, using the MTT and the MDT as the measures of trapping
efficiency and diffusion efficiency respectively, we analyze the effect of
trap's position on trapping efficiency and the effect of starting position on
diffusion efficiency. Comparing the trapping efficiency and diffusion
efficiency among all nodes of FSFT, we find the best (or worst) trapping sites
and the best (or worst) diffusing sites. Our results show that: the node which
is at the center of FSFT is the best trapping site, but it is also the worst
diffusing site. The nodes which are the farthest nodes from the two hubs are
the worst trapping sites, but they are also the best diffusion sites. Comparing
the maximum and minimum of MTT and MDT, we found that the maximum of MTT is
almost $\frac{20m^2+32m+12}{4m^2+4m+1}$ times of the minimum of MTT, but the
the maximum of MDT is almost equal to the minimum of MDT. These results shows
that the position of target node has big effect on trapping efficiency, but the
position of starting node almost has no effect on diffusion efficiency. We also
conducted numerical simulation to test the results we have derived, the results
we derived are consistent with those obtained by numerical simulation.


title:
Lesion Border Detection in Dermoscopy Images Using Ensembles of
  Thresholding Methods

abstract:
  Dermoscopy is one of the major imaging modalities used in the diagnosis of
melanoma and other pigmented skin lesions. Due to the difficulty and
subjectivity of human interpretation, automated analysis of dermoscopy images
has become an important research area. Border detection is often the first step
in this analysis. In many cases, the lesion can be roughly separated from the
background skin using a thresholding method applied to the blue channel.
However, no single thresholding method appears to be robust enough to
successfully handle the wide variety of dermoscopy images encountered in
clinical practice. In this paper, we present an automated method for detecting
lesion borders in dermoscopy images using ensembles of thresholding methods.
Experiments on a difficult set of 90 images demonstrate that the proposed
method is robust, fast, and accurate when compared to nine state-of-the-art
methods.


title: Bankruptcy Risk Induced by Career Concerns of Regulators

abstract:
  We introduce a model in which a regulator employs mechanism design to embed
her human capital beta signal(s) in a firm's capital structure, in order to
enhance the value of her post career change indexed executive stock option
contract with the firm. We prove that the agency cost of this revolving door
behavior increases the firm's financial leverage, bankruptcy risk, and affects
estimation of firm value at risk (VaR).


title: Minding the Gap in N=4 Super-Yang-Mills

abstract:
  We analyze fermionic response in the geometry holographically dual to
zero-temperature N=4 Super-Yang-Mills theory with two equal nonvanishing
chemical potentials, which is characterized by a singular horizon and zero
ground state entropy. We show that fermionic fluctuations are completely stable
within a gap in energy around a Fermi surface singularity, beyond which
non-Fermi liquid behavior returns. This gap disappears abruptly once the final
charge is turned on, and is associated to a discontinuity in the corresponding
chemical potential. We also show that the singular near-horizon geometry lifts
to a smooth AdS_3 x R^3, and interpret the gap as a region where the
quasiparticle momentum is spacelike in six dimensions due to the momentum
component in the Kaluza-Klein direction, corresponding to the final charge.


title:
A Simple Derivation of Finite-Temperature CFT Correlators from the BTZ
  Black Hole

abstract:
  We present a simple Lie-algebraic approach to momentum-space two-point
functions of two-dimensional conformal field theory at finite temperature dual
to the BTZ black hole. Making use of the real-time prescription of AdS/CFT
correspondence and ladder equations of the Lie algebra $\mathfrak{so}(2,2)
\cong \mathfrak{sl}(2,\mathbb{R})_{L} \oplus \mathfrak{sl}(2,\mathbb{R})_{R}$,
we show that the finite-temperature two-point functions in momentum space
satisfy linear recurrence relations with respect to the left and right momenta.
These recurrence relations are exactly solvable and completely determine the
momentum-dependence of retarded and advanced two-point functions of
finite-temperature conformal field theory.


title: Multi-particle eccentricities in collisions dominated by fluctuations

abstract:
  We compute analytically the multi-particle eccentricities, \epsilon_m {2n},
for systems dominated by fluctuations, such as proton-nucleus collisions at the
Large Hadron Collider. In particular, we derive a general relation for
<\epsilon_2^{2n}>. We further discuss the relations between various
multi-particle eccentricities and demonstrate that \epsilon_2{2} >
\epsilon_2{4} \simeq \epsilon_2{6} \simeq \epsilon_2{8}, in agreement with
recent numerical calculations in a Glauber model.


title: Compressed electroweakino spectra at the LHC

abstract:
  In this work, we examine the sensitivity of monojet searches at the LHC to
directly produced charginos and neutralinos (electroweakinos) in the limit of
small mass splitting, where the traditional multilepton plus missing energy
searches loose their sensitivity. We first recast the existing 8 TeV monojet
search at CMS in terms of a SUSY simplified model with only light gauginos
(winos and binos) or only light higgsinos. The current searches are not
sensitive to MSSM like production cross sections, but would be sensitive to
models with 2-20 times enhanced production cross section, for particle masses
between 100 GeV and 250 GeV. Then we explore the sensitivity in the 14 TeV run
of the LHC. Here we emphasise that in addition to the pure monojet search, soft
leptons present in the samples can be used to increase the sensitivity.
Exclusion of electroweakino masses up to 200 GeV is possible with 300 fb$^{-1}$
at the LHC, if the systematic error can be reduced to the 1% level. Discovery
is possible with 3000 fb$^{-1}$ in some regions of parameter space.


title: Borel Liftings of Graph Limits

abstract:
  The cut pseudo-metric on the space of graph limits induces an equivalence
relation. The quotient space obtained by collapsing each equivalence class to a
point is a metric space with appealing analytic properties. We show that the
equivalence relation admits a Borel lifting: There exists a Borel-measurable
mapping which maps each equivalence class to one of its elements.


title: Ideas for Advancing Code Sharing (A Different Kind of Hack Day)

abstract:
  How do we as a community encourage the reuse of software for telescope
operations, data processing, and calibration? How can we support making codes
used in research available for others to examine? Continuing the discussion
from last year Bring out your codes! BoF session, participants separated into
groups to brainstorm ideas to mitigate factors which inhibit code sharing and
nurture those which encourage code sharing. The BoF concluded with the sharing
of ideas that arose from the brainstorming sessions and a brief summary by the
moderator.


title:
A system's wave function is uniquely determined by its underlying
  physical state

abstract:
  We address the question of whether the quantum-mechanical wave function
$\Psi$ of a system is uniquely determined by any complete description $\Lambda$
of the system's physical state. We show that this is the case if the latter
satisfies a notion of "free choice". This notion requires that certain
experimental parameters---those that according to quantum theory can be chosen
independently of other variables---retain this property in the presence of
$\Lambda$. An implication of this result is that, among all possible
descriptions $\Lambda$ of a system's state compatible with free choice, the
wave function $\Psi$ is as objective as $\Lambda$.


title: Design of Reversible Random Access Memory

abstract:
  Reversible logic has become immensely popular research area and its
applications have spread in various technologies for their low power
consumption. In this paper we proposed an efficient design of random access
memory using reversible logic. In the way of designing the reversible random
access memory we proposed a reversible decoder and a write enable reversible
master slave D flip-flop. All the reversible designs are superior in terms of
quantum cost, delay and garbage outputs compared to the designs existing in
literature.


title: A Novel Approach for Designing Online Testable Reversible Circuits

abstract:
  Reversible logic is gaining interest of many researchers due to its low power
dissipating characteristic. In this paper we proposed a new approach for
designing online testable reversible circuits. The resultant testable
reversible circuit can detect any single bit error whiles it is operating.
Appropriate theorems and lemmas are presented to clarify the proposed design.
The experimental results show that our design approach is superior in terms of
number of number of gates, garbage outputs and quantum cost.


title:
Fitting the Continuum Component of A Composite SDSS Quasar Spectrum
  Using CMA-ES

abstract:
  Fitting the continuum component of a quasar spectrum in UV/optical band is
challenging due to contamination of numerous emission lines. Traditional
fitting algorithms such as the least-square fitting and the Levenberg-Marquardt
algorithm (LMA) are fast but are sensitive to initial values of fitting
parameters. They cannot guarantee to find global optimum solutions when the
object functions have multiple minima. In this work, we attempt to fit a
typical quasar spectrum using the Covariance Matrix Adaptation Evolution
Strategy (CMA-ES). The spectrum is generated by composing a number of real
quasar spectra from the Sloan Digital Sky Survey (SDSS) quasar catalog data
release 3 (DR3) so it has a higher signal-to-noise ratio. The CMA-ES algorithm
is an evolutionary algorithm that is designed to find the global rather than
the local minima. The algorithm we implemented achieves an improved fitting
result than the LMA and unlike the LMA, it is independent of initial parameter
values. We are looking forward to implementing this algorithm to real quasar
spectra in UV/optical band.


title: Tensor product algebras, Grassmannians and Khovanov homology

abstract:
  We discuss a new perspective on Khovanov homology, using categorifications of
tensor products. While in many ways more technically demanding than Khovanov's
approach (and its extension by Bar-Natan), this has distinct advantage of
directly connecting Khovanov homology to a categorification of
\$(\mathbb{C}^2)^{\otimes \ell}\$, and admitting a direct generalization to
other Lie algebras.
  While the construction discussed is a special case of that given in previous
work of the author, this paper contains new results about the special case of
\$\mathfrak{sl}_2\$ showing an explicit connection to Bar-Natan's approach to
Khovanov homology, to the geometry of Grassmannians, and to the categorified
Jones-Wenzl projectors of Cooper and Krushkal. In particular, we show that the
colored Jones homology defined by our approach coincides with that of Cooper
and Krushkal.


title: Oblique Alfv\'en instability driven by compensated currents

abstract:
  Compensated-current systems created by energetic ion beams are widespread in
space and astrophysical plasmas. The well-known examples are foreshock regions
in the solar wind and around supernova remnants. We found a new oblique
Alfv\'enic instability driven by compensated currents flowing along the
background magnetic field. Because of the vastly different electron and ion
gyroradii, oblique Alfv\'enic perturbations react differently on the currents
carried by the hot ion beams and the return electron currents. Ultimately, this
difference leads to a non-resonant aperiodic instability at perpendicular
wavelengths close to the beam ion gyroradius. The instability growth rate
increases with increasing beam current and temperature. In the solar wind
upstream of Earth's bow shock the instability growth time can drop below 10
proton cyclotron periods. Our results suggest that this instability can
contribute to the turbulence and ion acceleration in space and astrophysical
foreshocks.


title: Fraction of isospectral states exhibiting quantum correlations

abstract:
  For several types of correlations: mixed-state entanglement in systems of
distinguishable particles, particle entanglement in systems of
indistinguishable bosons and fermions and non-Gaussian correlations in
fermionic systems we estimate the fraction of non-correlated states among the
density matrices with the same spectra. We prove that for the purity exceeding
some critical value (depending on the considered problem) fraction of
non-correlated states tends to zero exponentially fast with the dimension of
the relevant Hilbert space. As a consequence a state randomly chosen from the
set of density matrices possessing the same spectra is asymptotically a
correlated one. To prove this we developed a systematic framework for detection
of correlations via nonlinear witnesses.


title:
A state-constrained differential game arising in optimal portfolio
  liquidation

abstract:
  We consider $n$ risk-averse agents who compete for liquidity in an
Almgren--Chriss market impact model. Mathematically, this situation can be
described by a Nash equilibrium for a certain linear-quadratic differential
game with state constraints. The state constraints enter the problem as
terminal boundary conditions for finite and infinite time horizons. We prove
existence and uniqueness of Nash equilibria and give closed-form solutions in
some special cases. We also analyze qualitative properties of the equilibrium
strategies and provide corresponding financial interpretations.


title: Electromagnetic field and cosmic censorship

abstract:
  We construct a gedanken experiment in which an extremal Kerr black hole
interacts with a test electromagnetic field. Using Teukolsky's solutions for
electromagnetic perturbations in Kerr spacetime, and the conservation laws
imposed by the energy momentum tensor of the electromagnetic field and the
Killing vectors of the spacetime, we prove that this interaction cannot convert
the black hole into a naked singularity, thus cosmic censorship conjecture is
not violated in this case.


title:
Characterization of low-temperature microwave loss of thin aluminum
  oxide formed by plasma oxidation

abstract:
  We report on the characterization of microwave loss of thin aluminum oxide
films at low temperatures using superconducting lumped resonators. The oxide
films are fabricated using plasma oxidation of aluminum and have a thickness of
5 nm. We measure the dielectric loss versus microwave power for resonators with
frequencies in the GHz range at temperatures from 54 to 303 mK. The power and
temperature dependence of the loss is consistent with the tunneling two-level
system theory. These results are relevant to understanding decoherence in
superconducting quantum devices. The obtained oxide films are thin and robust,
making them suitable for capacitors in compact microwave resonators.


title: How beta-skeletons lose their edges

abstract:
  A {\beta}-skeleton is a proximity graphs with node neighbourhood defined by
continuous-valued parameter {\beta}. Two nodes in a {\beta}-skeleton are
connected by an edge if their lune-based neighbourhood contains no other nodes.
With increase of {\beta} some edges a skeleton are disappear. We study how a
number of edges in {\beta}-skeleton depends on {\beta}. We speculate how this
dependence can be used to discriminate between random and non-random planar
sets. We also analyse stability of {\beta}-skeletons and their sensitivity to
perturbations.


title: Topology and field strength in spherical, anelastic dynamo simulations

abstract:
  Numerical modelling of convection driven dynamos in the Boussinesq
approximation revealed fundamental characteristics of the dynamo-generated
magnetic fields and the fluid flow. Because these results were obtained for an
incompressible fluid, their validity for gas planets and stars remains to be
assessed. A common approach is to take some density stratification into account
with the so-called anelastic approximation. The validity of previous results
obtained in the Boussinesq approximation is tested for anelastic models. We
point out and explain specific differences between both types of models, in
particular with respect to the field geometry and the field strength, but we
also compare scaling laws for the velocity amplitude, the magnetic dissipation
time, and the convective heat flux. Our investigation is based on a systematic
parameter study of spherical dynamo models in the anelastic approximation. We
make use of a recently developed numerical solver and provide results for the
test cases of the anelastic dynamo benchmark. The dichotomy of dipolar and
multipolar dynamos identified in Boussinesq simulations is also present in our
sample of anelastic models. Dipolar models require that the typical length
scale of convection is an order of magnitude larger than the Rossby radius.
However, the distinction between both classes of models is somewhat less
explicit than in previous studies. This is mainly due to two reasons: we found
a number of models with a considerable equatorial dipole contribution and an
intermediate overall dipole field strength. Furthermore, a large density
stratification may hamper the generation of dipole dominated magnetic fields.
Previously proposed scaling laws, such as those for the field strength, are
similarly applicable to anelastic models. It is not clear, however, if this
consistency necessarily implies similar dynamo processes in both settings.


title: Neutrino electromagnetic properties and new physics

abstract:
  New effects of nontrivial neutrino electromagnetic properties are
investigated on the basis of exact solutions of the modified Dirac equations
for neutrinos in dense magnetized rotating matter. The effect of spatial
separation of different types of neutrinos and antineutrinos (different in
flavors and energies) moving inside dense magnetized rotating matter is
predicted. We also describe a new mechanism of a star rotation frequency shift
by neutrinos escaping the star (termed "Neutrino Star Turning" mechanism, $\nu
S T$). The $\nu S T$ mechanism can explain the origin of pulsar "anti-glitches"
and ordinary glitches as well. Considering a possible effect of the $\nu S T$
mechanism on speeding up of a pulsar together with the observational data on
pulsars, we obtain a new limit on a neutrino millicharge
$q_{\nu}<1.3\times10^{-19}e_0$ that is one of the strongest limits on this
value obtained in astrophysics.


title:
Monte Carlo non local means: Random sampling for large-scale image
  filtering

abstract:
  We propose a randomized version of the non-local means (NLM) algorithm for
large-scale image filtering. The new algorithm, called Monte Carlo non-local
means (MCNLM), speeds up the classical NLM by computing a small subset of image
patch distances, which are randomly selected according to a designed sampling
pattern. We make two contributions. First, we analyze the performance of the
MCNLM algorithm and show that, for large images or large external image
databases, the random outcomes of MCNLM are tightly concentrated around the
deterministic full NLM result. In particular, our error probability bounds show
that, at any given sampling ratio, the probability for MCNLM to have a large
deviation from the original NLM solution decays exponentially as the size of
the image or database grows. Second, we derive explicit formulas for optimal
sampling patterns that minimize the error probability bound by exploiting
partial knowledge of the pairwise similarity weights. Numerical experiments
show that MCNLM is competitive with other state-of-the-art fast NLM algorithms
for single-image denoising. When applied to denoising images using an external
database containing ten billion patches, MCNLM returns a randomized solution
that is within 0.2 dB of the full NLM solution while reducing the runtime by
three orders of magnitude.


title: Comparing Double String Theory Actions

abstract:
  Aimed to a deeper comprehension of a manifestly T-dual invariant formulation
of string theory, in this paper a detailed comparison between the non-covariant
action proposed by Tseytlin and the covariant one proposed by Hull is done.
These are obtained by making both the string coordinates and their duals
explicitly appear, on the same foot, in the world-sheet action, so "doubling"
the string coordinates along the compact dimensions. After a discussion of the
nature of the constraints in both the models and the relative quantization, it
results that the string coordinates and their duals behave like "non-commuting"
phase space type coordinates but their expressions in terms of Fourier modes
generate the oscillator algebra of the standard bosonic string formulation. A
proof of the equivalence of the two formulations is given. Furthermore,
open-string solutions are also discussed.


title:
Totally normal cellular stratified spaces and applications to the
  configuration space of graphs

abstract:
  The notion of regular cell complexes plays a central role in topological
combinatorics because of its close relationship with posets. A generalization,
called totally normal cellular stratified spaces, was introduced by the third
author by relaxing two conditions; face posets are replaced by acyclic
categories and cells with incomplete boundaries are allowed. The aim of this
article is to demonstrate the usefulness of totally normal cellular stratified
spaces by constructing a combinatorial model for the configuration space of
graphs. As an application, we obtain a simpler proof of Ghrist's theorem on the
homotopy dimension of the configuration space of graphs. We also make sample
calculations of the fundamental group of ordered and unordered configuration
spaces of two points for small graphs.


title: Kinematics and dynamics in a Bipartite-Finsler spacetime

abstract:
  We study some properties of a recently proposed local Lorentz Violating
Finsler geometry, the so-called Bipartite space. This anisotropic structure
deforms the causal null surface to an elliptic cone and provides an anisotropy
to the inertia. The modified dispersion relations and the geodesic equation for
a massive particle are studied. For a weak directional-dependence we obtain the
dynamical and interaction terms analogous to the gravitational sector of the
Standard Model Extension.


title: Global thermal entanglement in n-qubit systems

abstract:
  We examine the entanglement of thermal states of n spins interacting through
different types of XY couplings in the presence of a magnetic field, by
evaluating the negativities of all possible bipartite partitions of the whole
system and of subsystems. We consider both the case where every qubit interacts
with all others and where just nearest neighbors interact in a one-dimensional
chain. Limit temperatures for non-zero negativities are also evaluated and
compared with the mean field critical temperature. It is shown that limit
temperatures of global negativities are strictly independent of the magnetic
field in all XXZ models, in spite of the quantum transitions that these models
may exhibit at zero temperature, while in anisotropic models they always
increase for sufficiently large fields. Results also show that these
temperatures are higher than those limiting pairwise entanglement.


title: Third Harmonic Generation in Cuprous Oxide: Efficiency Determination

abstract:
  The efficiency of third harmonic generation in cuprous oxide was measured.
Intensities followed a non-cubic power law which indicates nonperturbative
behavior. Polarization anisotropy of the harmonic generation was demonstrated
and related to the third order susceptibility. The results will influence the
understanding of harmonic generation in centrosymmetric materials and are
potentially relevant to device design and the interpretation of exciton
behavior.


title:
Unexpectedly Slow Two Particle Decay of Ultra-Dense Excitons in Cuprous
  Oxide

abstract:
  For an ultra-dense exciton gas in cuprous oxide (Cu$_2$O), exciton-exciton
interactions are the dominant cause of exciton decay. This study demonstrates
that the accepted Auger recombination model overestimates the exciton decay
rate following intense two photon excitation. Two exciton decay is relevant to
the search for collective quantum behavior of excitons in bulk systems. These
results suggest the existence of a new high density regime of exciton behavior.


title:
Extending Contexts with Ontologies for Multidimensional Data Quality
  Assessment

abstract:
  Data quality and data cleaning are context dependent activities. Starting
from this observation, in previous work a context model for the assessment of
the quality of a database instance was proposed. In that framework, the context
takes the form of a possibly virtual database or data integration system into
which a database instance under quality assessment is mapped, for additional
analysis and processing, enabling quality assessment. In this work we extend
contexts with dimensions, and by doing so, we make possible a multidimensional
assessment of data quality assessment. Multidimensional contexts are
represented as ontologies written in Datalog+-. We use this language for
representing dimensional constraints, and dimensional rules, and also for doing
query answering based on dimensional navigation, which becomes an important
auxiliary activity in the assessment of data. We show ideas and mechanisms by
means of examples.


title: The Bernstein presentation for general connected reductive groups

abstract:
  Let F be a non-Archimedean local field and let G be a connected reductive
affine algebraic F-group. Let I be an Iwahori subgroup of G(F) and denote by
H(G; I) the Iwahori-Hecke algebra, i.e. the convolution algebra of
complex-valued functions on G(F) which are left- and right-invariant by
I-translations. This article proves that the Iwahori-Hecke algebra H(G; I) has
both an Iwahori-Matsumoto Presentation and a Bernstein Presentation analogous
to those for affine Hecke algebras on root data found in Lusztig's "Affine
Hecke algebras and their graded version", and gives a basis (in other words, an
explicit Bernstein Isomorphism) for the center Z[H(G; I)] also analogous to
that found in loc. cit.


title: On the Identifiability Conditions in Some Nonlinear Time Series Models

abstract:
  In this study, we consider the identifiability problem for nonlinear time
series models. Special attention is paid to smooth transition GARCH, nonlinear
Poisson autoregressive, and multiple regime smooth transition autoregressive
models. Some sufficient conditions are obtained to establish the
identifiability of these models.


title:
Contact and first layer residues prediction in protein dimers using the
  Gaussian Network model with adjustable number of fast modes

abstract:
  Interactions between proteins are hard to decipher. Protein-protein
interactions are difficult problem to address because they are not based on
differences in charge type like protein-DNA or protein-lipid interactions. In
this manuscript we present a few methods aimed at recognizing contact and their
neighboring first layer residues. The methods are based on the simplified
analysis of normal modes via the Gaussian Network Model (GNM). The methods
adjust the number of modes used in analysis on the basis of the comparison of
predicted and expected number of targets (contact and first layer residues).
The number of modes used in weighted sum calculation is increased or decreased
if the number of predictions falls out of range for a given protein sequence
length. The methods are able to recognize more than 50% of targets on average.
At the same time they generate slightly more than 40% of false positives. They
are also fairly successful in recognizing near native decoys of the Vakser
decoy sets. The results depicted here show that kinetically active residues are
important in protein-protein interactions. The GNM analysis depicted also shows
that the two interacting chains usually exhibit opposite behavior. While the
binding surface of one of the partners is rigid and stable, the interfacial
area of the other partner is more flexible.


title:
Designing Fully Distributed Consensus Protocols for Linear Multi-agent
  Systems with Directed Graphs

abstract:
  This paper addresses the distributed consensus protocol design problem for
multi-agent systems with general linear dynamics and directed communication
graphs. Existing works usually design consensus protocols using the smallest
real part of the nonzero eigenvalues of the Laplacian matrix associated with
the communication graph, which however is global information. In this paper,
based on only the agent dynamics and the relative states of neighboring agents,
a distributed adaptive consensus protocol is designed to achieve
leader-follower consensus for any communication graph containing a directed
spanning tree with the leader as the root node. The proposed adaptive protocol
is independent of any global information of the communication graph and thereby
is fully distributed. Extensions to the case with multiple leaders are further
studied.


title:
Several almost critical regularity conditions based on one component of
  the solutions for 3D N-S Equations

abstract:
  In this article, we establish several almost critical regularity conditions
such that the weak solutions of the 3D Navier-Stokes equations become regular,
based on one component of the solutions, say $u_3$ and $\partial_3u_3$.


title:
Distributed Robust Consensus Control of Multi-agent Systems with
  Heterogeneous Matching Uncertainties

abstract:
  This paper considers the distributed consensus problem of linear multi-agent
systems subject to different matching uncertainties for both the cases without
and with a leader of bounded unknown control input. Due to the existence of
nonidentical uncertainties, the multi-agent systems discussed in this paper are
essentially heterogeneous. For the case where the communication graph is
undirected and connected, a distributed continuous static consensus protocol
based on the relative state information is first designed, under which the
consensus error is uniformly ultimately bounded and exponentially converges to
a small adjustable residual set. A fully distributed adaptive consensus
protocol is then designed, which, contrary to the static protocol, relies on
neither the eigenvalues of the Laplacian matrix nor the upper bounds of the
uncertainties. For the case where there exists a leader whose control input is
unknown and bounded, distributed static and adaptive consensus protocols are
proposed to ensure the boundedness of the consensus error. It is also shown
that the proposed protocols can be redesigned so as to ensure the boundedness
of the consensus error in the presence of bounded external disturbances which
do not satisfy the matching condition. A sufficient condition for the existence
of the proposed protocols is that each agent is stabilizable.


title: Strong Feller properties for degenerate SDEs with jumps

abstract:
  Under full H\"ormander's conditions, we prove the strong Feller property of
the semigroup determined by an SDE driven by additive subordinate Brownian
motion, where the drift is allowed to be arbitrarily growth. For this, we
extend a criterion due to Malicet-Poly \cite{Ma-Po} and Bally-Caramellino
\cite{Ba-Ca} about the convergence of the laws of Wiener functionals in total
variations. Moreover, the example of a chain of coupled oscillators is
verified.


title: Rate-Distortion Auto-Encoders

abstract:
  A rekindled the interest in auto-encoder algorithms has been spurred by
recent work on deep learning. Current efforts have been directed towards
effective training of auto-encoder architectures with a large number of coding
units. Here, we propose a learning algorithm for auto-encoders based on a
rate-distortion objective that minimizes the mutual information between the
inputs and the outputs of the auto-encoder subject to a fidelity constraint.
The goal is to learn a representation that is minimally committed to the input
data, but that is rich enough to reconstruct the inputs up to certain level of
distortion. Minimizing the mutual information acts as a regularization term
whereas the fidelity constraint can be understood as a risk functional in the
conventional statistical learning setting. The proposed algorithm uses a
recently introduced measure of entropy based on infinitely divisible matrices
that avoids the plug in estimation of densities. Experiments using
over-complete bases show that the rate-distortion auto-encoders can learn a
regularized input-output mapping in an implicit manner.


title:
The Structure Theorem for The cut locus of a Certain Class of Cylinders
  of Revolution II

abstract:
  In the previous paper, the structure of the cut locus was determined for a
class of surfaces of revolution homeomorphic to a cylinder. In this paper, we
prove the structure theorem of the cut locus for a wider class of surfaces of
revolution homeomorphic to a cylinder.


title:
Passive decoy-state quantum key distribution for the weak coherent
  photon source with intensity fluctuations

abstract:
  Passive decoy-state quantum key distribution (QKD) systems, proven to be more
desirable than active ones in some scenarios, also have the problem of device
imperfections like intensity fluctuations. In this paper the formular of key
generation rate of the passive decoy-state protocol using transformed weak
coherent pulse (WCP) source with intensity fluctuation is given, and then the
influence of intensity fluctuations on the performance of passive decoy-state
protocol is rigorously characterized. From numerical simulations, it can be
easily seen that intensity fluctuations have unignorable influence on
performance of the passive decoy-state QKD protocol with WCP source. Most
importantly, our simulations show that, under the same deviation of intensity
fluctuations, the passive decoy-state method performs better than the active
two-intensity decoy-state method and close to active three-intensity
decoy-state method.