title: E-polynomial of SL(2,C)-Character Varieties of Free groups

abstract:
  Let $\mathsf{F}_r$ be a free group of rank $r$, $\mathbb{F}_q$ a finite field
of order q, and let $\mathrm{SL}_n(\mathbb{F}_q)$ act on
$\mathrm{Hom}(\mathsf{F}_r, \mathrm{SL}_n(\mathbb{F}_q))$ by conjugation. We
describe a general algorithm to determine the cardinality of the set of orbits
$\mathrm{Hom}(\mathsf{F}_r,
\mathrm{SL}_n(\mathbb{F}_q))/\mathrm{SL}_n(\mathbb{F}_q)$. Our first main
theorem is the implementation of this algorithm in the case $n=2$. As an
application, we determine the $E$-polynomial of the character variety
$\mathrm{Hom}(\mathsf{F}_r,
\mathrm{SL}_2(\mathbb{C}))//!/\mathrm{SL}_2(\mathbb{C})$, and of its smooth and
singular locus. Thus we determine the Euler characteristic of these spaces.


title: CDENPROP: Transition matrix elements involving continuum states

abstract:
  Transition matrix elements between electronic states where one electron can
be in the continuum are required for a wide range of applications of the
molecular R-matrix method. These include photoionization, photorecombination
and photodetachment; electron-molecule scattering and photon-induced processes
in the presence of an external D.C. field, and time-dependent R-matrix
approaches to study the effect of the exposure of molecules to strong laser
fields. We present a new algorithm, implemented as a module (CDENPROP) in the
UKRmol electron-molecule scattering code suite.


title:
Lagrangian Framework for Systems Composed of High-Loss and Lossless
  Components

abstract:
  Using a Lagrangian mechanics approach, we construct a framework to study the
dissipative properties of systems composed of two components one of which is
highly lossy and the other is lossless. We have shown in our previous work that
for such a composite system the modes split into two distinct classes,
high-loss and low-loss, according to their dissipative behavior. A principal
result of this paper is that for any such dissipative Lagrangian system, with
losses accounted by a Rayleigh dissipative function, a rather universal
phenomenon occurs, namely, selective overdamping: The high-loss modes are all
overdamped, i.e., non-oscillatory, as are an equal number of low-loss modes,
but the rest of the low-loss modes remain oscillatory each with an extremely
high quality factor that actually increases as the loss of the lossy component
increases. We prove this result using a new time dynamical characterization of
overdamping in terms of a virial theorem for dissipative systems and the
breaking of an equipartition of energy.


title: Dynamics of the scenery flow and geometry of measures

abstract:
  We employ the ergodic theoretic machinery of scenery flows to address
classical geometric measure theoretic problems on Euclidean spaces. Our main
results include a sharp version of the conical density theorem, which we show
to be closely linked to rectifiability. Moreover, we show that the dimension
theory of measure-theoretical porosity can be reduced back to its set-theoretic
version, that Hausdorff and packing dimensions yield the same maximal dimension
for porous and even mean porous measures, and that extremal measures exist and
can be chosen to satisfy a generalized notion of self-similarity. These are
sharp general formulations of phenomena that had been earlier found to hold in
a number of special cases.


title:
On the Finiteness of Attractors for One-Dimensional Maps with
  Discontinuities

abstract:
  Since the proof, at the end of the 80's, of the finiteness of the number of
attractors for $C^3$ maps of the interval having negative Schwarzian
derivative, it has been generally considered that the same result could be true
for maps with discontinuities. In the present paper we show that this is indeed
the case.


title: A positive proportion of elliptic curves over $\mathbb{Q}$ have rank one

abstract:
  We prove that, when all elliptic curves over $\mathbb{Q}$ are ordered by
naive height, a positive proportion have both algebraic and analytic rank one.
It follows that the average rank and the average analytic rank of elliptic
curves are both strictly positive.


title: The Frobenius Complexity of a Local Ring of Prime Characteristic

abstract:
  We introduce a new invariant for local rings of prime characteristic, called
Frobenius complexity, that measures the abundance of Frobenius actions on the
injective hull of the residue field of a local ring. We present an important
case where the Frobenius complexity is finite, and prove that complete, normal
rings of dimension two or less have Frobenius complexity less than or equal to
zero. Moreover, we compute the Frobenius complexity for the determinantal ring
obtained by modding out the $2 \times 2$ minors of a $2 \times 3$ matrix of
indeterminates, showing that this number can be positive, irrational and
depends upon the characteristic. We also settle a conjecture of Katzman,
Schwede, Singh and Zhang on the infinite generation of the ring of Frobenius
operators of a local normal complete $\mathbb{Q}$-Gorenstein ring.


title: Partial Observability and its Consistency for PDEs

abstract:
  In this paper, a quantitative measure of partial observability is defined for
PDEs. The quantity is proved to be consistent if the PDE is approximated using
well-posed approximation schemes. A first order approximation of an
unobservability index using an empirical Gramian is introduced. Several
examples are presented to illustrate the concept of partial observability,
including Burgers' equation and a one-dimensional nonlinear shallow water
equation.


title:
Recent Advances in the Microscopic Calculations of Level Densities by
  the Shell Model Monte Carlo Method

abstract:
  The shell model Monte Carlo (SMMC) method enables calculations in model
spaces that are many orders of magnitude larger than those that can be treated
by conventional methods, and is particularly suitable for the calculation of
level densities in the presence of correlations. We review recent advances and
applications of SMMC for the microscopic calculation of level densities. Recent
developments include (i) a method to calculate accurately the ground-state
energy of an odd-mass nucleus, circumventing a sign problem that originates in
the projection on an odd number of particles, and (ii) a method to calculate
directly level densities, which, unlike state densities, do not include the
spin degeneracy of the levels. We calculated the level densities of a family of
nickel isotopes $^{59-64}$Ni and of a heavy deformed rare-earth nucleus
$^{162}$Dy and found them to be in close agreement with various experimental
data sets.


title: Complex zero strip decreasing operators

abstract:
  In this paper we study the effect of linear differential operators coming
from the Laguerre-Polya class that act on functions in the extended
Laguerre-Polya class with zeros in a horizontal strip in the complex plane.
These operator decrease the size of the strip containing the zeros.


title:
Stellar Populations and the Star Formation Histories of LSB Galaxies: IV
  Spitzer Surface Photometry of LSB Galaxies

abstract:
  Surface photometry at 3.6$\mu$m is presented for 61 low surface brightness
(LSB) galaxies ($\mu_o < 19$ 3.6$\mu$m mag arcsecs$^{-2}$). The sample covers a
range of luminosity from $-$11 to $-$22 in $M_{3.6}$ and size from 1 to 25 kpc.
The morphologies in the mid-IR are comparable to those in the optical with
3.6$\mu$m imaging reaches similar surface brightness depth as ground-based
optical imaging. A majority of the resulting surface brightness profiles are
single exponential in shape with very few displaying upward or downward breaks.
The mean $V-3.6$ color of LSB is 2.3 with a standard deviation of 0.5.
Color-magnitude and two color diagrams are well matched to models of constant
star formation, where the spread in color is due to small changes in the star
formation rate (SFR) over the last 0.5 Gyrs as also suggested by the specific
star formation rate measured by H$\alpha$.


title:
Microlensing Events by Proxima Centauri in 2014 and 2016: Opportunities
  for Mass Determination and Possible Planet Detection

abstract:
  We have found that Proxima Centauri, the star closest to our Sun, will pass
close to a pair of faint background stars in the next few years. Using Hubble
Space Telescope (HST) images obtained in 2012 October, we determine that the
passage close to a mag 20 star will occur in 2014 October (impact parameter
1.6"), and to a mag 19.5 star in 2016 February (impact parameter 0.5"). As
Proxima passes in front of these stars, the relativistic deflection of light
will cause shifts in the positions of the background stars by ~0.5 and 1.5 mas,
respectively, readily detectable by HST imaging, and possibly by Gaia and
ground-based facilities such as VLT. Measurement of these astrometric shifts
offers a unique and direct method to measure the mass of Proxima. Moreover, if
Proxima has a planetary system, the planets may be detectable through their
additional microlensing signals, although the probability of such detections is
small. With astrometric accuracies of 0.03 mas (achievable with HST spatial
scanning), centroid shifts caused by Jovian planets are detectable at
separations of up to 2.0" (corresponding to 2.6 AU at the distance of Proxima),
and centroid shifts by Earth-mass planets are detectable within a small band of
8 mas (corresponding to 0.01 AU) around the source trajectories. Jovian planets
within a band of about 28 mas (corresponding to 0.036 AU) around the source
trajectories would produce a brightening of the source by >0.01 mag and could
hence be detectable. Estimated timescales of the astrometric and photometric
microlensing events due to a planet range from a few hours to a few days, and
both methods would provide direct measurements of the planetary mass.


title:
Generation of Bright Isolated Attosecond Soft X-Ray Pulses Driven by
  Multi-Cycle Mid-Infrared Lasers

abstract:
  High harmonic generation driven by femtosecond lasers makes it possible to
capture the fastest dynamics in molecules and materials. However, to date the
shortest attosecond (as) pulses have been produced only in the extreme
ultraviolet (EUV) region of the spectrum below 100 eV, which limits the range
of materials and molecular systems that can be explored. Here we use advanced
experiment and theory to demonstrate a remarkable convergence of physics: when
mid-infrared lasers are used to drive the high harmonic generation process, the
conditions for optimal bright soft X-ray generation naturally coincide with the
generation of isolated attosecond pulses. The temporal window over which phase
matching occurs shrinks rapidly with increasing driving laser wavelength, to
the extent that bright isolated attosecond pulses are the norm for 2 \mu m
driving lasers. Harnessing this realization, we demonstrate the generation of
isolated soft X-ray attosecond pulses at photon energies up to 180 eV for the
first time, that emerge as linearly chirped 300 as pulses with a transform
limit of 35 as. Most surprisingly, we find that in contrast to as pulse
generation in the EUV, long-duration, multi-cycle, driving laser pulses are
required to generate isolated soft X-ray bursts efficiently, to mitigate group
velocity walk-off between the laser and the X-ray fields that otherwise limit
the conversion efficiency. Our work demonstrates a clear and straightforward
approach for robustly generating bright attosecond pulses of electromagnetic
radiation throughout the soft X ray region of the spectrum.


title:
Quantum phases in $p$-orbital degenerated attractive 1D fermionic
  optical lattices

abstract:
  We examine quantum phases emerged by double degeneracy of $p$-orbital bands
in attractive atomic Fermi gases loaded on a 1D optical lattice. Our numerical
simulations by the density-matrix renormalization group predict the emergence
of a state with a charge excitation gap, the Haldane insulator phase. A mapping
onto an effective spin-$1$ model reveals its physical origin. Moreover, we show
that population imbalance leads to richer diversity of the quantum phases,
including a phase-separated polarized state. Finally, we study the effects of
harmonic trap potential in this 1D chain.


title:
Unveiling Magnetic Dipole Radiation in Phase-Reversal Leaky-Wave
  Antennas

abstract:
  The radiation principle of travelling-wave type phase-reversal antennas is
explained in details, unveiling the presence of magnetic-dipole radiation in
addition to well-known electric dipole radiation. It is point out that such
magnetic dipole radiation is specific to the case of traveling-wave
phase-reversal antennas whereas only electric-dipole radiation exists in
resonant-type phase-reversal antennas. It is shown that a phase-reversal
travelling-wave antenna alternately operates as an array of magnetic dipoles
and an array of electric-dipoles during a time-harmonic period. This radiation
mechanism is confirmed through both full-wave and experimental results.


title: The Fibonacci Sequence via the sigma transform

abstract:
  In this short article, we study different problems described as initial value
problems of discrete differential equations and develop a a transform method
called the sigma transform, a discrete version of the continuous Laplace
transform to generate solutions as rational functions of integers to these
initial value problems. Particularly we look how the method generates the
traditionally known numbers called Fibonacci sequence as a solution to an
initial value problem of a discrete differential equation.


title: Kink instability evidenced by analyzing the leg rotation of a filament

abstract:
  Kink instability is a possible mechanism for solar filament eruption.
However, the twist of a solar filament is very difficult to directly measure
from observation. In this paper, we carried out the measurement of the twist of
a solar filament by analyzing its leg rotation. An inverse S-shaped filament in
active region NOAA 11485 was observed by the Atmospheric Imaging Assembly (AIA)
of Solar Dynamics Observatory (SDO) on 2012 May 22. During its eruption, the
leg of the filament exhibited a significant rotation motion. The 304 \AA\
images were used to uncurl along the circles, whose centers are the axis of the
filament's leg. The result shows that the leg of the filament rotated up to
about 510 degrees (about 2.83$\pi$) around the axis of the filament within
twenty-three minutes. The maximal rotation speed reached 100 degrees per minute
(about 379.9 km/s at radius 18$^\prime$$^\prime$), which is the fastest
rotation speed that has been reported. We also calculated the decay index along
the polarity inversion line in this active region and found that the decline of
the overlying field with height is not so fast enough to trigger the torus
instability. According to the condition of kink instability, it is indicating
that the kink instability is the trigger mechanism for the solar filament
eruption.


title: A Review: Expert System for Diagnosis of Myocardial Infarction

abstract:
  A computer Program Capable of performing at a human-expert level in a narrow
problem domain area is called an expert system. Management of uncertainty is an
intrinsically important issue in the design of expert systems because much of
the information in the knowledge base of a typical expert system is imprecise,
incomplete or not totally reliable. In this paper, the author present s the
review of past work that has been carried out by various researchers based on
development of expert systems for the diagnosis of cardiac disease


title:
Three Dimensional Metallic and Two Dimensional Insulating Behavior in
  Tantalum Dichalcogenides

abstract:
  Using density functional theory with added on-site interactions (DFT+U), we
study the electronic structure of bulk, monolayer, and bilayer of the layered
transition-metal dichalcogenide $1T-TaS_2$. We show that a two-dimensional
spin--$\frac{1}{2}$ Mott-phase exists for the monolayer in the charge-density
wave state (CDW) and that such a phase is systematically destroyed by packing
of the distorted layers leading to a one dimensional metal for bulk,
CDW-distorted TaS$_2$. The latter finding is in contrast with previous DMFT
predictions --disagreement we explain by the weak effective interaction felt by
the electrons in the CDW state. Experimental observations of insulating
behavior may arise from disorder due to stacking faults.


title: Robust Hierarchical Clustering

abstract:
  One of the most widely used techniques for data clustering is agglomerative
clustering. Such algorithms have been long used across many different fields
ranging from computational biology to social sciences to computer vision in
part because their output is easy to interpret. Unfortunately, it is well
known, however, that many of the classic agglomerative clustering algorithms
are not robust to noise. In this paper we propose and analyze a new robust
algorithm for bottom-up agglomerative clustering. We show that our algorithm
can be used to cluster accurately in cases where the data satisfies a number of
natural properties and where the traditional agglomerative algorithms fail. We
also show how to adapt our algorithm to the inductive setting where our given
data is only a small random sample of the entire data set. Experimental
evaluations on synthetic and real world data sets show that our algorithm
achieves better performance than other hierarchical algorithms in the presence
of noise.


title: Twofold fast summation

abstract:
  Debugging accumulation of floating-point errors is hard; ideally, computer
should track it automatically. Here we consider twofold approximation of an
exact real with value + error pair of floating-point numbers. Normally, value +
error sum is more accurate than value alone, so error can estimate deviation
between value and its exact target. Fast summation algorithm, that provides
twofold sum of x[1]+...+x[N] or dot product x[1]*y[1]+...+x[N]*y[N], can be
same fast as direct summation sometimes if leveraging processor underused
potential. This way, we can hit three goals: improve precision, track
inaccuracy, and do this with little if any loss in performance.


title: Dyadic Cantor set and its kinetic and stochastic counterpart

abstract:
  Firstly, we propose and investigate a dyadic Cantor set (DCS) and its kinetic
counterpart where a generator divides an interval into two equal parts and
removes one with probability $(1-p)$. The generator is then applied at each
step to all the existing intervals in the case of DCS and to only one interval,
picked with probability according to interval size, in the case of kinetic DCS.
Secondly, we propose a stochastic DCS in which, unlike the kinetic DCS, the
generator divides an interval randomly instead of equally into two parts.
Finally, the models are solved analytically; an exact expression for fractal
dimension in each case is presented and the relationship between fractal
dimension and the corresponding conserved quantity is pointed out. Besides, we
show that the interval size distribution function in both variants of DCS
exhibits dynamic scaling and we verify it numerically using the idea of
data-collapse.


title:
Precise photoproduction of the charged top-pions at the LHC with forward
  detector acceptances

abstract:
  We study the photoproduction of the charged top-pion predicted by the top
triangle moose ($TTM$) model (a deconstructed version of the topcolor-assisted
technicolor $TC2$ model) via the processes $pp\rightarrow p \gamma p
\rightarrow \pi^\pm_t t +X$ at the 14 $TeV$ Large Hadron Collider ($LHC$)
including next-to-leading order ($NLO$) $QCD$ corrections. Our results show
that the production cross sections and distributions are sensitive to the free
parameters $\sin\omega$ and $M_{\pi_t}$. Typical $QCD$ correction value is $7\%
\sim 11\%$ and does not depend much on $\sin\omega$ as well as the forward
detector acceptances.


title: The General Stationary Gaussian Markov Process

abstract:
  We find the class, ${\cal{C}}_k, k \ge 0$, of all zero mean stationary
Gaussian processes, $Y(t), ~t \in \reals$ with $k$ derivatives, for which
  \begin{equation} Z(t) \equiv (Y^{(0)}(t), Y^{(1)}(t), \ldots, Y^{(k)}(t) ), ~
t \ge 0 \end{equation}
  \noindent is a $(k+1)$-vector Markov process. (here, $Y^{(0)}(t) = Y(t)$).


title: Quadrupole Plasmon Excitations in Confined One-dimensional Systems

abstract:
  The existence and nature of a new mode of electronic collective excitations
(quadrupole plasmons) in confined one-dimensional electronic systems have been
predicted by an eigen-equation method. The eigen-equation based on the
time-dependent density-functional theory is presented for calculating the
collective excitations in confined systems. With this method, all modes of
collective excitations in the 1D systems may be found out. These modes include
dipole plasmons and quadrupole plasmons. The dipole plasmon mode corresponds to
the antisymmetric oscillation of induced charge, and can be shown as a
resonance of the dipole response. In the quadrupole plasmon modes, the induced
charge distribution is symmetric, and the dipole response vanishes. The motion
of the electrons in the quadrupole modes is similar to the vibration of atoms
in the breathing mode of phonons. This type of plasmons can be shown as a
resonance of the quadrupole response, and has to be excited by al non-uniform
field.


title: Capture of Irregular Satellites at Jupiter

abstract:
  The irregular satellites of outer planets are thought to have been captured
from heliocentric orbits. The exact nature of the capture process, however,
remains uncertain. We examine the possibility that irregular satellites were
captured from the planetesimal disk during the early Solar System instability
when encounters between the outer planets occurred (Nesvorny, Vokrouhlicky &
Morbidelli 2007, AJ 133; hereafter NVM07). NVM07 already showed that the
irregular satellites of Saturn, Uranus and Neptune were plausibly captured
during planetary encounters. Here we find that the current instability models
present favorable conditions for capture of irregular satellites at Jupiter as
well, mainly because Jupiter undergoes a phase of close encounters with an ice
giant. We show that the orbital distribution of bodies captured during
planetary encounters provides a good match to the observed distribution of
irregular satellites at Jupiter. The capture efficiency for each particle in
the original transplanetary disk is found to be (1.3-3.6)x10^-8. This is
roughly enough to explain the observed population of jovian irregular moons. We
also confirm NVM07's results for the irregular satellites of Saturn, Uranus and
Neptune.


title: Nonlocal Models of Cosmic Acceleration

abstract:
  I review a class of nonlocally modified gravity models which were proposed to
explain the current phase of cosmic acceleration without dark energy. Among the
topics considered are deriving causal and conserved field equations, adjusting
the model to make it support a given expansion history, why these models do not
require an elaborate screening mechanism to evade solar system tests, degrees
of freedom and kinetic stability, and the negative verdict of structure
formation. Although these simple models are not consistent with data on the
growth of cosmic structures many of their features are likely to carry over to
more complicated models which are in better agreement with the data.


title: Modeling Attractiveness and Multiple Clicks in Sponsored Search Results

abstract:
  Click models are an important tool for leveraging user feedback, and are used
by commercial search engines for surfacing relevant search results. However,
existing click models are lacking in two aspects. First, they do not share
information across search results when computing attractiveness. Second, they
assume that users interact with the search results sequentially. Based on our
analysis of the click logs of a commercial search engine, we observe that the
sequential scan assumption does not always hold, especially for sponsored
search results. To overcome the above two limitations, we propose a new click
model. Our key insight is that sharing information across search results helps
in identifying important words or key-phrases which can then be used to
accurately compute attractiveness of a search result. Furthermore, we argue
that the click probability of a position as well as its attractiveness changes
during a user session and depends on the user's past click experience. Our
model seamlessly incorporates the effect of externalities (quality of other
search results displayed in response to a user query), user fatigue, as well as
pre and post-click relevance of a sponsored search result. We propose an
efficient one-pass inference scheme and empirically evaluate the performance of
our model via extensive experiments using the click logs of a large commercial
search engine.


title:
A comment on the arguments about the reliability and convergence of
  chaotic simulations

abstract:
  Yao and Hughes commented (Tellus-A, 60: 803 - 805, 2008) that "all chaotic
responses are simply numerical noise and have nothing to do with the solutions
of differential equations". However, using 1200 CPUs of the National
Supercomputer TH-A1 and a parallel integral algorithm of the so-called "Clean
Numerical Simulation" (CNS) based on the 3500th-order Taylor expansion and data
in 4180-digit multiple precision, one can gain reliable, convergent chaotic
solution of Lorenz equation in a rather long interval [0,10000]. This supports
Lorenz's optimistic viewpoint (Tellus-A, 60: 806 - 807, 2008): "numerical
approximations can converge to a chaotic true solution throughout any finite
range of time".


title: Fast Scalable State Measurement with Superconducting Qubits

abstract:
  Progress in superconducting qubit experiments with greater numbers of qubits
or advanced techniques such as feedback requires faster and more accurate state
measurement. We have designed a multiplexed measurement system with a bandpass
filter that allows fast measurement without increasing environmental damping of
the qubits. We use this to demonstrate simultaneous measurement of four qubits
on a single superconducting integrated circuit, the fastest of which can be
measured to 99.8% accuracy in 140ns. This accuracy and speed is suitable for
advanced multi-qubit experiments including surface code error correction.


title:
Bauschinger Effect in Thin Metal Films: Discrete Dislocation Dynamics
  Study

abstract:
  The effects of dislocation climb on plastic deformation during loading and
unloading are studied using a two-dimensional discrete dislocation dynamics
model. Simulations are performed for polycrystalline thin films passivated on
both surfaces. Dislocation climb lowers the overall level of the stress inside
thin films and reduces the work hardening rate. Climb decreases the density of
dislocations in pile-ups and reduces back stresses. These factors result in a
smaller Bauschinger effect on unloading compared to simulations without climb.
As dislocations continue to climb at the onset of unloading and the dislocation
density continues to increase, the initial unloading slope increases with
decreasing unloading rate. Because climb disperses dislocations, fewer
dislocations are annihilated during unloading, leading to a higher dislocation
density at the end of the unloading step.


title:
Convolution properties of univalent harmonic mappings convex in one
  direction

abstract:
  Let $\ast$ and $\widetilde {\ast}$ denote the convolution of two analytic
maps and that of an analytic map and a harmonic map respectively. Pokhrel [1]
proved that if $f = h+\overline{g}$ is a harmonic map convex in the direction
of $e^{i\gamma}$ and $\phi$ is an analytic map in the class DCP, then
$f\widetilde{\ast} \phi= h\widetilde{\ast}\phi +
\overline{g\widetilde{\ast}\phi}$ is also convex in the direction of
$e^{i\gamma}$, provided $f\widetilde{\ast}\phi$ is locally univalent and
sense-preserving. In the present paper we obtain a general condition under
which $f\widetilde{\ast} \phi$ is locally univalent and sense-preserving. Some
interesting applications of the general result are also presented.


title: Models for the modern power grid

abstract:
  This article reviews different kinds of models for the electric power grid
that can be used to understand the modern power system, the smart grid. From
the physical network to abstract energy markets, we identify in the literature
different aspects that co-determine the spatio-temporal multilayer dynamics of
power system. We start our review by showing how the generation, transmission
and distribution characteristics of the traditional power grids are already
subject to complex behaviour appearing as a result of the the interplay between
dynamics of the nodes and topology, namely synchronisation and cascade effects.
When dealing with smart grids, the system complexity increases even more: on
top of the physical network of power lines and controllable sources of
electricity, the modernisation brings information networks, renewable
intermittent generation, market liberalisation, prosumers, among other aspects.
In this case, we forecast a dynamical co-evolution of the smart grid and other
kind of networked systems that cannot be understood isolated. This review
compiles recent results that model electric power grids as complex systems,
going beyond pure technological aspects. From this perspective, we then
indicate possible ways to incorporate the diverse co-evolving systems into the
smart grid model using, for example, network theory and multi-agent simulation.


title: Holographic R\'enyi entropy in AdS$_3$/LCFT$_2$ correspondence

abstract:
  The recent study in AdS$_3$/CFT$_2$ correspondence shows that the tree level
contribution and 1-loop correction of holographic R\'enyi entanglement entropy
(HRE) exactly match the direct CFT computation in the large central charge
limit. This allows the R\'enyi entanglement entropy to be a new window to study
the AdS/CFT correspondence. In this paper we generalize the study of R\'enyi
entanglement entropy in pure AdS$_3$ gravity to the massive gravity theories at
the critical points. For the cosmological topological massive gravity (CTMG),
the dual conformal field theory (CFT) could be a chiral conformal field theory
or a logarithmic conformal field theory (LCFT), depending on the asymptotic
boundary conditions imposed. In both cases, by studying the short interval
expansion of the R\'enyi entanglement entropy of two disjoint intervals with
small cross ratio $x$, we find that the classical and 1-loop HRE are in exact
match with the CFT results, up to order $x^6$. To this order, the difference
between the massless graviton and logarithmic mode can be seen clearly.
Moreover, for the cosmological new massive gravity (CNMG) at critical point,
which could be dual to a logarithmic CFT as well, we find the similar agreement
in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of
graviton and logarithmic mode to HRE from CFT computation. It has distinct
feature from the one in pure AdS$_3$ gravity.


title:
Persistent charge and spin currents in a quantum ring using Green's
  function technique: Interplay between magnetic flux and spin-orbit
  interactions

abstract:
  We put forward a new approach based on Green's function formalism to evaluate
precisely persistent charge and spin currents in an Aharonov-Bohm ring
subjected to Rashba and Dresselhaus spin-orbit interactions. Unlike
conventional methods our present scheme circumvents direct evaluation of
eigenvalues and eigenstates of the system Hamiltonian to determine persistent
currents which essentially reduces possible numerical errors, especially for
larger rings. The interplay of Aharonov-Bohm flux and spin-orbit interactions
in persistent charge and spin currents of quantum rings is analyzed in detail
and our results lead to a possibility of estimating the strength of any one of
the spin-orbit fields provided the other one is known. All these features are
exactly invariant even in presence of impurities, and therefore, can be
substantiated experimentally.


title: The Roads to LPA Based Free Electron Laser

abstract:
  In this paper, we simply outline the present status of the free electron
laser and the laser plasma based accelerator, and we simply discuss the
potential possible roads appearing in the accelerator community to use the
laser plasma based accelerator into the field of the free electron laser.


title:
Phonon spectrum of QCD vacuum in magnetic-field-induced superconducting
  phase

abstract:
  In the background of a sufficiently strong magnetic field the vacuum was
suggested to become an ideal electric conductor (highly anisotropic
superconductor) due to an interplay between the strong and electromagnetic
forces. The superconducting ground state resembles an Abrikosov lattice state
in an ordinary type--II superconductor: it is an inhomogeneous structure made
of a (charged vector) quark-antiquark condensate pierced by vortices. In this
paper the acoustic (phonon) vibrational modes of the vortex lattice are studied
at zero temperature. Using an effective model based on a vector meson
dominance, we show that in the infrared limit the longitudinal (transverse)
acoustic vibrations of the vortex lattice possess a linear (quadratic)
dispersion relation corresponding to type I (type II) Nambu--Goldstone modes.


title: Approximate Bayesian Computation for a Class of Time Series Models

abstract:
  In the following article we consider approximate Bayesian computation (ABC)
for certain classes of time series models. In particular, we focus upon
scenarios where the likelihoods of the observations and parameter are
intractable, by which we mean that one cannot evaluate the likelihood even
up-to a positive unbiased estimate. This paper reviews and develops a class of
approximation procedures based upon the idea of ABC, but, specifically
maintains the probabilistic structure of the original statistical model. This
idea is useful, in that it can facilitate an analysis of the bias of the
approximation and the adaptation of established computational methods for
parameter inference. Several existing results in the literature are surveyed
and novel developments with regards to computation are given.


title:
Normal zeta functions of the Heisenberg groups over number rings II --
  the non-split case

abstract:
  We compute explicitly the normal zeta functions of the Heisenberg groups
$H(R)$, where $R$ is a compact discrete valuation ring of characteristic zero.
These zeta functions occur as Euler factors of normal zeta functions of
Heisenberg groups of the form $H(\mathcal{O}_K)$, where $\mathcal{O}_K$ is the
ring of integers of an arbitrary number field~$K$, at the rational primes which
are non-split in~$K$. We show that these local zeta functions satisfy
functional equations upon the inversion of the prime.


title: Transformed sufficient dimension reduction

abstract:
  A novel general framework is proposed in this paper for dimension reduction
in regression to fill the gap between linear and fully nonlinear dimension
reduction. The main idea is to transform first each of the raw predictors
monotonically, and then search for a low-dimensional projection in the space
defined by the transformed variables. Both user-specified and data-driven
transformations are suggested. In each case, the methodology is discussed first
in a general manner, and a representative method, as an example, is then
proposed and evaluated by simulation. The proposed methods are applied to a
real data set for illustration.


title: Anisotropic merging and splitting of dipolar Bose-Einstein condensates

abstract:
  We study the merging and splitting of quasi-two-dimensional Bose-Einstein
condensates with strong dipolar interactions. We observe that if the dipoles
have a non-zero component in the plane of the condensate, the dynamics of
merging or splitting along two orthogonal directions, parallel and
perpendicular to the projection of dipoles on the plane of the condensate are
different. The anisotropic merging and splitting of the condensate is a
manifestation of the anisotropy of the roton-like mode in the dipolar system.
The difference in dynamics disappears if the dipoles are oriented at right
angles to the plane of the condensate as in this case the Bogoliubov
dispersion, despite having roton-like features, is isotropic.


title: A symplectic prolegomenon

abstract:
  A symplectic manifold gives rise to a triangulated A-infinity category, the
derived Fukaya category, which encodes information on Lagrangian submanifolds
and dynamics as probed by Floer cohomology. This survey aims to give some
insight into what the Fukaya category is, where it comes from and what
symplectic topologists want to do with it.


title: Measurement of the convective heat-transfer coefficient

abstract:
  We propose an experiment for investigating how objects cool down toward the
thermal equilibrium with its surrounding through convection. We describe the
time dependence of the temperature difference of the cooling object and the
environment with an exponential decay function. By measuring the thermal
constant tau, we determine the convective heat-transfer coefficient, which is a
characteristic constant of the convection system.


title: Solutions without any symmetry for semilinear elliptic problems

abstract:
  We prove the existence of infinitely many solitary waves for the nonlinear
Klein-Gordon or Schr\"odinger equation $$ \Delta u-u+ u^3 =0 , $$ in ${\bf
R}^2$, which have finite energy and whose maximal group of symmetry reduces to
the identity.


title:
Analytical solutions for quantum walks on 1D chain with different shift
  operators

abstract:
  In this paper, we study the discrete-time quantum walks on 1D Chain with the
moving and swapping shift operators. We derive analytical solutions for the
eigenvalues and eigenstates of the evolution operator $\hat{U}$ using the
Chebyshev polynomial technique, and calculate the long-time averaged
probabilities for the two different shift operators respectively. It is found
that the probability distributions for the moving and swapping shift operators
display completely different characteristics. For the moving shift operator,
the probability distribution exhibits high symmetry where the probabilities at
mirror positions are equal. The probabilities are inversely proportional to the
system size $N$ and approach to zero as $N\rightarrow \infty$. On the contrary,
for the swapping shift operator, the probability distribution is not symmetric,
the probability distribution approaches to a power-law stationary distribution
as $N\rightarrow \infty$ under certain coin parameter condition. We show that
such power-law stationary distribution is determined by the eigenstates of the
eigenvalues $\pm1$ and calculate the intrinsic probability for different
starting positions. Our findings suggest that the eigenstates corresponding to
eigenvalues $\pm1$ play an important role for the swapping shift operator.


title:
Valleytronics on the Surface of Topological Crystalline Insulator:
  Elliptic Dichroism and Valley-Selective Optical Pumping

abstract:
  The low-energy theory of the surface of the topological crystalline insulator
(TCI) is characterized by four Dirac cones anisotropic into the $x$ and $y$
directions. Recent experiments have shown that the band gap can be introduced
in these Dirac cones by crystal distortion by applying strain to the crystal
structure. The TCI surface provides us with a new way to valleytronics when
gaps are given to Dirac cones. Indeed the system has the Chern number and three
valley-Chern numbers. We investigate the optical absorption on the TCI surface.
It shows a strong elliptic dichroism though the four Dirac cones have the same
chiralities. Namely, it is found that the absorptions of the right- and
left-polarized light are different, depending on the sign of mass and the
location of the Dirac cones, owing to the anisotropy of the Dirac cone. By
measuring this elliptic dichroism it is possible to determine the anisotropy of
a Dirac cone experimentally.


title: Wavelets and Triebel type oscillation spaces

abstract:
  We apply wavelets to identify the Triebel type oscillation spaces with the
known Triebel-Lizorkin-Morrey spaces
$\dot{F}^{\gamma_1,\gamma_2}_{p,q}(\mathbb{R}^{n})$. Then we establish a
characterization of $\dot{F}^{\gamma_1,\gamma_2}_{p,q}(\mathbb{R}^{n})$ via the
fractional heat semigroup. Moreover, we prove the continuity of
Calder\'on-Zygmund operators on these spaces. The results of this paper also
provide necessary tools for the study of well-posedness of Navier-Stokes
equations.


title: Mutation pairs and triangulated quotients

abstract:
  We define mutation pair in a pseudo-triangulated category. We prove that
under certain conditions, for a mutation pair in a pseudo-triangulated
category, the corresponding quotient category carries a natural triangulated
structure. This result unifies many previous constructions of quotient
triangulated categories.


title: Theory and Phenomenology of Spacetime Defects

abstract:
  Whether or not space-time is fundamentally discrete is of central importance
for the development of the theory of quantum gravity. If the fundamental
description of space-time is discrete, typically represented in terms of a
graph or network, then the apparent smoothness of geometry on large scales
should be imperfect -- it should have defects. Here, we review a model for
space-time defects and summarize the constraints on the prevalence of these
defects that can be derived from observation.


title: A transmission problem for quasi-linear wave equations

abstract:
  We prove the local existence and uniqueness of solutions to a system of
quasi-linear wave equations involving a jump discontinuity in the lower order
terms. A continuation principle is also established.


title: On infinite dimensional algebraic transformation groups

abstract:
  We explore orbits, rational invariant functions, and quotients of the natural
actions of connected, not necessarily finite dimensional subgroups of the
automorphism groups of irreducible algebraic varieties. The applications of the
results obtained are given.


title:
On structural properties of trees with minimal atom-bond connectivity
  index

abstract:
  The {\em atom-bond connectivity (ABC) index} is a degree-based molecular
descriptor, that found chemical applications. It is well known that among all
connected graphs, the graphs with minimal ABC index are trees. A complete
characterization of trees with minimal $ABC$ index is still an open problem. In
this paper, we present new structural properties of trees with minimal ABC
index. Our main results reveal that trees with minimal ABC index do not contain
so-called {\em $B_k$-branches}, with $k \geq 5$, and that they do not have more
than four $B_4$-branches.


title: Failure Processes in Embedded Monolayer Graphene under Axial Compression

abstract:
  Exfoliated monolayer graphene flakes were embedded in a polymer matrix and
loaded under axial compression. By monitoring the shifts of the 2D Raman
phonons of rectangular flakes of various sizes under load, the critical strain
to failure was determined. Prior to loading care was taken for the examined
area of the flake to be free of residual stresses. The critical strain values
for first failure were found to be independent of flake size at a mean value of
-0.60 % corresponding to a yield stress of -6 GPa. By combining Euler mechanics
with a Winkler approach, we show that unlike buckling in air, the presence of
the polymer constraint results in graphene buckling at a fixed value of strain
with an estimated wrinkle wavelength of the order of 1-2 nm. These results were
compared with DFT computations performed on analogue coronene/ PMMA oligomers
and a reasonable agreement was obtained.


title: A unified description of solvent effects in the helix-coil transition

abstract:
  We analyze the problem of the helix-coil transition in explicit solvents
analytically by using spin-based models incorporating two different mechanisms
of solvent action: explicit solvent action through the formation of
solvent-polymer hydrogen bonds that can compete with the intrinsic
intra-polymer hydrogen bonded configurations (competing interactions) and
implicit solvent action, where the solvent-polymer interactions tune biopolymer
configurations by changing the activity of the solvent (non-competing
interactions). The overall spin Hamiltonian is comprised of three terms: the
background \emph{in vacuo} Hamiltonian of the "Generalized Model of Polypeptide
Chain" type and two additive terms that account for the two above mechanisms of
solvent action. We show that on this level the solvent degrees of freedom can
be {\sl explicitly} and {\sl exactly} traced over, the ensuing effective
partition function combining all the solvent effects in a unified framework. In
this way we are able to address helix-coil transitions for polypeptides,
proteins, and DNA, with different buffers and different external constraints.
Our spin-based effective Hamiltonian is applicable for treatment of such
diverse phenomena as cold denaturation, effects of osmotic pressure on the cold
and warm denaturation, complicated temperature dependence of the hydrophobic
effect as well as providing a conceptual base for understanding the behavior of
Intrinsically Disordered Proteins and their analogues.


title:
Design of a GIS-based Assistant Software Agent for the Incident
  Commander to Coordinate Emergency Response Operations

abstract:
  Problem: This paper addresses the design of an intelligent software system
for the IC (incident commander) of a team in order to coordinate actions of
agents (field units or robots) in the domain of emergency/crisis response
operations. Objective: This paper proposes GICoordinator. It is a GIS-based
assistant software agent that assists and collaborates with the human planner
in strategic planning and macro tasks assignment for centralized multi-agent
coordination. Method: Our approach to design GICoordinator was to: analyze the
problem, design a complete data model, design an architecture of GICoordinator,
specify required capabilities of human and system in coordination problem
solving, specify development tools, and deploy. Result: The result was an
architecture/design of GICoordinator that contains system requirements.
Findings: GICoordinator efficiently integrates geoinformatics with artifice
intelligent techniques in order to provide a spatial intelligent coordinator
system for an IC to efficiently coordinate and control agents by making
macro/strategic decisions. Results define a framework for future works to
develop this system.


title:
Wind braking of magnetars: to understand magnetar's multiwave radiation
  properties

abstract:
  Magnetars are proposed to be peculiar neutron stars powered by their super
strong magnetic field. Observationally, anomalous X-ray pulsars and soft
gamma-ray repeaters are believed to be magnetar candidates. While more and more
multiwave observations of magnetars are available, unfortunately, we see
accumulating failed predictions of the traditional magnetar model. These
challenges urge rethinking of magnetar. Wind braking of magnetars is one of the
alternative modelings. The release of magnetic energy may generate a particle
outflow (i.e., particle wind), that results in both an anomalous X-ray
luminosity and significantly high spindown rate. In this wind braking scenario,
only strong multipole field is necessary for a magnetar (a strong dipole field
is no longer needed). Wind braking of magnetars may help us to understand their
multiwave radiation properties, including (1) Non-detection of magnetars in
Fermi-LAT observations, (2) The timing behaviors of low magnetic field
magnetars, (3) The nature of anti-glitches, (4) The criterion for magnetar's
radio emission, etc. In the wind braking model of magentars, timing events of
magnetars should always be accompanied by radiative events. It is worth noting
that the wind engine should be the central point in the research since other
efforts with any reasonable energy mechanism may also reproduce the results.


title: Motivic Landweber exact theories and their effective covers

abstract:
  Let $k$ be a field of characteristic zero and let $(F,R)$ be a Landweber
exact formal group law. We consider a Landweber exact $T$-spectrum
$\mathcal{E}:=R\otimes_{\mathbb{L}}\text{MGL}$ and its effective cover
$f_0\mathcal{E}\to \mathcal{E}$ with respect to Voevodsky's slice tower. The
coefficient ring $R_0$ of $f_0\mathcal{E}$ is the subring of $R$ consisting of
elements of $R$ of non-positive degree; the power series $F\in R[[u,v]]$ has
coefficients in $R_0$ although $(F,R_0)$ is not necessarily Landweber exact. We
show that the geometric part $X\mapsto
f_0\mathcal{E}^*(X):=(f_0\mathcal{E})^{2*,*}(X)$ of $f_0\mathcal{E}$ is
canonically isomorphic to the oriented cohomology theory $X\mapsto R_0
\otimes_{\mathbb{L}} \Omega^*(X)$, where $\Omega^*$ is the theory of algebraic
cobordism, as defined by Levine-Morel. This recovers results of Dai-Levine as
the special case of algebraic $K$-theory and its effective cover, connective
algebraic $K$-theory.


title: Irregular shock waves formation as continuation of analytic solutions

abstract:
  This paper is devoted to the blow-up of analytic solutions with the emergence
of irregular solutions.


title: Testing Superdeterministic Conspiracy

abstract:
  Tests of Bell's theorem rule out local hidden variables theories. But any
theorem is only as good as the assumptions that go into it, and one of these
assumptions is that the experimenter can freely chose the detector settings.
Without this assumption, one enters the realm of superdeterministic hidden
variables theories and can no longer use Bell's theorem as a criterion. One can
like or not like such superdeterministic hidden variables theories and their
inevitable nonlocality, the real question is how one can test them. Here, we
propose a possible experiment that could reveal superdeterminism.


title:
A right and left truncated gamma distribution with application to the
  stars

abstract:
  The gamma density function is usually defined in interval between zero and
infinity. This paper introduces an upper and a lower boundary to this
distribution. The parameters which characterize the truncated gamma
distribution are evaluated. A statistical test is performed on two samples of
stars. A comparison with the lognormal and the four power law distribution is
made.


title: Disentangling the Black Hole Vacuum

abstract:
  We study the question whether disentanglement of Hawking radiation can be
achieved with any local operation. We assume that the operation we look for is
unitary and can be described by a Bogoliubov transformation. This allows to
formulate requirements on the operation of disentanglement. We then show that
these requirements can be fulfilled by a timelike boundary condition in the
near-horizon area and that the local observer does not notice the presence of
the boundary and does not encounter a firewall.


title:
Single Higgs boson production at $e^{+}e^{-}$ colliders in the Littlest
  Higgs Model with T-parity

abstract:
  In this work, we investigate the Higgs-boson production processes
$e^{+}e^{-}\rightarrow ZH$, $e^{+}e^{-}\rightarrow \nu_{e}\bar{\nu_{e}}H$ and
$e^{+}e^{-}\rightarrow e^{+}e^{-}H$ in the littlest Higgs model with T-parity.
We present the production cross sections, the relative corrections and some
distributions of the final states. In the allowed parameter space, we find that
the relative corrections of the three production channels are negative, the
relative correction of the $ZH$ production can reach $-7.5\%$ and the relative
corrections of the $\nu_{e}\bar{\nu_{e}}H$ and $e^{+}e^{-}H$ production can
both reach $-6.5\%$ for $\sqrt{s}=500$ GeV with the scale $f=$694 GeV.


title:
A real-space study of random extended defects in solids : application to
  disordered Stone-Wales defects in graphene

abstract:
  We propose here a first-principles, parameter free, real space method for the
study of disordered extended defects in solids. We shall illustrate the power
of the technique with an application to graphene sheets with randomly placed
Stone-Wales defects and shall examine the signature of such random defects on
the density of states as a function of their concentration. The technique is
general enough to be applied to a whole class of systems with lattice
translational symmetry broken not only locally but by extended defects and
defect clusters. The real space approach will allow us to distinguish
signatures of specific defects and defect clusters.


title: Analytic representation of critical equations of state

abstract:
  We propose a new form for equations of state (EOS) of thermodynamic systems
in the Ising universality class. The new EOS guarantees the correct
universality and scaling behavior close to critical points and is formulated in
terms of the scaling fields only -- unlike the traditional Schofield
representation, which uses a parametric form. Close to a critical point, the
new EOS expresses the square of the strong scaling field $\Sigma$ as an
explicit function $\Sigma^2=D^{2e_{-1}}\Gamma(D^{-e_0}\Theta)$ of the thermal
scaling field $\Theta$ and the dependent scaling field $D>0$, with a smooth,
universal function $\Gamma$ and the universal exponents
$e_{-1}=\delta/(\delta+1)$, $e_0=1/(2-\alpha)$. A numerical expression for
$\Gamma$ is derived, valid close to critical points. As a consequence of the
construction it is shown that the dependent scaling field can be written as an
explicit function of the relevant scaling fields without causing strongly
singular behavior of the thermodynamic potential in the one-phase region.
Augmented by additional scaling correction fields, the new EOS also describes
the state space further away from critical points. It is indicated how to use
the new EOS to model multiphase fluid mixtures, in particular for
vapor-liquid-liquid equilibrium (VLLE) where the traditional revised scaling
approach fails.


title:
Search for Sub-eV Sterile Neutrinos in the Precision Multiple Baselines
  Reactor Antineutrino Oscillation Experiments

abstract:
  According to different effects on neutrino oscillations, the unitarity
violation in the MNSP matrix can be classified into the direct unitarity
violation and the indirect unitarity violation which are induced by the
existence of the light and the heavy sterile neutrinos respectively. Of which
sub-eV sterile neutrinos are of most interesting. We study in this paper the
possibility of searching for sub-eV sterile neutrinos in the precision reactor
antineutrino oscillation experiments with three different baselines at around
500 m, 2 km and 60 km. We find that the antineutrino survival probabilities
obtained in the reactor experiments are sensitive only to the direct unitarity
violation and offer very concentrated sensitivity to the two parameters
$\theta^{}_{14}$ and $\Delta m^{2}_{41}$. If such light sterile neutrinos do
exist, the active-sterile mixing angle $\theta^{}_{14}$ could be acquired by
the combined rate analysis at all the three baselines and the mass-squared
difference $\Delta m^{2}_{41}$ could be obtained by taking the Fourier
transformation to the L / E spectrum. Of course, for such measurements to
succeed, both high energy resolution and large statistics are essentially
important.


title: Photon: New light on an old name

abstract:
  After G. N. Lewis (1875-1946) proposed the term "photon" in 1926, many
physicists adopted it as a more apt name for Einstein's light quantum. However,
Lewis' photon was a concept of a very different kind, something few physicists
knew or cared about. It turns out that Lewis' name was not quite the neologism
that it has usually been assumed to be. The same name was proposed or used
earlier, apparently independently, by at least four scientists. Three of the
four early proposals were related to physiology or visual perception, and only
one to quantum physics. Priority belongs to the American physicist and
psychologist L. T. Troland (1889-1932), who coined the word in 1916, and five
years later it was independently introduced by the Irish physicist J. Joly
(1857-1933). Then in 1925 a French physiologist, Rene Wurmser (1890-1993),
wrote about the photon, and in July 1926 his compatriot, the physicist F.
Wolfers (ca. 1890-1971), did the same in the context of optical physics. None
of the four pre-Lewis versions of "photon" was well known and they were soon
forgotten.


title: Complexity results for generating subgraphs

abstract:
  A graph G is well-covered if all its maximal independent sets are of the same
cardinality. Assume that a weight function w is defined on its vertices. Then G
is w-well-covered if all maximal independent sets are of the same weight.
  For every graph G, the set of weight functions w such that G is
w-well-covered is a vector space, denoted WCW(G). Let B be a complete bipartite
induced subgraph of G on vertex sets of bipartition B_X and B_Y. Then B is
generating if there exists an independent set S such that S \cup B_X and S \cup
B_Y are both maximal independent sets of G. A relating edge is a generating
subgraph in the restricted case that B = K_{1,1}.
  Deciding whether an input graph G is well-covered is co-NP-complete.
Therefore finding WCW(G) is co-NP-hard. Deciding whether an edge is relating is
co-NP-complete. Therefore, deciding whether a subgraph is generating is
co-NP-complete as well.
  In this article we discuss the connections among these problems, provide
proofs for NP-completeness for several restricted cases, and present polynomial
characterizations for some other cases.


title:
On a perturbation theory and on strong convergence rates for stochastic
  ordinary and partial differential equations with non-globally monotone
  coefficients

abstract:
  We develope a perturbation theory for stochastic differential equations
(SDEs) by which we mean both stochastic ordinary differential equations (SODEs)
and stochastic partial differential equations (SPDEs). In particular, we
estimate the $ L^p $-distance between the solution process of an SDE and an
arbitrary It\^o process, which we view as a perturbation of the solution
process of the SDE, by the $ L^q $-distances of the differences of the local
characteristics for suitable $ p, q > 0 $. As application of our perturbation
theory, we establish strong convergence rates for numerical approximations of a
class of SODEs with non-globally monotone coefficients. As another application
of our perturbation theory, we prove strong convergence rates for spectral
Galerkin approximations of solutions of semilinear SPDEs with non-globally
monotone nonlinearities including Cahn-Hilliard-Cook type equations and
stochastic Burgers equations. Further applications of the perturbation theory
include the regularity of solutions of SDEs with respect to the initial values
and small-noise analysis for ordinary and partial differential equations.


title:
Nereshennye voprosy teorii grupp. Kourovskaya tetrad'. 18-e izd.
  (Russian)

abstract:
  This is a collection of open problems in Group Theory proposed by more than
300 mathematicians from all over the world. It has been published every 2-4
years in Novosibirsk since 1965, now also in English. This is the 18th Russian
edition, which contains 120 new problems and a number of comments on about 1000
problems from the previous editions.


title: Gas Storage Potential of Li-decorated ExBox4+

abstract:
  The newly developed compound ExBox4+ is explored to check whether it is a
proficient hydrogen storage material. Both exoherdal and endohedral hydrogen
adsorption on ExBox4+ are studied. Endohedral hydrogen molecules interact
strongly than exohedral ones. The hydrogen adsorption energy is as good as the
recently studied charged fullerenes. The hydrogen storage capacity appears to
be ~4.3 wt%. The endohedral CO sorption is also analysed with the help of DFT.
The first principle DFT calculation and MD simulation are performed to
investigate the effect of lithium doping on the gas adsorbing capacity and
adsorption enthalpy as well as adsorption energy of ExBox4+.The metal atom
interaction with ExBox4+is found to be pretty strong, and the interaction
energy appears to be higher than the metal cohesive energy.The thermodynamic
parameters suggest that metal doping method is spontaneous in nature. The
analysis of adsorption energy, thermodynamic properties and MD simulation
results suggest that Li doped ExBox4+ can be a promising gas adsorbing
material. Lithium doping increases the gas adsorption capacity of ExBox4+. The
Li decorated ExBox4+ is found to adsorb twenty four hydrogen molecules with a
gravimetric wt% of 6.23. Adsorption of CO on the metal decorated ExBox4+ is
also studied. AIM analysis is performed to obtain a general idea of the bonding
interaction between Li-H and Li-C.


title:
Unfolding the electronic structure of
  Ca$_{10}$(Fe$_{1-x}$Pt$_x$As)$_{10}$(Pt$_n$As$_8$)

abstract:
  The platinum iron arsenides
Ca$_{10}$(Fe$_{1-x}$Pt$_x$As)$_{10}$(Pt$_n$As$_8$) are the first Fe based
superconductors with metallic spacer layers. Furthermore they display a large
variation in their critical temperatures depending on the amount of Pt in their
spacer layers: $(n=3,4)$. To gain more insight into the role of the spacer
layer the electronic structures of the iron arsenic platenides are represented
in the momentum space of the underlying Fe sublattice using a first principles
unfolding method. We find that Ca$_{10}$(FeAs)$_{10}$(Pt$_4$As$_8$), contrary
to Ca$_{10}$(FeAs)$_{10}$(Pt$_3$As$_8$), shows a net electron doping and a
non-negligible interlayer coupling. Both effects could account for the
difference in the critical temperatures.


title:
Disorder and magnetic-field induced breakdown of helical edge conduction
  in an inverted electron-hole bilayer

abstract:
  We calculate the conductance of a two-dimensional bilayer with inverted
electron-hole bands, to study the sensitivity of the quantum spin Hall
insulator (with helical edge conduction) to the combination of electrostatic
disorder and a perpendicular magnetic field. The characteristic breakdown field
for helical edge conduction splits into two fields with increasing disorder, a
field $B_{c}$ for the transition into a quantum Hall insulator (supporting
chiral edge conduction) and a smaller field $B'_{c}$ for the transition to bulk
conduction in a quasi-metallic regime. The spatial separation of the inverted
bands, typical for broken-gap InAs/GaSb quantum wells, is essential for the
magnetic-field induced bulk conduction --- there is no such regime in HgTe
quantum wells.


title: Unsolved Problems in Group Theory. The Kourovka Notebook

abstract:
  This is a collection of open problems in group theory proposed by hundreds of
mathematicians from all over the world. It has been published every 2-4 years
in Novosibirsk since 1965. This is the 20th edition, which contains 126 new
problems and a number of comments on problems from the previous editions.


title:
IIGHGINT: A generalization to the modified GHG intensity universal
  indicator toward a production/consumption insensitive border carbon tax

abstract:
  A global agreement on how to reduce and cap human footprint, especially their
GHG emissions, is very unlikely in near future. At the same time, bilateral
agreements would be inefficient because of their neural and balanced nature.
Therefore, unilateral actions would have attracted attention as a practical
option. However, any unilateral action would most likely fail if it is not fair
and also if it is not consistent with the world trade organization's (WTO's)
rules, considering highly heterogeneity of the global economy. The modified GHG
intensity (MGHGINT) indicator, hereafter called Inequality-adjusted
Production-based GHGINT (IPGHGINT), was put forward to address this need in the
form of a universal indicator applicable to every region regardless of its
economic and social status. Nonetheless, the original MGHGINT indicator ignores
hidden consumption-related emissions, and therefore it could be unfair to some
production-oriented regions in the current bipolar production/consumption
world. Here, we propose two generalizations, called Inequality-adjusted
Consumption-based GHGINT (ICGHGINT) and Inequality-adjusted
Production/Consumption-Insensitive GHGINT (IIGHGINT), to the IPGHGINT in order
to combine both production and consumption emissions in a unified and balanced
manner. The impact of this generalizations on the associated border carbon tax
rates is evaluated in order to validate their practicality.


title:
Arm locking for space-based laser interferometry gravitational wave
  observatories

abstract:
  Laser frequency stabilization is a critical part of the interferometry
measurement system of space-based gravitational wave observatories such as the
Laser Interferometer Space Antenna (LISA). Arm locking as a proposed frequency
stabilization technique, transfers the stability of the long arm lengths to the
laser frequency. The arm locking sensor synthesizes an adequately filtered
linear combination of the inter-spacecraft phase measurements to estimate the
laser frequency noise, which can be used to control the laser frequency. At the
University of Florida we developed the hardware-based University of Florida
LISA Interferometer Simulator (UFLIS) to study and verify laser frequency noise
reduction and suppression techniques under realistic LISA-like conditions.
These conditions include the variable Doppler shifts between the spacecraft,
LISA-like signal travel times, optical transponders, realistic laser frequency
and timing noise. We review the different types of arm locking sensors and
discuss their expected performance in LISA. The presented results are supported
by results obtained during experimental studies of arm locking under relevant
LISA-like conditions. We measured the noise suppression as well as initial
transients and frequency pulling in the presence of Doppler frequency errors.
This work has demonstrated the validity and \ feasibility of arm locking in
LISA.


title: Rediscovery of Good-Turing estimators via Bayesian nonparametrics

abstract:
  The problem of estimating discovery probabilities originated in the context
of statistical ecology, and in recent years it has become popular due to its
frequent appearance in challenging applications arising in genetics,
bioinformatics, linguistics, designs of experiments, machine learning, etc. A
full range of statistical approaches, parametric and nonparametric as well as
frequentist and Bayesian, has been proposed for estimating discovery
probabilities. In this paper we investigate the relationships between the
celebrated Good-Turing approach, which is a frequentist nonparametric approach
developed in the 1940s, and a Bayesian nonparametric approach recently
introduced in the literature. Specifically, under the assumption of a two
parameter Poisson-Dirichlet prior, we show that Bayesian nonparametric
estimators of discovery probabilities are asymptotically equivalent, for a
large sample size, to suitably smoothed Good-Turing estimators. As a by-product
of this result, we introduce and investigate a methodology for deriving exact
and asymptotic credible intervals to be associated with the Bayesian
nonparametric estimators of discovery probabilities. The proposed methodology
is illustrated through a comprehensive simulation study and the analysis of
Expressed Sequence Tags data generated by sequencing a benchmark complementary
DNA library.


title: Learning without Concentration

abstract:
  We obtain sharp bounds on the performance of Empirical Risk Minimization
performed in a convex class and with respect to the squared loss, without
assuming that class members and the target are bounded functions or have
rapidly decaying tails.
  Rather than resorting to a concentration-based argument, the method used here
relies on a `small-ball' assumption and thus holds for classes consisting of
heavy-tailed functions and for heavy-tailed targets.
  The resulting estimates scale correctly with the `noise level' of the
problem, and when applied to the classical, bounded scenario, always improve
the known bounds.


title:
Temperature-resolution anomalies in the reconstruction of time dynamics
  from energy-loss experiments

abstract:
  Inelastic scattering techniques provide a powerful approach to studying
electron and nuclear dynamics, via reconstruction of a propagator that
quantifies the time evolution of a system. There is now growing interest in
applying such methods to very low energy excitations, such as lattice
vibrations, but in this limit the cross section is no longer proportional to a
propagator. Significant deviations occur due to the finite temperature Bose
statistics of the excitations. Here we consider this issue in the context of
high-resolution electron energy loss experiments on the copper-oxide
superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$. We find that simple division of a
Bose factor yields an accurate propagator on energy scales greater than the
resolution width. However, at low energy scales, the effects of resolution and
finite temperature conspire to create anomalies in the dynamics at long times.
We compare two practical ways for dealing with such anomalies, and discuss the
range of validity of the technique in light of this comparison.


title:
New Maser Emission from Nonmetastable Ammonia in NGC 7538. IV.
  Coincident Masers in Adjacent States of Para-ammonia

abstract:
  We present the first detection of para-ammonia masers in NGC 7538: multiple
epochs of observation of the 14NH3 (J,K) = (10,8) and (9,8) lines. We detect
both thermal absorption and nonthermal emission in the (10,8) and (9,8)
transitions and the absence of a maser in the (11,8) transition. The (9,8)
maser is observed to increase in intensity by 40% over six months. Using
interferometric observations with a synthesized beam of 0.25", we find that the
(10,8) and (9,8) masers originate at the same sky position near IRS1. With
strong evidence that the (10,8) and (9,8) masers arise in the same volume, we
discuss the application of pumping models for the simultaneous excitation of
nonmetastable (J > K) para-ammonia states having the same value of K and
consecutive values of J. We also present detections of thermal absorption in
rotational states ranging in energy from E/k_B ~ 200 K to 2000 K, and several
non-detections in higher-energy states. In particular, we describe the
populations in eight adjacent rotational states with K=6, including two maser
transitions, along with the implications for ortho-ammonia pumping models. An
existing torus model for molecular gas in the environment of IRS1 has been
applied to the masers; a variety of maser species are shown to agree with the
model. Historical and new interferometric observations of 15NH3 (3,3) masers in
the region indicate a precession of the rotating torus at a rate comparable to
continuum-emission-based models of the region. We discuss the general necessity
of interferometric observations for diagnosing the excitation state of the
masers and for determining the geometry of the molecular environment.


title: New characterization of two-state normal distribution

abstract:
  In this article we give a purely noncommutative criterion for the
characterization of two-state normal distribution. We prove that families of
two-state normal distribution can be described by relations which is similar to
the conditional expectation in free probability, but has no classical analogue.
We also show a generalization of Bozejko, Leinert and Speicher's formula
(relating moments and noncommutative cumulants).


title: New non-arithmetic complex hyperbolic lattices

abstract:
  We produce a family of new, non arithmetic lattices in PU(2,1). All
previously known examples were commensurable with lattices constructed by
Picard, Mostow and Deligne-Mostow, and fell into 9 commensurability classes.
Our groups produce 5 new distinct commensurability classes. Most of the
techniques are completely general, and provide efficient geometric and
computational tools for constructing fundamental domains for discrete group
acting on the complex hyperbolic plane.


title:
Weak asymptotic methods for 3-D self-gravitating pressureless fluids.
  Application to the creation and evolution of solar systems from the fully
  nonlinear Euler-Poisson equations

abstract:
  We construct a family of classical continuous functions which tend to satisfy
asymptotically the system of self-gravitating pressureless fluids.


title: The Daniell Integral

abstract:
  The basic properties of the Daniell integral are presented. We do not use the
standard approach of introducing auxiliary spaces of the "over-functions" and
"under-functions." Instead, we use a simple and direct approach based on
approximating integrable functions by absolutely convergent series of simple
functions.


title: Variational Polaron Method for Bose-Bose Mixtures

abstract:
  We study degenerate mixtures of "heavy" bosons and "light" superfluid bosons
using a variational polaron transformation. We consider the Mott
insulator-superfluid transition of the heavy species and find that at $T=0$
interaction favors the superfluid phase of the heavy species. Our analytic
results agree well with numerically exact quantum Monte Carlo simulations in
two dimensions. We then show that in three dimensions the variational polaron
transformation can be combined with a Gutzwiller approximation to give good
results.


title:
Uniqueness of Conservative Solutions to the Camassa-Holm Equation via
  Characteristics

abstract:
  The paper provides a direct proof the uniqueness of solutions to the
Camassa-Holm equation, based on characteristics. Given a conservative solution
$u=u(t,x)$, an equation is introduced which singles out a unique characteristic
curve through each initial point. By studying the evolution of the quantities
$u$ and $v= 2\arctan u_x$ along each characteristic, it is proved that the
Cauchy problem with general initial data $u_0\in H^1(\mathbb{R})$ has a unique
solution, globally in time.


title:
Improving the kinematics for low-x QCD evolution equations in coordinate
  space

abstract:
  High-energy evolution equations, such as the BFKL, BK or JIMWLK equations,
aim at resumming the high-energy (next-to-)leading logarithms appearing in QCD
perturbative series. However, the standard derivations of those equations are
performed in a strict high-energy limit, whereas such equations are then
applied to scattering processes at large but finite energies. For that reason,
there is typically a slight mismatch between the leading logs resummed by those
evolution equations without finite-energy corrections and the leading logs
actually present in the perturbative expansion of any observable. That mismatch
is one of the sources of large corrections at NLO and NLL accuracy. In the case
of the BFKL equation in momentum space, that problem is solved by including a
kinematical constraint in the kernel, which is the most important finite-energy
correction. In this paper, such an improvement of kinematics is performed in
mixed-space (transverse positions and $k^+$) and with a factorization scheme in
the light-cone momentum $k^+$ (in a frame in which the projectile is
right-moving and the target left-moving). This is the usual choice of variables
and factorization scheme for the the BK equation. A kinematically improved
version of the BK equation is provided, consistent at finite energies. The
results presented here are also a necessary step towards having the high energy
limit of QCD (including gluon saturation) quantitatively under control beyond
strict leading logarithmic accuracy.


title:
Current-voltage characteristics of asymmetric double-barrier Josephson
  junctions

abstract:
  We develop a theory for the current-voltage characteristics of diffusive
superconductor-normal metal-superconductor Josephson junctions with resistive
interfaces and the distance between the electrodes smaller than the
superconducting coherence length. The theory allows for a quantitative
analytical and numerical analysis in the whole range of the interface
transparencies and asymmetry. We focus on the regime of large interface
resistance compared to the resistance of the normal region, when the
electron-hole dephasing in the normal region is significant and the finite
length of the junction plays a role. In the limit of strong asymmetry we find
pronounced current structures at the combination subharmonics of
$\Delta+\Delta_g$, where $\Delta_g$ is the proximity minigap in the normal
region, in addition to the subharmonics of the energy gap $2\Delta$ in the
electrodes. In the limit of rather transparent interfaces, our theory recovers
a known formula for the current in a short mesoscopic connector - a convolution
of the current through a single-channel point contact with the transparency
distribution for an asymmetric double-barrier potential.


title: Enriched factorization systems

abstract:
  In a paper of 1974, Brian Day employed a notion of factorization system in
the context of enriched category theory, replacing the usual diagonal lifting
property with a corresponding criterion phrased in terms of hom-objects. We set
forth the basic theory of such enriched factorization systems. In particular,
we establish stability properties for enriched prefactorization systems, we
examine the relation of enriched to ordinary factorization systems, and we
provide general results for obtaining enriched factorizations by means of wide
(co)intersections. As a special case, we prove results on the existence of
enriched factorization systems involving enriched strong monomorphisms or
strong epimorphisms.


title: Accounting for backflow in hydrodynamic-simulation interfaces

abstract:
  Methods for building a consistent interface between hydrodynamic and
simulation modules is presented. These methods account for the backflow across
the hydrodynamic/simulation hyper-surface. The algorithms are efficient,
relatively straight-forward to implement, and account for conservation laws
across the hyper-surface. The methods also account for the spurious
interactions between particles in the backflow and other particles by following
the subsequent impact of such particles. Since the number of altered
trajectories grows exponentially in time, a cutoff is built into the procedure
so that the effects of the backflow are ignored beyond a certain number of
collisions


title:
Full pseudoscalar mesonic chiral Lagrangian at p6 order under the
  unitary group

abstract:
  We construct the full p6 order chiral Lagrangians for the unitary group and
special unitary groups, including nf-, three- and two-flavor cases, all
bilinear currents (scalar, pseudoscalar, vector, axial-vector and tensor
currents) and theta parameter. The number of independent operators are 1391,
1326 and 969 for each of the flavor unitary groups. From these results, we find
one extra linear relation among the traditional p4 order low-energy constants
under the U(3) group, and some more linear relations with tensor sources for
the p6 order low-energy constants in the special unitary groups. We develop a
scheme to obtain the relations for the dependent operators in terms of
independent operators.


title: Particle diagrams and embedded many-body random matrix theory

abstract:
  We present a new method which uses Feynman-like diagrams to calculate the
statistical quantities of embedded many-body random matrix problems. The method
provides a promising alternative to existing techniques and offers many
important simplifications. We use it here to find the fourth, sixth and eighth
moments of the level density for k fermions or bosons interacting through a
random hermitian potential in the limit where the number of possible
single-particle states is taken to infinity. All share the same transition,
starting immediately after 2k = m, from moments arising from a semi-circular
level density to gaussian moments. The results also reveal a striking feature;
the domain of the 2n'th moment is naturally divided into n subdomains specified
by the points 2k = m, 3k = m, ..., nk = m.


title: Reply to M. Campisi [arXiv: 1310.5556]

abstract:
  In response to M. Campisi's comment [arXiv: 1310.5556] on our recent work
[Phys. Rev. E 88, 042126 (2013)], we first point out that the distribution used
by Campisi is not the correct escort distribution and further provide arguments
showing that the distributions obtained from the finite bath scenario are not
Tsallis distributions assuming the ergodicity of the total system. We also
comment on the role of evidence mentioned by M. Campisi.


title:
Existence and Stability of Almost Periodic Solutions of Differential
  Equations with Generalized Piecewise Constant Argument

abstract:
  This work deals with the existence of an almost periodic solution for certain
kind of differential equations with generalized piecewise constant argument,
almost periodic coefficients which are seen as a perturbation of a linear
equation of that kind satisfying an exponential dichotomy on a difference
equation. The stability of that solution in a semi-axis studied.


title: Giant black hole ringings induced by massive gravity

abstract:
  A distorted black hole radiates gravitational waves in order to settle down
in one of the geometries permitted by the no-hair theorem. During that
relaxation phase, a characteristic damped ringing is generated. It can be
theoretically constructed from the black hole quasinormal frequencies (which
govern its oscillating behavior and its decay) and from the associated
excitation factors (which determine intrinsically its amplitude) by carefully
taking into account the source of the distortion. Here, by considering the
Schwarzschild black hole in the framework of massive gravity, we show that the
excitation factors have an unexpected strong resonant behavior leading to giant
ringings which are, moreover, slowly decaying. Such extraordinary black hole
ringings could be observed by the next generations of gravitational wave
detectors and allow us to test the various massive gravity theories or their
absence could be used to impose strong constraints on the graviton mass.


title:
The $p$-adic Order of Power Sums, the Erd\"os-Moser Equation, and
  Bernoulli Numbers

abstract:
  The Erd\"os-Moser equation is a Diophantine equation proposed more than 60
years ago which remains unresolved to this day. In this paper, we consider the
problem in terms of divisibility of power sums and in terms of certain Egyptian
fraction equations. As a consequence, we show that solutions must satisfy
strong divisibility properties and a restrictive Egyptian fraction equation.
Our studies lead us to results on the Bernoulli numbers and allow us to
motivate Moser's original approach to the problem.


title: Analysis and Control of Beliefs in Social Networks

abstract:
  In this paper, we investigate the problem of how beliefs diffuse among
members of social networks. We propose an information flow model (IFM) of
belief that captures how interactions among members affect the diffusion and
eventual convergence of a belief. The IFM model includes a generalized Markov
Graph (GMG) model as a social network model, which reveals that the diffusion
of beliefs depends heavily on two characteristics of the social network
characteristics, namely degree centralities and clustering coefficients. We
apply the IFM to both converged belief estimation and belief control strategy
optimization. The model is compared with an IFM including the Barabasi-Albert
model, and is evaluated via experiments with published real social network
data.


title: Systematic of Particle Thermal Freeze-out in a Hadronic Fireball at RHIC

abstract:
  We attempt to describe the rapidity and transverse momentum spectra of
strange as well as non-strange hadrons e.g. cascade,cascadebar, lambda ,
lambdabar, proton, protonbar,(omega+omegabar, Kaon, anti-Kaon and their ratios
in the ultra-relativistic collisions of gold nuclei at (Root sNN)=200 GeV. This
is done by using a statistical thermal freeze-out model which incorporates the
rapidity (collision) axis as well as transverse direction boosts developed
within an expanding hot and dense hadronic fluid (fireball) till the final
freeze-out. We determine the thermo-chemical freeze-out conditions particularly
in terms of the temperature, baryon chemical potential and collective flow
effect parameters for different particle species. The parameters indicate
occurrence of freeze-out of the singly and doubly strange hyperon species at
somewhat earlier times during the evolution of the fireball. The experimental
data of the transverse momentum and rapidity distribution are well reproduced.
The contribution of heavier hadronic resonance decay is taken into account.


title:
Solutions and reductions for radiative energy transport in laser-heated
  plasma

abstract:
  A full symmetry classification is given for models of energy transport in
radiant plasma when the mass density is spatially variable and the diffusivity
is nonlinear. A systematic search for conservation laws also leads to some
potential symmetries, and to an integrable nonlinear model. Classical point
symmetries, potential symmetries and nonclassical symmetries are used to effect
variable reductions and exact solutions. The simplest time-dependent solution
is shown to be stable, and relevant to a closed system.


title: Local existence of solutions to Randomized Gross-Pitaevskii hierarchies

abstract:
  In this paper, we study the local-in-time existence of solutions to
randomized forms of the Gross-Pitaevskii hierarchy on periodic domains. In
particular, we study the independently randomized Gross-Pitaevskii hierarchy
and the dependently randomized Gross-Pitaevskii hierarchy, which were first
introduced in the author's joint work with Staffilani \cite{SoSt}. For these
hierarchies, we construct local-in-time low-regularity solutions in spaces
which contain a random component. The constructed density matrices will solve
the full randomized hierarchies, thus extending the results from \cite{SoSt},
where solutions solving arbitrarily long subhierarchies were given.
  Our analysis will be based on the truncation argument which was first used in
the deterministic setting in the work of T. Chen and Pavlovi\'{c} \cite{CP4}.
The presence of randomization in the problem adds additional difficulties, most
notably to estimating the Duhamel expansions that are crucial in the truncation
argument. These difficulties are overcome by a detailed analysis of the Duhamel
expansions. In the independently randomized case, we need to keep track of
which randomization parameters appear in the Duhamel terms, whereas in the
dependently randomized case, we express the Duhamel terms directly in terms of
the initial data. In both cases, we can obtain stronger results with respect to
the time variable if we assume additional regularity on the initial data.


title:
Quantum volume and length fluctuations in a midi-superspace model of
  Minkowski space

abstract:
  In a (1+1)-dimensional midi-superspace model for gravitational plane waves, a
flat space-time condition is imposed with constraints derived from null Killing
vectors. Solutions to a straightforward regularization of these constraints
have diverging length and volume expectation values. Physically acceptable
solutions in the kinematic Hilbert space are obtained from the original
constraint by multiplying with a power of the volume operator and by a similar
modification of the Hamiltonian constraint, which is used in a regularization
of the constraints. The solutions of the modified Killing constraint have
finite expectation values of geometric quantities. Further, the expectation
value of the original Killing constraint vanishes, but its moment is
non-vanishing. As the power of the volume grows the moment of the original
constraint grows, while the moments of volume and length both decrease. Thus,
these states provide possible kinematic states for flat space, with
fluctuations. As a consequence of the regularization of operators the quantum
uncertainty relations between geometric quantities such as length and its
conjugate momentum do not reflect naive expectations from the classical Poisson
bracket relations.


title: $\mathcal{L}^1$ limit solutions for control systems

abstract:
  For a control Cauchy problem $$\dot x= {f}(t,x,u,v) +\sum_{\alpha=1}^m
g_\alpha(x) \dot u_\alpha,\quad x(a)=\bar x, $$ on an interval $[a,b]$, we
propose a notion of limit solution $x,$ verifying the following properties: i)
$x$ is defined for $\mathcal{L}^1$ (impulsive) inputs $u$ and for standard,
bounded measurable, controls $v$; ii) in the commutative case (i.e. when
$[g_{\alpha},g_{\beta}]\equiv 0,$ for all $\alpha,\beta=1,...,m$), $x$
coincides with the solution one can obtain via the change of coordinates that
makes the $g_\alpha$ simultaneously constant; iii) $x$ subsumes former concepts
of solution valid for the generic, noncommutative case.
  In particular, when $u$ has bounded variation, we investigate the relation
between limit solutions and (single-valued) graph completion solutions.
Furthermore, we prove consistency with the classical Carath\'eodory solution
when $u$ and $x$ are absolutely continuous.
  Even though some specific problems are better addressed by means of special
representations of the solutions, we believe that various theoretical issues
call for a unified notion of trajectory. For instance, this is the case of
optimal control problems, possibly with state and endpoint constraints, for
which no extra assumptions (like e.g. coercivity, bounded variation,
commutativity) are made in advance.


title:
White Paper: Radio Emission and Polarization Properties of Galaxy
  Clusters with VLASS

abstract:
  We outline the science case for extended radio emission and polarization in
galaxy clusters which would be a scientifically important area of research for
an upcoming Jansky Very Large Array Sky Survey. The survey would provide a
major contribution in three key areas of the physics of clusters: 1) the active
galactic nucleus population and the impact of feedback on the evolution of the
intra-cluster medium, 2) the origin and evolution of diffuse cluster radio
sources to probe the physics of mergers with implications for cosmology, and 3)
the origin and role of magnetic fields in the ICM and in large scale
structures. Considering all three areas, a survey must have sufficient spatial
resolution to study the tailed galaxies which trace the cluster weather as well
as the radio lobes driving energy into the cluster from the central AGN. The
survey must also have sensitivity to low surface brightness emission and large
angular scales to probe radio halos and relics as well as the WHIM residing in
the large scale structure filaments. Finally, we note that full polarization
information would be a highly valuable tool to probe a number of
cluster-related issues. Due to the general steep spectral index of the emission
we consider the survey is best suited to this science when conducted in P, L,
or S bands. We conclude that the choices of S Band + D Configuration, L Band +
C Configuration, and P Band + B Configuration offer optimal resolutions for
constraining galactic interactions and feedback in cluster environments, while
still probing large scale structure and the bulk cluster environment itself.
While the push to probe higher redshifts and lower mass limits strongly favors
a narrow and deep (or even targeted) survey strategy, we note that a wide
survey covering roughly 1/4-2/3 of the sky will have significant scientific
return, discovery potential, and archival value.


title:
Nakayama automorphisms of double Ore extensions of Koszul regular
  algebras

abstract:
  Let $A$ be a Koszul Artin-Schelter regular algebra and $\sigma$ an algebra
homomorphism from $A$ to $M_{2\times 2}(A)$. We compute the Nakayama
automorphisms of a trimmed double Ore extension $A_P[y_1, y_2; \sigma]$
(introduced in \cite{ZZ08}). Using a similar method, we also obtain the
Nakayama automorphism of a skew polynomial extension $A[t; \theta]$, where
$\theta$ is a graded algebra automorphism of $A$. These lead to a
characterization of the Calabi-Yau property of $A_P[y_1, y_2; \sigma]$, the
skew Laurent extension $A[t^{\pm 1}; \theta]$ and $A[y_1^{\pm 1}, y_2^{\pm 1};
\sigma]$ with $\sigma$ a diagonal type.


title: Analytic theory of Hund's metals: a renormalization group perspective

abstract:
  We study the emergence of quasiparticles in Hund's metals with an
SU($M$)$\times$SU($N$)-symmetric Kondo impurity model carrying both spin and
orbital degrees of freedom. We show that the coupling of the impurity spin to
the conduction electrons can be \emph{ferromagnetic}, notably for hole-doped
iron pnictides. We derive the weak-coupling renormalization group (RG)
equations for arbitrary representations of SU($M$)$\times$SU($N$). A
ferromagnetic spin coupling results in a protracted RG flow, accounting for the
surprising particle-hole asymmetry that is observed in the iron-pnictide
systems. We establish the low coherence scale $T_{\rm K}$ which depends on the
filling through the impurity representation. We also discuss the temperature
dependence of the spin and orbital susceptibilities. Finally, we argue that
this mechanism explains the strong valence dependence of the coherence scale
observed in dilute transition-metal magnetic alloys.


title:
Relativistic Equation of Motion Coupled-Cluster Method: Application to
  the closed-shell atomic systems

abstract:
  We report our successful implementation of the full fledged relativistic
equation of motion coupled cluster (EOMCC) method. This method is employed to
compute the principal ionization potentials (IPs) of closed-shell rare gas
atoms, He-like ions, Be-like ions along with Na+, Al+, K+, Be, and Mg. Four
component Dirac spinors are used in the calculations and the one and two
electron integrals are evaluated using the Dirac Coulomb Hamiltonian. Our
results are in excellent agreement with those available measurements, which are
taken from the National Institute of Science and Technology database (NIST). We
also present results using the second order many-body perturbation theory
(MBPT(2)) and random phase approximation (RPA) in the EOMCC framework. These
results are compared with those of EOMCC at the level of single and double
excitations in order to assess the role of the electron correlation effects in
the intermediate schemes considered in our calculations .


title: Vibrational Spectroscopy of Methyl benzoate

abstract:
  Methyl benzoate (MB) is studied as a model compound for the development of
new IR pulse schemes with possible applicability to biomolecules. Anharmonic
vibrational modes of MB are calculated on different level (MP2, SCS, CCSD(T)
with varying basis sets) ab-initio PESs using the vibrational self-consistent
field (VSCF) method and its correlation corrected extensions. Dual level
schemes, combining different quantum chemical methods for diagonal and coupling
potentials, are systematically studied and applied successfully to reduce the
computational cost. Isotopic substitution of {\beta}-hydrogen by deuterium is
studied to obtain a better understanding of the molecular vibrational coupling
topology.


title: Convex optimization on Banach Spaces

abstract:
  Greedy algorithms which use only function evaluations are applied to convex
optimization in a general Banach space $X$. Along with algorithms that use
exact evaluations, algorithms with approximate evaluations are treated. A
priori upper bounds for the convergence rate of the proposed algorithms are
given. These bounds depend on the smoothness of the objective function and the
sparsity or compressibility (with respect to a given dictionary) of a point in
$X$ where the minimum is attained.


title: Pulsating variables from the OGLE and Araucaria projects

abstract:
  We present some results of long term studies of pulsating stars conducted in
the course of the OGLE and Araucaria projects. In particular very scarce
eclipsing binaries containing pulsating stars are discussed. Such systems
provide a unique opportunity to improve calibration of the cosmic distance
scale and to better calibrate stellar evolutionary models.


title: The Empirical Implications of Privacy-Aware Choice

abstract:
  This paper initiates the study of the testable implications of choice data in
settings where agents have privacy preferences. We adapt the standard
conceptualization of consumer choice theory to a situation where the consumer
is aware of, and has preferences over, the information revealed by her choices.
The main message of the paper is that little can be inferred about consumers'
preferences once we introduce the possibility that the consumer has concerns
about privacy. This holds even when consumers' privacy preferences are assumed
to be monotonic and separable. This motivates the consideration of stronger
assumptions and, to that end, we introduce an additive model for privacy
preferences that does have testable implications.


title:
Refining enumeration schemes to count according to permutation
  statistics

abstract:
  We consider the question of computing the distribution of a permutation
statistics over restricted permutations via enumeration schemes. The restricted
permutations are those avoiding sets of vincular patterns (which include both
classical and consecutive patterns), and the statistics are described in the
number of copies of certain vincular patterns such as the descent statistic and
major index. An enumeration scheme is a polynomial-time algorithm
(specifically, a system of recurrence relations) to compute the number of
permutations avoiding a given set of vincular patterns. Enumeration schemes'
most notable feature is that they may be discovered and proven via only finite
computation. We prove that when a finite enumeration scheme exists to compute
the number of permutations avoiding a given set of vincular patterns, the
scheme can also compute the distribution of certain permutation statistics with
very little extra computation.