title: Maximal subgroups of amalgams of finite inverse semigroups

abstract:
  We use the description of the Schutzenberger automata for amalgams of finite
inverse semigroups given by Cherubini, Meakin, Piochi to obtain structural
results for such amalgams. Schutzenberger automata, in the case of amalgams of
finite inverse semigroups, are automata with special structure possessing
finite subgraphs, that contain all essential information related to the whole
automaton. Using this crucial fact, and the Bass-Serre theory, we show that the
maximal subgroups of an amalgamated free-product are either isomorphic to
certain subgroups of the original semigroups or can be described as fundamental
groups of particular finite graphs of groups build from the maximal subgroups
of the original semigroups.


title:
Modified Bose-Einstein and Fermi-Dirac statistics if excitations are
  localized on an intermediate length scale: Application to non-Debye specific
  heat

abstract:
  Disordered systems show deviations from the standard Debye theory of specific
heat at low temperatures. These deviations are often attributed to two-level
systems of uncertain origin. We find that a source of excess specific heat
comes from correlations between quanta of energy if phonon-like excitations are
localized on an intermediate length scale. We use simulations of a simplified
Creutz model for a system of Ising-like spins coupled to a thermal bath of
Einstein-like oscillators. One feature of this model is that energy is
quantized in both the system and its bath, ensuring conservation of energy at
every step. Another feature is that the exact entropies of both the system and
its bath are known at every step, so that their temperatures can be determined
independently. We find that there is a mismatch in canonical temperature
between the system and its bath. In addition to the usual finite-size effects
in the Bose-Einstein and Fermi-Dirac distributions, if excitations in the heat
bath are localized on an intermediate length scale, this mismatch is
independent of system size up to at least 10^6 particles. We use a model for
correlations between quanta of energy to adjust the statistical distributions
and yield a thermodynamically consistent temperature. The model includes a
chemical potential for units of energy, as is often used for other types of
particles that are quantized and conserved. Experimental evidence for this
model comes from its ability to characterize the excess specific heat of
imperfect crystals at low temperatures.


title:
Gamma-ray pulsar physics: gap-model populations and light-curve analyses
  in the FERMI era

abstract:
  This thesis research focusses on the study of the young and energetic
isolated ordinary pulsar population detected by the Fermi gamma-ray space
telescope. We compared the model expectations of four emission models and the
LAT data. We found that all the models fail to reproduce the LAT detections, in
particular the large number of high spin-down power objects observed. This
inconsistency is not model dependent. A discrepancy between the
radio-loud/radio-quiet objects ratio was also found between the observed and
predicted samples. The gamma-ray luminosity proportional to the 0.5 power of
the spin-down power relation is robustly confirmed by all the assumed models
with particular agreement in the slot gap (SG) case. On luminosity bases, the
intermediate altitude emission of the two pole caustic SG model is favoured.
The beaming factor shows an spin-down power dependency that is slightly visible
in theSG case. Estimates of the pulsar orientations have been obtained to
explain the simultaneous gamma and radio light-curves. By analysing the
solutions we found a relation between the observed energy cutoff and the width
of the emission slot gap. This relation has been theoretically predicted. A
possible magnetic obliquity alignment with time is rejected -for all the
models- on timescale of the order of a million years. The light-curve
morphology study shows that the outer magnetosphere gap emission are favoured
to explain the observed radio-gamma lag. The light curve moment studies
(symmetry and sharpness) on the contrary favour a two pole caustic slot gap
emission. All the model predictions suggest a different magnetic field layout
with an hybrid two pole caustic and intermediate altitude emission to explain
both the pulsar luminosity and light curve morphology . The low magnetosphere
emission mechanism of the polar cap model, is systematically rejected by all
the tests done.


title: Remarks on the tensor degree of finite groups

abstract:
  The present paper is a note on the tensor degree of finite groups, introduced
recently in literature. This numerical invariant generalizes the commutativity
degree through the notion of nonabelian tensor square. We show two
inequalities, which correlate the tensor and the commutativity degree of finite
groups, and, indirectly, structural properties will be discussed.


title: An evolutionary approach to Function

abstract:
  Background: Understanding the distinction between function and role is vexing
and difficult. While it appears to be useful, in practice this distinction is
hard to apply, particularly within biology.
  Results: I take an evolutionary approach, considering a series of examples,
to develop and generate definitions for these concepts. I test them in practice
against the Ontology for Biomedical Investigations (OBI). Finally, I give an
axiomatisation and discuss methods for applying these definitions in practice.
  Conclusions: The definitions in this paper are applicable, formalizing
current practice. As such, they make a significant contribution to the use of
these concepts within biomedical ontologies.


title: On the Cookie Monster Problem

abstract:
  The Cookie Monster Problem supposes that the Cookie Monster wants to empty a
set of jars filled with various numbers of cookies. On each of his moves, he
may choose any subset of jars and take the same number of cookies from each of
those jars. The Cookie Monster number of a set is the minimum number of moves
the Cookie Monster must use to empty all of the jars. This number depends on
the initial distribution of cookies in the jars. We discuss bounds of the
Cookie Monster number and explicitly find the Cookie Monster number for jars
containing cookies in the Fibonacci, Tribonacci, n-nacci, and Super-n-nacci
sequences. We also construct sequences of k jars such that their Cookie Monster
numbers are asymptotically rk, where r is any real number between 0 and 1
inclusive.


title:
Experimental demonstration of near-infrared epsilon-near-zero multilayer
  metamaterial slabs

abstract:
  Near-infrared epsilon-near-zero (ENZ) metamaterial slabs based on
silver-germanium (Ag-Ge) multilayers are experimentally demonstrated.
Transmission, reflection and absorption spectra are characterized and used to
determine the complex refractive indices and the effective permittivities of
the ENZ metamaterial slabs, which match the results obtained from both the
numerical simulations and the optical nonlocalities analysis. A rapid
post-annealing process is used to reduce the collision frequency of silver and
therefore decrease the optical absorption loss of multilayer metamaterial
slabs. Furthermore, multilayer grating structures are studied to enhance the
optical transmission and also tune the location of ENZ wavelength. The
demonstrated near-infrared ENZ multilayer metamaterial slabs are important for
realizing many exotic applications, such as phase front shaping and engineering
of photonic density of states.


title: On Baker type lower bounds for linear forms

abstract:
  A criterion is given for studying (explicit) Baker type lower bounds of
linear forms in numbers $1,\Theta_1,...,\Theta_m\in\mathbb{C}^*$ over the ring
$\mathbb{Z}_{\mathbb{I}}$ of an imaginary quadratic field $\mathbb{I}$. This
work deals with the simultaneous auxiliary functions case.


title:
Development of an Optimization-Based Atomistic-to-Continuum Coupling
  Method

abstract:
  Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing
the properties of a discrete crystal structure, such as those containing
defects, that combine the accuracy of an atomistic (fully discrete) model with
the efficiency of a continuum model. In this note we extend the
optimization-based AtC, formulated in arXiv:1304.4976 for linear,
one-dimensional problems to multi-dimensional settings and arbitrary
interatomic potentials. We conjecture optimal error estimates for the
multidimensional AtC, outline an implementation procedure, and provide
numerical results to corroborate the conjecture for a 1D Lennard-Jones system
with next-nearest neighbor interactions.


title:
Photometry and Dynamics of the Minor Merger AM1219-430 with Gemini
  GMOS-S

abstract:
  We present an observational study of the interaction effect on the dynamics
and morphology of the minor merger AM1219-430. This work is based on r' and g'
images and long-slit spectra obtained with the Gemini Multi-Object Spectrograph
at the Gemini South Telescope. We detected a tidal tail in the main galaxy
(AM1219A) and a bridge of material connecting the galaxies. In luminosity,
AM1219A is about 3.8 times brighter than the secondary (AM1219B). The surface
brightness profile of AM1219A was decomposed into bulge and disc components.
The profile shows a light excess of ~ 53 % due to the contribution of
star-forming regions, which is typical of starburst galaxies. On the other
hand, the surface brightness profile of AM1219B shows a lens structure in
addition to the bulge and disc. The scale lengths and central magnitudes of the
disc structure of both galaxies agree with the average values derived for
galaxies with no sign of ongoing interaction or disturbed morphology. The
S\'ersic index (n<2), the effective and scale radii of the bulge of both
galaxies are typical of pseudo-bulges. The rotation curve of AM1219A derived
from the emission line of ionized gas is quite asymmetric, suggesting a gas
perturbed by interaction. We explore all possible values of stellar and dark
matter masses. The overall best-fitting solution for the mass distribution of
AM1219A was found with M/L for bulge and disc of M/L_b=2.8_-0.4^+0.4 and
M/L_d=2.4_-0.2^+0.3, respectively, and a Navarro, Frenk and White profile of
M_200=2.0_-0.4^+0.5 x10^12 M_sun and c=16.0_-1.1^+1.2. The estimated dynamical
mass is 1.6x10^11 M_sun, within a radius of ~ 10.6 kpc.


title: Backreaction of Localised Sources in String Compactifications

abstract:
  Localised sources such as D-branes or orientifold planes play an important
role in many string compactifications that are relevant for phenomenology. The
presence of these objects typically induces complicated dynamics in the compact
dimensions such that a full solution to the 10d equations of motion is often
out of reach. In order to still be able to make statements about the 4d
effective theory arising in the low-energy limit, the equations of motion are
usually only solved in an integrated sense, while the backreaction of the
localised sources on the internal fields is neglected. This simplification is
often referred to as smearing. In this work, we investigate to what extent
smearing may affect observables in the effective low-energy theory and whether
it may lead to fake solutions that would cease to exist once the backreaction
is properly taken into account. We analyse explicit examples for which smeared
solutions exist and find that the reliability of the smeared approximation
appears to depend on whether or not these solutions saturate a BPS bound. We
also address the proposal of placing anti-D3-branes at the tip of a warped
throat geometry like the Klebanov-Strassler solution in order to construct
meta-stable de Sitter vacua in string theory. We show that, under a few general
assumptions, the backreaction of the fully localised anti-branes yields a
singularity in fields that do not directly couple to them, and we give an
argument suggesting that the singularity is not resolved by brane polarisation.
We furthermore demonstrate that, in many string compactifications involving
non-trivial background fluxes, the effective lower-dimensional cosmological
constant is determined by the on-shell action of the localised sources present
in the solution. This often allows to compute the cosmological constant without
resorting to potentially unreliable approximations like smearing.


title:
Applications of Continuous Amortization to Bisection-based Root
  Isolation

abstract:
  Continuous amortization is a technique for computing the complexity of
algorithms, and it was first presented by the author in Burr, Krahmer, & Yap
(2009). Continuous amortization can result in simpler and more straight-forward
complexity analyses, and it was used in Burr, Krahmer, & Yap (2009), Burr &
Krahmer (2012), and Sharma & Yap (2012) to provide complexity bounds for simple
root isolation algorithms. This paper greatly extends the reach of continuous
amortization to serve as an overarching technique which can be used to compute
complexity of many root isolation techniques in a straight-forward manner.
Additionally, the technique of continuous amortization is extended to higher
dimensions and to the computation of the bit-complexity of algorithms. In this
paper, six continuous amortization calculations are performed to compute
complexity bounds (on either the size of the subdivision tree or the bit
complexity) for several algorithms (including algorithms based on Sturm
sequences, Descartes' rule of signs, and polynomial evaluation); in each case,
continuous amortization achieves an optimal complexity bound.


title:
Hydrodynamics of Euler incompressible fluid and the Fractional Quantum
  Hall Effect

abstract:
  We show that the Fractional Quantum Hall Effect can be phenomenologically
described as a special flow of a quantum incompressible Euler liquid. This flow
consists of a large number of vortices of the same chirality. In this approach
each vortex is identified with an electron while the fluid is neutral. We show
that the Laughlin wave function emerges as a stationary flow of the system of
vortices in quantum fluid dynamics. Subtle features of FQHE such as effects of
Lorentz shear stress, the spectral function, the Hall current in a modulated
electric fields, etc., naturally follow from the hydrodynamics approach. In the
paper we develop the hydrodynamics of the vortex liquid, and able consistently
quantize it. As a demonstration of the efficiency of the hydrodynamics we
discuss some new results for FQHE in a non-uniform magnetic field and a curved
space.


title:
Combining smart card data and household travel survey to analyze
  jobs-housing relationships in Beijing

abstract:
  Location Based Services (LBS) provide a new perspective for spatiotemporally
analyzing dynamic urban systems. Research has investigated urban dynamics using
GSM (Global System for Mobile Communications), GPS (Global Positioning System),
SNS (Social Networking Services) and Wi-Fi techniques. However, less attention
has been paid to the analysis of urban structure (especially commuting pattern)
using smart card data (SCD), which are widely available in most cities.
Additionally, ubiquitous LBS data, although providing rich spatial and temporal
information, lacks rich information on the social dimension, which limits its
in-depth application. To bridge this gap, this paper combines bus SCD for a
one-week period with a one-day household travel survey, as well as a
parcel-level land use map to identify job-housing locations and commuting trip
routes in Beijing. Two data forms (TRIP and PTD) are proposed, with PTD used
for jobs-housing identification and TRIP used for commuting trip route
identification. The results of the identification are aggregated in the bus
stop and traffic analysis zone (TAZ) scales, respectively. Particularly,
commuting trips from three typical residential communities to six main business
zones are mapped and compared to analyze commuting patterns in Beijing. The
identified commuting trips are validated on three levels by comparison with
those from the survey in terms of commuting time and distance, and the positive
validation results prove the applicability of our approach. Our experiment, as
a first step toward enriching LBS data using conventional survey and urban GIS
data, can obtain solid identification results based on rules extracted from
existing surveys or censuses.


title:
Simulation of inhomogeneous distributions of ultracold atoms in an
  optical lattice via a massively parallel implementation of nonequilibrium
  strong-coupling perturbation theory

abstract:
  We present a nonequilibrium strong-coupling approach to inhomogeneous systems
of ultracold atoms in optical lattices. We demonstrate its application to the
Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence
of a trap potential. Since the theory is formulated self-consistently, the
numerical implementation relies on a massively parallel evaluation of the
self-energy and the Green's function at each lattice site, employing thousands
of CPUs. While the computation of the self-energy is straightforward to
parallelize, the evaluation of the Green's function requires the inversion of a
large sparse $10^d\times 10^d$ matrix, with $d > 6$. As a crucial ingredient,
our solution heavily relies on the smallness of the hopping as compared to the
interaction strength and yields a widely scalable realization of a rapidly
converging iterative algorithm which evaluates all elements of the Green's
function. Results are validated by comparing with the homogeneous case via the
local-density approximation. These calculations also show that the
local-density approximation is valid in non-equilibrium setups without mass
transport.


title:
A Justification of the Modulation Approximation to the 3D Full Water
  Wave Problem

abstract:
  We consider small amplitude wave packet-like solutions to the 3D inviscid
incompressible irrotational infinite depth water wave problem neglecting
surface tension. Formal multiscale calculations suggest that the modulation of
such a solution is described by a profile traveling at group velocity and
governed by a hyperbolic cubic nonlinear Schr\"odinger equation. In this paper
we show that, given wave packet initial data, the corresponding solution exists
and retains the form of a wave packet on natural NLS time scales. Moreover, we
give rigorous error estimates between the true and formal solutions on the
appropriate time scale in Sobolev spaces using the energy method. The proof
proceeds by directly applying modulational analysis to the formulation of the
3D water wave problem developed by Sijue Wu.


title: Higher Classes of Ordinals induced by <_1

abstract:
  In this article we want to see that it is possible to iterate and generalize
the notions presented in "Carlson's <_1-relation on the class of epsilon
numbers" such that we can obtain the higher or thinner classes of ordinals
induced by the <_1-relation as solutions of conditions. Indeed, these results
are so general that in a future article we will be able to characterize the
ordinal |Pi_1^1 - CA_0 | as the smallest ordinal of the thinnest class induced
by <_1.


title: Extended Security Risks in IP Networks

abstract:
  Exploitation techniques targeting intermediate (transit) network nodes in
public and private networks have been theoretically known and empirically
proven to work for quite some time. However, very little effort has been made
to look into the network-specific risks of compromising the Internet
infrastructure to this date. In this publication, we describe several methods
of hijacking live network traffic following a successful attack on a router or
switch. We demonstrate that modern network platforms are capable of targeted
traffic replication and redirection for online and offline analysis and
modification, which can be a threat far greater than loss of service or other
risks frequently associated with such exploits.


title: Localized coherence in two interacting populations of social agents

abstract:
  We investigate the emergence of localized coherent behavior in a system
consisting of two populations of social agents possessing a condition for
non-interacting states, mutually coupled through global interaction fields. As
an example of such dynamics, we employ Axelrod's model for social influence.
The global interaction fields correspond to the statistical mode of the states
of the agents in each population. We find localized coherent states for some
values of parameters, consisting of one population in a homogeneous state and
the other in a disordered state. This situation can be considered as a social
analogue to a chimera state arising in two interacting populations of
oscillators. In addition, other asymptotic collective behaviors appear
depending on parameter values: a common homogeneous state, where both
populations reach the same state; different homogeneous states, where both
population reach homogeneous states different from each other; and a disordered
state, where both populations reach inhomogeneous states.


title:
Genetic Algorithm for Constrained Optimization with Stochastic
  Feasibility Region with Application to Vehicle Path Planning

abstract:
  In real-time trajectory planning for unmanned vehicles, on-board sensors,
radars and other instruments are used to collect information on possible
obstacles to be avoided and pathways to be followed. Since, in practice,
observations of the sensors have measurement errors, the stochasticity of the
data has to be incorporated into the models. In this paper, we consider using a
genetic algorithm for the constrained optimization problem of finding the
trajectory with minimum length between two locations, avoiding the obstacles on
the way. To incorporate the variability of the sensor readings, we propose a
more general framework, where the feasible regions of the genetic algorithm are
stochastic. In this way, the probability that a possible solution of the search
space, say x, is feasible can be derived from the random observations of
obstacles and pathways, creating a real-time data learning algorithm. By
building a confidence region from the observed data such that its border
intersects with the solution point x, the level of the confidence region
defines the probability that x is feasible. We propose using a smooth penalty
function based on the Gaussian distribution, facilitating the borders of the
feasible regions to be reached by the algorithm.


title:
A New Sentinel Approach for Energy Efficient and Hole Aware Wireless
  Sensor Networks

abstract:
  Recent advances in micro-sensor and communication technology have enabled the
emergence of a new technology, Wireless Sensor Networks (WSN). WSN have
emerging recently as a key solution to monitor remote or hostile environments
and concern a wide range of applications. These networks are faced with many
challenges such as energy efficiency usage, topology maintenance, network
lifetime maximization, etc. Experience shows that sensing and communications
tasks consume energy, therefore judicious power management can effectively
extend network lifetime. Moreover, the low cost of sensor devices will allows
deployment of huge number nodes that can permit a high redundancy degree. In
this paper, we focus on the problem of energy efficiency and topology
maintenance in a densely deployed network context. Hence we propose an energy
aware sleep scheduling and rapid topology healing scheme for long life wireless
sensor networks. Our scheme is a strong node scheduling based mechanism for
lifetime maximization in wireless sensor networks and has a fast maintenance
method to cover nodes failure. Our sentinel scheme is based on a probabilistic
model which provides a distributed sleep scheduling and topology control
algorithm. Simulations and experimental results are presented to verify our
approach and the performance of our mechanism.


title: Co-evolutionary dynamics in social networks: A case study of Twitter

abstract:
  Complex networks often exhibit co-evolutionary dynamics, meaning that the
network topology and the state of nodes or links are coupled, affecting each
other in overlapping time scales. We focus on the co-evolutionary dynamics of
online social networks, and on Twitter in particular. Monitoring the activity
of thousands of Twitter users in real-time, and tracking their followers and
tweets/retweets, we propose a method to infer new retweet-driven follower
relations. The formation of such relations is much more likely than the
exogenous creation of new followers in the absence of any retweets. We identify
the most significant factors (reciprocity and the number of retweets that a
potential new follower receives) and propose a simple probabilistic model of
this effect. We also discuss the implications of such co-evolutionary dynamics
on the topology and function of a social network.


title:
Assessing the adequacy of the bare optical potential in near-barrier
  fusion calculation

abstract:
  We critically examine the differences among the different bare nuclear
interactions used in near-barrier heavy ion fusion analysis and
Coupled-Channels calculations, and discuss the possibility of extracting the
barrier parameters of the bare potential from above-barrier data. We show that
the choice of the bare potential may be critical for the analysis of the fusion
cross sections. We show also that the barrier parameters taken from above
barrier data may be very wrong.


title: Zonoids and sparsification of quantum measurements

abstract:
  In this paper, we establish a connection between zonoids (a concept from
classical convex geometry) and the distinguishability norms associated to
quantum measurements, or POVMs (Positive Operator-Valued Measures), recently
introduced in quantum information theory.
  This correspondence allows us to state and prove the POVM version of
classical results from the local theory of Banach spaces about the
approximation of zonoids by zonotopes. We show that on $\mathbf{C}^d$, the
uniform POVM (the most symmetric POVM) can be sparsified, i.e. approximated by
a discrete POVM, the latter having only $O(d^2)$ outcomes. We also show that
similar (but weaker) approximation results actually hold for any POVM on
$\mathbf{C}^d$.
  By defining an appropriate notion of tensor product for zonoids, we are then
able to extend our results to the multipartite setting: we show, roughly
speaking, that local POVMs may be sparsified locally. In particular, the local
uniform POVM on $\mathbf{C}^{d_1}\otimes\cdots\otimes\mathbf{C}^{d_k}$ can be
approximated by a discrete POVM which is local and has
$O(d_1^2\times\cdots\times d_k^2)$ outcomes.


title:
Exact, molecular-shaped vortices with fractional and integer charges in
  the extended Skyrme-Faddeev model

abstract:
  We analytically construct vortex solutions in the integrable sector of the
extended Skyrme-Faddeev model. The solutions are holomorphic type which satisfy
the zero curvature condition. For the model parameter $\beta e^2=1$ there is a
lump solution, and for $\beta e^2 \neq 1$ new potentials are introduced for the
several molecular-shaped solutions with half-integer or integer charges. They
necessarily have infinite number of conserved currents and some of the examples
are shown. By performing an annealing simulation with our potentials, we verify
the existence of the solutions of the integrable sector.


title: ISAC LEBT

abstract: The ISAC electrostatic Low Energy Beam Transport (LEBT) system is described.


title:
Energy decay for systems of semilinear wave equations with dissipative
  structure in two space dimensions

abstract:
  We consider the Cauchy problem for systems of semilinear wave equations in
two space dimensions. We present a structural condition on the nonlinearity
under which the energy decreases to zero as time tends to infinity if the
Cauchy data are sufficiently small, smooth and compactly-supported.


title:
UAV Circumnavigation of an Unknown Target Without Location Information
  Using Noisy Range-based Measurements

abstract:
  This paper proposes a control algorithm for a UAV to circumnavigate an
unknown target at a fixed radius when the location information of the UAV is
unavailable. By assuming that the UAV has a constant velocity, the control
algorithm makes adjustments to the heading angle of the UAV based on range and
range rate measurements from the target, which may be corrupted by additive
measurement noise. The control algorithm has the added benefit of being
globally smooth and bounded. Exploiting the relationship between range rate and
bearing angle, we transform the system dynamics from Cartesian coordinate in
terms of location and heading to polar coordinate in terms of range and bearing
angle. We then formulate the addition of measurement errors as a stochastic
differential equation. A recurrence result is established showing that the UAV
will reach a neighborhood of the desired orbit in finite time. Some statistical
measures of performance are obtained to support the technical analysis.


title: Electrostatic Bender Optics

abstract:
  The relativistically-correct Hamiltonian and transfer matrix of electrostatic
benders is derived. This is the general case where the bender electrodes have
curvature in the non-bend direction.


title: Selections and their Absolutely Continuous Invariant Measures

abstract:
  Let $I=[0,1]$ and consider disjoint closed regions $G_{1},....,G_{n}$ in $%
I\times I$ and subintervals $I_{1},......,I_{n},$ such that $G_{i}$ projects
onto $I_{i.}$ We define the lower and upper maps $\tau_{1},$ $\tau_{2}$ by the
lower and upper boundaries of $G_{i},i=1,....,n,$ respectively. We assume
$\tau_{1}$, $\tau_{2}$ to be piecewise monotonic and preserving continuous
invariant measures $\mu_{1}$ and $\mu_{2}$, respectively. Let $% F^{(1)}$ and
$F^{(2)}$ be the distribution functions of $\mu_{1}$ and $\mu_{2}.$ The main
results shows that for any convex combination $F$ of $% F^{(1)} $ and $F^{(2)}$
we can find a map $\eta $ with values between the graphs of $\tau_{1}$ and
$\tau_{2}$ (that is, a selection) such that $F$ is the $\eta $-invariant
distribution function. Examples are presented. We also study the relationship
of the dynamics of multi-valued maps to random maps.


title: A birationality result for character varieties

abstract:
  Let M be an orientable, cusped hyperbolic 3-manifold of finite volume. We
show that the restriction map from a Dehn surgery component in the
PSL(2,C)-character variety of M to the character variety of the boundary of M
is a birational isomorphism onto its image. This generalises a result by Nathan
Dunfield. A key step in our proof is the exactness of Craig Hodgson's volume
differential on the eigenvalue variety.


title: Tropicalizing the positive semidefinite cone

abstract:
  We study the tropicalization of the cone of positive semidefinite matrices
over the ordered field of real Puiseux series. The tropical PSD matrices form
the normal cone of the Newton polytope of the symmetric determinant at the
vertex corresponding to the product of diagonal entries. We find generators and
defining inequalities of the cone. The PSD tropical quadratic forms are those
that induce the trivial subdivision on the standard simplex dilated by two. We
also show that the tropical PSD cone is the tropical convex hull of the set of
symmetric matrices of tropical rank one and that every tropical PSD matrix can
be factored as a tropical product of a matrix and its transpose.


title: Separating Invariants and Local Cohomology

abstract:
  The study of separating invariants is a recent trend in invariant theory. For
a finite group acting linearly on a vector space, a separating set is a set of
invariants whose elements separate the orbits of G. In some ways, separating
sets often exhibit better behavior than generating sets for the ring of
invariants. We investigate the least possible cardinality of a separating set
for a given G-action. Our main result is a lower bound that generalizes the
classical result of Serre that if the ring of invariants is polynomial then the
group action must be generated by pseudoreflections. We find these bounds to be
sharp in a wide range of examples.


title: A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion

abstract:
  We consider in this paper the problem of noisy 1-bit matrix completion under
a general non-uniform sampling distribution using the max-norm as a convex
relaxation for the rank. A max-norm constrained maximum likelihood estimate is
introduced and studied. The rate of convergence for the estimate is obtained.
Information-theoretical methods are used to establish a minimax lower bound
under the general sampling model. The minimax upper and lower bounds together
yield the optimal rate of convergence for the Frobenius norm loss.
Computational algorithms and numerical performance are also discussed.


title:
A Biomass-based Model to Estimate the Plausibility of Exoplanet
  Biosignature Gases

abstract:
  Biosignature gas detection is one of the ultimate future goals for exoplanet
atmosphere studies. We have created a framework for linking biosignature gas
detectability to biomass estimates, including atmospheric photochemistry and
biological thermodynamics. The new framework is intended to liberate predictive
atmosphere models from requiring fixed, Earth-like biosignature gas source
fluxes. New biosignature gases can be considered with a check that the biomass
estimate is physically plausible. We have validated the models on terrestrial
production of NO, H2S, CH4, CH3Cl, and DMS. We have applied the models to
propose NH3 as a biosignature gas on a "cold Haber World," a planet with a
N2-H2 atmosphere, and to demonstrate why gases such as CH3Cl must have too
large of a biomass to be a plausible biosignature gas on planets with Earth or
early-Earth-like atmospheres orbiting a Sun-like star. To construct the biomass
models, we developed a functional classification of biosignature gases, and
found that gases (such as CH4, H2S, and N2O) produced from life that extracts
energy from chemical potential energy gradients will always have false
positives because geochemistry has the same gases to work with as life does,
and gases (such as DMS and CH3Cl) produced for secondary metabolic reasons are
far less likely to have false positives but because of their highly specialized
origin are more likely to be produced in small quantities. The biomass model
estimates are valid to one or two orders of magnitude; the goal is an
independent approach to testing whether a biosignature gas is plausible rather
than a precise quantification of atmospheric biosignature gases and their
corresponding biomasses.


title:
A High-Performance Cellular Automaton Model of Tumor Growth with
  Dynamically Growing Domains

abstract:
  Tumor growth from a single transformed cancer cell up to a clinically
apparent mass spans many spatial and temporal orders of magnitude.
Implementation of cellular automata simulations of such tumor growth can be
straightforward but computing performance often counterbalances simplicity.
Computationally convenient simulation times can be achieved by choosing
appropriate data structures, memory and cell handling as well as domain setup.
We propose a cellular automaton model of tumor growth with a domain that
expands dynamically as the tumor population increases. We discuss memory
access, data structures and implementation techniques that yield
high-performance multi-scale Monte Carlo simulations of tumor growth. We
present simulation results of the tumor growth model and discuss tumor
properties that favor the proposed high-performance design.


title: Biosignature Gases in H2-Dominated Atmospheres on Rocky Exoplanets

abstract:
  (Abridged) Super Earth exoplanets are being discovered with increasing
frequency and some will be able to retain stable H2-dominated atmospheres. We
study biosignature gases on exoplanets with thin H2 atmospheres and habitable
surface temperatures, by using a model atmosphere with photochemistry, and
biomass estimate framework for evaluating the plausibilty of a range of
biosignature gas candidates. We find that photochemically produced H atoms are
the most abundant reactive species in H2 atmospheres. In atmospheres with high
CO2 levels, atomic O is the major destructive species for some molecules. In
sun-Earth-like UV radiation environments, H (and in some cases O) will rapidly
destroy nearly all biosignature gases of interest. The lower UV fluxes from UV
quiet M stars would produce a lower concentration of H (or O) for the same
scenario, enabling some biosignature gases to accumulate. The favorability of
low-UV radiation environments to in an H2 atmosphere is closely analogous to
the case of oxidized atmospheres, where photochemically produced OH is the
major destructive species. Most potential biosignature gases, such as DMS and
CH3Cl are therefore more favorable in low UV, as compared to solar-like UV,
environments. A few promising biosignature gas candidates, including NH3 and
N2O, are favorable even in solar-like UV environments, as these gases are
destroyed directly by photolysis and not by H (or O). A more subtle finding is
that most gases produced by life that are fully hydrogenated forms of an
element, such as CH4, H2S, are not effective signs of life in an H2-rich
atmosphere, because the dominant atmospheric chemistry will generate such gases
abiologically, through photochemistry or geochemistry. Suitable biosignature
gases in H2-rich atmospheres for super Earth exoplanets transiting M stars
could potentially be detected in transmission spectra with the JWST.


title: Linear stability of algebraic Ricci solitons

abstract:
  We consider a modified Ricci flow equation whose stationary solutions include
Einstein and Ricci soliton metrics, and we study the linear stability of those
solutions relative to the flow. After deriving various criteria that imply
linear stability, we turn our attention to left-invariant soliton metrics on
(non-compact) simply connected solvable Lie groups and prove linear stability
of many such metrics. These include an open set of two-step solvsolitons, all
two-step nilsolitons, two infinite families of three-step solvable Einstein
metrics, all nilsolitons of dimensions six or less, and all solvable Einstein
metrics of dimension seven or less with codimension-one nilradical. For each
linearly stable metric, dynamical stability follows a generalization of the
techniques of Guenther, Isenberg, and Knopf.


title: Collective Modes and Nonlinear Acoustics in Superfluid 3He-B

abstract:
  We discuss the relationship of collisionless sound propagation and
attenuation to the order parameter collective modes of superfluid 3He-B. These
modes, which reflect the symmetries of the normal state as well as the broken
gauge and relative rotational symmetries of the condensate, play a central role
in the high-frequency acoustic response of the superfluid. We review the theory
of acoustic spectroscopy based on the linear coupling of the J=2+/- modes. We
develop the theory of the nonlinear acoustic response of superfluid 3He-B for
the case of a three-wave resonance between two sound waves of different
frequencies and the J=2+/- modes, as well as the generation of higher harmonic
sound waves. The J=2+ modes couple nonlinearly to two zero-sound waves. The
predictions for the nonlinear absorption and velocity anomalies resulting from
the J=2+ modes depend on relatively well understood material properties of 3He.


title: Tunable single particle and many body physics in graphene

abstract:
  This thesis studies how the rudimentary attributes of graphene's charge
carriers, and local moments on its surface, can be directly manipulated and
controlled with electrostatic potentials. We first consider bilayer graphene
subject to a spatially varying electrostatic potential that forms two
neighbouring regions with opposite interlayer bias. Along the boundary, 1D
chiral "kink" states emerge. We find that these 1D modes behave as a strongly
interacting Luttinger liquid whose properties can be tuned via an external
gate. Next, we consider superlattices in bilayer graphene. Superlattices are
seen to have a more dramatic effect on bilayer graphene than monolayer graphene
because the quasi-particles are changed in a fundamental way; the dispersion
goes from a quadratic band touching point to linearly dispersing Dirac cones.
We illustrate that a 1D superlattice of either the chemical potential or an
interlayer bias generates multiple anisotropic Dirac cones. General arguments
delineate how certain symmetries protect the Dirac points. We then map the
Hamiltonian of an interlayer bias superlattice onto a chain model comprised of
"topological" modes. This is followed by another study that considers the
effect of a magnetic field on graphene superlattices. We show that
magnetotransport measurements in a weak perpendicular magnetic field probe the
number of emergent Dirac points and reveal details about the dispersion. In the
case of bilayer graphene, we also discuss the properties of kink states in an
applied magnetic field. Finally, we investigate local moment formation of
adatoms on bilayer graphene using an Anderson impurity model. We identify
regions where the local moments can be turned on or off by applying a external
electric fields. In addition, we compute the RKKY interaction between local
moments and show how it too can be controlled with electric fields.


title:
Simulating the Role of Stellar Rotation in the Spectroscopic Effects of
  Differential Limb Magnification

abstract:
  Finite-source effects of gravitationally microlensed stars have been well
discussed in the literature, but the role that stellar rotation plays has been
neglected. A differential magnification map applied to a differentially
Doppler-shifted surface alters the profiles of absorption lines, compromising
their ordinarily symmetric nature. Herein, we assess the degree to which this
finite-source effect of differential limb magnification (DLM), in combination
with stellar rotation, alters spectroscopically derived stellar properties. To
achieve this, we simulated a grid of high-magnification microlensing events
using synthetic spectra. Our analysis shows that rotation of the source
generates differences in the measured equivalent widths of absorption lines
supplementary to DLM alone, but only of the order of a few percent. Using the
wings of H alpha from the same simulated data, we confirmed the result of
Johnson et al. (2010) that DLM alters measurements of effective temperature by
< 100 K for dwarf stars, while showing rotation to bear no additional effect.


title: Rational exponential sums over the divisor function

abstract:
  We consider a problem posed by Shparlinski, of giving nontrivial bounds for
rational exponential sums over the arithmetic function $\tau(n)$, counting the
number of divisors of $n$. This is done using some ideas of Sathe concerning
the distribution in residue classes of the function $\omega(n)$, counting the
number of prime factors of $n$, to bring the problem into a form where, for
general modulus, we may apply a bound of Bourgain concerning exponential sums
over subgroups of finite abelian groups and for prime modulus some results of
Korobov and Shkredov.


title: New aspects of regions whose tilings are enumerated by perfect powers

abstract:
  In 2003, Ciucu presented a unified way to enumerate tilings of lattice
regions by using a certain Reduction Theorem (Ciucu, Perfect Matchings and
Perfect Powers, Journal of Algebraic Combinatorics, 2003). In this paper we
continue this line of work by investigating new families of lattice regions
whose tilings are enumerated by perfect powers or products of several perfect
powers. We prove a multi-parameter generalization of Bo-Yin Yang's theorem on
fortresses (B.-Y. Yang, Ph.D. thesis, Department of Mathematics, MIT, MA,
1991). On the square lattice with zigzag paths, we consider two particular
families of regions whose numbers of tilings are always a power of 3 or twice a
power of 3. The latter result provides a new proof for a conjecture of Matt
Blum first proved by Ciucu. We also consider several new lattices obtained by
periodically applying two simple subgraph replacement rules to the square
lattice. On some of those lattices, we get new families of regions whose
numbers of tilings are given by products of several perfect powers. In
addition, we prove a simple product formula for the number of tilings of a
certain family of regions on a variant of the triangular lattice.


title: Quantum Landau Spin Hall Insulator

abstract:
  We study theoretically the two-dimensional topological electric state in a
single band semiconductor with strong spin-orbit interactions under harmonic
scalar electrostatic potentials. The electronic states described by the spin
Landau levels are insulating in the bulk and host gapless edge states in the
presence of time-reversal symmetry. Such topological states show the properties
of the quantized electric conductivity and the quantized spin Hall conductivity
characterized by the spin Chern number $\mathbb{Z}$. The quantization of the
two conductivities are robust under various perturbations such as the potential
disorder, the Zeeman field, and the spin-orbit scatterings. Existing
semiconductor technologies would realize the topological states discussed in
the present paper.


title:
Asymptotic normality and optimalities in estimation of large Gaussian
  graphical models

abstract:
  The Gaussian graphical model, a popular paradigm for studying relationship
among variables in a wide range of applications, has attracted great attention
in recent years. This paper considers a fundamental question: When is it
possible to estimate low-dimensional parameters at parametric square-root rate
in a large Gaussian graphical model? A novel regression approach is proposed to
obtain asymptotically efficient estimation of each entry of a precision matrix
under a sparseness condition relative to the sample size. When the precision
matrix is not sufficiently sparse, or equivalently the sample size is not
sufficiently large, a lower bound is established to show that it is no longer
possible to achieve the parametric rate in the estimation of each entry. This
lower bound result, which provides an answer to the delicate sample size
question, is established with a novel construction of a subset of sparse
precision matrices in an application of Le Cam's lemma. Moreover, the proposed
estimator is proven to have optimal convergence rate when the parametric rate
cannot be achieved, under a minimal sample requirement. The proposed estimator
is applied to test the presence of an edge in the Gaussian graphical model or
to recover the support of the entire model, to obtain adaptive rate-optimal
estimation of the entire precision matrix as measured by the matrix $\ell_q$
operator norm and to make inference in latent variables in the graphical model.
All of this is achieved under a sparsity condition on the precision matrix and
a side condition on the range of its spectrum. This significantly relaxes the
commonly imposed uniform signal strength condition on the precision matrix,
irrepresentability condition on the Hessian tensor operator of the covariance
matrix or the $\ell_1$ constraint on the precision matrix. Numerical results
confirm our theoretical findings. The ROC curve of the proposed algorithm,
Asymptotic Normal Thresholding (ANT), for support recovery significantly
outperforms that of the popular GLasso algorithm.


title: Higher order log-monotonicity of combinatorial sequences

abstract:
  A sequence $\{z_n\}_{n\geq0}$ is called ratio log-convex in the sense that
the ratio sequence $\{\frac{z_{n+1}}{z_n}\}_{n\geq0}$ is log-convex. Based on a
three-term recurrence for sequences, we develop techniques for dealing with the
ratio log-convexity of ratio sequences. As applications, we prove that the
ratio sequences of numbers, including the derangement numbers, the Motzkin
numbers, the Fine numbers, Franel numbers and the Domb numbers are ratio
log-convex, respectively. Finally, we not only prove that the sequence of
derangement numbers is asymptotically infinitely log-monotonic, but also show
some infinite log-monotonicity of some numbers related to the Gamma function,
in particular, implying two results of Chen {\it et al.} on the infinite
log-monotonicity of the Catalan numbers and the central binomial coefficients.


title: A hadronic scenario for HESS J1818-154

abstract:
  Aims: G15.4+0.1 is a faint supernova remnant (SNR) that has recently been
associated with the gamma-ray source HESS J1818-154. We investigate a hadronic
scenario for the production of the gamma-ray emission. Methods: Molecular 13CO
(J=1-0) taken from the Galactic Ring Survey (GRS) and neutral hydrogen (HI)
data from the Southern Galactic Plane Survey (SGPS) have been used in
combination with new 1420 MHz radio continuum observations carried out with the
Giant Metrewave Radio Telescope (GMRT). Results: From the new observations and
analysis of archival data we provided for the first time a reliable estimate
for the distance to the SNR G15.4+0.1 and discovered molecular clouds located
at the same distance. On the basis of HI absorption features, we estimate the
distance to G15.4+0.1 in 4.8+/-1.0 kpc. The 13CO observations clearly show a
molecular cloud about 5 arcmin in size with two bright clumps, labeled A and B,
clump A positionally associated with the location of HESS J1818-154 and clump B
in coincidence with the brightest northern border of the radio SNR shell. The
HI absorption and the 13CO emission study indicates a possible interaction
between the molecular material and the remnant. We estimate the masses and
densities of the molecular gas as (1.2+/-0.5)X10^3 M_sun and (1.5+/-0.4)X10^3
cm^-3 for clump A and (3.0+/-0.7)X10^3 M_sun and (1.1+/-0.3)X10^3 cm^-3 for
clump B. Calculations show that the average density of the molecular clump A is
sufficient to produce the detected gamma-ray flux, thus favoring a hadronic
origin for the high-energy emission.


title:
Energy-Efficient Optimization for Wireless Information and Power
  Transfer in Large-Scale MIMO Systems Employing Energy Beamforming

abstract:
  In this letter, we consider a large-scale multiple-input multiple-output
(MIMO) system where the receiver should harvest energy from the transmitter by
wireless power transfer to support its wireless information transmission. The
energy beamforming in the large-scale MIMO system is utilized to address the
challenging problem of long-distance wireless power transfer. Furthermore,
considering the limitation of the power in such a system, this letter focuses
on the maximization of the energy efficiency of information transmission (bit
per Joule) while satisfying the quality-of-service (QoS) requirement, i.e.
delay constraint, by jointly optimizing transfer duration and transmit power.
By solving the optimization problem, we derive an energy-efficient resource
allocation scheme. Numerical results validate the effectiveness of the proposed
scheme.


title: The space of complete quotients

abstract:
  We introduce complete quotients over the projective line and prove that they
form smooth projective varieties. The resulting parameter spaces coincide with
the varieties constructed in [HLS11] and [Shao11]. Hence they provide modular
smooth compactifications with normal crossing boundaries of the spaces of
algebraic maps from the projective line to Grassmannian varieties.


title: Study of a WIMP dark matter model with the updated results of CDMS II

abstract:
  The new observation of CDMS II favors low mass WIMPs. Taking the CDMS II new
results as inputs, we consider a SM singlet: the darkon as the dark matter
candidate, which can be either scalar, fermion or vector. It is found that the
simplest scenario of DM+SM conflicts with the stringent constraint set by the
LHC data. New physics beyond the SM is needed, and in this work, we discuss an
extended standard model $SU_L(2)\otimes U_Y(1)\otimes U(1)'$ where $U(1)'$ only
couples to the darkon. The new gauge symmetry is broken into $U_{em}(1)$ and
two neutral bosons $Z^0$ and $Z'$ which are mixtures of $W^3_{\mu},\; B_{\mu}\;
X_{\mu}$ are resulted in. Following the literature and based on the CDMS data,
we make a complete analysis to testify the validity of the model. The cross
section of the elastic scattering between darkon and nucleon is calculated, and
the DM relic density is evaluated in the extended scenario as well. It is found
that considering the constraints from both cosmology and collider experiments,
only if $Z'$ is lighter than $Z^0$, one can reconcile all the presently
available data.


title: An adaptive GMsFEM for high-contrast flow problems

abstract:
  In this paper, we derive an a-posteriori error indicator for the Generalized
Multiscale Finite Element Method (GMsFEM) framework. This error indicator is
further used to develop an adaptive enrichment algorithm for the linear
elliptic equation with multiscale high-contrast coefficients. The GMsFEM, which
has recently been introduced in [12], allows solving multiscale
parameter-dependent problems at a reduced computational cost by constructing a
reduced-order representation of the solution on a coarse grid. The main idea of
the method consists of (1) the construction of snapshot space, (2) the
construction of the offline space, and (3) the construction of the online space
(the latter for parameter-dependent problems). In [12], it was shown that the
GMsFEM provides a flexible tool to solve multiscale problems with a complex
input space by generating appropriate snapshot, offline, and online spaces. In
this paper, we study an adaptive enrichment procedure and derive an
a-posteriori error indicator which gives an estimate of the local error over
coarse grid regions. We consider two kinds of error indicators where one is
based on the $L^2$-norm of the local residual and the other is based on the
weighted $H^{-1}$-norm of the local residual where the weight is related to the
coefficient of the elliptic equation. We show that the use of weighted
$H^{-1}$-norm residual gives a more robust error indicator which works well for
cases with high contrast media. The convergence analysis of the method is
given. In our analysis, we do not consider the error due to the fine-grid
discretization of local problems and only study the errors due to the
enrichment. Numerical results are presented that demonstrate the robustness of
the proposed error indicators.


title: Reconsidering Written Language

abstract:
  A number of elite thinkers in Europe during the 16th and 17th centuries
pursued an agenda which historian Paolo Rossi calls the "quest for a universal
language," a quest which was deeply interwoven with the emergence of the
scientific method. From a modern perspective, one of the many surprising
aspects of these efforts is that they relied on a diverse array of memorization
techniques as foundational elements. In the case of Leibniz's universal
calculus, the ultimate vision was to create a pictorial language that could be
learned by anyone in a matter of weeks and which would contain within it a
symbolic representation of all domains of contemporary thought, ranging from
the natural sciences, to theology, to law. In this brief article, I explore why
this agenda might have been appealing to thinkers of this era by examining
ancient and modern memory feats. As a thought experiment, I suggest that a
society built entirely upon memorization might be less limited than we might
otherwise imagine, and furthermore, that cultural norms discouraging the use of
written language might have had implications for the development of scientific
methodology. Viewed in this light, the efforts of Leibniz and others seem
significantly less surprising. I close with some general observations about
cross-cultural origins of scientific thought.


title:
Carbon and Oxygen Abundances in Cool Metal-rich Exoplanet Hosts: A Case
  Study of the C/O Ratio of 55 Cancri

abstract:
  The super-Earth exoplanet 55 Cnc e, the smallest member of a five-planet
system, has recently been observed to transit its host star. The radius
estimates from transit observations, coupled with spectroscopic determinations
of mass, provide constraints on its interior composition. The composition of
exoplanetary interiors and atmospheres are particularly sensitive to elemental
C/O ratio, which to first order can be estimated from the host stars. Results
from a recent spectroscopic study analyzing the 6300A [O I] line and two C I
lines suggest that 55 Cnc has a carbon-rich composition (C/O=1.12+/-0.09).
However oxygen abundances derived using the 6300A [O I] line are highly
sensitive to a Ni I blend, particularly in metal-rich stars such as 55 Cnc
([Fe/H]=0.34+/-0.18). Here, we further investigate 55 Cnc's composition by
deriving the carbon and oxygen abundances from these and additional C and O
absorption features. We find that the measured C/O ratio depends on the oxygen
lines used. The C/O ratio that we derive based on the 6300A [O I] line alone is
consistent with the previous value. Yet, our investigation of additional
abundance indicators results in a mean C/O ratio of 0.78+/-0.08. The lower C/O
ratio of 55 Cnc determined here may place this system at the sensitive boundary
between protoplanetary disk compositions giving rise to planets with high
(>0.8) versus low (<0.8) C/O ratios. This study illustrates the caution that
must applied when determining planet host star C/O ratios, particularly in
cool, metal-rich stars.


title:
Amino acid precursors from a simulated lower atmosphere of Titan:
  Experiments of cosmic ray energy source with 13 C- and 18 O-stable isotope
  probing mass spectrometry

abstract:
  The organic haze of aerosols that shrouds the Saturnian moon Titan has
previously been studied by both observations and laboratory simulation
experiments. Here we report the abiotic formation of amino acid precursors in
complex organic molecules during experimental simulation of the environment
near Titan's surface with proton irradiation. Pyrolysis of the organic
molecules formed in the simulated Titan atmosphere by proton irradiation at 600
degree-C yielded compounds that contained HCN and NH3. These experimental
results are consistent with the molecular information obtained by pyrolysis gas
chromatography-mass spectrometry (pyrolysis GC-MS) of samples collected by the
Huygens probe to Titan. Scanning electron microscopy (SEM) and
three-dimensional atomic force microscopy (AFM) images of the irradiation
products reveal nanometer-scale filaments and globules in complex amorphous
structures (approximately 1000 Da). Isotope probing experiments by
matrix-assisted laser desorption ionization time-of-flight mass spectrometry
(MALDI-TOF-MS) show that oxygen atoms were incorporated into the racemic amino
acids by hydrolysis of 18O- labeled water. We suggest that the amino acid
precursors possibly formed after water hydrolysis, as suggested in a previous
observational study (C. A. Griffith, T. Owen, T. R. Geballe, J. Rayner, and P.
Rannou, Science, 2003, 300, 628). We propose that cosmic rays are a significant
and effective energy source for producing complex organics and amino acid
precursors in Titan's atmospheric haze.


title: On The Hereditary Discrepancy of Homogeneous Arithmetic Progressions

abstract:
  We show that the hereditary discrepancy of homogeneous arithmetic
progressions is lower bounded by $n^{1/O(\log \log n)}$. This bound is tight up
to the constant in the exponent. Our lower bound goes via proving an
exponential lower bound on the discrepancy of set systems of subcubes of the
boolean cube $\{0, 1\}^d$.


title:
Mechanical design and analysis for a low beta squeezed half-wave
  resonator

abstract:
  A superconducting half-wave resonator (HWR) of frequency=162.5 MHz and
{\beta}=0.09 has been developed at Institute of Modern Physics. Mechanical
stability of the low beta HWR cavity is a big challenge in cavity design and
optimization. The mechanical deformations of a radio frequency superconducting
cavity could be a source of instability, both in continues wave(CW) operation
or in pulsed mode. Generally, the lower beta cavities have stronger Lorentz
force detuning than that of the higher beta cavities. In this paper, a basic
design consideration in the stiffening structure for the detuning effect caused
by helium pressure and Lorentz force has been presented. The mechanical modal
analysis has been investigated with finite element method(FEM). Based on these
considerations, a new stiffening structure has been promoted for the HWR
cavity. The computation results concerning the frequency shift show that the
low beta HWR cavity with new stiffening structure has low frequency sensitivity
coefficient, Lorentz force detuning coefficient KL and stable mechanical
property.


title: Almost Linear Complexity Methods for Delay-Doppler Channel Estimation

abstract:
  A fundamental task in wireless communication is channel estimation: Compute
the channel parameters a signal undergoes while traveling from a transmitter to
a receiver. In the case of delay-Doppler channel, i.e., a signal undergoes only
delay and Doppler shifts, a widely used method to compute delay-Doppler
parameters is the pseudo-random method. It uses a pseudo-random sequence of
length N; and, in case of non-trivial relative velocity between transmitter and
receiver, its computational complexity is O(N^2logN) arithmetic operations. In
[1] the flag method was introduced to provide a faster algorithm for
delay-Doppler channel estimation. It uses specially designed flag sequences and
its complexity is O(rNlogN) for channels of sparsity r. In these notes, we
introduce the incidence and cross methods for channel estimation. They use
triple-chirp and double-chirp sequences of length N, correspondingly. These
sequences are closely related to chirp sequences widely used in radar systems.
The arithmetic complexity of the incidence and cross methods is O(NlogN + r^3),
and O(NlogN + r^2), respectively.


title: False Theta Functions and the Verlinde formula

abstract:
  We discover new analytic properties of classical partial and false theta
functions and their potential applications to representation theory of
W-algebras and vertex algebras in general. More precisely, motivated by clues
from conformal field theory, first, we are able to determine modular-like
transformation properties of regularized partial and false theta functions.
Then, after suitable identification of regularized partial/false theta
functions with the characters of atypical modules for the singlet vertex
algebra W(2,2p-1), we formulate and prove a Verlinde-type formula for the
fusion rules of irreducible W(2,2p-1)-modules.


title:
Representation stability in cohomology and asymptotics for families of
  varieties over finite fields

abstract:
  We consider two families X_n of varieties on which the symmetric group S_n
acts: the configuration space of n points in C and the space of n linearly
independent lines in C^n. Given an irreducible S_n-representation V, one can
ask how the multiplicity of V in the cohomology groups H*(X_n;Q) varies with n.
We explain how the Grothendieck-Lefschetz Fixed Point Theorem converts a
formula for this multiplicity to a formula for the number of polynomials over
F_q (or maximal tori in GL_n(F_q), respectively) with specified properties
related to V. In particular, we explain how representation stability in
cohomology, in the sense of [CF, arXiv:1008.1368] and [CEF, arXiv:1204.4533],
corresponds to asymptotic stability of various point counts as n goes to
infinity.


title: Derived categories of $N$-complexes

abstract:
  We study the homotopy category $\mathsf{K}_{N}(\mathcal{B})$ of $N$-complexes
of an additive category $\mathcal{B}$ and the derived category
$\mathsf{D}_{N}(\mathcal{A})$ of an abelian category $\mathcal{A}$. First we
show that both $\mathsf{K}_N(\mathcal{B})$ and $\mathsf{D}_N(\mathcal{A})$ have
natural structures of triangulated categories. Then we establish a theory of
projective (resp., injective) resolutions and derived functors. Finally, under
some conditions of an abelian category $\mathcal{A}$, we show that
$\mathsf{D}_{N}(\mathcal{A})$ is triangle equivalent to the ordinary derived
category $\mathsf{D}(\mathsf{Morph}_{N-2}(\mathcal{A}))$ where
$\mathsf{Morph}_{N-2}(\mathcal{A})$ is the category of sequential $N-2$
morphisms of $\mathcal{A}$.


title:
Two-dimensional superconductivity at the interface of a Bi2Te3/FeTe
  heterostructure

abstract:
  Superconductivity at the interface of a heterostructure confined to
nanometer-sized scale offers unique opportunities to study the exotic physics
of two-dimensional superconductivity. The realization of superconductivity at
the interface between a topological insulator and an iron-chalcogenide compound
is highly attractive for exploring several recent theoretical predictions
involving these two new classes of materials. Here, we report transport
measurements on a Bi2Te3/FeTe heterostructure fabricated via van der Waals
epitaxy, which demonstrate superconductivity at the interface induced by the
Bi2Te3 epilayer with thickness even down to one quintuple layer. The
two-dimensional nature of the observed superconductivity with the highest
transition temperature around 12 K was verified by the existence of a
Berezinsky-Kosterlitz-Thouless transition and the diverging ratio of in-plane
to out-plane upper critical field on approaching the superconducting transition
temperature. With the combination of interface superconductivity and Dirac
surface states of Bi2Te3, the heterostructure studied in this work provides a
novel platform for realizing Majorana fermions.


title:
Persistent Monitoring of Events with Stochastic Arrivals at Multiple
  Stations

abstract:
  This paper introduces a new mobile sensor scheduling problem, involving a
single robot tasked with monitoring several events of interest that occur at
different locations. Of particular interest is the monitoring of transient
events that can not be easily forecast. Application areas range from natural
phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano
using a ground robot) to urban activities ({\em e.g.}, monitoring early
formations of traffic congestion using an aerial robot). Motivated by those and
many other examples, this paper focuses on problems in which the precise
occurrence times of the events are unknown {\em a priori}, but statistics for
their inter-arrival times are available. The robot's task is to monitor the
events to optimize the following two objectives: {\em (i)} maximize the number
of events observed and {\em (ii)} minimize the delay between two consecutive
observations of events occurring at the same location. The paper considers the
case when a robot is tasked with optimizing the event observations in a
balanced manner, following a cyclic patrolling route. First, assuming the
cyclic ordering of stations is known, we prove the existence and uniqueness of
the optimal solution, and show that the optimal solution has desirable
convergence and robustness properties. Our constructive proof also produces an
efficient algorithm for computing the unique optimal solution with $O(n)$ time
complexity, in which $n$ is the number of stations, with $O(\log n)$ time
complexity for incrementally adding or removing stations. Except for the
algorithm, most of the analysis remains valid when the cyclic order is unknown.
We then provide a polynomial-time approximation scheme that gives a
$(1+\epsilon)$-optimal solution for this more general, NP-hard problem.


title:
Numerical implementation of geodesic X-ray transforms and their
  inversion

abstract:
  We present a numerical implementation of the geodesic ray transform and its
inversion over functions and solenoidal vector fields on two-dimensional
Riemannian manifolds. For each problem, inversion formulas previously derived
in \cite{Pestov2004,Krishnan2010} are implemented in the case of simple and
some non-simple metrics. These numerical tools are also used to better
understand and gain intuition about non-simple manifolds, for which injectivity
and stability of the corresponding integral geometric problems are still under
active study.


title: Neutrinos from collapsars

abstract:
  Long gamma-ray bursts (GRBs) are associated with the gravitational collapse
of very massive stars. The central engine of a GRB can collimate relativistic
jets that propagate inside the stellar envelope. The shock waves produced when
the jet disrupts the stellar surface are capable of accelerating particles up
to very high energies. If the jet has hadronic content, neutrinos will be
produced via charged pion decays. The main goal of this work is to estimate the
neutrino emission produced in the region close to the surface of the star,
taking pion and muon cooling into account, along with subtle effects arising
from neutrino production in a highly magnetized medium. We estimate the maximum
energies of the different kinds of particles and solve the coupled transport
equations for each species. Once the particle distributions are known, we
calculate the intensity of neutrinos. We study the different effects on the
neutrinos that can change the relative weight of different flavors. In
particular, we consider the effects of neutrino oscillations, and of neutrino
spin precession caused by strong magnetic fields. The expected neutrino signals
from the shocks in the uncorking regions of Population III events is very weak,
but the neutrino signal produced by Wolf-Rayet GRBs with $z<0.5$ is not far
from the level of the atmospheric background. The IceCube experiment does not
have the sensitivity to detect neutrinos from the implosion of the earliest
stars, but a number of high-energy neutrinos may be detected from nearby long
GRBs. The cumulative signal should be detectable over several years ($\sim 10$
yr) of integration with the full 86-string configuration.


title:
Photometry Using Kepler "Superstamps" of Open Clusters NGC 6791 & NGC
  6819

abstract:
  The Kepler space telescope has proven to be a gold mine for the study of
variable stars. Unfortunately, Kepler only returns a handful of pixels
surrounding each star on the target list, which omits a large number of stars
in the Kepler field. For the open clusters NGC 6791 and NGC 6819, Kepler also
reads out larger superstamps which contain complete images of the central
region of each cluster. These cluster images can potentially be used to study
additional stars in the open clusters. We present preliminary results from
using traditional photometric techniques to identify and analyze additional
variable stars from these images.


title: Galois descent for completed Algebraic K-theory

abstract:
  In this paper we consider the problem of Galois descent for suitably
completed algebraic K-theory of fields. One of the main results is a suitable
form of rigidity for Borel-style generalized equivariant cohomology with
respect to certain spectra. In order to apply this to the problem at hand, we
need to invoke a derived Atiyah-Segal completion theorem for pro-groups. In the
present paper, the authors apply such a derived completion theorem proven by
the first author elsewhere. These two results provide a proof of the Galois
descent problem for equivariant algebraic K-theory as formulated by the first
author, at least when restricted to the case where the absolute Galois groups
are pro-$l$ groups for some prime $l$ different from the characteristic of the
base field and the K-theory spectrum is completed at the same prime $l$. Work
in progress hopes to remove these restrictions.


title:
Effect of Strain disorder on the magnetic glassy state in
  La5/8-yPryCa3/8MnO3 (y = 0.45) thin films

abstract:
  Present study reveals that the free energy landscape of the
La5/8-yPryCa3/8MnO3 (LPCMO) system could be modified by elastic strain
interaction in the epitaxial thin films. Epitaxial LPCMO thin films of various
thicknesses are grown on LaAlO3 substrate by pulsed laser deposition. With
increasing thickness, by virtue of island growth morphology, strain disorder is
invoked in thin films during strain relaxation process. The length-scale of
phase separation is found to be highly correlated with strain disorder.
Magneto-transport measurements demonstrate that coherent strain stabilizes
charge ordered insulating phase while strain disorder stabilizes metallic
phase. Resistivity under cooling and heating in unequal field (CHUF) protocol
exhibits lower value of freezing temperature for strain disordered films
compared to bulk system. Raman spectroscopy reveals that the charge ordered
insulating and ferromagnetic metallic phases are structurally dissimilar and
possess monoclinic and rhombohedral like symmetries respectively. Interfaces
between two phases strongly influence low temperature glassy metastable state
resulting in different phase separation states in the LPCMO thin films.


title:
Non-negative Matrix Factorization with Linear Constraints for
  Single-Channel Speech Enhancement

abstract:
  This paper investigates a non-negative matrix factorization (NMF)-based
approach to the semi-supervised single-channel speech enhancement problem where
only non-stationary additive noise signals are given. The proposed method
relies on sinusoidal model of speech production which is integrated inside NMF
framework using linear constraints on dictionary atoms. This method is further
developed to regularize harmonic amplitudes. Simple multiplicative algorithms
are presented. The experimental evaluation was made on TIMIT corpus mixed with
various types of noise. It has been shown that the proposed method outperforms
some of the state-of-the-art noise suppression techniques in terms of
signal-to-noise ratio.


title: On quantum conditional entropies defined in terms of the $f$-divergences

abstract:
  We consider a family of quantum conditional entropies based on the concept of
quantum $f$-divergences. First, we explicitly formulate conditions under which
the notion of quantum conditional entropy is well defined in this way. In
particular, we demand that the value of conditional entropy be independent of
any extension of the principal Hilbert space. Using fundamental properties of
the quantum $f$-divergences, several interesting relations for such conditional
entropies are formulated. We separately examine an especially important case of
quantum conditional entropies related to the Tsallis divergence.


title: A diagrammatic categorification of a Clifford algebra

abstract:
  We give a graphical calculus for a categorification of a Clifford algebra and
its Fock space representation via differential graded categories. The
categorical action is motivated by the gluing action between the contact
categories of infinite strips.


title:
The moduli space of 4-dimensional non-nilpotent complex associative
  algebras

abstract:
  In this paper we study the moduli space of 4-dimensional complex associative
algebras. We use extensions to compute the moduli space, and then give a
decomposition of this moduli space into strata consisting of complex projective
orbifolds, glued together through jump deformations. Because the space of
4-dimensional algebras is large, we only classify the non-nilpotent algebras in
this paper.


title: Precise Tully-Fisher Relations without Galaxy Inclinations

abstract:
  Power-law relations between tracers of baryonic mass and rotational
velocities of disk galaxies, so-called Tully-Fisher relations (TFRs), offer a
wealth of applications in galaxy evolution and cosmology. However, measurements
of rotational velocities require galaxy inclinations, which are difficult to
measure, thus limiting the range of TFR studies. This work introduces a maximum
likelihood estimation (MLE) method for recovering the TFR in galaxy samples
with limited or no information on inclinations. The robustness and accuracy of
this method is demonstrated using virtual and real galaxy samples.
Intriguingly, the MLE reliably recovers the TFR of all test samples, even
without using any inclination measurements - that is, assuming a
sin(i)-distribution for galaxy inclinations. Explicitly, this 'inclination-free
MLE' recovers the three TFR parameters (zero-point, slope, scatter) with
statistical errors only about 1.5-times larger than the best estimates based on
perfectly known galaxy inclinations with zero uncertainty. Thus, given
realistic uncertainties, the inclination-free MLE is highly competitive. If
inclination measurements have mean errors larger than 10 degrees, it is better
not to use any inclinations, than to consider the inclination measurements to
be exact. The inclination-free MLE opens interesting perspectives for future HI
surveys by the SKA and its pathfinders.


title:
Performance Analysis of Boron Nitride Embedded Armchair Graphene
  Nanoribbon MOSFET with Stone Wales Defects

abstract:
  We study the performance of a hybrid Graphene-Boron Nitride {GNR-BN} armchair
nanoribbon {a-GNR-BN} MOSFET at its ballistic transport limit. We consider
three geometric configurations 3p, 3p+1 and 3p+2 of a-GNR-BN with BN atoms
embedded on both sides {2, 4 and 6 BN on each side} on the GNR. The material
properties like band gap, effective mass and density of states of these
H-passivated structures have been evaluated using the Density Functional Theory
{DFT}. Using these material parameters, self-consistent Poisson-Schrodinger
simulations are carried out under the Non Equilibrium Greens Function {NEGF}
formalism to calculate the ballistic MOSFET device characteristics. For a
hybrid nanoribbon of width ~ 5 nm, the simulated ON current is found to be in
the range 276 uA - 291 uA with an ON/OFF ratio 7.1 x 10^6 - 7.4 x 10^6 for a
VDD = 0.68 V corresponds to 10 nm technology node. We further study the impact
of randomly distributed Stone Wales {SW} defects in these hybrid structures and
only 2.52% degradation of ON current is observed for SW defect density of
6.35%.


title: An explicit Baker type lower bound of exponential values

abstract:
  Let $\mathbb{I}$ denote an imaginary quadratic field or the field
$\mathbb{Q}$ of rational numbers and $\mathbb{Z}_{\mathbb{I}}$ its ring of
intergers. We shall prove an explicit Baker type lower bound for
$\mathbb{Z}_{\mathbb{I}}$-linear form of the numbers \begin{equation}\label{1}
1,\ e^{\alpha_1},...,\ e^{\alpha_m},\quad m\ge 2, \end{equation} where
$\alpha_0=0$, $\alpha_1,...,\alpha_m$, are $m+1$ different numbers from the
field $\mathbb{I}$. Our work gives gives some improvements to the existing
explicit versions of of Baker's work about exponential values at rational
points. In particilar, dependences on $m$ are improved.


title:
Matrix Fourier transform in dynamic theory of elasticity of piecewise
  homogeneous medium

abstract:
  The analytical solving dynamic problems of elasticity theory for piecewise
homogeneous half-space is found. The explicit construction of direct and
inverse Fourier's vector transform with discontinuous coefficients is
presented. The technique of applying Fourier's vector transform with
discontinuous coefficients for solving problems of mathematical physics in the
heterogeneous environments is developed on an example of the dynamic problems
of the elasticity theory.


title: An Equivalent Gauge and the Equivalence Theorem

abstract:
  I describe a novel covariant formulation of massive gauge theories in which
the longitudinal polarization vectors do not grow with the energy. Therefore in
the present formalism, differently from the ordinary one, the energy and
coupling power-counting is completely transparent at the level of individual
Feynman diagrams, with obvious advantages both at the conceptual and practical
level.
  Since power-counting is transparent, the high-energy limit of the amplitudes
involving longitudinal particles is immediately taken, and the Equivalence
Theorem is easily demonstrated at all orders in perturbation theory. Since the
formalism makes the Equivalence Theorem self-evident, and because it is based
on a suitable choice of the gauge, we can call it an "Equivalent Gauge".


title:
The Astronomical and Ethnological Components of the Cult of Bird-Man on
  Easter Island

abstract:
  The bird-man cult remains the main secret of Easter Island (Rapa Nui), a
remote plot of land in the Pacific. This paper includes not only necessary
ethnological data, but also some results on the archaeoastronomy. The research
of some lines marked on a stone calendar from the Mataveri area, an archaic
zone of the bird-man cult, allows to insist that the natives watched at least
the stars Canopus and Aldebaran. There are strong grounds for believing that,
among others, the Sun, the Moon as well as Beta and Alpha Centauri were the
matter for quasi-scientific enquiry. Several astronomical and calendar records
in the rock art and in the script have been decoded.


title: A logical loophole in the derivation of the CHSH Bell-type inequality

abstract:
  We point out a loophole in the derivation of the Bell inequalities in the
form proposed by Clauser, Horne, Shimony and Holt (CHSH). In this derivation it
is assumed that statistical independence is a necessary consequence of
locality, but this is not a logical necessity.


title:
Reduced-rank Regression in Sparse Multivariate Varying-Coefficient
  Models with High-dimensional Covariates

abstract:
  In genetic studies, not only can the number of predictors obtained from
microarray measurements be extremely large, there can also be multiple response
variables. Motivated by such a situation, we consider semiparametric dimension
reduction methods in sparse multivariate regression models. Previous studies on
joint variable and rank selection have focused on parametric models while here
we consider the more challenging varying-coefficient models which make the
investigation on nonlinear interactions of variables possible. Spline
approximation, rank constraints and concave group penalties are utilized for
model estimation. Asymptotic oracle properties of the estimators are presented.
We also propose reduced-rank independent screening to deal with the situation
when the dimension is so high that penalized estimation cannot be efficiently
applied. In simulations, we show the advantages of simultaneously performing
variable and rank selection. A real data set is analyzed to illustrate the good
prediction performance when incorporating interactions between genetic
variables and an index variable.


title: Theta dependence of 4D SU(N) gauge theories at finite temperature

abstract:
  We report a study of the dependence of 4D SU(N) gauge theories on the
topological theta term at finite temperature, and in particular in the large-N
limit. We show that the theta dependence drastically changes across the
deconfinement transition. The low-temperature phase is characterized by a
large-N scaling with theta/N as relevant variable, while in the
high-temperature phase the free energy is essentially determined by the dilute
instanton-gas approximation, with a simple theta dependence of the free-energy
density proportional to 1-Cos(theta).


title: Flat G-bundles and regular strata for reductive groups

abstract:
  Let LG be an algebraic loop group associated to a reductive group G. A
fundamental stratum is a triple consisting of a point x in the Bruhat-Tits
building of LG, a nonnegative real number r, and a character of the
corresponding depth r Moy-Prasad subgroup that satisfies a non-degeneracy
condition. The authors have shown in previous work how to associate a
fundamental stratum to a formal flat G-bundle and used this theory to define
its slope. In this paper, the authors study fundamental strata that satisfy an
additional regular semisimplicity condition. Flat G-bundles that contain
regular strata have a natural reduction of structure to a (not necessarily
split) maximal torus in LG, and the authors use this property to compute the
corresponding moduli spaces. This theory generalizes a natural condition on
algebraic connections (the GL_n case), which plays an important role in the
global analysis of meromorphic connections and isomonodromic deformations.


title: Piecewise deterministic Markov process - recent results

abstract:
  We give a short overview of recent results on a specific class of Markov
process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall
the definition of these processes and give some general results. On more
specific cases such as the TCP model or a model of switched vector fields,
better results can be proved, especially as regards long time behaviour. We
continue our review with an infinite dimensional example of neuronal activity.
From the statistical point of view, these models provide specific challenges:
we illustrate this point with the example of the estimation of the distribution
of the inter-jumping times. We conclude with a short overview on numerical
methods used for simulating PDMPs.


title: The early-type near-contact binary system V337 Aql revisited

abstract:
  The close binary V337 Aql consists of two early B-type components with an
orbital period of 2.7339 d. New multi-band photometric observations of the
system together with published radial velocities enabled us to derive the
absolute parameters of the components. The simultaneous light and radial
velocity curves solution yields masses and radii of
\emph{M$_{1}$}=17.44$\pm$0.31 \emph{M$_\odot$} and \emph{R$_{1}$}=9.86$\pm$0.06
\emph{R$_\odot$} for the primary and \emph{M$_{2}$}=7.83$\pm$0.18
\emph{M$_\odot$} and \emph{R$_{2}$}=7.48$\pm$0.04 \emph{R$_\odot$} for the
secondary component. Derived fundamental parameters allow us to calculate the
photometric distance as 1355$\pm$160 pc. The present analysis indicates that
the system is a near-contact semi-detached binary, in which a primary star is
inside its Roche lobe with a filling ratio of 92 percent and the secondary star
fills its Roche lobe. From \emph{O-C} data analysis, an orbital period decrease
was determined with a rate of -7.6 $\times$ 10$^{-8}$ yr$^{-1}$. Kinematic
analysis reveals that V337 Aql has a circular orbit in the Galaxy and belongs
to a young thin-disc population.


title: Summation of coefficients of polynomials on $\ell_{p}$ spaces

abstract:
  We investigate the summability of the coefficients of $m$-homogeneous
polynomials and $m$-linear mappings defined on $\ell_{p}$-spaces. In our
research we obtain results on the summability of the coefficients of $m$-linear
mappings defined on $\ell_{p_{1}} \times \cdots \times \ell_{p_{m}}$. The first
results in this respect go back to Littlewood and Bohnenblust and Hille (for
bilinear and $m$-linear forms on $c_{0}$) and Hardy and Littlewood and
Praciano-Pereira (for bilinear and $m$-linear forms on arbitrary
$\ell_{p}$-spaces). Our results recover and in some case complete these old
results through a general approach on vector valued $m$-linear mappings.


title:
Numerical solutions of a class of second order boundary value problems
  on using Bernoulli Polynomials

abstract:
  The aim of this paper is to find the numerical solutions of the second order
linear and nonlinear differential equations with Dirichlet, Neumann and Robin
boundary conditions. We use the Bernoulli polynomials as linear combination to
the approximate solutions of 2nd order boundary value problems. Here the
Bernoulli polynomials over the interval [0, 1] are chosen as trial functions so
that care has been taken to satisfy the corresponding homogeneous form of the
Dirichlet boundary conditions in the Galerkin weighted residual method. In
addition to that the given differential equation over arbitrary finite domain
[a, b] and the boundary conditions are converted into its equivalent form over
the interval [0, 1]. All the formulas are verified by considering numerical
examples. The approximate solutions are compared with the exact solutions, and
also with the solutions of the existing methods. A reliable good accuracy is
obtained in all cases.


title: Thermal and non-thermal emission in the Cygnus X region

abstract:
  Radio continuum observations detect non-thermal synchrotron and thermal
bremsstrahlung radiation. Separation of the two different emission components
is crucial to study the properties of diffuse interstellar medium. The Cygnus X
region is one of the most complex areas in the radio sky which contains a
number of massive stars and HII regions on the diffuse thermal and non-thermal
background. More supernova remnants are expected to be discovered. We aim to
develop a method which can properly separate the non-thermal and thermal radio
continuum emission and apply it to the Cygnus X region. The result can be used
to study the properties of different emission components and search for new
supernova remnants in the complex. Multi-frequency radio continuum data from
large-scale surveys are used to develop a new component separation method.
Spectral analysis is done pixel by pixel for the non-thermal synchrotron
emission with a realistic spectral index distribution and a fixed spectral
index of beta = -2.1 for the thermal bremsstrahlung emission. With the new
method, we separate the non-thermal and thermal components of the Cygnus X
region at an angular resolution of 9.5arcmin. The thermal emission component is
found to comprise 75% of the total continuum emission at 6cm. Thermal diffuse
emission, rather than the discrete HII regions, is found to be the major
contributor to the entire thermal budget. A smooth non-thermal emission
background of 100 mK Tb is found. We successfully make the large-extent known
supernova remnants and the HII regions embedded in the complex standing out,
but no new large SNRs brighter than Sigma_1GHz = 3.7 x 10^-21 W m^-2 Hz^-1
sr^-1 are found.


title:
Bridging physiological and evolutionary time scales in a gene regulatory
  network

abstract:
  Gene regulatory networks (GRN) govern phenotypic adaptations and reflect the
trade-offs between physiological responses and evolutionary adaptation that act
at different time scales. To identify patterns of molecular function and
genetic diversity in GRNs, we studied the drought response of the common
sunflower, Helianthus annuus, and how the underlying GRN is related to its
evolution. We examined the responses of 32,423 expressed sequences to drought
and to abscisic acid and selected 145 co-expressed transcripts. We
characterized their regulatory relationships in nine kinetic studies based on
different hormones. From this, we inferred a GRN by meta-analyses of a Gaussian
graphical model and a random forest algorithm and studied the genetic
differentiation among populations (FST) at nodes. We identified two main hubs
in the network that transport nitrate in guard cells. This suggests that
nitrate transport is a critical aspect of sunflower physiological response to
drought. We observed that differentiation of the network genes in elite
sunflower cultivars is correlated with their position and connectivity. This
systems biology approach combined molecular data at different time scales and
identified important physiological processes. At the evolutionary level, we
propose that network topology could influence responses to human selection and
possibly adaptation to dry environments.


title:
Semiempirical pseudopotential approach for nitride-based nanostructures
  and {\it ab initio} based passivation of free surfaces

abstract:
  We present a semiempirical pseudopotential method based on screened atomic
pseudopotentials and derived from \textit{ab initio} calculations. This
approach is motivated by the demand for pseudopotentials able to address
nanostructures, where \textit{ab initio} methods are both too costly and
insufficiently accurate at the level of the local-density approximation, while
mesoscopic effective-mass approaches are inapplicable due to the small size of
the structures along, at least, one dimension. In this work we improve the
traditional pseudopotential method by a two-step process: First, we invert a
set of self-consistently determined screened {\it ab initio} potentials in
wurtzite GaN for a range of unit cell volumes, thus determining
spherically-symmetric and structurally averaged atomic potentials. Second, we
adjust the potentials to reproduce observed excitation energies. We find that
the adjustment represents a reasonably small perturbation over the potential,
so that the ensuing potential still reproduces the original wave functions,
while the excitation energies are significantly improved. We furthermore deal
with the passivation of the dangling bonds of free surfaces which is relevant
for the study of nanowires and colloidal nanoparticles. We present a
methodology to derive passivant pseudopotentials from {\it ab initio}
calculations. We apply our pseudopotential approach to the exploration of the
confinement effects on the electronic structure of GaN nanowires.


title: Off-Criticality and the Massive Brownian Loop Soup

abstract:
  We introduce a natural "massive" version of the Brownian loop soup of Lawler
and Werner which displays conformal covariance and exponential decay. We show
that this massive Brownian loop soup arises as the near-critical scaling limit
of a random walk loop soup with killing and is related to the massive SLE(2)
identified by Makarov and Smirnov as the near-critical scaling limit of a
loop-erased random walk with killing. We conjecture that the massive Brownian
loop soup describes the zero level lines of the massive Gaussian free field,
and discuss possible relations to other models, such as Ising, in the
off-critical regime.

categories: math.PR cond-mat.stat-mech math-ph math.MP


title: Beyond the Shannon's Bound

abstract:
  Let $G=(V,E)$ be a multigraph of maximum degree $\Delta$. The edges of $G$
can be colored with at most $\frac{3}{2}\Delta$ colors by Shannon's theorem. We
study lower bounds on the size of subgraphs of $G$ that can be colored with
$\Delta$ colors.
  Shannon's Theorem gives a bound of
$\frac{\Delta}{\lfloor\frac{3}{2}\Delta\rfloor}|E|$. However, for $\Delta=3$,
Kami\'{n}ski and Kowalik [SWAT'10] showed that there is a 3-edge-colorable
subgraph of size at least $\frac{7}{9}|E|$, unless $G$ has a connected
component isomorphic to $K_3+e$ (a $K_3$ with an arbitrary edge doubled). Here
we extend this line of research by showing that $G$ has a $\Delta$-edge
colorable subgraph with at least
$\frac{\Delta}{\lfloor\frac{3}{2}\Delta\rfloor-1}|E|$ edges, unless $\Delta$ is
even and $G$ contains $\frac{\Delta}{2}K_3$ or $\Delta$ is odd and $G$ contains
$\frac{\Delta-1}{2}K_3+e$. Moreover, the subgraph and its coloring can be found
in polynomial time.
  Our results have applications in approximation algorithms for the Maximum
$k$-Edge-Colorable Subgraph problem, where given a graph $G$ (without any bound
on its maximum degree or other restrictions) one has to find a
$k$-edge-colorable subgraph with maximum number of edges. In particular, for
every even $k \ge 4$ we obtain a $\frac{2k+2}{3k+2}$-approximation and for
every odd $k\ge 5$ we get a $\frac{2k+1}{3k}$-approximation. When $4\le k \le
13$ this improves over earlier algorithms due to Feige et al. [APPROX'02]


title: Orders on free groups induced by oriented words

abstract:
  For every finite rank k, k>1, we explicitly construct (2k)! left orders on
the free group F_k of rank k. Each order is induced by a word of length 2k in
which each generator of F_k and its inverse appear exactly once. For each of
these (2k)! words we define a real valued function on F_k, which is shown to be
a quasi-character with small relative defect and which is used as a weight
function to define the corresponding order (the elements of F_k which evaluate
to positive real numbers are declared positive in the group). Some of the
orders we define on F_k are extensions of the usual lexicographic order on the
positive monoid and some have word reversible positive cones. We characterize
the defining words leading to orders of either of these two types.


title:
Boundedness of the Bergman projection on $L^p$ spaces with exponential
  weights

abstract:
  Let $v(r)=\exp\left(-\frac{\alpha}{1-r}\right)$ with $\alpha>0$, and let
$\mathbb{D}$ be the unit disc in the complex plane. Denote by $A^p_v$ the
subspace of analytic functions of $L^p(\mathbb{D},v)$ and let $P_v$ be the
orthogonal projection from $L^2(\mathbb{D},v)$ onto $A^2_v$. In 2004, Dostanic
revealed the intriguing fact that $P_v$ is bounded from $L^p(\mathbb{D},v)$ to
$A^p_v$ only for $p=2$, and he posed the related problem of identifying the
duals of $A^p_v$ for $p\ge 1$, $p\neq 2$. In this paper we propose a solution
to this problem by proving that $P_v$ is bounded from $\,L^p(\D,v^{p/2})$ to
$A^p_{v^{p/2}}$ whenever $1\le p <\infty$, and, consequently, the dual of
$A^p_{v^{p/2}}$ for $p\ge 1$ can be identified with $A^{q}_{v^{q/2}}$, where
$1/p+1/q=1$. In addition, we also address a similar question on some classes of
weighted Fock spaces.


title:
Reproducing kernel estimates, bounded projections and duality on large
  weighted Bergman spaces

abstract:
  We obtain ceratin estimates for the reproducing kernels of large weighted
Bergman spaces. Applications of these estimates to boundedness of the Bergman
projection on $L^p(\D,\omega ^{p/2})$, complex interpolation and duality of
weighted Bergman spaces are given.


title:
Improved Analyses for SP and CoSaMP Algorithms in Terms of Restricted
  Isometry Constants

abstract:
  In the context of compressed sensing (CS), both Subspace Pursuit (SP) and
Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative
greedy recovery algorithms which could reduce the recovery complexity greatly
comparing with the well-known $\ell_1$-minimization. Restricted isometry
property (RIP) and restricted isometry constant (RIC) of measurement matrices
which ensure the convergency of iterative algorithms play key roles for the
guarantee of successful reconstructions. In this paper, we show that for the
$s$-sparse recovery, the RICs are enlarged to $\delta_{3s}<0.4859$ for SP and
$\delta_{4s}<0.5$ for CoSaMP, which improve the known results significantly.
The proposed results also apply to almost sparse signal and corrupted
measurements.