title:
Collision detection or nearest-neighbor search? On the computational
  bottleneck in sampling-based motion planning

abstract:
  The complexity of nearest-neighbor search dominates the asymptotic running
time of many sampling-based motion-planning algorithms. However, collision
detection is often considered to be the computational bottleneck in practice.
Examining various asymptotically optimal planning algorithms, we characterize
settings, which we call NN-sensitive, in which the practical computational role
of nearest-neighbor search is far from being negligible, i.e., the portion of
running time taken up by nearest-neighbor search is comparable, or sometimes
even greater than the portion of time taken up by collision detection. This
reinforces and substantiates the claim that motion-planning algorithms could
significantly benefit from efficient and possibly specifically-tailored
nearest-neighbor data structures. The asymptotic (near) optimality of these
algorithms relies on a prescribed connection radius, defining a ball around a
configuration $q$, such that $q$ needs to be connected to all other
configurations in that ball. To facilitate our study, we show how to adapt this
radius to non-Euclidean spaces, which are prevalent in motion planning. This
technical result is of independent interest, as it enables to compare the
radial-connection approach with the common alternative, namely, connecting each
configuration to its $k$ nearest neighbors ($k$-NN). Indeed, as we demonstrate,
there are scenarios where using the radial connection scheme, a solution path
of a specific cost is produced ten-fold (and more) faster than with $k$-NN.


title: Complex symmetric composition operators with automorphic symbols

abstract:
  In this paper we show that a composition operator $C_\varphi$ cannot be
complex symmetric on Hardy-Hilbert space $H^2(D)$ when $\varphi$ is an elliptic
automorphism of order $3$ and not a rotation. This completes the project of
finding all invertible composition operators which are complex symmetric
$H^2(D)$.


title:
Heat production and error probability relation in Landauer reset at
  effective temperature

abstract:
  The erasure of a classical bit of information is a dissipative process. The
minimum heat produced during this operation has been theorized by Rolf Landauer
in 1961 to be equal to $k_B T \ln 2$ and takes the name of Landauer limit,
Landauer reset or Landauer principle. Despite its fundamental importance, the
Landauer limit remained untested experimentally for more than fifty years until
recently when it has been tested using colloidal particles and magnetic dots.
Experimental measurements on different devices, like micro-mechanical systems
or nano-electronic devices are still missing. Here we show the results obtained
in performing the Landauer reset operation in a micro-mechanical system,
operated at an effective temperature. The measured heat exchange is in
accordance with the theory reaching values close to the expected limit. The
data obtained for the heat production is then correlated to the probability of
error in accomplishing the reset operation.


title:
A combinatorial approach for small and strong formulations of
  disjunctive constraints

abstract:
  We present a framework for constructing strong mixed-integer programming
formulations for logical disjunctive constraints. Our approach is a
generalization of the logarithmically-sized formulations of Vielma and
Nemhauser for SOS2 constraints, and we offer a complete characterization of its
expressive power. We apply the framework to a variety of disjunctive
constraints, producing novel small and strong formulations for outer
approximations of multilinear terms, generalizations of special ordered sets,
piecewise linear functions over a variety of domains, and obstacle avoidance
constraints.


title:
Source reconstruction using a bilevel optimisation method with a smooth
  weighted distance function

abstract:
  We consider a bilevel optimatisation method for inverse linear atmospheric
dispersion problems where both linear and non-linear model parameters are to be
determined. We propose that a smooth weighted Mahalanobis distance function is
used and derive sufficient conditions for when the follower problem has local
strict convexity. A few toy-models are presented where local strict convexity
and ill-posedness of the inverse problem are explored, indeed the smooth
distance function is compared and contrasted to linear and piecewise linear
ones. The bilevel optimisation method is then applied to sensor data collected
in wind tunnel experiments of a neutral gas release in urban environments
(MODITIC).


title:
Inferring solutions of differential equations using noisy multi-fidelity
  data

abstract:
  For more than two centuries, solutions of differential equations have been
obtained either analytically or numerically based on typically well-behaved
forcing and boundary conditions for well-posed problems. We are changing this
paradigm in a fundamental way by establishing an interface between
probabilistic machine learning and differential equations. We develop
data-driven algorithms for general linear equations using Gaussian process
priors tailored to the corresponding integro-differential operators. The only
observables are scarce noisy multi-fidelity data for the forcing and solution
that are not required to reside on the domain boundary. The resulting
predictive posterior distributions quantify uncertainty and naturally lead to
adaptive solution refinement via active learning. This general framework
circumvents the tyranny of numerical discretization as well as the consistency
and stability issues of time-integration, and is scalable to high-dimensions.


title: Spin- and orbital-Hall effect in cyclic group symmetric metasurface

abstract:
  Light possesses both spin and orbital angular momentum (AM). While spin AM is
determined by helicity of circular-polarization, orbital AM is characterized by
topological charge of vortex beam. Interaction of AM with optical beam orbit
leads to optical spin Hall or orbital Hall effect, exhibited as spin-dependent
or topological charge-dependent transverse shift of optical beam. Conservation
of AM enables spin-to-orbital AM conversion, where circular-polarized Gaussian
beam is converted to opposite-helicity circular-polarized vortex beam with
topological charge $\pm 2$, an example of controlling spatial beam profiling by
spin flip. However, the resultant vortex beam has the beam center of gravity
unchanged, the same as that of incident Gaussian beam, meaning a null
transverse shift. Here we introduce a cyclic group symmetric metasurface to
demonstrate generation of vortex beam exhibiting spin-dependent transverse
shift, namely, spin- and orbital-Hall effect, attributed to an alteration of
dynamical phase of scattered beam according to the order $n$ of cyclic group
while keeping geometric phase constant. Capability of spin-controlled spatial
beam profiling with a transverse shift via spin- and orbital-Hall effect has
important implications for spatial demultiplexing in optical communication
utilizing orbital AM mode division multiplexing as well as for optical vortex
tweezer and signal processing involving vortex beams.


title: Progress on a Conjecture Regarding the Triangular Distribution

abstract:
  Triangular distributions are a well-known class of distributions that are
often used as an elementary example of a probability model. Maximum likelihood
estimation of the mode parameter of the triangular distribution over the unit
interval can be performed via an order statistics-based method. It had been
conjectured that such a method can be conducted using only a constant number of
likelihood function evaluations, on average, as the sample size becomes large.
We prove two theorems that validate this conjecture. Graphical and numerical
results are presented to supplement our proofs.


title: Fast Ewald summation for free-space Stokes potentials

abstract:
  We present a spectrally accurate method for the rapid evaluation of
free-space Stokes potentials, i.e. sums involving a large number of free space
Green's functions. We consider sums involving stokeslets, stresslets and
rotlets that appear in boundary integral methods and potential methods for
solving Stokes equations. The method combines the framework of the Spectral
Ewald method for periodic problems, with a very recent approach to solving the
free-space harmonic and biharmonic equations using fast Fourier transforms
(FFTs) on a uniform grid. Convolution with a truncated Gaussian function is
used to place point sources on a grid. With precomputation of a scalar grid
quantity that does not depend on these sources, the amount of oversampling of
the grids with Gaussians can be kept at a factor of two, the minimum for
aperiodic convolutions by FFTs. The resulting algorithm has a computational
complexity of O(N log N) for problems with N sources and targets. Comparison is
made with a fast multipole method (FMM) to show that the performance of the new
method is competitive.


title:
Knowledge Representation on the Web revisited: Tools for Prototype Based
  Ontologies

abstract:
  In recent years RDF and OWL have become the most common knowledge
representation languages in use on the Web, propelled by the recommendation of
the W3C. In this paper we present a practical implementation of a different
kind of knowledge representation based on Prototypes. In detail, we present a
concrete syntax easily and effectively parsable by applications. We also
present extensible implementations of a prototype knowledge base, specifically
designed for storage of Prototypes. These implementations are written in Java
and can be extended by using the implementation as a library. Alternatively,
the software can be deployed as such. Further, results of benchmarks for both
local and web deployment are presented. This paper augments a research paper,
in which we describe the more theoretical aspects of our Prototype system.


title:
Investigation of the Ground and Excited States of the 3H and 4He Nuclei
  by Using the Methods of Group Theory

abstract:
  The method of group theory is applied to investigate the ground and the
excited states of the triton and helium nuclei by using the translation
invariant shell model with basis functions corresponding to even number of
quanta of excitations in the range 0 less than or equal to N less than or equal
to 20. Accordingly, the ground and first excited state wave functions and
energies, the S, P and D state probabilities, the root mean square radius and
the magnetic dipole moment of triton have been investigated. Also, the energies
and wave functions of the ground and the even parity excited states and the
root mean square radius of helium have been investigated. Two residual two body
interactions together with two three nucleon interactions have been used in the
calculations. Moreover, the convergence of calculations has been examined by
extrapolating the results with N less than or equals to 20 step by step to
reach N equals to 30 for the two nuclei.


title: Cyber Attack Surface Analysis of Advanced Metering Infrastructure

abstract:
  Cyber attacks on critical infrastructure have been an issue of importance in
industry over the past several years, as well as a focus of academic research.
Cyber attacks of various types and magnitude have been on the rise targeted
specifically at power grids. A successful attack on the power grid could result
in significant impacts including grid shutdown, cascading failures, damage to
the infrastructure, and potential harm to people. Power grid infrastructure are
critical in nature, they enable operations for residential, commercial,
industrial, and government users across critical infrastructure such as water,
communication, banking, transportation, manufacturing, and more. The compromise
of these operations introduces threats, which span from economic to public
safety. The Advanced Metering Infrastructure (AMI) is now being rapidly
deployed throughout the power grid, and is an enabling technology for smart
grid. Identifying the attack surface is a necessary step in achieving cyber
security in smart grids and AMI. The purpose of this paper is to quantify and
examine the cyber attack surface of AMI in order to lay the foundation for
mitigating approaches to AMI cyber security.


title: Coordinated Optimization at a Hydro Generating Plant by Software Agents

abstract:
  The architecture is developed for incorporating a software agent into the
existing control system of a river-based hydro generating plant. The software
agent will utilize a rule-based system for ease of integration. Optimization
for increased power production is presented, initially for a single generating
unit. An enhancement to facilitate the constraints of river level and flow by
an external user as well as the goals of corporate dispatching is then
developed through the existing SCADA system. Finally, expansion to coordinate
multiple hydro units at a single location is presented.


title: Infinite families of 2-designs and 3-designs from linear codes

abstract:
  The interplay between coding theory and $t$-designs started many years ago.
While every $t$-design yields a linear code over every finite field, the
largest $t$ for which an infinite family of $t$-designs is derived directly
from a linear or nonlinear code is $t=3$. Sporadic $4$-designs and $5$-designs
were derived from some linear codes of certain parameters. The major objective
of this paper is to construct many infinite families of $2$-designs and
$3$-designs from linear codes. The parameters of some known $t$-designs are
also derived. In addition, many conjectured infinite families of $2$-designs
are also presented.


title:
New Software Metrics for Evaluation and Comparison of Advanced Power
  Management Systems

abstract:
  A set of software metrics for the evaluation of power management systems
(PMSs) is presented. Such systems for managing power need to be autonomous,
scalable, low in complexity, and comprised of portable algorithms in order to
be well applied across the varying implementations that utilize power systems.
Although similar metrics exist for software in general, their definitions do
not readily lend themselves to the unique characteristics of power management
systems or systems of similar architecture.


title: Infinite families of $t$-designs from a type of five-weight codes

abstract:
  It has been known for a long time that $t$-designs can be employed to
construct both linear and nonlinear codes and that the codewords of a fixed
weight in a code may hold a $t$-design. While a lot of progress in the
direction of constructing codes from $t$-designs has been made, only a small
amount of work on the construction of $t$-designs from codes has been done. The
objective of this paper is to construct infinite families of $2$-designs and
$3$-designs from a type of binary linear codes with five-weights. The total
number of $2$-designs and $3$-designs obtained in this paper are exponential in
any odd $m$ and the block size of the designs varies in a huge range.


title:
Microgrid Reference Methodology for Understanding Utility and Customer
  Interactions in Microgrid Projects

abstract:
  The purpose of this paper is to introduce a holistic and systematic approach,
based in key concepts of systems thinking, systems of systems and management
science; to completely represent, model and analyze microgrid systems. In this
paper we propose a Microgrid Reference Methodology (MRM) that guides the
cooperation and mutual benefits between electric utilities and industrial
customers for microgrid projects. We sketch a four-level socio-technical system
in which the {\delta} (business) level is added to the other three levels that
are traditionally analyzed in microgrid design and planning. This MRM clearly
specifies the steps and processes necessary for determining actors in the
system, their interrelations, interests, goals and undesired effects. Finally,
the MRM makes possible the evaluation of the impact of different alternatives
on the objectives of both parties through the determination of criteria and
factors. These factors can be influenced by the electric utility and customer;
or they can be external, but still influenced by other actors such as
regulators and government, to incentivize the implementation of microgrid
projects.


title: Global Continuous Optimization with Error Bound and Fast Convergence

abstract:
  This paper considers global optimization with a black-box unknown objective
function that can be non-convex and non-differentiable. Such a difficult
optimization problem arises in many real-world applications, such as parameter
tuning in machine learning, engineering design problem, and planning with a
complex physics simulator. This paper proposes a new global optimization
algorithm, called Locally Oriented Global Optimization (LOGO), to aim for both
fast convergence in practice and finite-time error bound in theory. The
advantage and usage of the new algorithm are illustrated via theoretical
analysis and an experiment conducted with 11 benchmark test functions. Further,
we modify the LOGO algorithm to specifically solve a planning problem via
policy search with continuous state/action space and long time horizon while
maintaining its finite-time error bound. We apply the proposed planning method
to accident management of a nuclear power plant. The result of the application
study demonstrates the practical utility of our method.


title: Asynchronous Parallel Algorithms for Nonconvex Optimization

abstract:
  We propose a new asynchronous parallel block-descent algorithmic framework
for the minimization of the sum of a smooth nonconvex function and a nonsmooth
convex one, subject to both convex and nonconvex constraints. The proposed
framework hinges on successive convex approximation techniques and a novel
probabilistic model that captures key elements of modern computational
architectures and asynchronous implementations in a more faithful way than
current state-of-the-art models. Other key features of the framework are: i) it
covers in a unified way several specific solution methods; ii) it accommodates
a variety of possible parallel computing architectures; and iii) it can deal
with nonconvex constraints. Almost sure convergence to stationary solutions is
proved, and theoretical complexity results are provided, showing nearly ideal
linear speedup when the number of workers is not too large.


title: A Faster Algorithm for Asymptotic Communication for Omniscience

abstract:
  We propose a modified decomposition algorithm (MDA) to solve the asymptotic
communication for omniscience (CO) problem where the communication rates could
be real or fractional. By starting with a lower estimation of the minimum
sum-rate, the MDA algorithm iteratively updates the estimation by the optimizer
of a Dilworth truncation problem until the minimum is reached with a
corresponding optimal rate vector. We also propose a fusion method
implementation of the coordinate-wise saturation capacity algorithm
(CoordSatCapFus) for solving the Dilworth truncation problem, where the
minimization is done over a fused user set with a cardinality smaller than the
original one. We show that the MDA algorithm is less complex than the existing
ones. In addition, we show that the non-asymptotic CO problem, where the
communication rates are integral, can be solved by one more call of the
CoordSatCapfus algorithm. By choosing a proper linear ordering of the user
indices in the MDA algorithm, the optimal rate vector is also the one with the
minimum weighted sum-rate.


title: A note on Atiyah's $\Gamma$-index theorem in Heisenberg calculus

abstract:
  In this note, we prove an index theorem on Galois covering for Heisenberg
elliptic differential operators, which is not elliptic, analogous to Atiyah's
$\Gamma$-index theorem. This note also contains an example of Heisenberg
differential operators with non-trivial $\Gamma$-index.


title:
Dirac equation in 2-dimensional curved spacetime, particle creation, and
  coupled waveguide arrays

abstract:
  When quantum fields are coupled to gravitational fields, spontaneous particle
creation may occur similarly to when they are coupled to external
electromagnetic fields. Gravitational fields can be incorporated as background
spacetime if the back-action of matter on it can be neglected, yielding
modified Dirac or Klein-Gordon equations for elementary fermions and bosons
respectively. The semi-classical description predicts particle creation in many
scenarios including expanding universe, near the event horizon of a black hole
(the Hawking effect), and an accelerating observer in flat spacetime (the Unruh
effect). In this work, we give a pedagogical introduction to the Dirac equation
in a general 2D spacetime and show examples of spinor wave packet dynamics in
some background spacetimes. In particular, we cover the phenomenon of particle
creation in a time-dependent metric. Photonic analogs of these effects are then
proposed, where classical light propagating in an array of coupled waveguides
provides a visualisation of the Dirac spinor propagating in curved 2D
spacetime. The extent to which such a single-particle description can be said
to mimic particle creation is discussed.


title: HoTTSQL: Proving Query Rewrites with Univalent SQL Semantics

abstract:
  Every database system contains a query optimizer that performs query
rewrites. Unfortunately, developing query optimizers remains a highly
challenging task. Part of the challenges comes from the intricacies and rich
features of query languages, which makes reasoning about rewrite rules
difficult. In this paper, we propose a machine-checkable denotational semantics
for SQL, the de facto language for relational database, for rigorously
validating rewrite rules. Unlike previously proposed semantics that are either
non-mechanized or only cover a small amount of SQL language features, our
semantics covers all major features of SQL, including bags, correlated
subqueries, aggregation, and indexes. Our mechanized semantics, called HoTTSQL,
is based on K-Relations and homotopy type theory, where we denote relations as
mathematical functions from tuples to univalent types. We have implemented
HoTTSQL in Coq, which takes only fewer than 300 lines of code and have proved a
wide range of SQL rewrite rules, including those from database research
literature (e.g., magic set rewrites) and real-world query optimizers (e.g.,
subquery elimination). Several of these rewrite rules have never been
previously proven correct. In addition, while query equivalence is generally
undecidable, we have implemented an automated decision procedure using HoTTSQL
for conjunctive queries: a well-studied decidable fragment of SQL that
encompasses many real-world queries.


title:
Realizing Giant Magneto-Optical Effects in 3D Topological Insulators
  Without Magnetic Fields

abstract:
  Topological insulators display unusual light-matter interactions due to the
helical nature of surface electronic states. We study the near-field
interaction of light propagating in an optical fiber with crystals of Sb2Te3, a
3D topological insulator (TI), and observe a large apparent Faraday rotation.
The origin of this unexpected polarization rotation in the optical fiber is
attributed to a magneto-optical Kerr effect at the TI-fiber interface. We show
that the combined effects of time-reversal symmetry breaking, which arises from
Zeeman coupling of the electromagnetic field with the surface electrons of the
TI, and inversion symmetry breaking of optical excitations, which arises from
the exponential decay of the evanescent light across the TI crystal, are
central to realizing this giant polarization rotation. Our work demonstrates a
facile approach for realizing large magneto-optical effects without any
magnetic fields by exploiting the unique physics of light-matter interactions
at TI surfaces.


title: On Properties of Geometric Preduals of ${\mathbf C^{k,\omega}}$ Spaces

abstract:
  Let $C_b^{k,\omega}(\mathbb R^n)$ be the Banach space of $C^k$ functions on
$\mathbb R^n$ bounded together with all derivatives of order $\le k$ and with
derivatives of order $k$ having moduli of continuity majorated by
$c\cdot\omega$, $c\in\mathbb R_+$, for some $\omega\in C(\mathbb R_+)$. Let
$C_b^{k,\omega}(S):=C_b^{k,\omega}(\mathbb R^n)|_S$ be the trace space to a
closed subset $S\subset\mathbb R^n$. The geometric predual $G_b^{k,\omega}(S)$
of $C_b^{k,\omega}(S)$ is the minimal closed subspace of the dual
$\bigl(C_b^{k,\omega}(\mathbb R^n)\bigr)^*$ containing evaluation functionals
of points in $S$. We study geometric properties of spaces $G_b^{k,\omega}(S)$
and their relations to the classical Whitney problems on the characterization
of trace spaces of $C^k$ functions on $\mathbb R^n$.


title: New Results on CGR/CUR Approximation of a Matrix

abstract:
  CUR and low-rank approximations are among most fundamental subjects of
numerical linear algebra, with a wide range of applications to a variety of
highly important areas of modern computing, which range from the machine
learning theory and neural networks to data mining and analysis. We first
dramatically accelerate computation of such approximations for the average
input matrix, then show some narrow classes of hard inputs for our algorithms,
and finally point out a tentative direction to narrowing such classes further
by means of pre-processing with quasi Gaussian structured multipliers. Our
extensive numerical tests with a variety of real world inputs for
regularization from Singular Matrix Database have consistently produced
reasonably close CUR approximations at a low computational cost. There is a
variety of efficient applications of our results and our techniques to
important subjects of matrix computations. Our study provides new insights and
enable design of faster algorithms for low-rank approximation by means of
sampling and oversampling, for Gaussian elimination with no pivoting and block
Gaussian elimination, and for the approximation of railing singular spaces
associated with the $\nu$ smallest singular values of a matrix having numerical
nullity. We conclude the paper with novel extensions of our acceleration to the
Fast Multipole Method and the Conjugate Gradient Algorithms. (This report is an
outline of our paper in arXiv:1611.01391.)


title:
Regular and limiting normal cones for the subdifferential mapping graph
  of nuclear norm

abstract:
  This paper focuses on the characterization for the regular and limiting
normal cones to the graph of the subdifferential mapping of the nuclear norm,
which is essential to derive optimality conditions for the equivalent MPEC
(mathematical program with equilibrium constraints) reformulation of rank
minimization problems.


title:
Forced acoustical response of an open cavity coupled with a
  semi-infinite space

abstract:
  This paper presents a study of the forced acoustical response of an open
cavity from the perspective of modal expansion. Based on the coupled mode
theory, it is shown that the sound pressure distribution of an open cavity
excited by a point source placed within the cavity can be expanded by a set of
frequency-dependent eigenmodes, which are derived from the coupling between the
cavity and a semi-infinite space. The calculation of the acoustical responses
for baffled and unbaffled open cavities indicates that the proposed modal
expansion converges with only a few frequency-dependent eigenmodes in the
frequency range of interest. The results of this study eliminate the ambiguity
involving the selection of appropriate basis functions, in modal expansion for
the forced response problem in open cavities.


title:
Using 21-cm absorption surveys to measure the average HI spin
  temperature in distant galaxies

abstract:
  We present a statistical method for measuring the average HI spin temperature
in distant galaxies using the expected detection yields from future wide-field
21cm absorption surveys. As a demonstrative case study we consider a simulated
all-southern-sky survey of 2-h per pointing with the Australian Square
Kilometre Array Pathfinder for intervening HI absorbers at intermediate
cosmological redshifts between $z = 0.4$ and $1$. For example, if such a survey
yielded $1000$ absorbers we would infer a harmonic-mean spin temperature of
$\overline{T}_\mathrm{spin} \sim 100$K for the population of damped Lyman
$\alpha$ (DLAs) absorbers at these redshifts, indicating that more than $50$
per cent of the neutral gas in these systems is in a cold neutral medium (CNM).
Conversely, a lower yield of only 100 detections would imply
$\overline{T}_\mathrm{spin} \sim 1000$K and a CNM fraction less than $10$ per
cent. We propose that this method can be used to provide independent
verification of the spin temperature evolution reported in recent 21cm surveys
of known DLAs at high redshift and for measuring the spin temperature at
intermediate redshifts below $z \approx 1.7$, where the Lyman-$\alpha$ line is
inaccessible using ground-based observatories. Increasingly more sensitive and
larger surveys with the Square Kilometre Array should provide stronger
statistical constraints on the average spin temperature. However, these will
ultimately be limited by the accuracy to which we can determine the HI column
density frequency distribution, the covering factor and the redshift
distribution of the background radio source population.


title:
Logic Programming with Graph Automorphism: Integrating naut with Prolog
  (Tool Description)

abstract:
  This paper presents the plnauty~library, a Prolog interface to the nauty
graph-automorphism tool. Adding the capabilities of nauty to Prolog combines
the strength of the "generate and prune" approach that is commonly used in
logic programming and constraint solving, with the ability to reduce symmetries
while reasoning over graph objects. Moreover, it enables the integration of
nauty in existing tool-chains, such as SAT-solvers or finite domain constraints
compilers which exist for Prolog. The implementation consists of two
components: plnauty, an interface connecting \nauty's C library with Prolog,
and plgtools, a Prolog framework integrating the software component of nauty,
called gtools, with Prolog. The complete tool is available as a SWI-Prolog
module. We provide a series of usage examples including two that apply to
generate Ramsey graphs. This paper is under consideration for publication in
TPLP.


title: Topological complexity of subgroups of Artin's braid groups

abstract:
  We consider the topological complexity of subgroups of Artin's braid group
consisting of braids whose associated permutations lie in some specified
subgroup of the symmetric group. We give upper and lower bounds for the
topological complexity of such mixed braid groups. In particular we show that
the topological complexity of any subgroup of the n-strand braid group which
fixes any two strands is 2n-3, extending a result of Farber and Yuzvinsky in
the pure braid case. In addition, we generalise our results to the setting of
higher topological complexity.


title:
A transition in the spectral statistics of quantum optical model by
  different electromagnetic fields

abstract:
  The effects of the quantized electromagnetic fields on the spectral
statistics of two-level atoms are considered. We have used the Berry- Robnik
distribution and Maximum Likelihood estimation technique to analyze the effect
of mean photon and two level atoms numbers and also the quantum number of
considered states. Results suggest the intensity of electromagnetic fields as
control parameter which the spectral statistics change due to its variation in
the 0-1200 region. Also, we observed the universality in the spectral
statistics of considered systems when the number of two level atoms is
approached to unrealistic limits and there are some suggestions about the
effect of the quantum number of selected levels and the atom-field coupling
constant on level statistics.


title: Phases of kinky holographic nuclear matter

abstract:
  Holographic QCD at finite baryon number density and zero temperature is
studied within the five-dimensional Sakai-Sugimoto model. We introduce a new
approximation that models a smeared crystal of solitonic baryons by assuming
spatial homogeneity to obtain an effective kink theory in the holographic
direction. The kink theory correctly reproduces a first order phase transition
to lightly bound nuclear matter. As the density is further increased the kink
splits into a pair of half-kink constituents, providing a concrete realization
of the previously suggested dyonic salt phase, where the bulk soliton splits
into constituents at high density. The kink model also captures the phenomenon
of baryonic popcorn, in which a first order phase transition generates an
additional soliton layer in the holographic direction. We find that this
popcorn transition takes place at a density below the dyonic salt phase, making
the latter energetically unfavourable. However, the kink model predicts only
one pop, rather than the sequence of pops suggested by previous approximations.
In the kink model the two layers produced by the single pop form the surface of
a soliton bag that increases in size as the baryon chemical potential is
increased. The interior of the bag is filled with abelian electric potential
and the instanton charge density is localized on the surface of the bag. The
soliton bag may provide a holographic description of a quarkyonic phase.


title:
Belief propagation decoding of quantum channels by passing quantum
  messages

abstract:
  Belief propagation is a powerful tool in statistical physics, machine
learning, and modern coding theory. As a decoding method, it is ubiquitous in
classical error correction and has also been applied to stabilizer-based
quantum error correction. The algorithm works by passing messages between nodes
of the factor graph associated with the code and enables efficient decoding, in
some cases even up to the Shannon capacity of the channel. Here we construct a
belief propagation algorithm which passes quantum messages on the factor graph
and is capable of decoding the classical-quantum channel with pure state
outputs. This gives explicit decoding circuits whose number of gates is
quadratic in the blocklength of the code. We also show that this decoder can be
modified to work with polar codes for the pure state channel and as part of a
polar decoder for transmitting quantum information over the amplitude damping
channel. These represent the first explicit capacity-achieving decoders for
non-Pauli channels.


title: On non-existence of full exceptional collections on some relative flags

abstract:
  In this paper we show that certain relative flags cannot have full
exceptional collections. We also prove that some of these flags are categorical
representable in dimension zero if and only if they admit a full exceptional
collection. As a consequence, these flags are categorical representable in
dimension zero if and only if they have $k$-rational points if and only if they
are $k$-rational. Moreover, we calculate the categorical representability
dimension for the flags under consideration.


title:
Generalized Aubry-Andr\'e-Harper model with p-wave superconducting
  pairing

abstract:
  We investigate a generalized Aubry-Andr\'e-Harper (AAH) model with p-wave
superconducting pairing. Both the hopping amplitudes between the nearest
neighboring lattice sites and the on-site potentials in this system are
modulated by a cosine function with a periodicity of $1/\alpha$. In the
incommensurate case [$\alpha=(\sqrt{5}-1)/2$], due to the modulations on the
hopping amplitudes, the critical region of this quasiperiodic system is
significantly reduced and the system becomes more easily to be turned from
extended states to localized states. In the commensurate case ($\alpha = 1/2$),
we find that this model shows three different phases when we tune the system
parameters: Su-Schrieffer-Heeger (SSH)-like trivial, SSH-like topological, and
Kitaev-like topological phases. The phase diagrams and the topological quantum
numbers for these phases are presented in this work. This generalized AAH model
combined with superconducting pairing provides us with a useful testfield for
studying the phase transitions from extended states to Anderson localized
states and the transitions between different topological phases.


title: Can Bioinformatics Be Considered as an Experimental Biological Science?

abstract:
  The objective of this short report is to reconsider the subject of
bioinformatics as just being a tool of experimental biological science. To do
that, we introduce three examples to show how bioinformatics could be
considered as an experimental science. These examples show how the development
of theoretical biological models generates experimentally verifiable computer
hypotheses, which necessarily must be validated by experiments in vitro or in
vivo.


title: New physics in neutral $\textbf{D}\rightarrow\textbf{VV}$ modes

abstract:
  We show that it is possible to construct observables to test the existence of
new physics in a model independent way for the $D^0\rightarrow VV$ modes using
a time-dependent analysis of the neutral $D$ meson. We show that it is possible
to identify whether the NP is due to decay, mixing or a combination of both. We
also provide numerical estimates for the polarization amplitudes for the
$D^0\rightarrow\overline{K^{*0}}\rho^0$ mode and show that our analysis is
consistent with the present data.


title: Budding Transition of Asymmetric Two-component Lipid Domains

abstract:
  We propose a model that accounts for the budding transition of asymmetric
two-component lipid domains, where the two monolayers (leaflets) have different
average compositions controlled by independent chemical potentials. Assuming a
coupling between the local curvature and local lipid composition in each of the
leaflets, we discuss the morphology and thermodynamic behavior of asymmetric
lipid domains. The membrane free-energy contains three contributions: the
bending energy, the line tension, and a Landau free-energy for a lateral phase
separation. Within a mean-field treatment, we obtain various phase diagrams
containing fully budded, dimpled, and flat states as a function of the two
leaflet compositions. The global phase behavior is analyzed, and depending on
system parameters, the phase diagrams include one-phase, two-phase and
three-phase regions. In particular, we predict various phase coexistence
regions between different morphologies of domains, which may be observed in
multi-component membranes or vesicles.

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


title: Vacuum energy of the Bukhvostov-Lipatov model

abstract:
  Bukhvostov and Lipatov have shown that weakly interacting instantons and
anti-instantons in the $O(3)$ non-linear sigma model in two dimensions are
described by an exactly soluble model containing two coupled Dirac fermions. We
propose an exact formula for the vacuum energy of the model for twisted
boundary conditions, expressing it through a special solution of the classical
sinh-Gordon equation. The formula perfectly matches predictions of the standard
renormalized perturbation theory at weak couplings as well as the conformal
perturbation theory at short distances. Our results also agree with the Bethe
ansatz solution of the model. A complete proof the proposed expression for the
vacuum energy based on a combination of the Bethe ansatz techniques and the
classical inverse scattering transform method is presented in the second part
of this work [40].


title: Reanalysis of the $X(3915)$, $X(4500)$ and $X(4700)$ with QCD sum rules

abstract:
  In this article, we study the $C\gamma_5\otimes \gamma_5C$ type and $C\otimes
C$ type scalar $cs\bar{c}\bar{s}$ tetraquark states with the QCD sum rules by
calculating the contributions of the vacuum condensates up to dimension 10 in a
consistent way. The ground state masses $M_{C\gamma_5\otimes \gamma_5C}=3.89\pm
0.05\,\rm{GeV}$ and $M_{C\otimes C}=5.48\pm0.10\,\rm{GeV}$ support assigning
the $X(3915)$ to be the ground state $C\gamma_5\otimes \gamma_5C$ type
tetraquark state with $J^{PC}=0^{++}$, but do not support assigning the
$X(4700)$ to be the ground state $C\otimes C$ type $cs\bar{c}\bar{s}$
tetraquark state with $J^{PC}=0^{++}$. Then we tentatively assign the $X(3915)$
and $X(4500)$ to be the 1S and 2S $C\gamma_5\otimes \gamma_5C$ type scalar
$cs\bar{c}\bar{s}$ tetraquark states respectively, and obtain the 1S mass
$M_{\rm 1S}=3.85^{+0.18}_{-0.17}\,\rm{GeV}$ and 2S mass $M_{\rm
2S}=4.35^{+0.10}_{-0.11}\,\rm{GeV}$ from the QCD sum rules, which support
assigning the $X(3915)$ to be the 1S $C\gamma_5\otimes \gamma_5C$ type
tetraquark state, but do not support assigning the $X(4500)$ to be the 2S
$C\gamma_5\otimes \gamma_5C$ type tetraquark state.


title: Kauffman type invariants for tied links

abstract:
  We define two new invariants for tied links. One of them can be thought as an
extension of the Kauffman polynomial and the other one as an extension of the
Jones polynomial which is constructed via a bracket polynomial for tied links.
These invariants are more powerful than both the Kauffman and the bracket
polynomials when evaluated on classical links. Further, the extension of the
Kauffman polynomial is more powerful of the Homflypt polynomial, as well as of
certain new invariants introduced recently. Also we propose a new algebra which
plays in the case of tied links the same role as the BMW algebra for the
Kauffman polynomial in the classical case. Moreover, we prove that the Markov
trace on this new algebra can be recovered from the extension of the Kauffman
polynomial defined here.


title: The Minrank of Random Graphs

abstract:
  The minrank of a graph $G$ is the minimum rank of a matrix $M$ that can be
obtained from the adjacency matrix of $G$ by switching some ones to zeros
(i.e., deleting edges) and then setting all diagonal entries to one. This
quantity is closely related to the fundamental information-theoretic problems
of (linear) index coding (Bar-Yossef et al., FOCS'06), network coding and
distributed storage, and to Valiant's approach for proving superlinear circuit
lower bounds (Valiant, Boolean Function Complexity '92).
  We prove tight bounds on the minrank of random Erd\H{o}s-R\'enyi graphs
$G(n,p)$ for all regimes of $p\in[0,1]$. In particular, for any constant $p$,
we show that $\mathsf{minrk}(G) = \Theta(n/\log n)$ with high probability,
where $G$ is chosen from $G(n,p)$. This bound gives a near quadratic
improvement over the previous best lower bound of $\Omega(\sqrt{n})$ (Haviv and
Langberg, ISIT'12), and partially settles an open problem raised by Lubetzky
and Stav (FOCS '07). Our lower bound matches the well-known upper bound
obtained by the "clique covering" solution, and settles the linear index coding
problem for random graphs.
  Finally, our result suggests a new avenue of attack, via derandomization, on
Valiant's approach for proving superlinear lower bounds for logarithmic-depth
semilinear circuits.


title:
Influence of electron-neutral elastic collisions on the instability of
  an ion-contaminated cylindrical electron cloud: 2D3V PIC-with-MCC simulations

abstract:
  This paper is a simulation based investigation of the effect of elastic
collisions and effectively elastic-like excitation collisions between electrons
and background neutrals on the dynamics of a cylindrically trapped electron
cloud that also has an ion contaminant mixed in it. Effects of the collisions
on the instability are evident from alteration in the growth rate and
energetics of the ion resonance instability caused by the presence of
background neutrals as compared to a vacuum background. Further in order to
understand if the non-ionizing collisions can independently be a cause of
destabilization of an electron cloud, a second set of numerical experiments
were performed with pure electron plasmas making non-ionizing collisions with
different densities of background neutrals. These experiments reveal that the
nature of potential energy extraction from the electron cloud by the
non-ionizing collisions is not similar to the potential energy extraction of
other destabilizing processes \textit{e.g.} a resistive wall instability. This
difference in the energy extraction process renders these non-ionizing
collisions incapable of independently triggering an instability of the cloud.


title: Molecular beam brightening by shock-wave suppression

abstract:
  Supersonic beams are a prevalent source of cold molecules utilized in the
study of chemical reactions, atom interferometry, gas-surface interactions,
precision spectroscopy, molecular cooling and more. The triumph of this method
emanates from the high densities produced in relation to other methods, however
beam density remains fundamentally limited by interference with shock waves
reflected from collimating surfaces. Here we show experimentally that this
shock interaction can be reduced or even eliminated by cryo-cooling the
interacting surface. An increase in beam density of nearly an order of
magnitude was measured at the lowest surface temperature, with no further
fundamental limitation reached. Visualization of the shock waves by plasma
discharge and reproduction with direct simulation Monte Carlo calculations both
indicate that the suppression of the shock structure is partially caused by
lowering the momentum flux of reflected particles, and significantly enhanced
by the adsorption of particles to the surface. We observe that the scaling of
beam density with source pressure is recovered, paving the way to order of
magnitude brighter cold molecular beams.

categories: physics.atom-ph physics.atm-clus physics.chem-ph quant-ph


title: Magnetic fields and chiral asymmetry in the early hot universe

abstract:
  In this paper, we study analytically the process of external generation and
subsequent free evolution of the lepton chiral asymmetry and helical magnetic
fields in the early hot universe. This process is known to be affected by the
Abelian anomaly of the electroweak gauge interactions. As a consequence, chiral
asymmetry in the fermion distribution generates magnetic fields of non-zero
helicity, and vice versa. We take into account the presence of thermal bath,
which serves as a seed for the development of instability in magnetic field in
the presence of externally generated lepton chiral asymmetry. The developed
helical magnetic field and lepton chiral asymmetry support each other,
considerably prolonging their mutual existence, in the process of `inverse
cascade' transferring magnetic-field power from small to large spatial scales.
For cosmologically interesting initial conditions, the chiral asymmetry and the
energy density of helical magnetic field are shown to evolve by scaling laws,
effectively depending on a single combined variable. In this case, the
late-time asymptotics of the conformal chiral chemical potential reproduces the
universal scaling law previously found in the literature for the system under
consideration. This regime is terminated at lower temperatures because of
scattering of electrons with chirality change, which exponentially washes out
chiral asymmetry. We derive an expression for the termination temperature as a
function of the chiral asymmetry and energy density of helical magnetic field.


title: Dimer Metadynamics

abstract:
  Sampling complex potential energies is one of the most pressing challenges of
contemporary computational science. Inspired by recent efforts that use quantum
effects and discretized Feynman's path integrals to overcome large barriers we
propose a replica exchange method. In each replica two copies of the same
system with halved potential strengths interact via inelastic springs. The
strength of the spring is varied in the different replicas so as to bridge the
gap between the infinitely strong spring, that corresponds to the Boltzmann
replica and the less tight ones. We enhance the spring length fluctuations
using Metadynamics. We test the method on simple yet challenging problems.


title: Designs for 24-vertex snarks

abstract:
  The design spectrum problem is solved for the thirty-eight 24-vertex
non-trivial snarks.


title: A note on the asymptotic normality of sums of extreme values

abstract:
  Let $X_1$, $X_2$,... be a sequence of independent random variables with
common distribution function $F$ in the domain of attraction of a Gumbel
extreme value distribution and for each integer $n\geq 1$, let $X_{1,n} \leq
... X_{n,n}$ denote the order statistics based on the first $n$ of these random
variables. Along with related results it is shown that for any sequence of
positive integers $k_n \rightarrow +\infty$ and $k_{n}/n \rightarrow 0$ as $n
\rightarrow 0$ the sum of the upper $k_n$ extreme values
$X_{n-k_{n},n}+...+X_{n,n}$, when properly centered and normalized, converges
in distribution to a standard normal random variable $N(0, 1)$. These results
constitute an extension of results by S. Cs\"{o}rg\H{o} and D.M. Mason (1985).


title: Secure Group Testing

abstract:
  The principal goal of Group Testing (GT) is to identify a small subset of
"defective" items from a large population, by grouping items into as few test
pools as possible. The test outcome of a pool is positive if it contains at
least one defective item, and is negative otherwise. GT algorithms are utilized
in numerous applications, and in many of them maintaining the privacy of the
tested items, namely, keeping secret whether they are defective or not, is
critical.
  In this paper, we consider a scenario where there is an eavesdropper (Eve)
who is able to observe a subset of the GT outcomes (pools). We propose a new
non-adaptive Secure Group Testing (SGT) scheme based on information-theoretic
principles. The new proposed test design keeps the eavesdropper ignorant
regarding the items' status. Specifically, when the fraction of tests observed
by Eve is $0 \leq \delta <1$, we prove that with the naive Maximum Likelihood
(ML) decoding algorithm the number of tests required for both correct
reconstruction at the legitimate user (with high probability) and negligible
information leakage to Eve is $\frac{1}{1-\delta}$ times the number of tests
required with no secrecy constraint for the fixed $K$ regime. By a matching
converse, we completely characterize the Secure GT capacity. Moreover, we
consider the Definitely Non-Defective (DND) computationally efficient decoding
algorithm, proposed in the literature for non-secure GT. We prove that with the
new secure test design, for $\delta < 1/2$, the number of tests required,
without any constraint on $K$, is at most $\frac{1}{1/2-\delta}$ times the
number of tests required with no secrecy constraint.


title:
Identities involving (doubly) symmetric polynomials and integrals over
  Grassmannians

abstract:
  We obtain identities involving symmetric and doubly symmetric polynomials.
These identities provide a way of handling expressions appearing in the
Atiyah-Bott-Berline-Vergne formula for Grassmannians. As corollaries, we obtain
formulas for integrals over Grassmannians of characteristic classes of the
tautological bundles. Moreover, we provide a valid proof of the Martin formula
for the classical Grassmannian.


title:
Covariant representations of subproduct systems: Invariant subspaces and
  curvature

abstract:
  Let $X=(X(n))_{n \in \mathbb{Z_+}}$ be a standard subproduct system of
$C^*$-correspondences over a $C^*$-algebra $\mathcal M.$ Assume $T=(T_n)_{n \in
\mathbb{Z_+}}$ to be a pure completely contractive, covariant representation of
$X$ on a Hilbert space $\mathcal H,$ and $\mathcal S$ to be a non-trivial
closed subspace of $\mathcal H.$ Then $\mathcal{S}$ is invariant for $T$ if and
only if there exist a Hilbert space $\mathcal{D},$ a representation $\pi$ of
$\mathcal M$ on $\mathcal D,$ and a partial isometry $\Pi:
\mathcal{F}_X\bigotimes_{\pi}\mathcal{D}\to \mathcal{H} $ such that $$\Pi
(S_n(\zeta)\otimes I_{\mathcal{D}})=T_n(\zeta)\Pi~\mbox{whenever}~\zeta\in
X(n), ~n\in \mathbb{Z_+},~\mbox{and}$$ $\mathcal S$ is the range of $\Pi,$ or
equivalently, $P_{\mathcal S}=\Pi\Pi^*.$ This result leads us to many important
consequences including Beurling type theorem and other general observations on
wandering subspaces. We extend the notion of curvature for completely
contractive, covariant representations and analyze it in terms of the above
results.


title:
p-adic Generalized Hypergeometric Equations from the Viewpoint of
  Arithmetic D-modules

abstract:
  We study the $p$-adic (generalized) hypergeometric equations by using the
theory of multiplicative convolution of arithmetic $\mathscr{D}$-modules. As a
result, we prove that the hypergeometric isocrystals with suitable rational
parameters have a structure of overconvergent $F$-isocrystals.


title:
An Empirical Evaluation of various Deep Learning Architectures for
  Bi-Sequence Classification Tasks

abstract:
  Several tasks in argumentation mining and debating, question-answering, and
natural language inference involve classifying a sequence in the context of
another sequence (referred as bi-sequence classification). For several single
sequence classification tasks, the current state-of-the-art approaches are
based on recurrent and convolutional neural networks. On the other hand, for
bi-sequence classification problems, there is not much understanding as to the
best deep learning architecture. In this paper, we attempt to get an
understanding of this category of problems by extensive empirical evaluation of
19 different deep learning architectures (specifically on different ways of
handling context) for various problems originating in natural language
processing like debating, textual entailment and question-answering. Following
the empirical evaluation, we offer our insights and conclusions regarding the
architectures we have considered. We also establish the first deep learning
baselines for three argumentation mining tasks.


title:
Bohmian mechanics in the exact factorization of electron-nuclear
  wavefunction

abstract:
  The exact factorization of an electron-nuclear wavefunction [A. Abedi, N. T.
Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] allows us to
define the rigorous nuclear time-dependent Schr\"{o}dinger equation (TDSE) with
a time-dependent potential-energy surface (TDPES) that fully accounts for the
coupling to the electronic motion and drives the nuclear wavepacket dynamics.
Here, we study whether the propagation of multiple classical trajectories can
reproduce the quantum nuclear motion in strong-field processes when their
motions are governed by the quantum Hamilton-Jacobi equation derived by
applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that
multiple classical trajectories propagated by the force from the gradient of
the exact TDPES plus the Bohmian quantum potential can reproduce the
strong-field dissociation dynamics of a one-dimensional model of the H$_2^+$
molecule. Our results show that the force from the Bohmian quantum potential
plays a non-negligible role in yielding quantum nuclear dynamics in the
strong-field process studied here, where ionization and/or splitting of nuclear
probability density occurs.


title:
Minimal generating systems and properties of Sylow 2-subgroups of
  alternating group

abstract:
  The background of this paper is the following: search of the minimal systems
of generators for this class of group which still was not founded also problem
of representation for this class of group, exploration of systems of generators
for Sylow 2-subgroups $Syl_2{A_{2^k}}$ and $Syl_2{A_{n}}$ of alternating group,
finding structure these subgroups.
  The aim of this paper is to research the structure of Sylow 2-subgroups and
to construct a minimal generating system for such subgroups. In other words,
the problem is not simply in the proof of existence of a generating set with
elements for Sylow 2-subgroup of alternating group of degree $2^k $ and its
constructive proof and proof its minimality. For the construction of minimal
generating set we used the representation of elements of group by automorphisms
of portraits for binary tree.
  The main result is the proof of minimality of this generating set of the
above described subgroups and also the description of their structure. Key
words: minimal system of generators, wreath product, Sylow subgroups, group,
semidirect product.


title:
Exciton formation assisted by longitudinal optical phonons in monolayer
  transition metal dichalcogenides

abstract:
  We examine a mechanism by which excitons are generated via the LO
(longitudinal optical) phonon-assisted scattering process after optical
excitation of monolayer transition metal dichalcogenides. The exciton formation
time is computed as a function of the exciton center-of-mass wavevector,
electron and hole temperatures, and carrier densities for known values of the
Fr\"ohlich coupling constant, LO phonon energy, lattice temperature, and the
exciton binding energy in layered structures. For the monolayer MoS$_2$, we
obtain ultrafast exciton formation times on the sub-picosecond time scale at
charge densities of 5 $\times$ 10$^{11}$ cm$^{-2}$ and carrier temperatures
less than 300 K, in good agreement with recent experimental findings ($\approx$
0.3 ps). While excitons are dominantly created at zero center-of-mass
wavevectors at low charge carrier temperatures ($\approx$ 30 K), the exciton
formation time is most rapid at non-zero wavevectors at higher temperatures
($\ge $ 120 K) of charge carriers. The results show the inverse square-law
dependence of the exciton formation times on the carrier density, consistent
with a square-law dependence of photoluminescence on the excitation density.
Our results show that excitons are formed more rapidly in exemplary monolayer
selenide-based dichalcogenides (MoSe$_2$ and WSe$_2$) than sulphide-based
dichalcogenides (MoS$_2$ and WS$_2$).


title:
Explanation of $B \to K^{(*)} \ell^+ \ell^-$ and muon $g-2$, and
  implications at the LHC

abstract:
  More than $3\sigma$ deviations from the standard model are observed in the
angular observable $P'_5$ of $B\to K^* \mu^+ \mu^-$ and muon $g-2$. To resolve
these anomalies, we extend the standard model by adding two leptoquarks. It is
found that the signal strength of the diphoton Higgs decay can exhibit a
significant deviation from unity and is within the data errors. Although
$\ell_i \to \ell_j \gamma$ puts severe bounds on some couplings, it is found
that the excesses of $P'_5$ and muon $g-2$ can still be explained and can be
accommodated to the measurement of $B_s\to \mu^+ \mu^-$ in this model. In
addition, the leptoquark effects can also explain the LHCb measurement of $R_K
= BR(B^+ \to K^+ \mu^+\mu^-)/BR(B^+ \to K^+ e^+e^-)=0.745^{+0.090}_{-0.074} \pm
0.036$, which shows a $2.6\sigma$ deviation from the standard model prediction.


title:
Chemical Reaction Rates from Ring Polymer Molecular Dynamics: Theory and
  Practical Applications

abstract:
  This Feature Article presents an overview of the current status of Ring
Polymer Molecular Dynamics (RPMD) rate theory. We first analyze the RPMD
approach and its connection to quantum transition-state theory. We then focus
on its practical applications to prototypical chemical reactions in the gas
phase, which demonstrate how accurate and reliable RPMD is for calculating
thermal chemical reaction rate coefficients in multifarious cases. This review
serves as an important checkpoint in RPMD rate theory development, which shows
that RPMD is shifting from being just one of recent novel ideas to a
well-established and validated alternative to conventional techniques for
calculating thermal chemical rate coefficients. We also hope it will motivate
further applications of RPMD to various chemical reactions.


title: First Passage Time Densities through H\"older curves

abstract:
  We prove that for a standard Brownian motion, there exists a
first-passage-time density function through a locally H\"older continuous curve
with exponent greater than 1/2. By using a property of local time of a standard
Brownian motion and the theories of partial differential equations in Cannon
[2], we find a sufficient condition for existence of the density function. We
also show that this density function is proportional to the space derivative of
the Green function of the heat equation with Dirichlet boundary condition at
the moving boundary.


title: Intersection multiplicity, Milnor number and Bernstein's theorem

abstract:
  We explicitly characterize when the Milnor number at the origin of a
polynomial or power series (over an algebraically closed field k of arbitrary
characteristic) is the minimum of all polynomials with the same Newton diagram,
which completes works of Kushnirenko (Invent. Math., 1976) and Wall (J. Reine
Angew. Math., 1999). Given a fixed collection of n convex integral polytopes in
R^n, we also give an explicit characterization of systems of n polynomials
supported at these polytopes which have the maximum number (counted with
multiplicity) of isolated zeroes on k^n, or more generally, on a union of torus
orbits on k^n; this completes the program (undertaken by many authors including
Khovanskii (Funkcional. Anal. i Prilozen, 1978), Huber and Sturmfels (Discrete
Comput. Geom., 1997), Rojas (J. Pure Appl. Algebra, 1999)) of the extension to
k^n of Bernstein's theorem (Funkcional. Anal. i Prilozen, 1975) on number of
solutions of n polynomials on (k^*)^n. Our solutions to these two problems are
connected by the computation of the intersection multiplicity at the origin of
n hypersurfaces determined by n generic polynomials.


title: Cutkosky Rules from Outer Space

abstract:
  We overview recent results on the mathematical foundations of Cutkosky rules.
We emphasize that the two operations of shrinking an internal edge or putting
internal lines on the mass-shell are natural operation on the cubical chain
complex studied in the context of geometric group theory. This together with
Cutkosky's theorem regarded as a theorem which informs us about variations
connected to the monodromy of Feynman amplitudes allows for a systematic
approach to normal and anomalous thresholds, dispersion relations and the
optical theorem. In this report we follow [1] closely.


title: On the average volume of sections of convex bodies

abstract:
  The average section functional ${\rm as}(K)$ of a centered convex body in
${\mathbb R}^n$ is the average volume of central hyperplane sections of $K$:
\begin{equation*}{\rm as}(K)=\int_{S^{n-1}}|K\cap \xi^{\perp }|\,d\sigma (\xi
).\end{equation*} We study the question if there exists an absolute constant
$C>0$ such that for every $n$, for every centered convex body $K$ in ${\mathbb
R}^n$ and for every 0<k<n, $${\rm as}(K)\ls C^k|K|^{\frac{k}{n}}\,\max_{E\in
{\rm Gr}_{n-k}}{\rm as}(K\cap E).$$ We observe that the case $k=1$ is
equivalent to the hyperplane conjecture. We show that this inequality holds
true in full generality if one replaces $C$ by $CL_K$ or $Cd_{\rm
ovr}(K,{\cal{BP}}_k^n)$, where $L_K$ is the isotropic constant of $K$ and
$d_{\rm ovr}(K,{\cal{BP}}_k^n)$ is the outer volume ratio distance from $K$ to
the class ${\cal{BP}}_k^n$ of generalized $k$-intersection bodies. We also
compare ${\rm as}(K)$ to the average of ${\rm as}(K\cap E)$ over all
$k$-codimensional sections of $K$. We examine separately the dependence of the
constants on the dimension in the case where $K$ is in some of the classical
positions as well as the natural lower dimensional analogue of the average
section functional.


title:
An experimental review on elliptic flow of strange and multi-strange
  hadrons in relativistic heavy ion collisions

abstract:
  Strange hadrons, especially multi-strange hadrons are good probes for the
early partonic stage of heavy ion collisions due to their small hadronic cross
sections. In this paper, I give a brief review on the elliptic flow
measurements of strange and multi-strange hadrons in relativistic heavy ion
collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider
(LHC).


title:
Thermodynamic limit for directed polymers and stationary solutions of
  the Burgers equation

abstract:
  The first goal of this paper is to prove multiple asymptotic results for a
time-discrete and space-continuous polymer model of a random walk in a random
potential. These results include: existence of deterministic free energy
density in the infinite volume limit for every fixed asymptotic slope;
concentration inequalities for free energy implying a bound on its fluctuation
exponent; straightness estimates implying a bound on the transversal
fluctuation exponent. The culmination of this program is almost sure existence
and uniqueness of polymer measures on one-sided infinite paths with given
endpoint and slope, and interpretation of these infinite-volume Gibbs measures
as thermodynamic limits. Moreover, we prove that marginals of polymer measures
with the same slope and different endpoints are asymptotic to each other.
  The second goal of the paper is to develop ergodic theory of the Burgers
equation with positive viscosity and random kick forcing on the real line
without any compactness assumptions. Namely, we prove a One Force -- One
Solution principle, using the infinite volume polymer measures to construct a
family of stationary global solutions for this system, and proving that each of
those solutions is a one-point pullback attractor on the initial conditions
with the same spatial average. This provides a natural extension of the same
program realized for the inviscid Burgers equation with the help of action
minimizers that can be viewed as zero temperature limits of polymer measures.


title: Quest for magicity in hypernuclei

abstract:
  In present study, we search the lambda magic number in hypernuclei within the
framework of relativistic mean field theory (RMF) with inclusion of
hyperon-nucleon and hyperon-hyperon potentials. Based on one- and two-lambda
separation energy and two-lambda shell gap, 2, 8, 14, 18, 20, 28, 34, 40, 50,
58, 68, 70 and 82 are suggested to be the $\Lambda$ magic number within the
present approach. The weakening strength of $\Lambda$ spin-orbit interaction is
responsible for emerging the new lambda shell closure other than the model
scheme. The predicted $\Lambda$ magic numbers are in remarkable agreement with
earlier predictions and hypernuclear magicity quite resembles with nuclear
magicity. %Our results also support the nuclear magicity, Our results are
supported by nuclear magicity, where neutron number N = 34 is experimentally
observed as a magic which is one of the $\Lambda$ closed shell in our
predictions. In addition, the stability of hypernuclei is also examined by
calculating the binding energy per particle, where Ni hypernucleus is found to
be most tightly bound triply magic system in considered hypernuclei. Nucleon
and lambda density distributions are observed and it is found that introduced
$\Lambda$'s have significant impact on total density and reduces the central
depression of the core nucleus. Nucleon and lambda mean field potentials and
spin-orbit interaction potentials are also observed for predicted triply magic
hypernuclei and the addition of $\Lambda$'s affect the both the potentials to a
large extent. The single-particle energy levels are also analyzed to explain
the shell gaps for triply magic multi-$\Lambda$ hypernuclei.


title:
Materials Pushing the Application Limits of Wire Grid Polarizers further
  into the Deep Ultraviolet Spectral Range

abstract:
  Wire grid polarizers (WGPs), periodic nano-optical meta-surfaces, are
convenient polarizing elements for many optical applications. However, they are
still inadequate in the deep ultraviolet spectral range. We show that to
achieve high performance ultraviolet WGPs a material with large absolute value
of the complex permittivity and extinction coefficient at the wavelength of
interest has to be utilized. This requirement is compared to refractive index
models considering intraband and interband absorption processes. We elucidate
why the extinction ratio of metallic WGPs intrinsically humble in the deep
ultraviolet, whereas wide bandgap semiconductors are superior material
candidates in this spectral range. To demonstrate this, we present the design,
fabrication and optical characterization of a titanium dioxide WGP. At a
wavelength of 193 nm an unprecedented extinction ratio of 384 and a
transmittance of 10 % is achieved.


title:
Robust Automated Human Activity Recognition and its Application to Sleep
  Research

abstract:
  Human Activity Recognition (HAR) is a powerful tool for understanding human
behaviour. Applying HAR to wearable sensors can provide new insights by
enriching the feature set in health studies, and enhance the personalisation
and effectiveness of health, wellness, and fitness applications. Wearable
devices provide an unobtrusive platform for user monitoring, and due to their
increasing market penetration, feel intrinsic to the wearer. The integration of
these devices in daily life provide a unique opportunity for understanding
human health and wellbeing. This is referred to as the "quantified self"
movement. The analyses of complex health behaviours such as sleep,
traditionally require a time-consuming manual interpretation by experts. This
manual work is necessary due to the erratic periodicity and persistent
noisiness of human behaviour. In this paper, we present a robust automated
human activity recognition algorithm, which we call RAHAR. We test our
algorithm in the application area of sleep research by providing a novel
framework for evaluating sleep quality and examining the correlation between
the aforementioned and an individual's physical activity. Our results improve
the state-of-the-art procedure in sleep research by 15 percent for area under
ROC and by 30 percent for F1 score on average. However, application of RAHAR is
not limited to sleep analysis and can be used for understanding other health
problems such as obesity, diabetes, and cardiac diseases.


title: Vectors of matroids over tracts

abstract:
  We enrich Baker and Bowler's theory of matroids over tracts with notions of
vectors and covectors. In the case of oriented matroids, these $F$-vectors and
$F$-covectors coincide with the usual signed vectors and signed covectors. In
the case of matroids over a field $F$, the $F$-covector set resp. $F$-vector
set of an $F$-matroid is a linear subspace of $F^E$ resp. its orthogonal
complement.


title:
A quantum version of the algebra of distributions of
  $\operatorname{SL}_2$

abstract:
  Let $\lambda$ be a primitive root of unity of order $\ell$. We introduce a
family of finite-dimensional algebras
$\{\mathcal{D}_{\lambda,N}(\mathfrak{sl}_2)\}_{N\in\mathbb{N}_0}$ over the
complex numbers, such that $\mathcal{D}_{\lambda,N}(\mathfrak{sl}_2)$ is a
subalgebra of $\mathcal{D}_{\lambda,M}(\mathfrak{sl}_2)$ if $N<M$, and
$\mathcal{D}_{\lambda,N-1}(\mathfrak{sl}_2)\subset
\mathcal{D}_{\lambda,N}(\mathfrak{sl}_2)$ is a
$\mathfrak{u}_{\lambda}(\mathfrak{sl}_2)$-cleft extension.
  The simple $\mathcal{D}_{\lambda,N}(\mathfrak{sl}_2)$-modules
$(\mathcal{L}_{N}(p))_{0\le p<\ell^{N+1}}$ are highest weight modules, which
admit a tensor product decomposition: the first factor is a simple
$\mathfrak{u}_{\lambda}(\mathfrak{sl}_2)$-module and the second factor is a
simple $\mathcal{D}_{\lambda,N-1}(\mathfrak{sl}_2)$-module. This factorization
resembles the corresponding Steinberg decomposition, and the family of algebras
resembles the presentation of algebra of distributions of $\operatorname{SL}_2$
as a filtration by finite-dimensional subalgebras.


title: Weakly globular Tamsamani N-categories and their rigidification

abstract:
  We introduce a new class of higher categorical structures called weakly
globular Tamsamani n-categories. These generalize the Tamsamani-Simpson model
of higher categories by using the new paradigm of weak globularity to weaken
higher categorical structures. We prove this new structure is suitably
equivalent to a simpler one previously introduced by the author, called weakly
globular n-fold categories.


title: Self dual reflexive simplices with Eulerian polynomials

abstract:
  A lattice polytope $\mathcal{P}$ is called reflexive if its dual
$\mathcal{P}^\vee$ is a lattice polytope. The property that $\mathcal{P}$ is
unimodularly equivalent to $\mathcal{P}^\vee$ does not hold in general, and in
fact there are few examples of such polytopes. In this note, we introduce a new
reflexive simplex $Q_n$ which has this property. Additionally, we show that
$\delta$-polynomalial of $Q_n$ is the Eulerian polynomial and show the
existence of a regular, flag, unimodular triangulation.


title:
Cell averaging two-scale convergence: Applications to periodic
  homogenization

abstract:
  The aim of the paper is to introduce an alternative notion of two-scale
convergence which gives a more natural modeling approach to the homogenization
of partial differential equations with periodically oscillating coefficients:
while removing the bother of the admissibility of test functions, it
nevertheless simplifies the proof of all the standard compactness results which
made classical two-scale convergence very worthy of interest: bounded sequences
in $L^2_{\sharp}[Y,L^2(\Omega)]$ and $L^2_{\sharp}[Y,H^1(\Omega)]$ are proven
to be relatively compact with respect to this new type of convergence. The
strengths of the notion are highlighted on the classical homogenization problem
of linear second-order elliptic equations for which first order boundary
corrector-type results are also established. Eventually, possible weaknesses of
the method are pointed out on a nonlinear problem: the weak two-scale
compactness result for $\mathbb{S}^2$-valued stationary harmonic maps.


title: Uniform determinantal representations

abstract:
  The problem of expressing a specific polynomial as the determinant of a
square matrix of affine-linear forms arises from algebraic geometry,
optimisation, complexity theory, and scientific computing. Motivated by recent
developments in this last area, we introduce the notion of a uniform
determinantal representation, not of a single polynomial but rather of all
polynomials in a given number of variables and of a given maximal degree. We
derive a lower bound on the size of the matrix, and present a construction
achieving that lower bound up to a constant factor as the number of variables
is fixed and the degree grows. This construction marks an improvement upon a
recent construction due to Plestenjak-Hochstenbach, and we investigate the
performance of new representations in their root-finding technique for
bivariate systems. Furthermore, we relate uniform determinantal representations
to vector spaces of singular matrices, and we conclude with a number of future
research directions.


title:
Cosmological implications of modified gravity induced by quantum metric
  fluctuations

abstract:
  We investigate the cosmological implications of modified gravities induced by
the quantum fluctuations of the gravitational metric. If the metric can be
decomposed as the sum of the classical and of a fluctuating part, of quantum
origin, then the corresponding Einstein quantum gravity generates at the
classical level modified gravity models with a nonminimal coupling between
geometry and matter. As a first step in our study, after assuming that the
expectation value of the quantum correction can be generally expressed in terms
of an arbitrary second order tensor constructed from the metric and from the
thermodynamic quantities characterizing the matter content of the Universe, we
derive the (classical) gravitational field equations in their general form. We
analyze in detail the cosmological models obtained by assuming that the quantum
correction tensor is given by the coupling of a scalar field and of a scalar
function to the metric tensor, and by a term proportional to the matter
energy-momentum tensor. For each considered model we obtain the gravitational
field equations, and the generalized Friedmann equations for the case of a flat
homogeneous and isotropic geometry. In some of these models the divergence of
the matter energy-momentum tensor is non-zero, indicating a process of matter
creation, which corresponds to an irreversible energy flow from the
gravitational field to the matter fluid, and which is direct consequence of the
nonminimal curvature-matter coupling. The cosmological evolution equations of
these modified gravity models induced by the quantum fluctuations of the metric
are investigated in detail by using both analytical and numerical methods, and
it is shown that a large variety of cosmological models can be constructed,
which, depending on the numerical values of the model parameters, can exhibit
both accelerating and decelerating behaviors.


title: A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991-2014

abstract:
  The law of allometric scaling based on Zipf distributions can be employed to
research hierarchies of cities in a geographical region. However, the
allometric patterns are easily influenced by random disturbance from the noises
in observational data. In theory, both the allometric growth law and Zipf's law
are related to the hierarchical scaling laws associated with fractal structure.
In this paper, the scaling laws of hierarchies with cascade structure are used
to study Chinese cities, and the method of R/S analysis is applied to analyzing
the change trend of the allometric scaling exponents. The results show that the
hierarchical scaling relations of Chinese cities became clearer and clearer
from 1991 to 2014 year; the global allometric scaling exponent values
fluctuated around 0.85, and the local scaling exponent approached to 0.85. The
Hurst exponent of the allometric parameter change is greater than 0.5,
indicating persistence and a long-term memory of urban evolution. The main
conclusions can be reached as follows: the allometric scaling law of cities
represents an evolutionary order rather than an invariable rule, which emerges
from self-organized process of urbanization, and the ideas from allometry and
fractals can be combined to optimize spatial and hierarchical structure of
urban systems in future city planning.


title: Understanding Fractal Dimension of Urban Form through Spatial Entropy

abstract:
  Spatial patterns and processes of cities can be described with various
entropy functions. However, spatial entropy always depends on the scale of
measurement, and it is difficult to find a characteristic value for it. In
contrast, fractal parameters can be employed to characterize scale-free
phenomena. This paper is devoted to exploring the similarities and differences
between spatial entropy and fractal dimension in urban description. Drawing an
analogy between cities and growing fractals, we illustrate the definitions of
fractal dimension based on different entropy concepts. Three representative
fractal dimensions in the multifractal dimension set are utilized to make
empirical analyses of urban form of two cities. The results show that the
entropy values are not determinate, but the fractal dimension value is certain;
if the linear size of boxes is small enough (e.g., <1/25), the linear
correlation between entropy and fractal dimension is clear. Further empirical
analysis indicates that fractal dimension is close to the characteristic values
of spatial entropy. This suggests that the physical meaning of fractal
dimension can be interpreted by the ideas from entropy and scales and the
conclusion is revealing for future spatial analysis of cities. Key words:
fractal dimension; entropy; mutlifractals; scaling; urban form; Chinese cities


title: Gabriel localization theory and its applications

abstract:
  In this article first we develop the Gabriel localizations (abbreviated as
G-localizations) for commutative rings, specially some new results in this
direction are proven. Then, as an application, it is shown that a ring map is a
flat epimorphism if and only if it corresponds to a kind of the
G-localizations. As a by-product of this study, a characterization for the
flatness of the quotient rings is given. The exactness of the G-localization
functor are characterized. The structure of prime ideals in the G-localization
rings are also studied. Finally, it is shown that the Gabriel localization
theory is a natural generalization of the usual localization theory.


title:
From Planck data to Planck era: Observational tests of Holographic
  Cosmology

abstract:
  We test a class of holographic models for the very early universe against
cosmological observations and find that they are competitive to the standard
$\Lambda$CDM model of cosmology. These models are based on three dimensional
perturbative super-renormalizable Quantum Field Theory (QFT), and while they
predict a different power spectrum from the standard power-law used in
$\Lambda$CDM, they still provide an excellent fit to data (within their regime
of validity). By comparing the Bayesian evidence for the models, we find that
$\Lambda$CDM does a better job globally, while the holographic models provide a
(marginally) better fit to data without very low multipoles (i.e. $l\lesssim
30$), where the dual QFT becomes non-perturbative. Observations can be used to
exclude some QFT models, while we also find models satisfying all
phenomenological constraints: the data rules out the dual theory being
Yang-Mills theory coupled to fermions only, but allows for Yang-Mills theory
coupled to non-minimal scalars with quartic interactions. Lattice simulations
of 3d QFT's can provide non-perturbative predictions for large-angle statistics
of the cosmic microwave background, and potentially explain its apparent
anomalies.


title:
Converse results, saturation and quasi-optimality for Lavrentiev
  regularization of accretive problems

abstract:
  This paper deals with Lavrentiev regularization for solving linear ill-posed
problems, mostly with respect to accretive operators on Hilbert spaces. We
present converse and saturation results which are an important part in
regularization theory. As a byproduct we obtain a new result on the
quasi-optimality of a posteriori parameter choices. Results in this paper are
formulated in Banach spaces whenever possible.


title: Integral transform of the Galue type Struve function

abstract:
  This paper refers to the study of generalized Struve type function. Using
generalized Galue type Struve function (GTSF) by Nisar et al. [13], we derive
various integral transform, including Euler transform, Laplace transform,
Whittakar transform, K-transform and Fractional Fourier transform. The results
are expressed in terms of generalized Wright function. The transform
established here are general in nature and are likely to find useful in applied
problem of Sciences, engineering and technology. Certain interesting special
cases of the main results are also considered.


title: Stochastic Broadcast Control of Multi-Agent Swarms

abstract:
  We present a model for controlling swarms of mobile agents via broadcast
control, assumed to be detected by a random set of agents in the swarm. The
agents that detect the control signal become ad-hoc leaders of the swarm. The
agents are assumed to be velocity controlled, identical, anonymous, memory-less
units with limited capabilities of sensing their neighborhood. Each agent is
programmed to behave according to a linear local gathering process, based on
the relative position of all its neighbors. The detected exogenous control,
which is a desired velocity vector, is added by the leaders to the local
gathering control. The graph induced by the agents adjacency is referred to as
the visibility graph. We show that for piece-wise constant system parameters
and a connected visibility graph, the swarm asymptotically aligns in each
time-interval on a line in the direction of the exogenous control signal, and
all the agents move with identical speed. These results hold for two models of
pairwise influence in the gathering process, uniform and scaled. The impact of
the influence model is mostly evident when the visibility graph is incomplete.
These results are conditioned by the preservation of the connectedness of the
visibility graph. In the second part of the report we analyze sufficient
conditions for preserving the connectedness of the visibility graph. We show
that if the visibility graph is complete then certain bounds on the control
signal suffice to preserve the completeness of the graph. However, when the
graph is incomplete, general conditions, independent of the leaders topology,
could not be found.


title:
Stationarity of asymptotically flat non-radiating electrovacuum
  spacetimes

abstract:
  It is proven that a solution to the Einstein-Maxwell equations whose
gravitational and electromagnetic radiation fields vanish is in fact stationary
in a neighbourhood of spatial infinity. That is, if the Weyl and Faraday
tensors decay suitably fast, then there exists a time-like Killing vector field
in the region outside the bifurcate horizon of a sphere of sufficiently large
radius. In particular, truly dynamical time-periodic electrovacuum spacetimes
do not exist. This is an extension of earlier work by Alexakis and Schlue and
Bi\v{c}\'{a}k, Sholtz and Tod to include electromagnetism.


title: Statistical Industry Classification

abstract:
  We give complete algorithms and source code for constructing (multilevel)
statistical industry classifications, including methods for fixing the number
of clusters at each level (and the number of levels). Under the hood there are
clustering algorithms (e.g., k-means). However, what should we cluster?
Correlations? Returns? The answer turns out to be neither and our backtests
suggest that these details make a sizable difference. We also give an algorithm
and source code for building "hybrid" industry classifications by improving
off-the-shelf "fundamental" industry classifications by applying our
statistical industry classification methods to them. The presentation is
intended to be pedagogical and geared toward practical applications in
quantitative trading.


title:
Modeling the coevolution between citations and coauthorships in
  scientific papers

abstract:
  Collaborations and citations within scientific research grow simultaneously
and interact dynamically. Modelling the coevolution between them helps to study
many phenomena that can be approached only through combining citation and
coauthorship data. A geometric graph for the coevolution is proposed, the
mechanism of which synthetically expresses the interactive impacts of authors
and papers in a geometrical way. The model is validated against a data set of
papers published on PNAS during 2007-2015. The validation shows the ability to
reproduce a range of features observed with citation and coauthorship data
combined and separately. Particularly, in the empirical distribution of
citations per author there exist two limits, in which the distribution appears
as a generalized Poisson and a power-law respectively. Our model successfully
reproduces the shape of the distribution, and provides an explanation for how
the shape emerges via the decisions of authors. The model also captures the
empirically positive correlations between the numbers of authors' papers,
citations and collaborators.


title: On a conjecture of Imrich and M\"uller

abstract:
  A conjecture of Imrich and M\"uller on rank of the intersection of subgroups
of free groups is disproved.


title: Neural scaling laws for an uncertain world

abstract:
  Autonomous neural systems must efficiently process information in a wide
range of novel environments, which may have very different statistical
properties. We consider the problem of how to optimally distribute receptors
along a one-dimensional continuum consistent with the following design
principles. First, neural representations of the world should obey a neural
uncertainty principle---making as few assumptions as possible about the
statistical structure of the world. Second, neural representations should
convey, as much as possible, equivalent information about environments with
different statistics. The results of these arguments resemble the structure of
the visual system and provide a natural explanation of the behavioral
Weber-Fechner law, a foundational result in psychology. Because the derivation
is extremely general, this suggests that similar scaling relationships should
be observed not only in sensory continua, but also in neural representations of
``cognitive' one-dimensional quantities such as time or numerosity.


title: Two charmoniumlike charged axial resonances near 3885 MeV

abstract:
  It is argued that the charged $Z^+_c(3885)$ resonance, treated as a
`molecular' state of charmed $D$ and $D^*$ mesons, is likely to consist of two
peaks unequally coupled to the $D^{*+} \bar D^0$ and $D^+ \bar D^{*0}$
channels. The peaks should be split in mass by at least approximately 1.5 MeV.
This behavior arises from an enhancement of the effect of isospin violation in
the masses of the $D$ and $D^*$ mesons due to apparent suppression of forces
between the mesons depending on the spins of the heavy as well as of the light
quarks. The suggested double-peak structure can be studied either by direct
shape measurement in the channels with heavy mesons, or by isospin-violating
transitions from $Z_c^\pm(3885)$ to the states of charmonium plus a light
meson.


title: New Upper Bound for Sums of Dilates

abstract:
  For $\lambda \in \mathbb{Z}$, let $\lambda \cdot A = \{ \lambda a : a \in
A\}$. Suppose $r, h\in \mathbb{Z}$ are sufficiently large and comparable to
each other. We prove that if $|A+A| \le K |A|$ and $\lambda_1, \ldots,
\lambda_h \le 2^r$, then \[ |\lambda_1 \cdot A + \ldots + \lambda_h \cdot A |
\le K^{ 7 rh /\ln (r+h) } |A|. \] This improves upon a result of Bukh who shows
that \[ |\lambda_1 \cdot A + \ldots + \lambda_h \cdot A | \le K^{O(rh)} |A|. \]
Our main technique is to combine Bukh's idea of considering the binary
expansion of $\lambda_i$ with a result on biclique decompositions of bipartite
graphs.lique decompositions.


title: Gland Instance Segmentation by Deep Multichannel Neural Networks

abstract:
  In this paper, we propose a new image instance segmentation method that
segments individual glands (instances) in colon histology images. This is a
task called instance segmentation that has recently become increasingly
important. The problem is challenging since not only do the glands need to be
segmented from the complex background, they are also required to be
individually identified. Here we leverage the idea of image-to-image prediction
in recent deep learning by building a framework that automatically exploits and
fuses complex multichannel information, regional, location and boundary
patterns in gland histology images. Our proposed system, deep multichannel
framework, alleviates heavy feature design due to the use of convolutional
neural networks and is able to meet multifarious requirement by altering
channels. Compared to methods reported in the 2015 MICCAI Gland Segmentation
Challenge and other currently prevalent methods of instance segmentation, we
observe state-of-the-art results based on a number of evaluation metrics.


title: On joins and intersections of subgroups in free groups

abstract:
  We study graphs of (generalized) joins and intersections of finitely
generated subgroups of a free group. We show how to disprove a lemma of Imrich
and M\"uller on these graphs and how to repair this lemma.


title: Planetary engulfment as a trigger for white dwarf pollution

abstract:
  The presence of a planetary system can shield a planetesimal disk from the
secular gravitational perturbations due to distant outer massive objects
(planets or stellar companions). As the host star evolves off the main sequence
to become a white dwarf, these planets can be engulfed, triggering secular
instabilities and leading to the tidal disruptions of small rocky bodies. These
disrupted bodies can feed the white dwarfs with rocky material and possibly
explain the high-metallicity material in their atmospheres. We illustrate how
this mechanism can operate when the gravitational perturbations are due to the
Kozai-Lidov mechanism from a stellar binary companion. We show that this
mechanism can explain the observed levels of accretion if: (1) the planetary
engulfment happens fast compared to the secular timescale, which is generally
the case for wide binaries ($>100$ AU) and planetary engulfment during the
Asymptotic Giant Branch; (2) the planetesimal disk has a total mass of
$\sim10^{-4}-10^{-2}M_\oplus$. We show that this new mechanism can provide a
steady supply of material throughout the entire life of the white dwarfs for
all cooling ages and can account for a large fraction (up to nearly half) of
the observed polluted WDs.


title: Observation of the photon-blockade breakdown phase transition

abstract:
  Non-equilibrium phase transitions exist in damped-driven open quantum
systems, when the continuous tuning of an external parameter leads to a
transition between two robust steady states. In second-order transitions this
change is abrupt at a critical point, whereas in first-order transitions the
two phases can co-exist in a critical hysteresis domain. Here we report the
observation of a first-order dissipative quantum phase transition in a driven
circuit quantum electrodynamics (QED) system. It takes place when the photon
blockade of the driven cavity-atom system is broken by increasing the drive
power. The observed experimental signature is a bimodal phase space
distribution with varying weights controlled by the drive strength. Our
measurements show an improved stabilization of the classical attractors up to
the milli-second range when the size of the quantum system is increased from
one to three artificial atoms. The formation of such robust pointer states
could be used for new quantum measurement schemes or to investigate
multi-photon quantum many-body phases.


title: Testing the Kerr metric with the iron line and the KRZ parametrization

abstract:
  The spacetime geometry around astrophysical black holes is supposed to be
well approximated by the Kerr metric, but deviations from the Kerr solution are
predicted in a number of scenarios involving new physics. Broad iron K$\alpha$
lines are commonly observed in the X-ray spectrum of black holes and originate
by X-ray fluorescence of the inner accretion disk. The profile of the iron line
is sensitively affected by the spacetime geometry in the strong gravity region
and can be used to test the Kerr black hole hypothesis. In this paper, we
extend previous work in the literature. In particular: i) as test-metric, we
employ the parametrization recently proposed by Konoplya, Rezzolla, and
Zhidenko, which has a number of subtle advantages with respect to the existing
approaches; ii) we perform simulations with specific X-ray missions, and we
consider NuSTAR as a prototype of current observational facilities and eXTP as
an example of the next generation of X-ray observatories. We find a significant
difference between the constraining power of NuSTAR and eXTP. With NuSTAR, it
is difficult or impossible to constrain deviations from the Kerr metric. With
eXTP, in most cases we can obtain quite stringent constraints (modulo we have
the correct astrophysical model).


title:
Caching as a Service: Small-cell Caching Mechanism Design for Service
  Providers

abstract:
  Wireless network virtualization has been well recognized as a way to improve
the flexibility of wireless networks by decoupling the functionality of the
system and implementing infrastructure and spectrum as services. Recent studies
have shown that caching provides a better performance to serve the content
requests from mobile users. In this paper, we propose that \emph{caching can be
applied as a service} in mobile networks, i.e., different service providers
(SPs) cache their contents in the storages of wireless facilities that owned by
mobile network operators (MNOs). Specifically, we focus on the scenario of
\emph{small-cell networks}, where cache-enabled small-cell base stations (SBSs)
are the facilities to cache contents. To deal with the competition for storages
among multiple SPs, we design a mechanism based on multi-object auctions, where
the time-dependent feature of system parameters and the frequency of content
replacement are both taken into account. Simulation results show that our
solution leads to a satisfactory outcome.


title: Distant Solar System Objects identified in the Pan-STARRS1 survey

abstract:
  We present a method to identify distant solar system objects in long-term
wide-field asteroid survey data, and conduct a search for them in the
Pan-STARRS1 (PS1) image data acquired from 2010 to mid-2015. We demonstrate
that our method is able to find multi-opposition orbital links, and we present
the resulting orbital distributions which consist of 154 Centaurs, 255
classical Trans-Neptunian Objects (TNOs), 121 resonant TNOs, 89 Scattered Disc
Objects (SDOs) and 10 comets. Our results show more than half of these are new
discoveries, including a newly discovered 19th magnitude TNO. Our identified
objects do not show clustering in their argument of perihelia, which if
present, might support the existence of a large unknown planetary-sized object
in the outer solar system.


title: Scalable GaSb/InAs tunnel FETs with non-uniform body thickness

abstract:
  GaSb/InAs heterojunction tunnel field-effect transistors are strong
candidates in building future low-power integrated circuits, as they could
provide both steep subthreshold swing and large ON-state current
($I_{\rm{ON}}$). However, at short channel lengths they suffer from large
tunneling leakage originating from the small band gap and small effective
masses of the InAs channel. As proposed in this article, this problem can be
significantly mitigated by reducing the channel thickness meanwhile retaining a
thick source-channel tunnel junction, thus forming a design with a non-uniform
body thickness. Because of the quantum confinement, the thin InAs channel
offers a large band gap and large effective masses, reducing the ambipolar and
source-to-drain tunneling leakage at OFF state. The thick GaSb/InAs tunnel
junction, instead, offers a low tunnel barrier and small effective masses,
allowing a large tunnel probability at ON state. In addition, the confinement
induced band discontinuity enhances the tunnel electric field and creates a
resonant state, further improving $I_{\rm{ON}}$. Atomistic quantum transport
simulations show that ballistic $I_{\rm{ON}}=284$A/m is obtained at 15nm
channel length, $I_{\rm{OFF}}=1\times10^{-3}$A/m, and $V_{\rm{DD}}=0.3$V. While
with uniform body thickness, the largest achievable $I_{\rm{ON}}$ is only
25A/m. Simulations also indicate that this design is scalable to sub-10nm
channel length.