title: The physics and the mixed Hodge structure of Feynman integrals

abstract:
  This expository text is an invitation to the relation between quantum field
theory Feynman integrals and periods. We first describe the relation between
the Feynman parametrization of loop amplitudes and world-line methods, by
explaining that the first Symanzik polynomial is the determinant of the period
matrix of the graph, and the second Symanzik polynomial is expressed in terms
of world-line Green's functions. We then review the relation between Feynman
graphs and variations of mixed Hodge structures. Finally, we provide an
algorithm for generating the Picard-Fuchs equation satisfied by the all equal
mass banana graphs in a two-dimensional space-time to all loop orders.


title: Insulators of ABC Solutions

abstract:
  This note studies various ways of measuring the complexity of primitive
solutions to the equation $A \,+\, B\, + \,C = 0$ and conjectures relating
them. We define the insulator $\mathcal I(A,B,C)$ of a primitive solution as
the smallest positive integer $\mathcal I$ such that the primes dividing the
product $ABC \cdot \mathcal I$ are exactly those below a given bound. We show
that the strong XYZ Conjecture of Lagarias and Soundararajan implies there are
only finitely many primitive solutions $(A,B,C)$ with a given insulator.


title:
Schottky barriers at hexagonal boron nitride/metal interfaces: a first
  principles study

abstract:
  The formation of a Schottky barrier at the interface between a metal and
hexagonal boron nitride (h-BN) is studied using density functional theory. For
metals whose work functions range from 4.2 to 6.0 eV, we find Schottky barrier
heights for holes between 1.2 and 2.3 eV. A central role in determining the
Schottky barrier height is played by a potential step of between 0.4 and 1.8 eV
that is formed at the metal|h-BN interface and effectively lowers the metal
work function. If h-BN is physisorbed, as is the case on fcc Cu, Al, Au, Ag and
Pt(111) substrates, the interface potential step is described well by a
universal function that depends only on the distance separating h-BN from the
metal surface. The interface potential step is largest when h-BN is
chemisorbed, which is the case for hcp Co and Ti (0001) and for fcc Ni and Pd
(111) substrates.


title: A new vacuum for Loop Quantum Gravity

abstract:
  We construct a new vacuum for loop quantum gravity, which is dual to the
Ashtekar-Lewandowski vacuum. Because it is based on BF theory, this new vacuum
is physical for $(2+1)$-dimensional gravity, and much closer to the spirit of
spin foam quantization in general. To construct this new vacuum and the
associated representation of quantum observables, we introduce a modified
holonomy-flux algebra which is cylindrically consistent with respect to the
notion of refinement by time evolution suggested in [1]. This supports the
proposal for a construction of a physical vacuum made in [1,2], also for
$(3+1)$-dimensional gravity. We expect that the vacuum introduced here will
facilitate the extraction of large scale physics and cosmological predictions
from loop quantum gravity.


title:
Linear automorphisms of vertex operator algebras associated with formal
  changes of variable and Bernoulli-type numbers

abstract:
  We study a certain linear automorphism of a vertex operator algebra induced
by the formal change of variable $f(x)=e^x-1$ and describe examples showing how
this relates the theory of vertex operator algebras to Bernoulli numbers,
Bernoulli polynomial values, and related numbers. We give a recursion for such
numbers derived using vertex operator relations, and study the Jacobi identity
for modified vertex operators that was introduced in work of Lepowsky.


title:
A one-phase problem for the fractional Laplacian: regularity of flat
  free boundaries

abstract:
  We consider a one-phase free boundary problem involving a fractional
Laplacian $(-\Delta)^\alpha$, $0<\alpha <1,$ and we prove that ``flat free
boundaries" are $C^{1,\gamma}$. We thus extend the known result for the case
$\alpha=1/2.$


title: Android Anti-forensics: Modifying CyanogenMod

abstract:
  Mobile devices implementing Android operating systems inherently create
opportunities to present environments that are conducive to anti-forensic
activities. Previous mobile forensics research focused on applications and data
hiding anti-forensics solutions. In this work, a set of modifications were
developed and implemented on a CyanogenMod community distribution of the
Android operating system. The execution of these solutions successfully
prevented data extractions, blocked the installation of forensic tools, created
extraction delays and presented false data to industry accepted forensic
analysis tools without impacting normal use of the device. The research
contribution is an initial empirical analysis of the viability of operating
system modifications in an anti-forensics context along with providing the
foundation for future research.


title:
Theoretical Analysis of Dynamic Processes for Interacting Molecular
  Motors

abstract:
  Biological transport is supported by collective dynamics of enzymatic
molecules that are called motor proteins or molecular motors. Experiments
suggest that motor proteins interact locally via short-range potentials. We
investigate the fundamental role of these interactions by analyzing a new class
of totally asymmetric exclusion processes where interactions are accounted for
in a thermodynamically consistent fashion. Theoretical analysis that combines
various mean-field cal- culations and computer simulations suggests that
dynamic properties of molecular motors strongly depend on interactions, and
correlations are stronger for interacting motor proteins. Surprisingly, it is
found that there is an optimal strength of interactions (weak repulsion) that
leads to a maxi- mal particle flux. It is also argued that molecular motors
transport is more sensitive to attractive interactions. Applications of these
results for kinesin motor proteins are discussed.


title: Cluster Polylogarithms for Scattering Amplitudes

abstract:
  Motivated by the cluster structure of two-loop scattering amplitudes in N=4
Yang-Mills theory we define "cluster polylogarithm functions". We find that all
such functions of weight 4 are made up of a single simple building block
associated to the A_2 cluster algebra. Adding the requirement of locality on
generalized Stasheff polytopes, we find that these A_2 building blocks arrange
themselves to form a unique function associated to the A_3 cluster algebra.
This A_3 function manifests all of the cluster algebraic structure of the
two-loop n-particle MHV amplitudes for all n, and we use it to provide an
explicit representation for the most complicated part of the n=7 amplitude as
an example.


title:
Semiclassical analysis for a Schr\"odinger operator with a U(2)
  artificial gauge: the periodic case

abstract:
  We consider a Schr\"odinger operator with a Hermitian 2x2 matrix-valued
potential which is lattice periodic and can be diagonalized smoothly on the
whole $R^n.$ In the case of potential taking its minimum only on the lattice,
we prove that the well-known semiclassical asymptotic of first band spectrum
for a scalar potential remains valid for our model.


title: An ADER-WENO Finite Volume AMR code for Astrophysics

abstract:
  A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh
Refinement (AMR) in multiple space dimensions is presented. A high order
one-step time discretization is achieved using a local space-time discontinuous
Galerkin predictor method, while a high order spatial accuracy is obtained
through a WENO reconstruction. Thanks to the one-step nature of the underlying
scheme, the resulting algorithm can be efficiently imported within an AMR
framework on space-time adaptive meshes. We provide convincing evidence that
the presented high order AMR scheme behaves better than traditional second
order AMR methods. Tests are shown of the new scheme for nonlinear systems of
hyperbolic conservation laws, including the classical Euler equations and the
equations of ideal magnetohydrodynamics. The proposed scheme is likely to
become a useful tool in several astrophysical scenarios.


title: A statistical network analysis of the HIV/AIDS epidemics in Cuba

abstract:
  The Cuban contact-tracing detection system set up in 1986 allowed the
reconstruction and analysis of the sexual network underlying the epidemic
(5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168
edges), shedding light onto the spread of HIV and the role of contact-tracing.
Clustering based on modularity optimization provides a better visualization and
understanding of the network, in combination with the study of covariates. The
graph has a globally low but heterogeneous density, with clusters of high
intraconnectivity but low interconnectivity. Though descriptive, our results
pave the way for incorporating structure when studying stochastic SIR epidemics
spreading on social networks.


title: Phase Transitions in Nonlinear Filtering

abstract:
  It has been established under very general conditions that the ergodic
properties of Markov processes are inherited by their conditional distributions
given partial information. While the existing theory provides a rather complete
picture of classical filtering models, many infinite-dimensional problems are
outside its scope. Far from being a technical issue, the infinite-dimensional
setting gives rise to surprising phenomena and new questions in filtering
theory. The aim of this paper is to discuss some elementary examples,
conjectures, and general theory that arise in this setting, and to highlight
connections with problems in statistical mechanics and ergodic theory. In
particular, we exhibit a simple example of a uniformly ergodic model in which
ergodicity of the filter undergoes a phase transition, and we develop some
qualitative understanding as to when such phenomena can and cannot occur. We
also discuss closely related problems in the setting of conditional Markov
random fields.


title: Tilting theory via stable homotopy theory

abstract:
  We show that certain tilting results for quivers are formal consequences of
stability, and as such are part of a formal calculus available in any abstract
stable homotopy theory. Thus these results are for example valid over arbitrary
ground rings, for quasi-coherent modules on schemes, in the differential-graded
context, in stable homotopy theory and also in the equivariant, motivic or
parametrized variant thereof. In further work, we will continue developing this
calculus and obtain additional abstract tilting results. Here, we also deduce
an additional characterization of stability, based on Goodwillie's strongly
(co)cartesian n-cubes.
  As applications we construct abstract Auslander-Reiten translations and
abstract Serre functors for the trivalent source and verify the relative
fractionally Calabi-Yau property. This is used to offer a new perspective on
May's axioms for monoidal, triangulated categories.


title: Gromov compactness in non-archimedean analytic geometry

abstract:
  Gromov's compactness theorem for pseudo-holomorphic curves is a foundational
result in symplectic geometry. It controls the compactness of the moduli space
of pseudo-holomorphic curves with bounded area in a symplectic manifold.
  In this paper, we prove the analog of Gromov's compactness theorem in
non-archimedean analytic geometry. We work in the framework of Berkovich
spaces.
  First, we introduce a notion of K\"ahler structure in non-archimedean
analytic geometry using metrizations of virtual line bundles. Second, we
introduce formal stacks and non-archimedean analytic stacks. Then we construct
the moduli stack of non-archimedean analytic stable maps using formal models,
Artin's representability criterion and the geometry of stable curves. Finally,
we reduce the non-archimedean problem to the known compactness results in
algebraic geometry. The motivation of this paper is to provide the foundations
for non-archimedean enumerative geometry.


title: Zero-modes and global antiferromagnetism in strained graphene

abstract:
  A novel magnetic ground state is reported for the Hubbard Hamiltonian in
strained graphene. When the chemical potential lies close to the Dirac point,
the ground state exhibits locally both the N\'{e}el and ferromagnetic orders,
even for weak Hubbard interaction. Whereas the N\'{e}el order parameter remains
of the same sign in the entire system, the magnetization at the boundary takes
the opposite sign from the bulk. The total magnetization this way vanishes, and
the magnetic ground state is globally only an antiferromagnet. This peculiar
ordering stems from the nature of the strain-induced single particle
zero-energy states, which have support on one sublattice of the honeycomb
lattice in the bulk, and on the other sublattice near the boundary of a finite
system. We support our claim with the self-consistent numerical calculation of
the order parameters, as well as by the Monte Carlo simulations of the Hubbard
model in both uniformly and non-uniformly strained honeycomb lattice. The
present result is contrasted with the magnetic ground state of the same Hubbard
model in the presence of a true magnetic field (and for vanishing Zeeman
coupling), which is exclusively N\'{e}el ordered, with zero local magnetization
everywhere in the system.


title: A fast pneumatic sample-shuttle with attenuated shocks

abstract:
  We describe a home-built pneumatic shuttle suitable for the fast displacement
of samples in the vicinity of a highly sensitive atomic magnetometer. The
samples are magnetized at 1 T using a Halbach assembly of magnets. The device
enables the remote detection of free induction decay in ultra-low-field and
zero-field NMR experiments, in relaxometric measurements and in other
applications involving the displacement of magnetized samples within time
intervals as short as a few tens of milliseconds. Other possible applications
of fast sample shuttling exist in radiological studies, where samples have to
be irradiated and then analyzed in a 'cold' environment.


title:
Motivating Smartphone Collaboration in Data Acquisition and Distributed
  Computing

abstract:
  This paper analyzes and compares different incentive mechanisms for a master
to motivate the collaboration of smartphone users on both data acquisition and
distributed computing applications. To collect massive sensitive data from
users, we propose a reward-based collaboration mechanism, where the master
announces a total reward to be shared among collaborators, and the
collaboration is successful if there are enough users wanting to collaborate.
We show that if the master knows the users' collaboration costs, then he can
choose to involve only users with the lowest costs. However, without knowing
users' private information, then he needs to offer a larger total reward to
attract enough collaborators. Users will benefit from knowing their costs
before the data acquisition. Perhaps surprisingly, the master may benefit as
the variance of users' cost distribution increases.
  To utilize smartphones' computation resources to solve complex computing
problems, we study how the master can design an optimal contract by specifying
different task-reward combinations for different user types. Under complete
information, we show that the master involves a user type as long as the
master's preference characteristic outweighs that type's unit cost. All
collaborators achieve a zero payoff in this case. If the master does not know
users' private cost information, however, he will conservatively target at a
smaller group of users with small costs, and has to give most benefits to the
collaborators.


title:
A rapid evolving region in the Galactic Center: Why S-stars thermalize
  and more massive stars are missing

abstract:
  The existence of "S-stars" within a distance of 1" from SgrA$^*$ contradicts
our understanding of star formation, due to the forbiddingly violent
environment. A suggested possibility is that they form far and have been
brought in by some fast dynamical process, since they are young. Nonetheless,
all conjectured mechanisms either fail to reproduce their eccentricities
--without violating their young age-- or cannot explain the problem of "inverse
mass segregation": The fact that lighter stars (the S-stars) are closer to
SgrA$^*$ and more massive ones, Wolf-Rayet (WR) and O-stars, are farther out.
In this Letter we propose that the responsible for both, the distribution of
the eccentricities and the paucity of massive stars, is the Kozai-Lidov-{\em
like} resonance induced by a sub-parsec disk recently discovered in the
Galactic center. Considering that the disk probably extended to smaller radius
in the past, we show that in as short as (a few) $10^6$ years, the stars
populating the innermost 1" region would redistribute in angular-momentum space
and recover the observed "super-thermal" distribution. Meanwhile, WR and
O-stars in the same region intermittently attain ample eccentricities that will
lead to their tidal disruptions by the central massive black hole. Our results
provide new evidences that SgrA$^*$ was powered several millions years ago by
an accretion disk as well as by tidal stellar disruptions.


title: Loopy Constraints on Leptophilic Dark Matter and Internal Bremsstrahlung

abstract:
  A sharp and spatially extended peak in an astrophysical gamma ray spectrum
would provide very strong evidence for the existence of dark matter (DM), given
that there are no known astrophysical processes that could mimic such a signal.
From the particle physics perspective, perhaps the simplest explanation for a
gamma ray peak is internal bremsstrahlung in DM annihilation through a charged
t-channel mediator eta close in mass to the DM particle chi. Since DM
annihilation to quarks is already tightly constrained in this scenario, we
focus here on the leptophilic case. We compute the electromagnetic anapole and
dipole moments that DM acquires at 1-loop, and we find an interesting
enhancement of these moments if the DM particle and the mediator are close in
mass. We constrain the DM anapole and dipole moments using direct detection
data, and then translate these limits into bounds on the DM annihilation cross
section. Our bounds are highly competitive with those from astrophysical gamma
ray searches. In the second part of the paper, we derive complementary
constraints on internal bremsstrahlung in DM annihilation using LEP mono-photon
data, measurements of the anomalous magnetic moments of the electron and the
muon, and searches for lepton flavor violation. We also comment on the impact
of the internal bremsstrahlung scenario on the hyperfine splitting of true
muonium.


title: Extended gamma-ray emission from Coy Dark Matter

abstract:
  We show that it is possible for WIMP dark matter to produce a large signal in
indirect dark matter searches without producing signals elsewhere. We
illustrate our point by fitting the Fermi-LAT extended galactic gamma-ray
excess with a simple model of Dirac dark matter that annihilates primarily into
b quarks via a pseudoscalar. Current collider constraints are weak while the 14
TeV LHC run will constrain a limited portion of the parameter space. No signal
is expected in additional indirect searches or at future direct detection
experiments. Our results emphasise the importance of fully understanding
potential indirect signals of dark matter as they may provide the only
information about the dark matter particle.


title: The Local Void: for or against LCDM?

abstract:
  The emptiness of the Local Void has been put forward as a serious challenge
to the current standard paradigm of structure formation in LCDM. We use a high
resolution cosmological N-body simulation, the Millennium-II run, combined with
a sophisticated semi-analytic galaxy formation model, to explore statistically
whether the local void is allowed within our current knowledge of galaxy
formation in LCDM. We find that about 15 percent of the Local Group analogue
systems (11 of 77) in our simulation are associated with nearby low density
regions having size and 'emptiness' similar to those of the observed Local
Void. This suggests that, rather than a crisis of the LCDM, the emptiness of
the Local Void is indeed a success of the standard LCDM theory. The paucity of
faint galaxies in such voids results from a combination of two factors: a lower
amplitude of the halo mass function in the voids than in the field, and a lower
galaxy formation efficiency in void haloes due to halo assembly bias effects.
While the former is the dominated factor, the later also plays a sizable role.
The halo assembly bias effect results in a stellar mass fraction 25 percent
lower for void galaxies when compared to field galaxies with the same halo
mass.


title: Constraining Axion Dark Matter with Big Bang Nucleosynthesis

abstract:
  We show that Big Bang Nucleosynthesis (BBN) significantly constrains
axion-like dark matter. The axion acts like an oscillating QCD $\theta$ angle
that redshifts in the early universe, increasing the neutron-proton mass
difference at neutron freeze-out. An axion-like particle that couples too
strongly to QCD results in the underproduction of 4He during BBN and is thus
excluded. The BBN bound overlaps with much of the parameter space that would be
covered by proposed searches for time-varying neutron EDMs. The QCD axion does
not couple strongly enough to affect BBN.


title: Families of weighted sum formulas for multiple zeta values

abstract:
  Euler's sum formula and its multi-variable and weighted generalizations form
a large class of the identities of multiple zeta values. In this paper we prove
a family of identities involving Bernoulli numbers and apply them to obtain
infinitely many weighted sum formulas for double zeta values and triple zeta
values where the weight coefficients are given by symmetric polynomials. We
give a general conjecture in arbitrary depth at the end of the paper.


title: Mirror Symmetry in Flavored Affine D-type Quivers

abstract:
  We present non-trivial checks of three dimensional mirror symmetry for
$\mathcal{N}=4$, $\hat{D}_N$ quiver gauge theories with unitary gauge groups
using partition function on a round sphere. Type IIB (Hanany-Witten)
realization of these theories and their mirror duals (as world volume gauge
theories on coincident D3 branes) involve 1/2-BPS boundary conditions
associated with orbifold and orientifold 5-planes respectively, in addition to
NS5 and D5 branes. We demonstrate that partition function for a given quiver in
this class may be decomposed into distinct contributions from the
aforementioned Type IIB ingredients. As a byproduct of this computation, we
find a convenient way of deriving the mirror map for a given pair of dual
theories.


title:
Dynamic Average Consensus under Limited Control Authority and Privacy
  Requirements

abstract:
  This paper introduces a novel continuous-time dynamic average consensus
algorithm for networks whose interaction is described by a strongly connected
and weight-balanced directed graph. The proposed distributed algorithm allows
agents to track the average of their dynamic inputs with some steady-state
error whose size can be controlled using a design parameter. This steady-state
error vanishes for special classes of input signals. We analyze the asymptotic
correctness of the algorithm under time-varying interaction topologies and
characterize the requirements on the stepsize for discrete-time
implementations. We show that our algorithm naturally preserves the privacy of
the local input of each agent. Building on this analysis, we synthesize an
extension of the algorithm that allows individual agents to control their own
rate of convergence towards agreement and handle saturation bounds on the
driving command. Finally, we show that the proposed extension additionally
preserves the privacy of the transient response of the agreement states and the
final agreement value from internal and external adversaries. Numerical
examples illustrate the results.


title:
Suite of Hydrodynamical Simulations for the Lyman-Alpha Forest with
  Massive Neutrinos

abstract:
  The signature left in quasar spectra by the presence of neutral hydrogen in
the Universe allows one to constrain the sum of the neutrino masses with
improved sensitivity, with respect to laboratory experiments, and may shed a
new light on the neutrino mass hierarchy and on the absolute mass scale of
neutrinos. Constraints on cosmological parameters and on the dark energy
equation of state can also be derived, from a joint parameter estimation
procedure. However, this requires a detailed modeling of the line-of-sight
power spectrum of the transmitted flux in the Lyman-Alpha (LyA) forest on
scales ranging from a few to hundreds of Mpcs, which in turns demands the
inclusion and careful treatment of cosmological neutrinos. To this end, we
present here a suite of state-of-the-art hydrodynamical simulations with cold
dark matter, baryons and massive neutrinos, specifically targeted for modeling
the low-density regions of the IGM as probed by the LyA forest at
high-redshift. The simulations span volumes ranging from (25 Mpc/h)^3 to (100
Mpc/h)^3, and are made using either 3 X 192^3~21 millions or 3 X 768^3~1.4
billion particles. The resolution of the various runs can be further enhanced,
so that we can reach the equivalent of 3 X 3072^3~87 billion particles in a
(100 Mpc/h)^3 box size. The chosen cosmological parameters are compatible with
the latest Planck (2013) results, although we also explore the effect of slight
variations in the main cosmological and astrophysical parameters. We adopt a
particle-type implementation of massive neutrinos, and consider three
degenerate species having masses M_nu =0.1, 0.2, 0.3, 0.4 and 0.8 eV,
respectively. We improve on previous studies in several ways, in particular
with updated routines for IGM radiative cooling and heating processes, and
initial conditions based on 2LPT rather than the Zeldovich approximation.


title:
Extended Order Parameter and Conjugate Field for the Dynamic Phase
  Transition in a Ginzburg-Landau Mean-Field Model in an Oscillating Field

abstract:
  We present numerical evidence for an extended order parameter and conjugate
field for the dynamic phase transition in a Ginzburg-Landau mean-field model
driven by an oscillating field. The order parameter, previously taken to be the
time-averaged magnetization, comprises the deviations of the Fourier components
of the magnetization from their values at the critical period. The conjugate
field, previously taken to be the time-averaged magnetic field, comprises the
even Fourier components of the field. The scaling exponents beta and delta
associated with the extended order parameter and conjugate field are shown
numerically to be consistent with their values in the equilibrium mean-field
model.


title:
Periodic ordering of clusters and stripes in a two-dimensional lattice
  model. II. Results of Monte Carlo simulation

abstract:
  The triangular lattice model with nearest-neighbor attraction and
third-neighbor repulsion, introduced in [J. Pekalski, A. Ciach and N. G.
Almarza, arXiv:1401.0801 [cond-mat.soft]] is studied by Monte Carlo simulation.
Introduction of appropriate order parameters allowed us to construct a phase
diagram, where different phases with patterns made of clusters, bubbles or
stripes are thermodynamically stable. We observe, in particular, two distinct
lamellar phases - the less ordered one with global orientational order and the
more ordered one with both orientational and translational order. Our results
concern spontaneous pattern formation on solid surfaces, fluid interfaces or
membranes that is driven by competing interactions between adsorbing particles
or molecules.


title: Wavenumber-dependent Gilbert damping in metallic ferromagnets

abstract:
  New terms to the dynamical equation of magnetization motion, associated with
spin transport, have been reported over the past several years. Each newly
identified term is thought to possess both a real and an imaginary effective
field leading to fieldlike and dampinglike torques on magnetization. Here we
show that three metallic ferromagnets possess an imaginary effective-field term
which mirrors the well-known real effective-field term associated with exchange
in spin waves. Using perpendicular standing spin wave resonance between 2-26
GHz, we evaluate the magnitude of the finite-wavenumber ($k$) dependent Gilbert
damping $\alpha$ in three typical device ferromagnets, Ni$_{79}$Fe$_{21}$, Co,
and Co$_{40}$Fe$_{40}$B$_{20}$, and demonstrate for the first time the presence
of a $k^2$ term as $\Delta\alpha=\Delta\alpha_0+A_{k}\cdot k^2$ in all three
metals. We interpret the new term as the continuum analog of spin pumping,
predicted recently, and show that its magnitude, $A_{k}$=0.07-0.1 nm$^2$, is
consistent with transverse spin relaxation lengths as measured by conventional
(interlayer) spin pumping.


title: Coherent laminar and turbulent motion of toroidal vortex bundles

abstract:
  Motivated by experiments performed in superfluid helium, we study numerically
the motion of toroidal bundles of vortex filaments in an inviscid fluid. We
find that the evolution of these large-scale vortex structures involves the
generalised leapfrogging of the constituent vortex rings. Despite three
dimensional perturbations in the form of Kelvin waves and vortex reconnections,
toroidal vortex bundles retain their coherence over a relatively large distance
(compared to their size), in agreement with experimental observations.


title:
Phase-sensitive detection of spin pumping via the ac inverse spin Hall
  effect

abstract:
  An intriguing feature of spintronics is the use of pure spin-currents to
manipulate magnetization, e.g., spin-currents can switch magnetization in
spin-torque MRAM, a next-generation DRAM alternative. Giant spin-currents via
the spin Hall effect greatly expand the technological opportunities.
Conversely, a ferromagnet/normal metal junction emits spin-currents under
microwave excitation, i.e. spin-pumping. While such spin-currents are modulated
at the excitation frequency, there is also a non-linear, rectified component
that is commonly detected using the corresponding inverse spin Hall effect
(iSHE) dc voltage. However, the ac component should be more conducive for
quantitative analysis, as it is up to two orders of magnitude larger and
linear. But any device that uses the ac iSHE is also sensitive to inductive
signals via Faraday's Law and discrimination of the ac iSHE signal must rely on
phase-sensitive measurements. We use the inductive signal as a reference for a
quantitative measurement of the magnitude and phase of the ac iSHE.


title: r-Dynamic Chromatic Number of Graphs

abstract:
  An $r$-dynamic $k$-coloring of a graph $G$ is a proper vertex $k$-coloring
such that the neighbors of any vertex $v$ receive at least $\min\{r,{\rm
deg}(v)\}$ different colors. The $r$-dynamic chromatic number of $G$,
$\chi_r(G)$, is defined as the smallest $k$ such that $G$ admits an $r$-dynamic
$k$-coloring. In this paper we introduce an upper bound for $\chi_r(G)$ in
terms of $r$, chromatic number, maximum degree and minimum degree. In 2001,
Montgomery \cite{MR2702379} conjectured that, for a $d$-regular graph $G$,
$\chi_2(G)-\chi(G)\leq 2$. In this regard, for a $d$-regular graph $G$, we
present two upper bounds for $\chi_2(G)-\chi(G)$, one of them, $\lceil
5.437\log d+2.721\rceil$, is an improvement of the bound $14.06\log d +1$,
proved by Alishahi (2011) \cite{MR2746973}. Also, we give an upper bound for
$\chi_2(G)$ in terms of chromatic number, maximum degree and minimum degree.


title: The Galois action on Hurwitz curves

abstract:
  We make some observations concerning the Galois actions on Hurwitz curves and
on the closely related but lesser-known Hurwitz origamis.


title:
New approach for precise computation of Lyman-alpha forest power
  spectrum with hydrodynamical simulations

abstract:
  We present a suite of cosmological N-body simulations with cold dark matter
and baryons aiming at modeling the low-density regions of the IGM as probed by
the Lyman-$\alpha$ forests at high redshift. The simulations are designed to
match the requirements imposed by the quality of BOSS and eBOSS data. They are
made using either 2x768$^3$ or 2x192$^3$ particles, spanning volumes ranging
from (25 Mpc.h$^{-1})^3$ for high-resolution simulations to (100
Mpc.h$^{-1})^3$ for large-volume ones. Using a splicing technique, the
resolution is further enhanced to reach the equivalent of simulations with
2x3072$^3$= 58 billion particles in a (100 Mpc.h$^{-1}$)^3 box size, i.e. a
mean mass per gas particle of 1.2x10$^5$M_sun.h$^{-1}$. We show that the
resulting power spectrum is accurate at the 2% level over the full range from a
few Mpc to several tens of Mpc. We explore the effect on the one-dimensional
transmitted-flux power spectrum of 4 cosmological parameters ($n_s, \sigma_8,
\Omega_m, H_0$) and 2 astrophysical parameters ($T_0, \gamma$) related to the
heating rate of the IGM. By varying the input parameters around a central model
chosen to be in agreement with the latest Planck results, we built a grid of
simulations that allows the study of the impact on the flux power spectrum of
these six relevant parameters. We improve upon previous studies by not only
measuring the effect of each parameter individually, but also probing the
impact of the simultaneous variation of each pair of parameters. We thus
provide a full second-order expansion, including cross-terms, around our
central model. We check the validity of the second-order expansion with
independent simulations obtained either with different cosmological parameters
or different seeds. Finally, a comparison to the one-dimensional Ly-$\alpha$
forest power spectrum obtained with BOSS shows an excellent agreement.


title: Hausdorff dimension of unique beta expansions

abstract:
  Given an integer $N\ge 2$ and a real number ${\beta}>1$, let
$\Gamma_{{\beta},N}$ be the set of all $x=\sum_{i=1}^\infty {d_i}/{{\beta}^i}$
with $d_i\in\{0,1,\cdots,N-1\}$ for all $i\ge 1$. The infinite sequence $(d_i)$
is called a ${\beta}$-expansion of $x$. Let $\mathbf{U}_{{\beta},N}$ be the set
of all $x$'s in $\Gamma_{{\beta},N}$ which have unique ${\beta}$-expansions. We
give explicit formula of the Hausdorff dimension of $\mathbf{U}_{{\beta},N}$
for ${\beta}$ in any admissible interval $[{{\beta}}_L,{{\beta}}_U]$, where
${{\beta}_L}$ is a purely Parry number while ${{\beta}_U}$ is a transcendental
number whose quasi-greedy expansion of $1$ is related to the classical
Thue-Morse sequence. This allows us to calculate the Hausdorff dimension of
$\U{N}$ for almost every $\beta>1$. In particular, this improves the main
results of G{\'a}bor Kall{\'o}s (1999, 2001). Moreover, we find that the
dimension function $f({\beta})=\dim_H\mathbf{U}_{{\beta},N}$ fluctuates
frequently for ${\beta}\in(1,N)$.


title: Cycle 23 Variation in Solar Flare Productivity

abstract:
  The NOAA listings of solar flares in cycles 21-24, including the GOES soft
X-ray magnitudes, enable a simple determination of the number of flares each
flaring active region produces over its lifetime. We have studied this measure
of flare productivity over the interval 1975-2012. The annual averages of flare
productivity remained approximately constant during cycles 21 and 22, at about
two reported M or X flares per region, but then increased significantly in the
declining phase of cycle 23 (the years 2004-2005). We have confirmed this by
using the independent RHESSI flare catalog to check the NOAA events listings
where possible. We note that this measure of solar activity does not correlate
with the solar cycle. The anomalous peak in flare productivity immediately
preceded the long solar minimum between cycles 23 and 24.


title:
Density and Level Set-XFEM Schemes for Topology Optimization of 3-D
  Structures

abstract:
  As the capabilities of additive manufacturing techniques increase, topology
optimization provides a promising approach to design geometrically
sophisticated structures which can be directly manufactured. Traditional
topology optimization methods aim at finding the conceptual design but often
lack a sufficient resolution of the geometry and structural response, needed to
directly use the optimized design for manufacturing. To overcome these
limitations, this paper studies the viability and characteristics of the
eXtended Finite Element Method (XFEM) in combination with the Level-Set Method
(LSM) for topology optimization of three dimensional structural design
problems. The LSM describes the geometry by defining the nodal level set values
via explicit functions of the optimization variables. The structural response
is predicted by a generalized version of the XFEM. The LSM-XFEM approach is
compared against results from a traditional Solid Isotropic Material with
Penalization (SIMP) method for two-phase ``solid-void'' and ``solid-solid''
problems. The numerical results demonstrate that the LSM-XFEM approach can
describe crisply the geometry and predict the structural response of complex
three-dimensional structures with acceptable accuracy even on coarse meshes.
However, the LSM-XFEM studied here lacks a robust and intuitive formulation to
control the minimum feature size, and the optimization results may depend on
the initial design.


title: Adaptive Video Streaming in MU-MIMO Networks

abstract:
  We consider extensions and improvements on our previous work on dynamic
adaptive video streaming in a multi-cell multiuser ``small cell'' wireless
network. Previously, we treated the case of single-antenna base stations and,
starting from a network utility maximization (NUM) formulation, we devised a
``push'' scheduling policy, where users place requests to sequential video
chunks to possibly different base stations with adaptive video quality, and
base stations schedule their downlink transmissions in order to stabilize their
transmission queues. In this paper we consider a ``pull'' strategy, where every
user maintains a request queue, such that users keep track of the video chunks
that are effectively delivered. The pull scheme allows to download the chunks
in the playback order without skipping or missing them. In addition, motivated
by the recent/forthcoming progress in small cell networks (e.g., in wave-2 of
the recent IEEE 802.11ac standard), we extend our dynamic streaming approach to
the case of base stations capable of multiuser MIMO downlink, i.e., serving
multiple users on the same time-frequency slot by spatial multiplexing. By
exploiting the ``channel hardening'' effect of high dimensional MIMO channels,
we devise a low complexity user selection scheme to solve the underlying
max-weighted rate scheduling, which can be easily implemented and runs
independently at each base station. Through simulations, we show MIMO gains in
terms of video streaming QoE metrics like the pre-buffering and re-buffering
times.


title:
Charge-exchange limits on low-energy alpha-particle fluxes in solar
  flares

abstract:
  This paper reports on a search for flare emission via charge-exchange
radiation in the wings of the Lyman-alpha line of He ii at 304 A, as originally
suggested for hydrogen by Orrall and Zirker. Via this mechanism a primary alpha
particle that penetrates into the neutral chromosphere can pick up an atomic
electron and emit in the He ii bound-bound spectrum before it stops. The
Extreme-ultraviolet Variability Experiment (EVE) on board the Solar Dynamics
Observatory (SDO) gives us our first chance to search for this effect
systematically. The Orrall-Zirker mechanism has great importance for flare
physics because of the essential roles that particle acceleration plays; this
mechanism is one of the few proposed that would allow remote sensing of primary
accelerated particles below a few MeV/nucleon. We study ten events in total,
including the gamma-ray events SOL2010-06-12 (M2.0) and SOL2011-02-24 (M3.5)
(the latter a limb flare), seven X-class flares, and one prominent M-class
event that produced solar energetic particles (SEPs). The absence of
charge-exchange line wings may point to a need for more complete theoretical
work. Some of the events do have broad-band signatures, which could correspond
to continua from other origins, but these do not have the spectral signatures
expected from the Orrall-Zirker mechanism.


title: Energy-aware Vehicle Routing in Networks with Charging Nodes

abstract:
  We study the problem of routing vehicles with energy constraints through a
network where there are at least some charging nodes. We seek to minimize the
total elapsed time for vehicles to reach their destinations by determining
routes as well as recharging amounts when the vehicles do not have adequate
energy for the entire journey. For a single vehicle, we formulate a
mixed-integer nonlinear programming (MINLP) problem and derive properties of
the optimal solution allowing it to be decomposed into two simpler problems.
For a multi-vehicle problem, where traffic congestion effects are included, we
use a similar approach by grouping vehicles into subflows. We also provide an
alternative flow optimization formulation leading to a computationally simpler
problem solution with minimal loss in accuracy. Numerical results are included
to illustrate these approaches.


title: Charged black holes in Horava gravity

abstract:
  We explore static spherically symmetric black hole solutions allowing a bulk
U(1) vector field in the khronometric formulation of Horava gravity by way of
Einstein-Aether. We examine analytic solutions and study numerical results in
the limit that the khronon does not backreact on the metric.


title: A new proof of Savin's theorem on Allen-Cahn equations

abstract:
  In this paper we establish an improvement of tilt-excess decay estimate for
the Allen-Cahn equation, and use this to give a new proof of Savin's theorem on
the uniform $C^{1,\alpha}$ regularity of flat level sets, which then implies
the one dimensional symmetry of minimizers in $\mathbb{R}^n$ for $n\leq 7$.
This generalizes Allard's $\varepsilon$-regularity theorem for stationary
varifolds to the setting of Allen-Cahn equations.


title: Reducibility in the Four-Color Theorem

abstract:
  In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of
the Four-Color Theorem. The proof is computer-assisted in the sense that for
two lemmas in the article we did not give proofs, and instead asserted that we
have verified those statements using a computer. Here we give additional
details for one of those lemmas, and we include the original computer programs
and data as "ancillary files" accompanying this submission.


title:
Nested Polar Codes Achieve the Shannon Rate-Distortion Function and the
  Shannon Capacity

abstract:
  It is shown that nested polar codes achieve the Shannon rate-distortion
function for arbitrary (binary or non-binary) discrete memoryless sources and
the Shannon capacity of arbitrary discrete memoryless channels.


title:
Branch-and-price-and-cut for the Split-collection Vehicle Routing
  Problem with Time Windows and Linear Weight-related Cost

abstract:
  This paper addresses a new vehicle routing problem that simultaneously
involves time windows, split collection and linear weight-related cost, which
is a generalization of the split delivery vehicle routing problem with time
windows (SDVRPTW). This problem consists of determining least-cost vehicle
routes to serve a set of customers while respecting the restrictions of vehicle
capacity and time windows. The travel cost per unit distance is a linear
function of the vehicle weight and the customer demand can be fulfilled by
multiple vehicles. To solve this problem, we propose a exact
branch-and-price-and-cut algorithm, where the pricing subproblem is a
resource-constrained elementary least-cost path problem. We first prove that at
least an optimal solution to the pricing subproblem is associated with an
extreme collection pattern, and then design a tailored and novel label-setting
algorithm to solve it. Computational results show that our proposed algorithm
can handle both the SDVRPTW and our problem effectively.


title:
Identification of Protein Coding Regions in Genomic DNA Using
  Unsupervised FMACA Based Pattern Classifier

abstract:
  Genes carry the instructions for making proteins that are found in a cell as
a specific sequence of nucleotides that are found in DNA molecules. But, the
regions of these genes that code for proteins may occupy only a small region of
the sequence. Identifying the coding regions play a vital role in understanding
these genes. In this paper we propose a unsupervised Fuzzy Multiple Attractor
Cellular Automata (FMCA) based pattern classifier to identify the coding region
of a DNA sequence. We propose a distinct K-Means algorithm for designing FMACA
classifier which is simple, efficient and produces more accurate classifier
than that has previously been obtained for a range of different sequence
lengths. Experimental results confirm the scalability of the proposed
Unsupervised FCA based classifier to handle large volume of datasets
irrespective of the number of classes, tuples and attributes. Good
classification accuracy has been established.


title: Discharging cartwheels


title: Bilinear Forms on Frobenius Algebras

abstract:
  We analyze the homothety types of associative bilinear forms that can occur
on a Hopf algebra or on a local Frobenius \(k\)-algebra \(R\) with residue
field \(k\). If \(R\) is symmetric, then there exists a unique form on \(R\) up
to homothety iff \(R\) is commutative. If \(R\) is Frobenius, then we introduce
a norm based on the Nakayama automorphism of \(R\). We show that if two forms
on \(R\) are homothetic, then the norm of the unit separating them is central,
and we conjecture the converse. We show that if the dimension of \(R\) is even,
then the determinant of a form on \(R\), taken in \(\dot k/\dot k^2\), is an
invariant for \(R\).
  \textit{Key words}: bilinear form, Frobenius algebra, homothety, Hopf
algebra, isometry, local algebra, Nakayama automorphism, Ore extension,
symmetric algebra


title:
Holographic fluid from nonminimally coupled scalar-tensor theory of
  gravity

abstract:
  We establish the gravity/fluid correspondence in the nonminimally coupled
scalar-tensor theory of gravity. Imposing Petrov-like boundary conditions over
the gravitational field, we find that, for a certain class of background
metrics, the boundary fluctuations obey the standard Navier-Stokes equation for
an incompressible fluid without any external force term in the leading order
approximation under the near horizon expansion. That is to say, the scalar
field fluctuations does not contribute in the leading order approximation
regardless of what kind of boundary condition we impose on it.


title: Chasing diagrams in cryptography

abstract:
  Cryptography is a theory of secret functions. Category theory is a general
theory of functions. Cryptography has reached a stage where its structures
often take several pages to define, and its formulas sometimes run from page to
page. Category theory has some complicated definitions as well, but one of its
specialties is taming the flood of structure. Cryptography seems to be in need
of high level methods, whereas category theory always needs concrete
applications. So why is there no categorical cryptography? One reason may be
that the foundations of modern cryptography are built from probabilistic
polynomial-time Turing machines, and category theory does not have a good
handle on such things. On the other hand, such foundational problems might be
the very reason why cryptographic constructions often resemble low level
machine programming. I present some preliminary explorations towards
categorical cryptography. It turns out that some of the main security concepts
are easily characterized through the categorical technique of *diagram
chasing*, which was first used Lambek's seminal `Lecture Notes on Rings and
Modules'.


title:
Absence of Cartan subalgebras in continuous cores of free product von
  Neumann algebras

abstract:
  We show that the continuous core of any type III free product factor has no
Cartan subalgebra. This is a complement to previous works due to
Houdayer--Ricard and Boutonnet--Houdayer--Raum.


title:
The Relation between the Radial Temperature Profile in the Chromosphere
  and the Solar Spectrum at Centimeter, Millimeter, Sub-millimeter, and
  Infrared Wavelengths

abstract:
  Solar observations from millimeter to ultraviolet wavelengths show that there
is a temperature minimum between photosphere and chromosphere. Analysis based
on semi-empirical models locate this point at about 500 km over the
photosphere. The consistency of these models has been tested by means of
millimeter to infrared observations.
  In the present work, we show that variations of the theoretical radial
temperature profile near the temperature minimum impacts the brightness
temperature at centimeter, submillimeter, and infrared wavelengths, but the
millimeter wavelength emission remains unchanged. We found a region between 500
and 1000 km over the photosphere that remains hidden to observations at the
frequencies under study in this work.


title:
A Deep Chandra Observation of Oxygen-Rich Supernova Remnant B0049-73.6
  in the Small Magellanic Cloud

abstract:
  We report on the initial results from our deep Chandra observation (450 ks)
of O-rich supernova remnant (SNR) B0049-73.6 in the Small Magellanic Cloud. We
detect small metal-rich ejecta features extending out to the outermost boundary
of B0049-73.6, which were not seen in the previous data with a shorter
exposure. The central nebula is dominated by emission from reverse-shocked
ejecta material enriched in O, Ne, Mg, and Si. O-rich ejecta distribution is
relatively smooth throughout the central nebula. In contrast the Si-rich
material is highly structured. These results suggest that B0049-73.6 was
produced by an asymmetric core-collapse explosion of a massive star. The
estimated abundance ratios among these ejecta elements are in plausible
agreement with the nucleosynthesis products from the explosion of a
13-15$M_{\odot}$ progenitor. The central ring-like (in projection) ejecta
nebula extends to $\sim$9 pc from the SNR center. This suggests that the
contact discontinuity may be located at a further distance from the SNR center
than the previous estimate. We estimate the Sedov age of $\sim$17000 yr and an
explosion energy of $E_0$ $\sim1.7 \times~10^{51}$ erg for B0049-73.6. We place
a stringent upper limit on the 2-7 keV band luminosity of $L_{X}\sim$ 8.5
$\times 10^{31}$ erg s$^{-1}$ for the embedded compact stellar remnant at the
center of B0049-73.6.


title:
The Limb Brightening and its Relationship with the Millimeter-wave
  Cavity

abstract:
  Through a detailed theoretical analysis of the local emission at
millimeter,sub-millimeter and infrared wavelength regimes (from \~ 10 GHz up to
\~ 10 THz), we found that, associated with the temperature minimum, there is an
optically thin cavity surrounded by two regions of high local emissivity. We
call this structure the Chromospheric Solar Millimeter Cavity (CSMC). In order
to search for traces of this cavity in the available radio observations on the
solar limb, we have developed a robust method to associate the radiation at
different heights with the observed brightness temperatures. We foresee that
this approach will allow us to determine the relationship between the CSMC and
the solar limb brightening.


title:
Uniform close-to-convexity radius of sections of functions in the
  close-to-convex family

abstract:
  The authors consider the class $\F$ of normalized functions $f$ analytic in
the unit disk $\ID$ and satisfying the condition $${\rm
Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>-\frac{1}{2},\quad z\in\D. $$ Recently,
Ponnusamy et al. \cite{samy-hiroshi-swadesh} have shown that $1/6$ is the
uniform sharp bound for the radius of convexity of every section of each
function in the class $\F$. They conjectured that $1/3$ is the uniform
univalence radius of every section of $f\in \F$. In this paper, we solve this
conjecture affirmatively.


title: On the Yang-Baxter equation for the six-vertex model

abstract:
  In this paper we review the theory of the Yang-Baxter equation related to the
6-vertex model and its higher spin generalizations. We employ a 3D approach to
the problem. Starting with the 3D R-matrix, we consider a two-layer projection
of the corresponding 3D lattice model. As a result, we obtain a new expression
for the higher spin $R$-matrix associated with the affine quantum algebra
$U_q(\widehat{sl(2)})$. In the simplest case of the spin $s=1/2$ this
$R$-matrix naturally reduces to the $R$-matrix of the 6-vertex model. Taking a
special limit in our construction we also obtain new formulas for the
$Q$-operators acting in the representation space of arbitrary (half-)integer
spin. Remarkably, this construction can be naturally extended to any complex
values of spin $s$. We also give all functional equations satisfied by the
transfer-matrices and $Q$-operators.


title:
User Participation in an Academic Social Networking Service: A Survey of
  Open Group Users on Mendeley

abstract:
  Although there are a number of social networking services that specifically
target scholars, little has been published about the actual practices and the
usage of these so-called academic social networking services (ASNSs). To fill
this gap, we explore the populations of academics who engage in social
activities using an ASNS; as an indicator of further engagement, we also
determine their various motivations for joining a group in ASNSs. Using groups
and their members in Mendeley as the platform for our case study, we obtained
146 participant responses from our online survey about users' common
activities, usage habits, and motivations for joining groups. Our results show
that 1) participants did not engage with social-based features as frequently
and actively as they engaged with research-based features, and 2) users who
joined more groups seemed to have a stronger motivation to increase their
professional visibility and to contribute the research articles they had read
to the group reading list. Our results generate interesting insights into
Mendeley's user populations, their activities, and their motivations relative
to the social features of Mendeley. We also argue that further design of ASNSs
is needed to take greater account of disciplinary differences in scholarly
communication and to establish incentive mechanisms for encouraging user
participation.


title: Generalized Sphere Packing Bound

abstract:
  Kulkarni and Kiyavash recently introduced a new method to establish upper
bounds on the size of deletion-correcting codes. This method is based upon
tools from hypergraph theory. The deletion channel is represented by a
hypergraph whose edges are the deletion balls (or spheres), so that a
deletion-correcting code becomes a matching in this hypergraph. Consequently, a
bound on the size of such a code can be obtained from bounds on the matching
number of a hypergraph. Classical results in hypergraph theory are then invoked
to compute an upper bound on the matching number as a solution to a
linear-programming problem.
  The method by Kulkarni and Kiyavash can be applied not only for the deletion
channel but also for other error channels. This paper studies this method in
its most general setup. First, it is shown that if the error channel is regular
and symmetric then this upper bound coincides with the sphere packing bound and
thus is called the generalized sphere packing bound. Even though this bound is
explicitly given by a linear programming problem, finding its exact value may
still be a challenging task. In order to simplify the complexity of the
problem, we present a technique based upon graph automorphisms that in many
cases reduces the number of variables and constraints in the problem. We then
apply this method on specific examples of error channels. We start with the $Z$
channel and show how to exactly find the generalized sphere packing bound for
this setup. Next studied is the non-binary limited magnitude channel both for
symmetric and asymmetric errors, where we focus on the single-error case. We
follow up on the deletion and grain-error channels and show how to improve upon
the existing upper bounds for single deletion/error. Finally, we apply this
method for projective spaces and find its generalized sphere packing bound for
the single-error case.


title:
Bayesian CP Factorization of Incomplete Tensors with Automatic Rank
  Determination

abstract:
  CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful
technique for tensor completion through explicitly capturing the multilinear
latent factors. The existing CP algorithms require the tensor rank to be
manually specified, however, the determination of tensor rank remains a
challenging problem especially for CP rank. In addition, existing approaches do
not take into account uncertainty information of latent factors, as well as
missing entries. To address these issues, we formulate CP factorization using a
hierarchical probabilistic model and employ a fully Bayesian treatment by
incorporating a sparsity-inducing prior over multiple latent factors and the
appropriate hyperpriors over all hyperparameters, resulting in automatic rank
determination. To learn the model, we develop an efficient deterministic
Bayesian inference algorithm, which scales linearly with data size. Our method
is characterized as a tuning parameter-free approach, which can effectively
infer underlying multilinear factors with a low-rank constraint, while also
providing predictive distributions over missing entries. Extensive simulations
on synthetic data illustrate the intrinsic capability of our method to recover
the ground-truth of CP rank and prevent the overfitting problem, even when a
large amount of entries are missing. Moreover, the results from real-world
applications, including image inpainting and facial image synthesis,
demonstrate that our method outperforms state-of-the-art approaches for both
tensor factorization and tensor completion in terms of predictive performance.


title: On the Power of Cooperation: Can a Little Help a Lot? (Extended Version)

abstract:
  In this paper, we propose a new cooperation model for discrete memoryless
multiple access channels. Unlike in prior cooperation models (e.g.,
conferencing encoders), where the transmitters cooperate directly, in this
model the transmitters cooperate through a larger network. We show that under
this indirect cooperation model, there exist channels for which the increase in
sum-capacity resulting from cooperation is significantly larger than the rate
shared by the transmitters to establish the cooperation. This result contrasts
both with results on the benefit of cooperation under prior models and results
in the network coding literature, where attempts to find examples in which
similar small network modifications yield large capacity benefits have to date
been unsuccessful.


title:
Transmitter Optimization in MISO Broadcast Channel with Common and
  Secret Messages

abstract:
  In this paper, we consider transmitter optimization in multiple-input
single-output (MISO) broadcast channel with common and secret messages. The
secret message is intended for $K$ users and it is transmitted with perfect
secrecy with respect to $J$ eavesdroppers which are also assumed to be
legitimate users in the network. The common message is transmitted at a fixed
rate $R_{0}$ and it is intended for all $K$ users and $J$ eavesdroppers. The
source operates under a total power constraint. It also injects artificial
noise to improve the secrecy rate. We obtain the optimum covariance matrices
associated with the common message, secret message, and artificial noise, which
maximize the achievable secrecy rate and simultaneously meet the fixed rate
$R_{0}$ for the common message.


title: Holographic Transformation for Quantum Factor Graphs

abstract:
  Recently, a general tool called a holographic transformation, which
transforms an expression of the partition function to another form, has been
used for polynomial-time algorithms and for improvement and understanding of
the belief propagation. In this work, the holographic transformation is
generalized to quantum factor graphs.

categories: cs.IT cond-mat.stat-mech math.IT quant-ph


title: A holographic superconductor model in a spatially anisotropic background

abstract:
  We investigate an anisotropic model of superconductors in the
Einstein-Maxwell-dilaton theory with a charged scalar field. It is found that
the critical temperature decreases as the anisotropy becomes large. We then
estimate the energy gap of the superconductor, and find that the ratio of the
energy gap to the critical temperature increases as the anisotropy increases
and so it is larger than that in the isotropic case. We also find that peudogap
appears due to the anisotropy.


title:
Final state effects on charge asymmetry of pion elliptic flow in
  high-energy heavy-ion collisions

abstract:
  Within a multi-phase transport (AMPT) model with the string melting mechanism
and imported initial electric quadrupole moment, the difference between the
elliptic flow of positive and negative pions is calculated. The slope parameter
$r$ of the linear dependence of $\Delta v_{2}=v_{2}(\pi^{-})-v_{2}(\pi^{+})$ on
$A_{ch}=(N^{+}-N^{-})/(N^{+}+N^{-})$ is yielded owing to the parton cascade,
which converts the initial electric quadrupole distribution into the final
charge-dependent elliptic flow. The slope parameter $r$ is found to be
increased by the hadronization given by the coalescence, and decreased by the
resonance decays. The slope parameter $r$ is very sensitive to both the initial
electric quadrupole percentage and centrality bin and consequently a helpful
constraint on the quadrupole moment of the chiral magnetic wave is obtained for
Au+Au collisions at the top RHIC energy.


title:
Kerr Metric, Geodesic Motion, and Flyby Anomaly in Fourth-Order
  Conformal Gravity

abstract:
  In this paper we analyze the Kerr geometry in the context of Conformal
Gravity, an alternative theory of gravitation, which is a direct extension of
General Relativity. Following previous studies in the literature, we introduce
an explicit expression of the Kerr metric in Conformal Gravity, which naturally
reduces to the standard General Relativity Kerr geometry in the absence of
Conformal Gravity effects. As in the standard case, we show that the
Hamilton-Jacobi equation governing geodesic motion in a space-time based on
this geometry is indeed separable and that a fourth constant of motion-similar
to Carter's constant-can also be introduced in Conformal Gravity. Consequently,
we derive the fundamental equations of geodesic motion and show that the
problem of solving these equations can be reduced to one of quadratures. In
particular, we study the resulting time-like geodesics in Conformal Gravity
Kerr geometry by numerically integrating the equations of motion for Earth
flyby trajectories of spacecraft. We then compare our results with the existing
data of the Flyby Anomaly in order to ascertain whether Conformal Gravity
corrections are possibly the origin of this gravitational anomaly. Although
Conformal Gravity slightly affects the trajectories of geodesic motion around a
rotating spherical object, we show that these corrections are minimal and are
not expected to be the origin of the Flyby Anomaly, unless conformal parameters
are drastically different from current estimates. Therefore, our results
confirm previous analyses, showing that modifications due to Conformal Gravity
are not likely to be detected at the Solar System level, but might affect
gravity at the galactic or cosmological scale.


title:
Inferring gene-gene interactions and functional modules using sparse
  canonical correlation analysis

abstract:
  Networks pervade many disciplines of science for analyzing complex systems
with interacting components. In particular, this concept is commonly used to
model interactions between genes and identify closely associated genes forming
functional modules. In this paper, we focus on gene group interactions and
infer these interactions using appropriate partial correlations between genes,
that is, the conditional dependencies between genes after removing the
influences of a set of other functionally related genes. We introduce a new
method for estimating group interactions using sparse canonical correlation
analysis (SCCA) coupled with repeated random partition and subsampling of the
gene expression data set. By considering different subsets of genes and ways of
grouping them, our interaction measure can be viewed as an aggregated estimate
of partial correlations of different orders. Our approach is unique in
evaluating conditional dependencies when the correct dependent sets are unknown
or only partially known. As a result, a gene network can be constructed using
the interaction measures as edge weights and gene functional groups can be
inferred as tightly connected communities from the network. Comparisons with
several popular approaches using simulated and real data show our procedure
improves both the statistical significance and biological interpretability of
the results. In addition to achieving considerably lower false positive rates,
our procedure shows better performance in detecting important biological
pathways.


title:
Holographic entanglement entropy in insulator/superconductor transition
  with Born-Infeld electrodynamics

abstract:
  We investigate the holographic entanglement entropy in the
insulator/superconductor phase transition for the Born-Infeld electrodynamics
with full backreaction in five-dimensional AdS soliton spacetime. We note that
the holographic entanglement entropy is a good probe to study the properties of
the phase transition, and the Born-Infeld factor $b$ has no effect on the
critical chemical potential $\mu_c$. We find that both in the half space and
the belt one, the non-monotonic behavior of the entanglement entropy versus the
chemical potential is a general property, and the entanglement entropy
increases with the increase of the Born-Infeld factor in the superconductor
phase. Particularly, there exists confinement/deconfinement phase transition in
the strip geometry and the critical width $\ell_c$ is dependent of the
Born-Infeld parameter.


title: Moment bounds in spde's with application to the stochastic wave equation

abstract:
  We exhibit a class of properties of an spde that guarantees existence,
uniqueness and bounds on moments of the solution. These moment bounds are
expressed in terms of quantities related to the associated deterministic
homogeneous p.d.e. With these, we can, for instance, obtain solutions to the
stochastic heat equation on the real line for initial data that falls in a
certain class of Schwartz distributions, but our main focus is the stochastic
wave equation on the real line with irregular initial data. We give bounds on
higher moments, and for the hyperbolic Anderson model, explicit formulas for
second moments. We establish weak intermittency and obtain sharp bounds on
exponential growth indices for certain classes of initial conditions with
unbounded support. Finally, we relate H\"older-continuity properties of the
stochastic integral part of the solution to the stochastic wave equation to
integrability properties of the initial data, obtaining the optimal H\"older
exponent.


title: The Heisenberg Relation - Mathematical Formulations

abstract:
  We study some of the possibilities for formulating the Heisenberg relation of
quantum mechanics in mathematical terms. In particular, we examine the
framework discussed by Murray and von Neumann, the family (algebra) of
operators affiliated with a finite factor (of infinite linear dimension).


title:
The Effect of Network and Infrastructural Variables on SPDY's
  Performance

abstract:
  HTTP is a successful Internet technology on top of which a lot of the web
resides. However, limitations with its current specification, i.e. HTTP/1.1,
have encouraged some to look for the next generation of HTTP. In SPDY, Google
has come up with such a proposal that has growing community acceptance,
especially after being adopted by the IETF HTTPbis-WG as the basis for
HTTP/2.0. SPDY has the potential to greatly improve web experience with little
deployment overhead. However, we still lack an understanding of its true
potential in different environments. This paper seeks to resolve these issues,
offering a comprehensive evaluation of SPDY's performance using extensive
experiments. We identify the impact of network characteristics and website
infrastructure on SPDY's potential page loading benefits, finding that these
factors are decisive for SPDY and its optimal deployment strategy. Through
this, we feed into the wider debate regarding HTTP/2.0, exploring the key
aspects that impact the performance of this future protocol.


title: Linear Convergence of the Douglas-Rachford Method for Two Closed Sets

abstract:
  In this paper, we investigate the Douglas-Rachford method for two closed
(possibly nonconvex) sets in Euclidean spaces. We show that under certain
regularity conditions, the Douglas-Rachford method converges locally with
R-linear rate. In convex settings, we prove that the linear convergence is
global. Our study recovers recent results on the same topic.


title:
Asymmetric Velocity Distributions from Halo Density Profiles in the
  Eddington Approach

abstract:
  In the present paper we show how obtain the energy distribution f(E) in our
vicinity starting from WIMP density profiles in a self consistent way by
employing the Eddington approach and adding reasonable angular momentum
dependent terms in the expression of the energy. We then show how we can obtain
the velocity dispersion and the asymmetry parameter {\beta} in terms of the
parameters describing the angular momentum dependence. From this expression for
f(E) we proceed to construct an axially symmetric WIMP velocity distributions,
which for a gravitationally bound system automatically has an velocity upper
bound and is characterized by the the same asymmetries. This approach is tested
and clarified by constructing analytic expressions in a simple model, with
adequate structure. We then show how such velocity distributions can be used in
determining the event rates, including modulation, both in the standard as well
directional WIMP searches. find that some density profiles lead to approximate
Maxwell-Boltzmann distributions, which are automatically defined in a finite
domain, i.e. the escape velocity need not be put by hand. The role of such
distributions in obtaining the direct WIMP detection rates, including the
modulation, is studied in some detail and, in particular, the role of the
asymmetry is explored.


title:
Investigation of thermoelectric properties of half-metallic Co2 MnGe by
  using first principles calculations

abstract:
  By combining the electronic structures obtained from first principles
calculations with Boltzmann transport theory we have investigated the
electronic, magnetic and transport properties of Co$_{2}$MnGe Heusler compound.
The density of states plots, dispersion curves and total energy of paramagnetic
and ferromagnetic (FM) phases clearly show the half-metallic FM ground state
for the compound with an indirect band gap of about 400 meV in the minority
spin channel. It has integer value of the magnetic moment equal to 5 $\mu_{B}$.
In the FM phase a very large value ($\sim$550 $\mu$V/K) of Seebeck coefficient
(S) is obtained for down-spin electrons due to the existence of almost flat
conduction band along X to $\Gamma$ direction. The two current model has been
used to find the total S and the obtained value is about 10 $\mu$V/K. The
calculated values of Seebeck coefficient, resistivity and electronic thermal
conductivity show nice agreement with the experimental results.


title:
Achievable Degrees of Freedom in MIMO Correlatively Changing Fading
  Channels

abstract:
  The relationship between the transmitted signal and the noiseless received
signals in correlatively changing fading channels is modeled as a nonlinear
mapping over manifolds of different dimensions. Dimension counting argument
claims that the dimensionality of the neighborhood in which this mapping is
bijective with probability one is achievable as the degrees of freedom of the
system.We call the degrees of freedom achieved by the nonlinear decoding
methods the nonlinear degrees of freedom.


title:
Virtual Interpolation Point Method for Viscous Flows in Complex
  Geometries

abstract:
  A new approach for simulating flows over complex geometries is developed by
introducing an accurate virtual interpolation point scheme as well as a virtual
local stencil approach. The present method is based on the concept of point
collocation on a virtual staggered structure together with a fractional step
method. The use of a virtual staggered structure arrangement, which stores all
the variables at the same physical location and employs only one set of nodes
using virtual interpolation points, reduces the geometrical complexity. The
virtual staggered structure consists of the virtual interpolation points and
the virtual local stencil. Also, computational enhancement of the virtual
interpolation point method is considerable since the present method directly
discretizes the strong forms of the incompressible Navier-Stokes equations
without numerical integration. It makes a key difference from others. In the
virtual interpolation point method, the choice of an accurate interpolation
scheme satisfying the spatial approximation in the complex domain is important
because there is the virtual staggered structure for computation of the
velocities and pressure since there is no explicit staggered structure for
stability. In our proposed method, the high order derivative approximations for
constructing node-wise difference equations are easily obtained. Several
different flow problems (decaying vortices, lid-driven cavity, triangular
cavity, flow over a circular cylinder and a bumpy cylinder) are simulated using
the virtual interpolation point method and the results agree very well with
previous numerical and experimental results. They verify the accuracy of the
present method.


title: Relative derived equivalences and relative homological dimensions

abstract:
  Let $\mathscr{A}$ be a small abelian category. For a closed subbifunctor $F$
of $\Ext_{\mathscr{A}}^{1}(-,-)$, Buan has generalized the construction of the
Verdier's quotient category to get a relative derived category, where he
localized with respect to $F$-acyclic complexes. In this paper, the homological
properties of relative derived categories are discussed, and the relation with
derived categories is given. For Artin algebras, using relatively derived
categories, we give a relative version on derived equivalences induced by
$F$-tilting complexes. We discuss the relationships between relative
homological dimensions and relative derived equivalences.


title:
Spin-Orbit Interaction Effects in the Electronic Structure of B20-type
  CoSi: First-Principles Density Functional Study

abstract:
  We have performed fully relativistic first-principles density functional
calculations for non-magnetic B20-type CoSi. The spin-orbit interaction has
crucial effects on the electronic structures of a chiral crystal. The
calculated band structure around the Fermi energy shows Bloch vector $k$-linear
dispersion expressed by a $real$-$spin$ Weyl Hamiltonian, i.e., a mass-less
Dirac Hamiltonian. We found the hedgehog-like spin texture in Bloch
$\boldsymbol k$-vector space (momentum space) on the isoenergy surface around
the $\Gamma$ point. The Fermi velocity for $k$-linear dispersion is about
0.22$v^g_F$, where $v^g_F$ is the Fermi velocity of graphene.


title: Inversions and the Gog-Magog problem

abstract:
  We consider the problem of finding a bijection between the sets of
alternating sign matrices and of totally symmetric self complementary plane
partitions, which can be reformulated using Gog and Magog triangles. In a
previous work we introduced GOGAm triangles, which are images of Magog
triangles by the Sch\"utzenberger involution. In this paper we introduce left
Gog and GOGAm trapezoids. We conjecture that they are equienumerated, and we
give an explicit bijection between such trapezoids with one or two diagonals.
We also study the distribution of inversions and coinversions in Gog triangles.


title:
Kinematics analysis and three-dimensional simulation of the
  rehabilitation lower extremity exoskeleton robot

abstract:
  The kinematics recursive equation was built by using the modified D-H method
after the structure of rehabilitation lower extremity exoskeleton was analyzed.
The numerical algorithm of inverse kinematics was given too. Then the
three-dimensional simulation model of the exoskeleton robot was built using
MATLAB software, based on the model, 3D reappearance of a complete gait was
achieved. Finally, the reliability of numerical algorithm of inverse kinematics
was verified by the simulation result. All jobs above lay a foundation for
developing a three-dimensional simulation platform of exoskeleton robot.


title: F-finite embeddabilities of sets and ultrafilters

abstract:
  Let $S$ be a semigroup, let $n\in\mathbb{N}$ be a positive natural number,
let $A,B\subseteq S$, let $\mathcal{U},\mathcal{V}\in\beta S$ and let let
$\mathcal{F}\subseteq\{f:S^{n}\rightarrow S\}$. We say that $A$ is
$\mathcal{F}$-finitely embeddable in $B$ if for every finite set $F\subseteq A$
there is a function $f\in\mathcal{F}$ such that $f\left(A^{n}\right)\subseteq
B$, and we say that $\mathcal{U}$ is $\mathcal{F}$-finitely embeddable in
$\mathcal{V}$ if for every set $B\in\mathcal{V}$ there is a set
$A\in\mathcal{U}$ such that $A$ is $\mathcal{F}$-finitely embeddable in $B$. We
show that $\mathcal{F}$-finite embeddabilities can be used to study certain
combinatorial properties of sets and ultrafilters related with finite
structures. We introduce the notions of set and of ultrafilter maximal for
$\mathcal{F}$-finite embeddability, whose existence is proved under very mild
assumptions. Different choices of $\mathcal{F}$ can be used to characterize
many combinatorially interesting sets/ultrafilters as maximal
sets/ultrafilters, for example thick sets, AP-rich sets, $\overline{K(\beta
S)}$ and so on. The set of maximal ultrafilters for $\mathcal{F}$-finite
embeddability can be characterized algebraically in terms of $\mathcal{F}$.
This property can be used to give an algebraic characterization of certain
interesting sets of ultrafilters, such as the ultrafilters whose elements
contain, respectively, arbitrarily long arithmetic, geoarithmetic or polynomial
progressions. As a consequence of the connection between sets and ultrafilters
maximal for $\mathcal{F}$-finite embeddability we are able to prove a general
result that entails, for example, that given a finite partition of a set that
contains arbitrarily long geoarithmetic (resp. polynomial) progressions, one
cell must contain arbitrarily long geoarithmetic (resp. polynomial)
progressions.


title: An internal characterisation of radiality

abstract:
  In this paper, we will investigate how radiality occurs in topological spaces
by considering neighbourhood bases generated by nests. We will define a new
subclass of radial spaces, called the independently-based spaces, that contains
LOTS, GO-spaces and spaces with well-ordered neighbourhood bases. We show that
first-countable spaces are precisely the independently-based, strongly
Fr\'echet spaces and we give an example of a Fr\'echet-Urysohn space that is
neither independently-based nor strongly Fr\'echet.


title: Approximation Resistance by Disguising Biased Distributions

abstract:
  In this short note, the author shows that the gap problem of some 3-XOR is
NP-hard and can be solved by running Charikar\&Wirth's SDP algorithm for two
rounds. To conclude, the author proves that $P=NP$.


title: Temporal and spatial heterogeneity in aging colloids: a mesoscopic model

abstract:
  A coarse-grained model of dense hard sphere colloids building on simple
notions of particle mobility and spatial coherence is presented and shown to
reproduce results of experiments and simulations for key quantities such as the
intermediate scattering function, the particle mean-square displacement and the
$\chi_{4}$ mobility correlation function. All results are explained by two
emerging and interrelated dynamical properties: i) a rate of intermittent
events, quakes, which decreases as the inverse of the system age t; ii) a
length scale characterizing correlated domains, which increases linearly in log
t. This leads to simple and accurate scaling forms expressed in terms of a
single scaling variable Finally, we propose a method to experimentally extract
the growing length scale of an aging colloid and suggest that a suitable
scaling of the probability density function of particle displacement can
experimentally reveal the rate of quakes.


title:
Existence and stability in a virtual interpolation method of the Stokes
  equations

abstract:
  In this paper, we propose a new virtual interpolation point method to
formulate the discrete Stokes equations. We form virtual staggered structure
for the velocity and pressure from the actual computation node set. The virtual
interpolation point method by a point collocation scheme is well suited to
meshfree scheme since the approximation comes from smooth kernel and we can
differentiate directly the kernels. The focus of this paper is laid on the
contribution to a stable flow computation without explicit structure of
staggered grid. In our method, we don't have to construct explicitly the
staggered grid at all. Instead, there exists only virtual interpolation points
at each computational node which play a key role in discretizing the
conservative quantities of the Stokes equations.
  We prove the inf-sup condition for virtual interpolation point method with
virtual structure of staggered grid and the existence and stability of discrete
solutions.


title:
Strategic aspects of the probabilistic serial rule for the allocation of
  goods

abstract:
  The probabilistic serial (PS) rule is one of the most prominent randomized
rules for the assignment problem. It is well-known for its superior fairness
and welfare properties. However, PS is not immune to manipulative behaviour by
the agents. We examine computational and non-computational aspects of
strategising under the PS rule. Firstly, we study the computational complexity
of an agent manipulating the PS rule. We present polynomial-time algorithms for
optimal manipulation. Secondly, we show that expected utility best responses
can cycle. Thirdly, we examine the existence and computation of Nash
equilibrium profiles under the PS rule. We show that a pure Nash equilibrium is
guaranteed to exist under the PS rule. For two agents, we identify two
different types of preference profiles that are not only in Nash equilibrium
but can also be computed in linear time. Finally, we conduct experiments to
check the frequency of manipulability of the PS rule under different
combinations of the number of agents, objects, and utility functions.


title:
The emergence of the rescue effect from the interaction of local
  stochastic dynamics within a metapopulation

abstract:
  Immigration can rescue local populations from extinction, helping to
stabilise a metapopulation. Local population dynamics is important for
determining the strength of this rescue effect, but the mechanistic link
between local demographic parameters and the rescue effect at the
metapopulation level has received very little attention by modellers. We
develop an analytical framework that allows us to describe the emergence of the
rescue effect from interacting local stochastic dynamics. We show this
framework to be applicable to a wide range of spatial scales, providing a
powerful and convenient alternative to individual-based models for making
predictions concerning the fate of metapopulations. We show that the rescue
effect plays an important role in minimising the increase in local extinction
probability associated with high demographic stochasticity, but its role is
more limited in the case of high local environmental stochasticity of
recruitment or survival. While most models postulate the rescue effect, our
framework provides an explicit mechanistic link between local dynamics and the
emergence of the rescue effect, and more generally the stability of the whole
metapopulation.


title:
An approach to normal forms of Kuramoto model with distributed delays
  and the effect of minimal delay

abstract:
  Heterogeneous delays with positive lower bound (gap) are taken into
consideration in Kuramoto oscillators. We first establish a perturbation
technique, by which universal normal forms and detailed dynamical behavior of
this model can be obtained easily. Theoretically, a hysteresis loop is found
near the subcritically bifurcated coherent state on the Ott-Antonsen's
manifold. For Gamma distributed delay with fixed variance and mean, we find
large gap destroys the loop and significantly increases in the number of
coexisted coherent attractors. This result is also explained in the viewpoint
of excess kurtosis.


title:
Derivation of equations for scalar and fermion fields using properties
  of dispersion-codispersion operators

abstract:
  We establish equations for scalar and fermion fields using results obtained
from a study on a phase space representation of quantum theory that we have
performed in a previous work. Our approaches are similar to the historical ones
to obtain Klein-Gordon and Dirac equations but the main difference is that ours
are based on the use of properties of operators called dispersion-codispersion
operators. We begin with a brief recall about the dispersion-codispersion
operators. Then, introducing a mass operator with its canonical conjugate
coordinate and applying rules of quantization, based on the use of dispersion -
codispersion operators, we deduce a second order differential operator relation
from the relativistic expression relying energy, momentum and mass. Using Dirac
matrices, we derive from this second order differential operator relation a
first order one. The application of the second order differential operator
relation on a scalar function gives the equation for the scalar field and the
use of the first order differential operator relation leads to the equation for
fermion field.


title: Evidence for the direct decay of the 125 GeV Higgs boson to fermions

abstract:
  The discovery of a new boson with a mass of approximately 125 GeV in 2012 at
the LHC has heralded a new era in understanding the nature of electroweak
symmetry breaking and possibly completing the standard model of particle
physics. Since the first observation in decays to gamma gamma, WW, and ZZ boson
pairs, an extensive set of measurements of the mass and couplings to W and Z
bosons, as well as multiple tests of the spin-parity quantum numbers, have
revealed that the properties of the new boson are consistent with those of the
long-sought agent responsible for electroweak symmetry breaking. An important
open question is whether the new particle also couples to fermions, and in
particular to down-type fermions, since the current measurements mainly
constrain the couplings to the up-type top quark. Determination of the
couplings to down-type fermions requires direct measurement of the
corresponding Higgs boson decays, as recently reported by the CMS experiment in
the study of Higgs decays to bottom quarks and tau leptons. In this paper we
report the combination of these two channels which results, for the first time,
in strong evidence for the direct coupling of the 125 GeV Higgs boson to
down-type fermions, with an observed significance of 3.8 standard deviations,
when 4.4 are expected.


title: Linear Boolean classification, coding and "the critical problem"

abstract:
  The problem of constructing a minimal rank matrix over GF(2) whose kernel
does not intersect a given set S is considered. In the case where S is a
Hamming ball centered at 0, this is equivalent to finding linear codes of
largest dimension. For a general set, this is an instance of "the critical
problem" posed by Crapo and Rota in 1970. This work focuses on the case where S
is an annulus. As opposed to balls, it is shown that an optimal kernel is
composed not only of dense but also of sparse vectors, and the optimal mixture
is identified in various cases. These findings corroborate a proposed
conjecture that for annulus of inner and outer radius nq and np respectively,
the optimal relative rank is given by (1-q)H(p/(1-q)), an extension of the
Gilbert-Varshamov bound H(p) conjectured for Hamming balls of radius np.


title:
On the convergence of an algorithm constructing the normal form for
  lower dimensional elliptic tori in planetary systems

abstract:
  We give a constructive proof of the existence of lower dimensional elliptic
tori in nearly integrable Hamiltonian systems. In particular we adapt the
classical Kolmogorov's normalization algorithm to the case of planetary
systems, for which elliptic tori may be used as replacements of elliptic
keplerian orbits in Lagrange-Laplace theory. With this paper we support with
rigorous convergence estimates the semi-analytical work in our previous article
(2011), where an explicit calculation of an invariant torus for a planar model
of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous
works on the same subject we exploit the characteristic of Lie series giving a
precise control of all terms generated by our algorithm. This allows us to
slightly relax the non-resonance conditions on the frequencies.


title:
Evidence of residual Doppler shift on three pulsars, PSR B1259-63,
  4U1627-67 and PSR J2051-0827

abstract:
  The huge derivative of orbital period observed in binary pulsar PSR B1259-63,
the torque reversal displaying on low mass X-ray binary, 4U1627-67 and the long
term change of orbital period of PSR J2051-0827, seem totally unrelated
phenomena occurring at totally different pulsar systems. In this paper, they
are simply interpreted by the same mechanism, residual Doppler shift. In a
binary system with periodic signals sending to an observer, the drift of the
signal frequency actually changes with the varying orbital velocity, projected
to line of sight at different phases of orbit. And it has been taken for
granted that the net red-shift and blue-shift of an full orbit circle be
cancelled out, so that the effect of Doppler shift to the signal in binary
motion cannot be accumulated over the orbital period. However, taking the
propagation time at each velocity state into account, the symmetry of the
velocity distribution over the orbital phase is broken. Consequently, the net
Doppler shift left in an orbit is non-zero. Understanding this Newtonian second
Doppler effect not only makes pulsars better laboratory in the test of
gravitational effects, but also allows us to extract the angular momentum of
the pulsar of PSR J2051-0827, $\leq 2\times 10^{43}gcm^2$; and the accretion
disc of 4U 1627-67, $7\times 10^{50} gcm^2/s$, respectively, which are of
importance in the study of structure of neutron stars and the physics of
accretion disc of X-ray binaries.


title: Solutions to the quantum Rabi model with two equivalent qubits

abstract:
  Using extended coherent states, an analytically exact study has been carried
out for the quantum Rabi model with two equivalent qubits. Compact
transcendental functions of one variable have been derived leading to exact
solutions. The energy spectrum is clearly identified and analyzed. Also
obtained analytically is the necessary and sufficient conditions for the
occurrence of isolated exceptional solutions, which are not doubly degenerate
as in the one-qubit quantum Rabi model.


title:
The nilpotent variety and invariant polynomial functions in the
  Hamiltonian algebra

abstract:
  Premet has conjectured that the nilpotent variety of any finite-dimensional
restricted Lie algebra is an irreducible variety. In this paper, we prove this
conjecture in the case of Hamiltonian Lie algebra. and show that its nilpotent
variety is normal and a complete intersection. In addition, we generalize the
Chevalley Restriction theorem to Hamiltonian Lie algebra. Accordingly, we give
the generators of the invariant polynomial ring.


title: A Robust Compressive Quantum State Tomography Algorithm Using ADMM

abstract:
  The possible state space dimension increases exponentially with respect to
the number of qubits. This feature makes the quantum state tomography expensive
and impractical for identifying the state of merely several qubits. The recent
developed approach, compressed sensing, gives us an alternative to estimate the
quantum state with fewer measurements. It is proved that the estimation then
can be converted to a convex optimization problem with quantum mechanics
constraints. In this paper we present an alternating augmented Lagrangian
method for quantum convex optimization problem aiming for recovering pure or
near pure quantum states corrupted by sparse noise given observables and the
expectation values of the measurements. The proposed algorithm is much faster,
robust to outlier noises (even very large for some entries) and can solve the
reconstruction problem distributively. The simulations verify the superiority
of the proposed algorithm and compare it to the conventional least square and
compressive quantum tomography using Dantzig method.


title: A suspended rope wrapped around a cylinder

abstract:
  The problem of a suspended rope wrapped around a fixed cylinder is studied.
If the suspension force is larger than a certain threshold (which is larger
than the weight of the rope), the rope would remain tightly wrapped around the
cylinder. For suspension forces smaller than that threshold but larger than
another threshold, the rope becomes loose (loses contact with the cylinder) at
some points, but still remains at rest. Theses thresholds are obtained when
there is no friction. The system is then analyzed also with friction, and the
threshold of tight-wrapping is obtained for that case as well.


title: On Keisler singular-like models II

abstract:
  Keisler proved that if $\theta$ is a strong limit cardinal and $\lambda$ is a
singular cardinal, then the transfer relation $\theta\longrightarrow\lambda$
holds. In a previous paper, we studied initial elementary submodels of the
$\lambda$-like models produced in the proof of Keisler's transfer theorem when
$\theta$ is further assumed to be regular i.e., $\theta$ is strongly
inaccessible. In this paper we deal with a much more difficult situation. Some
years ago Ali Enayat asked the author whether Keisler's singular-like models
can have elementary end extensions. We give a positive answer to this question.


title: Infinite square-free self-shuffling words

abstract:
  In this paper we answer two recent questions from Charlier et al. and Harju
about self-shuffling words. An infinite word $w$ is called self-shuffling, if
$w=\prod_{i=0}^\infty U_iV_i=\prod_{i=0}^\infty U_i=\prod_{i=0}^\infty V_i$ for
some finite words $U_i$, $V_i$. Harju recently asked whether square-free
self-shuffling words exist. We answer this question affirmatively. Besides
that, we build an infinite word such that no word in its shift orbit closure is
self-shuffling, answering positively a question from Charlier et al.


title: Phonon Diodes and Transistors from Magneto-acoustics

abstract:
  By sculpting the magnetic field applied to magneto-acoustic materials,
phonons can be used for information processing. Using a combination of analytic
and numerical techniques, we demonstrate designs for diodes (isolators) and
transistors that are independent of their conventional, electronic formulation.
We analyze the experimental feasibility of these systems, including the
sensitivity of the circuits to likely systematic and random errors.


title: Flare Ribbon Energetics in the Early Phase of an SDO Flare

abstract:
  The sites of chromospheric excitation during solar flares are marked by
extended extreme ultraviolet ribbons and hard X-ray footpoints. The standard
interpretation is that these are the result of heating and bremsstrahlung
emission from non-thermal electrons precipitating from the corona. We examine
this picture using multi-wavelength observations of the early phase of an
M-class flare SOL2010-08-07T18:24. We aim to determine the properties of the
heated plasma in the flare ribbons, and to understand the partition of the
power input into radiative and conductive losses. Using GOES, SDO/EVE, SDO/AIA
and RHESSI we measure the temperature, emission measure and differential
emission measure of the flare ribbons, and deduce approximate density values.
The non-thermal emission measure, and the collisional thick target energy input
to the ribbons are obtained from RHESSI using standard methods. We deduce the
existence of a substantial amount of plasma at 10 MK in the flare ribbons,
during the pre-impulsive and early-impulsive phase of the flare. The average
column emission measure of this hot component is a few times 10^28/cm^5, and we
can calculate that its predicted conductive losses dominate its measured
radiative losses. If the power input to the hot ribbon plasma is due to
collisional energy deposition by an electron beam from the corona then a
low-energy cutoff of around 5 keV is necessary to balance the conductive
losses, implying a very large electron energy content. Independent of the
standard collisional thick-target electron beam interpretation, the observed
non-thermal X-rays can be provided if one electron in 10^3 - 10^4 in the 10 MK
(1 keV) ribbon plasma has an energy above 10 keV. We speculate that this could
arise if a non-thermal tail is generated in the ribbon plasma which is being
heated by other means, for example by waves or turbulence.


title:
Tomographic and improved subadditivity conditions for two qubits and
  qudit with j = 3=2

abstract:
  New entropic inequality for quantum and tomographic Shannon information for
system of two qubits is obtained. The inequality relating quantum information
and spin-tomographic information for particle with spin j = 3=2 is found. The
method to extend the obtained new entropic and information inequalities for one
qudit and arbitrary composite system of qudits is suggested.