title: Frustrated double ionization in two-electron triatomic molecules

abstract:
  Using a semi-classical model, we investigate frustrated double ionization
(FDI) in $\mathrm{D_3^+}$, a two-electron triatomic molecule, when driven by an
intense, linearly polarized, near-infrared (800 nm) laser field. We compute the
kinetic energy release of the nuclei and find a good agreement between
experiment and our model. We explore the two pathways of FDI and show that,
with increasing field strength, over-the-barrier ionization overtakes tunnel
ionization as the underlying mechanism of FDI. Moreover, we compute the angular
distribution of the ion fragments for FDI and identify a feature that can
potentially be observed experimentally and is a signature of only one of the
two pathways of FDI.


title: Sparse Representations of Clifford and Tensor algebras in Maxima

abstract:
  Clifford algebras have broad applications in science and engineering. The use
of Clifford algebras can be further promoted in these fields by availability of
computational tools that automate tedious routine calculations. We offer an
extensive demonstration of the applications of Clifford algebras in
electromagnetism using the geometric algebra G3 = Cl(3,0) as a computational
model in the Maxima computer algebra system. We compare the geometric
algebra-based approach with conventional symbolic tensor calculations supported
by Maxima, based on the itensor package. The Clifford algebra functionality of
Maxima is distributed as two new packages called clifford - for basic
simplification of Clifford products, outer products, scalar products and
inverses; and cliffordan - for applications of geometric calculus.


title: Agnostic Estimation of Mean and Covariance

abstract:
  We consider the problem of estimating the mean and covariance of a
distribution from iid samples in $\mathbb{R}^n$, in the presence of an $\eta$
fraction of malicious noise; this is in contrast to much recent work where the
noise itself is assumed to be from a distribution of known type. The agnostic
problem includes many interesting special cases, e.g., learning the parameters
of a single Gaussian (or finding the best-fit Gaussian) when $\eta$ fraction of
data is adversarially corrupted, agnostically learning a mixture of Gaussians,
agnostic ICA, etc. We present polynomial-time algorithms to estimate the mean
and covariance with error guarantees in terms of information-theoretic lower
bounds. As a corollary, we also obtain an agnostic algorithm for Singular Value
Decomposition.


title: Observation of Quantum Equilibration in Dilute Bose Gases

abstract:
  We investigate experimentally the dynamical relaxation of a non-integrable
quantum many-body system to its equilibrium state. A Bose-Einstein condensate
is loaded into the first excited band of an optical lattice and let to evolve
up to a few hundreds of milliseconds. Signs of quantum equilibration are
observed. There is a period of time, roughly 40 ms long, during which both the
aspect ratio of the cloud and its momentum distribution remain constant. In
particular, the momentum distribution has a flat top and is not a Gaussian
thermal distribution. After this period, the cloud becomes classical as its
momentum distribution becomes Gaussian.


title:
Bayesian Inference of Recursive Sequences of Group Activities from
  Tracks

abstract:
  We present a probabilistic generative model for inferring a description of
coordinated, recursively structured group activities at multiple levels of
temporal granularity based on observations of individuals' trajectories. The
model accommodates: (1) hierarchically structured groups, (2) activities that
are temporally and compositionally recursive, (3) component roles assigning
different subactivity dynamics to subgroups of participants, and (4) a
nonparametric Gaussian Process model of trajectories. We present an MCMC
sampling framework for performing joint inference over recursive activity
descriptions and assignment of trajectories to groups, integrating out
continuous parameters. We demonstrate the model's expressive power in several
simulated and complex real-world scenarios from the VIRAT and UCLA Aerial Event
video data sets.


title: On principles of large deviation and selected data compression

abstract:
  The Shannon Noiseless coding theorem (the data-compression principle) asserts
that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell
-1\}$ and an asymptotic equipartition property, one can reduce the number of
stored strings $(x_0,\ldots ,x_{n-1})\in {\mathcal X}^n$ to $\ell^{nh}$ with an
arbitrary small error-probability. Here $h$ is the entropy rate of the source
(calculated to the base $\ell$). We consider further reduction based on the
concept of utility of a string measured in terms of a rate of a weight
function. The novelty of the work is that the distribution of memory is
analyzed from a probabilistic point of view. A convenient tool for assessing
the degree of reduction is a probabilistic large deviation principle. Assuming
a Markov-type setting, we discuss some relevant formulas, including the case of
a general alphabet.


title: Acceleration of Thermal Protons By Generic Phenomenological Mechanisms

abstract:
  We investigate heating and acceleration of protons from a thermal gas with a
generic diffusion and acceleration model, and subject to Coulomb scattering and
energy loss, as was carried out in Petrosian & East (2008) for electrons. As
protons gain energy their loss to electrons becomes important. Thus, we need to
solve the coupled proton-electron kinetic equation. We numerically solve the
coupled Fokker-Plank equations and computes the time evolution of the spectra
of both particles. We show that this can lead to a quasi-thermal component plus
a high energy nonthermal tail. We determine the evolution of nonthermal tail
and the quasi-thermal component. The results may be used to explore the
possibility of inverse bremsstrahlung radiation as a source of hard X-ray
emissions from hot sources such as solar flares, accretion disk coronas and the
intracluster medium of galaxy clusters. We find that emergence of nonthermal
protons is accompanied by excessive heating of the entire plasma, unless the
turbulence needed for scattering and acceleration is steeper than Kolmogorov
and the acceleration parameters, the duration of the acceleration, and/or the
initial distributions are significantly fine-tuned. These results severely
constraint the feasibility of nonthermal inverse bremsstrahlung process
producing hard X-ray emissions. However the nonthermal tail may be the seed
particles for further re-acceleration to relativistic energies, say by a shock.
In the Appendix we present some tests of the integrity of the algorithm used
and present a new formula for the energy loss rate due to inelastic
proton-proton interactions.


title: Wigner's theorem for an infinite set

abstract:
  It is well known that the closed subspaces of a Hilbert space form an
orthomodular lattice. Elements of this orthomodular lattice are the
propositions of a quantum mechanical system represented by the Hilbert space,
and by Gleason's theorem atoms of this orthomodular lattice correspond to pure
states of the system. Wigner's theorem says that the automorphism group of this
orthomodular lattice corresponds to the group of unitary and anti-unitary
operators of the Hilbert space. This result is of basic importance in the use
of group representations in quantum mechanics.
  The closed subspaces $A$ of a Hilbert space $\mathcal{H}$ correspond to
direct product decompositions $\mathcal{H}\simeq A\times A^\perp$ of the
Hilbert space, a result that lies at the heart of the superposition principle.
It has been shown that the direct product decompositions of any set, group,
vector space, and topological space form an orthomodular poset. This is the
basis for a line of study in foundational quantum mechanics replacing Hilbert
spaces with other types of structures. It is the purpose of this note to prove
a version of Wigner's theorem: for an infinite set $X$, the automorphism group
of the orthomodular poset Fact $(X)$ of direct product decompositions of $X$ is
isomorphic to the permutation group of $X$.
  The structure Fact $(X)$ plays the role for direct product decompositions of
a set that the lattice of equivalence relations plays for surjective images of
a set. So determining its automorphism group is of interest independent of its
application to quantum mechanics. Other properties of Fact $(X)$ are determined
in proving our version of Wigner's theorem, namely that Fact $(X)$ is atomistic
in a very strong way.


title:
Quasiprobability representations of quantum mechanics with minimal
  negativity

abstract:
  Quasiprobability representations, such as the Wigner function, play an
important role in various research areas. The inevitable appearance of
negativity in such representations is often regarded as a signature of
nonclassicality, which has profound implications for quantum computation.
However, little is known about the minimal negativity that is necessary in
general quasiprobability representations. Here we focus on a natural class of
quasiprobability representations that is distinguished by simplicity and
economy. We introduce three measures of negativity concerning the
representations of quantum states, unitary transformations, and quantum
channels, respectively. Quite surprisingly, all three measures lead to the same
representations with minimal negativity, which are in one-to-one correspondence
with the elusive symmetric informationally complete measurements. In addition,
most representations with minimal negativity are automatically covariant with
respect to the Heisenberg-Weyl groups. Furthermore, our study reveals an
interesting tradeoff between negativity and symmetry in quasiprobability
representations.


title: The scaling limit of critical Ising interfaces is CLE(3)

abstract:
  In this paper, we consider the set of interfaces between + and - spins
arising for the critical planar Ising model on a domain with + boundary
conditions, and show that it converges towards CLE(3).
  Our proof relies on the study of the coupling between the Ising model and its
random cluster (FK) representation, and of the interactions between FK and
Ising interfaces. The main idea is to construct an exploration process starting
from the boundary of the domain, to discover the Ising loops and to establish
its convergence to a conformally invariant limit. The challenge is that Ising
loops do not touch the boundary; we use the fact that FK loops touch the
boundary (and hence can be explored from the boundary) and that Ising loops in
turn touch FK loops, to construct a recursive exploration process that visits
all the macroscopic loops.
  A key ingredient in the proof is the convergence of Ising free arcs to the
Free Arc Ensemble (FAE), established in [BDH16]. Qualitative estimates about
the Ising interfaces then allow one to identify the scaling limit of Ising
loops as a conformally invariant collection of simple, disjoint SLE(3)-like
loops and thus by the Markovian characterization of [ShWe12] as a CLE(3).
  A technical point of independent interest contained in this paper is an
investigation of double points of interfaces in the scaling limit of critical
FK-Ising. It relies on the technology of [KeSm12].


title: Extracted Social Network Mining

abstract:
  In this paper we study the relationship between the resources of social
networks by exploring the Web as big data based on a simple search engine. We
have used set theory by utilizing the occurrence and co-occurrence for defining
the singleton or doubleton spaces of event in a search engine model, and then
provided them as representation of social actors and their relationship in
clusters. Thus, there are behaviors of social actors and their relation based
on Web.


title: Vanishing Absorption and Blueshifted Emission in FeLoBAL Quasars

abstract:
  We study the dramatic decrease in iron absorption strength in the iron
low-ionization broad absorption line quasar SDSS J084133.15+200525.8. We report
on the continued weakening of absorption in the prototype of this class of
variable broad absorption line quasar, FBQS J140806.2+305448. We also report a
third example of this class, SDSS J123103.70+392903.6; unlike the other two
examples, it has undergone an increase in observed continuum brightness (at
3000~\AA\ rest-frame) as well as a decrease in iron absorption strength. These
changes could be caused by absorber transverse motion or by ionization
variability. We note that the \mgii\ and UV \feii\ lines in several FeLoBAL
quasars are blueshifted by thousands of \kms\ relative to the \Hb\ emission
line peak. We suggest that such emission arises in the outflowing winds
normally seen only in absorption.


title: Finite groups with star-free noncyclic graphs

abstract:
  For a finite noncyclic group $G$, let $\Cyc(G)$ be a set of elements $a$ of
$G$ such that $\langle a,b\rangle$ is cyclic for each $b$ of $G$. The noncyclic
graph of $G$ is a graph with the vertex set $G\setminus \Cyc(G)$, having an
edge between two distinct vertices $x$ and $y$ if $\langle x, y\rangle$ is not
cyclic. In this paper, we classify all finite noncyclic groups whose noncyclic
graphs are $K_{1,n}$-free, where $3\leq n\leq 6$.


title: Cardiac Motion Analysis by Temporal Flow Graphs

abstract:
  Cardiac motion analysis from B-mode ultrasound sequence is a key task in
assessing the health of the heart. The paper proposes a new methodology for
cardiac motion analysis based on the temporal behaviour of points of interest
on the myocardium. We define a new signal called the Temporal Flow Graph (TFG)
which depicts the movement of a point of interest over time. It is a graphical
representation derived from a flow field and describes the temporal evolution
of a point. We prove that TFG for an object undergoing periodic motion is also
periodic. This principle can be utilized to derive both global and local
information from a given sequence. We demonstrate this for detecting motion
irregularities at the sequence, as well as regional levels on real and
synthetic data. A coarse localisation of anatomical landmarks such as centres
of left/right cavities and valve points is also demonstrated using TFGs.


title: On exact and optimal recovering of missing values for sequences

abstract:
  The paper studies recoverability of missing values for sequences in a
pathwise setting without probabilistic assumptions. This setting is oriented on
a situation where the underlying sequence is considered as a sole sequence
rather than a member of an ensemble with known statistical properties.
Sufficient conditions of recoverability are obtained; it is shown that
sequences are recoverable if there is a certain degree of degeneracy of the
Z-transforms. We found that, in some cases, this degree can be measured as the
number of the derivatives of Z-transform vanishing at a point. For processes
with non-degenerate Z-transform, an optimal recovering based on the projection
on a set of recoverable sequences is suggested. Some robustness of the solution
with respect to noise contamination and truncation is established.


title: Sharp bounds for Boltzmann and Landau collision operators

abstract:
  The aim of the work is to provide a stable method to get sharp bounds for
Boltzmann and Landau operators in weighted Sobolev spaces and in anisotropic
spaces. All the sharp bounds are given for the original Boltzmann and Landau
operators. The sharpness means the lower and upper bounds for the operators are
consistent with the behavior of the linearized operators. Moreover, we make
clear the difference between the bounds for the original operators and those
for the linearized ones.
  According to the Bobylev's formula, we introduce two types of dyadic
decompositions performed in both phase and frequency spaces to make full use of
the interaction and the cancellation. It allows us to see clearly which part of
the operator behaves like a Laplace type operator and which part is dominated
by the anisotropic structure. It is the key point to get the sharp bounds in
weighted Sobolev spaces and in anisotropic spaces. Based on the geometric
structure of the elastic collision, we make a geometric decomposition to
capture the anisotropic structure of the collision operator. More precisely, we
make it explicit that the fractional Laplace-Beltrami operator really exists in
the structure of the collision operator. It enables us to derive the sharp
bounds in anisotropic spaces and then complete the entropy dissipation
estimates. The structures mentioned above are so stable that we can apply them
to the rescaled Boltzmann collision operator in the process of the grazing
collisions limit. Then we get the sharp bounds for the Landau collision
operator by passing to the limit. We remark that our analysis used here will
shed light on the investigation of the asymptotics from Boltzmann equation to
Landau equation.


title:
Competition between Alkalide Characteristics and Nonlinear Optical
  Properties in OLi3-M-Li3O (M=Li, Na and K) Complexes

abstract:
  Alkalides possess enhanced nonlinear optical (NLO) responses due to
localization of excess electrons on alkali metals. We have proposed a new class
of alkalides by sandwiching alkali atoms (M) between two Li3O superalkali
clusters at MP2/6-311++G(d,p) level. We notice a competition between alkalide
characteristics and NLO properties in OLi3-M-Li3O (M=Li, Na and K) isomers. For
instance, the atomic charge on M (qM) in D2h structure is -0.58e for M=Li and
its first static mean hyperpolarizablity (\b{eta}o) is 1 a.u., but in C2v
structure, qM=-0.12e and \b{eta}o= 3.4*103 a.u. More interestingly, the
\b{eta}o value for M=K (C2v) increases to 1.9*104 a.u. in which qM=0.24e. These
findings may provide new insights into the design of alkalides, an unusual
class of salts and consequently, lead to further researches in this direction.


title:
An Arithmetic Coding Scheme for Blocked-based Compressive Sensing of
  Images

abstract:
  Differential pulse-code modulation (DPCM) is recently coupled with uniform
scalar quantization (SQ) to improve the rate-distortion (RD) performance for
the block-based quantized compressive sensing (CS) of images. In this
framework, for each block's CS measurements, a prediction is generated based on
the reconstructed CS measurements of the previous blocks and subtracted from
measurements of the current block in the measurement domain. The resulting
residual is then quantized by uniform SQ to generate the quantization index.
However, the entropy coding is still required to remove the statistical
redundancies between the quantization indices and generate the bitstream. Thus,
in this paper, we proposed an arithmetic coding scheme for the quantization
index within DPCM-plus-SQ framework by analyzing their statistics. Experimental
results demonstrate that further RD performance can be achieved compared to
original DPCM-plus-SQ scheme and transform coefficient coding in CABAC.


title:
PFO: A Parallel Friendly High Performance System for Online Query and
  Update of Nearest Neighbors

abstract:
  Nearest Neighbor(s) search is the fundamental computational primitive to
tackle massive dataset. Locality Sensitive Hashing (LSH) has been a bracing
tool for Nearest Neighbor(s) search in high dimensional spaces. However,
traditional LSH systems cannot be applied in online big data systems to handle
a large volume of query/update requests, because most of the systems optimize
the query efficiency with the assumption of infrequent updates and missing the
parallel-friendly design. As a result, the state-of-the-art LSH systems cannot
adapt the system response to the user behavior interactively.
  In this paper, we propose a new LSH system called PFO. It handles
query/update requests in RAM and scales the system capacity by using flash
memory. To achieve high streaming data throughput, PFO adopts a
parallel-friendly indexing structure while preserving the distance between data
points. Further, it accommodates inbound data in real-time and dispatches
update requests intelligently to eliminate the cross-threads synchronization.
We carried out extensive evaluations with large synthetic and standard
benchmark datasets. Results demonstrate that PFO delivers shorter latency and
offers scalable capacity compared with the existing LSH systems. PFO serves
with higher throughput than the state-of-the-art LSH indexing structure when
dealing with online query/update requests to nearest neighbors. Meanwhile, PFO
returns neighbors with much better quality, thus being efficient to handle
online big data applications, e.g. streaming recommendation system, interactive
machine learning systems.


title: Deep Learning with Eigenvalue Decay Regularizer

abstract:
  This paper extends our previous work on regularization of neural networks
using Eigenvalue Decay by employing a soft approximation of the dominant
eigenvalue in order to enable the calculation of its derivatives in relation to
the synaptic weights, and therefore the application of back-propagation, which
is a primary demand for deep learning. Moreover, we extend our previous
theoretical analysis to deep neural networks and multiclass classification
problems. Our method is implemented as an additional regularizer in Keras, a
modular neural networks library written in Python, and evaluated in the
benchmark data sets Reuters Newswire Topics Classification, IMDB database for
binary sentiment classification, MNIST database of handwritten digits and
CIFAR-10 data set for image classification.


title:
Quantitative Volume Space Form Rigidity Under Lower Ricci Curvature
  Bound

abstract:
  Let $M$ be a compact $n$-manifold of $\operatorname{Ric}_M\ge (n-1)H$ ($H$ is
a constant). We are concerned with the following space form rigidity: $M$ is
isometric to a space form of constant curvature $H$ under either of the
following conditions:
  (i) There is $\rho>0$ such that for any $x\in M$, the open $\rho$-ball at
$x^*$ in the (local) Riemannian universal covering space, $(U^*_\rho,x^*)\to
(B_\rho(x),x)$, has the maximal volume i.e., the volume of a $\rho$-ball in the
simply connected $n$-space form of curvature $H$.
  (ii) For $H=-1$, the volume entropy of $M$ is maximal i.e. $n-1$ ([LW1]).
  The main results of this paper are quantitative space form rigidity i.e.,
statements that $M$ is diffeomorphic and close in the Gromov-Hausdorff topology
to a space form of constant curvature $H$, if $M$ almost satisfies, under some
additional condition, the above maximal volume condition. For $H=1$, the
quantitative spherical space form rigidity improves and generalizes the
diffeomorphic sphere theorem in [CC2].


title:
Theoretical constraints on masses of heavy particles in Left-Right
  Symmetric Models

abstract:
  Left-Right symmetric models with general $g_L \neq g_R$ gauge couplings which
include bidoublet and triplet scalar multiplets are studied. Possible scalar
mass spectra are outlined by imposing Tree-Unitarity, and Vacuum Stability
criteria and also using the bounds on neutral scalar masses $M_{\rm H^{ FCNC}}$
which assure the absence of Flavour Changing Neutral Currents (FCNC). We are
focusing on mass spectra relevant for the LHC analysis, i.e., the scalar masses
are around TeV scale. As all non-standard heavy particle masses are related to
the vacuum expectation value (VEV) of the right-handed triplet ($v_R$), the
combined effects of relevant Higgs potential parameters and $M_{\rm H^{ FCNC}}$
regulate the lower limits of heavy gauge boson masses. The complete set of
Renormalization Group Evolutions for all couplings are provided at the 1-loop
level, including the mixing effects in the Yukawa sector. Most of the scalar
couplings suffer from the Landau poles at the intermediate scale $Q \sim
10^{6.5}$ GeV, which in general coincides with violation of the Tree-Unitarity
bounds.


title: Integral cohomology groups of real toric manifolds and small covers

abstract:
  For a simplicial complex $K$ with $m$ vertices, there is a canonical $\mathbb
Z_2^m$-space known as a real moment angle complex $\mathbb R \mathcal Z_K$. In
this paper, we consider the quotient spaces $Y=\mathbb R \mathcal Z_K / \mathbb
Z_2^{k}$, where $K$ is a pure shellable complex and $\mathbb Z_2^k \subset
\mathbb Z_2^m$ is a maximal free action on $\mathbb R \mathcal Z_K$. A typical
example of such spaces is a small cover, where a small cover is known as a
topological analog of a real toric manifold. We compute the integral cohomology
group of $Y$ by using the PL cell decomposition obtained from a shelling of
$K$. In addition, we compute the Bockstein spectral sequence of $Y$ explicitly.


title:
Study on the high spectral intensity at the Dirac energy of single-layer
  graphene on an SiC substrate

abstract:
  We have investigated electron band structure of epitaxially grown graphene on
an SiC(0001) substrate using angle-resolved photoemission spectroscopy. In
single-layer graphene, abnormal high spectral intensity is observed at the
Dirac energy whose origin has been questioned between in-gap states induced by
the buffer layer and plasmaron bands induced by electron-plasmon interactions.
With the formation of double-layer graphene, the Dirac energy does not show the
high spectral intensity any longer different from the single-layer case. The
inconsistency between the two systems suggests that the main ingredient of the
high spectral intensity at the Dirac energy of single-layer graphene is the
electronic states originating from the coupling of the graphene $\pi$ bands to
the localized $\pi$ states of the buffer layer, consistent with the theoretical
prediction on the presence of in-gap states.


title:
Holographic insulator/superconductor transitions in the three
  dimensional AdS soliton

abstract:
  We investigate the holographic description of a superconductor constructed in
the (2+1)-dimensional AdS soliton background in the probe limit. We study the
holographic properties through both analytical and numerical methods. With
analytical methods, we are the first to obtain the exact formula for critical
phase transition points as $\mu_{c}=1+\sqrt{1+m^2}$. Around the transition
points, we find a correspondence between the value of the scalar field at the
tip and the scalar operator at infinity. We also generalize the front
properties to holographic models in higher dimensional AdS soliton spacetime.
Moreover, we examine effects of the scalar mass on stability of phase
transitions with numerical methods. With $m^{2}\in (-0.38,0]$, we arrive at the
classical second order insulator/superconductor phase transition. Surprisingly,
there is no stable superconducting phases in cases of $m^{2}\in (-1,-0.38]$. In
other words, superconductor only exists in a certain range of the scalar mass
in the (2+1)-dimensional AdS soliton spacetime, which is very different from
properties in other spacetime.


title: Statistical and Deterministic Dynamics of Maps with Memory

abstract:
  We consider a dynamical system to have memory if it remembers the current
state as well as the state before that. The dynamics is defined as follows:
$x_{n+1}=T_{\alpha}(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha)\cdot
x_{n-1}),$ where $\tau$ is a one-dimensional map on $I=[0,1]$ and $0<\alpha <1$
determines how much memory is being used. $T_{\alpha}$ does not define a
dynamical system since it maps $U=I\times I$ into $I$. In this note we let
$\tau $ to be the symmetric tent map. We shall prove that for $0<\alpha <0.46,$
the orbits of $\{x_{n}\}$ are described statistically by an absolutely
continuous invariant measure (acim) in two dimensions. As $\alpha $ approaches
$0.5 $ from below, that is, as we approach a balance between the memory state
and the present state, the support of the acims become thinner until at $\alpha
=0.5$, all points have period 3 or eventually possess period 3. For $0.5<\alpha
<0.75$, we have a global attractor: for all starting points in $U$ except
$(0,0)$, the orbits are attracted to the fixed point $(2/3,2/3).$ At
$\alpha=0.75,$ we have slightly more complicated periodic behavior.


title:
A Revisit on Commutators of linear and bilinear Fractional Integral
  Operator

abstract:
  Let $I_{\alpha}$ be the linear and $\mathcal{I}_{\alpha}$ be the bilinear
fractional integral operators. In the linear setting, it is known that the
two-weight inequality holds for the first order commutators of $I_{\alpha}$.
But the method can't be used to obtain the two weighted norm inequality for the
higher order commutators of $I_{\alpha}$. In this paper, we first give an
alternative proof for the first order commutators of $I_{\alpha}$. This new
approach allows us to consider the higher order commutators. This was done by
showing that the commutator $[b,I_{\alpha}]$ can be represented as a finite
linear combination of some paraproducts. Then, by using the Cauchy integral
theorem, we show that the two-weight inequality holds for the higher order
commutators of $I_{\alpha}$. In the bilinear setting, we present a dyadic proof
for the characterization between $BMO$ and the boundedness of
$[b,\mathcal{I}_{\alpha}]$. Moreover, some bilinear paraproducts are also
treated in order to obtain the boundedness of $[b,\mathcal{I}_{\alpha}]$.


title:
Moment Generating Functions of Generalized Wireless Fading Channels and
  Applications in Wireless Communication Theory

abstract:
  In this paper, new exact and approximate moment generating functions (MGF)
expression for generalized fading models are derived. Specifically, we consider
the ${\eta}-{\lambda}-{\mu}$, ${\alpha}-{\mu}$, ${\alpha}-{\eta}-{\mu}$,
${\alpha}-{\lambda}-{\mu}$, ${\alpha}-{\kappa}-{\mu}$, and
${\alpha}-{\lambda}-{\eta}-{\mu}$ generalized fading distributions to derive
approximate MGF expressions. The new expressions are very accurate and, in
contrast to earlier results in the literature, avoid any complicated special
functions, e.g. the Meijer-$G$ and Fox $H$-functions. As such, the new MGF
expressions allow easier and more efficient analytical manipulations, which
also apply for their special cases such as the Rayleigh, Rice, and Nakagami-m
fading. As an illustrative application, the average bit error rates for each of
the fading models are evaluated using the new derived MGF expressions. The
accuracy of the analytical results by using the numerically computed results as
a basis of comparison as well as published results from the literature.


title: Spectral flow for real skew-adjoint Fredholm operators

abstract:
  An analytic definition of a $\mathbb{Z}_2$-valued spectral flow for paths of
real skew-adjoint Fredholm operators is given. It counts the parity of the
number of changes in the orientation of the eigenfunctions at eigenvalue
crossings through $0$ along the path. The $\mathbb{Z}_2$-valued spectral flow
is shown to satisfy a concatenation property and homotopy invariance, and it
provides an isomorphism on the fundamental group of the real skew-adjoint
Fredholm operators. Moreover, it is connected to a $\mathbb{Z}_2$-index pairing
for suitable paths. Applications concern the zero energy bound states at
defects in a Majorana chain and a spectral flow interpretation for the
$\mathbb{Z}_2$-polarization in these models.


title: Miquel point and isogonal conjugation

abstract:
  We study the possible positions of the Miquel point in the plane of a given
triangle, which Miquel triangles are similar to the given one. We found out
that these positions are eleven. We also study the possible positions of the
Miquel point in the plane of a given triangle, where among the families of
Miquel triangles there are triangles, which are similar to the given triangle.
We study which of them are isogonal conjugated.


title:
Parity check systems of nonlinear codes over finite commutative
  Frobenius rings

abstract:
  The concept of parity check matrices of linear binary codes has been extended
by Heden [9] to parity check systems of nonlinear binary codes. In the present
paper we extend this concept to parity check systems of nonlinear codes over
finite commutative Frobenius rings. Using parity check systems, results on how
to get some fundamental properties of the codes are given. Moreover, parity
check systems and its connection to characters is investigated and a
MacWilliams type theorem on the distance distribution is given.


title: Better Analysis of GREEDY Binary Search Tree on Decomposable Sequences

abstract:
  In their seminal paper [Sleator and Tarjan, J.ACM, 1985], the authors
conjectured that the splay tree is dynamically optimal binary search tree
(BST). In spite of decades of intensive research, the problem remains open.
Perhaps a more basic question, which has also attracted much attention, is if
there exists any dynamically optimal BST algorithm. One such candidate is
GREEDY which is a simple and intuitive BST algorithm [Lucas, Rutgers Tech.
Report, 1988; Munro, ESA, 2000; Demaine, Harmon, Iacono, Kane and Patrascu,
SODA, 2009]. [Demaine et al., SODA, 2009] showed a novel connection between a
geometric problem.
  Since dynamic optimality conjecture in its most general form remains elusive
despite much effort, researchers have studied this problem on special
sequences. Recently, [Chalermsook, Goswami, Kozma, Mehlhorn and Saranurak,
FOCS, 2015] studied a type of sequences known as $k$-{\em decomposable
sequences} in this context, where $k$ parametrizes easiness of the sequence.
Using tools from forbidden submatrix theory, they showed that GREEDY takes
$n2^{O(k^2)}$ time on this sequence and explicitly raised the question of
improving this bound.
  In this paper, we show that GREEDY takes $O(n \log{k})$ time on
$k$-decomposable sequences. In contrast to the previous approach, ours is based
on first principles. One of the main ingredients of our result is a new
construction of a lower bound certificate on the performance of any algorithm.
This certificate is constructed using the execution of GREEDY, and is more
nuanced and possibly more flexible than the previous independent set
certificate of Demaine et al. This result, which is applicable to all
sequences, may be of independent interest and may lead to further progress in
analyzing GREEDY on $k$-decomposable as well as general sequences.


title:
Phase transition and thermodynamic stability of topological black holes
  in Ho\v{r}ava-Lifshitz gravity

abstract:
  On the basis of horizon thermodynamics, we study the thermodynamic stability
and $P-V$ criticality of topological black holes constructed in
Ho\v{r}ava-Lifshitz (HL) gravity without the detailed-balance condition (with
general $\epsilon$). In the framework of horizon thermodynamics, we do not need
the concrete black hole solution (the metric function) and the concrete matter
fields. It is shown that the HL black hole for $k=0$ is always
thermodynamically stable. For $k=1$, the thermodynamic behaviors and $P-V$
criticality of the HL black hole are similar to those of RN-AdS black hole for
some $\epsilon$. For $k=-1$, the temperature is classified into six types by
their different features. Among them, we mainly focus on the type with triply
degenerate thermodynamic state. It is also shown that there is a "thermodynamic
singularity" for the $k=-1$ HL black hole, where the temperature and Gibbs free
energy both diverge apart from a special pressure $P_s$.


title:
Heijal's theorem for parabolic projective structures on non compact
  surfaces

abstract:
  In this note, we prove that the holonomy map from the set of equivalence
classes of projective structures of parabolic type on non compact surfaces to
the set of equivalence classes of parabolic representations of the fundamental
group of the surface to P SL 2 (C) is a local biholomorphism.


title:
An accurate scheme to solve cluster dynamics equations using a
  Fokker-Planck approach

abstract:
  We present a numerical method to accurately simulate particle size
distributions within the formalism of rate equation cluster dynamics. This
method is based on a discretization of the associated Fokker-Planck equation.
We show that particular care has to be taken to discretize the advection part
of the Fokker-Planck equation, in order to avoid distortions of the
distribution due to numerical diffusion. For this purpose we use the
Kurganov-Noelle-Petrova scheme coupled with the monotonicity-preserving
reconstruction MP5, which leads to very accurate results. The interest of the
method is highlighted on the case of loop coarsening in aluminum. We show that
the choice of the models to describe the energetics of loops does not
significantly change the normalized loop distribution, while the choice of the
models for the absorption coefficients seems to have a significant impact on
it.


title:
Convergence of weak K\"ahler-Ricci Flows on minimal models of positive
  Kodaira dimension

abstract:
  Studying the behavior of the K\"ahler-Ricci flow on mildly singular
varieties, one is naturally lead to study weak solutions of degenerate
parabolic complex Monge-Amp\`ere equations.
  In this article, the third of a series on this subject, we study the long
term behavior of the normalized K\"ahler-Ricci flow on mildly singular
varieties of positive Kodaira dimension, generalizing results of Song and Tian
who dealt with smooth minimal models.


title:
AUV Rendezvous Online Path Planning in a Highly Cluttered Undersea
  Environment Using Evolutionary Algorithms

abstract:
  In this study, a single autonomous underwater vehicle (AUV) aims to
rendezvous with a submerged leader recovery vehicle through a cluttered and
variable operating field. The rendezvous problem is transformed into a
nonlinear optimal control problem (NOCP) and then numerical solutions are
provided. A penalty function method is utilized to combine the boundary
conditions, vehicular and environmental constraints with the performance index
that is final rendezvous time.Four evolutionary based path planning methods
namely particle swarm optimization (PSO), biogeography-based optimization
(BBO), differential evolution (DE) and Firefly algorithm (FA) are employed to
establish a reactive planner module and provide a numerical solution for the
proposed NOCP. The objective is to synthesize and analysis the performance and
capability of the mentioned methods for guiding an AUV from loitering point
toward the rendezvous place through a comprehensive simulation study.The
proposed planner module entails a heuristic for refining the path considering
situational awareness of underlying environment, encompassing static and
dynamic obstacles overwhelmed in spatiotemporal current vectors.This leads to
accommodate the unforeseen changes in the operating field like emergence of
unpredicted obstacles or variability of current vector filed and turbulent
regions. The simulation results demonstrate the inherent robustness and
significant efficiency of the proposed planner in enhancement of the vehicle's
autonomy in terms of using current force, coping undesired current disturbance
for the desired rendezvous purpose. Advantages and shortcoming of all utilized
methods are also presented based on the obtained results.


title: Differential rotation in K, G, F and A stars

abstract:
  Rotational light modulation in Kepler photometry of K - A stars is used to
estimate the absolute rotational shear. The rotation frequency spread in 2562
carefully selected stars with known rotation periods is measured using
time-frequency diagrams. The variation of rotational shear as a function of
effective temperature in restricted ranges of rotation period is determined.
The shear increases to a maximum in F stars, but decreases somewhat in the A
stars. Theoretical models reproduce the temperature variation quite well. The
dependence of rotation shear on rotation rate in restricted temperature ranges
is also determined. The dependence of the shear on the rotation rate is weak in
K and G stars, increases rapidly for F stars and is strongest in A stars. For
stars earlier than type K, a discrepancy exists between the predicted and
observed variation of shear with rotation rate. There is a strong increase in
the fraction of stars with zero frequency spread with increasing effective
temperature. The time-frequency diagrams for A stars are no different from
those in cool stars, further supporting the presence of spots in stars with
radiative envelopes.


title: Around the Thom-Sebastiani theorem

abstract:
  For germs of holomorphic functions $f : (\mathbf{C}^{m+1},0) \to
(\mathbf{C},0)$, $g : (\mathbf{C}^{n+1},0) \to (\mathbf{C},0)$ having an
isolated critical point at 0 with value 0, the classical Thom-Sebastiani
theorem describes the vanishing cycles group $\Phi^{m+n+1}(f \oplus g)$ (and
its monodromy) as a tensor product $\Phi^m(f) \otimes \Phi^n(g)$, where $(f
\oplus g)(x,y) = f(x) + g(y), x = (x_0,...,x_m), y = (y_0,...,y_n)$. We prove
algebraic variants and generalizations of this result in \'etale cohomology
over fields of any characteristic, where the tensor product is replaced by a
certain local convolution product, as suggested by Deligne. They generalize
arXiv:1105.5210. The main ingredient is a K\"unneth formula for $R\Psi$ in the
framework of Deligne's theory of nearby cycles over general bases. In the last
section, we study the tame case, and the relations between tensor and
convolution products, in both global and local situations.


title:
Continuous homomorphisms between algebras of iterated Laurent series
  over a ring

abstract:
  We study continuous homomorphisms between algebras of iterated Laurent series
over a commutative ring. We give a full description of such homomorphisms in
terms of a discrete data determined by the images of parameters. In similar
terms, we give a criterion of invertibility of an endomorphism and provide an
explicit formula for the inverse endomorphism. We study the behavior of the
higher-dimensional residue under continuous homomorphisms.


title: Spectral flow and resonance index

abstract:
  It has been shown recently that spectral flow admits a natural integer-valued
extension to essential spectrum. This extension admits four different
interpretations; two of them are singular spectral shift function and total
resonance index. In this work we study resonance index outside essential
spectrum.
  Among results of this paper are the following.
  1. Total resonance index satisfies Robbin-Salamon axioms for spectral flow.
  2. Direct proof of equality "total resonance index = intersection number".
  3. Direct proof of equality "total resonance index = total Fredholm index".
  4. (a) Criteria for a perturbation~$V$ to be tangent to the~resonance set at
a point~$H,$ where the resonance set is the infinite-dimensional variety of
self-adjoint perturbations of the initial self-adjoint operator~$H_0$ which
have~$\lambda$ as an eigenvalue. (b) Criteria for the order of tangency of a
perturbation~$V$ to the resonance set.
  5. Investigation of the root space of the compact operator
$(H_0+sV-\lambda)^{-1}V$ corresponding to an eigenvalue $(s-r_\lambda)^{-1},$
where $H_0+r_\lambda V$ is a point of the resonance set.
  This analysis gives a finer information about behaviour of discrete spectrum
compared to spectral flow.
  Finally, many results of this paper are non-trivial even in finite
dimensions, in which case they can be and were tested in numerical experiments.


title: Torsional rigidity for regions with a Brownian boundary

abstract:
  Let $T^m$ be the $m$-dimensional unit torus, $m \in N$. The torsional
rigidity of an open set $\Omega \subset T^m$ is the integral with respect to
Lebesgue measure over all starting points $x \in \Omega$ of the expected
lifetime in $\Omega$ of a Brownian motion starting at $x$. In this paper we
consider $\Omega = T^m \backslash \beta[0,t]$, the complement of the path
$\beta[0,t]$ of an independent Brownian motion up to time $t$. We compute the
leading order asymptotic behaviour of the expectation of the torsional rigidity
in the limit as $t \to \infty$. For $m=2$ the main contribution comes from the
components in $T^2 \backslash \beta [0,t]$ whose inradius is comparable to the
largest inradius, while for $m=3$ most of $T^3 \backslash \beta [0,t]$
contributes. A similar result holds for $m \geq 4$ after the Brownian path is
replaced by a shrinking Wiener sausage $W_{r(t)}[0,t]$ of radius
$r(t)=o(t^{-1/(m-2)})$, provided the shrinking is slow enough to ensure that
the torsional rigidity tends to zero. Asymptotic properties of the capacity of
$\beta[0,t]$ in $R^3$ and $W_1[0,t]$ in $R^m$, $m \geq 4$, play a central role
throughout the paper. Our results contribute to a better understanding of the
geometry of the complement of Brownian motion on $T^m$, which has received a
lot of attention in the literature in past years.


title:
A comprehensive characterization of the set of polynomial curves with
  rational rotation-minimizing frames

abstract:
  A rotation-minimizing frame $({\bf f}_1,{\bf f}_2,{\bf f}_3)$ on a space
curve ${\bf r}(\xi)$ defines an orthonormal basis for $\mathbb{R}^3$ in which
${\bf f}_1={\bf r}'/|{\bf r}'|$ is the curve tangent, and the normal-plane
vectors ${\bf f}_2$, ${\bf f}_3$ exhibit no instantaneous rotation about ${\bf
f}_1$. Polynomial curves that admit rational rotation-minimizing frames (or
RRMF curves) form a subset of the Pythagorean-hodograph (PH) curves, specified
by integrating the form ${\bf r}'(\xi)={\cal A}(\xi)\,{\bf i}\,{\cal A}^*(\xi)$
for some quaternion polynomial ${\cal A}(\xi)$. By introducing the notion of
rotation indicatrix and of core of the quaternion polynomial ${\cal A}(\xi)$, a
comprehensive characterization of the complete space of RRMF curves is
developed, that subsumes all previously known special cases. This novel
characterization helps clarify the structure of the complete space of RRMF
curves, distinguishes the spatial RRMF curves from trivial (planar) cases, and
paves the way toward new construction algorithms.


title:
Numerical Evaluation of the Bose-Ghost Propagator in Minimal Landau
  Gauge on the Lattice

abstract:
  We present numerical details of the evaluation of the so-called Bose-ghost
propagator in lattice minimal Landau gauge, for the SU(2) case in four
Euclidean dimensions. This quantity has been proposed as a carrier of the
confining force in the Gribov-Zwanziger approach and, as such, its infrared
behavior could be relevant for the understanding of color confinement in
Yang-Mills theories. Also, its nonzero value can be interpreted as direct
evidence of BRST-symmetry breaking, which is induced when restricting the
functional measure to the first Gribov region Omega. Our simulations are done
for lattice volumes up to 120^4 and for physical lattice extents up to 13.5 fm.
We investigate the infinite-volume and continuum limits.


title:
The early gaseous and stellar mass assembly of Milky Way-type galaxy
  halos

abstract:
  How the Milky Way has accumulated its mass over the Hubble time, whether
significant amounts of gas and stars were accreted from satellite galaxies, or
whether the Milky Way has experienced an initial gas assembly and then evolved
more-or-less in isolation is one of the burning questions in modern astronomy,
because it has consequences for our understanding of galaxy formation in the
cosmological context. Here we present the evolutionary model of a Milky
Way-type satellite system zoomed into a cosmological large-scale simulation.
Embedded into Dark Matter halos and allowing for baryonic processes these
chemo-dynamical simulations aim at studying the gas and stellar loss from the
satellites to feed the Milky Way halo and the stellar chemical abundances in
the halo and the satellite galaxies.


title:
Self-consistent relativistic quasiparticle random-phase approximation
  and its applications to charge-exchange excitations and $\beta$-decay
  half-lives

abstract:
  The self-consistent quasiparticle random-phase approximation (QRPA) approach
is formulated in the canonical single-nucleon basis of the relativistic
Hatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study the
isobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Sn
isotopes as examples. It is found that self-consistent treatment of the
particle-particle residual interaction is essential to concentrate the IAS in a
single peak for open-shell nuclei and the Coulomb exchange term is very
important to predict the IAS energies. For the GTR, the isovector pairing can
increase the calculated GTR energy, while the isoscalar pairing has an
important influence on the low-lying tail of the GT transition. Furthermore,
the QRPA approach is employed to predict nuclear $\beta$-decay half-lives. With
an isospin-dependent pairing interaction in the isoscalar channel, the
RHFB+QRPA approach almost completely reproduces the experimental $\beta$-decay
half-lives for nuclei up to the Sn isotopes with half-lives smaller than one
second. Large discrepancies are found for the Ni, Zn, and Ge isotopes with
neutron number smaller than $50$, as well as the Sn isotopes with neutron
number smaller than $82$. The potential reasons for these discrepancies are
discussed in detail.


title:
Turbulent mixing and a generalized phase transition in shear-thickening
  fluids

abstract:
  This paper presents a new theory of turbulent mixing in stirred reactors. The
degree of homogeneity of a mixed fluid may be characterized by the Kolmogorov
micro-scale. The smaller its value, the better homogeneity. The micro-scale
scales inversely with the fourth root of the energy dissipation rate in the
stirring process. The higher this rate, the smaller lambda, and the better the
homogeneity in the reactor. This is true for Newtonian fluids. In non-Newtonian
fluids the situation is different. For instance, in shear-thickening fluids it
is plausible that high shear rates thicken the fluid and might strangle the
mixing. The internal interactions between different fluid-mechanical and
colloidal variables are subtle, namely due to the (until recently) very limited
understanding of turbulence. Starting from a qualitatively new turbulence
theory for inviscid fluids [Baumert, 2013], giving e.g. the Karman constant as
$(2\pi)^{-1/2} = 0.40$ [the super-pipe in Princeton gave 0.40 p/m 0.02, Bailey
et al., 2014], we generalize this approach to the case of viscous fluids and
derive equations which in the steady state exhibit two solutions. One solution
branch describes a state of good mixing, the other a state of strangled
turbulence. The physical system cannot be in two different steady states at the
same time. But it is physically admissible to switch between the two steady
states by non-stationary transitions, maybe in a chaotic fashion.


title: The Dolgopyat inequality in \BV\ for non-Markov maps

abstract:
  Let $F$ be a (non-Markov) countably piecewise expanding interval map
satisfying certain regularity conditions, and $\tilde\L$ the corresponding
transfer operator. We prove the Dolgopyat inequality for the twisted operator
$\tilde\L_s(v) = \tilde\L_s(e^{s\varphi}v)$ acting on the space BV of functions
of bounded variation, where $\varphi$ is a piecewise $C^1$ roof function.


title: Design and stability of a family of deployable structures

abstract:
  A large family of deployable filamentary structures can be built by
connecting two elastic rods along their length. The resulting structure has
interesting shapes that can be stabilized by tuning the material properties of
each rod. To model this structure and study its stability, we show that the
equilibrium equations describing unloaded states can be derived from a
variational principle. We then use a novel geometric method to study the
stability of the resulting equilibria. As an example we apply the theory to
establish the stability of all possible equilibria of the Bristol ladder.


title: A new summability method for divergent series

abstract:
  The theory of summability of divergent series is a major branch of
mathematical analysis that has found important applications in engineering and
science. It addresses methods of assigning natural values to divergent sums,
whose prototypical examples include the Abel summation method, the Cesaro
means, and Borel summability method. In this paper, we introduce a new
summability method for divergent series, and derive an asymptotic expression to
its error term. We show that it is both regular and linear, and that it arises
quite naturally in the study of local polynomial approximations of analytic
functions. Because the proposed summability method is conceptually simple and
can be implemented in a few lines of code, it can be quite useful in practice
for computing the values of divergent sums.


title: Uniquely Restricted Matchings in Interval Graphs

abstract:
  A matching $M$ in a graph $G$ is said to be uniquely restricted if there is
no other matching in $G$ that matches the same set of vertices as $M$. We
describe a polynomial-time algorithm to compute a maximum cardinality uniquely
restricted matching in an interval graph, thereby answering a question of
Golumbic et al. ("Uniquely restricted matchings", M. C. Golumbic, T. Hirst and
M. Lewenstein, Algorithmica, 31:139--154, 2001). Our algorithm actually solves
the more general problem of computing a maximum cardinality "strong independent
set" in an interval nest digraph, which may be of independent interest.
Further, we give linear-time algorithms for computing maximum cardinality
uniquely restricted matchings in proper interval graphs and bipartite
permutation graphs.


title: Interpretation of the Omori Law

abstract:
  The known Omori law is presented in the form of differential equation that
describes the evolution of the aftershock activity. This equation is derived
hypothetically with taking into account deactivation of the faults in
epicentral zone of the main shock. A generalization of the Omori law is
proposed.


title: Ridigity of Ricci Solitons with Weakly Harmonic Weyl Tensors

abstract:
  In this paper, we prove rigidity results on gradient shrinking Ricci solitons
with weakly harmonic Weyl curvature tensors. Let $(M^n, g)$ be a compact
gradient shrinking Ricci soliton satisfying ${\rm Ric}_g + Ddf = \rho g$ with
$\rho >0$ constant. We show that if $(M,g)$ satisfies $\delta \mathcal W
(\cdot, \cdot, \nabla f) = 0$, then $(M, g)$ is Einstein. Here $\mathcal W$
denotes the Weyl curvature tensor. In the case of noncompact, if $M$ is
complete and satisfies the same condition, then $M$ is rigid in the sense that
$M$ is given by a quotient of product of an Einstein manifold with Euclidean
space. These are generalizations of the previous known results in
  \cite{l-r}, \cite{m-s} and \cite{p-w3}.


title: Time Varying Isotropic Vector Random Fields on Spheres

abstract:
  For a vector random field that is isotropic and mean square continuous on a
sphere and stationary on a temporal domain, this paper derives a general form
of its covariance matrix function and provides a series representation for the
random field, which involve the ultraspherical polynomials. The series
representation is somehow an imitator of the covariance matrix function, but
differs from the the spectral representation in terms of the ordinary spherical
harmonics, and is useful for modeling and simulation. Some semiparametric
models are also illustrated.


title: Lower estimation of the difference among quasi-arithmetic means

abstract:
  Quasi-arithmetic means are defined for every continuous, strictly monotone
function $f \colon U \rightarrow \mathbb{R}$, ($U$ -- an interval). For an
$n$-tuple $a \in U^n$ with corresponding vector of weights $w=(w_1,\dots,w_n)$
($w_i>0$, $\sum w_i=1$) it equals $f^{-1}\left( \sum_{i=1}^{n} w_i
f(a_i)\right)$. In 1960s Cargo and Shisha defined a metric in a family of
quasi-arithmetic means defined on a common interval as the maximal possible
difference between these means taken over all admissible vectors with
corresponding weights. During the years 2013--16 we proved that, having two
quasi-arithmetic means, we can majorized distance between them in terms of
Arrow-Pratt index $f''/f'$. In this paper we are going to proof that this
operator can be also used to establish certain lower boundaries of this
distance.


title: Tableaux for First Order Logic of Proofs

abstract:
  In this paper we present a tableau proof system for first order logic of
proofs FOLP. We show that the tableau system is sound and complete with respect
to Mkrtychev models of FOLP.


title: Direct numerical approach to one-loop amplitudes

abstract:
  We present a completely numerical method of calculating one-loop amplitudes.
Our approach is built upon two different existing methods: the contour
deformation and the extrapolation methods. Taking the best features of each of
them, we devise an intuitive, stable and robust procedure which circumvents the
problem of large cancellations and related numerical instabilities by
calculating the complete amplitude at once. As a proof of concept, we use our
method to calculate the $2\gamma \to (N - 2)\gamma$ benchmark process, as well
as the Higgs decay amplitude $H \to \gamma \gamma$.


title: Shifts of the Stable Kneser Graphs and Hom-Idempotence

abstract:
  A graph $G$ is said to be {\em hom-idempotent} if there is a homomorphism
from $G^2$ to $G$, and {\em weakly hom-idempotent} if for some $n \geq 1$ there
is a homomorphism from $G^{n+1}$ to $G^n$. Larose et al. [{\em Eur. J. Comb.
19:867-881, 1998}] proved that Kneser graphs $\operatorname{KG}(n,k)$ are not
weakly hom-idempotent for $n \geq 2k+1$, $k\geq 2$. For $s \geq 2$, we
characterize all the shifts (i.e., automorphisms of the graph that map every
vertex to one of its neighbors) of $s$-stable Kneser graphs
$\operatorname{KG}(n,k)_{s-\operatorname{stab}}$ and we show that $2$-stable
Kneser graphs are not weakly hom-idempotent, for $n \geq 2k+2$, $k \geq 2$.
Moreover, for $s,k\geq 2$, we prove that $s$-stable Kneser graphs
$\operatorname{KG}(ks+1,k)_{s-\operatorname{stab}}$ are circulant graphs and so
hom-idempotent graphs. Finally, for $s \geq 3$, we show that $s$-stable Kneser
graphs $\operatorname{KG}(2s+2,2)_{s-\operatorname{stab}}$ are cores, not
$\chi$-critical, not hom-idempotent and their chromatic number is equal to
$s+2$.


title:
Cooling rate dependence of simulated ${\rm Cu_{64.5}Zr_{35.5}}$ metallic
  glass structure

abstract:
  Using molecular dynamics simulations with embedded atom model potential, we
study structural evolution of ${\rm Cu_{64.5}Zr_{35.5}}$ alloy during the
cooling in a wide range of cooling rates $\gamma\in(1.5\cdot 10^{9},10^{13})$
K/s. Investigating short- and medium-range order, we show that structure of
${\rm Cu_{64.5}Zr_{35.5}}$ metallic glass essentially depends on cooling rate.
In particular, a decrease of the cooling rate leads to a increase of abundances
of both the icosahedral-like clusters and Frank-Kasper Z16 polyhedra. The
amounts of these clusters in the glassy state drastically increase at the
$\gamma_{\rm min}=1.5\cdot 10^{9}$ K/s. Analysing the structure of the glass at
$\gamma_{\rm min}$, we observe the formation of nano-sized crystalline grain of
${\rm Cu_2Zr}$ intermetallic compound with the structure of ${\rm Cu_2Mg}$
Laves phase. The structure of this compound is isomorphous with that for ${\rm
Cu_5Zr}$ intermetallic compound. Both crystal lattices consist of two type of
clusters: Cu-centered 13-atom icosahedral-like cluster and Zr-centered 17-atom
Frank-Kasper polyhedron Z16. That suggests the same structural motifs for the
metallic glass and intermetallic compounds and explains the drastic increase of
the abundances of these clusters observed at $\gamma_{\rm min}$.

categories: cond-mat.dis-nn cond-mat.mtrl-sci cond-mat.soft physics.chem-ph


title:
Who pumps spin current into nonmagnetic-metal (NM) layer in YIG/NM
  multilayers at ferromagnetic resonance?

abstract:
  Spin pumping in Yttrium-iron-garnet (YIG)/nonmagnetic-metal (NM) layer
systems under ferromagnetic resonance (FMR) conditions is a popular method of
generating spin current in the NM layer. A good understanding of the spin
current source is essential in extracting spin Hall angle of the NM and in
potential spintronics applications. It is widely believed that spin current is
pumped from precessing YIG magnetization into NM layer. Here, by combining
microwave absorption and DC-voltage measurements on YIG/Pt and YIG/NM1/NM2
(NM1=Cu or Al, NM2=Pt or Ta), we unambiguously showed that spin current in NM
came from the magnetized NM surface (in contact with YIG) due to the magnetic
proximity effect (MPE), rather than the precessing YIG magnetization. This
conclusion is reached through our unique detecting method where the FMR
microwave absorption of the magnetized NM surface, hardly observed in the
conventional FMR experiments, was greatly amplified when the electrical
detection circuit was switched on.


title:
On Multiple-Input Multiple-Output OFDM with Index Modulation for Next
  Generation Wireless Networks

abstract:
  Multiple-input multiple-output orthogonal frequency division multiplexing
with index modulation (MIMO-OFDM-IM) is a novel multicarrier transmission
technique which has been proposed recently as an alternative to classical
MIMO-OFDM. In this scheme, OFDM with index modulation (OFDM-IM) concept is
combined with MIMO transmission to take advantage of the benefits of these two
techniques. In this paper, we shed light on the implementation and error
performance analysis of the MIMO-OFDM-IM scheme for next generation 5G wireless
networks. Maximum likelihood (ML), near-ML, simple minimum mean square error
(MMSE) and ordered successive interference cancellation (OSIC) based MMSE
detectors of MIMO-OFDM-IM are proposed and their theoretical performance is
investigated. It has been shown via extensive computer simulations that
MIMO-OFDM-IM scheme provides an interesting trade-off between error performance
and spectral efficiency as well as it achieves considerably better error
performance than classical MIMO-OFDM using different type detectors and under
realistic conditions.


title:
Approximate Bayesian Computation and Model Validation for Repulsive
  Spatial Point Processes

abstract:
  In many applications involving spatial point patterns, we find evidence of
inhibition or repulsion. The most commonly used class of models for such
settings are the Gibbs point processes. A recent alternative, at least to the
statistical community, is the determinantal point process. Here, we examine
model fitting and inference for both of these classes of processes in a
Bayesian framework. While usual MCMC model fitting can be available, the
algorithms are complex and are not always well behaved. We propose using
approximate Bayesian computation (ABC) for such fitting. This approach becomes
attractive because, though likelihoods are very challenging to work with for
these processes, generation of realizations given parameter values is
relatively straightforward. As a result, the ABC fitting approach is
well-suited for these models. In addition, such simulation makes them
well-suited for posterior predictive inference as well as for model assessment.
We provide details for all of the above along with some simulation
investigation and an illustrative analysis of a point pattern of tree data
exhibiting repulsion. R-code and datasets are included in the supplementary
material.


title: Dilepton production with the SMASH model

abstract:
  In this work the SMASH model is presented ("Simulating Many Accelerated
Strongly-Interacting Hadrons"), a next-generation hadronic transport approach,
which is designed to describe the non-equilibrium evolution of hadronic matter
in heavy-ion collisions. We discuss first dilepton spectra obtained with SMASH
in the few-GeV energy range of GSI/FAIR, where the dynamics of hadronic matter
is dominated by the production and decay of various resonance states. In
particular we show how electromagnetic transition form factors can emerge in a
transport picture under the hypothesis of vector-meson dominance.


title:
Continuity in a parameter of solutions to generic boundary-value
  problems

abstract:
  We introduce the most general class of linear boundary-value problems for
systems of first-order ordinary differential equations whose solutions belong
to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and
$0\leq\alpha\leq1$. The boundary conditions can contain derivatives $y^{(r)}$,
with $1\leq r\leq n+1$, of the solution $y$ to the system. For
parameter-dependent problems from this class, we obtain constructive criterion
under which their solutions are continuous in the normed space $C^{n+1,\alpha}$
with respect to the parameter.


title:
Linear Depth Increase of Lambda Terms along Leftmost-Outermost
  Beta-Reduction

abstract:
  Performing $n$ steps of $\beta$-reduction to a given term in the
$\lambda$-calculus can lead to an increase in the size of the resulting term
that is exponential in $n$. The same is true for the possible depth increase of
terms along a $\beta$-reduction sequence. We explain that the situation is
different for the leftmost-outermost strategy for $\beta$-reduction: while
exponential size increase is still possible, depth increase is bounded linearly
in the number of steps. For every $\lambda$-term $M$ with depth $d$, in every
step of a leftmost-outermost $\beta$-reduction rewrite sequence starting from
$M$ the term depth increases by at most $d$. Hence the depth of the $n$-th
reduct of $M$ in such a rewrite sequence is bounded by $d\cdot (n+1)$.
  We prove the lifting of this result to $\lambda$-term representations as
orthogonal first-order term rewriting systems, which can be obtained by the
lambda-lifting transformation. For the transfer to lambda-calculus, we rely on
correspondence statements via lambda-lifting. We argue that the
linear-depth-increase property can be a stepping stone for an alternative proof
of, and so can shed new light on, a result by Accattoli and Dal Lago (2015)
that states: leftmost-outermost $\beta$-reduction rewrite sequences of length
$n$ in the lambda-calculus can be implemented on a reasonable machine with an
overhead that is polynomial in $n$ and the size of the initial term.


title:
Predictive Hierarchical Clustering: Learning clusters of CPT codes for
  improving surgical outcomes

abstract:
  We develop a novel algorithm, Predictive Hierarchical Clustering (PHC), for
agglomerative hierarchical clustering of current procedural terminology (CPT)
codes. Our predictive hierarchical clustering aims to cluster subgroups, not
individual observations, found within our data, such that the clusters
discovered result in optimal performance of a classification model. Therefore,
merges are chosen based on a Bayesian hypothesis test, which chooses pairings
of the subgroups that result in the best model fit, as measured by held out
predictive likelihoods. We place a Dirichlet prior on the probability of
merging clusters, allowing us to adjust the size and sparsity of clusters. The
motivation is to predict patient-specific surgical outcomes using data from ACS
NSQIP (American College of Surgeon's National Surgical Quality Improvement
Program). An important predictor of surgical outcomes is the actual surgical
procedure performed as described by a CPT code. We use PHC to cluster CPT
codes, represented as subgroups, together in a way that enables us to better
predict patient-specific outcomes compared to currently used clusters based on
clinical judgment.


title: Note on a new parametrization for testing the Kerr metric

abstract:
  We propose a new parametrization for testing the Kerr nature of astrophysical
black hole candidates. The common approaches focus on the attempt to constrain
possible deviations from the Kerr solution described by new terms in the
metric. Here we adopt a different perspective. The mass and the spin of a black
hole make the spacetime curved and we want to check whether they do it with the
strength predicted by general relativity. As an example, we apply our
parametrization to the black hole shadow, an observation that may be possible
in a not too distant future.


title:
MOCCA code for star cluster simulations - V. Initial globular cluster
  conditions influence on blue stragglers

abstract:
  The paper presents an analysis of properties of populations of blue
stragglers (BSs) in evolving globular clusters, based on numerical simulations
done with the MOCCA code for various initial globular clusters conditions.
  We find that various populations of BSs strongly depend on the initial
semi-major axes distributions. With a significant number of compact binaries,
the number of evolutionary BSs can be also significant. In turn, for semi-major
axes distributions preferring binaries with wider orbits, dynamical BSs are the
dominant ones. Their formation scenario is very distinct: for wide binaries the
number of dynamical interactions is significantly larger. Most interactions are
weak and increase only slightly the eccentricities. However, due to a large
number of such interactions, the eccentricities of a number of binaries finally
get so large that the stars collide.
  We study how larger initial clusters' concentrations influence the BSs.
Besides the expected increase of the number of dynamically created BSs (for
denser GCs the probabilities of strong dynamical interactions and collisions
are higher), we find that the number of the evolutionary BSs is not affected
even by very high initial concentrations. This has a very important implication
on observations - it supports the theory that the evolutionary BSs are the
result of the unperturbed evolution of the primordial binaries.
  In addition, the paper presents the evolution of the ratio between the number
of BSs in binaries and as single stars R_B/S. For a vast diversity of models,
the ratio R_B/S approaches the value ~0.4. Additionally, we identified two
subgroups which differ in the initial semi-major axes distributions. The first
group starts with a high ratio R_B/S, it decreases with time and settles around
0.4. The second group starts with lower values of the ratio R_B/S ... . (etc.,
abstract continues)


title: The free group has the dimensional order property

abstract:
  We prove that the common theory of nonabelian free groups has the dimensional
order property, or DOP, implying, for example, that there is no reasonable
structure theorem for $\aleph_1$-saturated models of this theory.


title: Tight bounds and conjectures for the isolation lemma

abstract:
  Given a hypergraph $H$ and a weight function $w: V \rightarrow \{1, \dots,
M\}$ on its vertices, we say that $w$ is isolating if there is exactly one edge
of minimum weight $w(e) = \sum_{i \in e} w(i)$. The Isolation Lemma is a
combinatorial principle introduced in Mulmuley et. al (1987) which gives a
lower bound on the number of isolating weight functions. Mulmuley used this as
the basis of a parallel algorithm for finding perfect graph matchings. It has a
number of other applications to parallel algorithms and to reductions of
general search problems to unique search problems (in which there are one or
zero solutions).
  The original bound given by Mulmuley et al. was recently improved by Ta-Shma
(2015). In this paper, we show improved lower bounds on the number of isolating
weight functions, and we conjecture that the extremal case is when $H$ consists
of $n$ singleton edges. When $M \gg n$ our improved bound matches this extremal
case asymptotically.
  We are able to show that this conjecture holds in a number of special cases:
when $H$ is a linear hypergraph or is 1-degenerate, or when $M = 2$. We also
show that it holds asymptotically when $M \gg n \gg 1$.


title:
A Radix Representation for each van der Waerden number $W(r, k)$ with
  $r$ colors: Why $\log_{r}W(r, k) < k^{2}$ is true whenever $k$ is the number
  of terms in the arithmetic progression

abstract:
  Here we show that by expressing a van der Waerden number $W(r, k)$ by its
radix polynomial representation, it not only is possible to locate each proper
subset on $\mathbb{R}$ in which the van der Waerden number lies, but also to
show that conditions exist for which the logarithm of the van der Waerden
number necessarily is bounded above by the square of the number of terms $k$ in
the arithmetic progression. Furthermore we also use the method to find a
mathematical expression or formula for the ratio of two "consecutive" van der
Waerden numbers of the kind $W(r, k)$, $W(r, k + 1)$.


title: Non-homogeneous $Tb$ Theorem for Bi-parameter $g$-Function

abstract:
  The main result of this paper is a bi-parameter $Tb$ theorem for
Littlewood-Paley $g$-function, where $b$ is a tensor product of two
pseudo-accretive functions. Instead of the doubling measure, we work with a
product measure $\mu = \mu_n \times \mu_m$, where the measures $\mu_n$ and
$\mu_m$ are only assumed to be upper doubling. The main techniques of the proof
include a bi-parameter $b$-adapted Haar function decomposition and an averaging
identity over good double Whitney regions. Moreover, the non-homogeneous
analysis and probabilistic methods are used again.


title: A Local Algorithm for Constructing Spanners in Minor-Free Graphs

abstract:
  Constructing a spanning tree of a graph is one of the most basic tasks in
graph theory. We consider this problem in the setting of local algorithms: one
wants to quickly determine whether a given edge $e$ is in a specific spanning
tree, without computing the whole spanning tree, but rather by inspecting the
local neighborhood of $e$. The challenge is to maintain consistency. That is,
to answer queries about different edges according to the same spanning tree.
Since it is known that this problem cannot be solved without essentially
viewing all the graph, we consider the relaxed version of finding a spanning
subgraph with $(1+\epsilon)n$ edges (where $n$ is the number of vertices and
$\epsilon$ is a given sparsity parameter). It is known that this relaxed
problem requires inspecting $\Omega(\sqrt{n})$ edges in general graphs, which
motivates the study of natural restricted families of graphs. One such family
is the family of graphs with an excluded minor. For this family there is an
algorithm that achieves constant success probability, and inspects
$(d/\epsilon)^{poly(h)\log(1/\epsilon)}$ edges (for each edge it is queried
on), where $d$ is the maximum degree in the graph and $h$ is the size of the
excluded minor. The distances between pairs of vertices in the spanning
subgraph $G'$ are at most a factor of $poly(d, 1/\epsilon, h)$ larger than in
$G$.
  In this work, we show that for an input graph that is $H$-minor free for any
$H$ of size $h$, this task can be performed by inspecting only $poly(d,
1/\epsilon, h)$ edges. The distances between pairs of vertices in the spanning
subgraph $G'$ are at most a factor of $\tilde{O}(h\log(d)/\epsilon)$ larger
than in $G$. Furthermore, the error probability of the new algorithm is
significantly improved to $\Theta(1/n)$. This algorithm can also be easily
adapted to yield an efficient algorithm for the distributed setting.


title: Finite sample breakdown point of Tukey's halfspace median

abstract:
  Tukey's halfspace median ($\HM$), servicing as the {multivariate} counterpart
of the univariate median, has been introduced and extensively studied in the
literature. It is supposed and expected to preserve robustness property (the
most outstanding property) of the univariate median. One of prevalent
quantitative assessments of robustness is finite sample breakdown point (FSBP).
Indeed, the FSBP of many multivariate medians have been identified, except for
the most prevailing one---the Tukey's halfspace median. This paper presents a
precise result on FSBP for Tukey's halfspace median. The result here depicts
the complete prospect of the global robustness of $\HM$ in the \emph{finite
sample} practical scenario, revealing the dimension effect on the breakdown
point robustness and complimenting the existing \emph{asymptotic} breakdown
point result.


title:
Study of the ${\Upsilon}(1S)$ ${\to}$ $B_{c}D_{s}^{\ast}$ decay with
  pQCD approach

abstract:
  The ${\Upsilon}(1S)$ ${\to}$ $B_{c}D_{s}^{\ast}$ weak decay is studied with
the perturbative QCD approach firstly. It is found that (1) main contributions
to branching ratio come from the longitudinal and parallel helicity amplitudes,
(2) branching ratio, longitudinal and parallel polarization fractions are
sensitive to the wave functions of the ${\Upsilon}(1S)$ meson, (3) branching
ratio for the ${\Upsilon}(1S)$ ${\to}$ $B_{c}D_{s}^{\ast}$ decay can reach up
to $10^{-9}$, which might be promisingly measured by the future experiments.


title:
Positive solutions for infinite semipositone/positone quasilinear
  elliptic systems with singular and superlinear terms

abstract:
  We establish existence and regularity of positive solutions for a class of
quasilinear elliptic systems with singular and superlinear terms. The approach
is based on sub-supersolution methods for systems of quasilinear singular
equations and the Schauder's fixed point Theorem.


title: Entropy and credit risk in highly correlated markets

abstract:
  We compare two models of corporate default by calculating the
Jeffreys-Kullback-Leibler divergence between their predicted default
probabilities when asset correlations are either high or low. Our main results
show that the divergence between the two models increases in highly correlated,
volatile, and large markets, but that it is closer to zero in small markets,
when asset correlations are low and firms are highly leveraged. These findings
suggest that during periods of financial instability the single-and
multi-factor models of corporate default will generate increasingly
inconsistent predictions.


title: Towards Better Analysis of Deep Convolutional Neural Networks

abstract:
  Deep convolutional neural networks (CNNs) have achieved breakthrough
performance in many pattern recognition tasks such as image classification.
However, the development of high-quality deep models typically relies on a
substantial amount of trial-and-error, as there is still no clear understanding
of when and why a deep model works. In this paper, we present a visual
analytics approach for better understanding, diagnosing, and refining deep
CNNs. We formulate a deep CNN as a directed acyclic graph. Based on this
formulation, a hybrid visualization is developed to disclose the multiple
facets of each neuron and the interactions between them. In particular, we
introduce a hierarchical rectangle packing algorithm and a matrix reordering
algorithm to show the derived features of a neuron cluster. We also propose a
biclustering-based edge bundling method to reduce visual clutter caused by a
large number of connections between neurons. We evaluated our method on a set
of CNNs and the results are generally favorable.


title: Analyzing User Preference for Social Image Recommendation

abstract:
  With the incredibly growing amount of multimedia data shared on the social
media platforms, recommender systems have become an important necessity to ease
users' burden on the information overload. In such a scenario, extensive amount
of heterogeneous information such as tags, image content, in addition to the
user-to-item preferences, is extremely valuable for making effective
recommendations. In this paper, we explore a novel hybrid algorithm termed {\em
STM}, for image recommendation. STM jointly considers the problem of image
content analysis with the users' preferences on the basis of sparse
representation. STM is able to tackle the challenges of highly sparse user
feedbacks and cold-start problmes in the social network scenario. In addition,
our model is based on the classical probabilistic matrix factorization and can
be easily extended to incorporate other useful information such as the social
relationships. We evaluate our approach with a newly collected 0.3 million
social image data set from Flickr. The experimental results demonstrate that
sparse topic modeling of the image content leads to more effective
recommendations, , with a significant performance gain over the
state-of-the-art alternatives.


title:
Rotation-Invariant Restricted Boltzmann Machine Using Shared Gradient
  Filters

abstract:
  Finding suitable features has been an essential problem in computer vision.
We focus on Restricted Boltzmann Machines (RBMs), which, despite their
versatility, cannot accommodate transformations that may occur in the scene. As
a result, several approaches have been proposed that consider a set of
transformations, which are used to either augment the training set or transform
the actual learned filters. In this paper, we propose the Explicit
Rotation-Invariant Restricted Boltzmann Machine, which exploits prior
information coming from the dominant orientation of images. Our model extends
the standard RBM, by adding a suitable number of weight matrices, associated
with each dominant gradient. We show that our approach is able to learn
rotation-invariant features, comparing it with the classic formulation of RBM
on the MNIST benchmark dataset. Overall, requiring less hidden units, our
method learns compact features, which are robust to rotations.


title: Tune the topology to create or destroy patterns

abstract:
  We consider the dynamics of a reaction-diffusion system on a multigraph. The
species share the same set of nodes but can access different links to explore
the embedding spatial support. By acting on the topology of the networks we can
control the ability of the system to self-organise in macroscopic patterns,
emerging as a symmetry breaking instability of an homogeneous fixed point. Two
different cases study are considered: on the one side, we produce a global
modification of the networks, starting from the limiting setting where species
are hosted on the same graph. On the other, we consider the effect of inserting
just one additional single link to differentiate the two graphs. In both cases,
patterns can be generated or destroyed, as follows the imposed, small,
topological perturbation. Approximate analytical formulae allows to grasp the
essence of the phenomenon and can potentially inspire innovative control
strategies to shape the macroscopic dynamics on multigraph networks


title: Adaptative decomposition: the case of the Drury-Arveson space

abstract:
  The maximum selection principle allows to give expansions, in an adaptive
way, of functions in the Hardy space $\mathbf H_2$ of the disk in terms of
Blaschke products. The expansion is specific to the given function. Blaschke
factors and products have counterparts in the unit ball of $\mathbb C^N$, and
this fact allows us to extend in the present paper the maximum selection
principle to the case of functions in the Drury-Arveson space of functions
analytic in the unit ball of $\mathbb C^N$. This will give rise to an algorithm
which is a variation in this higher dimensional case of the greedy algorithm.
We also introduce infinite Blaschke products in this setting and study their
convergence.


title: Nested Lattice Codes for Vector Perturbation Systems

abstract:
  Vector perturbation is an encoding method for broadcast channels in which the
transmitter solves a shortest vector problem in a lattice to create a
perturbation vector, which is then added to the data before transmission. In
this work, we introduce nested lattice codes into vector perturbation systems,
resulting in a strategy which we deem matrix perturbation. We propose design
criteria for the nested lattice codes, and show empirically that lattices
satisfying these design criteria can improve the performance of vector
perturbation systems. The resulting design criteria are the same as those
recently proposed for the Compute-and-Forward protocol.


title:
Fast Approximation Algorithms for the Generalized Survivable Network
  Design Problem

abstract:
  In a standard $f$-connectivity network design problem, we are given an
undirected graph $G=(V,E)$, a cut-requirement function $f:2^V \rightarrow
{\mathbb{N}}$, and non-negative costs $c(e)$ for all $e \in E$. We are then
asked to find a minimum-cost vector $x \in {\mathbb{N}}^E$ such that
$x(\delta(S)) \geq f(S)$ for all $S \subseteq V$. We focus on the class of such
problems where $f$ is a proper function. This encodes many well-studied NP-hard
problems such as the generalized survivable network design problem.
  In this paper we present the first strongly polynomial time FPTAS for solving
the LP relaxation of the standard IP formulation of the $f$-connectivity
problem with general proper functions $f$. Implementing Jain's algorithm, this
yields a strongly polynomial time $(2+\epsilon)$-approximation for the
generalized survivable network design problem (where we consider rounding up of
rationals an arithmetic operation).


title:
Ab initio computational study on the lattice thermal conductivity of
  Zintl clathrates [Si$_{19}$P$_{4}$]Cl$_{4}$ and Na$_{4}$[Al$_{4}$Si$_{19}$]

abstract:
  The lattice thermal conductivity of silicon clathrate framework Si$_{23}$ and
two Zintl clathrates, [Si$_{19}$P$_{4}$]Cl$_{4}$ and
Na$_{4}$[Al$_{4}$Si$_{19}$], is investigated by using an iterative solution of
the linearized Boltzmann transport equation (BTE) in conjuntion with ab initio
lattice dynamical techniques. At 300 K, the lattice thermal conductivities for
Si$_{23}$, [Si$_{19}$P$_{4}$]Cl$_{4}$, and Na$_{4}$[Al$_{4}$Si$_{19}$] were
found to be 43 W/(m K), 25 W/(m K), and 2 W/(m K), respectively. In the case of
Na$_{4}$[Al$_{4}$Si$_{19}$], the order-of-magnitude reduction in the lattice
thermal conductivity was found to be mostly due to relaxation times and group
velocities differing from Si$_{23}$ and [Si$_{19}$P$_{4}$]Cl$_{4}$. The
difference in the relaxation times and group velocities arises primarily due to
the phonon spectrum at low frequencies, resulting eventually from the
differences in the second-order interatomic force constants (IFCs). The
obtained third-order IFCs were rather similar for all materials considered
here.


title: Lossless Intra Coding in HEVC with Adaptive 3-tap Filters

abstract:
  In pixel-by-pixel spatial prediction methods for lossless intra coding, the
prediction is obtained by a weighted sum of neighbouring pixels. The proposed
prediction approach in this paper uses a weighted sum of three neighbor pixels
according to a two-dimensional correlation model. The weights are obtained
after a three step optimization procedure. The first two stages are offline
procedures where the computed prediction weights are obtained offline from
training sequences. The third stage is an online optimization procedure where
the offline obtained prediction weights are further fine-tuned and adapted to
each encoded block during encoding using a rate-distortion optimized method and
the modification in this third stage is transmitted to the decoder as side
information. The results of the simulations show average bit rate reductions of
12.02% and 3.28% over the default lossless intra coding in HEVC and the
well-known Sample-based Angular Prediction (SAP) method, respectively.


title: Optomagnonics in Magnetic Solids

abstract:
  Coherent conversion of photons to magnons, and back, provides a natural
mechanism for rapid control of interactions between stationary spins with long
coherence times and high-speed photons. Despite the large frequency difference
between optical photons and magnons, coherent conversion can be achieved
through a three-particle interaction between one magnon and two photons whose
frequency difference is resonant with the magnon frequency, as in optomechanics
with two photons and a phonon. The large spin density of a transparent
ferromagnetic insulator (such as the ferrite yttrium iron garnet) in an optical
cavity provides an intrinsic photon-magnon coupling strength that we calculate
to exceed reported optomechanical couplings. A large cavity photon number and
properly selected cavity detuning produce a predicted effective coupling
strength sufficient for observing electromagnetically induced transparency and
the Purcell effect, and even to reach the ultra-strong coupling regime.


title: Coupled Spin-Light dynamics in Cavity Optomagnonics

abstract:
  Experiments during the past two years have shown strong resonant
photon-magnon coupling in microwave cavities, while coupling in the optical
regime was demonstrated very recently for the first time. Unlike with
microwaves, the coupling in optical cavities is parametric, akin to
optomechanical systems. This line of research promises to evolve into a new
field of optomagnonics, aimed at the coherent manipulation of elementary
magnetic excitations by optical means. In this work we derive the microscopic
optomagnonic Hamiltonian. In the linear regime the system reduces to the
well-known optomechanical case, with remarkably large coupling. Going beyond
that, we study the optically induced nonlinear classical dynamics of a
macrospin. In the fast cavity regime we obtain an effective equation of motion
for the spin and show that the light field induces a dissipative term
reminiscent of Gilbert damping. The induced dissipation coefficient however can
change sign on the Bloch sphere, giving rise to self-sustained oscillations.
When the full dynamics of the system is considered, the system can enter a
chaotic regime by successive period doubling of the oscillations.


title:
MOCCA code for star cluster simulations - VI. Bimodal spatial
  distribution of blue stragglers

abstract:
  The paper presents an analysis of formation mechanism and properties of
spatial distributions of blue stragglers in evolving globular clusters, based
on numerical simulations done with the MOCCA code. First, there are presented
N-body and MOCCA simulations which try to reproduce the simulations presented
by Ferraro (2012). Then, the agreement between N-body and the MOCCA code is
shown. Finally, we discuss the formation process of the bimodal distribution.
We report that so-called bimodal spatial distribution of blue stragglers is a
very transient feature. It is formed for one snapshot in time and it can easily
vanish in the next one. Moreover, we show that the radius of avoidance proposed
by Ferraro (2012) goes out of sync with the apparent minimum of the bimodal
distribution after about two half-mass relaxation times. This finding creates a
real challenge for the dynamical clock, which uses this radius to determine the
dynamical age of globular clusters. Additionally, the paper discusses a few
important problems concerning the apparent visibilities of the bimodal
distributions which have to be taken into account while studying the spatial
distributions of blue stragglers.


title: On the index of reducibility of powers of a standard parameter ideal

abstract:
  In this paper we study the index of reducibility of powers of a standard
parameter ideal. An explicit formula is proved for the extremely case. We apply
the main result to compute Hilbert polynomials of socle ideals of standard
parameter ideals.


title:
Accessing many-body localized states through the Generalized Gibbs
  Ensemble

abstract:
  We show how the thermodynamic properties of large many-body localized systems
can be studied using quantum Monte Carlo simulations. To this end we devise a
heuristic way of constructing local integrals of motion of very high quality,
which are added to the Hamiltonian in conjunction with Lagrange multipliers.
The ground state simulation of the shifted Hamiltonian corresponds to a
high-energy state of the original Hamiltonian in case of exactly known local
integrals of motion. We can show that the inevitable mixing between eigenstates
as a consequence of non-perfect integrals of motion is weak enough such that
the characteristics of many-body localized systems are not averaged out in our
approach, unlike the standard ensembles of statistical mechanics. Our method
paves the way to study higher dimensions and indicates that a full many-body
localized phase in 2d, where (nearly) all eigenstates are localized, is likely
to exist.


title:
Multi-Fold Gabor, PCA and ICA Filter Convolution Descriptor for Face
  Recognition

abstract:
  This paper devises a new means of filter diversification, dubbed multi-fold
filter convolution (M-FFC), for face recognition. On the assumption that M-FFC
receives single-scale Gabor filters of varying orientations as input, these
filters are self-cross convolved by M-fold to instantiate a filter offspring
set. The M-FFC flexibility also permits cross convolution amongst Gabor filters
and other filter banks of profoundly dissimilar traits, e.g., principal
component analysis (PCA) filters, and independent component analysis (ICA)
filters. The 2-FFC of Gabor, PCA and ICA filters thus yields three offspring
sets: (1) Gabor filters solely, (2) Gabor-PCA filters, and (3) Gabor-ICA
filters, to render the learning-free and the learning-based 2-FFC descriptors.
To facilitate a sensible Gabor filter selection for M-FFC, the 40 multi-scale,
multi-orientation Gabor filters are condensed into 8 elementary filters. Aside
from that, an average histogram pooling operator is employed to leverage the
2-FFC histogram features, prior to the final whitening PCA compression. The
empirical results substantiate that the 2-FFC descriptors prevail over, or on
par with, other face descriptors on both identification and verification tasks.


title:
Singular quasilinear elliptic systems with (super-) homogeneous
  conditions

abstract:
  In this paper we establish existence, nonexitence and regularity of positive
solutions for a class of singular quasilinear elliptic systems subject to
(super-) homogeneous condition. The approach is based on sub-supersolution
methods for systems of quasilinear singular equations combined with
perturbation arguments involving singular terms.


title: Hilbert-Schmidt Hankel operators over semi-Reinhardt domains

abstract:
  Let $\Omega$ be an arbitrary bounded semi-Reinhardt domain in
$\mathbb{C}^{m+n}$. We show that for $m \geq 2$, if a Hankel operator with an
anti-holomorphic symbol is Hilbert-Schmidt on the Bergman space
$L_a^2(\Omega)$, then it must equal zero. This fact has previously been proved
for Reinhardt domains.


title: Binary Codes for Tagging X-Ray Images via Deep De-Noising Autoencoders

abstract:
  A Content-Based Image Retrieval (CBIR) system which identifies similar
medical images based on a query image can assist clinicians for more accurate
diagnosis. The recent CBIR research trend favors the construction and use of
binary codes to represent images. Deep architectures could learn the non-linear
relationship among image pixels adaptively, allowing the automatic learning of
high-level features from raw pixels. However, most of them require class
labels, which are expensive to obtain, particularly for medical images. The
methods which do not need class labels utilize a deep autoencoder for binary
hashing, but the code construction involves a specific training algorithm and
an ad-hoc regularization technique. In this study, we explored using a deep
de-noising autoencoder (DDA), with a new unsupervised training scheme using
only backpropagation and dropout, to hash images into binary codes. We
conducted experiments on more than 14,000 x-ray images. By using class labels
only for evaluating the retrieval results, we constructed a 16-bit DDA and a
512-bit DDA independently. Comparing to other unsupervised methods, we
succeeded to obtain the lowest total error by using the 512-bit codes for
retrieval via exhaustive search, and speed up 9.27 times with the use of the
16-bit codes while keeping a comparable total error. We found that our new
training scheme could reduce the total retrieval error significantly by 21.9%.
To further boost the image retrieval performance, we developed Radon
Autoencoder Barcode (RABC) which are learned from the Radon projections of
images using a de-noising autoencoder. Experimental results demonstrated its
superior performance in retrieval when it was combined with DDA binary codes.


title: Testing the Higgs sector directly in the nonrelativistic domain

abstract:
  Directly measuring the Higgs self-coupling is of great importance for testing
the Brout-Englert-Higgs mechanism in the Standard Model. As a scattering that
contains the direct information from the Higgs self-coupling, we investigate
the process $\mu^-\mu^+\rightarrow HH$ in the threshold region. We calculate
the one-loop corrections to the cross section and consider the non-perturbative
contribution from the Higgs self-interactions in the final state. It is found
that the scattering in the nonrelativistic domain could be an especial process
to testing the Higgs sector directly.


title: Extension Complexity of Independent Set Polytopes

abstract:
  We exhibit an $n$-node graph whose independent set polytope requires extended
formulations of size exponential in $\Omega(n/\log n)$. Previously, no explicit
examples of $n$-dimensional $0/1$-polytopes were known with extension
complexity larger than exponential in $\Theta(\sqrt{n})$. Our construction is
inspired by a relatively little-known connection between extended formulations
and (monotone) circuit depth.


title:
The Dichotomy for Conservative Constraint Satisfaction is Polynomially
  Decidable

abstract:
  Given a fixed constraint language $\Gamma$, the conservative CSP over
$\Gamma$ (denoted by c-CSP($\Gamma$)) is a variant of CSP($\Gamma$) where the
domain of each variable can be restricted arbitrarily. A dichotomy is known for
conservative CSP: for every fixed language $\Gamma$, c-CSP($\Gamma$) is either
in P or NP-complete. However, the characterization of conservatively tractable
languages is of algebraic nature and the naive recognition algorithm is
super-exponential in the domain size. The main contribution of this paper is a
polynomial-time algorithm that, given a constraint language $\Gamma$ as input,
decides if c-CSP($\Gamma$) is tractable. In addition, if $\Gamma$ is proven
tractable the algorithm also outputs its coloured graph, which contains
valuable information on the structure of $\Gamma$.