title: Some positive conclusions related to the Embrechts-Goldie' conjecture

abstract:
  In this paper, we give some conditions, under which, if an infinitely
divisible distribution supported on $[0,\infty)$ belongs to the intersection of
exponential distribution class $\mathcal{L}(\gamma)$ for some $\gamma\ge0$ and
generalised subexponential distribution class $\mathcal{OS}$, then its
L$\rm\acute{e}$vy spectral distribution or convolution of the distribution with
itself also belongs to the same one. To this end, we discuss the closure under
the compound convolution roots for the class. In addition, we do some in-depth
discussion about the above-mentioned conditions, and provide some types of
distributions satisfying them. Further, we obtain some local versions of the
above-mentioned results by the Esscher transform of distributions. Therefore,
some positive conclusions related to the Embrechts-Goldie conjecture are
obtained. Prior to this, all corresponding results are negative


title: Quantum coherence of Gaussian states

abstract:
  We introduce a geometric quantification of quantum coherence in single-mode
Gaussian states and we investigate the behavior of distance measures as
functions of different physical parameters. In the case of squeezed thermal
states, we observe that re-quantization yields an effect of noise-enhanced
quantum coherence for increasing thermal photon number.


title: Random simplicial complexes - around the phase transition

abstract:
  This article surveys some of the work done in recent years on random
simplicial complexes. We mostly consider higher-dimensional analogs of the well
known phase transition in $G(n, p)$ theory that occurs at $p = \frac 1n$ . Our
main objective is to provide a more streamlined and unified perspective of some
of the papers in this area.


title: Basic Celestial Mechanics

abstract:
  These are lecture notes of the lecture on elementary celestial mechanics read
at Technische Universitaet Dresden, Dresden, Germany from 2000 till 2011.


title: A correction to collision rates of droplets in turbulent flows

abstract:
  This paper makes a correction to the collision rates of small droplets in
turbulent fluid derived by Saffman and Turner(1956). Not only the distortion
but also the rotation of the fluid is taken into account between two close
droplets. A rotation reference is fixed on one drop, and the fluxes of the
other drops moving towards the fixed one are carried out based on this new
reference. The behaviors of turbulent flow are analyzed within the smallest
eddies under the rotation reference, and a correction is made to the collision
rates by multiplying a factor sqrt(2).


title: Asymptotic non-Markovianity

abstract:
  We investigate the asymptotic dynamics of exact quantum Brownian motion. We
find that non-Markovianity can persist in the long-time limit, and that in
general the asymptotic behaviour depends strongly on the system-environment
coupling and the spectral density of the bath.


title:
Velocity statistics inside coherent vortices generated by the inverse
  cascade of $2d$ turbulence

abstract:
  We analyze velocity fluctuations inside coherent vortices generated as a
result of the inverse cascade in the two-dimensional ($2d$) turbulence in a
finite box. As we demonstrated in \cite{16KL}, the universal velocity profile,
established in \cite{14LBFKL}, corresponds to the passive regime of flow
fluctuations. The property enables one to calculate correlation functions of
the velocity fluctuations in the universal region. We present results of the
calculations that demonstrate a non-trivial scaling of the structure function.
In addition the calculations reveal strong anisotropy of the structure
function.


title: Automated Mutual Explicit Induction Proof in Separation Logic

abstract:
  We present a sequent-based deductive system for automatically proving
entailments in separation logic by using mathematical induction. Our technique,
called mutual explicit induction proof, is an instance of Noetherian induction.
Specifically, we propose a novel induction principle on a well-founded relation
of separation logic model and follow the explicit induction methods to
implement this principle as inference rules, so that it can be easily
integrated into a deductive system. We also support mutual induction, a natural
feature of implicit induction, where the goal entailment and other entailments
derived during the proof search can be used as hypotheses to prove each other.
We have implemented a prototype prover and evaluated it on a benchmark of
handcrafted entailments as well as benchmarks from a separation logic
competition.


title: Death and extended persistence in computational algebraic topology

abstract:
  The main aim of this paper is to explore the ideas of persistent homology and
extended persistent homology, and their stability theorems, using ideas from
[Bubenik and Scott, 2014; Cohen-Steiner, Edelsbrunner, and Harer, 2007; and
Cohen-Steiner, Edelsbrunner, and Harer, 2009], as well as other sources. The
secondary aim is to explore the homology (and cohomology) of non-orientable
surfaces, using the Klein bottle as an example. We also use the Klein bottle as
an example for the computation of (extended) persistent homology, referring to
it throughout the paper.


title:
Decoding visual stimuli in human brain by using Anatomical Pattern
  Analysis on fMRI images

abstract:
  A universal unanswered question in neuroscience and machine learning is
whether computers can decode the patterns of the human brain. Multi-Voxels
Pattern Analysis (MVPA) is a critical tool for addressing this question.
However, there are two challenges in the previous MVPA methods, which include
decreasing sparsity and noises in the extracted features and increasing the
performance of prediction. In overcoming mentioned challenges, this paper
proposes Anatomical Pattern Analysis (APA) for decoding visual stimuli in the
human brain. This framework develops a novel anatomical feature extraction
method and a new imbalance AdaBoost algorithm for binary classification.
Further, it utilizes an Error-Correcting Output Codes (ECOC) method for
multi-class prediction. APA can automatically detect active regions for each
category of the visual stimuli. Moreover, it enables us to combine homogeneous
datasets for applying advanced classification. Experimental studies on 4 visual
categories (words, consonants, objects and scrambled photos) demonstrate that
the proposed approach achieves superior performance to state-of-the-art
methods.


title:
Renormalized solutions of semilinear elliptic equations with general
  measure data

abstract:
  In the paper, we first propose a definition of renormalized solution of
semilinear elliptic equation involving operator corresponding to a general
(possibly nonlocal) symmetric regular Dirichlet form satisfying the so-called
absolute continuity condition and general (possibly nonsmooth) measure data.
Then we analyze the relationship between our definition and other concepts of
solutions considered in the literature (probabilistic solutions, solution
defined via the resolvent kernel of the underlying Dirichlet form,
Stampacchia's definition by duality). We show that under mild integrability
assumption on the data all these concepts coincide.


title:
Raman spectroscopic characterization of stacking configuration and
  interlayer coupling of twisted multilayer graphene grown by chemical vapor
  deposition

abstract:
  Multilayer graphene (MLG) grown by chemical vapor deposition (CVD) is a
promising material for electronic and optoelectronic devices. Understanding the
stacking configuration and interlayer coupling of MLGs is technologically
relevant and of importance for the device applications. Here, we reported a
kind of twisted MLGs (tMLGs), which are formed by stacking one graphene
monolayer on the top of AB-stacked MLG by rotating a certain angle between
them. The twist angle of tMLGs are identified by the twist-related modes, R and
R'. With increasing the total layer number of N, the observed interlayer shear
modes in the tMLG flake always follow those of AB-stacked (N-1)LG, while the
observed interlayer breathing modes always follow those of AB-stacked NLG,
independent of its twist angle. The layer breathing coupling of the tMLGs is
almost identical to that of mechanically-exfoliated tMLGs, which demonstrates
the high quality of MLGs grown by CVD. This study provides an applicable
approach to probe the stacking configuration and interlayer coupling of MLGs
grown by CVD or related methods. This work also demonstrates the possibility to
grow MLG flakes with a fixed stacking configuration, $e.g.$, t(1+$n$)LG, by the
CVD method.


title:
Quantum elasticity of graphene: Thermal expansion coefficient and
  specific heat

abstract:
  We explore thermodynamics of a quantum membrane, with a particular
application to suspended graphene membrane and with a particular focus on the
thermal expansion coefficient. We show that an interplay between quantum and
classical anharmonicity-controlled fluctuations leads to unusual elastic
properties of the membrane. The effect of quantum fluctuations is governed by
the dimensionless coupling constant, $g_0 \ll 1$, which vanishes in the
classical limit ($\hbar \to 0$) and is equal to $\simeq 0.05$ for graphene. We
demonstrate that the thermal expansion coefficient $\alpha_T$ of the membrane
is negative and remains nearly constant down to extremely low temperatures,
$T_0\propto \exp (-2/g_0)$. We also find that $\alpha_T$ diverges in the
classical limit: $\alpha_T \propto - \ln(1/g_0)$ for $g_0 \to 0$. For graphene
parameters, we estimate the value of the thermal expansion coefficient as
$\alpha_T \simeq - 0.23\:{\rm eV}^{-1}$, which applies below the temperature
$T_{\rm uv} \sim g_0 \varkappa_0 \sim 500$\:K (where $\varkappa_0 \sim 1$\:eV
is the bending rigidity) down to $T_0 \sim 10^{-14}$\:K. For $T<T_0$, the
thermal expansion coefficient slowly (logarithmically) approaches zero with
decreasing temperature. This behavior is surprising since typically the thermal
expansion coefficient goes to zero as a power-law function. We discuss possible
experimental consequences of this anomaly. We also evaluate classical and
quantum contributions to the specific heat of the membrane and investigate the
behavior of the Gr\"uneisen parameter.


title: Majorana fermions in the nonuniform Ising-Kitaev chain: exact solution

abstract:
  A quantum computer based on Majorana qubits would contain a large number of
zero-energy Majorana states. This system can be modelled as a connected network
of the Ising-Kitaev chains alternating the "trivial" and "topological" regions,
with the zero-energy Majorana fermions localized at their interfaces. The
low-energy sector of the theory describing such a network can be formulated in
terms of leading-order couplings between the Majorana zero modes. I consider a
minimal model exhibiting effective couplings between four Majorana zero modes -
the nonuniform Ising-Kitaev chain, containing two "topological" regions
separated by a "trivial" region. Solving the model exactly, I show that for
generic values of the model parameters the four zero modes are localized at the
four interface points of the chain. In the special case where additional
inversion symmetry is present, the Majorana zero modes are "delocalized"
between two interface points. In both cases, the low-energy sector of the
theory can be formulated in terms of the localized Majorana fermions, but the
couplings between some of them are independent of their respective separations:
the exact solution does not support the "nearest-neighbor" form of the
effective low-energy Hamiltonian.


title: Multivariate Mixed Tempered Stable Distribution

abstract:
  The multivariate version of the Mixed Tempered Stable is proposed. It is a
generalization of the Normal Variance Mean Mixtures. Characteristics of this
new distribution and its capacity in fitting tails and capturing dependence
structure between components are investigated. We discuss a random number
generating procedure and introduce an estimation methodology based on the
minimization of a distance between empirical and theoretical characteristic
functions. Asymptotic tail behavior of the univariate Mixed Tempered Stable is
exploited in the estimation procedure in order to obtain a better model
fitting. Advantages of the multivariate Mixed Tempered Stable distribution are
discussed and illustrated via simulation study.


title:
Asymptotic Analysis of Second Order Nonlocal Cahn-Hilliard-Type
  Functionals

abstract:
  In this paper the study of a nonlocal second order Cahn-Hilliard-type
singularly perturbed family of functions is undertaken. The kernels considered
include those leading to Gagliardo fractional seminorms for gradients. Using
Gamma convergence the integral representation of the limit energy is
characterized leading to an anisotropic surface energy on interfaces separating
different phases.


title: Hyperfine and crystal field interactions in multiferroic HoCrO${_3}$

abstract:
  We report a comprehensive specific heat and inelastic neutron scattering
study to explore the possible origin of multiferroicity in HoCrO$_3$. We have
performed specific heat measurements in the temperature range 100 mK - 290 K
and inelastic neutron scattering measurements were performed in the temperature
range 1.5 - 200 K. From the specific heat data we determined hyperfine
splitting at 22.5(2) $\mu$eV and crystal field transitions at 1.379(5) meV,
10.37(4) meV, 15.49(9) meV and 23.44(9) meV, indicating the existence of strong
hyperfine and crystal field interactions in HoCrO$_3$. Further, an effective
hyperfine field is determined to be 600(3) T. The quasielastic scattering
observed in the inelastic scattering data and a large linear term
$\gamma=6.3(8)$ mJmol$^{-1}$K$^{-2}$ in the specific heat is attributed to the
presence of short range exchange interactions, which is understood to be
contributing to the observed ferroelectricity. Further the nuclear and magnetic
entropies were computed to be, $\sim$$17.2$ Jmol$^{-1}$K$^{-1}$ and $\sim$34
Jmol$^{-1}$K$^{-1}$, respectively. The entropy values are in excellent
agreement with the limiting theoretical values. An anomaly is observed in peak
position of the temperature dependent crystal field spectra around 60 K, at the
same temperature an anomaly in the pyroelectric current is reported. From this
we could elucidate a direct correlation between the crystal electric field
excitations of Ho$^{3+}$ and ferroelectricity in HoCrO$_3$. Our present study
along with recent reports confirm that HoCrO$_3$, and $R$CrO$_3$ ($R=$ Rare
earth) in general, possess more than one driving force for the ferroelectricity
and multiferroicity.


title: Detecting fast radio bursts at decametric wavelengths

abstract:
  Fast radio bursts (FRBs) are highly dispersed, sporadic radio pulses that are
likely extragalactic in nature. Here we investigate the constraints on the
source population from surveys carried out at frequencies $<1$~GHz. All but one
FRB has so far been discovered in the 1--2~GHz band, but new and emerging
instruments look set to become valuable probes of the FRB population at sub-GHz
frequencies in the near future. In this paper, we consider the impacts of
free-free absorption and multi-path scattering in our analysis via a number of
different assumptions about the intervening medium. We consider previous low
frequency surveys alongwith an ongoing survey with the University of Technology
digital backend for the Molonglo Observatory Synthesis Telescope (UTMOST) as
well as future observations with the Canadian Hydrogen Intensity Mapping
Experiment (CHIME) and the Hydrogen Intensity and Real-Time Analysis Experiment
(HIRAX). We predict that CHIME and HIRAX will be able to observe $\sim$ 30 or
more FRBs per day, even in the most extreme scenarios where free-free
absorption and scattering can significantly impact the fluxes below 1~GHz. We
also show that UTMOST will detect 1--2 FRBs per month of observations. For
CHIME and HIRAX, the detection rates also depend greatly on the assumed FRB
distance scale. Some of the models we investigated predict an increase in the
FRB flux as a function of redshift at low frequencies. If FRBs are truly
cosmological sources, this effect may impact future surveys in this band,
particularly if the FRB population traces the cosmic star formation rate.


title:
Multi-region relaxed magnetohydrodynamics in plasmas with slowly
  changing boundaries --- resonant response of a plasma slab

abstract:
  The adiabatic limit of a recently proposed dynamical extension of Taylor
relaxation, \emph{multi-region relaxed magnetohydrodynamics} (MRxMHD) is
summarized, with special attention to the appropriate definition of relative
magnetic helicity. The formalism is illustrated using a simple two-region,
sheared-magnetic-field model similar to the Hahm--Kulsrud--Taylor (HKT)
rippled-boundary slab model. In MRxMHD a linear Grad--Shafranov equation
applies, even at finite ripple amplitude. The adiabatic switching on of
boundary ripple excites a shielding current sheet opposing reconnection at a
resonant surface. The perturbed magnetic field as a function of ripple
amplitude is calculated by invoking conservation of magnetic helicity in the
two regions separated by the current sheet. At low ripple amplitude "half
islands" appear on each side of the current sheet, locking the rotational
transform at the resonant value. Beyond a critical amplitude these islands
disappear and the rotational transform develops a discontinuity across the
current sheet.


title:
An intermediate-luminosity-optical-transient (ILOT) model for the young
  stellar object ASASSN-15qi

abstract:
  We construct a scenario where the outburst of the young-stellar-object
ASASSN-15qi is an intermediate luminosity optical transient (ILOT). In this
scenario a sub-Jupiter young planet was tidally destructed on to a young
main-sequence star. The system is young, therefore the radius of the planet is
larger than its final value, and consequently its density is smaller. The lower
density allows the tidal destruction of the young Saturn-like planet on to the
main-sequence star of mass $\approx 2.4~\rm{M_\odot}$, resulting in a formation
of a disc and a gravitationally-powered ILOT. Unlike the case of the more
energetic ILOT V838~Mon, the mass of the destructed planet is too low to
inflate a giant envelope, and hence the merger remnant stays hot. If our
suggested model holds, this ILOT possesses two interesting properties: (1) its
luminosity and total energy are below those of novae, and (2) it is not as red
as other ILOTs. The unusual outburst of ASASSN-15qi, if indeed is an ILOT,
further increases the diversity of the already heterogeneous group of ILOTs. We
mark the region on the energy-time diagram occupied by such young ILOTs.


title: Spectral learning of dynamic systems from nonequilibrium data

abstract:
  Observable operator models (OOMs) and related models are one of the most
important and powerful tools for modeling and analyzing stochastic systems.
They exactly describe dynamics of finite-rank systems and can be efficiently
and consistently estimated through spectral learning under the assumption of
identically distributed data. In this paper, we investigate the properties of
spectral learning without this assumption due to the requirements of analyzing
large-time scale systems, and show that the equilibrium dynamics of a system
can be extracted from nonequilibrium observation data by imposing an
equilibrium constraint. In addition, we propose a binless extension of spectral
learning for continuous data. In comparison with the other continuous-valued
spectral algorithms, the binless algorithm can achieve consistent estimation of
equilibrium dynamics with only linear complexity.

categories: cs.LG cs.AI cs.SY math.PR physics.data-an


title: Graph-Like Compacta: Characterizations and Eulerian Loops

abstract:
  A compact graph-like space is a triple $(X,V,E)$ where $X$ is a compact,
metrizable space, $V \subseteq X$ is a closed zero-dimensional subset, and $E$
is an index set such that $X \setminus V \cong E \times (0,1)$. New
characterizations of compact graph-like spaces are given, connecting them to
certain classes of continua, and to standard subspaces of Freudenthal
compactifications of locally finite graphs. These are applied to characterize
Eulerian graph-like compacta.


title: Dispersion Compensation using High-Positive Dispersive Optical Fibers

abstract:
  The common and traditional method for dispersion compensation in optical
domain is concatenating the transmit optical fiber by a compensating optical
fiber having high-negative dispersion coefficient. In this paper, we take an
opposite direction and show how an optical fiber with high-positive dispersion
coefficient can also be used for dispersion compensation. Our optical
dispersion compensating structure is the optical implementation of an iterative
algorithm in signal processing. The proposed dispersion compensating system is
constructed by cascading a number of compensating sub-systems and its
compensation capability is improved by increasing the number of embedded
sub-systems. We also show that the compensation capability is a trade-off
between transmission length and bandwidth. We use simulation results to
validate the performance of the introduced dispersion compensating module.
Photonic crystal fibers with high-positive dispersion coefficient can be used
for constructing the proposed optical dispersion compensating module.


title: Strict local martingales: examples

abstract:
  We show that a continuous local martingale is a strict local martingale if
its supremum process is not in $ L_\alpha$ for a positive number $\alpha $
smaller than $1$. Using this we construct a family of strict local martingales.


title: Duality and Stability for Functional Inequalities

abstract:
  We develop a general framework for using duality to "transfer" stability
results for a functional inequality to its dual inequality. As an application,
we prove a stability bound for the Hardy-Littlewood-Sobolev inequality, which
is related by duality, and the results proved here, to a stability inequality
for the Sobolev inequality proved by Bianchi and Egnell, and extended by Chen,
Frank and Weth. We also discuss how the results proved here can be combined
with the proof of functional inequalities by means of flows to prove stability
bounds with computable constants


title:
Gamma strength function and level density of $^{208}$Pb from
  forward-angle proton scattering at 295 MeV

abstract:
  Gamma strength functions (GSFs) and level densities (LDs) are essential
ingredients of statistical nuclear reaction theory with many applications in
astrophysics, reactor design, and waste transmutation. The aim of the present
work is a test of systematic parametrizations of the GSF recommended by the
RIPL-3 data base for the case of $^{208}$Pb. The upward GSF and LD in
$^{208}$Pb are compared to gamma decay data from an Oslo-type experiment to
examine the validity of the Brink-Axel (BA) hypothesis. The E1 and M1 parts of
the total GSF are determined from high-resolution forward angle inelastic
proton scattering data taken at 295 MeV at RCNP, Osaka, Japan. The total LD in
$^{208}$Pb is derived from the $1^-$ LD extracted with a fluctuation analysis
in the energy region of the isovector giant dipole resonance. The E1 GSF is
compared to parametrizations recommended by the RIPL-3 data base showing
systematic deficiencies of all models in the energy region around neutron
threshold. The new data for the poorly known spinflip M1 resonance call for a
substantial revision of the model suggested in RIPL-3. The total GSF derived
from the present data is larger in the PDR energy region than the Oslo data but
the strong fluctuations due to the low LD resulting from the double shell
closure of $^{208}$Pb prevent a conclusion on a possible violation of the BA
hypothesis. Using the parameters suggested by RIPL-3 for a description of the
LD in $^{208}$Pb with the back-shifted Fermi gas model, remarkable agreement
between the two experiments spanning a wide excitation energy range is
obtained. Systematic parametrizations of the E1 and M1 GSF parts need to be
reconsidered at low excitation energies. The good agreement of LD provides an
independent confirmation of the approach underlying the decomposition of GSF
and LDs in Oslo-type experiments.


title: Shear dynamics of an inverted nematic emulsion

abstract:
  Here we study theoretically the dynamics of a 2D and a 3D isotropic droplet
in a nematic liquid crystal under a shear flow. We find a large repertoire of
possible nonequilibrium steady states as a function of the shear rate and of
the anchoring of the nematic director field at the droplet surface. We first
discuss homeotropic anchoring. For weak anchoring, we recover the typical
behaviour of a sheared isotropic droplet in a binary fluid, which rotates,
stretches and can be broken by the applied flow. For intermediate anchoring,
new possibilities arise due to elastic effects in the nematic fluid. We find
that in this regime the 2D droplet can tilt and move in the flow, or tumble
incessantly at the centre of the channel. For sufficiently strong anchoring,
finally, one or both of the topological defects which form close to the surface
of the isotropic droplet in equilibrium detach from it and get dragged deep
into the nematic state by the flow. In 3D, instead, the Saturn ring associated
with normal anchoring disclination line can be deformed and shifted downstream
by the flow, but remains always localized in proximity of the droplet, at least
for the parameter range we explored. Tangential anchoring in 2D leads to a
different dynamic response, as the boojum defects characteristic of this
situation can unbind from the droplet under a weaker shear with respect to the
normal anchoring case. Our results should stimulate further experiments with
inverted liquid crystal emulsions under shear, as most of the predictions can
be testable in principle by monitoring the evolution of liquid crystalline
orientation patterns or by tracking the position and shape of the droplet over
time.


title: Quadratic Capelli operators and Okounkov polynomials

abstract:
  Let $Z$ be the symmetric cone of $r \times r$ positive definite Hermitian
matrices over a real division algebra $\mathbb F$. Then $Z$ admits a natural
family of invariant differential operators -- the Capelli operators $C_\lambda$
-- indexed by partitions $\lambda$ of length at most $r$, whose eigenvalues are
given by specialization of Knop--Sahi interpolation polynomials.
  In this paper we consider a double fibration $Y \longleftarrow X
\longrightarrow Z$ where $Y$ is the Grassmanian of $r$-dimensional subspaces of
$\mathbb F^n $ with $n \geq 2r$. Using this we construct a family of invariant
differential operators $D_{\lambda,s}$ on $Y$ that we refer to as quadratic
Capelli operators. Our main result shows that the eigenvalues of the
$D_{\lambda,s}$ are given by specializations of Okounkov interpolation
polynomials.


title: Non-asymptotic Bayesian Minimax Adaptation

abstract:
  This paper studies a Bayesian approach to non-asymptotic minimax adaptation
in nonparametric estimation. Estimating an input function on the basis of
output functions in a Gaussian white-noise model is discussed. The input
function is assumed to be in a Sobolev ellipsoid with an unknown smoothness and
an unknown radius. Our purpose in this paper is to present a Bayesian approach
attaining minimaxity up to a universal constant without any knowledge regarding
the smoothness and the radius. Our Bayesian approach provides not only a
rate-exact minimax adaptive estimator in large sample asymptotics but also a
risk bound for the Bayes estimator quantifying the effects of both the
smoothness and the ratio of the squared radius to the noise variance, where the
smoothness and the ratio are the key parameters to describe the minimax risk in
this model. Application to non-parametric regression models is also discussed.


title:
Flaring of Blazars from an Analytical, Time-dependent Model for Combined
  Synchrotron and Synchrotron Self-Compton Radiative Losses of Multiple
  Ultrarelativistic Electron Populations

abstract:
  We present a fully analytical, time-dependent leptonic one-zone model that
describes a simplified radiation process of multiple interacting
ultrarelativistic electron populations, accounting for the flaring of GeV
blazars. In this model, several mono-energetic, ultrarelativistic electron
populations are successively and instantaneously injected into the emission
region, i.e., a magnetized plasmoid propagating along the blazar jet, and
subjected to linear, time-independent synchrotron radiative losses, which are
caused by a constant magnetic field, and nonlinear, time-dependent synchrotron
self-Compton radiative losses in the Thomson limit. Considering a general
multiple-injection scenario is, from a physical point of view, more realistic
than the usual single-injection scenario invoked in common blazar models, as
blazar jets may extend over tens of kiloparsecs and, thus, most likely pick up
several particle populations from intermediate clouds. We analytically compute
the electron number density by solving a kinetic equation using Laplace
transformations and the method of matched asymptotic expansions. Moreover, we
explicitly calculate the optically thin synchrotron intensity, the synchrotron
self-Compton intensity in the Thomson limit, as well as the associated total
fluences. In order to mimic injections of finite duration times and radiative
transport, we model flares by sequences of these instantaneous injections,
suitably distributed over the entire emission region. Finally, we present a
parameter study for the total synchrotron and synchrotron self-Compton fluence
spectral energy distributions for a generic three-injection scenario, varying
the magnetic field strength, the Doppler factor, and the initial electron
energy of the first injection in realistic parameter domains, demonstrating
that our model can reproduce the typical broad-band behavior seen in
observational data.


title: The Age of the KIC 7177553 System

abstract:
  KIC 7177553 is a quadruple system containing two binaries of orbital periods
16.5 and 18 d. All components have comparable masses and are slowly rotating,
non-evolved stars of spectral type near G2V. The longer period binary is
eclipsing with component masses and radii, M1 = 1.043 +/- 0.014 M_sun, R1 =
0.940 +/- 0.005 R_sun, and M2 = 0.986 +/- 0.015 M_sun, R2 = 0.941 +/- 0.005
R_sun. The essentially equal radii measurements are inconsistent with the two
stars being on the main sequence at the same age using standard stellar
evolution models. Instead a consistent scenario is found if the stars are in
their pre-main sequence phase of evolution and have age 33 - 36 Myr. Such a
young age has important implications for the detectability of the massive
planet indicated by eclipse time variations.


title: Probing CP violation in $h\to \tau^{-}\tau^{+}$ at the LHC

abstract:
  We propose a novel method to reconstruct event by event the full kinematics
of the cascade decay process, $h \to \tau^+\tau^- \to (\pi^+ \bar{\nu}) (\pi^-
\nu)$, which allows us to measure the $\tau^+\tau^-$ spin correlation, a
measure of the CP property of the Higgs boson. By noting that the $\tau^{\pm}$
momenta lie on the plane spanned by the accurately measured impact parameter
and momentum vectors of charged pions, we can obtain the most likely momenta of
the two missing neutrinos by using the probability distribution functions of
the $\met$ vector and the location of the primary vertex. A simple detector
level simulation shows an excellent agreement between the reconstructed and the
true kinematics, both in the $\tau^+\tau^-$ and the $\pi^+\pi^-$ rest frames.
The method can be tested in $Z \to \tau^+\tau^-$ events, which should exhibit
no correlation.


title: Armendariz ring with weakly semicommutativity

abstract:
  In this article, we introduce the weak ideal-Armendariz ring which combines
Armendariz ring and weakly semicommutative properties of rings. In fact, it is
a generalisation of an ideal-Armendariz ring. We investigate some properties of
weak ideal Armendariz rings and prove that R is a weak ideal-Armendariz ring if
and only if R[x] is weak ideal-Armendariz ring. Also, we generalise weak
ideal-Armendariz as strongly nil-IFP and a number of properties are discussed
which distinguishes it from other existing structures. We prove that if I is a
semicommutative ideal of a ring R and R/I is a strongly nil-IFP, then R is
strongly nil-IFP. Moreover, if R is 2-primal, then R[x]/<x^{n}> is a strongly
nil-IFP.


title:
MmmTurkey: A Crowdsourcing Framework for Deploying Tasks and Recording
  Worker Behavior on Amazon Mechanical Turk

abstract:
  Internal HITs on Mechanical Turk can be programmatically restrictive, and as
a result, many requesters turn to using external HITs as a more flexible
alternative. However, creating such HITs can be redundant and time-consuming.
We present MmmTurkey, a framework that enables researchers to not only quickly
create and manage external HITs, but more significantly also capture and record
detailed worker behavioral data characterizing how each worker completes a
given task.


title: Gradient dynamics models for liquid films with soluble surfactant

abstract:
  In this paper we propose equations of motion for the dynamics of liquid films
of surfactant suspensions that consist of a general gradient dynamics framework
based on an underlying energy functional. This extends the gradient dynamics
approach to dissipative non-equilibrium thin film systems with several
variables, and casts their dynamic equations into a form that reproduces
Onsager's reciprocity relations. We first discuss the general form of gradient
dynamics models for an arbitrary number of fields and discuss simple well-known
examples with one or two fields. Next, we develop the gradient dynamics (three
field) model for a thin liquid film covered by soluble surfactant and discuss
how it automatically results in consistent convective (driven by pressure
gradients, Marangoni forces and Korteweg stresses), diffusive,
adsorption/desorption, and evaporation fluxes. We then show that in the dilute
limit, the model reduces to the well-known hydrodynamic form that includes
Marangoni fluxes due to a linear equation of state. In this case the energy
functional incorporates wetting energy, surface energy of the free interface
(constant contribution plus an entropic term) and bulk mixing entropy.
Subsequently, as an example, we show how various extensions of the energy
functional result in consistent dynamical models that account for nonlinear
equations of state, concentration-dependent wettability and surfactant and film
bulk decomposition phase transitions. We conclude with a discussion of further
possible extensions towards systems with micelles, surfactant adsorption at the
solid substrate and bioactive behaviour.


title: New methods toward the patch and flat topologies with applications

abstract:
  In this paper, we use elementary and simple ideas which are based on the
significant applications of the power set ring to rebuild and study the patch
topology on the prime spectrum from a completely different and new point of
view. Specially, the proof of a major result in the literature on the
comparison of topologies greatly simplified and shortened. Then we develop more
natural and simple methods to obtain the flat topology and its properties. In
particular, it is shown that the minimal spectrum of a commutative ring is
quasi-compact with respect to the flat topology. Then as an application of this
result, all of the related results of Kaplansky, Anderson, Gilmer-Heinzer,
Bahmanpour-Khojali-Naghipour and Naghipour on the finiteness of the minimal
primes are deduced as special cases of this result. Dually, a similar result is
also obtained for maximal ideals.


title:
Diffusive escape through a narrow opening: new insights into a classic
  problem

abstract:
  We study the mean first exit time $T_{\ve}$ of a particle diffusing in a
circular or a spherical micro-domain with an impenetrable confining boundary
containing a small escape window (EW) of an angular size $\ve$. Focusing on the
effects of an energy/entropy barrier at the EW, and of the long-range
interactions (LRI) with the boundary on the diffusive search for the EW, we
develop a self-consistent approximation to derive for $T_{\ve}$ a general
expression, akin to the celebrated Collins-Kimball relation in chemical
kinetics and accounting for both rate-controlling factors in an explicit way.
Our analysis reveals that the barrier-induced contribution to $T_{\ve}$ is the
dominant one in the limit $\ve \to 0$, implying that the narrow escape problem
is not "diffusion-limited" but rather "barrier-limited". We present the
small-$\ve$ expansion for $T_{\ve}$, in which the coefficients in front of the
leading terms are expressed via some integrals and derivatives of the LRI
potential. On example of a triangular-well potential, we show that $T_{\ve}$ is
non-monotonic with respect to the extent of the attractive LRI, being minimal
for the ones having an intermediate extent, neither too concentrated on the
boundary nor penetrating too deeply into the bulk. Our analytical predictions
are in a good agreement with the numerical simulations.


title:
The adjoint map of the Serre derivative and special values of shifted
  Dirichlet series

abstract:
  We compute the adjoint of the Serre derivative map with respect to the
Petersson scalar product by using existing tools of nearly holomorphic modular
forms. The Fourier coefficients of a cusp form of integer weight $k$,
constructed using this method, involve special values of certain shifted
Dirichlet series associated with a given cusp form $f$ of weight $k+2$. As
application, we get an asymptotic bound for the special values of these shifted
Dirichlet series and also relate these special values with the Fourier
coefficients of $f$. We also give a formula for the Ramanujan tau function in
terms of the special values of the shifted Dirichlet series associated to the
Ramanujan delta function.


title:
Braiding without Braiding: Teleportation-Based Quantum Information
  Processing with Majorana Zero Modes

abstract:
  We present a new measurement-based scheme for performing braiding operations
on Majorana zero modes and for detecting their non-Abelian statistics without
moving or hybridizing them. In our scheme, the topological qubit encoded in any
pair of well-separated Majorana zero modes in a mesoscopic superconductor
island is read out from the transmission phase shift in electron teleportation
through the island in the Coulomb blockade regime. We propose experimental
setups to measure the teleportation phase shift via conductance in an electron
interferometer or persistent current in a closed loop.


title:
A Unified Convergence Analysis of the Multiplicative Update Algorithm
  for Regularized Nonnegative Matrix Factorization

abstract:
  The multiplicative update (MU) algorithm has been extensively used to
estimate the basis and coefficient matrices in nonnegative matrix factorization
(NMF) problems under a wide range of divergences and regularizers. However,
theoretical convergence guarantees have only been derived for a few special
divergences without regularization. In this work, we provide a conceptually
simple, self-contained, and unified proof for the convergence of the MU
algorithm applied on NMF with a wide range of divergences and regularizers. Our
main result shows the sequence of iterates (i.e., pairs of basis and
coefficient matrices) produced by the MU algorithm converges to the set of
stationary points of the non-convex NMF optimization problem. Our proof
strategy has the potential to open up new avenues for analyzing similar
problems in machine learning and signal processing.


title: The non-Lefschetz locus

abstract:
  We study the weak Lefschetz property of artinian Gorenstein algebras and in
particular of artinian complete intersections. In codimension four and higher,
it is an open problem whether all complete intersections have the weak
Lefschetz property. For a given artinian Gorenstein algebra $A$ we ask what
linear forms are Lefschetz elements for this particular algebra, i.e., which
linear forms $\ell$ give maximal rank for all the multiplication maps $\times
\ell: [A]_i \longrightarrow [A]_{i+1}$. This is a Zariski open set and its
complement is the \emph{non-Lefschetz locus}. For monomial complete
intersections, we completely describe the non-Lefschetz locus. For general
complete intersections of codimension three and four we prove that the
non-Lefschetz locus has the expected codimension, which in particular means
that it is empty in a large family of examples. For general Gorenstein algebras
of codimension three with a given Hilbert function, we prove that the
non-Lefschetz locus has the expected codimension if the first difference of the
Hilbert function is of decreasing type. For completeness we also give a full
description of the non-Lefschetz locus for artinian algebras of codimension
two.


title:
On the solutions of the $Z_n$-Belavin model with arbitrary number of
  sites

abstract:
  The periodic $Z_n$-Belavin model on a lattice with an arbitrary number of
sites $N$ is studied via the off-diagonal Bethe Ansatz method (ODBA). The
eigenvalues of the corresponding transfer matrix are given in terms of an
unified inhomogeneous $T-Q$ relation. In the special case of $N=nl$ with $l$
being also a positive integer, the resulting $T-Q$ relation recovers the
homogeneous one previously obtained via algebraic Bethe Ansatz.

categories: math-ph cond-mat.stat-mech hep-th math.MP


title: On the dynamics of the mean-field polaron in the weak-coupling limit

abstract:
  We consider the dynamics of the mean-field polaron in the weak-coupling limit
of vanishing electron-phonon interaction, $\varepsilon \to 0$. This is a
singular limit formally leading to a Schr\"odinger--Poisson system that is
equivalent to the nonlinear Choquard equation. By establishing estimates
between the approximation obtained via the Choquard equation and true solutions
of the original system we show that the Choquard equation makes correct
predictions about the dynamics of the polaron mean-field model for small values
of $\varepsilon > 0$.


title: The large sum graph related to comultiplication modules

abstract:
  Let R be a commutative ring and M be an R-module. We define the large sum
graph, denoted by \acute{G}(M), as a graph with the vertex set of non-large
submodules of M and two distinct vertices are adjacent if and only if N + K is
a non-large submodule of M. In this article, we investigate the connection
between the graph-theoretic properties of \acute{G}(M) and some algebraic
properties of M when M is a comultiplication R-module.


title: Factorial hypersurfaces

abstract:
  In this paper the codimension of the complement to the set of factorial
hypersurfaces of degree $d$ in ${\mathbb P}^N$ is estimated for $d\geqslant 4$,
$N\geqslant 7$.


title: $N(p, q, s)$-type spaces in the unit ball of $C^n$

abstract:
  In this paper, we consider a new class of space, called $N(p, q, s)$-type
spaces, in the unit ball $B$ of $C^n$. We study some basic properties, Hadamard
gaps, Hadamard products, Random power series, Korenblum's inequality, Gleason's
problem, atomic decomposition of $N(p, q, s)$-type spaces. Moreover, we also
establish several equivalent characterizations, including Carleson measure
characterization and various derivative characterizations. Finally, we also
characterize the distance between Bergman-type spaces and $N(p, q, s)$-type
spaces, Riemann-Stieltjes operators and multipliers on $N(p, q, s)$-type
spaces.


title:
High performance volume ray casting: A branchless generalized Joseph
  projector

abstract:
  A concise and highly performant branchless formulation of a Joseph-type
interpolating ray-casting algorithm for the computation of X-ray projections is
presented. It efficiently utilizes the hardware resources of modern graphics
processing units at the scale of their theoretic maximum performance reaching
access rates of 600 GB/s within read-and-write memory, and is further shown to
do so without compromising on image quality. The computation of X-ray
projections from discrete voxel grids is an ubiquitous task in many problems
related to volume image processing, including tomographic reconstruction and
visualization. Although its central role has given rise to numerous
publications discussing the optimal modeling of ray-volume intersections, a
unique benchmark in this respect does not exist. Here, a 3D Shepp-Logan phantom
is used, which allows the computation of analytic reference projections that
can further serve as input to iterative reconstructions without committing the
inverse crime. The proposed algorithm (GJP) is compared to the competing and
widely adopted digital differential analyzer (DDA), which computes exact
line-box intersections. It is thereby found to outperform the DDA on recent
graphics processors in all respects: Despite accessing twice as much memory,
the GJP is still able to calculate projections twice as fast. It further
exhibits considerably less discretization artifacts, and neither oversampling
of the DDA nor a smooth interpolation kernel within the GJP are able to improve
on these results in any respect.


title:
Selecting between-sample RNA-Seq normalization methods from the
  perspective of their assumptions

abstract:
  RNA-Seq is a widely-used method for studying the behavior of genes under
different biological conditions. An essential step in an RNA-Seq study is
normalization, in which raw data are adjusted to account for factors that
prevent direct comparison of expression measures. Errors in normalization can
have a significant impact on downstream analysis, such as inflated false
positives in differential expression analysis. An under-emphasized feature of
normalization is the assumptions upon which the methods rely and how the
validity of these assumptions can have a substantial impact on the performance
of the methods. In this paper, we explain how assumptions provide the link
between raw RNA-Seq read counts and meaningful measures of gene expression. We
examine normalization methods from the perspective of their assumptions, as an
understanding of methodological assumptions is necessary for choosing methods
appropriate for the data at hand. Furthermore, we discuss why normalization
methods perform poorly when their assumptions are violated and how this causes
problems in subsequent analysis. To analyze a biological experiment,
researchers must select a normalization method with assumptions that are met
and that produces a meaningful measure of expression for the given experiment.


title:
Planet formation with envelope enrichment: new insights on planetary
  diversity

abstract:
  We compute, for the first time, self-consistent models of planet growth
including the effect of envelope enrichment. The change of envelope metallicity
is assumed to be the result of planetesimal disruption or icy pebble
sublimation. We solve internal structure equations taking into account global
energy conservation for the envelope to compute in-situ planetary growth. We
consider different opacities and equations of state suited for a wide range of
metallicities. We find that envelope enrichment speeds up the formation of gas
giants. It also explains naturally the formation of low and intermediate mass
objects with large fractions of H-He (~ 20 - 30 % in mass). High opacity models
explain well the metallicity of the giant planets of the solar system, whereas
low opacity models are suited for forming small mass objects with thick H-He
envelopes and gas giants with sub-solar envelope metallicities. We find good
agreement between our models and the estimated water abundance for WASP-43b.
For HD 189733b, HD 209458b and WASP-12b we predict fractions of water larger
than what is estimated from observations, by at least a factor ~ 2. Envelope
enrichment by icy planetesimals is the natural scenario to explain the
formation of a large variety of objects, ranging from mini-Neptunes, to gas
giants. We predict that the total and envelope metallicity decrease with
planetary mass.


title:
Power Series Representations for Complex Bosonic Effective Actions. III.
  Substitution and Fixed Point Equations

abstract:
  We have previously developed a polymer-like expansion that applies when the
(effective) action in a functional integral is an analytic function of the
fields being integrated. Here, we develop methods to aid the application of
this technique when the method of steepest descent is used to analyze the
functional integral. We develop a version of the Banach fixed point theorem
that can be used to construct and control the critical fields, as analytic
functions of external fields, and substitution formulae to control the change
in norms that occurs when one replaces the integration fields by the sum of the
critical fields and the fluctuation fields.


title: Two-color Soergel calculus and simple transitive 2-representations

abstract:
  In this paper we complete the $\mathrm{ADE}$-like classification of simple
transitive $2$-representations of Soergel bimodules in finite dihedral type,
under the assumption of gradeability. In particular, we use bipartite graphs
and zigzag algebras of $\mathrm{ADE}$ type to give an explicit construction of
a graded (non-strict) version of all these $2$-representations.
  Moreover, we give simple combinatorial criteria for when two such
$2$-representations are equivalent and for when their Grothendieck groups give
rise to isomorphic representations.
  Finally, our construction also gives a large class of simple transitive
$2$-representations in infinite dihedral type for general bipartite graphs.


title: Classification of reductive real spherical pairs I. The simple case

abstract:
  This paper gives a classification of all pairs $(\mathfrak g, \mathfrak h)$
with $\mathfrak g$ a simple real Lie algebra and $\mathfrak h < \mathfrak g$ a
reductive subalgebra for which there exists a minimal parabolic subalgebra
$\mathfrak p < \mathfrak g$ such that $\mathfrak g = \mathfrak h + \mathfrak p$
as vector sum.


title: Bloch Theory for Periodic Block Spin Transformations

abstract:
  Block spin renormalization group is the main tool used in our program to see
symmetry breaking in a weakly interacting many Boson system on a three
dimensional lattice at low temperature. It generates operators, like the
fluctuation integral covariance, that act on some lattice but are translation
invariant only with respect to a proper sublattice. This paper constructs a
Bloch/Floquet framework that is appropriate for bounding such operators.


title: A note on Brehm's extension theorem

abstract:
  Brehm's extension theorem states that a non-expansive map on a finite subset
of a Euclidean space can be extended to a piecewise-linear map on the entire
space. In this note, it is verified that the proof of the theorem is
constructive provided that the finite subset consists of points with rational
coordinates. Additionally, the initial non-expansive map needs to send points
with rational coordinates to points with rational coordinates. The
two-dimensional case is considered.


title: The Algebra of Block Spin Renormalization Group Transformations

abstract:
  Block spin renormalization group is the main tool used in our program to see
symmetry breaking in a weakly interacting many Boson system on a three
dimensional lattice at low temperature. In this paper, we discuss some of its
purely algebraic aspects in an abstract setting. For example, we derive some
"well known" identities like the composition rule and the relation between
critical fields and background fields.


title: Vanishing point detection with convolutional neural networks

abstract:
  Inspired by the finding that vanishing point (road tangent) guides driver's
gaze, in our previous work we showed that vanishing point attracts gaze during
free viewing of natural scenes as well as in visual search (Borji et al.,
Journal of Vision 2016). We have also introduced improved saliency models using
vanishing point detectors (Feng et al., WACV 2016). Here, we aim to predict
vanishing points in naturalistic environments by training convolutional neural
networks in an end-to-end manner over a large set of road images downloaded
from Youtube with vanishing points annotated. Results demonstrate effectiveness
of our approach compared to classic approaches of vanishing point detection in
the literature.


title:
Complex Bosonic Many-body Models: Overview of the Small Field Parabolic
  Flow

abstract:
  This paper is a contribution to a program to see symmetry breaking in a
weakly interacting many Boson system on a three dimensional lattice at low
temperature. It provides an overview of our analysis of the "small field"
approximation to the "parabolic flow" which exhibits the formation of a
"Mexican hat" potential well.


title: Adaptive Distributional Extensions to DFR Ranking

abstract:
  Divergence From Randomness (DFR) ranking models assume that informative terms
are distributed in a corpus differently than non-informative terms. Different
statistical models (e.g. Poisson, geometric) are used to model the distribution
of non-informative terms, producing different DFR models. An informative term
is then detected by measuring the divergence of its distribution from the
distribution of non-informative terms. However, there is little empirical
evidence that the distributions of non-informative terms used in DFR actually
fit current datasets. Practically this risks providing a poor separation
between informative and non-informative terms, thus compromising the
discriminative power of the ranking model. We present a novel extension to DFR,
which first detects the best-fitting distribution of non-informative terms in a
collection, and then adapts the ranking computation to this best-fitting
distribution. We call this model Adaptive Distributional Ranking (ADR) because
it adapts the ranking to the statistics of the specific dataset being processed
each time. Experiments on TREC data show ADR to outperform DFR models (and
their extensions) and be comparable in performance to a query likelihood
language model (LM).


title:
Astrophysical constraints on dark-matter $Q$-balls in the presence of
  baryon-violating operators

abstract:
  Supersymmetric extensions of the standard model predict the existence of
non-topological solitons, $Q$-balls. Assuming the standard cosmological history
preceded by inflation, $Q$-balls can form in the early universe and can make up
the dark matter. The relatively large masses of such dark-matter particles
imply a low number density, making direct detection very challenging. The
strongest limits come from the existence of neutron stars because, if a
baryonic $Q$-ball is captured by a neutron star, the $Q$-ball can absorb the
baryon number releasing energy and eventually destroying a neutron star.
However, in the presence of baryon number violating higher-dimension operators,
the growth of a $Q$-ball inside a neutron star is hampered once the $Q$-ball
reaches a certain size. We re-examine the limits and identify some classes of
higher-dimensional operators for which supersymmetric $Q$-balls can account for
dark matter. The present limits leave a wide range of parameters available for
dark matter in the form of supersymmetric $Q$-balls.


title: Operators for Parabolic Block Spin Transformations

abstract:
  This paper is a contribution to a program to see symmetry breaking in a
weakly interacting many Boson system on a three dimensional lattice at low
temperature. It is part of an analysis of the "small field" approximation to
the "parabolic flow" which exhibits the formation of a "Mexican hat" potential
well. Bounds on the fluctuation integral covariance, as well as on some other
linear operators, are an important ingredient in our renormalization group step
analysis. These bounds are proven here.


title: Curl Forces and the Nonlinear Fokker-Planck Equation

abstract:
  Nonlinear Fokker-Planck equations endowed with curl drift forces are
investigated. The conditions under which these evolution equations admit
stationary solutions, which are $q$-exponentials of an appropriate potential
function, are determined. It is proved that when these stationary solutions
exist, the nonlinear Fokker-Planck equations satisfy an $H$-theorem in terms of
a free-energy like quantity involving the $S_q$ entropy. A particular two
dimensional model admitting analytical, time-dependent, $q$-Gaussian solutions
is discussed in detail. This model describes a system of particles with
short-range interactions, performing overdamped motion under drag effects, due
to a rotating resisting medium. It is related to models that have been recently
applied to the study of type-II superconductors. The relevance of the present
developments to the study of complex systems in physics, astronomy, and
biology, is discussed.


title: Bernstein and Kantorovich polynomials diminish the $\Lambda$-variation

abstract:
  We prove the $\Lambda$-variation diminishing property of the Bernstein and
Kantorovich polynomials. Next we apply this result to characterize the space
$C\Lambda BV_c$ as the closure of the space of polynomials in the $\Lambda BV$
norm. A new proof of the separability of $C\Lambda BV_c$ is given.


title:
Hybrid semiclassical theory of quantum quenches in one dimensional
  systems

abstract:
  We develop a hybrid semiclassical method to study the time evolution of one
dimensional quantum systems in and out of equilibrium. Our method handles
internal degrees of freedom completely quantum mechanically by a modified time
evolving block decimation method, while treating orbital quasiparticle motion
classically. We can follow dynamics up to timescales well beyond the reach of
standard numerical methods to observe the crossover between pre-equilibrated
and locally phase equilibrated states. As an application, we investigate the
quench dynamics and phase fluctuations of a pair of tunnel coupled one
dimensional Bose condensates. We demonstrate the emergence of soliton-collision
induced phase propagation, soliton-entropy production and multistep
thermalization. Our method can be applied to a wide range of gapped
one-dimensional systems.


title: One-loop divergences in the 6D, N=(1,0) abelian gauge theory

abstract:
  We consider, in the harmonic superspace approach, the six-dimensional N=(1,0)
supersymmetric model of abelian gauge multiplet coupled to a hypermultiplet.
The superficial degree of divergence is evaluated and the structure of possible
one-loop divergences is analyzed. Using the superfield proper-time and
background-field technique, we compute the divergent part of the one-loop
effective action depending on both the gauge multiplet and the hypermultiplet.
The corresponding counterterms contain the purely gauge multiplet contribution
together with the mixed contributions of the gauge multiplet and
hypermultiplet. We show that the theory is on-shell one-loop finite in the
gauge multiplet sector in agreement with the results of [1]. The divergences in
the mixed sector cannot be eliminated by any field redefinition, implying the
theory to be UV divergent at one loop.


title: Oscillatory Integrals and Fractal Dimension

abstract:
  We study geometrical representation of oscillatory integrals with an analytic
phase function and a smooth amplitude with compact support. Geometrical
properties of the curves defined by the oscillatory integral depend on the type
of a critical point of the phase. We give explicit formulas for the box
dimension and the Minkowski content of these curves. Methods include Newton
diagrams and the resolution of singularities.


title: Modeling sRNA-regulated Plasmid Maintenance

abstract:
  We study a theoretical model for the toxin-antitoxin (hok/sok) mechanism for
plasmid maintenance in bacteria. Toxin-antitoxin systems enforce the
maintenance of a plasmid through post-segregational killing of cells that have
lost the plasmid. Key to their function is the tight regulation of expression
of a protein toxin by an sRNA antitoxin. Here, we focus on the nonlinear nature
of the regulatory circuit dynamics of the toxin-antitoxin mechanism. The
mechanism relies on a transient increase in protein concentration rather than
on the steady state of the genetic circuit. Through a systematic analysis of
the parameter dependence of this transient increase, we confirm some known
design features of this system and identify new ones: for an efficient
toxin-antitoxin mechanism, the synthesis rate of the toxin's mRNA template
should be lower that of the sRNA antitoxin, the mRNA template should be more
stable than the sRNA antitoxin, and the mRNA-sRNA complex should be more stable
than the sRNA antitoxin. Moreover, a short half-life of the protein toxin is
also beneficial to the function of the toxin-antitoxin system. In addition, we
study a therapeutic scenario in which a competitor mRNA is introduced to
sequester the sRNA antitoxin, causing the toxic protein to be expressed.


title:
Local Maxima in the Likelihood of Gaussian Mixture Models: Structural
  Results and Algorithmic Consequences

abstract:
  We provide two fundamental results on the population (infinite-sample)
likelihood function of Gaussian mixture models with $M \geq 3$ components. Our
first main result shows that the population likelihood function has bad local
maxima even in the special case of equally-weighted mixtures of well-separated
and spherical Gaussians. We prove that the log-likelihood value of these bad
local maxima can be arbitrarily worse than that of any global optimum, thereby
resolving an open question of Srebro (2007). Our second main result shows that
the EM algorithm (or a first-order variant of it) with random initialization
will converge to bad critical points with probability at least
$1-e^{-\Omega(M)}$. We further establish that a first-order variant of EM will
not converge to strict saddle points almost surely, indicating that the poor
performance of the first-order method can be attributed to the existence of bad
local maxima rather than bad saddle points. Overall, our results highlight the
necessity of careful initialization when using the EM algorithm in practice,
even when applied in highly favorable settings.


title:
N-barrier maximum principle for degenerate elliptic systems and its
  application

abstract:
  In this paper, we prove the N-barrier maximum principle, which extends the
result in [5] from linear diffusion equations to nonlinear diffusion equations,
for a wide class of degenerate elliptic systems of porous medium type. The
N-barrier maximum principle provides a priori upper and lower bounds of the
solutions to the above-mentioned degenerate nonlinear diffusion equations
including the Shigesada-Kawasaki-Teramoto model as a special case. As an
application of the N-barrier maximum principle to a coexistence problem in
ecology, we show the nonexistence of waves in a three-species degenerate
elliptic systems.


title: Some Notes on Pairs in Binary Strings

abstract:
  Seth (Mathematics Stack Exchange, http://math.stackexchange.com/q/1812699)
posed a problem that is equivalent to the following: how many binary strings of
length n have exactly k pairs of consecutive 0s and exactly m pairs of
consecutive 1s, where the first and last bits are considered as being
consecutive? In this paper, we provide a closed form solution which also solves
a related problem with some interesting connections to other combinatorial
sequences.


title: Allometric scaling in-vitro

abstract:
  The quarter power allometric scaling of mammalian metabolic rate is largely
regarded as a universal law of biology. However, it is well known that cell
cultures do not obey this law. The current thinking is that were in-vitro
cultures to obey quarter power scaling, they would have more predictive power
and could for instance provide a viable substitute for animals in research.
About two decades ago, West and coworkers established a model which predicts
that metabolic rate follows a quarter power relationship with the mass of an
organism, based on the premise that tissues are supplied nutrients through a
fractal distribution network. This paper outlines a theoretical and
computational framework for establishing quarter power scaling in-vitro,
starting where fractal distribution ends. Allometric scaling in non-vascular
spherical tissue constructs was assessed using models of Michaelis Menten
oxygen consumption and diffusion. The results demonstrate that physiological
scaling is maintained when about 5 to 60% of the construct is exposed to oxygen
concentrations less than the Michaelis Menten constant. In these conditions the
Thiele modulus is between 8 and 80, with a significant concentration gradient
in the sphere. The results have important implications for the design of
downscaled in-vitro systems with physiological relevance.


title: The IRAS 08589-4714 star-forming region

abstract:
  We present an analysis of the IRAS 08589-4714 star-forming region. This
region harbors candidate young stellar objects identified in the WISE and
Herschel images using color index criteria and spectral energy distributions
(SEDs). The SEDs of some of the infrared sources and the 70 microns radial
intensity profile of the brightest source (IRS 1) are modeled from Herschel
fluxes using the one-dimensional radiative transfer DUSTY code. For these
objects, we estimate the envelope masses, sizes, densities, and luminosities
which suggest that they are very young, massive and luminous objects at early
stages of the formation process. Color-color diagrams in the bands of WISE and
2MASS are used to identify potential young objects in the region. Those
identified in the bands of WISE would be contaminated by the emission of PAHs.
We use the emission distribution in the infrared at 70 and 160 microns, to
estimate the dust temperature gradient. This suggests that the nearby massive
star-forming region RCW 38, located ~ 10 pc of the IRAS source position may be
contributing to the photodissociation of the molecular gas and to the heating
of the interstellar dust in the environs of the IRAS source.


title: Unit Hypercube Visibility Numbers of Trees

abstract:
  A visibility representation of a graph $G$ is an assignment of the vertices
of $G$ to geometric objects such that vertices are adjacent if and only if
their corresponding objects are "visible" each other, that is, there is an
uninterrupted channel, usually axis-aligned, between them. Depending on the
objects and definition of visibility used, not all graphs are visibility
graphs. In such situations, one may be able to obtain a visibility
representation of a graph $G$ by allowing vertices to be assigned to more than
one object. The {\it visibility number} of a graph $G$ is the minimum $t$ such
that $G$ has a representation in which each vertex is assigned to at most $t$
objects.
  In this paper, we explore visibility numbers of trees when the vertices are
assigned to unit hypercubes in $\mathbb{R}^n$. We use two different models of
visibility: when lines of sight can be parallel to any standard basis vector of
$\mathbb{R}^n$, and when lines of sight are only parallel to the $n$th standard
basis vector in $\mathbb{R}^n$. We establish relationships between these
visibility models and their connection to trees with certain cubicity values.


title: Atiyah classes of strongly homotopy Lie pairs

abstract:
  The subject of this paper is strongly homotopy (SH) Lie algebras, also known
as $L_\infty$-algebras. We extract an intrinsic character, the Atiyah class,
which measures the nontriviality of an (SH) Lie algebra $A$ when it is extended
to $L$. In fact, given such an SH Lie pair $(L, A)$, and any $A$-module $E$,
there associates a canonical cohomology class, the Atiyah class $[\alpha^E]$,
which generalizes earlier known Atiyah classes out of Lie algebra pairs. We
show that the Atiyah class $[\alpha^{L/A}]$ induces a graded Lie algebra
structure on $\operatorname{H}^\bullet_{\mathrm{CE}}(A,L/A[-2])$, and the
Atiyah class $[\alpha^E]$ of any $A$-module $E$ induces a Lie algebra module
structure on $\operatorname{H}^\bullet_{\mathrm{CE}}(A,E)$. Moreover, Atiyah
classes are invariant under gauge equivalent $A$-compatible infinitesimal
deformations of $L$.


title: Symmetry Enrichment in Three-Dimensional Topological Phases

abstract:
  While two-dimensional symmetry-enriched topological phases ($\mathsf{SET}$s)
have been studied intensively and systematically, three-dimensional ones are
still open issues. We propose an algorithmic approach of imposing global
symmetry $G_s$ on gauge theories (denoted by $\mathsf{GT}$) with gauge group
$G_g$. The resulting symmetric gauge theories are dubbed "symmetry-enriched
gauge theories" ($\mathsf{SEG}$), which may be served as low-energy effective
theories of three-dimensional symmetric topological quantum spin liquids. We
focus on $\mathsf{SEG}$s with gauge group
$G_g=\mathbb{Z}_{N_1}\times\mathbb{Z}_{N_2}\times\cdots$ and on-site unitary
symmetry group $G_s=\mathbb{Z}_{K_1}\times\mathbb{Z}_{K_2}\times\cdots$ or
$G_s=\mathrm{U(1)}\times \mathbb{Z}_{K_1}\times\cdots$. Each
$\mathsf{SEG}(G_g,G_s)$ is described in the path integral formalism associated
with certain symmetry assignment. From the path-integral expression, we propose
how to physically diagnose the ground state properties (i.e., $\mathsf{SET}$
orders) of $\mathsf{SEG}$s in experiments of charge-loop braidings (patterns of
symmetry fractionalization) and the \emph{mixed} multi-loop braidings among
deconfined loop excitations and confined symmetry fluxes. From these
symmetry-enriched properties, one can obtain the map from $\mathsf{SEG}$s to
$\mathsf{SET}$s. By giving full dynamics to background gauge fields,
$\mathsf{SEG}$s may be eventually promoted to a set of new gauge theories
(denoted by $\mathsf{GT}^*$). Based on their gauge groups, $\mathsf{GT}^*$s may
be further regrouped into different classes each of which is labeled by a gauge
group ${G}^*_g$. Finally, a web of gauge theories involving $\mathsf{GT}$,
$\mathsf{SEG}$, $\mathsf{SET}$ and $\mathsf{GT}^*$ is achieved. We demonstrate
the above symmetry-enrichment physics and the web of gauge theories through
many concrete examples.


title: On the Uniqueness of the Solution to a Strongly Competing System

abstract:
  This work is devoted to prove uniqueness result for the positive solution to
a strongly competing system of Lotka - Volterra type in the limiting
configuration, when the competition rate tends to infinity.


title:
Non-Gaussian analytic option pricing: a closed formula for the
  L\'evy-stable model

abstract:
  We establish an explicit pricing formula for the class of L\'evy-stable
models with maximal negative asymmetry (Log-L\'evy model with finite moments
and stability parameter $1<\alpha\leq 2$) in the form of rapidly converging
series. The series is obtained with help of Mellin transform and the residue
theory in $\mathbb{C}^2$. The resulting formula enables the straightforward
evaluation of an European option with arbitrary accuracy without the use of
numerical techniques. The formula can be used by any practitioner, even if not
familiar with the underlying mathematical techniques. We test the efficiency of
the formula, and compare it with numerical methods.


title:
A clustering-based data reduction for very large spatio-temporal
  datasets

abstract:
  Today, huge amounts of data are being collected with spatial and temporal
components from sources such as meteorological, satellite imagery etc.
Efficient visualisation as well as discovery of useful knowledge from these
datasets is therefore very challenging and becoming a massive economic need.
Data Mining has emerged as the technology to discover hidden knowledge in very
large amounts of data. Furthermore, data mining techniques could be applied to
decrease the large size of raw data by retrieving its useful knowledge as
representatives. As a consequence, instead of dealing with a large size of raw
data, we can use these representatives to visualise or to analyse without
losing important information. This paper presents a new approach based on
different clustering techniques for data reduction to help analyse very large
spatio-temporal data. We also present and discuss preliminary results of this
approach.


title:
Mass concentration and aging in the parabolic Anderson model with
  doubly-exponential tails

abstract:
  We study the solutions $u=u(x,t)$ to the Cauchy problem on $\mathbb
Z^d\times(0,\infty)$ for the parabolic equation $\partial_t u=\Delta u+\xi u$
with initial data $u(x,0)=1_{\{0\}}(x)$. Here $\Delta$ is the discrete
Laplacian on $\mathbb Z^d$ and $\xi=(\xi(z))_{z\in\mathbb Z^d}$ is an i.i.d.\
random field with doubly-exponential upper tails. We prove that, for large $t$
and with large probability, a majority of the total mass $U(t):=\sum_x u(x,t)$
of the solution resides in a bounded neighborhood of a site $Z_t$ that achieves
an optimal compromise between the local Dirichlet eigenvalue of the Anderson
Hamiltonian $\Delta+\xi$ and the distance to the origin. The processes
$t\mapsto Z_t$ and $t \mapsto \tfrac1t \log U(t)$ are shown to converge in
distribution under suitable scaling of space and time. Aging results for $Z_t$,
as well as for the solution to the parabolic problem, are also established. The
proof uses the characterization of eigenvalue order statistics for $\Delta+\xi$
in large sets recently proved by the first two authors.


title:
A data mining-based solution for detecting suspicious money laundering
  cases in an investment bank

abstract:
  Today, money laundering poses a serious threat not only to financial
institutions but also to the nation. This criminal activity is becoming more
and more sophisticated and seems to have moved from the clichy of drug
trafficking to financing terrorism and surely not forgetting personal gain.
Most international financial institutions have been implementing anti-money
laundering solutions to fight investment fraud. However, traditional
investigative techniques consume numerous man-hours. Recently, data mining
approaches have been developed and are considered as well-suited techniques for
detecting money laundering activities. Within the scope of a collaboration
project for the purpose of developing a new solution for the anti-money
laundering Units in an international investment bank, we proposed a simple and
efficient data mining-based solution for anti-money laundering. In this paper,
we present this solution developed as a tool and show some preliminary
experiment results with real transaction datasets.


title: Higher-Spin Algebras, Holography and Flat Space

abstract:
  In this article we study the algebra generated by the holographically
reconstructed cubic couplings for the type A minimal bosonic higher-spin theory
on AdS$_{d+1}$, which were recently extracted from the free scalar $O(N)$
model. We demonstrate that it is equal to the unique higher-spin algebra for
bosonic totally symmetric higher-spin fields in generic dimensions. This
provides an explicit check of the holographic reconstruction and of the duality
between higher-spin theories and the free $O(N)$ model in general dimensions,
extending the result of Giombi and Yin in AdS$_4$. For completeness, we also
address the same problem in the flat space for the cubic couplings derived by
Metsaev in 1991, which are recovered in the flat limit of the AdS type-A cubic
couplings. We observe that both flat and AdS$_4$ higher-spin Lorentz
subalgebras coincide, hinting towards the existence of a full higher-spin
symmetry behind the flat-space cubic couplings of Metsaev.


title:
Performance Evaluation of a Natural Language Processing approach applied
  in White Collar crime investigation

abstract:
  In today world we are confronted with increasing amounts of information every
day coming from a large variety of sources. People and co-operations are
producing data on a large scale, and since the rise of the internet, e-mail and
social media the amount of produced data has grown exponentially. From a law
enforcement perspective we have to deal with these huge amounts of data when a
criminal investigation is launched against an individual or company. Relevant
questions need to be answered like who committed the crime, who were involved,
what happened and on what time, who were communicating and about what? Not only
the amount of available data to investigate has increased enormously, but also
the complexity of this data has increased. When these communication patterns
need to be combined with for instance a seized financial administration or
corporate document shares a complex investigation problem arises. Recently,
criminal investigators face a huge challenge when evidence of a crime needs to
be found in the Big Data environment where they have to deal with large and
complex datasets especially in financial and fraud investigations. To tackle
this problem, a financial and fraud investigation unit of a European country
has developed a new tool named LES that uses Natural Language Processing (NLP)
techniques to help criminal investigators handle large amounts of textual
information in a more efficient and faster way. In this paper, we present
briefly this tool and we focus on the evaluation its performance in terms of
the requirements of forensic investigation: speed, smarter and easier for
investigators. In order to evaluate this LES tool, we use different performance
metrics. We also show experimental results of our evaluation with large and
complex datasets from real-world application.


title: Tail asymptotics of maximums on trees in the critical case

abstract:
  We consider solutions to the maximum recursion on weighted branching trees
given by$$X\,{\buildrel d\over=}\,\bigvee_{i=1}^{N}{A_iX_i}\vee B,$$where $N$
is a random natural number, $B$ and $\{A_i\}_{i\in\mathbb{N}}$ are random
positive numbers and $X_i$ are independent copies of $X$, also independent of
$N$, $B$, $\{A_i\}_{i\in\mathbb{N}}$. Properties of solutions to this equation
are governed mainly by the function
$m(s)=\mathbb{E}\big[\sum_{i=1}^NA_i^s\big]$. Recently, Jelenkovi\'c and
Olvera-Cravioto proved, assuming e.g. $m(s)<1$ for some $s$, that the
asymptotic behavior of the endogenous solution $R$ to the above equation is
power-law, i.e.$$\mathbb{P}[R>t]\sim Ct^{-\alpha}$$for some $\alpha>0$ and
$C>0$. In this paper we assume $m(s)\ge 1$ for all $s$ and prove analogous
results.


title: Gauge invariants from the powers of antipodes

abstract:
  We prove that the trace of the $n$th power of the antipode of a Hopf algebra
with the Chevalley property is a gauge invariant, for each integer $n$. As a
consequence, the order of the antipode, and its square, are invariant under
Drinfeld twists. The invariance of the order of the antipode is closely related
to a question of Shimizu on the pivotal covers of finite tensor categories,
which we affirmatively answer for representation categories of Hopf algebras
with the Chevalley property.


title: Preliminary design of the INPE's Solar Vector Magnetograph

abstract:
  We describe the preliminary design of a magnetograph and visible-light imager
instrument to study the solar dynamo processes through observations of the
solar surface magnetic field distribution. The instrument will provide
measurements of the vector magnetic field and of the line-of-sight velocity in
the solar photosphere. As the magnetic field anchored at the solar surface
produces most of the structures and energetic events in the upper solar
atmosphere and significantly influences the heliosphere, the development of
this instrument plays an important role in reaching the scientific goals of The
Atmospheric and Space Science Coordination (CEA) at the Brazilian National
Institute for Space Research (INPE). In particular, the CEA's space weather
program will benefit most from the development of this technology. We expect
that this project will be the starting point to establish a strong research
program on Solar Physics in Brazil. Our main aim is acquiring progressively the
know-how to build state-of-art solar vector magnetograph and visible-light
imagers for space-based platforms to contribute to the efforts of the
solar-terrestrial physics community to address the main unanswered questions on
how our nearby Star works.


title:
New Equation for Bending Development of Arbitrary Rods and Application
  to Palm Fronds Bending

abstract:
  A new general equation to explain bending of arbitrary rods (from arbitrary
materials, cross sections, densities, strengthnesses, bending angles, etc) was
proposed. This equation can solve several problems found in classical
equations, which have many limitations such as only applies for small bending
angles or must be solved using very complex schemes. Experiments were also
conducted to confirm the theoretical predictions. The equation might be used to
explain bending of palm fronds in a very simple way. The proposed equation may
be used to obtain solution of several problems which are usually obtain with
iteration procedures.


title: Hodge locus and Brill-Noether type locus

abstract:
  Given a family $\pi:\mc{X} \rightarrow B$ of smooth projective varieties, a
closed fiber $\mc{X}_o$ and an invertible sheaf $\mc{L}$ on $\mc{X}_o$, we
compare the Hodge locus in $B$ corresponding to the Hodge class $c_1(\mc{L})$
with the locus of points $b\,\in\, B$ such that $\mc{L}$ deforms to an
invertible sheaf $\mc{L}_b$ on $\mc{X}_b$ with at least
$h^0(\mc{L})$--dimensional space of global sections (it is a Brill-Noether type
locus associated to $\mc{L}$). We finally give an application by comparing the
Brill-Noether locus to a family of curves on a surface passing through a fixed
set of points.


title:
Effect of thermal annealing on the heat transfer properties of reduced
  graphite oxide flakes: a nanoscale characterization via scanning thermal
  microscopy

abstract:
  This paper reports on the thermal properties of reduced graphite oxide (RGO)
flakes, studied by means of scanning thermal microscopy (SThM). This technique
was demonstrated to allow thermal characterization of the flakes with a spatial
resolution of the order of a few tens of nanometers, while recording nanoscale
topography at the same time. Several individual RGO flakes were analyzed by
SThM, both as obtained after conventional thermal reduction and after a
subsequent annealing at 1700{\deg}C. Significant differences in the thermal
maps were observed between pristine and annealed flakes, reflecting higher heat
dissipation on annealed RGO flakes compared with pristine ones. This result was
correlated with the reduction of RGO structure defectiveness. In particular, a
substantial reduction of oxidized groups and sp3 carbons upon annealing was
proven by X-ray photoelectron and Raman spectroscopies, while the increase of
crystalline order was demonstrated by X-ray diffraction, in terms of higher
correlation lengths both along and perpendicular to the graphene planes.
Results presented in this paper provide experimental evidence for the
qualitative correlation between the defectiveness of graphene-related materials
and their thermal conductivity, which is clearly crucial for the exploitation
of these materials into thermally conductive nanocomposites.


title: Automatic Generation of Vectorized Montgomery Algorithm

abstract:
  Modular arithmetic is widely used in crytography and symbolic computation.
This paper presents a vectorized Montgomery algorithm for modular
multiplication, the key to fast modular arithmetic, that fully utilizes the
SIMD instructions. We further show how the vectorized algorithm can be
automatically generated by the {\SPIRAL} system, as part of the effort for
automatic generation of a modular polynomial multiplication library.


title: Convexified Convolutional Neural Networks

abstract:
  We describe the class of convexified convolutional neural networks (CCNNs),
which capture the parameter sharing of convolutional neural networks in a
convex manner. By representing the nonlinear convolutional filters as vectors
in a reproducing kernel Hilbert space, the CNN parameters can be represented as
a low-rank matrix, which can be relaxed to obtain a convex optimization
problem. For learning two-layer convolutional neural networks, we prove that
the generalization error obtained by a convexified CNN converges to that of the
best possible CNN. For learning deeper networks, we train CCNNs in a layer-wise
manner. Empirically, CCNNs achieve performance competitive with CNNs trained by
backpropagation, SVMs, fully-connected neural networks, stacked denoising
auto-encoders, and other baseline methods.


title: Transference for the Erd\H{o}s-Ko-Rado theorem

abstract:
  For natural numbers $n,r \in \mathbb{N}$ with $n\ge r$, the Kneser graph
$K(n,r)$ is the graph on the family of $r$-element subsets of $\{1,\dots,n\}$
in which two sets are adjacent if and only if they are disjoint. Delete the
edges of $K(n,r)$ with some probability, independently of each other: is the
independence number of this random graph equal to the independence number of
the Kneser graph itself? We answer this question affirmatively as long as $r/n$
is bounded away from $1/2$, even when the probability of retaining an edge of
the Kneser graph is quite small. This gives us a random analogue of the
Erd\H{o}s-Ko-Rado theorem since an independent set in the Kneser graph is the
same as a uniform intersecting family. To prove our main result, we give some
new estimates for the number of disjoint pairs in a family in terms of its
distance from an intersecting family, these might be of independent interest.


title: Catching a fast robber on the grid

abstract:
  We study the problem of cops and robbers on the grid where the robber is
allowed to move faster than the cops. It is well known that two cops are
necessary and sufficient to catch the robber on any finite grid when the robber
has unit speed. Here, we prove that when the speed of the robber is a
sufficiently large constant, the number of cops needed to catch the robber on
an $n \times n$ grid is $\exp(\Omega(\log n / \log \log n))$.


title: Connections in randomly oriented graphs

abstract:
  Given an undirected graph $G$, let us randomly orient $G$ by tossing
independent (possibly biased) coins, one for each edge of $G$. Writing
$a\rightarrow b$ for the event that there exists a directed path from a vertex
$a$ to a vertex $b$ in such a random orientation, we prove that
$\mathbb{P}(s\rightarrow a \cap s\rightarrow b) \ge \mathbb{P}(s\rightarrow a)
\mathbb{P}(s\rightarrow b)$ for any three vertices $s$, $a$ and $b$ of $G$.


title:
Note on "Equivalence Between Different Auxiliary Field Formulations of
  ${\cal N}=1$ Supergravity Coupled to Matter"

abstract:
  In the version 1 of this paper, we claimed that 4D ${\cal N}=1$ supergravity
formulations with different auxiliary fields can be unified using U(1) gauge
symmetry, whose gauge superfield does not have a kinetic term. However, after
submission, we found a critical error in our statement. This is the note on the
paper of the version 1.


title: The third moment for the parabolic Anderson model

abstract:
  In this paper, we study the {\it parabolic Anderson model} starting from the
Dirac delta initial data: \[ \left(\frac{\partial}{\partial t}
-\frac{\nu}{2}\frac{\partial^2}{\partial x^2} \right) u(t,x) = \lambda u(t,x)
\dot{W}(t,x), \qquad u(0,x)=\delta_0(x), \quad x\in\mathbb{R}, \] where
$\dot{W}$ denotes the space-time white noise. By evaluating the threefold
contour integral in the third moment formula by Borodin and Corwin [2], we
obtain some explicit formulas for $\mathbb{E}[u(t,x)^3]$. One application of
these formulas is given to show the exact phase transition for the
intermittency front of order three.


title:
Combining Fully Convolutional and Recurrent Neural Networks for 3D
  Biomedical Image Segmentation

abstract:
  Segmentation of 3D images is a fundamental problem in biomedical image
analysis. Deep learning (DL) approaches have achieved state-of-the-art
segmentation perfor- mance. To exploit the 3D contexts using neural networks,
known DL segmentation methods, including 3D convolution, 2D convolution on
planes orthogonal to 2D image slices, and LSTM in multiple directions, all
suffer incompatibility with the highly anisotropic dimensions in common 3D
biomedical images. In this paper, we propose a new DL framework for 3D image
segmentation, based on a com- bination of a fully convolutional network (FCN)
and a recurrent neural network (RNN), which are responsible for exploiting the
intra-slice and inter-slice contexts, respectively. To our best knowledge, this
is the first DL framework for 3D image segmentation that explicitly leverages
3D image anisotropism. Evaluating using a dataset from the ISBI Neuronal
Structure Segmentation Challenge and in-house image stacks for 3D fungus
segmentation, our approach achieves promising results comparing to the known
DL-based 3D segmentation approaches.


title: Domain and range symmetries of operator fractional Brownian fields

abstract:
  An operator fractional Brownian field (OFBF) is a Gaussian, stationary
increment R^n-valued random field on R^m that satisfies the operator
self-similarity property {X(c^E t)}_{t in R^m} L= {c^H X(t)}_{t in R^m}, c > 0,
for two matrix exponents (E,H). In this paper, we characterize the domain and
range symmetries of OFBF, respectively, as maximal groups with respect to
equivalence classes generated by orbits and, based on a new anisotropic
polar-harmonizable representation of OFBF, as intersections of centralizers. We
also describe the sets of possible pairs of domain and range symmetry groups in
dimensions (m,1) and (2,2).


title: An integral formula for affine connections

abstract:
  In this article, we introduce a $2$-parameter family of affine connections
and derive the Ricci curvature. We first establish an integral Bochner
technique. On one hand, this technique yields a new proof to our recent work in
\cite{LX} for substatic manifolds. On the other hand, this technique leads to
various geometric inequalities and eigenvalue estimates under a much more
general Ricci curvature conditions. The new Ricci curvature condition
interpolates between static Ricci tensor and $1$-Bakry-Emery Ricci, and also
includes the conformal Ricci as an intermediate case.


title:
Equidistribution with an error rate and Diophantine approximation over
  function fields

abstract:
  We prove pointwise equidistribution with an error rate of each $H$-orbit in
$SL(d,\mathbf{K})/SL(d,\mathbf{Z})$ for a certain proper subgroup $H$ of
horospherical group over a function field $\mathbf{K}$, extending a work of
Kleinbock-Shi-Weiss. Moreover, we obtain an asymptotic formula for the number
of integral solutions to the Diophantine inequalities with weights,
generalizing a result of Dodson-Kristensen-Levesley. This result enables us to
show pointwise equidistribution for unbounded functions of class $C_\alpha$,
which was first introduced by Eskin-Margulis-Mozes.


title: Automatic Library Generation for Modular Polynomial Multiplication

abstract:
  Polynomial multiplication is a key algorithm underlying computer algebra
systems (CAS) and its efficient implementation is crucial for the performance
of CAS. In this paper we design and implement algorithms for polynomial
multiplication using approaches based the fast Fourier transform (FFT) and the
truncated Fourier transform (TFT). We improve on the state-of-the-art in both
theoretical and practical performance. The {\SPIRAL} library generation system
is extended and used to automatically generate and tune the performance of a
polynomial multiplication library that is optimized for memory hierarchy,
vectorization and multi-threading, using new and existing algorithms. The
performance tuning has been aided by the use of automation where many code
choices are generated and intelligent search is utilized to find the "best"
implementation on a given architecture. The performance of autotuned
implementations is comparable to, and in some cases better than, the best
hand-tuned code.


title:
Robin spectral rigidity of strictly convex domains with a reflectional
  symmetry

abstract:
  This is a note on a recent paper of De Simoi-Kaloshin-Wei \cite{DKW}. We show
that using their results combined with wave trace invariants of
Guillemin-Melrose and the heat trace invariants of Zayed for the Laplacian with
Robin boundary conditions, one can extend the Dirichlet/Neumann spectral
rigidity results of \cite{DKW} to the case of Robin boundary conditions. We
will consider the same generic subset as in \cite{DKW} of smooth strictly
convex $\mathbb Z_2$-symmetric planar domains sufficiently close to a circle,
however we pair them with arbitrary $\mathbb Z_2$-symmetric smooth Robin
functions on the boundary and of course allow deformations of Robin functions
as well.


title:
Design of FELiChEM, the first infrared free-electron laser user facility
  in China

abstract:
  FELiChEM is a new experimental facility under construction at University of
Science and Technology of China (USTC), whose core device is two free electron
laser oscillators generating middle-infrared and far-infrared laser and
covering the spectral range of 2.5-200 $\mu$m. It will be a dedicated infrared
light source aiming at energy chemistry research. We present the brief design
of FEL oscillators with the emphasis put on the middle-infrared oscillator.
Most of the basic parameters are determined and the anticipated performance of
the output radiation is given. The first light of FELiChEM is targeted for the
end of 2017.


title:
Electromagnetic cascade masquerade: a way to mimic $\gamma$--axion-like
  particle mixing effects in blazar spectra

abstract:
  Context. Most of the studies on extragalactic {\gamma}-ray propagation
performed up to now only accounted for primary gamma-ray absorption and
adiabatic losses ("absorption-only model"). However, there is growing evidence
that this model is oversimplified and must be modified in some way. In
particular, it was found that the intensity extrapolated from the
optically-thin energy range of some blazar spectra is insufficient to explain
the optically-thick part of these spectra. This effect was interpreted as an
indication for {\gamma}-axion-like particle (ALP) oscillation. On the other
hand, there are many hints that a secondary component from electromagnetic
cascades initiated by primary {\gamma}-rays or nuclei may be observed in the
spectra of some blazars. Aims. We study the impact of electromagnetic cascades
from primary {\gamma}-rays or protons on the physical interpretation of blazar
spectra obtained with imaging Cherenkov telescopes. Methods. We use the
publicly-available code ELMAG to compute observable spectra of electromagnetic
cascades from primary {\gamma}-rays. For the case of primary proton, we develop
a simple, fast and reasonably accurate hybrid method to calculate the
observable spectrum. We perform the fitting of the observed spectral energy
distributions (SEDs) with various physical models: the absorption-only model,
the "electromagnetic cascade model" (for the case of primary {\gamma}-rays),
and several versions of the hadronic cascade model (for the case of primary
proton). We distinguish the following species of hadronic cascade models: 1)
"basic hadronic model", where it is assumed that the proton beam travels
undisturbed by extragalactic magnetic field and that all observable
{\gamma}-rays are produced by primary protons through photohadronic processes
with subsequent development of electromagnetic cascades /abridged


title:
Compact star forming galaxies as the progenitors of compact quiescent
  galaxies: clustering result

abstract:
  We present a measurement of the spatial clustering of massive compact
galaxies at $1.2\le z \le 3$ in CANDELS/3D-HST fields. We obtain the
correlation length for compact quiescent galaxies (cQGs) at $z\sim1.6$ of
$r_{0}=7.1_{-2.6}^{+2.3}\ h^{-1}Mpc$ and compact star forming galaxies (cSFGs)
at $z\sim2.5$ of $r_{0}=7.7_{-2.9}^{+2.7}\ h^{-1}Mpc$ assuming a power-law
slope $\gamma =1.8$. The characteristic dark matter halo masses $M_H$ of cQGs
at $z\sim1.6$ and cSFGs at $z\sim2.5$ are $\sim7.1\times 10^{12}\ h^{-1}
M_\odot$ and $\sim4.4\times10^{12}\ h^{-1} M_\odot$, respectively. Our
clustering result suggests that cQGs at $z\sim1.6$ are possibly the progenitors
of local luminous ETGs and the descendants of cSFGs and SMGs at $z>2$. Thus an
evolutionary connection involving SMGs, cSFGs, QSOs, cQGs and local luminous
ETGs has been indicated by our clustering result.


title:
The Energy Landscape Underpinning Module Dynamics in the Human Brain
  Connectome

abstract:
  Human brain dynamics can be profitably viewed through the lens of statistical
mechanics, where neurophysiological activity evolves around and between local
attractors representing preferred mental states. Many physically-inspired
models of these dynamics define the state of the brain based on instantaneous
measurements of regional activity. Yet, recent work in network neuroscience has
provided initial evidence that the brain might also be well-characterized by
time-varying states composed of locally coherent activity or functional
modules. Here we study this network-based notion of brain state to understand
how functional modules dynamically interact with one another to perform
cognitive functions. We estimate the functional relationships between regions
of interest (ROIs) by fitting a pair-wise maximum entropy model to each ROI's
pattern of allegiance to functional modules. Local minima in this model
represent attractor states characterized by specific patterns of modular
structure. The clustering of local minima highlights three classes of ROIs with
similar patterns of allegiance to community states. Visual, attention,
sensorimotor, and subcortical ROIs tend to form a single functional community.
The remaining ROIs tend to form a putative executive control community or a
putative default mode and salience community. We simulate the brain's dynamic
transitions between these community states using a Markov Chain Monte Carlo
random walk. We observe that simulated transition probabilities between basins
resemble empirically observed transitions between community allegiance states
in resting state fMRI data. These results collectively offer a view of the
brain as a dynamical system that transitions between basins of attraction
characterized by coherent activity in small groups of brain regions, and that
the strength of these attractors depends on the cognitive computations being
performed.