title:
M\"obius strips before M\"obius: Topological hints in ancient
  representations

abstract:
  August M\"obius discovered his eponymous strip --- also found almost
contemporaneously by Johann Listing --- in 1858, so a pre-1858 M\"obius band
would be an interesting object. It turns out there were lots of them.


title:
Linear kernels for edge deletion problems to immersion-closed graph
  classes

abstract:
  Suppose $\mathcal{F}$ is a finite family of graphs. We consider the following
meta-problem, called $\mathcal{F}$-Immersion Deletion: given a graph $G$ and
integer $k$, decide whether the deletion of at most $k$ edges of $G$ can result
in a graph that does not contain any graph from $\mathcal{F}$ as an immersion.
This problem is a close relative of the $\mathcal{F}$-Minor Deletion problem
studied by Fomin et al. [FOCS 2012], where one deletes vertices in order to
remove all minor models of graphs from $\mathcal{F}$.
  We prove that whenever all graphs from $\mathcal{F}$ are connected and at
least one graph of $\mathcal{F}$ is planar and subcubic, then the
$\mathcal{F}$-Immersion Deletion problem admits: a constant-factor
approximation algorithm running in time $O(m^3 \cdot n^3 \cdot \log m)$; a
linear kernel that can be computed in time $O(m^4 \cdot n^3 \cdot \log m)$; and
a $O(2^{O(k)} + m^4 \cdot n^3 \cdot \log m)$-time fixed-parameter algorithm,
where $n,m$ count the vertices and edges of the input graph.
  These results mirror the findings of Fomin et al. [FOCS 2012], who obtained a
similar set of algorithmic results for $\mathcal{F}$-Minor Deletion, under the
assumption that at least one graph from $\mathcal{F}$ is planar. An important
difference is that we are able to obtain a linear kernel for
$\mathcal{F}$-Immersion Deletion, while the exponent of the kernel of Fomin et
al. for $\mathcal{F}$-Minor Deletion depends heavily on the family
$\mathcal{F}$. In fact, this dependence is unavoidable under plausible
complexity assumptions, as proven by Giannopoulou et al. [ICALP 2015]. This
reveals that the kernelization complexity of $\mathcal{F}$-Immersion Deletion
is quite different than that of $\mathcal{F}$-Minor Deletion.


title:
Unidirectional Quorum-based Cycle Planning for Efficient Resource
  Utilization and Fault-Tolerance

abstract:
  In this paper, we propose a greedy cycle direction heuristic to improve the
generalized $\mathbf{R}$ redundancy quorum cycle technique. When applied using
only single cycles rather than the standard paired cycles, the generalized
$\mathbf{R}$ redundancy technique has been shown to almost halve the necessary
light-trail resources in the network. Our greedy heuristic improves this
cycle-based routing technique's fault-tolerance and dependability.
  For efficiency and distributed control, it is common in distributed systems
and algorithms to group nodes into intersecting sets referred to as quorum
sets. Optimal communication quorum sets forming optical cycles based on
light-trails have been shown to flexibly and efficiently route both
point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle
routing techniques will use pairs of cycles to achieve both routing and
fault-tolerance, which uses substantial resources and creates the potential for
underutilization. Instead, we use a single cycle and intentionally utilize
$\mathbf{R}$ redundancy within the quorum cycles such that every point-to-point
communication pairs occur in at least $\mathbf{R}$ cycles. Without the paired
cycles the direction of the quorum cycles becomes critical to the fault
tolerance performance. For this we developed a greedy cycle direction heuristic
and our single fault network simulations show a reduction of missing pairs by
greater than 30%, which translates to significant improvements in fault
coverage.


title:
Asymptotic solution for high vorticity regions in incompressible 3D
  Euler equations

abstract:
  Incompressible 3D Euler equations develop high vorticity in very thin
pancake-like regions from generic large-scale initial conditions. In this work
we propose an exact solution of the Euler equations for the asymptotic pancake
evolution. This solution combines a shear flow aligned with an asymmetric
straining flow, and is characterized by a single asymmetry parameter and an
arbitrary transversal vorticity profile. The analysis is based on detailed
comparison with numerical simulations performed using a pseudo-spectral method
in anisotropic grids of up to 972 x 2048 x 4096.


title:
Self-Organized Stationary Patterns in Networks of Bistable Chemical
  Reactions

abstract:
  Experiments with networks of discrete reactive bistable electrochemical
elements organized in regular and nonregular tree networks are presented to
confirm an alternative to the Turing mechanism for the formation of
self-organized stationary patterns. The results show that the pattern formation
can be described by the identification of domains that can be activated
individually or in combinations. The method also enabled the localization of
chemical reactions to network substructures and the identification of critical
sites whose activation results in complete activation of the system. Although
the experiments were performed with a specific nickel electrodissolution
system, they reproduced all the salient dynamic behavior of a general network
model with a single nonlinearity parameter. Thus, the considered
pattern-formation mechanism is very robust, and similar behavior can be
expected in other natural or engineered networked systems that exhibit, at
least locally, a treelike structure.


title:
Spin correlation tensor for measurement of quantum entanglement in
  electron-electron scattering

abstract:
  We consider the problem of correct measurement of a quantum entanglement in
the two-body electron-electron scattering. An expression is derived for a spin
correlation tensor of a pure two-electron state. A geometrical measure of a
quantum entanglement as the distance between two forms of this tensor in
entangled and separable cases is presented. We prove that this measure
satisfies properties of a valid entanglement measure: nonnegativity,
discriminance, normalization, non-growth under local operations and classical
communication. This measure is calculated for a problem of electron-electron
scattering. We prove that it does not depend on the azimuthal rotation angle of
the second electron spin relative to the first electron spin before scattering.
Finally, we specify how to find a spin correlation tensor and the related
measure of a quantum entanglement in an experiment with electron-electron
scattering.


title: Charge puddles in a completely compensated topological insulator

abstract:
  Compensation of intrinsic charges is widely used to reduce the bulk
conductivity of 3D topological insulators (TIs). Here we use low temperature
electron irradiation-induced defects paired with in-situ electrical transport
measurements to fine-tune the degree of compensation in Bi2Te3. The coexistence
of electrons and holes at the point of optimal compensation can only be
explained by bulk carriers forming charge puddles. These need to be considered
to understand the electric transport in compensated TI samples, irrespective of
the method of compensation.


title: Extended Learning Graphs for Triangle Finding

abstract:
  We present new quantum algorithms for Triangle Finding improving its best
previously known quantum query complexities for both dense and spare
instances.For dense graphs on $n$ vertices, we get a query complexity of
$O(n^{5/4})$ without any of the extra logarithmic factors present in the
previous algorithm of Le Gall [FOCS'14]. For sparse graphs with $m\geq n^{5/4}$
edges, we get a query complexity of $O(n^{11/12}m^{1/6}\sqrt{\log n})$, which
is better than the one obtained by Le Gall and Nakajima [ISAAC'15] when $m \geq
n^{3/2}$. We also obtain an algorithm with query complexity ${O}(n^{5/6}(m\log
n)^{1/6}+d_2\sqrt{n})$ where $d_2$ is the variance of the degree distribution.
Our algorithms are designed and analyzed in a new model of learning graphs that
we call extended learning graphs. In addition, we present a framework in order
to easily combine and analyze them. As a consequence we get much simpler
algorithms and analyses than previous algorithms of Le Gall {\it et al} based
on the MNRS quantum walk framework [SICOMP'11].


title:
Modulus stabilisation in a backreacted warped geometry model via
  Goldberger-Wise mechanism

abstract:
  In the context of higher dimensional braneworld scenario, the stabilisation
of extra dimensional modulus is an essential requirement for resolving the
gauge hierarchy problem in the context of Standard Model of elementary particle
Physics. For Randall-Sundrum (RS) warped extra dimensional model, Goldberger
and Wise (GW) proposed a much useful mechanism to achieve this using a scalar
field in the bulk spacetime ignoring the effects of backreaction of the scalar
field on the background metric. In this article we examine the influence of the
backreaction of the stabilising field on the stabilisation condition as well as
that on the Physics of the extra dimensional modulus namely radion. In
particular we obtain the modifications of the mass and the coupling of the
radion with the Standard Model (SM) matter fields on the TeV brane due to
backreaction effect. Our calculation also brings out an important equivalence
between the treatments followed by Csaki et.al. in \cite{kribs} and
Goldberger-Wise in \cite{GW1,GW_radion}.


title:
Impact of the Photon-Initiated process on Z'-boson searches in di-lepton
  final states at the LHC

abstract:
  We discuss the effect of the Photon Initiated (PI) process on the dilepton
channel at the LHC. Adopting various QED PDF sets, we evaluate the contribution
produced by two resolved photons which is not included in the Equivalent Photon
Approximation (EPA). We compare the PI central value as predicted by the CTEQ,
MRST and NNPDF collaborations. With the NNPDF2.3QED set of replicas we also
estimate the PDF uncertainties on the PI central value. We show the effect of
the inclusion of the PI contribution and its PDF uncertainties on neutral heavy
Z'-boson searches. We explore the two scenarios of narrow and broad resonances,
including in the analysis the reconstructed Forward-Backward Asymmetry
observable, the latter being less affected by systematics effects.


title: Total domination polynomial of graphs from primary subgraphs

abstract:
  Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is
a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of
$D$. The total domination number of $G$ is equal to minimum cardinality of
total dominating set in $G$ and denoted by $\gamma_t(G)$. The total domination
polynomial of $G$ is the polynomial $D_t(G,x)=\sum d_t(G,i)$, where $d_t(G,i)$
is the number of total dominating sets of $G$ of size $i$. Let $G$ be a
connected graph constructed from pairwise disjoint connected graphs $G_1,\ldots
,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identify these two
vertices. Then continue in this manner inductively. We say that $G$ is obtained
by point-attaching from $G_1, \ldots ,G_k$ and that $G_i$'s are the primary
subgraphs of $G$. In this paper, we consider some particular cases of these
graphs that most of them are of importance in chemistry and study their total
domination polynomials.


title:
Theory of interaction-induced renormalization of Drude weight and
  plasmon frequency in chiral multilayer graphene

abstract:
  We develop a theory for the optical conductivity of doped multilayer graphene
including the effects of electron-electron interactions. Applying the quantum
kinetic formalism, we formulate a set of pseudospin Bloch equations that
governs the dynamics of the nonequilibrium density matrix driven by an external
\emph{a.c.} electric field under the influence of Coulomb interactions. These
equations reveal a dynamical mechanism that couples the Drude and interband
responses arising from the chirality of pseudospin textures in multilayer
graphene systems. We demonstrate that this results in an interaction-induced
enhancement of the Drude weight and plasmon frequency strongly dependent on the
pseudospin winding number. Using bilayer graphene as an example, we also study
the influence of higher-energy bands and find that they contribute considerable
renormalization effects not captured by a low-energy two-band description. We
argue that this enhancement of Drude weight and plasmon frequency occurs
generally in materials characterized by electronic chirality.


title:
General Stieltjes moment problems for rapidly decreasing smooth
  functions

abstract:
  We give (necessary and sufficient) conditions over a sequence $\left\{
f_{n}\right\} _{n=0}^{\infty}$ of functions under which every generalized
Stieltjes moment problem \[ \int_{0}^{\infty} f_{n}(x)\phi(x)\mathrm{d}
x=a_{n}, \ \ \ n\in\mathbb{N}, \] has solutions
$\phi\in\mathcal{S}(\mathbb{R})$ with $\operatorname*{supp}
\phi\subseteq[0,\infty)$. Furthermore, we consider more general problems of
this kind for measure or distribution sequences $\left\{ f_{n}\right\}
_{n=0}^{\infty}$. We also study vector moment problems with values in Frechet
spaces and multidimensional moment problems.


title:
A Hierarchical Bayesian Model Accounting for Endmember Variability and
  Abrupt Spectral Changes to Unmix Multitemporal Hyperspectral Images

abstract:
  Hyperspectral unmixing is a blind source separation problem which consists in
estimating the reference spectral signatures contained in a hyperspectral
image, as well as their relative contribution to each pixel according to a
given mixture model. In practice, the process is further complexified by the
inherent spectral variability of the observed scene and the possible presence
of outliers. More specifically, multi-temporal hyperspectral images, i.e.,
sequences of hyperspectral images acquired over the same area at different time
instants, are likely to simultaneously exhibit moderate endmember variability
and abrupt spectral changes either due to outliers or to significant time
intervals between consecutive acquisitions. Unless properly accounted for,
these two perturbations can significantly affect the unmixing process. In this
context, we propose a new unmixing model for multitemporal hyperspectral images
accounting for smooth temporal variations, construed as spectral variability,
and abrupt spectral changes interpreted as outliers. The proposed hierarchical
Bayesian model is inferred using a Markov chain Monte-Carlo (MCMC) method
allowing the posterior of interest to be sampled and Bayesian estimators to be
approximated. A comparison with unmixing techniques from the literature on
synthetic and real data allows the interest of the proposed approach to be
appreciated.


title:
On the Ground State Energy of the Delta-Function Fermi Gas II: Further
  Asymptotics

abstract:
  Building on previous work of the authors, we here derive the weak coupling
asymptotics to order $\gamma^2$ of the ground state energy of the
delta-function Fermi gas. We use a method that can be applied to a large class
of finite convolution operators.


title: On two-sided monogenic functions of axial type

abstract:
  In this paper we study two-sided (left and right) axially symmetric solutions
of a generalized Cauchy-Riemann operator. We present three methods to obtain
special solutions: via the Cauchy-Kowalevski extension theorem, via plane wave
integrals and Funk-Hecke's formula and via primitivation. Each of these methods
is effective enough to generate all the polynomial solutions.


title: Non-compact groups, tensor operators and applications to quantum gravity

abstract:
  This work focuses on non-compact groups and their applications to quantum
gravity, mainly through the use of tensor operators. First, the mathematical
theory of tensor operators for a Lie group is recast in a new way which is used
to generalise the Wigner-Eckart theorem to non-compact groups. The result
relies on the knowledge of the recoupling theory between finite-dimensional and
infinite-dimensional irreducible representations of the group; here the
previously unconsidered cases of the 3D and 4D Lorentz groups are investigated
in detail. As an application, the Wigner-Eckart theorem is used to generalise
the Jordan-Schwinger representation of SU(2) to both groups, for all
representation classes. Next, the results obtained for the 3D Lorentz group are
applied to (2+1) Lorentzian loop quantum gravity to develop an analogue of the
well-known spinorial approach used in the Euclidean case. Tensor operators are
used to construct observables and to generalise the Hamiltonian constraint
introduced by Bonzom and Livine (2012) for 3D gravity to the Lorentzian case.
The Ponzano-Regge amplitude is shown to be a solution of this constraint by
recovering the (opportunely generalised) Biedenharn-Elliott relations. Finally,
the focus is shifted on the intertwiner space based on SU(2) representations,
widely used in loop quantum gravity. When working in the spinorial formalism,
it has been shown that the Hilbert space of n-valent intertwiners with fixed
total area is a representation of U(n). Here it is shown that the full space of
all n-valent intertwiners forms an irreducible representation of the
non-compact group SO*(2n). This fact is used to construct a new kind of
coherent intertwiner state (in the sense of Perelomov). Hints of how these
coherent states can be interpreted in the semi-classical limit as convex
polyhedra are provided.


title:
Error Correction Coding Meets Cyber-Physical Systems: Message-Passing
  Analysis of Self-Healing Interdependent Networks

abstract:
  Coupling cyber and physical systems gives rise to numerous engineering
challenges and opportunities. An important challenge is the contagion of
failure from one system to another, which can lead to large-scale cascading
failures. However, the self-healing ability emerges as a valuable opportunity
where the overlaying cyber network can cure failures in the underlying physical
network. To capture both self-healing and contagion, this paper considers a
graphical model representation of an interdependent cyber-physical system, in
which nodes represent various cyber or physical functionalities, and edges
capture the interactions between the nodes. A message-passing algorithm is
proposed for this representation to study the dynamics of failure propagation
and healing. By conducting a density evolution analysis for this algorithm,
network reaction to initial disruptions is investigated. It is proved that as
the number of message-passing iterations increases, the network reaches a
steady-state condition that would be either a complete healing or a complete
collapse. Then, a sufficient condition is derived to select the network
parameters to guarantee the complete healing of the system. The result of the
density evolution analysis is further employed to jointly optimize the design
of cyber and physical networks for maximum resiliency. This analytical
framework is then extended to the cases where propagation of failures in the
physical network is faster than the healing responses of the cyber network.
Such scenarios are of interest in many real-life applications such as smart
grid. Finally, extensive numerical results are presented to verify the analysis
and investigate the impact of the network parameters on the resiliency of the
network.


title: On nef subvarieties

abstract:
  The goal of this work is to study positivity of subvarieties with nef normal
bundle in the sense of intersection theory. After Ottem's work on ample
subschemes, we introduce the notion of a nef subscheme, which generalizes the
notion of a subvariety with nef normal bundle. We show that restriction of a
pseudoeffective (resp. big) divisor to a nef subvariety is pseudoeffective
(resp. big). We also show that ampleness and nefness are transitive properties.
We define the weakly movable cone as the cone generated by the pushforward of
cycle classes of nef subvarieties via proper surjective maps. This cone
contains the movable cone and shares similar intersection-theoretic properties
with it, thanks to the aforementioned properties of nef subvarieties. On the
other hand, we prove that if $Y\subset X$ is an ample subscheme of codimension
$r$ and $D|_Y$ is $q$-ample, then $D$ is $(q+r)$-ample. This is analogous to a
result proved by Demailly-Peternell-Schneider. We use the theory of $q$-ample
divisors, as developed by Totaro, throughout the paper.


title: Branes and the Kraft-Procesi Transition

abstract:
  The Coulomb and Higgs branches of certain 3d N=4 gauge theories can be
understood as closures of nilpotent orbits. Recently, a new theorem by Namikawa
suggests that this is the simplest possible case, thus giving this class a
special role. In this note we use branes to reproduce the mathematical work by
Kraft and Procesi. It studies the classification of all nilpotent orbits for
classical groups and it characterizes an inclusion relation via minimal
singularities. We show how these minimal singularities arise naturally in the
Type IIB superstring embedding of the 3d A-type theories. The Higgs mechanism
can be used to remove the minimal singularity, corresponding to a transition in
the brane configuration that induces a new effective 3d theory. This reproduces
the Kraft-Procesi results, endowing the family of gauge theories with a new
underlying structure. We provide an efficient procedure for computing such
brane transitions.


title:
Strategies for the Simulation of Sea Ice Organic Chemistry: Arctic Tests
  and Development

abstract:
  A mechanism connecting ice algal ecodynamics with the buildup of organic
macromolecules in brine channels is tested offline in a reduced model of pack
geochemistry. Driver physical quantities are extracted from the global sea ice
dynamics code CICE, including snow height, column thickness and internal
temperature. The variables are averaged at the regional scale over ten Arctic
biogeographic zones and treated as input matrices at four vertical habitat
levels. Nutrient-light-salt limited ice algal growth is computed along with the
associated grazing plus mortality. Vertical transport is diffusive but responds
to pore structure. Simulated bottom layer chlorophyll maxima are reasonable,
though delayed by about a month relative to observations. This highlights major
uncertainties deriving from snow thickness variability. Upper level biota are
generated intermittently through flooding. Macromolecular injections are
represented by the compound classes humics, proteins, polysaccharides and
lipids. The fresh biopolymers behave in a successional manner and are removed
by bacteria. In baseline runs, organics are introduced solely through cell
disruption, and internal carbon is biased low. Continuous exudation is
therefore appended, and agreement with dissolved organic or individual
biopolymer measurements is achieved when strong release is coupled to light
availability. Detrital carbon then reaches hundreds of micromolar, sufficient
to support physical changes to the ice matrix. Through this optimized model
version we address the question, are high molecular weight organics added to
the brine network over and above background spillage? The mechanism is
configured for ready extension to the Antarctic, so that global ice organic
chemistry issues can be targeted.


title: Schottky Groups over Valuation Rings

abstract:
  Given a non-trivial complete valued field $K$ with value group $\Lambda$, we
construct a $\Lambda$-tree space associated to $K$ analog of the Bruhat-Tits
tree, and locally finite trees associated to compact subsets of the projective
line. We propose a definition of hyperbolic matrix and Schottky group over such
field $K$. To any such Schottky group $\Gamma$, we associate a compact set with
an action of $\Gamma$, such that the quotient graph of the associated tree is a
finite graph, and $\Gamma$ is identified with its fundamental group. Finally
explain a method to construct such groups. This results extend the classical
ones for discrete valuations of Mumford and non-archimedean rank 1 valuations
of Gerritzen and Van der Put.


title:
Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via
  Nanomechanical Multimode Resonance Spectromicroscopy

abstract:
  Black phosphorus (P) has emerged as a layered semiconductor with a unique
crystal structure featuring corrugated atomic layers and strong in-plane
anisotropy in its physical properties. Here, we demonstrate that the crystal
orientation and mechanical anisotropy in free-standing black P thin layers can
be precisely determined by spatially resolved multimode nanomechanical
resonances. This offers a new means for resolving important crystal orientation
and anisotropy in black P device platforms in situ beyond conventional optical
and electrical calibration techniques. Furthermore, we show that
electrostatic-gating-induced straining can continuously tune the mechanical
anisotropic effects on multimode resonances in black P electromechanical
devices. Combined with finite element modeling (FEM), we also determine the
Young's moduli of multilayer black P to be 116.1 and 46.5 GPa in the zigzag and
armchair directions, respectively.


title:
On Furstenberg's intersection conjecture, self-similar measures, and the
  $L^q$ norms of convolutions

abstract:
  We study a class of measures on the real line with a kind of self-similar
structure, which we call dynamically driven self-similar measures, and contain
proper self-similar measures such as Bernoulli convolutions as special cases.
Our main result gives an expression for the $L^q$-dimensions of such
dynamically driven self-similar measures, under certain conditions. As an
application, we settle Furstenberg's long-standing conjecture on the dimension
of the intersections of $\times p$ and $\times q$-invariant sets. Among several
other applications, we also show that Bernoulli convolutions have an $L^q$
density for all finite $q$, outside of a zero-dimensional set of exceptions.
  The proof of the main result is inspired by M. Hochman's approach to the
dimensions of self-similar measures and his inverse theorem for entropy. Our
method can be seen as an extension of Hochman's theory from entropy to $L^q$
norms, and likewise relies on an inverse theorem for the decay of $L^q$ norms
of discrete measures under convolution. This central piece of our approach may
be of independent interest, and is an application of well-known methods and
results in additive combinatorics: the asymmetric version of the
Balog-Szemer\'{e}di-Gowers Theorem due to Tao-Vu, and some constructions of
Bourgain.


title: Sterile Neutrinos: An Introduction to Experiments

abstract:
  This paper is written as one chapter in a collection of essays on neutrino
physics for beginning graduate students. The text presents important
experimental methods and issues for those interested in searches for sterile
neutrinos. Other essays in the collection, written by other authors, will cover
introduction to neutrinos in the Standard Model, a description of the theory,
and discussion of details of detectors, thus these aspects are not covered
here. However, beyond these points, this represents a self-contained tutorial
on experimental studies of sterile neutrino oscillations, covering such issues
as signals vs. limits, designing experiments, and performing and interpreting
global fits to the oscillation data.


title:
The Bekenstein-Hawking Corpuscular Cascading from the Backreacted Black
  Hole

abstract:
  Exciting peculiarities of Planck-scale physics have immediate effects on the
Bekenstein-Hawking radiation emitted from black holes (BHs). In this paper,
using the tunneling formalism, we determine the Bekenstein-Hawking temperature
for the vector particles from a backreacted black hole (BBH) constructed from a
conformal scalar field surrounded by a BTZ (Banados-Teitelboim-Zanelli) BH.
Then, under the effect of the generalized uncertainty principle, we extend our
calculations for scalar particles to understand the effects of quantum gravity.
Then, we calculate an evaporation time for the BBH, the total number of
Bekenstein-Hawking particles, and the quantum corrections of the number. We
observe that remnants of the BH evaporation occur and that they affect the
Bekenstein-Hawking temperature of the BBH as well as the total number of
Bekenstein-Hawking particles.


title: $L^2$-Euler characteristics and the Thurston norm

abstract:
  We assign to a finite $CW$-complex and an element in its first cohomology
group a twisted version of the $L^2$-Euler characteristic and study its main
properties. In the case of an irreducible orientable $3$-manifold with empty or
toroidal boundary and infinite fundamental group we identify it with the
Thurston norm. We will use the $L^2$-Euler characteristic to address the
problem whether the existence of a map inducing an epimorphism on fundamental
groups implies an inequality of the Thurston norms.


title:
Application of Bootstrap Re-sampling Method to a Categorical Data of
  HIV/AIDS Spread across different Social-Economic Classes

abstract:
  This research reports on the relationship and significance of social-economic
factors (age, sex, employment status) and modes of HIV/AIDS transmission to the
HIV/AIDS spread. Logistic regression model, a form of probabilistic function
for binary response was used to relate social-economic factors (age, sex,
employment status) to HIV/AIDS spread. The statistical predictive model was
used to project the likelihood response of HIV/AIDS spread with a larger
population using 10,000 Bootstrap re-sampling observations.


title:
Charge Effects and Nanoparticle Pattern Formation in Electrohydrodynamic
  NanoDrip Printing of Colloids

abstract:
  Advancing open atmosphere printing technologies to produce features in the
nanoscale range has important and broad applications ranging from electronics,
to photonics, plasmonics and biology. Recently an electrohydrodynamic printing
regime has been demonstrated in a rapid dripping mode (termed NanoDrip), where
the ejected colloidal droplets from nozzles of diameters of O(1 {\mu}m) can
controllably reach sizes an order of magnitude smaller than the nozzle and can
generate planar and out-of-plane structures of similar sizes. Despite
demonstrated capabilities, our fundamental understanding of important aspects
of the physics of NanoDrip printing needs further improvement. Here we address
the topics of charge content and transport in NanoDrip printing. We employ
quantum dot and gold nanoparticle dispersions in combination with a specially
designed, auxiliary, asymmetric electric field, targeting the understanding of
charge locality (particles vs. solvent) and particle distribution in the
deposits as indicated by the dried nanoparticle patterns (footprints) on the
substrate. We show that droplets of alternating charge can be spatially
separated when applying an ac field to the nozzle. The nanoparticles within a
droplet are distributed asymmetrically under the influence of the auxiliary
lateral electric field, indicating that they are the main carriers. We also
show that the ligand length of the nanoparticles in the colloid affects their
mobility after deposition (in the sessile droplet state).


title: Levi-flat hypersurfaces and their complement in complex surfaces

abstract:
  In this work we study analytic Levi-flat hypersurfaces in complex algebraic
surfaces. First, we show that if this foliation admits chaotic dynamics (i.e.
if it does not admit a transverse invariant measure), then the connected
components of the complement of the hypersurface are modifications of Stein
domains. This allows us to extend the CR foliation to a singular algebraic
foliation on the ambient complex surface. We apply this result to prove, by
contradiction, that analytic Levi-flat hypersurfaces admitting a transverse
affine structure in a complex algebraic surface have a transverse invariant
measure. This leads us to conjecture that Levi-flat hypersurfaces in complex
algebraic surfaces that are diffeomorphic to a hyperbolic torus bundle over the
circle are fibrations by algebraic curves.


title: Universal $L^2$-torsion, polytopes and applications to $3$-manifolds

abstract:
  Given an $L^2$-acyclic connected finite $CW$-complex, we define its universal
$L^2$-torsion in terms of the chain complex of its universal covering. It takes
values in the weak Whitehead group $\operatorname{Wh}^w(G)$. We study its main
properties such as homotopy invariance, sum formula, product formula and
Poincar\'e duality. Under certain assumptions, we can specify certain
homomorphisms from the weak Whitehead group $\operatorname{Wh}^w(G)$ to abelian
groups such as the real numbers or the Grothendieck group of integral
polytopes, and the image of the universal $L^2$-torsion can be identified with
many invariants such as the $L^2$-torsion, the $L^2$-torsion function, twisted
$L^2$-Euler characteristics and, in the case of a $3$-manifold, the dual
Thurston norm polytope.


title: Characterization of embedded free boundary surfaces in the ball

abstract:
  We prove that the only embedded free boundary minimal surface $\Sigma$ in
$\mathbb{B}^3$ with index $4$ is the critical catenoid. This extends
fundamental work of A. Fraser and R. Schoen, as well as the work of H. Tran.


title: Regularity properties of the Zakharov system on the half line

abstract:
  In this paper we study the local and global regularity properties of the
Zakharov system on the half line with rough initial data. These properties
include local and global wellposedness results, local and global smoothing
results and the behavior of higher order Sobolev norms of the solutions.
Smoothing means that the nonlinear part of the solution on the half line is
smoother than the initial data. The gain in regularity coincides with the gain
that was observed for the periodic Zakharov and the Zakharov on the real line.
Uniqueness is proved in the class of smooth solutions. When the boundary value
of the Schr\"odinger part of the solution is zero, uniqueness can be extended
to the full range of local solutions. Under the same assumptions on the initial
data we also prove global-in-time existence and uniqueness of energy solutions.
For more regular data we prove that all higher Sobolev norms grow at most
polynomially-in-time.


title: Fully robust qubit in atomic and molecular three-level systems

abstract:
  We present a new method of constructing a fully robust qubit in a three-level
system. By the application of continuous driving fields, robustness to both
external and controller noise is achieved. Specifically, magnetic noise and
power fluctuations do not operate within the robust qubit subspace. Whereas all
the continuous driving based constructions of such a fully robust qubit
considered so far have required at least four levels, we show that in fact only
three levels are necessary. This paves the way for simple constructions of a
fully robust qubit in many atomic and solid state systems that are controlled
by either microwave or optical fields. We focus on the NV-center in diamond and
analyze the implementation of the scheme, by utilizing the electronic spin
sub-levels of its ground state. In current state-of-the-art experimental setups
the scheme leads to improvement of more than two orders of magnitude in
coherence time, pushing it towards the lifetime limit. We show how the fully
robust qubit can be used to implement quantum sensing, and in particular, the
sensing of high frequency signals.


title: Hom-Novikov color algebras

abstract:
  The aim of this paper is to introduce Hom-Novikov color algebras and give
some constructions of Hom-Novikov color algebras from a given one and a (weak)
morphism. Other interesting constructions using averaging operators, centroids,
derivations and tensor product are given. We also proved that any Hom-Novikov
color algebra is Hom-Lie admissible. Moreover, we introduce Hom-quadratic
Hom-Novikov color algebras and provide some properties by twisting. It is also
shown that the Hom-Lie color algebra associated to a given quadratic
Hom-Novikov color algebra is also quadratic.


title: Singularities and n-dimensional black holes in torsion theories

abstract:
  In this work we have studied the singular behaviour of gravitational theories
with non symmetric connections. For this purpose we introduce a new criteria
for the appearance of singularities based on the existence of black/white hole
regions of arbitrary codimension defined inside a spacetime of arbitrary
dimension. We discuss this prescription by increasing the complexity of the
particular torsion theory under study. In this sense, we start with
Teleparallel Gravity, then we analyse Einstein-Cartan theory, and finally
dynamical torsion models.


title:
Effects of Spin-Orbit Coupling on Jaynes-Cummings and Tavis-Cummings
  Models

abstract:
  We consider ultracold atoms inside a ring optical cavity that supports a
single plane-wave mode. The cavity field, together with an external coherent
laser field, drives a two-photon Raman transition between two internal
pseudo-spin states of the atom. This gives rise to an effective coupling
between atom's pseudo-spin and external center-of-mass (COM) motion. For the
case of a single atom inside the cavity, We show how the spin-orbit coupling
modifies the static and dynamic properties of the Jaynes-Cummings (JC) model.
In the case of many atoms in thermodynamic limit, we show that the spin-orbit
coupling modifies the Dicke superradiance phase transition boundary and the
non-superradiant normal phase may become reentrant in some regimes.

categories: cond-mat.quant-gas physics.atom-ph physics.optics quant-ph


title:
A Study of the Impact of High Cross Section ILC Processes on the SiD
  Detector Design

abstract:
  The SiD concept is one of two proposed detectors to be mounted at the
interaction region of the International Linear Collider (ILC). A substantial
ILC background arises from low transverse momentum
$\mathrm{e}^{+}\mathrm{e}^{-}$ pairs created by the interaction of the
colliding beams' electromagnetic fields. In order to provide hermeticity and
sensitivity to beam targeting parameters, a forward Beamline Calorimeter
(BeamCal) is being designed that will provide coverage down to 5 mrad from the
outgoing beam trajectory, and intercept the majority of this pair background.
Using the SiD simulation framework, the effect of this pair background on the
SiD detector components, especially the vertex detector (VXD) and forward
electromagnetic calorimeter (FCAL), is explored. In the case of the FCAL,
backgrounds from Bhabha and two-photon processes are also considered. The
consequence of several variants of the BeamCal geometry and ILC interaction
region configuration are considered for both the vertex detector and BeamCal
performance.


title: The Exact Rate-Memory Tradeoff for Caching with Uncoded Prefetching

abstract:
  We consider a basic cache network, in which a single server is connected to
multiple users via a shared bottleneck link. The server has a database of files
(content). Each user has an isolated memory that can be used to cache content
in a prefetching phase. In a following delivery phase, each user requests a
file from the database, and the server needs to deliver users' demands as
efficiently as possible by taking into account their cache contents. We focus
on an important and commonly used class of prefetching schemes, where the
caches are filled with uncoded data. We provide the exact characterization of
the rate-memory tradeoff for this problem, by deriving both the minimum average
rate (for a uniform file popularity) and the minimum peak rate required on the
bottleneck link for a given cache size available at each user. In particular,
we propose a novel caching scheme, which strictly improves the state of the art
by exploiting commonality among user demands. We then demonstrate the exact
optimality of our proposed scheme through a matching converse, by dividing the
set of all demands into types, and showing that the placement phase in the
proposed caching scheme is universally optimal for all types. Using these
techniques, we also fully characterize the rate-memory tradeoff for a
decentralized setting, in which users fill out their cache content without any
coordination.


title:
Programming the Universe: The First Commandment of Software Engineering
  for all Varieties of Information Systems

abstract:
  Since the early days of computers and programs, the process and outcomes of
software development has been a minefield plagued with problems and failures,
as much as the complexity and complication of software and its development has
increased by a thousandfold in half a century. Over the years, a number of
theories, laws, best practices, manifestos and methodologies have emerged, with
varied degrees of (un)success. Our experience as software engineers of complex
and large-scale systems shows that those guidelines are bound to previously
defined and often narrow scopes. Enough is enough. Nowadays, nearly every
company is in the software and services business and everything is - or is
managed by - software. It is about time, then, that the laws that govern our
universe ought to be redefined. In this context, we discuss and present a set
of universal laws that leads us to propose the first commandment of software
engineering for all varieties of information systems.


title: A note on Riley polynomials of $2$-bridge knots

abstract:
  In this short note we show the existence of an epimorphism between groups of
$2$-bridge knots by means of an elementary argument using the Riley polynomial.
As a corollary, we give a classification of $2$-bridge knots by Riley
polynomials.


title: Conditionally Bi-Free Independence with Amalgamation

abstract:
  In this paper, we introduce the notion of conditionally bi-free independence
in an amalgamated setting. We define operator-valued conditionally
bi-multiplicative pairs of functions and construct operator-valued
conditionally bi-free moment and cumulant functions. It is demonstrated that
conditionally bi-free independence with amalgamation is equivalent to the
vanishing of mixed operator-valued bi-free and conditionally bi-free cumulants.
Furthermore, an operator-valued conditionally bi-free partial
$\mathcal{R}$-transform is constructed and various operator-valued
conditionally bi-free limit theorems are studied.


title:
The Rotation-Metallicity Relation for the Galactic Disk as Measured in
  the Gaia DR1 TGAS and APOGEE Data

abstract:
  Previous studies have found that the Galactic rotation velocity-metallicity
(V-[Fe/H]) relations for the thin and thick disk populations show negative and
positive slopes, respectively. The first Gaia Data Release includes the
Tycho-Gaia Astrometric Solution (TGAS) information, which we use to analyze the
V-[Fe/H] relation for a strictly selected sample with high enough astrometric
accuracy. We aim to arrive at an explanation for the slopes of the V-[Fe/H]
relationship. We measure the V-[Fe/H] relation for thin and thick disk stars
classified on the basis of their [$\alpha$/Fe] and [Fe/H] abundances. We find
dV/d[Fe/H]= -18 +/- 2 km/s/dex for stars in the thin disk and dV/d[Fe/H]= +23
+/- 10 km/s/dex for thick disk stars, so we confirm the different signs for the
slopes. The negative value of dV/d[Fe/H] for thick disk stars is consistent
with previous studies, but the combination of TGAS and APOGEE data provide
higher precision, even though systematic errors could exceed +/-5 km/s/dex .
Our average measurement of dV/d[Fe/H] for local thick disk stars shows a
somewhat flatter slope than the previous studies, but we confirm a significant
spread and a dependence of the slope on the [alpha/Fe] ratio of the stars.
Using a simple N-body model, we demonstrate that the observed trend for the
thick and thin disk can be explained by the observed radial metallicity
gradients and the correlation between orbital eccentricity and metallicity in
the thick disk.


title:
Disorder effect on chiral edge modes and anomalous Hall conductance in
  Weyl semimetals

abstract:
  Typical Weyl semimetals host chiral surface states and hence show an
anomalous Hall response. Although a Weyl semimetal phase is known to be robust
against weak disorder, the influence of disorder on chiral states is not fully
clarified so far. We study the behavior of such chiral states in the presence
of disorder and its consequences on an anomalous Hall response, focusing on a
thin slab of Weyl semimetal with chiral surface states along its edge. It is
shown that weak disorder does not disrupt chiral edge states but crucially
affects them owing to the renormalization of a mass parameter: the number of
chiral edge states changes depending on the strength of disorder. It is also
shown that the Hall conductance is quantized when the Fermi level is located
near Weyl nodes within a finite-size gap. This quantization of the Hall
conductance collapses once the strength of disorder exceeds a critical value,
suggesting that it serves as a probe to distinguish a Weyl semimetal phase from
a diffusive anomalous Hall metal phase.


title:
Optimizations and Heuristics to improve Compression in Columnar Database
  Systems

abstract:
  In-memory columnar databases have become mainstream over the last decade and
have vastly improved the fast processing of large volumes of data through
multi-core parallelism and in-memory compression thereby eliminating the usual
bottlenecks associated with disk-based databases. For scenarios, where the data
volume grows into terabytes and petabytes, keeping all the data in memory is
exorbitantly expensive. Hence, the data is compressed efficiently using
different algorithms to exploit the multi-core parallelization technologies for
query processing. Several compression methods are studied for compressing the
column array, post Dictionary Encoding. In this paper, we will present two
novel optimizations in compression techniques - Block Size Optimized Cluster
Encoding and Block Size Optimized Indirect Encoding - which perform better than
their predecessors. In the end, we also propose heuristics to choose the best
encoding amongst common compression schemes.


title:
Near-Infrared Photometry of Globular Clusters Towards the Galactic
  Bulge: Observations and Photometric Metallicity Indicators

abstract:
  We present wide field JHKs photometry of 16 Galactic globular clusters
located towards the Galactic bulge, calibrated on the 2MASS photometric system.
Differential reddening corrections and statistical field star decontamination
are employed for all of these clusters before fitting fiducial sequences to the
cluster red giant branches (RGBs). Observed values and uncertainties are
reported for several photometric features, including the magnitude of the RGB
bump, tip, the horizontal branch (HB) and the slope of the upper RGB. The
latest spectroscopically determined chemical abundances are used to build
distance- and reddening-independent relations between observed photometric
features and cluster metallicity, optimizing the sample size and metallicity
baseline of these relations by supplementing our sample with results from the
literature. We find that the magnitude different between the HB and the RGB
bump can be used to predict metallicities, in terms of both iron abundance
[Fe/H] and global metallicity [M/H], with a precision of better than 0.1 dex in
all three near-IR bandpasses for relative metal-rich ([M/H]$\gtrsim$-1)
clusters. Meanwhile, both the slope of the upper RGB and the magnitude
difference between the RGB tip and bump are useful metallicity indicators over
the entire sampled metallicity range (-2$\lesssim$[M/H]$\lesssim$0) with a
precision of 0.2 dex or better, despite model predictions that the RGB slope
may become unreliable at high (near-solar) metallicities. Our results agree
with previous calibrations in light of the relevant uncertainties, and we
discuss implications for clusters with controversial metallicities as well as
directions for further investigation.


title: Conservation laws of the generalized Riemann equations at $N=2,3,4$

abstract:
  In this paper, we present infinitely many conserved densities satisfying
particular conservation law $F_{t}=(2uF)_{x}$ for the generalized Riemann
equations at $N=2,3,4$. In the $N=2$ case, we also construct conserved
densities corresponding to new conservation laws containing an arbitrary smooth
function. In virtue of reductions and/or changes of variables, related
conserved densities are obtained for two component Hunter-Saxton equation,
Hunter-Saxton equation, Gurevich-Zybin equation and Monge-Ampere equation.


title: Multiview RGB-D Dataset for Object Instance Detection

abstract:
  This paper presents a new multi-view RGB-D dataset of nine kitchen scenes,
each containing several objects in realistic cluttered environments including a
subset of objects from the BigBird dataset. The viewpoints of the scenes are
densely sampled and objects in the scenes are annotated with bounding boxes and
in the 3D point cloud. Also, an approach for detection and recognition is
presented, which is comprised of two parts: i) a new multi-view 3D proposal
generation method and ii) the development of several recognition baselines
using AlexNet to score our proposals, which is trained either on crops of the
dataset or on synthetically composited training images. Finally, we compare the
performance of the object proposals and a detection baseline to the Washington
RGB-D Scenes (WRGB-D) dataset and demonstrate that our Kitchen scenes dataset
is more challenging for object detection and recognition. The dataset is
available at: http://cs.gmu.edu/~robot/gmu-kitchens.html.


title:
Semantic Information Measure with Two Types of Probability for
  Falsification and Confirmation

abstract:
  Logical Probability (LP) is strictly distinguished from Statistical
Probability (SP). To measure semantic information or confirm hypotheses, we
need to use sampling distribution (conditional SP function) to test or confirm
fuzzy truth function (conditional LP function). The Semantic Information
Measure (SIM) proposed is compatible with Shannon's information theory and
Fisher's likelihood method. It can ensure that the less the LP of a predicate
is and the larger the true value of the proposition is, the more information
there is. So the SIM can be used as Popper's information criterion for
falsification or test. The SIM also allows us to optimize the true-value of
counterexamples or degrees of disbelief in a hypothesis to get the optimized
degree of belief, i. e. Degree of Confirmation (DOC). To explain confirmation,
this paper 1) provides the calculation method of the DOC of universal
hypotheses; 2) discusses how to resolve Raven Paradox with new DOC and its
increment; 3) derives the DOC of rapid HIV tests: DOC of
test-positive=1-(1-specificity)/sensitivity, which is similar to Likelihood
Ratio (=sensitivity/(1-specificity)) but has the upper limit 1; 4) discusses
negative DOC for excessive affirmations, wrong hypotheses, or lies; and 5)
discusses the DOC of general hypotheses with GPS as example.

categories: cs.IT math.IT math.LO math.PR math.ST stat.TH


title: Magnetically Charged Superdomain Walls In Square Artificial Spin Ice

abstract:
  We report direct evidence that magnetically charged superdomain walls form
spontaneously in two dimensional square artificial spin ice nanostructures in
response to external magnetic fields. These extended magnetic defects were
revealed by the development of internal structure, which varies as a function
of applied magnetic field, within the Bragg peaks of resonant soft x-ray
magnetic scattering patterns. Magnetically charged superdomain walls extend
over tens of lattice sites and do not necessarily align with the applied field.
Our results illustrate a novel approach to detect hierarchical magnetic
structures within spin textures.


title:
Phase Transition of Iron-based Single Crystals at Extreme Strain Rates
  under Dynamic Loadings

abstract:
  Phase transition of iron, as a prototype of martensite phase transition under
dynamic loadings, exhibits huge diverges in its TP among experiments with
different pressure medium and loading rates, even in the same initial samples.
Great achievements are made in understanding strain or stress dependence of the
TP under dynamic loadings. However, present understandings on the strain rate
dependence of the TP are far from clear, even a virgin for extreme high strain
rates. In this work, large scale NEMD simulations are conducted to study the
effects of strain rates on the phase transition of iron-based single crystals.
Our results show that the phase transition is preceded by lattice instabilities
under ramp compressions, but present theory, represented by modified Born
criteria, cannot correctly predict observed onsets of the instability. Through
considering both strain and strain gradient disturbances, new instability
criteria are proposed, which could be generally applied for studying
instabilities under either static or dynamic loadings. For the ramp with a
strain rate smaller than about 1010s-1, the observed onset of instabilities is
indeed equal to the one predicted by the new instability criteria under small
gradient disturbances. The observed onsets deviates from the predicted one at
lager strain rates because of finite strain gradient effect. Interestingly, the
strain rate dependence of the TP also exhibits an obvious change at the same
strain rate, i.e., 1010 s-1. When 1010 s-1, a certain power law is obeyed, but
it is not applicable at larger strain rates. This strain rate effect on the TP
is well interpreted with nucleation time and the finite strain gradient effect.
According to these basic understandings, the roles of strain rates on
nucleation and growth of the phase transition are studied.


title:
Friendship-based Cooperative Jamming for Secure Communication in Poisson
  Networks

abstract:
  Wireless networks with the consideration of social relationships among
network nodes are highly appealing for lots of important data communication
services. Ensuring the security of such networks is of great importance to
facilitate their applications in supporting future social-based services with
strong security guarantee. This paper explores the physical layer
security-based secure communication in a finite Poisson network with social
friendships among nodes, for which a social friendship-based cooperative
jamming scheme is proposed. The jamming scheme consists of a Local Friendship
Circle (LFC) and a Long-range Friendship Annulus (LFA), where all legitimate
nodes in the LFC serve as jammers, but the legitimate nodes in the LFA are
selected as jammers through three location-based policies. To understand both
the security and reliability performance of the proposed jamming scheme, we
first model the sum interference at any location in the network by deriving its
Laplace transform under two typical path loss scenarios. With the help of the
interference Laplace transform results, we then derive the exact expression for
the transmission outage probability (TOP) and determine both the upper and
lower bounds on the secrecy outage probability (SOP), such that the overall
outage performances of the proposed jamming scheme can be depicted. Finally, we
present extensive numerical results to validate the theoretical analysis of TOP
and SOP and also to illustrate the impacts of the friendship-based cooperative
jamming on the network performances.


title:
Mechanical force involved multiple fields switching of both local
  ferroelectric and magnetic domain in a Bi5Ti3FeO15 thin film

abstract:
  Multiferroics have received intense attention due to their great application
potential in multi-state information storage devices and new types of sensors.
Coupling among ferroic orders such as ferroelectricity, (anti-)ferromagnetism,
ferroelasticity, etc. will enable dynamic interaction between these ordering
parameters. Direct visualization of such coupling behaviour in single phase
multiferroic materials is highly desirable for both applications and
fundamental study. Manipulation of both ferroelectric and magnetic domains of
Bi5Ti3FeO15 thin film using electric field and external mechanical force is
reported, which confirms the magnetoelectric coupling in Bi5Ti3FeO15, indicates
the electric and magnetic orders are coupled through ferroelasticity. Due to
the anisotropic relaxation of ferroelastic strain, the back-switching of
out-of-plane electric domains is not as obvious as in-plane. An inevitable
destabilization of the coupling between elastic and magnetic ordering happens
because of the elastic strain relaxation, which result in a subsequent decay of
magnetic domain switching. Mechanical force applied on the surface of
Bi5Ti3FeO15 film generates by an AFM tip will effectively drive a transition of
the local ferroelastic strain state, reverse both the polarization and
magnetization in a way similar to an electric field. Current work provides a
framework for exploring cross-coupling among multiple orders and potential for
developing novel nanoscale functional devices.


title:
Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev
  models

abstract:
  The Sachdev-Ye-Kitaev model is a $(0+1)$-dimensional model describing
Majorana fermions or complex fermions with random interactions. This model has
various interesting properties such as approximate local criticality (power law
correlation in time), zero temperature entropy, and quantum chaos. In this
article, we propose a higher dimensional generalization of the
Sachdev-Ye-Kitaev model, which is a lattice model with $N$ Majorana fermions at
each site and random interactions between them. Our model can be defined on
arbitrary lattices in arbitrary spatial dimensions. In the large $N$ limit, the
higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev
model such as local criticality in two-point functions, zero temperature
entropy and chaos measured by the out-of-time-ordered correlation functions. In
addition, we obtain new properties unique to higher dimensions such as
diffusive energy transport and a "butterfly velocity" describing the
propagation of chaos in space. We mainly present results for a
$(1+1)$-dimensional example, and discuss the general case near the end.


title: Finite flag-transitive affine planes with a solvable automorphism group

abstract:
  In this paper, we consider finite flag-transitive affine planes with a
solvable automorphism group. Under a mild number-theoretic condition involving
the order and dimension of the plane, the translation complement must contain a
linear cyclic subgroup that either is transitive or has two equal-sized orbits
on the line at infinity. We develop a new approach to the study of such planes
by associating them with planar functions and permutation polynomials in the
odd order and even order case respectively. In the odd order case, we
characterize the Kantor-Suetake family by using Menichetti's classification of
generalized twisted fields and Blokhuis, Lavrauw and Ball's classifcation of
rank two commutative semifields. In the even order case, we develop a technique
to study permutation polynomials of DO type by quadratic forms and characterize
such planes that have dimensions up to four over their kernels.


title: The Directions of Selection Bias

abstract:
  We show that if the exposure and the outcome affect the selection indicator
in the same direction and have non-positive interaction on the risk difference,
risk ratio or odds ratio scale, the exposure-outcome odds ratio in the selected
population is a lower bound for true odds ratio.


title: From Monocular SLAM to Autonomous Drone Exploration

abstract:
  Micro aerial vehicles (MAVs) are strongly limited in their payload and power
capacity. In order to implement autonomous navigation, algorithms are therefore
desirable that use sensory equipment that is as small, low-weight, and
low-power consuming as possible. In this paper, we propose a method for
autonomous MAV navigation and exploration using a low-cost consumer-grade
quadrocopter equipped with a monocular camera. Our vision-based navigation
system builds on LSD-SLAM which estimates the MAV trajectory and a semi-dense
reconstruction of the environment in real-time. Since LSD-SLAM only determines
depth at high gradient pixels, texture-less areas are not directly observed so
that previous exploration methods that assume dense map information cannot
directly be applied. We propose an obstacle mapping and exploration approach
that takes the properties of our semi-dense monocular SLAM system into account.
In experiments, we demonstrate our vision-based autonomous navigation and
exploration system with a Parrot Bebop MAV.


title:
The Breaking $\mu \leftrightarrow \tau$ Symmetry through the ${\bf
  Q}_{6}$ Flavour Group

abstract:
  In a supersymmetric scenario, we study masses and mixings for leptons through
the ${\bf Q}_{6}$ flavour symmetry. In the simplest case, the ${\bf M}_{\nu}$
effective neutrino mass matrix, that comes from the type I see-saw mechanism,
breaks the $\mu \leftrightarrow \tau$ interchange symmetry. As consequence, the
reactor and atmospheric angles deviate from $0^{\circ}$ and $45^{\circ}$,
respectively. At first glance, the model might accommodate very well the
reactor and atmospheric angles in good agreement with the experimental data.


title:
Uplink Performance Analysis of Dense Cellular Networks with LoS and NLoS
  Transmissions

abstract:
  In this paper, we analyse the coverage probability and the area spectral
efficiency (ASE) for the uplink (UL) of dense small cell networks (SCNs)
considering a practical path loss model incorporating both line-of-sight (LoS)
and non-line-of-sight (NLoS) transmissions. Compared with the existing work, we
adopt the following novel approaches in our study: (i) we assume a practical
user association strategy (UAS) based on the smallest path loss, or
equivalently the strongest received signal strength; (ii) we model the
positions of both base stations (BSs) and the user equipments (UEs) as two
independent Homogeneous Poisson point processes (HPPPs); and (iii) the
correlation of BSs' and UEs' positions is considered, thus making our
analytical results more accurate. The performance impact of LoS and NLoS
transmissions on the ASE for the UL of dense SCNs is shown to be significant,
both quantitatively and qualitatively, compared with existing work that does
not differentiate LoS and NLoS transmissions. In particular, existing work
predicted that a larger UL power compensation factor would always result in a
better ASE in the practical range of BS density, i.e., 10^1-10^3 BSs/km^2.
However, our results show that a smaller UL power compensation factor can
greatly boost the ASE in the UL of dense SCNs, i.e., 10^2-10^3 BSs/km^2, while
a larger UL power compensation factor is more suitable for sparse SCNs, i.e.,
10^1-10^2 BSs/km^2.


title: Solutions for dissipative quadratic open systems: part II - fermions

abstract:
  This is the second part of a work in which we show how to solve a large class
of Lindblad master equations for non-interacting particles on $L$ sites. Here
we concentrate on fermionic particles. In parallel to part I for bosons, but
with important differences, we show how to reduce the problem to diagonalizing
an $L \times L$ non-Hermitian matrix which, for boundary dissipative driving of
a uniform chain, is a tridiagonal bordered Toeplitz matrix. In this way, both
for fermionic and spin systems alike, we can obtain analytical expressions for
the normal master modes and their relaxation rates (rapidities) and we show how
to construct the non-equilibrium steady state.


title: Lipschitz properties of convex mappings

abstract:
  The present paper is concerned with Lipschitz properties of convex mappings.
One considers the general context of mappings defined on an open convex subset
$\Omega$ of a locally convex space $X$ and taking values in a locally convex
space $Y$ ordered by a normal cone. One proves also equi-Lipschitz properties
for pointwise bounded families of continuous convex mappings, provided the
source space $X$ is barrelled.
  Some results on Lipschitz properties of continuous convex functions defined
on metrizable topological vector spaces are included as well.
  The paper has a methodological character - its aim is to show that some
geometric properties (monotonicity of the slope, the normality of the
seminorms) allow to extend the proofs from the scalar case to the vector one.
In this way the proofs become more transparent and natural.


title: Asymptotic $r$-log-convexity and P-recursive sequences

abstract:
  A sequence $\{ a_n \}_{n \ge 0}$ is said to be asymptotically $r$-log-convex
if it is $r$-log-convex for $n$ sufficiently large. We present a criterion on
the asymptotical $r$-log-convexity based on the asymptotic behavior of $a_n
a_{n+2}/a_{n+1}^2$. As an application, we show that most P-recursive sequences
are asymptotic $r$-log-convexity for any integer $r$ once they are log-convex.
Moreover, for a concrete integer $r$, we present a systematic method to find
the explicit integer $N$ such that a P-recursive sequence $\{a_n\}_{n \ge N}$
is $r$-log-convex. This enable us to prove the $r$-log-convexity of some
combinatorial sequences.


title: Dark Matter Relic Abundance and Light Sterile Neutrinos

abstract:
  In this paper, we calculate the relic abundance of the dark matter particles
when they can annihilate into sterile neutrinos with the mass $\lesssim 100
\text{ GeV}$ in a simple model. Unlike the usual standard calculations, the
sterile neutrino may fall out of the thermal equilibrium with the thermal bath
before the dark matter freezes out. In such a case, if the Yukawa coupling
$y_N$ between the Higgs and the sterile neutrino is small, this process gives
rise to a larger $\Omega_{\text{DM}} h^2$ so we need a larger coupling between
the dark matter and the sterile neutrino for a correct relic abundance.


title:
Migration of a surfactant-laden droplet in non-isothermal Poiseuille
  flow

abstract:
  The motion of a surfactant-laden viscous droplet in the presence of
background non-isothermal Poiseuille flow is studied analytically and
numerically. Specifically, the effect of interfacial Marangoni stress due to
non-uniform distribution of surfactants and temperature at the droplet
interface on the velocity and direction of motion of the droplet along the
centerline of imposed Poiseuille flow is investigated in the presence of
linearly varying temperature field. In the absence of thermal convection, fluid
inertia and shape deformation, the interfacial transport of bulk-insoluble
surfactants is governed by the surface Peclet number which represents the
relative strength of the advective transport of surfactant over the diffusive
transport. We obtain analytical solution for small and large values of the
surface Peclet number. Numerical solution is obtained for arbitrary surface
Peclet number, which compares well with the analytical solution. Depending on
the direction of temperature gradient with respect to the imposed Poiseuille
flow, the surfactant-induced Marangoni stress affects the droplet velocity
differently. When the imposed temperature increases in the direction of imposed
Poiseuille flow, surfactants retard the droplet motion as compared with a
surfactant-free droplet. However, when the imposed temperature decreases in the
direction of imposed Poiseuille flow, presence of surfactants may increase or
decrease the magnitude of droplet velocity depending on the relevant governing
parameters. Further, for particular values of governing parameters, we observe
change in direction of droplet motion due to presence of surfactants, which may
bear significant consequences in the design of droplet based microfluidic
systems.


title: Pointer Sentinel Mixture Models

abstract:
  Recent neural network sequence models with softmax classifiers have achieved
their best language modeling performance only with very large hidden states and
large vocabularies. Even then they struggle to predict rare or unseen words
even if the context makes the prediction unambiguous. We introduce the pointer
sentinel mixture architecture for neural sequence models which has the ability
to either reproduce a word from the recent context or produce a word from a
standard softmax classifier. Our pointer sentinel-LSTM model achieves state of
the art language modeling performance on the Penn Treebank (70.9 perplexity)
while using far fewer parameters than a standard softmax LSTM. In order to
evaluate how well language models can exploit longer contexts and deal with
more realistic vocabularies and larger corpora we also introduce the freely
available WikiText corpus.


title:
Calculating higher-order moments of phylogenetic stochastic mapping
  summaries in linear time

abstract:
  Stochastic mapping is a simulation-based method for probabilistically mapping
substitution histories onto phylogenies according to continuous-time Markov
models of evolution. This technique can be used to infer properties of the
evolutionary process on the phylogeny and, unlike parsimony-based mapping,
conditions on the observed data to randomly draw substitution mappings that do
not necessarily require the minimum number of events on a tree. Most stochastic
mapping applications simulate substitution mappings only to estimate the mean
and/or variance of two commonly used mapping summaries: the number of
particular types of substitutions (labeled substitution counts) and the time
spent in a particular group of states (labeled dwelling times) on the tree.
Fast, simulation-free algorithms for calculating the mean of stochastic mapping
summaries exist. Importantly, these algorithms scale linearly in the number of
tips/leaves of the phylogenetic tree. However, to our knowledge, no such
algorithm exists for calculating higher-order moments of stochastic mapping
summaries. We present one such simulation-free dynamic programming algorithm
that calculates prior and posterior mapping variances and scales linearly in
the number of phylogeny tips. Our procedure suggests a general framework that
can be used to efficiently compute higher-order moments of stochastic mapping
summaries without simulations. We demonstrate the usefulness of our algorithm
by extending previously developed statistical tests for rate variation across
sites and for detecting evolutionarily conserved regions in genomic sequences.


title:
Decentralized Non-communicating Multiagent Collision Avoidance with Deep
  Reinforcement Learning

abstract:
  Finding feasible, collision-free paths for multiagent systems can be
challenging, particularly in non-communicating scenarios where each agent's
intent (e.g. goal) is unobservable to the others. In particular, finding time
efficient paths often requires anticipating interaction with neighboring
agents, the process of which can be computationally prohibitive. This work
presents a decentralized multiagent collision avoidance algorithm based on a
novel application of deep reinforcement learning, which effectively offloads
the online computation (for predicting interaction patterns) to an offline
learning procedure. Specifically, the proposed approach develops a value
network that encodes the estimated time to the goal given an agent's joint
configuration (positions and velocities) with its neighbors. Use of the value
network not only admits efficient (i.e., real-time implementable) queries for
finding a collision-free velocity vector, but also considers the uncertainty in
the other agents' motion. Simulation results show more than 26 percent
improvement in paths quality (i.e., time to reach the goal) when compared with
optimal reciprocal collision avoidance (ORCA), a state-of-the-art collision
avoidance strategy.


title: Device-independent tests of quantum measurements

abstract:
  We consider the problem of characterizing the set of input-output
correlations that can be generated by an arbitrarily given quantum measurement.
Our main result is to provide a closed-form, full characterization of such a
set for any qubit measurement, and to discuss its geometrical interpretation.
As applications, we further specify our results to the cases of real and
complex symmetric, informationally complete measurements and mutually unbiased
bases of a qubit, in the presence of isotropic noise. Our results provide the
optimal device-independent tests of quantum measurements.


title: Pseudo-binomial Approximation to $(k_1, k_2)$-runs

abstract:
  ($k_1,k_2$)-runs have received a special attention in the literature and its
distribution can be obtained using combinatorial method (Huang and Tsai) and
Markov chain approach (Dafnis et al). But the formulae are difficult to use
when the number of Bernoulli trials is too large under identical setup and is
generally intractable under non-identical setup. So, it is useful to
approximate it with a suitable random variable. In this paper, it is
demonstrated that pseudo-binomial is most suitable distribution for
approximation and the approximation results are derived using Stein's method.
Also, application of these results is demonstrated through real-life problems.
It is shown that the bounds obtained are either comparable to or improvement
over bounds available in the literature.


title: Location-Based and Audience-Aware Storytelling

abstract:
  While the daily user of digital, Internet-enabled devices has some explicit
control over what they read and see, the providers fulfilling searches,
offering options, and presenting material are using increasingly sophisticated
real-time algorithms that tune and target content for the particular user. They
redefine the historical relationships between tellers and users, providing a
responsiveness paralleled only by forms of live performance incorporating
elements of improvisation and audience interaction. The general accessibility
of algorithmically driven content delivery techniques suggests significant
untapped potential for new approaches to narrative beyond advertising and
commercially orientated customization.


title: Meaningful Maps With Object-Oriented Semantic Mapping

abstract:
  For intelligent robots to interact in meaningful ways with their environment,
they must understand both the geometric and semantic properties of the scene
surrounding them. The majority of research to date has addressed these mapping
challenges separately, focusing on either geometric or semantic mapping. In
this paper we address the problem of building environmental maps that include
both semantically meaningful, object-level entities and point- or mesh-based
geometrical representations. We simultaneously build geometric point cloud
models of previously unseen instances of known object classes and create a map
that contains these object models as central entities. Our system leverages
sparse, feature-based RGB-D SLAM, image-based deep-learning object detection
and 3D unsupervised segmentation.


title: A fiber-bundle model for the continuum deformation of brittle material

abstract:
  The deformation of brittle material is primarily accompanied by
micro-cracking and faulting. However, it has often been found that continuum
fluid models, usually based on a non-Newtonian viscosity, are applicable. To
explain this rheology, we use a fiber-bundle model, which is a model of damage
mechanics. In our analyses, yield stress was introduced. Above this stress, we
hypothesize that the fibers begin to fail and a failed fiber is replaced by a
new fiber. This replacement is analogous to a micro-crack or an earthquake and
its iteration is analogous to stick-slip motion. Below the yield stress, we
assume that no fiber failure occurs, and the material behaves elastically. We
show that deformation above yield stress under a constant strain rate for a
sufficient amount of time can be modeled as an equation similar to that used
for non-Newtonian viscous flow. We expand our rheological model to treat
viscoelasticity and consider a stress relaxation problem. The solution can be
used to understand aftershock temporal decay following an earthquake. Our
results provide justification for the use of a non-Newtonian viscous flow to
model the continuum deformation of brittle materials.


title:
Testing MOG, Non-Local Gravity and MOND with rotation curves of dwarf
  galaxies

abstract:
  Modified Gravity (MOG) and Non-Local Gravity (NLG) are two alternative
theories to General Relativity. They are able to explain the rotation curves of
spiral galaxies and clusters of galaxies without including dark matter (Moffat
& Rahvar 2013, 2014; Rahvar & Mashhoon 2014). In the weak-field approximation
these two theories have similar forms, with an effective gravitational
potential that has two components: (i) Newtonian gravity with the gravitational
constant enhanced by a factor $(1+\alpha)$ and (ii) a Yukawa type potential
that produces a repulsive force with length scale $1/\mu$. In this work we
compare the rotation curves of dwarf galaxies in the LITTLE THINGS catalog with
predictions of MOG, NLG and Modified Newtonian Dynamics (MOND). We find that
the universal parameters of these theories, can fit the rotation curve of dwarf
galaxies with a larger stellar mass to the light ratio compared to the nearby
stars in the Milky Way galaxy. Future direct observations of mass function of
stars in the dwarf galaxies can examine different modified gravity models.


title: Semi-cubic hyponormality of weighted shifts with stampfli recursive tail

abstract:
  Let $\alpha :\sqrt{x_{m}},\cdots ,\sqrt{x_{1}},(\sqrt{u},\sqrt{v},\sqrt{w}%
)^{\wedge}$ be a backward $m$-step extension of a recursive weight sequence and
let $% W_{\alpha }$ be the weighted shift associated with $\alpha $. In this
paper we characterize the semi-cubic hyponormality of $W_{\alpha }$ having the
positive determinant coefficient property and discuss some related examples.


title:
Variance-corrected Michaelis-Menten equation predicts transient rates of
  single-enzyme reactions and response times in bacterial gene-regulation

abstract:
  Many chemical reactions in biological cells occur at very low concentrations
of constituent molecules. Thus, transcriptional gene-regulation is often
controlled by poorly expressed transcription-factors, such as E.coli lac
repressor with few tens of copies. Here we study the effects of inherent
concentration fluctuations of substrate-molecules on the seminal
Michaelis-Menten scheme of biochemical reactions. We present a universal
correction to the Michaelis-Menten equation for the reaction-rates. The
relevance and validity of this correction for enzymatic reactions and
intracellular gene-regulation is demonstrated. Our analytical theory and
simulation results confirm that the proposed variance-corrected
Michaelis-Menten equation predicts the rate of reactions with remarkable
accuracy even in the presence of large non-equilibrium concentration
fluctuations. The major advantage of our approach is that it involves only the
mean and variance of the substrate-molecule concentration. Our theory is
therefore accessible to experiments and not specific to the exact source of the
concentration fluctuations.


title: A parabolic Monge-Amp\`ere type equation of Gauduchon metrics

abstract:
  We prove the long time existence and uniqueness of solution to a parabolic
Monge-Amp\`ere type equation on compact Hermitian manifolds. We also show that
the normalization of the solution converges to a smooth function in the smooth
topology as $t$ approaches infinity which, up to scaling, is the solution to a
Monge-Amp\`ere type equation. This gives a parabolic proof of the Gauduchon
conjecture based on the solution of Sz\'ekelyhidi, Tosatti and Weinkove to this
conjecture.


title:
A single predator charging a herd of prey: effects of self volume and
  predator-prey decision-making

abstract:
  We study the degree of success of a single predator hunting a herd of prey on
a two dimensional square lattice landscape. We explicitly consider the self
volume of the prey restraining their dynamics on the lattice. The movement of
both predator and prey is chosen to include an intelligent, decision making
step based on their respective sighting ranges, the radius in which they can
detect the other species (prey cannot recognise each other besides the self
volume interaction): after spotting each other the motion of prey and predator
turns from a nearest neighbour random walk into direct escape or chase,
respectively. We consider a large range of prey densities and sighting ranges
and compute the mean first passage time for a predator to catch a prey as well
as characterise the effective dynamics of the hunted prey. We find that the
prey's sighting range dominates their life expectancy and the predator profits
more from a bad eyesight of the prey than from his own good eye sight. We
characterise the dynamics in terms of the mean distance between the predator
and the nearest prey. It turns out that effectively the dynamics of this
distance coordinate can be captured in terms of a simple Ornstein-Uhlenbeck
picture. Reducing the many-body problem to a simple two-body problem by
imagining predator and nearest prey to be connected by a Hookean bond, all
features of the model such as prey density and sighting ranges merge into the
effective binding constant.


title: Formation of Non-uniform Double Helices for Elastic Rods under Torsion

abstract:
  The spontaneous formation of double helices for filaments under torsion is
common and significant. For example, the research on the supercoiling of DNA is
helpful for understanding the replication and transcription of DNA. Similar
double helices can appear in polymer chains, carbon nanotube yarns, cables,
telephone wires and so forth. We noticed that non-uniform double helices can be
produced due to the surface friction induced by the self-contact. Therefore an
ideal model was presented to investigate the formation of double helices for
elastic rods under torque. A general equilibrium condition which is valid for
both the smooth surface and the rough surface situations is derived by using
the variational method. Based on this, by adding further constraints, the
smooth and rough surface situations are investigated in detail respectively.
Additionally, the model showed that the specific process of how to twist and
slack the rod can determine the surface friction and hence influence the
configuration of the double helix formed by rods with rough surfaces. Based on
this principle, a method of manufacturing double helices with designed
configurations was proposed and demonstrated. Finally, experiments were
performed to verify the model and the results agreed well with the theory.


title:
Spectrally resolved single-photon imaging with hybrid superconducting -
  nanophotonic circuits

abstract:
  The detection of individual photons is an inherently binary mechanism,
revealing either their absence or presence while concealing their spectral
information. For multi-color imaging techniques, such as single photon
spectroscopy, fluorescence resonance energy transfer microscopy and
fluorescence correlation spectroscopy, wavelength discrimination is essential
and mandates spectral separation prior to detection. Here, we adopt an approach
borrowed from quantum photonic integration to realize a compact and scalable
waveguide-integrated single-photon spectrometer capable of parallel detection
on multiple wavelength channels, with temporal resolution below 50 ps and dark
count rates below 10 Hz. We demonstrate multi-detector devices for
telecommunication and visible wavelengths and showcase their performance by
imaging silicon vacancy color centers in diamond nanoclusters. The fully
integrated hybrid superconducting-nanophotonic circuits enable simultaneous
spectroscopy and lifetime mapping for correlative imaging and provide the
ingredients for quantum wavelength division multiplexing on a chip.


title:
Exact optimal values of step-size coefficients for boundedness of linear
  multistep methods

abstract:
  Linear multistep methods (LMMs) applied to approximate the solution of
initial value problems---typically arising from method-of-lines
semidiscretizations of partial differential equations---are often required to
have certain monotonicity or boundedness properties (e.g.
strong-stability-preserving, total-variation-diminishing or
total-variation-boundedness properties). These properties can be guaranteed by
imposing step-size restrictions on the methods. To qualitatively describe the
step-size restrictions, one introduces the concept of step-size coefficient for
monotonicity (SCM, also referred to as the strong-stability-preserving (SSP)
coefficient) or its generalization, the step-size coefficient for boundedness
(SCB). A LMM with larger SCM or SCB is more efficient, and the computation of
the maximum SCM for a particular LMM is now straightforward. However, it is
more challenging to decide whether a positive SCB exists, or determine if a
given positive number is a SCB. Theorems involving sign conditions on certain
linear recursions associated to the LMM have been proposed in the literature
that allow us to answer the above questions: the difficulty with these theorems
is that there are in general infinitely many sign conditions to be verified. In
this work we present methods to rigorously check the sign conditions. As an
illustration, we confirm some recent numerical investigations concerning the
existence of SCBs in the BDF and in the extrapolated BDF (EBDF) families. As a
stronger result, we determine the optimal values of the SCBs as exact algebraic
numbers in the BDF family (with $1\le k\le 6$ steps) and in the
Adams--Bashforth family (with $1\le k\le 3$ steps).


title: Visual Fashion-Product Search at SK Planet

abstract:
  We build a large-scale visual search system which finds similar product
images given a fashion item. Defining similarity among arbitrary
fashion-products is still remains a challenging problem, even there is no exact
ground-truth. To resolve this problem, we define more than 90 fashion-related
attributes, and combination of these attributes can represent thousands of
unique fashion-styles. The fashion-attributes are one of the ingredients to
define semantic similarity among fashion-product images. To build our system at
scale, these fashion-attributes are again used to build an inverted indexing
scheme. In addition to these fashion-attributes for semantic similarity, we
extract colour and appearance features in a region-of-interest (ROI) of a
fashion item for visual similarity. By sharing our approach, we expect active
discussion on that how to apply current computer vision research into the
e-commerce industry.


title: The Dating Problem and Optimal Ordering of Sequential Opportunities

abstract:
  In this paper, we discuss a stochastic decision problem of optimally
selecting the order in which to try $n$ opportunities that may yield an
uncertain reward in the future. The motivation came out from pure curiosity,
after an informal conversation about what could be the best way to date
friends. The problem structure turned out to be suitable also for other
situations, such as the problem of optimally selecting the order of submission
of a paper to journals. Despite the seemingly combinatorial nature of the
problem, we show that optimal-tradeoff solutions can be found by simply
ordering a sequence of $n$ real numbers.


title:
Broadband and energy-concentrating terahertz coherent perfect absorber
  based on a self-complementary metasurface

abstract:
  We demonstrate that a self-complementary checkerboard-like metasurface works
as a broadband coherent perfect absorber (CPA) when symmetrically illuminated
by two counter-propagating incident waves. A theoretical analysis based on wave
interference and results of numerical simulations of the proposed metasurface
are provided. In addition, we experimentally demonstrate the proposed CPA in
the terahertz regime by using a time-domain spectroscopy technique. We observe
that the metasurface can work as a CPA below its lowest diffraction frequency.
The size of the absorptive areas of the proposed CPA can be much smaller than
the incident wavelength. Unlike conventional CPAs, the presented one
simultaneously achieves the broadband operation and energy concentration of
electromagnetic waves at the deep-subwavelength scale.


title:
Quadratic residue codes over the ring $\mathbb{F}_{p}[u]/\langle
  u^m-u\rangle$ and their Gray images

abstract:
  Let $m\geq 2$ be any natural number and let
$\mathcal{R}=\mathbb{F}_{p}+u\mathbb{F}_{p}+u^2\mathbb{F}_{p}+\cdots+u^{m-1}\mathbb{F}_{p}$
be a finite non-chain ring, where $u^m=u$ and $p$ is a prime congruent to $1$
modulo $(m-1)$. In this paper we study quadratic residue codes over the ring
$\mathcal{R}$ and their extensions. A gray map from $\mathcal{R}$ to
$\mathbb{F}_{p}^m$ is defined which preserves self duality of linear codes. As
a consequence self dual, formally self dual and self orthogonal codes are
constructed. To illustrate this several examples of self-dual, self orthogonal
and formally self-dual codes are given. Among others a [9,3,6] linear code over
$\mathbb{F}_{7}$ is constructed which is self-orthogonal as well as nearly MDS.
The best known linear code with these parameters (ref. Magma) is not self
orthogonal.


title:
Ferromagnetic resonance study of composite Co/Ni - FeCoB free layers
  with perpendicular anisotropy

abstract:
  We study the properties of composite free layers with perpendicular
anisotropy. The free layers are made of a soft FeCoB layer ferromagnetically
coupled by a variable spacer (Ta, W, Mo) to a very anisotropic [Co/Ni]
multilayer embodied in a magnetic tunnel junction meant for spin torque memory
applications. For this we use broadband ferromagnetic resonance to follow the
field dependence of the acoustical and optical excitation of the composite free
layer in both in-plane and out-of-plane applied fields. The modeling provides
the interlayer exchange coupling, the anisotropies and the damping factors. The
popular Ta spacer are outperformed by W and even more by Mo, which combines the
strongest interlayer exchange coupling without sacrificing anisotropies,
damping factors and transport properties.


title:
The motivic class of the classifying stack of the special orthogonal
  group

abstract:
  We compute the class of the classifying stack of the special orthogonal group
in the Grothendieck ring of stacks, and check that it is equal to the
multiplicative inverse of the class of the group.


title: On a good reduction criterion for proper polycurves with sections

abstract:
  We give a good reduction criterion for proper polycurves with sections,i.e.,
successive extensions of family of curves with section, under mild assumption.
This criterion is a higher dimensional version of the good reduction criterion
for hyperbolic curves given by Oda and Tamagawa.


title: Role of Interference Alignment in Wireless Cellular Network Optimization

abstract:
  The emergence of interference alignment (IA) as a degrees-of-freedom optimal
strategy motivates the need to investigate whether IA can be leveraged to aid
conventional network optimization algorithms that are only capable of finding
locally optimal solutions. To test the usefulness of IA in this context, this
paper proposes a two-stage optimization framework for the downlink of a
$G$-cell multi-antenna network with $K$ users/cell. The first stage of the
proposed framework focuses on nulling interference from a set of dominant
interferers using IA, while the second stage optimizes transmit and receive
beamformers to maximize a network-wide utility using the IA solution as the
initial condition. Further, this paper establishes a set of new feasibility
results for partial IA that can be used to guide the number of dominant
interferers to be nulled in the first stage. Through simulations on specific
topologies of a cluster of base-stations, it is observed that the impact of IA
depends on the choice of the utility function and the presence of
out-of-cluster interference. In the absence of out-of-cluster interference, the
proposed framework outperforms straightforward optimization when maximizing the
minimum rate, while providing marginal gains when maximizing sum-rate. However,
the benefit of IA is greatly diminished in the presence of significant
out-of-cluster interference.


title:
Temporal variability from the two-component advective flow solution and
  its observational evidence

abstract:
  In the propagating oscillatory shock model, the oscillation of the post-shock
region, i.e., the Compton cloud, causes the observed low-frequency
quasi-periodic oscillations (QPOs). The evolution of QPO frequency is explained
by the systematic variation of the Compton cloud size, i.e., the steady radial
movement of the shock front, which is triggered by the cooling of the
post-shock region. Thus, analysis of energy-dependent temporal properties in
different variability time scales can diagnose the dynamics and geometry of
accretion flows around black holes. We study these properties for the high
inclination black hole source XTE J1550-564 during its 1998 outburst and the
low-inclination black hole source GX 339-4 during its 2006-07 outburst using
RXTE/PCA data, and we find that they can satisfactorily explain the time lags
associated with the QPOs from these systems. We find a smooth decrease of the
time lag as a function of time in the rising phase of both sources. In the
declining phase the time lag increases with time. We find a systematic
evolution of QPO frequency and hard lags in these outbursts. In XTE J1550-564,
the lag changes from hard to soft (i.e., from a positive to a negative value)
at a crossing frequency ($\nu_C$) of $\sim 3.4$ Hz. We present possible
mechanisms to explain the lag behavior of high and low-inclination sources
within the framework of a single two-component advective flow model (TCAF).


title:
One loop effects of natural SUSY in third generation fermion production
  at the ILC

abstract:
  Within the framework of the Minimal Supersymmetric Standard Model, we
investigate the 1-loop effects of supersymmetric particles on the
third-generation fermion-pair production at the ILC. Three sets of the SUSY
parameters are proposed which are consistent with the observed Higgs mass, the
muon g-2, the Dark Matter abundance and the decay branching ratio of B meson.
We discuss on the possibility of discovering the signals consistent with SUSY
as well as of experimentally distinguishing the proposed sets of SUSY
parameters.


title: Spin current relaxation time in thermally evaporated pentacene films

abstract:
  The spin current relaxation time [tau] in thermally evaporated pentacene
films was evaluated with the spin-pump-induced spin transport properties and
the charge current transport properties in pentacene films. Under an assumption
of a diffusive transport of the spin current in pentacene films, the zero-field
mobility and the diffusion constant of holes in pentacene films were
experimentally obtained to be ~8.0x10^-7 m^2/Vs and ~2.0x10^-8 m^2/s,
respectively. Using those values and the previously obtained spin diffusion
length in pentacene films of 42{plus-minus}10 nm, the [tau] in pentacene films
was estimated to be 150{plus-minus}120 ns at room temperature. This estimated
[tau] in pentacene films is long enough for practical use as a spintronic
material.


title: On Morita and derived equivalences for cohomological Mackey algebras

abstract:
  By results of the second author, a source algebra equivalence between two
$p$-blocks of finite groups induces an equivalence between the categories of
cohomological Mackey functors associated with these blocks, and a splendid
derived equivalence between two blocks induces a derived equivalence between
the corresponding categories of cohomological Mackey functors. The main result
of this paper proves a partial converse: an equivalence (resp. Rickard
equivalence) between the categories of cohomological Mackey functors of two
blocks of finite groups induces a permeable Morita (resp. derived) equivalence
between the two block algebras.


title:
Morphing graphene-based systems for applications: perspectives from
  simulations

abstract:
  Graphene, the one-atom-thick sp2 hybridized carbon crystal, displays unique
electronic, structural and mechanical properties, which promise a large number
of interesting applications in diverse high tech fields. Many of these
applications require its functionalization, e.g. with substitution of carbon
atoms or adhesion of chemical species, creation of defects, modification of
structure of morphology, to open electronic band gap to use it in electronics,
or to create 3D frameworks for volumetric applications. Understanding the
morphology-properties relationship is the first step to efficiently
functionalize graphene. Therefore a great theoretical effort has been recently
devoted to model graphene in different conditions and with different approaches
involving different level of accuracy and resolution. Here we review the
modeling approaches to graphene systems, with a special focus on atomistic
level methods, but extending our analysis onto coarser scales. We illustrate
the methods by means of applications with possible potential impact.


title: Every linear order isomorphic to its cube is isomorphic to its square

abstract:
  In 1958, Sierpinski asked whether there exists a linear order $X$ that is
isomorphic to its lexicographically ordered cube but is not isomorphic to its
square. The main result of this paper is that the answer is negative. More
generally, if $X$ is isomorphic to any one of its finite powers $X^n$, $n>1$,
it is isomorphic to all of them.