title:
A Class of Nonconvex Penalties Preserving Overall Convexity in
  Optimization-Based Mean Filtering

abstract:
  $\ell_1$ mean filtering is a conventional, optimization-based method to
estimate the positions of jumps in a piecewise constant signal perturbed by
additive noise. In this method, the $\ell_1$ norm penalizes sparsity of the
first-order derivative of the signal. Theoretical results, however, show that
in some situations, which can occur frequently in practice, even when the jump
amplitudes tend to $\infty$, the conventional method identifies false change
points. This issue is referred to as stair-casing problem and restricts
practical importance of $\ell_1$ mean filtering. In this paper, sparsity is
penalized more tightly than the $\ell_1$ norm by exploiting a certain class of
nonconvex functions, while the strict convexity of the consequent optimization
problem is preserved. This results in a higher performance in detecting change
points. To theoretically justify the performance improvements over $\ell_1$
mean filtering, deterministic and stochastic sufficient conditions for exact
change point recovery are derived. In particular, theoretical results show that
in the stair-casing problem, our approach might be able to exclude the false
change points, while $\ell_1$ mean filtering may fail. A number of numerical
simulations assist to show superiority of our method over $\ell_1$ mean
filtering and another state-of-the-art algorithm that promotes sparsity tighter
than the $\ell_1$ norm. Specifically, it is shown that our approach can
consistently detect change points when the jump amplitudes become sufficiently
large, while the two other competitors cannot.


title:
Constraining Magnetization of Gamma-Ray Bursts Outflows using Prompt
  Emission Fluence

abstract:
  I consider here acceleration and heating of relativistic outflow by local
magnetic energy dissipation process in Poynting flux dominated outflow.
Adopting the standard assumption that the reconnection rate scales with the
Alfven speed, I show here that the fraction of energy dissipated as thermal
photons cannot exceed (13 $\hat \gamma -14)^{-1} = 30$% (for adiabatic index
$\hat \gamma = 4/3$) of the kinetic energy at the photosphere. Even in the most
radiatively efficient scenario, the energy released as non-thermal photons
during the prompt phase is at most equal to the kinetic energy of the outflow.
These results imply that calorimetry of the kinetic energy that can be done
during the afterglow phase, could be used to constrain the magnetization of
gamma-ray bursts (GRB) outflows. I discuss the recent observational status, and
its implications on constraining the magnetization in GRB outflows.


title: Stability of stationary solutions in models of the Calvin cycle

abstract:
  In this paper results are obtained concerning the number of positive
stationary solutions in simple models of the Calvin cycle of photosynthesis and
the stability of these solutions. It is proved that there are open sets of
parameters in a model of Zhu et. al. for which there exist two positive
stationary solutions. There are never more than two isolated positive
stationary solutions but under certain explicit special conditions on the
parameters there is a whole continuum of positive stationary solutions. It is
also shown that in the set of parameter values for which two isolated positive
stationary solutions exist there is an open subset where one of the solutions
is asymptotically stable and the other is unstable. In related models , for
which it was known that more that one positive stationary solution exists, it
is proved that there are parameter values for which one of these solutions is
asymptotically stable and the other unstable. A key technical aspect of the
proofs is to exploit the fact that there is a bifurcation where the centre
manifold is one-dimensional.


title:
Honest elementary degrees and degrees of relative provability without
  the cupping property

abstract:
  An element $a$ of a lattice cups to an element $b > a$ if there is a $c < b$
such that $a \cup c = b$. An element of a lattice has the cupping property if
it cups to every element above it. We prove that there are non-zero honest
elementary degrees that do not have the cupping property, which answers a
question of Kristiansen, Schlage-Puchta, and Weiermann. In fact, we show that
if $\mathbf b$ is a sufficiently large honest elementary degree, then there is
a non-zero honest elementary degree $\mathbf a <_{\mathrm E} \mathbf b$ that
does not cup to $\mathbf b$. For comparison, we modify a result of Cai to show
that in several versions of the related degrees of relative provability the
preceding property holds for all non-zero $\mathbf b$, not just sufficiently
large $\mathbf b$.


title:
The interstellar medium in Andromeda's dwarf spheroidal galaxies: I.
  Content and origin of the interstellar dust

abstract:
  Dwarf spheroidal galaxies are among the most numerous galaxy population in
the Universe, but their main formation and evolution channels are still not
well understood. The three dwarf spheroidal satellites (NGC147, NGC185, and
NGC205) of the Andromeda galaxy are characterised by very different
interstellar medium (ISM) properties, which might suggest them being at
different galaxy evolutionary stages. While the dust content of NGC205 has been
studied in detail by De Looze et al. (2012), we present new Herschel dust
continuum observations of NGC147 and NGC185. The non-detection of NGC147 in
Herschel SPIRE maps puts a strong constraint on its dust mass (< 128 Msun). For
NGC185, we derive a total dust mass M_d = 5.1 x 10^3 Msun, which is a factor of
~2-3 higher than that derived from ISO and Spitzer observations and confirms
the need for longer wavelength observations to trace more massive cold dust
reservoirs. We, furthermore, estimate the dust production by asymptotic giant
branch (AGB) stars and supernovae (SNe). For NGC147, the upper limit on the
dust mass is consistent with expectations of the material injected by the
evolved stellar population. In NGC185 and NGC205, the observed dust content is
one order of magnitude higher compared to the estimated dust production by AGBs
and SNe. Efficient grain growth, and potentially longer dust survival times
(3-6 Gyr) are required to account for their current dust content. Our study
confirms the importance of grain growth in the gas phase to account for the
current dust reservoir in galaxies.


title: Gaussian approximations for transition paths in Brownian dynamics

abstract:
  This paper is concerned with transition paths within the framework of the
overdamped Langevin dynamics model of chemical reactions. We aim to give an
efficient description of typical transition paths in the small temperature
regime. We adopt a variational point of view and seek the best Gaussian
approximation, with respect to Kullback-Leibler divergence, of the non-Gaussian
distribution of the diffusion process. We interpret the mean of this Gaussian
approximation as the "most likely path" and the covariance operator as a means
to capture the typical fluctuations around this most likely path.
  We give an explicit expression for the Kullback-Leibler divergence in terms
of the mean and the covariance operator for a natural class of Gaussian
approximations and show the existence of minimisers for the variational
problem. Then the low temperature limit is studied via $\Gamma$-convergence of
the associated variational problem. The limiting functional consists of two
parts: The first part only depends on the mean and coincides with the
$\Gamma$-limit of the Freidlin-Wentzell rate functional. The second part
depends on both, the mean and the covariance operator and is minimized if the
dynamics are given by a time-inhomogenous Ornstein-Uhlenbeck process found by
linearization of the Langevin dynamics around the Freidlin-Wentzell minimizer.


title: The decays $\Lambda_{b,c}\to N^*\, l\,\nu$ in QCD

abstract:
  We present an exploratory study of the $\Lambda_{c,b}\to N^*$-form factors
and the semileptonic decay width within the framework of light-cone sum rules.
We use two different methods and two different interpolating currents for the
$\Lambda_{c,b}$. As interpolating currents we choose an axial-vector like and a
pseudoscalar like current. Our results show that the procedure of eliminating
negative parity partners is not well suited for the case at hand and that the
second approach using structures with highest powers of $p_+$ with an
axial-vector like interpolating current gives the most reliable results. Our
predictions are based on the models obtained in
\cite{Anikin:2015ita,Braun:2014wpa}. The largest uncertainty comes from the
uncertainty of the twist 4 parameters $\eta_{10},\,\eta_{11}$ and we take the
spread between the two models in \cite{Anikin:2015ita} as a measure for this.
We get \begin{eqnarray} \Gamma(\Lambda_b\to N^*(1535) l
\nu)&=&\left(0.0058^{+0.0010}_{-0.0009}\right)\cdot\left(\dfrac{V_{ub}}{3.5\cdot10^{-3}}\right)^2,\quad\mbox{LCSR(1)}
\nonumber \Gamma(\Lambda_b\to N^*(1535) l
\nu)&=&\left(0.00070^{+0.00012}_{-0.00011}\right)\cdot\left(\dfrac{V_{ub}}{3.5\cdot10^{-3}}\right)^2,\quad\mbox{LCSR(2)}
\nonumber \Gamma(\Lambda_c\to N^*(1535) l
\nu)&=&\left(0.0064^{+0.0012}_{-0.0011}\right)\cdot
\left(\dfrac{V_{cd}}{0.225}\right)^2,\quad\mbox{LCSR(1)}\nonumber
\Gamma(\Lambda_c\to N^*(1535) l
\nu)&=&\left(0.00077^{+0.00016}_{-0.00014}\right)\cdot
\left(\dfrac{V_{cd}}{0.225}\right)^2,\quad\mbox{LCSR(2)}\nonumber
\end{eqnarray} as predictions for the respective decay widths, where LCSR(1)
and LCSR(2) refer to the two different models of the distribution amplitudes of
the $N^*$. It is seen that even a rough measurement of these decays will
greatly help to discriminate different models.


title: The Quantization of the Rabi Hamiltonian

abstract:
  The Bargmann-Fock representation of the Rabi Hamiltonian is expressed by a
system of two coupled first-order differential equations in the complex field,
which may be rewritten in a canonical form under the Birkhoff transformation.
The transformation gives rise to leapfrog recurrence relations, from which the
eigenvalues and eigenvectors could be obtained. The interesting feature of this
approach is that it generates integer quantum numbers, which relate the
solutions to the Juddian baselines. The relationship with Braak's integrability
claim [PRL 107, 100401 (2011)] is discussed


title: A Note on a Map from Knots to $2$-Knots

abstract:
  We construct a map from knots to (abstract) 2-knots which can be extended to
higher dimensions; this map is the natural "knot" counterpart for "braid"
theory of groups $G_{n}^{k}$.


title:
Direct Base-to-Base Transitions in ssDNA Revealed by Tip-Enhanced Raman
  Scattering

abstract:
  In the present contribution, specifically designed single-stranded DNA
(ssDNA) sequences composed of adenine and cytosine were used as nanometric
rulers to target the maximum achievable spatial resolution of tip-enhanced
Raman spectroscopy (TERS) under ambient conditions. By stepping along a strand
with a TERS tip, the obtained spectra allowed for a clear spectral
discrimination including conformational information of the nucleobases, and
even sharp adenine-cytosine transitions were detected repeatedly with a spatial
resolution below 1 nm.


title:
Application of Cross-correlation Greens Function along with FDTD for
  Fast Computation of Envelope Correlation Coefficient over Wideband for MIMO
  Antennas

abstract:
  In this paper, the concept of cross-correlation Green's functions (CGF) is
used in conjunction with the finite difference time domain (FDTD) technique for
calculation of envelope correlation coefficient (ECC) of any arbitrary MIMO
antenna system over wide frequency band. Both frequency-domain (FD) and
time-domain (TD) post-processing techniques are proposed for possible
application with this FDTD-CGF scheme. The FDTD-CGF time-domain (FDTD-CGF-TD)
scheme utilizes time-domain signal processing methods and exhibits significant
reduction in ECC computation time as compared to the FDTD-CGF frequency domain
(FDTD-CGF-FD) scheme, for high frequency-resolution requirements. The proposed
FDTD-CGF based schemes can be applied for accurate and fast prediction of
wideband ECC response, instead of the conventional scattering parameter based
techniques which have several limitations. Numerical examples of the proposed
FDTD-CGF techniques are provided for two-element MIMO systems involving
thin-wire half-wavelength dipoles in parallel side-by-side as well as
orthogonal arrangements. The results obtained from the FDTD-CGF techniques are
compared with results from commercial electromagnetic solver Ansys HFSS, to
verify the validity of proposed approach.


title: On Number Conservation of Non-uniform Cellular Automata

abstract:
  This paper studies the number conservation property of 1-dimensional
non-uniform cellular automata (CAs). In a non-uniform cellular automaton (CA),
different cells may follow different rules. The present work considers that the
cells follow Wolfram's CAs rules. A characterization tool, named Reachability
tree is used to discover the number conservation property of non-uniform CAs.
Then a decision algorithm is reported to conclude whether a given non-uniform
CA with $n$ cells is number conserving or not. Finally, a synthesis scheme is
developed to get an $n$-cell number conserving non-uniform CA.


title: The Scales of Gravitational Lensing

abstract:
  After exactly a century since the formulation of the general theory of
relativity, the phenomenon of gravitational lensing is still an extremely
powerful method for investigating in astrophysics and cosmology. Indeed, it is
adopted to study the distribution of the stellar component in the Milky Way, to
study dark matter and dark energy on very large scales and even to discover
exoplanets. Moreover, thanks to technological developments, it will allow the
measure of the physical parameters (mass, angular momentum and electric charge)
of supermassive black holes in the center of ours and nearby galaxies.


title:
Clustering with Missing Features: A Penalized Dissimilarity Measure
  based approach

abstract:
  Many real-world clustering problems are plagued by incomplete data
characterized by missing or absent features for some or all of the data
instances. Traditional clustering methods cannot be directly applied to such
data without preprocessing by imputation or marginalization techniques. In this
article, we overcome this drawback by utilizing a penalized dissimilarity
measure which we refer to as the Feature Weighted Penalty based Dissimilarity
(FWPD). Using the FWPD measure, we modify the traditional k-means clustering
algorithm and the standard hierarchical agglomerative clustering algorithms so
as to make them directly applicable to datasets with missing features. We
present time complexity analyses for these new techniques and also undertake a
detailed theoretical analysis showing that the new FWPD based k-means algorithm
converges to a local optimum within a finite number of iterations. We also
present a detailed method for simulating random as well as feature dependent
missingness. We report extensive experiments on various benchmark datasets for
different types of missingness showing that the proposed clustering techniques
have generally better results compared to some of the most well-known
imputation methods which are commonly used to handle such incomplete data. We
append a possible extension of the proposed dissimilarity measure to the case
of absent features (where the unobserved features are known to be undefined).


title: Traveling phase waves in asymmetric networks of noisy chaotic attractors

abstract:
  We explore identical R\"ossler systems organized into two equally-sized
groups, among which differing positive and negative in- and out-coupling
strengths are allowed. Patterns of distinctly synchronized phase dynamics are
observed, which coexist with chaotically evolving amplitudes. In particular, we
report the emergence of traveling phase waves, i.e. states in which the
oscillators settle on a new rhythm different from their own. We further
elucidate our findings through phase-coupled R\"ossler systems, establishing a
connection with the Kuramoto model. Together with the study of noise effects,
our results suggest a promising new avenue towards the coexistence of chaotic,
noisy and regular collective dynamics.


title: Rogue wavefunctions due to noisy quantum tunneling potentials

abstract:
  In this paper we study the effects of white-noised potentials on nonlinear
quantum tunneling. We use a split-step scheme to numerically solve the
nonlinear Schrodinger equation (NLSE) with a tunneling potential. We consider
three different types of potentials, namely; the single rectangular barrier,
double rectangular barrier and triangular barrier. For all these three cases we
show that white-noise given to potentials do not trigger modulation instability
for tunneling of the sech type soliton solutions of the NLSE. However
white-noised potentials trigger modulation instability for tunneling of the
sinusoidal wavefunctions, thus such a wavefield turns into a chaotic one with
many apparent peaks. We argue that peaks of such a field may be in the form of
rational rogue wave solutions of the NLSE. Our results can be used to examine
the effects of noise on quantum tunneling. Since a rogue wavefunction means a
higher probability of the tunneling particle to be at a given (x,t) coordinate,
our results may also be used for developing the quantum science and technology
with many possible applications including but are not limited to increasing the
resolution and efficiency of scanning tunneling microscopes, enhancing proton
tunneling for DNA mutation and enhancing superconducting properties of
junctions.


title: Indexing Variation Graphs

abstract:
  Variation graphs, which represent genetic variation within a population, are
replacing sequences as reference genomes. Path indexes are one of the most
important tools for working with variation graphs. They generalize text indexes
to graphs, allowing one to find the paths matching the query string. We propose
using de Bruijn graphs as path indexes, compressing them by merging redundant
subgraphs, and encoding them with the Burrows-Wheeler transform. The resulting
fast, space-efficient, and versatile index is used in the variation graph
toolkit vg.


title: Reduced normal form of local integral bases

abstract:
  We introduce a canonical form for reduced bases of integral closures of
discrete valuation rings, and we describe an algorithm for computing a basis in
reduced normal form. This normal form has the same applications as the Hermite
normal form: identification of isomorphic objects, construction of global bases
by patching local ones, etc. but in addition the bases are reduced, which is a
crutial property for several important applications. Except for very particular
cases, a basis in Hermite normal form cannot be reduced.


title: K-Bit-Swap: A New Operator For Real-Coded Evolutionary Algorithms

abstract:
  There has been a variety of crossover operators proposed for Real-Coded
Genetic Algorithms (RCGAs), which recombine values from the same location in
pairs of strings. In this article we present a recombination operator for RC-
GAs that selects the locations randomly in both parents, and compare it to
mainstream crossover operators in a set of experiments on a range of standard
multidimensional optimization problems and a clustering problem. We present two
variants of the operator, either selecting both bits uniformly at random in the
strings, or sampling the second bit from a normal distribution centered at the
selected location in the first string. While the operator is biased towards
exploitation of fitness space, the random selection of the second bit for swap-
ping makes it slightly less exploitation-biased. Extensive statistical analysis
using a non-parametric test shows the advantage of the new recombination
operators on a range of test functions.


title:
Ship waves on uniform shear current at finite depth: wave resistance and
  critical velocity

abstract:
  We present a comprehensive theory for linear gravity-driven ship waves in the
presence of a shear current with uniform vorticity, including the effects of
finite water depth. The wave resistance in the presence of shear current is
calculated for the first time, containing in general a non-zero lateral
component. While formally apparently a straightforward extension of existing
deep water theory, the introduction of finite water depth is physically
non-trivial, since the surface waves are now affected by a subtle interplay of
the effects of the current and the sea bed. This becomes particularly
pronounced when considering the phenomenon of critical velocity, the velocity
at which transversely propagating waves become unable to keep up with the
moving source. The phenomenon is well known for shallow water, and was recently
shown to exist also in deep water in the presence of a shear current
[Ellingsen, J.~Fluid Mech.\ {\bf 742} R2 (2014)]. We derive the exact criterion
for criticality as a function of an intrinsic shear Froude number $S\sqrt{b/g}$
($S$ is uniform vorticity, $b$ size of source), the water depth, and the angle
between the shear current and the ship's motion. Formulae for both the normal
and lateral wave resistance force are derived, and we analyse its dependence on
the source velocity (or Froude number $Fr$) for different amounts of shear and
different directions of motion. The effect of the shear current is to increase
wave resistance for upstream ship motion and decrease it for downstream motion.
Also the value of $Fr$ at which $R$ is maximal is lowered for upstream and
increased for downstream directions of ship motion. For oblique angles between
ship motion and current there is a lateral wave resistance component which can
amount to $10$-$20\%$ of the normal wave resistance for side-on shear and
$S\sqrt{b/g}$ of order unity. (Continues...)


title:
Linear quadratic optimal control of conditional McKean-Vlasov equation
  with random coefficients and applications *

abstract:
  We consider the optimal control problem for a linear conditional
McKean-Vlasov equation with quadratic cost functional. The coefficients of the
system and the weigh-ting matrices in the cost functional are allowed to be
adapted processes with respect to the common noise filtration. Semi closed-loop
strategies are introduced, and following the dynamic programming approach in
[32], we solve the problem and characterize time-consistent optimal control by
means of a system of decoupled backward stochastic Riccati differential
equations. We present several financial applications with explicit solutions,
and revisit in particular optimal tracking problems with price impact, and the
conditional mean-variance portfolio selection in incomplete market model.


title: Homogeneous affine surfaces: Moduli spaces

abstract:
  We analyze the moduli space of non-flat homogeneous affine connections on
surfaces. For Type $\mathcal{A}$ surfaces, we write down complete sets of
invariants that determine the local isomorphism type depending on the rank of
the Ricci tensor and examine the structure of the associated moduli space. For
Type $\mathcal{B}$ surfaces which are not Type $\mathcal{A}$ we show the
corresponding moduli space is a simply connected real analytic 4-dimensional
manifold with second Betti number equal to $1$.


title:
Quasi-optimality of Petrov-Galerkin discretizations of parabolic
  problems with random coefficients

abstract:
  We consider a linear parabolic problem with random elliptic operator in the
usual Gelfand triple setting. We do not assume uniform bounds on the coercivity
and boundedness constants, but allow them to be random variables. The parabolic
problem is studied in a weak space-time formulation, where we can derive
explicit formulas for the inf-sup constants. Under suitable assumptions we
prove existence of moments of the solution. We also prove quasi-optimal error
estimates for piecewise polynomial Petrov-Galerkin discretizations.


title: Limit theorems for counting large continued fraction digits

abstract:
  We establish a central limit theorem for counting large continued fraction
digits $(a_n)$, i.e. we count occurrences $\{a_n>b_n\}$, where $(b_n)$ is a
sequence of positive integers. Our result improves a similar result by Philipp
which additionally assumes that $b_n$ tends to infinity. Moreover, we give a
refinement of the famous Borel-Bernstein Theorem for continued fractions
regarding the event that the $n$-th continued fraction digit lies infinitely
often between $d_n$ and $d_n(1+1/c_n)$ for given sequences $(c_n)$ and $(d_n)$.
Also for these sets we obtain a central limit theorem. As an interesting side
result we determine the first $\phi$-mixing coefficient for the Gauss system
explicitly.


title:
Could the static properties of nuclei be deduced from the dynamics of a
  single quark?

abstract:
  We show that the static properties of a nucleus could arise from a single
quark moving in a mean field generated by all other constituents of this
nucleus. The resulting model provides a way for determining the nuclear sizes
characteristic of the liquid drop model, and reasonably accurate values of
magnetic moments of different nuclei with the aid of two parameters $\alpha_s$
and $\sigma$ appearing in the Cornell potential intended for use in quarkonium
physics.


title: Agenda Separability in Judgment Aggregation

abstract:
  One of the better studied properties for operators in judgment aggregation is
independence, which essentially dictates that the collective judgment on one
issue should not depend on the individual judgments given on some other
issue(s) in the same agenda. Independence, although considered a desirable
property, is too strong, because together with mild additional conditions it
implies dictatorship. We propose here a weakening of independence, named agenda
separability: a judgment aggregation rule satisfies it if, whenever the agenda
is composed of several independent sub-agendas, the resulting collective
judgment sets can be computed separately for each sub-agenda and then put
together. We show that this property is discriminant, in the sense that among
judgment aggregation rules so far studied in the literature, some satisfy it
and some do not. We briefly discuss the implications of agenda separability on
the computation of judgment aggregation rules.


title:
Nullspace Property for Optimality of Minimum Frame Angle Under
  Invertible Linear Operators

abstract:
  Orthogonal Matching Pursuit and Basis Pursuit are popular reconstruction
algorithms for recovery of sparse signals. The exact recovery property of both
the methods has a relation with the coherence of the underlying redundant
dictionary, i.e. a frame. A frame with low coherence provides better guarantees
for exact recovery. An equivalent formulation of the associated linear system
is obtained via premultiplication by a non-singular matrix. In view of bounds
that guarantee sparse recovery, it is very useful to generate the
preconditioner in such way that the preconditioned frame has low coherence as
compared to the original. In this paper, we discuss the impact of
preconditioning on sparse recovery. Further, we formulate a convex optimization
problem for designing the preconditioner that yields a frame with improved
coherence. In addition to reducing coherence, we focus on designing well
conditioned frames and numerically study the relationship between the condition
number of the preconditioner and the coherence of the new frame. Alongside
theoretical justifications, we demonstrate through simulations the efficacy of
the preconditioner in reducing coherence as well as recovering sparse signals.


title:
On the interior regularity of weak solutions to the 2-D incompressible
  Euler equations

abstract:
  We consider the 2-D incompressible Euler equations in a bounded domain and
show that local weak solutions are exponentially integrable, uniformly in time,
under minimal integrability conditions. This is a Serrin-type interior
regularity result $$u \in L_{\rm loc}^{2+\varepsilon}(\Omega_T) \implies {\rm
regularity}$$ for weak solutions in the energy space $L_t^\infty L_x^2$
satisfying appropriate vorticity estimates. The argument is completely local in
nature as the result follows from the structural properties of the equation
alone, while completely avoiding all sorts of boundary conditions and related
gradient estimates. To the best of our knowledge, the approach we follow is new
in the context of Euler equations and provides an alternative look at interior
regularity issues. We also show how our method can be used to give a modified
proof of the classical Serrin condition for the regularity of the Navier-Stokes
equations in any dimension.


title: Descriptive Complexity of $\#\textrm{AC}^0$ Functions

abstract:
  We introduce a new framework for a descriptive complexity approach to
arithmetic computations. We define a hierarchy of classes based on the idea of
counting assignments to free function variables in first-order formulae. We
completely determine the inclusion structure and show that #P and #AC^0 appear
as classes of this hierarchy. In this way, we unconditionally place #AC^0
properly in a strict hierarchy of arithmetic classes within #P. We compare our
classes with a hierarchy within #P defined in a model-theoretic way by Saluja
et al. We argue that our approach is better suited to study arithmetic circuit
classes such as #AC^0 which can be descriptively characterized as a class in
our framework.


title:
Split Form Nodal Discontinuous Galerkin Schemes with Summation-By-Parts
  Property for the Compressible Euler Equations

abstract:
  Fisher and Carpenter (\textit{High-order entropy stable finite difference
schemes for non-linear conservation laws: Finite domains, Journal of
Computational Physics, 252:518--557, 2013}) found a remarkable equivalence of
general diagonal norm high-order summation-by-parts operators to a subcell
based high-order finite volume formulation. This equivalence enables the
construction of provably entropy stable schemes by a specific choice of the
subcell finite volume flux. We show that besides the construction of entropy
stable high order schemes, a careful choice of subcell finite volume fluxes
generates split formulations of quadratic or cubic terms. Thus, by changing the
subcell finite volume flux to a specific choice, we are able to generate, in a
systematic way, all common split forms of the compressible Euler advection
terms, such as the Ducros splitting and the Kennedy and Gruber splitting.
Although these split forms are not entropy stable, we present a systematic way
to prove which of those split forms are at least kinetic energy preserving.
With this, we show we construct a unified high-order split form DG framework.
We investigate with three dimensional numerical simulations of the inviscid
Taylor-Green vortex and show that the new split forms enhance the robustness of
high order simulations in comparison to the standard scheme when solving
turbulent vortex dominated flows. In fact, we show that for certain test cases,
the novel split form discontinuous Galerkin schemes are more robust than the
discontinuous Galerkin scheme with over-integration.


title:
Mass and angular momentum of black holes in low-energy heterotic string
  theory

abstract:
  We investigate conserved charges in the low-energy effective field theory
describing heterotic string theory. Starting with a general Lagrangian that
consists of a metric, a scalar field, a vector gauge field, together with a
two-form potential, we derive off-shell Noether potentials of the Lagrangian
and generalize the Abbott-Deser-Tekin (ADT) formalism to the off-shell level by
establishing one-to-one correspondence between the ADT potential and the
off-shell Noether potential. It is proved that the off-shell generalized ADT
formalism is conformally invariant. Then we apply the formulation to compute
mass and angular momentum of the four-dimensional Kerr-Sen black hole and the
five-dimensional rotating charged black string in the string frame without a
necessity to transform the metrics into the Einstein frame.


title:
Optimizing Top Precision Performance Measure of Content-Based Image
  Retrieval by Learning Similarity Function

abstract:
  In this paper we study the problem of content-based image retrieval. In this
problem, the most popular performance measure is the top precision measure, and
the most important component of a retrieval system is the similarity function
used to compare a query image against a database image. However, up to now,
there is no existing similarity learning method proposed to optimize the top
precision measure. To fill this gap, in this paper, we propose a novel
similarity learning method to maximize the top precision measure. We model this
problem as a minimization problem with an objective function as the combination
of the losses of the relevant images ranked behind the top-ranked irrelevant
image, and the squared Frobenius norm of the similarity function parameter.
This minimization problem is solved as a quadratic programming problem. The
experiments over two benchmark data sets show the advantages of the proposed
method over other similarity learning methods when the top precision is used as
the performance measure.


title:
Effective medium approximation for lattice random walks with long-range
  jumps

abstract:
  We consider the random walk on a lattice with random transition rates and
arbitrarily long-range jumps. We employ Bruggeman's effective medium
approximation (EMA) to find the disorder averaged (coarse-grained) dynamics.
The EMA procedure replaces the disordered system with a cleverly guessed
reference system in a self-consistent manner. We give necessary conditions on
the reference system and discuss possible physical mechanisms of anomalous
diffusion. In case of a power-law scaling between transition rates and
distance, lattice variants of Levy-ights emerge as the effective medium, and
the problem is solved analytically, bearing the effective anomalous
diffusivity. Finally, we discuss several example distributions, and demonstrate
very good agreement with numerical simulations.


title: The hyperbolic Brownian plane

abstract:
  We introduce and study a new random surface which we call the hyperbolic
Brownian plane and which is the near-critical scaling limit of the hyperbolic
triangulations constructed in arXiv:1401.3297. The law of the hyperbolic
Brownian plane is obtained after biasing the law of the Brownian plane
arXiv:1204.5921 by an explicit martingale depending on its perimeter and volume
processes studied in arXiv:1409.4026. Although the hyperbolic Brownian plane
has the same local properties as those of the Brownian plane, its large scale
structure is much different since we prove e.g. that is has exponential volume
growth.


title:
Finite temperature QCD: Quarkonium survival at and beyond $T_c$ and
  dimuon production in heavy ion collisions

abstract:
  Finite temperature QCD sum rules are applied to the behaviour of charmonium
and bottonium states, leading to their survival at and beyond the critical
temperature for deconfinement. Di-muon production in heavy-ion collisions in
the $\rho$-region is also discussed.


title:
Direct measurements of quantum kinetic energy tensor in stable and
  metastable water near the triple point: an experimental benchmark

abstract:
  This study presents the first direct and quantitative measurements of the
nuclear momentum distribution anisotropy and the quantum kinetic energy tensor
in stable and metastable (supercooled) water near its triple point using Deep
Inelastic Neutron Scattering (DINS). From the experimental spectra accurate
lineshapes of the hydrogen momentum distributions are derived using an
anisotropic Gaussian and a model independent framework. The experimental
results, benchmarked with those obtained for the solid phase, provide the state
of the art directional values of the hydrogen mean kinetic energy in metastable
water. The determinations of the direction kinetic energies in the supercooled
phase, benchmarked with ice at the same temperature, provide accurate and
quantitative measurements of these dynamical observables in metastable and
stable phases, {i.e.} key insight in the physical mechanisms of the hydrogen
quantum state in both disordered and polycrystalline systems. The remarkable
findings of this study establish novel insight to further expand the capacity
and accuracy of DINS investigations of the nuclear quantum effects in water and
represent reference experimental values for theoretical investigations.


title:
Accelerated micropolar fluid--flow past an uniformly rotating circular
  cylinder

abstract:
  In this paper, we formulated the non-steady flow due to the uniformly
accelerated and rotating circular cylinder from rest in a stationary, viscous,
incompressible and micropolar fluid. This flow problem is examined numerically
by adopting a special scheme comprising the Adams-Bashforth Temporal Fourier
Series method and the Runge-Kutta Temporal Special Finite-Difference method.
This numerical scheme transforms the governing equation for micropolar fluids
for this problem into system of finite-difference equations. This system was
further solved numerically by point SOR-method. These results were also further
extrapolated by the Richardson extrapolation method. This scheme is valid for
all values of the flow and fluid-parameters and for all time. Moreover the
boundary conditions of the vorticity and the spin at points far from the
cylinder are being imposed and encountered too. The results are compared with
existing results (for non-rotating circular cylinder in Newtonian fluids). The
comparison is good. The enhancement of lift and reduction in drag was observed
if the micropolarity effects are intensified. Same is happened if the rotation
of a cylinder increases. Furthermore, the vortex-pair in the wake is delayed to
successively higher times as rotation parameter increases. In addition, the
rotation helps not only in dissolving vortices adjacent to the cylinder and
adverse pressure region but also in dissolving the boundary layer separation.
Furthermore, the rotation reduces the micropolar spin boundary layer also.


title: The Mean Partition Theorem of Consensus Clustering

abstract:
  To devise efficient solutions for approximating a mean partition in consensus
clustering, Dimitriadou et al. [3] presented a necessary condition of
optimality for a consensus function based on least square distances. We show
that their result is pivotal for deriving interesting properties of consensus
clustering beyond optimization. For this, we present the necessary condition of
optimality in a slightly stronger form in terms of the Mean Partition Theorem
and extend it to the Expected Partition Theorem. To underpin its versatility,
we show three examples that apply the Mean Partition Theorem: (i) equivalence
of the mean partition and optimal multiple alignment, (ii) construction of
profiles and motifs, and (iii) relationship between consensus clustering and
cluster stability.


title: Resetting of fluctuating interfaces at power-law times

abstract:
  What happens when the time evolution of a fluctuating interface is
interrupted with resetting to a given initial configuration after random time
intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};~\alpha >
0$? For an interface of length $L$ in one dimension, and an initial flat
configuration, we show that depending on $\alpha$, the dynamics as $L \to
\infty$ exhibits a rich long-time behavior. Without resetting, the interface
width grows unbounded with time as $t^\beta$, where $\beta$ is the so-called
growth exponent. We show that introducing resetting induces for $\alpha>1$ and
at long times fluctuations that are bounded in time. Corresponding to such a
stationary state is a distribution of fluctuations that is strongly
non-Gaussian, with tails decaying as a power-law. The distribution exhibits a
cusp for small argument, implying that the stationary state is out of
equilibrium. For $\alpha<1$, resetting is unable to counter the otherwise
unbounded growth of fluctuations in time, so that the distribution of
fluctuations remains time dependent with an ever-increasing width even at long
times. Although stationary for $\alpha>1$, the width of the interface grows
forever with time as a power-law for $1<\alpha < \alpha^{({\rm w})}$, and
converges to a finite constant only for larger $\alpha$, thereby exhibiting a
crossover at $\alpha^{({\rm w})}=1+2\beta$. The time-dependent distribution of
fluctuations for $\alpha<1$ exhibits for small argument another interesting
crossover behavior, from cusp to divergence, across $\alpha^{({\rm
d})}=1-\beta$. We demonstrate these results by exact analytical results for the
paradigmatic Edwards-Wilkinson (EW) dynamical evolution of the interface, and
further corroborate our findings by extensive numerical simulations of
interface models in the EW and the Kardar-Parisi-Zhang universality class.


title:
About oscillation method to study crystallization and melting in
  multicomponent system

abstract:
  It is shown that the oscillation method to study liquid viscosity of
[1-3,7-34], which is the basis of oscillation method to study crystallization
and melting in multicomponent system, is based on incorrect consideration of
one dimensional forced (constrained) )vibrations of plate in viscous liquid,
because additional (apparent) mass of liquid and surface forces are incorrectly
taken into account, and Archimedes force did not taken into account. It is
shown that the vibrations cannot be one dimensional, and torsional vibrations
need to be taken into account. It is shown also that the characteristics of
vibrating system depend on time, the system has no isothermal conditions, the
system cannot reach metastable conditions therefore one cannot observe
homogeneous crystallization and melting, the results obtained with the use of
the method are not reliable and incorrect.


title: Entangling credit and funding shocks in interbank markets

abstract:
  Credit and liquidity risks represent main channels of financial contagion for
interbank lending markets. On one hand, banks face potential losses whenever
their counterparties are under distress and thus unable to fulfill their
obligations. On the other hand, solvency constraints may force banks to recover
lost fundings by selling their illiquid assets, resulting in effective losses
in the presence of fire sales - that is, when funding shortcomings are
widespread over the market. Because of the complex structure of the network of
interbank exposures, these losses reverberate among banks and eventually get
amplified, with potentially catastrophic consequences for the whole financial
system. Building on Debt Rank [Battiston et al., 2012], in this work we define
a systemic risk metric that estimates the potential amplification of losses in
interbank markets accounting for both credit and liquidity contagion channels:
the Debt-Solvency Rank. We implement this framework on a dataset of 183
European banks that were publicly traded between 2004 and 2013, showing indeed
that liquidity spillovers substantially increase systemic risk, and thus cannot
be neglected in stress-test scenarios. We also provide additional evidence that
the interbank market was extremely fragile up to the 2008 financial crisis,
becoming slightly more robust only afterwards.


title: Superradiance induced particle flow via dynamical gauge coupling

abstract:
  We study fermions that are gauge-coupled to a cavity mode via Raman-assisted
hopping in a one dimensional lattice. For an infinite lattice, we find a
superradiant phase with infinitesimal pumping threshold which induces a
directed particle flow. We explore the fate of this flow in a finite lattice
with boundaries, studying the non-equilibrium dynamics including fluctuation
effects. The short time dynamics is dominated by superradiance, while the long
time behaviour is governed by cavity fluctuations. We show that the steady
state in the finite lattice is not unique, and can be understood in terms of
coherent bosonic excitations above a Fermi surface in real space.


title: The two-loop n-point all-plus helicity amplitude

abstract:
  We propose a compact analytic expression for the polylogarithmic part of the
n-point two-loop all-plus helicity amplitude in gauge theory.


title: About oscillation method to study liquid viscosity

abstract:
  It is shown that the oscillation method to study liquid viscosity of
[1-3,7-34] is based on incorrect consideration of one dimensional forced
(constrained) )vibrations of plate in viscous liquid, because additional
(apparent) mass of liquid and surface forces are incorrectly taken into
account, and Archimedes force did not taken into account. It is shown the
vibrations cannot be one dimensional, and torsional vibrations need to be take
into account, the results obtained with the use of the method are not reliable
and incorrect.


title: Phase reduction theory for hybrid nonlinear oscillators

abstract:
  Hybrid dynamical systems characterized by discrete switching of smooth
dynamics have been used to model various rhythmic phenomena. However, the phase
reduction theory, a fundamental framework for analyzing the synchronization of
limit-cycle oscillations in rhythmic systems, has mostly been restricted to
smooth dynamical systems. Here we develop a general phase reduction theory for
weakly perturbed limit cycles in hybrid dynamical systems that facilitates
analysis, control, and optimization of nonlinear oscillators whose smooth
models are unavailable or intractable. On the basis of the generalized theory,
we analyze injection locking of hybrid limit-cycle oscillators by periodic
forcing and reveal their characteristic synchronization properties, such as
ultrafast and robust entrainment to the periodic forcing and logarithmic
scaling at the synchronization transition. We also illustrate the theory by
analyzing the synchronization dynamics of a simple physical model of biped
locomotion.


title: Forman-Ricci flow for change detection in large dynamic data sets

abstract:
  We present a viable solution to the challenging question of change detection
in complex networks inferred from large dynamic data sets. Building on Forman's
discretization of the classical notion of Ricci curvature, we introduce a novel
geometric method to characterize different types of real-world networks with an
emphasis on peer-to-peer networks. Furthermore we adapt the classical Ricci
flow that already proved to be a powerful tool in image processing and
graphics, to the case of undirected and weighted networks. The application of
the proposed method on peer-to-peer networks yields insights into topological
properties and the structure of their underlying data.


title: Bridging LSTM Architecture and the Neural Dynamics during Reading

abstract:
  Recently, the long short-term memory neural network (LSTM) has attracted wide
interest due to its success in many tasks. LSTM architecture consists of a
memory cell and three gates, which looks similar to the neuronal networks in
the brain. However, there still lacks the evidence of the cognitive
plausibility of LSTM architecture as well as its working mechanism. In this
paper, we study the cognitive plausibility of LSTM by aligning its internal
architecture with the brain activity observed via fMRI when the subjects read a
story. Experiment results show that the artificial memory vector in LSTM can
accurately predict the observed sequential brain activities, indicating the
correlation between LSTM architecture and the cognitive process of story
reading.


title:
The origin of the near-IR line emission from molecular, low and high
  ionization gas in the inner kiloparsec of NGC6240

abstract:
  The understating of the origin of the H2 line emission from the central
regions of galaxies represent an important key to improve our knowledge about
the excitation and ionization conditions of the gas in these locations. Usually
these lines can be produced by Starburts, shocks and/or radiation from an
active galactic nucleus (AGN). Luminous Infrared Galaxies (LIRG) represent
ideal and challenging objects to investigate the origin of the H2 emission, as
all processes above can be observed in a single object. In this work, we use
K-band integral field spectroscopy to map the emission line flux distributions
and kinematics and investigate the origin of the molecular and ionized gas line
emission from inner 1.4x2.4 kpc2 of the LIRG NGC6240, known to be the galaxy
with strongest H2 line emission. The emission lines show complex profiles at
locations between both nuclei and surrounding the northern nucleus, while at
locations near the southern nucleus and at 1" west of the northern nucleus,
they can be reproduced by a single gaussian component. We found that the H2
emission is originated mainly by thermal processes, possible being dominated by
heating of the gas by X-rays from the AGN at locations near both nuclei. For
the region between the northern and southern nuclei shocks due to the
interacting process may be the main excitation mechanism, as indicated by the
high values of the H2l2.12um/Brg line ratio. A contribution of fluorescent
excitation may also be important at locations near 1" west of the northern
nucleus, which show the lowest line ratios. The [FeII]l2.072um/Brg ratio show a
similar trend as observed for H2l2.12um/Brg, suggesting that [FeII] and H2 line
emission have similar origins. Finally, the [CaVIII]l2.32um coronal line
emission is observed mainly in regions next to the nuclei, suggesting it is
originated gas ionized by the radiation from the AGN.


title: Robust and Sparse Regression via $\gamma$-divergence

abstract:
  In high-dimensional data, many sparse regression methods have been proposed.
However, they may not be robust against outliers. Recently, the use of density
power weight has been studied for robust parameter estimation and the
corresponding divergences have been discussed. One of such divergences is the
$\gamma$-divergence and the robust estimator using the $\gamma$-divergence is
known for having a strong robustness. In this paper, we consider the robust and
sparse regression based on $\gamma$-divergence. We extend the
$\gamma$-divergence to the regression problem and show that it has a strong
robustness under heavy contamination even when outliers are heterogeneous. The
loss function is constructed by an empirical estimate of the
$\gamma$-divergence with sparse regularization and the parameter estimate is
defined as the minimizer of the loss function. To obtain the robust and sparse
estimate, we propose an efficient update algorithm which has a monotone
decreasing property of the loss function. Particularly, we discuss a linear
regression problem with $L_1$ regularization in detail. In numerical
experiments and real data analyses, we see that the proposed method outperforms
past robust and sparse methods.


title:
Decoherence of an impurity in a one-dimensional fermionic bath with mass
  imbalance

abstract:
  We study the transport, decoherence and dissipation of an impurity
interacting with a bath of free fermions in a one-dimensional lattice.
Numerical simulations are made with the time-evolving block decimation method.
We introduce a mass imbalance between the impurity and bath particles and find
that the fastest decoherence occurs for a light impurity in a bath of heavy
particles. By contrast, the fastest dissipation of energy occurs when the
masses are equal. We present a simple model for decoherence in the heavy bath
limit, and a linear density response description of the interaction which
predicts maximum dissipation for equal masses.


title: Polychromatic Arm Exponents for the Critical Planar FK-Ising model

abstract:
  Schramm Loewner Evolution (SLE) is a one-parameter family of random planar
curves introduced by Oded Schramm in 1999 as the candidates for the scaling
limits of the interfaces in the planar critical lattice models. This is the
only possible process with conformal invariance and a certain "domain Markov
property". In 2010, Chelkak and Smirnov proved the conformal invariance of the
scaling limits of the critial planar FK-Ising model which gave the convergence
of the interface to SLE$_{16/3}$. We derive the arm exponents of SLE$_{\kappa}$
for $\kappa\in (4,8)$. Combining with the convergence of the interface, we
derive the arm exponents of the critical FK-Ising model. We obtain six
different patterns of boundary arm exponents and three different patterns of
interior arm exponents of the critical planar FK-Ising model on the square
lattice.


title:
Correction to Nambu-Jona-Lasinio model from QCD at the next-to-leading
  order

abstract:
  We evaluate the next-to-leading order correction to the Nambu-Jona-Lasinio
model starting from quantum chromodynamics. We show that a systematic expansion
exists, starting from a given set of exact classical solutions, so that higher
order corrections could in principle be computed at any order. In this way, we
are able to fix the constants of the Nambu-Jona-Lasinio model from quantum
chromodynamics and analyze the behavior of strong interactions at low energies.
The technique is to expand in powers of currents of the generating functional.
We apply it to a simple Yukawa model with self-interaction showing how this has
a Nambu-Jona-Lasinio model and its higher order corrections as a low-energy
limit. The same is shown to happen for quantum chromodynamics in the chiral
limit with two quarks. We prove stability of the NJL model so obtained. Then,
we prove that the correction term we obtained does not change the critical
temperature of the chiral transition of the Nambu-Jona-Lasinio model at zero
chemical potential.


title:
Compact-Table: Efficiently Filtering Table Constraints with Reversible
  Sparse Bit-Sets

abstract:
  In this paper, we describe Compact-Table (CT), a bitwise algorithm to enforce
Generalized Arc Consistency (GAC) on table con- straints. Although this
algorithm is the default propagator for table constraints in or-tools and
OscaR, two publicly available CP solvers, it has never been described so far.
Importantly, CT has been recently improved further with the introduction of
residues, resetting operations and a data-structure called reversible sparse
bit-set, used to maintain tables of supports (following the idea of tabular
reduction): tuples are invalidated incrementally on value removals by means of
bit-set operations. The experimentation that we have conducted with OscaR shows
that CT outperforms state-of-the-art algorithms STR2, STR3, GAC4R, MDD4R and
AC5-TC on standard benchmarks.


title: Pairing effects on neutrino transport in low-density stellar matter

abstract:
  We investigate the impact of pairing correlations on neutrino transport in
stellar matter. Our analysis is extended to nuclear matter conditions where
large density fluctuations develop, associated with the onset of the
liquid-vapor phase transition, and clustering phenomena occur. Within a
thermodynamical treatment, we show that at moderate temperatures, where pairing
effects are still active, the scattering of neutrinos in the nuclear medium is
significantly affected by pairing correlations, which increase the neutrino
trapping, thus modifying the cooling mechanism, by neutrino emission, of
neutron stars.


title: Sampling cluster point processes: a review

abstract:
  The theme of this article is the sampling of cluster and iterated cluster
point processes. It is partially a review, mainly of the Brix-Kendall exact
sampling method for cluster point processes and its adaptation by M{\o}ller and
Rasmussen to Hawkes branching point processes on the real line with light-tail
fertility rate are reviewed. The main novel aspect of this review is the
extension to non-Poissonian germ point processes. For this, a slight adaptation
is needed. A formal proof via Laplace transforms of the validity of the method
in terms of general clusters that are not necessarily point processes fits this
purpose and allows to include the exact sampling of Boolean models.


title: Derivative-Based Diagnosis of Regular Expression Ambiguity

abstract:
  Regular expressions are often ambiguous. We present a novel method based on
Brzozowski's derivatives to aid the user in diagnosing ambiguous regular
expressions. We introduce a derivative-based finite state transducer to
generate parse trees and minimal counter-examples. The transducer can be easily
customized to either follow the POSIX or Greedy disambiguation policy and based
on a finite set of examples it is possible to examine if there are any
differences among POSIX and Greedy.


title:
Search for magnetic monopoles with the MoEDAL prototype trapping
  detector in 8 TeV proton-proton collisions at the LHC

abstract:
  The MoEDAL experiment is designed to search for magnetic monopoles and other
highly-ionising particles produced in high-energy collisions at the LHC. The
largely passive MoEDAL detector, deployed at Interaction Point 8 on the LHC
ring, relies on two dedicated direct detection techniques. The first technique
is based on stacks of nuclear-track detectors with surface area $\sim$18 m$^2$,
sensitive to particle ionisation exceeding a high threshold. These detectors
are analysed offline by optical scanning microscopes. The second technique is
based on the trapping of charged particles in an array of roughly 800 kg of
aluminium samples. These samples are monitored offline for the presence of
trapped magnetic charge at a remote superconducting magnetometer facility. We
present here the results of a search for magnetic monopoles using a 160 kg
prototype MoEDAL trapping detector exposed to 8 TeV proton-proton collisions at
the LHC, for an integrated luminosity of 0.75 fb$^{-1}$. No magnetic charge
exceeding $0.5g_{\rm D}$ (where $g_{\rm D}$ is the Dirac magnetic charge) is
measured in any of the exposed samples, allowing limits to be placed on
monopole production in the mass range 100 GeV$\leq m \leq$ 3500 GeV.
Model-independent cross-section limits are presented in fiducial regions of
monopole energy and direction for $1g_{\rm D}\leq|g|\leq 6g_{\rm D}$, and
model-dependent cross-section limits are obtained for Drell-Yan pair production
of spin-1/2 and spin-0 monopoles for $1g_{\rm D}\leq|g|\leq 4g_{\rm D}$. Under
the assumption of Drell-Yan cross sections, mass limits are derived for
$|g|=2g_{\rm D}$ and $|g|=3g_{\rm D}$ for the first time at the LHC, surpassing
the results from previous collider experiments.


title: Synthetic Data for Text Localisation in Natural Images

abstract:
  In this paper we introduce a new method for text detection in natural images.
The method comprises two contributions: First, a fast and scalable engine to
generate synthetic images of text in clutter. This engine overlays synthetic
text to existing background images in a natural way, accounting for the local
3D scene geometry. Second, we use the synthetic images to train a
Fully-Convolutional Regression Network (FCRN) which efficiently performs text
detection and bounding-box regression at all locations and multiple scales in
an image. We discuss the relation of FCRN to the recently-introduced YOLO
detector, as well as other end-to-end object detection systems based on deep
learning. The resulting detection network significantly out performs current
methods for text detection in natural images, achieving an F-measure of 84.2%
on the standard ICDAR 2013 benchmark. Furthermore, it can process 15 images per
second on a GPU.


title: On the CPT-even Lorentz-breaking extension of the QED

abstract:
  In this paper, we describe the quantum electrodynamics added by
Lorentz-violating CPT-even terms in the context of the standard model
extension. We focus our attention on the fermion sector, represented by the
CPT-even symmetric Lorentz-breaking tensor $c_{\mu\nu}$. We adopt a generic
form that parametrizes the components of $c_{\mu\nu}$ in terms of one
four-vector, namely, $c_{\mu\nu}=u_\mu u_\nu - \zeta \frac{u^2}{4}g_{\mu\nu}$.
We then generate perturbatively, up to the third order in this tensor, the
aether-like term for the gauge field. Finally, we discuss the renormalization
scheme for the gauge propagator, by taking into account $c_{\mu\nu}$ traceless
($\zeta=1)$ and, trivially, $c_{\mu\nu}=u_\mu u_\nu$ ($\zeta=0$).


title:
Automatic verbal aggression detection for Russian and American
  imageboards

abstract:
  The problem of aggression for Internet communities is rampant. Anonymous
forums usually called imageboards are notorious for their aggressive and
deviant behaviour even in comparison with other Internet communities. This
study is aimed at studying ways of automatic detection of verbal expression of
aggression for the most popular American (4chan.org) and Russian (2ch.hk)
imageboards. A set of 1,802,789 messages was used for this study. The machine
learning algorithm word2vec was applied to detect the state of aggression. A
decent result is obtained for English (88%), the results for Russian are yet to
be improved.


title:
The origin of unequal bond lengths in the $\mathrm{\tilde{C}}$ $^1$B$_2$
  state of SO$_2$: Signatures of high-lying potential energy surface crossings
  in the low-lying vibrational structure

abstract:
  The $\mathrm{\tilde{C}}$ $^1$B$_2$ state of SO$_2$ has a double-minimum
potential in the antisymmetric stretch coordinate, such that the minimum energy
geometry has nonequivalent SO bond lengths. The asymmetry in the potential
energy surface is expressed as a staggering in the energy levels of the
$\nu_3'$ progression. We have recently made the first observation of low-lying
levels with odd quanta of $v_3'$, which allows us--in the current work--to
characterize the origins of the level staggering. Our work demonstrates the
usefulness of low-lying vibrational level structure, where the character of the
wavefunctions can be relatively easily understood, to extract information about
dynamically important potential energy surface crossings that occur at much
higher energy. The measured staggering pattern is consistent with a vibronic
coupling model for the double-minimum, which involves direct coupling to the
bound 2$^1$A$_1$ state and indirect coupling with the repulsive 3$^1$A$_1$
state. The degree of staggering in the $\nu_3'$ levels increases with quanta of
bending excitation, which is consistent with the approach along the
$\mathrm{\tilde{C}}$ state potential energy surface to a conical intersection
with the 2$^1$A$_1$ surface at a bond angle of $\sim$145$^{\circ}$.


title: Detecting state of aggression in sentences using CNN

abstract:
  In this article we study verbal expression of aggression and its detection
using machine learning and neural networks methods. We test our results using
our corpora of messages from anonymous imageboards. We also compare Random
forest classifier with convolutional neural network for "Movie reviews with one
sentence per review" corpus.


title: General and specific utility measures for synthetic data

abstract:
  Data holders can produce synthetic versions of datasets when concerns about
potential disclosure restrict the availability of the original records. This
paper is concerned with methods to judge whether such synthetic data have a
distribution that is comparable to that of the original data, what we will term
general utility. We consider how general utility compares with specific
utility, the similarity of results of analyses from the synthetic data and the
original data. We adapt a previous general measure of data utility, the
propensity score mean-squared-error (pMSE), to the specific case of synthetic
data and derive its distribution for the case when the correct synthesis model
is used to create the synthetic data. Our asymptotic results are confirmed by a
simulation study. We also consider two specific utility measures, confidence
interval overlap and standardized difference in summary statistics, which we
compare with the general utility results. We present two examples examining
this comparison of general and specific utility to real data syntheses and make
recommendations for their use for evaluating synthetic data.


title: Quantum features of natural cellular automata

abstract:
  Cellular automata can show well known features of quantum mechanics, such as
a linear rule according to which they evolve and which resembles a discretized
version of the Schroedinger equation. This includes corresponding conservation
laws. The class of "natural" Hamiltonian cellular automata is based exclusively
on integer-valued variables and couplings and their dynamics derives from an
Action Principle. They can be mapped reversibly to continuum models by applying
Sampling Theory. Thus, "deformed" quantum mechanical models with a finite
discreteness scale $l$ are obtained, which for $l\rightarrow 0$ reproduce
familiar continuum results. We have recently demonstrated that such automata
can form "multipartite" systems consistently with the tensor product structures
of nonrelativistic many-body quantum mechanics, while interacting and
maintaining the linear evolution. Consequently, the Superposition Principle
fully applies for such primitive discrete deterministic automata and their
composites and can produce the essential quantum effects of interference and
entanglement.


title:
Shallow acceptor state in ZnO realized by simple irradiation and
  annealing route

abstract:
  Activation of shallow acceptor state has been observed in ion irradiated and
subsequently air annealed polycrystalline ZnO material. Low temperature
photoluminescence (PL) spectrum of the sample exhibits clear signature of
acceptor bound exciton (ABX) emission at 3.360 eV. The other two samples,
pristine and ion irradiated (without annealing), however, do not show acceptor
related PL emission in the nearby energy region. Electron transition from
shallow donor (most probable site is interstitial zinc for undoped ZnO) to such
newly formed shallow acceptor state creates new donor-acceptor pair (DAP)
luminescence peak ~ 3.229 eV. ABX and DAP peak energy positions confirm that
the acceptor is N related. The acceptor exciton binding energy has been
estimated to be 180 +/- 15 meV which is in conformity with earlier reports. The
activation of shallow acceptors without any source of atomic nitrogen can only
be possible through diffusion of molecular nitrogen inside the sample during
annealing. The N2 molecules get trapped at bulk defect sites incorporated by
ion irradiation and subsequent annealing. X-ray diffraction (XRD) and Raman
spectroscopic (RS) investigation have been employed to probe the changing
defective nature of the ZnO samples. Irradiation induced increased disorder has
been detected (both by XRD and RS) which is partially removed/modified by
annealing at 300 oC. Simultaneous activation of molecular nitrogen acceptor in
purposefully defective ZnO is the key finding of this work. Results presented
here provide a simple but controlled way of producing shallow acceptor state in
ZnO. If optimized through suitable choice of ion, its energy and fluence as
well as the annealing temperature, this methodology can trigger further scope
to fabricate devices using ZnO epitaxial thin films or nanowires.


title: Numerically stable conditions on rational and essential singularities

abstract:
  This paper demonstrates some connections between the coefficients of a Taylor
series $f(z)=\ds\sum_{n=0}^\infty a_n z^n$ and singularities of the function.
There are many known results of this type, for example, counting the number of
poles on the circle of convergence, and doing convergence or overconvergence
for $f$ on any arc of holomorphy. A new approach proposed here is that these
kinds of results are extended by relaxing the classical conditions for
singularities and convergence theorems. This is done by allowing the
coefficients to be sufficiently small instead of being zero.


title:
Interface asymptotics of partial Bergman kernels on $S^1$-symmetric
  Kaehler manifolds

abstract:
  This article is concerned with asymptotics of equivariant Bergman kernels and
partial Bergman kernels for polarized projective Kahler manifolds invariant
under a Hamiltonian holomorphic $S^1$ action. Asymptotics of partial Bergman
kernel are obtained in the allowed region $\mathcal{A}$ resp. forbidden region
$\mathcal{F}$, generalizing results of Shiffman-Zelditch,
Shiffman-Tate-Zelditch and Pokorny-Singer for toric Kahler manifolds. The main
result gives scaling asymptotics of equivariant Bergman kernels and partial
Bergman kernels in the transition region around the interface $\partial
\mathcal{A}$, generalizing recent work of Ross-Singer on partial Bergman
kernels, and refining the Ross-Singer transition asymptotics to apply to
equivariant Bergman kernels.


title:
Coherent Coupling of WS_2 Monolayers with Metallic Photonic
  Nanostructures at Room Temperature

abstract:
  Room temperature strong coupling of WS_2 monolayer exciton transitions to
metallic Fabry-Perot and plasmonic optical cavities is demonstrated. A Rabi
splitting of 101 meV is observed for the Fabry-Perot cavity, more than double
those reported to date in other 2D materials. The enhanced magnitude and
visibility of WS_2 monolayer strong coupling is attributed to the larger
absorption coefficient, the narrower linewidth of the A exciton transition, and
greater spin-orbit coupling. For WS_2 coupled to plasmonic arrays, the Rabi
splitting still reaches 60 meV despite the less favorable coupling conditions,
and displays interesting photoluminescence features. The unambiguous signature
of WS_2 monolayer strong coupling in easily fabricated metallic resonators at
room temperature suggests many possibilities for combining light-matter
hybridization with spin and valleytronics.


title:
Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical
  Gauss map

abstract:
  We give a complete classification of Riemannian and Lorentzian surfaces of
arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are
of 1-type or, in particular, harmonic. In some cases a concrete global
classification is obtained, while in other cases the solutions are described by
an explicit system of partial differential equations.


title: Confining continuous manipulations of accelerator beamline optics

abstract:
  Altering the optics in one section of a linear accelerator beamline will in
general cause an alteration of the optics in all downstream sections. In
circular accelerators, changing the optical properties of any beamline element
will have an impact on the optical functions throughout the whole machine. In
many cases, however, it is desirable to change the optics in a certain beamline
section without disturbing any other parts of the machine. Such a local optics
manipulation can be achieved by adjusting a number of additional corrector
magnets that restore the initial optics after the manipulated section. In that
case, the effect of the manipulation is confined in the region between the
manipulated and the correcting beamline elements. Introducing a manipulation
continuously, while the machine is operating, therefore requires continuous
correction functions to be applied to the correcting quadrupole magnets.
  In this paper we present an analytic approach to calculate such continuous
correction functions for six quadrupole magnets by means of a homotopy method.
Besides a detailed derivation of the method, we present its application to an
algebraic example, as well as its implementation at the seeding experiment
sFLASH at the free-electron laser FLASH located at DESY in Hamburg.


title:
On the Closed-Form Solution of a Nonlinear Difference Equation and
  Another Proof to Sroysang's Conjecture

abstract:
  The purpose of this paper is twofold. First, we derive theoretically, using
appropriate transformation on $x_n$, the closed-form solution of the nonlinear
difference equation \[ x_{n+1} = \frac{1}{\pm 1 + x_n},\qquad n\in
\mathbb{N}_0. \] We mention that the solution form of this equation was already
obtained by Tollu et al. in 2013, but through induction principle, and one of
our purpose is to clearly explain how was the formula appeared in such
structure. After that, with the solution form of the above equation at hand, we
prove a case of Sroysang's conjecture (2013); i.e., given a fixed positive
integer $k$, we verify the validity of the following claim: \[ \lim_{x
\rightarrow \infty}\left\{ \frac{f(x+k)}{f(x)}\right\}= \phi, \] where
$\phi=(1+\sqrt{5})/2$ denotes the well-known golden ratio and the real valued
function $f$ on $\mathbb{R}$ satisfies the functional equation $f(x+2k)=f(x+k)
+ f(x)$ for every $x\in \mathbb{R}$. We complete the proof of the conjecture by
giving out an entirely different approach for the other case.


title: Excluded volume effects in on- and off-lattice reaction-diffusion models

abstract:
  Mathematical models are important tools to study the excluded volume effects
on reaction-diffusion systems, which are known to play an important role inside
living cells. Detailed microscopic simulations with off-lattice Brownian
dynamics become computationally expensive in crowded environments. In this
paper we therefore investigate to which extent on-lattice approximations, so
called Cellular Automata models, can be used to simulate reactions and
diffusion in the presence of crowding molecules. We show that the diffusion is
most severely slowed down in the off-lattice model, since randomly distributed
obstacles effectively exclude more volume than those ordered on an artificial
grid. Crowded reaction rates can be both increased and decreased by the grid
structure and it proves important to model the molecules with realistic sizes
when excluded volume is taken into account. The grid artifacts increase with
increasing crowder density and we conclude that the computationally more
efficient on-lattice simulations are accurate approximations only for low
crowder densities.


title:
Manipulating superconductivity in ruthenates through Fermi surface
  engineering

abstract:
  The key challenge in superconductivity research is to go beyond the
historical mode of discovery-driven research. We put forth a new strategy,
which is to combine theoretical developments in the weak-coupling
renormalization group approach with the experimental developments in lattice
strain driven Fermi surface-engineering. For concreteness we theoretically
investigate how superconducting tendencies will be affected by strain
engineering of ruthenates' Fermi surface. We first demonstrate that our
approach qualitatively reproduces recent experiments under uniaxial strain. We
then note that order few $\%$ strain readily accessible to epitaxial thin
films, can bring the Fermi surface close to van Hove singularity. Using the
experimental observation of the change in the Fermi surface under biaxial
epitaxial strain and ab-initio calculations, we predict ${\rm T}_{\rm c}$ for
triplet pairing to be maximized by getting close to the van Hove singularities
without tuning on to the singularity.


title:
Possible formation of high temperature superconductor at early stage of
  heavy-ion collisions

abstract:
  We investigate the effect of the inverse magnetic catalysis (IMC) on the
charged $\rho$ meson condensation at finite temperature in the framework of the
Nambu--Jona-Lasinio model, where mesons are calculated to the leading order of
$1/N_c$ expansion by summing up infinity quark-loops. IMC for chiral condensate
has been considered in three different ways, i.e. fitting Lattice data, using
the running coupling constant and introducing the chiral chemical potential,
respectively. It is observed that, with no IMC effect included, the critical
magnetic field $eB_c$ for charged $\rho$ condensation increases monotonically
with the temperature. However, including IMC substantially affects the
polarized charged $\rho$ condensation around the critical temperature $T_c$ of
chiral phase transition, the critical magnetic field $eB_c$ for charged $\rho$
condensation decreases with the temperature firstly, reaches to a minimum value
around $T_c$, then increases with the temperature. Our calculation indicates
that the charged $\rho$ condensation can exist in the temperature region of
$1-1.5 T_c$ with critical magnetic field $eB_c\sim 0.15-0.3 {\rm GeV}^2$, which
suggests that high temperature superconductor might be created through
non-central heavy ion collisions at LHC energies. We also show that a growing
electric conductivity in early stage of non-central heavy-ion collisions
substantially delays the decay of strong magnetic field, which is helpful for
the formation of the high temperature superconductor.


title: Small oscillations of the pendulum, Euler's method, and adequality

abstract:
  Small oscillations evolved a great deal from Klein to Robinson. We propose a
concept of solution of differential equation based on Euler's method with
infinitesimal mesh, with well-posedness based on a relation of adequality
following Fermat and Leibniz. The result is that the period of infinitesimal
oscillations is independent of their amplitude.
  Keywords: harmonic motion; infinitesimal; pendulum; small oscillations


title:
Optimal scaling of the Random Walk Metropolis algorithm under Lp mean
  differentiability

abstract:
  This paper considers the optimal scaling problem for high-dimensional random
walk Metropolis algorithms for densities which are differentiable in Lp mean
but which may be irregular at some points (like the Laplace density for
example) and/or are supported on an interval. Our main result is the weak
convergence of the Markov chain (appropriately rescaled in time and space) to a
Langevin diffusion process as the dimension d goes to infinity. Because the
log-density might be non-differentiable, the limiting diffusion could be
singular. The scaling limit is established under assumptions which are much
weaker than the one used in the original derivation of [6]. This result has
important practical implications for the use of random walk Metropolis
algorithms in Bayesian frameworks based on sparsity inducing priors.


title:
Multiscale Segmentation via Bregman Distances and Nonlinear Spectral
  Analysis

abstract:
  In biomedical imaging reliable segmentation of objects (e.g. from small cells
up to large organs) is of fundamental importance for automated medical
diagnosis. New approaches for multi-scale segmentation can considerably improve
performance in case of natural variations in intensity, size and shape. This
paper aims at segmenting objects of interest based on shape contours and
automatically finding multiple objects with different scales. The overall
strategy of this work is to combine nonlinear segmentation with scales spaces
and spectral decompositions recently introduced in literature. For this we
generalize a variational segmentation model based on total variation using
Bregman distances to construct an inverse scale space. This offers the new
model to be accomplished by a scale analysis approach based on a spectral
decomposition of the total variation. As a result we obtain a very efficient,
(nearly) parameter-free multiscale segmentation method that comes with an
adaptive regularization parameter choice. The added benefit of our method is
demonstrated by systematic synthetic tests and its usage in a new biomedical
toolbox for identifying and classifying circulating tumor cells. Due to the
nature of nonlinear diffusion underlying, the mathematical concepts in this
work offer promising extensions to nonlocal classification problems.


title:
Theory of the Evolution of Superconductivity in Sr$_2$RuO$_4$ under
  Anisotropic Strain

abstract:
  Sr$_2$RuO$_4$ is a leading candidate for chiral $p$-wave superconductivity.
The detailed mechanism of superconductivity in this material is still the
subject of intense investigations. Since superconductivity is sensitive to the
topology of the Fermi surface (the contour of zero-energy quasi-particle
excitations in the momentum space in the normal state), changing this topology
can provide a strong test of theory. Recent experiments tuned the Fermi surface
topology efficiently by applying planar anisotropic strain. Using functional
renormalization group theory, we study the superconductivity and competing
orders in Sr$_2$RuO$_4$ under strain. We find a rapid initial increase in the
superconducting transition temperature $T_c$, which can be associated with the
evolution of the Fermi surface toward a Lifshitz reconstruction under
increasing strain. Before the Lifshitz reconstruction is reached, however, the
system switches from the superconducting state to a spin density wave state.
The theory agrees well with recent strain experiments showing an enhancement of
$T_c$ followed by an intriguing sudden drop.


title:
Cygrid: A fast Cython-powered convolution-based gridding module for
  Python

abstract:
  Data gridding is a common task in astronomy and many other science
disciplines. It refers to the resampling of irregularly sampled data to a
regular grid. We present cygrid, a library module for the general purpose
programming language Python. Cygrid can be used to resample data to any
collection of target coordinates, although its typical application involves
FITS maps or data cubes. The FITS world coordinate system standard is
supported. The regridding algorithm is based on the convolution of the original
samples with a kernel of arbitrary shape. We introduce a lookup table scheme
that allows us to parallelize the gridding and combine it with the HEALPix
tessellation of the sphere for fast neighbor searches. We show that for $n$
input data points, cygrids runtime scales between O(n) and O(n log n) and
analyze the performance gain that is achieved using multiple CPU cores. We also
compare the gridding speed with other techniques, such as nearest-neighbor, and
linear and cubic spline interpolation. Cygrid is a very fast and versatile
gridding library that significantly outperforms other third-party Python
modules, such as the linear and cubic spline interpolation provided by SciPy.


title:
Test of the Weak Equivalence Principle using LIGO observations of
  GW150914 and Fermi observations of GBM transient 150914

abstract:
  About 0.4s after the Laser Interferometer Gravitational-Wave Observatory
(LIGO) detected a transient gravitational-wave (GW) signal GW150914, the Fermi
Gamma-ray Burst Monitor (GBM) also found a weak electromagnetic transient (GBM
transient 150914). Time and location coincidences favor a possible association
between GW150904 and GBM transient 150914. Under this possible association, we
adopt Fermi's electromagnetic (EM) localization and derive constraints on
possible violations of the Weak Equivalence Principle (WEP) from the
observations of two events. Our calculations are based on four comparisons:
(1)The first is the comparison of the initial GWs detected at the two LIGO
sites. From the different polarizations of these initial GWs, we obtain a limit
on any difference in the parametrized post-Newtonian (PPN) parameter
$\Delta\gamma\lesssim 10^{-10}$. (2) The second is a comparison of GWs and
possible EM waves. Using a traditional super-Eddington accretion model for GBM
transient 150914, we again obtain an upper limit $\Delta\gamma\lesssim
10^{-10}$. Compared with previous results for photons and neutrinos, our limits
are five orders of magnitude stronger than those from PeV neutrinos in blazar
flares, and seven orders stronger than those from MeV neutrinos in SN1987A. (3)
The third is a comparison of GWs with different frequencies in the range [35
Hz, 250 Hz]. (4) The fourth is a comparison of EM waves with different energies
in the range [1 keV, 10 MeV]. These last two comparisons lead to an even
stronger limit, $\Delta\gamma\lesssim 10^{-8}$. Our results highlight the
potential of multi-messenger signals exploiting different emission channels to
strengthen existing tests of the WEP.


title: Strong Peak in $T_c$ of Sr$_2$RuO$_4$ Under Uniaxial Pressure

abstract:
  We report a combined experimental and theoretical study of the dependence of
the superconductivity of the unconventional superconductor Sr$_2$RuO$_4$ on
anisotropic strain. Novel piezoelectric apparatus is used to apply uniaxial
pressures of up to $\sim$1~GPa along a $\langle 100 \rangle$ direction
($a$-axis) of the crystal lattice. $T_c$ increases from 1.5~K in unstrained
material to 3.4~K at compression by $\approx$0.6\%, then falls steeply. The
$c$-axis upper critical field for the strained $T_c$ = 3.4~K material is a
factor of twenty larger than that of the unstrained crystal, whereas the
in-plane ($a$-axis) critical field increases by only a factor of three.
First-principles electronic structure calculations give evidence that the
observed maximum $T_c$ occurs at or near a Lifshitz transition when the Fermi
level passes through a van Hove singularity. Finally, we perform order
parameter analyses using three-band renormalization group calculations. These,
combined with the unexpectedly low in-plane critical field, open the
possibility that the highly strained $T_c$=3.4~K Sr$_2$RuO$_4$ has an even-
rather than an odd-parity order parameter. Potential implications such as a
transition at nonzero strain between odd- and even-parity order parameters are
discussed.


title: Non-stationary resonance dynamics of the harmonically forced pendulum

abstract:
  The stationary and highly non-stationary resonant dynamics of the
harmonically forced pendulum are described in the framework of a semi-inverse
procedure combined with the Limiting Phase Trajectory concept. This procedure,
implying only existence of slow time scale, permits to avoid any restriction on
the oscillation amplitudes. The main results relating to the dynamical
bifurcation thresholds are represented in a closed form. The small parameter
defining the separation of the time scales is naturally identified in the
analytical procedure. Considering the pendulum frequency as the control
parameter we reveal two qualitative transitions. One of them corresponding to
stationary instability with formation of two additional stationary states, the
other, associated with the most intense energy drawing from the source, at
which the amplitude of pendulum oscillations abruptly grows.
  Analytical predictions of both bifurcations are verified by numerical
integration of original equation.
  It is also shown that occurrence of chaotic domains may be strongly connected
with the second transition.


title:
Eigenvalue placement for regular matrix pencils with rank one
  perturbations

abstract:
  A regular matrix pencil sE-A and its rank one perturbations are considered.
We determine the sets in the extended complex plane which are the eigenvalues
of the perturbed pencil. We show that the largest Jordan chains at each
eigenvalue of sE-A may disappear and the sum of the length of all destroyed
Jordan chains is the number of eigenvalues (counted with multiplicities) which
can be placed arbitrarily in the extended complex plane. We prove sharp upper
and lower bounds of the change of the algebraic and geometric multiplicity of
an eigenvalue under rank one perturbations. Finally we apply our results to a
pole placement problem for a single-input differential algebraic equation with
feedback.


title:
Oscillating line source in a shear flow with a free surface: critical
  layer-like contributions

abstract:
  The linearized water-wave radiation problem for an oscillating submerged line
source in an inviscid shear flow with a free surface is investigated
analytically at finite, constant depth in the presence of a shear flow varying
linearly with depth. The surface velocity is taken to be zero relative to the
oscillating source, so that Doppler effects are absent. The radiated wave out
from the source is calculated based on Euler's equation of motion with the
appropriate boundary and radiation conditions, and differs substantially from
the solution obtained by assuming potential flow. To wit, an additional wave is
found in the downstream direction in addition to the previously known
dispersive wave solutions; this wave is non-dispersive and we show how it is
the surface manifestation of a critical layer-like flow generated by the
combination of shear and mass flux at the source, passively advected with the
flow. As seen from a system moving at the fluid velocity at the source's depth,
streamlines form closed curves in a manner similar to Kelvin's cat's eye
vortices. A resonant frequency exists at which the critical wave resonates with
the downstream propagating wave, resulting in a downstream wave pattern
diverging linearly in amplitude away from the source.


title:
Stability and chaos in Kustaanheimo-Stiefel space induced by the Hopf
  fibration

abstract:
  The need for the extra dimension in Kustaanheimo-Stiefel (KS) regularization
is explained by the topology of the Hopf fibration, which defines the geometry
and structure of KS space. A trajectory in Cartesian space is represented by a
four-dimensional manifold, called the fundamental manifold. Based on geometric
and topological aspects classical concepts of stability are translated to KS
language. The separation between manifolds of solutions generalizes the concept
of Lyapunov stability. The dimension-raising nature of the fibration transforms
fixed points, limit cycles, attractive sets, and Poincar\'e sections to
higher-dimensional subspaces. From these concepts chaotic systems are studied.
In strongly perturbed problems the numerical error can break the topological
structure of KS space: points in a fiber are no longer transformed to the same
point in Cartesian space. An observer in three dimensions will see orbits
departing from the same initial conditions but diverging in time. This apparent
randomness of the integration can only be understood in four dimensions. The
concept of topological stability results in a simple method for estimating the
time scale in which numerical simulations can be trusted. Ideally all
trajectories departing from the same fiber should be KS transformed to a unique
trajectory in three-dimensional space, because the fundamental manifold that
they constitute is unique. By monitoring how trajectories departing from one
fiber separate from the fundamental manifold a critical time, equivalent to the
Lyapunov time, is estimated. These concepts are tested on N-body examples: the
Pythagorean problem, and an example of field stars interacting with a binary.

categories: math-ph astro-ph.GA astro-ph.SR math.AT math.MP physics.space-ph


title: A new ordering principle in quantum field theory and its consequences

abstract:
  The ad-hoc imposition of normal ordering on the Lagrangian, energy-momentum
tensor and currents is a standard tool in quantum field theory (QFT) to
eliminate infinite vacuum expectation values (v.e.v.) However, for fermionic
expressions these infinite terms are due to anti-particles only. This exposes
an asymmetry in standard QFT, which can be traced back to a bias towards
particles in the Dirac bra-ket notation. To counter this bias a new ordering
principle (called the $\mathbb{R}$-product) is required which restores the
symmetry (or rather duality) between particles and anti-particles and
eliminates the infinite v.e.v. While this $\mathbb{R}$-product was already used
in a bound-state application, this paper aims to give it a more general
foundation and analyze its overall impact in QFT.
  For boson fields the particle bias is hidden and the fields must first be
expanded into bilinear particle-anti-particle fermion operators. This new
representation also leads to vanishing v.e.v.'s and avoids some common
technical problems in the quantization of vector fields, while it admits new
constant contributions that mimic the Higgs mechanism without unacceptable
contributions to the cosmological constant.
  Since the $\mathbb{R}$-product does not apply between operators belonging to
different space- time coordinates (e.g. propagators and vacuum condensates),
most standard QFT calculations remain unaffected by this new principle,
preserving those quantitative successes. The boson propagator also retains a
standard bosonic form despite the fermionic representation. However, the
foundations of QFT are affected strongly as the new principle suggests that the
Standard Model is an effective theory built (partly?) on massless bare quarks.


title:
Gr\"obner-Shirshov bases for Lie $\Omega$-algebras and free Rota-Baxter
  Lie algebras

abstract:
  In this paper, we generalize the Lyndon-Shirshov words to Lyndon-Shirshov
$\Omega$-words on a set $X$ and prove that the set of all non-associative
Lyndon-Shirshov $\Omega$-words forms a linear basis of the free Lie
$\Omega$-algebra on the set $X$. From this, we establish Gr\"{o}bner-Shirshov
bases theory for Lie $\Omega$-algebras. As applications, we give
Gr\"{o}bner-Shirshov bases for free $\lambda$-Rota-Baxter Lie algebras, free
modified $\lambda$-Rota-Baxter Lie algebras and free Nijenhuis Lie algebras and
then linear bases of such three free algebras are obtained.


title: On free Gelfand-Dorfman-Novikov-Poisson algebras and a PBW theorem

abstract:
  In 1997, X. Xu \cite{Xiaoping Xu Poisson} invented a concept of
Novikov-Poisson algebras (we call them Gelfand-Dorfman-Novikov-Poisson
(GDN-Poisson) algebras). We construct a linear basis of a free GDN-Poisson
algebra. We define a notion of a special GDN-Poisson admissible algebra, based
on X. Xu's definition and an S.I. Gelfand's observation (see \cite{Gelfand}).
It is a differential algebra with two commutative associative products and some
extra identities. We prove that any GDN-Poisson algebra is embeddable into its
universal enveloping special GDN-Poisson admissible algebra. Also we prove that
any GDN-Poisson algebra with the identity $x\circ(y\cdot z)=(x\circ y )\cdot z
+(x\circ z) \cdot y$ is isomorphic to a commutative associative differential
algebra.


title:
On polarization parameters of spin-$1$ particles and anomalous couplings
  in $e^+e^-\to ZZ/Z\gamma$

abstract:
  We study the anomalous trilinear gauge couplings of $Z$ and $\gamma$ using a
complete set of polarization asymmetries for the $Z$ boson in $e^+e^-\to
ZZ/Z\gamma$ processes with unpolarized initial beams. We use these polarization
asymmetries, along with the cross section, to obtain a simultaneous limit on
all the anomalous couplings using the Markov-Chain--Monte-Carlo (MCMC) method.
For an $e^+e^-$ collider running at $500$ GeV center-of-mass energy and $100$
fb$^{-1}$ of integrated luminosity the simultaneous limits on the anomalous
couplings are $1\sim3\times 10^{-3}$.


title:
Wall-crossing functors for quantized symplectic resolutions: perversity
  and partial Ringel dualities

abstract:
  In this paper we study wall-crossing functors between categories of modules
over quantizations of symplectic resolutions. We prove that wall-crossing
functors through faces are perverse equivalences and use this to verify an
Etingof type conjecture for quantizations of Nakajima quiver varieties
associated to affine quivers. In the case when there is a Hamiltonian torus
action on the resolution with finitely many fixed points so that it makes sense
to speak about categories $\mathcal{O}$ over quantizations, we introduce new
standardly stratified structures on these categories $\mathcal{O}$ and relate
the wall-crossing functors to the Ringel duality functors associated to these
standardly stratified structures.


title: Modeling of nanoparticle coatings for medical applications

abstract:
  Gold nanoparticles (AuNPs) have been shown to possess properties beneficial
for the treatment of cancerous tumors by acting as radiosensitizers for both
photon and ion radiation. Blood circulation time is usually increased by
coating the AuNPs with poly(ethylene glycol) (PEG) ligands. The effectiveness
of the PEG coating, however, depends on both the ligand surface density and
length of the PEG molecules, making it important to understand the structure of
the coating. In this paper the thickness, ligand surface density, and density
of the PEG coating is studied with classical molecular dynamics using the
software package MBN Explorer. AuNPs consisting of 135 atoms (approximately 1.4
nm diameter) in a water medium have been studied with the number of PEG ligands
varying between 32 and 60. We find that the thickness of the coating is only
weakly dependent on the surface ligand density and that the degree of water
penetration increased when there is a smaller number of attached ligands.


title:
Waves from an oscillating point source with a free surface in the
  presence of a shear current

abstract:
  We investigate analytically the linearized water wave radiation problem for
an oscillating submerged point source in an inviscid shear flow with a free
surface. A constant depth is taken into account and the shear flow increases
linearly with depth. The surface velocity relative to the source is taken to be
zero, so that Doppler effects are absent. We solve the linearized Euler
equations to calculate the resulting wave field as well as its far-field
asymptotics. For values of the Froude number $F^2=\omega^2 D/g$ ($\omega$:
oscillation frequency, $D$ submergence depth) below a resonant value
$F^2_\text{res}$ the wave field splits cleanly into separate contributions from
regular dispersive propagating waves and non-dispersive "critical waves"
resulting from a critical layer-like street of flow structures directly
downstream of the source. In the sub-resonant regime the regular waves behave
like sheared ring waves while the critical layer wave forms a street of a
constant width of order $D\sqrt{S/\omega}$ ($S$ is the shear flow vorticity)
and is convected downstream at the fluid velocity at the depth of the source.
When the Froude number approaches its resonant value, the the downstream
critical and regular waves resonate, producing a train of waves of linearly
increasing amplitude contained within a downstream wedge.


title: Dynamics of the verge and foliot clock escapement

abstract:
  The verge and foliot escapement has received relatively little attention in
horology, despite the fact that it has been used in clocks for ages. We analyse
the operation of a verge and foliot escapement in stationary swing. It is
driven by a torque $m=\pm\mu$, switching sign at fixed swing angles
$\pm\phi_0$, and $\mu$ is taken to be constant. Friction is assumed to exert a
torque proportional to the angular speed. We determine the shape of the swing
angle $\varphi(t)$, and compute the period and the swing amplitude of the
foliot analytically, as a function of the model parameters. We find that the
period of the foliot scales as $P\propto\mu^{-1}$ for weak driving, gradually
changing into $P\propto\mu^{-1/3}$ for strong driving (large $\mu$).