title: Topological Polarization in Graphene-like Systems

abstract:
  In this article we investigate the possibility of generating piezoelectric
orbital polarization in graphene-like systems which are deformed periodically.
We start with discrete two-level models which depend on control parameters; in
this setting, time-dependent model hamiltonians are described by loops in
parameter space. Then, the gap structure at a given Fermi energy generates a
non-trivial topology on parameter space which then leads to possibly
non-trivial polarizations. More precisely, we show the polarization, as given
by the *King-Smith--Vanderbilt formula*, depends only on the homotopy class of
the loop; hence, a necessary condition for non-trivial piezo effects is that
the fundamental group of the gapped parameter space must not be trivial. The
use of the framework of non-commutative geometry implies our results extend to
systems with weak disorder. We then apply this analysis to the uniaxial strain
model for graphene which includes nearest-neighbor hopping and a stagger
potential, and show that it supports non-trivial piezo effects; this is in
agreement with recent physics literature.

categories: math-ph cond-mat.mes-hall cond-mat.mtrl-sci math.MP


title:
Augmenting the Immersed Boundary Method with Radial Basis Functions
  (RBFs) for the Modeling of Platelets in Hemodynamic Flows

abstract:
  We present a new computational method by extending the Immersed Boundary (IB)
method with a spectrally-accurate geometric model based on Radial Basis
Function (RBF) interpolation of the Lagrangian structures. Our specific
motivation is the modeling of platelets in hemodynamic flows, though we
anticipate that our method will be useful in other applications as well. The
efficacy of our new RBF-IB method is shown through a series of numerical
experiments. Specifically, we compare our method with the traditional IB method
in terms of convergence and accuracy, computational cost, maximum stable
time-step size and volume loss. We conclude that the RBF-IB method has
advantages over the traditional Immersed Boundary method, and is well-suited
for modeling of platelets in hemodynamic flows.


title:
The Ergodic Capacity of the Multiple Access Channel Under Distributed
  Scheduling - Order Optimality of Linear Receivers

abstract:
  Consider the problem of a Multiple-Input Multiple-Output (MIMO)
Multiple-Access Channel (MAC) at the limit of large number of users. Clearly,
in practical scenarios, only a small subset of the users can be scheduled to
utilize the channel simultaneously. Thus, a problem of user selection arises.
However, since solutions which collect Channel State Information (CSI) from all
users and decide on the best subset to transmit in each slot do not scale when
the number of users is large, distributed algorithms for user selection are
advantageous.
  In this paper, we analyse a distributed user selection algorithm, which
selects a group of users to transmit without coordinating between users and
without all users sending CSI to the base station. This threshold-based
algorithm is analysed for both Zero-Forcing (ZF) and Minimum Mean Square Error
(MMSE) receivers, and its expected sum-rate in the limit of large number of
users is investigated. It is shown that for large number of users it achieves
the same scaling laws as the optimal centralized scheme.


title: Lifshitz Hydrodynamics

abstract:
  We construct the hydrodynamics of quantum critical points with Lifshitz
scaling. There are new dissipative effects allowed by the lack of boost
invariance. The formulation is applicable, in general, to any fluid with an
explicit breaking of boost symmetry. We use a Drude model of a strange metal to
study the physical effects of the new transport coefficient. It can be measured
using electric fields with non-zero gradients, or via the heat production when
an external force is turned on. Scaling arguments fix the resistivity to be
linear in the temperature.


title: Affine projective Osserman structures

abstract:
  By considering the projectivized spectrum of the Jacobi operator, we
introduce the concept of projective Osserman manifold in both the affine and in
the pseudo-Riemannian settings. If M is an affine projective Osserman manifold,
then the modified Riemannian extension metric on the cotangent bundle is both
spacelike and timelike projective Osserman. Since any rank 1 symmetric space is
affine projective Osserman, this provides additional information concerning the
cotangent bundle of a rank 1 Riemannian symmetric space with the modified
Riemannian extension metric. We construct other examples of affine projective
Osserman manifolds where the Ricci tensor is not symmetric and thus the
connection is not the Levi-Civita connection of any metric. If M is an affine
projective Osserman manifold of odd dimension, we use methods of algebraic
topology to show the Jacobi operator has only one non-zero eigenvalue and that
eigenvalue is real.


title: A new perspective on MOND

abstract:
  A novel interpretation of MOND is presented. For galactic data, in addition
to Newtonian acceleration, there is an attractive acceleration peaking at
Milgrom's parameter a_0. The peak lies within experimental error where a_0 =
cH_0/2\pi; H_0 is the present-time value of the Hubble constant and c the
velocity of light. The physical interpretation of this relation and its
connection to Dark Energy are discussed.


title: Holomorphic functions on certain K\"{a}hler manifolds

abstract:
  We investigate Liouville theorems and dimension estimates for the space of
exponentially growing holomorphic functions on complete K\"{a}hler manifolds.
While our work is motivated by the study of gradient Ricci solitons in the
theory of Ricci flow, the most general results we prove here do not require any
knowledge of curvature.


title:
Optical control of coherent and squeezed phonons: major differences and
  similarities

abstract:
  Coherent and squeezed phonon oscillations can be excited in solids
impulsively by a single femtosecond pulse whose duration is shorter that a
phonon period. By applying the second ultrafast pump pulse these oscillations
can be significantly, but differently modified.


title:
Hidden Fermi Liquid, Scattering Rate Saturation and Nernst Effect: a
  DMFT Perspective

abstract:
  We investigate the transport properties of a correlated metal within
dynamical mean field theory. Canonical Fermi liquid behavior emerges only below
a very low temperature scale $T_{FL}$. Surprisingly the quasiparticle
scattering rate follows a quadratic temperature dependence up to much higher
temperatures and crosses over to saturated behavior around a temperature scale
$T_{sat}$. We identify these quasiparticles as constituents of the hidden Fermi
liquid. The non-Fermi liquid transport above $T_{FL}$, in particular the
linear-in-$T$ resistivity, is shown to be a result of a strongly temperature
dependent band dispersion. We derive simple expressions for resistivity, Hall
angle, thermoelectric power and Nernst coefficient in terms of a temperature
dependent renormalized band structure and the quasiparticle scattering rate. We
discuss possible tests of the DMFT picture of transport using ac measurements.


title: Design of Non-Binary Quasi-Cyclic LDPC Codes by ACE Optimization

abstract:
  An algorithm for constructing Tanner graphs of non-binary irregular
quasi-cyclic LDPC codes is introduced. It employs a new method for selection of
edge labels allowing control over the code's non-binary ACE spectrum and
resulting in low error-floor. The efficiency of the algorithm is demonstrated
by generating good codes of short to moderate length over small fields,
outperforming codes generated by the known methods.


title: Emission spectrum of soft massless states from heavy superstring

abstract:
  We calculate emission rates of various bosonic/fermionic soft massless states
of open/closed superstring from an ensemble of a highly excited open/closed
superstring in the flat background. The resulting spectrum shows thermal
distributions at the Hagedorn temperature. We find greybody factors for each
process and observe their relation to the ones from blackholes.


title: An extension theorem for planar semimodular lattices

abstract:
  We prove that every finite distributive lattice $D$ can be represented as the
congruence lattice of a rectangular lattice $K$ in which all congruences are
principal. We verify this result in a stronger form as an extension theorem.


title:
A note on the structure theory of groups acting on the Bruhat Tits tree
  associated to $\mathrm{PGL}_{2}(F)$

abstract:
  In this note we prove the classical decomposition theorems for certain
subgroups of the automorphism group of the Bruhat-Tits tree associated to
$\mathrm{PGL}_{2}(F)$, where $F$ is a local field. The results can be used to
understand the representation theory of these subgroups. Moreover, we can also
use the results to obtain similar decompositions for \textit{any} closed
transitive subgroup of the automorphism group of \textit{any} Bruhat-Tits tree.


title: A row space method for solving a system of linear equations

abstract:
  A new algorithm is presented for computing a direct solution to a system of
consistent linear equations. It produces a minimum norm particular solution, a
generalized inverse (of type {124}), and a null space projection operator. In
addition, the algorithm permits an online formulation so that computations may
proceed as the data become available. The algorithm does not require the
solution of a triangular system of equations, nor does it rely on block
partitioned matrices.


title: Decaying Asymmetric Dark Matter Relaxes the AMS-Fermi Tension

abstract:
  The first result of AMS-02 confirms the positron fraction excess observed by
PAMELA, but the spectrum is somewhat softer than that of PAMELA. In the dark
matter (DM) interpretation it brings a tension between AMS-02 and Fermi-LAT,
which reported an excess of the electron plus positron flux. In this work we
point out that the asymmetric cosmic ray from asymmetric dark matter (ADM)
decay relaxes the tension. It is found that in the case of two-body decay a
bosonic ADM around 2.4 TeV and decaying into $\mu^-\tau^+$ can significantly
improve the fits. Based on the $R-$parity-violating supersymmetry with
operators $LLE^c$, we propose a minimal model to realize that ADM. The model
introduces only a pair of singlets $(X,\bar X)$ with a tiny coupling $LH_uX$,
which makes the ADM share the lepton asymmetry and decay into $\mu^-\tau^+$
along the operator $LLE^c$.


title: A metric characterization of Carnot groups

abstract:
  We give a short axiomatic introduction to Carnot groups and their
subRiemannian and subFinsler geometry. We explain how such spaces can be
metrically described as exactly those proper geodesic spaces that admit
dilations and are isometrically homogeneous.


title:
Third-order relativistic dynamics: classical spinning particle
  travelling in a plane

abstract:
  Mathisson's 'new mechanics' of a relativistic spinning particle is shown to
follow, in the case of planar motion, from only general requirements of
relativistic invariance and of the dependence on third order derivatives along
with the 'variationality' feature. The Hamiltonian counterpart ultimately
recovers the Dixon system of equations for this case with the Mathisson-Pirani
supplementary condition.


title:
Measurement of the Lambda(b)0 lifetime in pp collisions at sqrt(s) = 7
  TeV

abstract:
  A measurement of the Lambda(b)0 lifetime using the decay Lambda(b)0 to J/Psi
Lambda in proton-proton collisions at sqrt(s) = 7 TeV is presented. The data
set, corresponding to an integrated luminosity of about 5 inverse femtobarns,
was recorded with the CMS experiment at the Large Hadron Collider using
triggers that selected dimuon events in the J/Psi mass region. The Lambda(b)0
lifetime is measured to be 1.503 +/- 0.052 (stat.) +/- 0.031 (syst.) ps.


title:
A Systems Model of the Eco-physiological Response of Plants to
  Environmental Heavy Metal Concentrations

abstract:
  The ecophysiological response of plants to environmental heavy metal stress
is indicated by the profile of its tissue HM concentrations (Cp) versus the
concentration of the HM in the substrate (Cs). We report a systems biology
approach to the modelling of the Cp- Cs profile using as loose analogy, the
Verhulst model of population dynamics but formulated in the concentration
domain. The HM is conceptualized as an ecological organism that `colonizes' the
resource zone of the plant cells driven by the potential supplied by the higher
HM concentration in the substrate. The infinite occupation by the HM is limited
by the eventual saturation of the cellular binding sites. The solution of the
differential equation results in the logistic equation, the r-K model. The
model is tested for 3 metalophillic plants T.erecta, S. vulgaris and E.
splendens growing in different types of substrates, contaminated to varying
extents by different copper compounds. The model fitted the experimental Cp- Cs
profiles well. The r, K parameter values and secondary quantities derived from
them, allowed a quantification of the number of Cu binding sites per cell at
saturation, the sensitivities (affinities) of these sites for Cu in the 3
experimental systems as well as the extraction of information related to the
substrate phyto-availability of the Cu. Thus even though the model operates at
the systems level it permits useful insights into underlying processes that
ultimately derive from the cumulative molecular processes of HM homeostasis.
The chief advantages of the model are its simplicity, fewer arbitrary
parameters, and the non-specification of constraints on substrate and plant
type.


title:
Dispersive and dissipative errors in the DPG method with scaled norms
  for Helmholtz equation

abstract:
  We consider the discontinuous Petrov-Galerkin (DPG) method, wher the test
space is normed by a modified graph norm. The modificatio scales one of the
terms in the graph norm by an arbitrary positive scaling parameter. Studying
the application of the method to the Helmholtz equation, we find that better
results are obtained, under some circumstances, as the scaling parameter
approaches a limiting value. We perform a dispersion analysis on the multiple
interacting stencils that form the DPG method. The analysis shows that the
discrete wavenumbers of the method are complex, explaining the numerically
observed artificial dissipation in the computed wave approximations. Since the
DPG method is a nonstandard least-squares Galerkin method, we compare its
performance with a standard least-squares method.


title:
Measurement of the ratio of the inclusive 3-jet cross section to the
  inclusive 2-jet cross section in pp collisions at sqrt(s) = 7 TeV and first
  determination of the strong coupling constant in the TeV range

abstract:
  A measurement is presented of the ratio of the inclusive 3-jet cross section
to the inclusive 2-jet cross section as a function of the average transverse
momentum, <pT[1,2]>, of the two leading jets in the event. The data sample was
collected during 2011 at a proton-proton centre-of-mass energy of 7 TeV with
the CMS detector at the LHC, corresponding to an integrated luminosity of 5.0
inverse femtobarns. The strong coupling constant at the scale of the Z boson
mass is determined to be alphaS[MZ] = 0.1148 +/- 0.0014 (exp.) +/- 0.0018 (PDF)
+/- 0.0050 (theory), by comparing the ratio in the range 0.42 < <pT[1,2]> <
1.39 TeV to the predictions of perturbative QCD at next-to-leading order. This
is the first determination of alphaS[MZ] from measurements at momentum scales
beyond 0.6 TeV. The predicted ratio depends only indirectly on the evolution of
the parton distribution functions of the proton such that this measurement also
serves as a test of the evolution of the strong coupling constant. No deviation
from the expected behaviour is observed.


title:
On genus expansion of knot polynomials and hidden structure of Hurwitz
  tau-functions

abstract:
  In the genus expansion of the HOMFLY polynomials their representation
dependence is naturally captured by symmetric group characters. This
immediately implies that the Ooguri-Vafa partition function (OVPF) is a Hurwitz
tau-function. In the planar limit involving factorizable special polynomials,
it is actually a trivial exponential tau-function. In fact, in the double
scaling Kashaev limit (the one associated with the volume conjecture) dominant
in the genus expansion are terms associated with the symmetric representations
and with the integrability preserving Casimir operators, though we stop one
step from converting this fact into a clear statement about the OVPF behavior
in the vicinity of q=1. Instead, we explain that the genus expansion provides a
hierarchical decomposition of the Hurwitz tau-function, similar to the
Takasaki-Takebe expansion of the KP tau-functions. This analogy can be helpful
to develop a substitute for the universal Grassmannian description in the
Hurwitz tau-functions.


title:
Generalized Chern-Simons action and maximally supersymmetric gauge
  theories

abstract:
  We study observables and deformations of generalized Chern-Simons action and
show how to apply these results to maximally supersymmetric gauge theories. We
describe a construction of large class of deformations based on some results on
the cohomology of super Lie algebras proved in the Appendix.


title:
Integral operators, embedding theorems and a Littlewood-Paley formula on
  weighted Fock spaces

abstract:
  We obtain a complete characterization of the entire functions $g$ such that
the integral operator $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ is
bounded or compact, on a large class of Fock spaces $\mathcal{F}^\phi_p$,
induced by smooth radial weights that decay faster than the classical Gaussian
one. In some respects, these spaces turn out to be significantly different than
the classical Fock spaces. Descriptions of Schatten class integral operators
are also provided. En route, we prove a Littlewood-Paley formula for
$||\cdot||_{\mathcal{F}^\phi_p}$ and we characterize the positive Borel
measures for which $\mathcal{F}^\phi_p\subset L^q(\mu)$, $0<p,q<\infty$. In
addition, we also address the question of describing the subspaces of
$\mathcal{F}^\phi_p$ that are invariant under the classical Volterra integral
operator.


title: Guiding Isotopies and Holomorphic Motions

abstract:
  We develop an isotopy principle for holomorphic motions. Our main result
concerns the extendability of a holomorphic motion of a finite subset $E$ of a
Riemann surface $Y$ parameterized by a point $t$ in a pointed hyperbolic
surface $(X, t_{0})$. If a holomorphic motion from $E$ to $E_{t}$ in $Y$ has a
guiding quasiconformal isotopy, then there is a holomorphic extension to any
new point $p$ in $Y-E$ that follows the guiding isotopy. The proof gives a
canonical way to replace a quasiconformal motion of the $(n+1)^{th}$ point by a
holomorphic motion while leaving unchanged the given holomorphic motion of the
first $n$ points. In particular, our main result gives a new proof of
Slodkowski's theorem which concerns the special case when the parameter space
is the open unit disk with base point $0$ and the dynamical space $Y$ is the
Riemann sphere.


title: 100-year DASCH Light Curves of Kepler Planet-Candidate Host Stars

abstract:
  We present 100 year light curves of Kepler planet-candidate host stars from
the Digital Access to a Sky Century at Harvard (DASCH) project. 261 out of 997
host stars have at least 10 good measurements on DASCH scans of the Harvard
plates. 109 of them have at least 100 good measurements, including 70% (73 out
of 104) of all host stars with g<=13 mag, and 44% (100 out of 228) of all host
stars with g<=14 mag. Our typical photometric uncertainty is ~0.1-0.15 mag. No
variation is found at 3-sigma level for these host stars, including 21
confirmed or candidate hot Jupiter systems which might be expected to show
enhanced flares from magnetic interactions between dwarf primaries and their
close and relatively massive planet companions.


title: Improved Photometry for the DASCH Pipeline

abstract:
  The Digital Access to a Sky Century@Harvard (DASCH) project is digitizing the
~500,000 glass plate images obtained (full sky) by the Harvard College
Observatory from 1885-1992. Astrometry and photometry for each resolved object
are derived with photometric rms values of ~0.15mag for the initial photometry
analysis pipeline. Here we describe new developments for DASCH photometry,
applied to the Kepler field, that has yielded further improvements, including
better identification of image blends and plate defects by measuring image
profiles and astrometric deviations. A local calibration procedure using nearby
stars in a similar magnitude range as the program star (similar to what has
been done for visual photometry from the plates) yields additional improvement
for a net photometric rms ~0.1mag. We also describe statistical measures of
light curves that are now used in the DASCH pipeline processing to autonomously
identify new variables. The DASCH photometry methods described here are used in
the pipeline processing for the Data Releases of DASCH data (Grindlay et al.
2012; http://dasch.rc.fas.harvard.edu), as well as for the long-term variables
discovered by DASCH in the Kepler field (Tang et al, in preparation).


title: Linear Time Parameterized Algorithms via Skew-Symmetric Multicuts

abstract:
  A skew-symmetric graph $(D=(V,A),\sigma)$ is a directed graph $D$ with an
involution $\sigma$ on the set of vertices and arcs. In this paper, we
introduce a separation problem, $d$-Skew-Symmetric Multicut, where we are given
a skew-symmetric graph $D$, a family of $\cal T$ of $d$-sized subsets of
vertices and an integer $k$. The objective is to decide if there is a set
$X\subseteq A$ of $k$ arcs such that every set $J$ in the family has a vertex
$v$ such that $v$ and $\sigma(v)$ are in different connected components of
$D'=(V,A\setminus (X\cup \sigma(X))$. In this paper, we give an algorithm for
this problem which runs in time $O((4d)^{k}(m+n+\ell))$, where $m$ is the
number of arcs in the graph, $n$ the number of vertices and $\ell$ the length
of the family given in the input.
  Using our algorithm, we show that Almost 2-SAT has an algorithm with running
time $O(4^kk^4\ell)$ and we obtain algorithms for {\sc Odd Cycle Transversal}
and {\sc Edge Bipartization} which run in time $O(4^kk^4(m+n))$ and
$O(4^kk^5(m+n))$ respectively. This resolves an open problem posed by Reed,
Smith and Vetta [Operations Research Letters, 2003] and improves upon the
earlier almost linear time algorithm of Kawarabayashi and Reed [SODA, 2010].
  We also show that Deletion q-Horn Backdoor Set Detection is a special case of
3-Skew-Symmetric Multicut, giving us an algorithm for Deletion q-Horn Backdoor
Set Detection which runs in time $O(12^kk^5\ell)$. This gives the first
fixed-parameter tractable algorithm for this problem answering a question posed
in a paper by a superset of the authors [STACS, 2013]. Using this result, we
get an algorithm for Satisfiability which runs in time $O(12^kk^5\ell)$ where
$k$ is the size of the smallest q-Horn deletion backdoor set, with $\ell$ being
the length of the input formula.


title: Dynamics of electric transport in interacting Weyl semimetals

abstract:
  The response to an electric field (DC and AC) of electronic systems in which
the Fermi "surface" consists of a number of 3D Weyl points (such as some
pyrochlore iridates) exhibits a peculiar combination of characteristics usually
associated with insulating and conducting behaviour. Generically a neutral
plasma in clean materials can be described by a tight binding model with a
strong spin-orbit interaction. A system of that type has a vanishing DC
conductivity; however the current response to the DC field is very slow: the
current decays with time in a powerwise manner, different from an insulator.
The AC conductivity, in addition to a finite real part which is linear in
frequency, exhibits an imaginary part that increases logarithmically as
function of the UV cutoff (atomic scale). This leads to substantial dielectric
response like a large dielectric constant at low frequencies. This is in
contrast to a 2D Weyl semimetal like graphene at neutrality point where the AC
conductivity is purely pseudo-dissipative. The Coulomb interaction between
electrons is long range and sufficiently strong to make a significant impact on
transport. The interaction contribution to the AC conductivity is calculated
within the tight binding model.


title:
Measuring Cultural Relativity of Emotional Valence and Arousal using
  Semantic Clustering and Twitter

abstract:
  Researchers since at least Darwin have debated whether and to what extent
emotions are universal or culture-dependent. However, previous studies have
primarily focused on facial expressions and on a limited set of emotions. Given
that emotions have a substantial impact on human lives, evidence for cultural
emotional relativity might be derived by applying distributional semantics
techniques to a text corpus of self-reported behaviour. Here, we explore this
idea by measuring the valence and arousal of the twelve most popular emotion
keywords expressed on the micro-blogging site Twitter. We do this in three
geographical regions: Europe, Asia and North America. We demonstrate that in
our sample, the valence and arousal levels of the same emotion keywords differ
significantly with respect to these geographical regions --- Europeans are, or
at least present themselves as more positive and aroused, North Americans are
more negative and Asians appear to be more positive but less aroused when
compared to global valence and arousal levels of the same emotion keywords. Our
work is the first in kind to programatically map large text corpora to a
dimensional model of affect.


title: Emptying Sets: The Cookie Monster Problem

abstract:
  Given a set of integers $S = \{k_1,\ k_2,...,\ k_n\}$, the Cookie Monster
Problem is the problem of making all elements of the set equal 0 in the minimum
number of moves. Consider the analogy of cookie jars with distinct numbers of
cookies, such that $k_i$ is the number of cookies in the $i$th jar. The "Cookie
Monster" wants to eat all the cookies, but at each move he must choose some
subset of the jars and eat the same amount from each jar. The \emph{Cookie
Monster Number of $S$}, $CM(S)$, is the minimum number of such moves necessary
to empty the jars. It has been shown previously that $\lceil \log_2(|S|+1)
\rceil \leq CM(S) \leq |S|$. In this paper we classify sets by determining what
conditions are necessary for $CM(S)$ to equal 2 or 3 and what effect certain
restrictions have on $CM(S)$. We also provide an alternative interpretation of
the problem in the form of a combinatorial game and analyze the losing
positions.


title: Optimized Backhaul Compression for Uplink Cloud Radio Access Network

abstract:
  This paper studies the uplink of a cloud radio access network (C-RAN) where
the cell sites are connected to a cloud-computing-based central processor (CP)
with noiseless backhaul links with finite capacities. We employ a simple
compress-and-forward scheme in which the base-stations(BSs) quantize the
received signals and send the quantized signals to the CP using either
distributed Wyner-Ziv coding or single-user compression. The CP decodes the
quantization codewords first, then decodes the user messages as if the remote
users and the cloud center form a virtual multiple-access channel (VMAC). This
paper formulates the problem of optimizing the quantization noise levels for
weighted sum rate maximization under a sum backhaul capacity constraint. We
propose an alternating convex optimization approach to find a local optimum
solution to the problem efficiently, and more importantly, establish that
setting the quantization noise levels to be proportional to the background
noise levels is near optimal for sum-rate maximization when the
signal-to-quantization-noise ratio (SQNR) is high. In addition, with Wyner-Ziv
coding, the approximate quantization noise level is shown to achieve the
sum-capacity of the uplink C-RAN model to within a constant gap. With
single-user compression, a similar constant-gap result is obtained under a
diagonal dominant channel condition. These results lead to an efficient
algorithm for allocating the backhaul capacities in C-RAN. The performance of
the proposed scheme is evaluated for practical multicell and heterogeneous
networks. It is shown that multicell processing with optimized quantization
noise levels across the BSs can significantly improve the performance of
wireless cellular networks.


title: Remarks on factorization property of some stochastic integrals

abstract:
  In the paper Sato (2006) there are introduced two families of improper random
integrals and the corresponding two convolution semigroups of infinitely
divisible laws on $\Rset^d$. Theorem 3.1 gives a relation (a factorization
property) between those two integrals. Here, using \emph{the random integral
mappings} $I^{h,r}_{(a,b]}$ (cf. the survey article Jurek (2011)), we give a
simpler proof that is also valid for measures on Banach spaces. Furthermore,
using our technique we establish yet other relations between those two families
of improper stochastic integrals.


title:
Extrinsic spin Hall effect induced by resonant skew scattering in
  graphene

abstract:
  We show that the extrinsic spin Hall effect can be engineered in monolayer
graphene by decoration with small doses of adatoms, molecules, or nanoparticles
originating local spin-orbit perturbations. The analysis of the single impurity
scattering problem shows that intrinsic and Rashba spin-orbit local couplings
enhance the spin Hall effect via skew scattering of charge carriers in the
resonant regime. The solution of the transport equations for a random ensemble
of spin-orbit impurities reveals that giant spin Hall currents are within the
reach of the current state of the art in device fabrication. The spin Hall
effect is robust with respect to thermal fluctuations and disorder averaging.


title: Non-positive curvature, and the planar embedding conjecture

abstract:
  The planar embedding conjecture asserts that any planar metric admits an
embedding into L_1 with constant distortion. This is a well-known open problem
with important algorithmic implications, and has received a lot of attention
over the past two decades. Despite significant efforts, it has been verified
only for some very restricted cases, while the general problem remains elusive.
  In this paper we make progress towards resolving this conjecture. We show
that every planar metric of non-positive curvature admits a constant-distortion
embedding into L_1. This confirms the planar embedding conjecture for the case
of non-positively curved metrics.


title:
Thresholdless discrete surface solitons and stability switchings in
  periodically curved waveguides

abstract:
  We study numerically a parametrically driven discrete nonlinear Schr\"odinger
equation modelling periodically curved waveguide arrays. We show that discrete
surface solitons persist, but their threshold power is altered by the drive.
There are critical drives at which the threshold values vanish. We also show
that parametric drives can create resonance with a phonon making a new barrier
for discrete solitons. By calculating the corresponding Floquet multipliers, we
find that the stability of symmetric and antisymmetric off-side discrete
surface solitons switches approximately at the critical drives for
thresholdless solitons.


title:
Asymmetric multi-segmented conjugated polymer-metal nanowires for
  engineering of non-linear electrical behavior

abstract:
  In this paper, we report on the impact of metal/polymer interfaces on the
rectifying behavior of novel multi-segmented hybrid nanowires (HNWs) made of
metallic and conjugated polymer (CP) segments. Using HNWs integrated in
micromachined devices, the relationship between electronic properties and
original structure is revealed. By combining transmission electron microscopy
(TEM) and current-voltage (I-V) spectroscopy studies performed on several
symmetric and asymmetric HNWs structures, we show that rectifying I-V
characteristics are observed only for asymmetric HNWs. Moreover, it is shown
that the rectification ratio can be improved up to 3 orders of magnitude by a
proper selection of the HNW composition. While the rectifying behavior is
observed in HNWs after oxidative or acid doping, the charge transport mechanism
in as-synthesized HNWs is bulk-limited and independent from their structure.
Both symmetric and asymmetric HNWs exhibit Ohmic and non-linear I-V curves
above and below T~120 K, respectively. These electrical behaviors are
consistent with a smooth transition from an Ohmic to a non-Ohmic
variable-range-hopping (VRH) mechanism. We discuss the origin of these
nonlinearities comparing the two- and four-probe measurements on single HNWs
and we propose a simple model based on dual back-to-back Schottky diodes to
explain qualitatively the rectifying properties.


title: A short note on short pants

abstract:
  It is a theorem of Bers that any closed hyperbolic surface admits a pants
decomposition consisting of curves of bounded length where the bound only
depends on the topology of the surface. The question of the quantification of
the optimal constants has been well studied and the best upper bounds to date
are linear in genus, a theorem of Buser and Sepp\"al\"a. The goal of this note
is to give a short proof of an linear upper bound which slightly improves the
best known bounds.


title:
Quantum Circuits for GCD Computation with $O(n \log n)$ Depth and O(n)
  Ancillae

abstract:
  GCD computations and variants of the Euclidean algorithm enjoy broad uses in
both classical and quantum algorithms. In this paper, we propose quantum
circuits for GCD computation with $O(n \log n)$ depth with O(n) ancillae. Prior
circuit construction needs $O(n^2)$ running time with O(n) ancillae. The
proposed construction is based on the binary GCD algorithm and it benefits from
log-depth circuits for 1-bit shift, comparison/subtraction, and managing
ancillae. The worst-case gate count remains $O(n^2)$, as in traditional
circuits.


title: A New Analysis of the DS-CDMA Cellular Uplink Under Spatial Constraints

abstract:
  A new analysis is presented for the direct-sequence code-division multiple
access (DS-CDMA) cellular uplink. For a given network topology, closed-form
expressions are found for the outage probability and rate of each uplink in the
presence of path-dependent Nakagami fading and log-normal shadowing. The
topology may be arbitrary or modeled by a random spatial distribution for a
fixed number of base stations and mobiles placed over a finite area with the
separations among them constrained to exceed a minimum distance. The analysis
is more detailed and accurate than existing ones and facilitates the resolution
of network design issues, including the influence of the minimum base-station
separation, the role of the spreading factor, and the impact of various
power-control and rate-control policies. It is shown that once power control is
established, the rate can be allocated according to a fixed-rate or
variable-rate policy with the objective of either meeting an outage constraint
or maximizing throughput. An advantage of the variable-rate policy is that it
allows an outage constraint to be enforced on every uplink, whereas the
fixed-rate policy can only meet an average outage constraint.


title: Meta-centralizers of non locally compact group algebras

abstract:
  Meta-centralizers of non-locally compact group algebras are studied. Theorems
about their representations with the help of families of generalized measures
are proved. Isomorphisms of group algebras are investigated in relation with
meta-centralizers.


title: Homogenization Techniques for Periodic Structures

abstract:
  In this chapter we describe a selection of mathematical techniques and
results that suggest interesting links between the theory of gratings and the
theory of homogenization, including a brief introduction to the latter. By no
means do we purport to imply that homogenization theory is an exclusive method
for studying gratings, neither do we hope to be exhaustive in our choice of
topics within the subject of homogenization. Our preferences here are motivated
most of all by our own latest research, and by our outlook to the future
interactions between these two subjects. We have also attempted, in what
follows, to contrast the "classical" homogenization (Section 11.1.2), which is
well suited for the description of composites as we have known them since their
advent until about a decade ago, and the "non-standard" approaches,
high-frequency homogenization (Section 11.2) and high-contrast homogenization
(Section 11.3), which have been developing in close relation to the study of
photonic crystals and metamaterials, which exhibit properties unseen in
conventional composite media, such as negative refraction allowing for
super-lensing through a flat heterogeneous lens, and cloaking, which
considerably reduces the scattering by finite size objects (invisibility) in
certain frequency range. These novel electromagnetic paradigms have renewed the
interest of physicists and applied mathematicians alike in the theory of
gratings.


title: Speed calculations for random walks in degenerate random environments

abstract:
  We calculate explicit speeds for random walks in uniform degenerate random
environments. For certain non-uniform random environments, we calculate speeds
that are non-monotone.


title: Dark matter and dark energy from quark bag model

abstract:
  We calculate the present expansion of our Universe endowed with relict
colored objects - quarks and gluons - that survived hadronization either as
isolated islands of quark-gluon "nuggets", or spread uniformly in the Universe.
In the first scenario, the QNs can play the role of dark matter. In the second
scenario, we demonstrate that uniform colored objects can play the role of dark
energy providing the late-time accelerating expansion of the Universe.


title: Radical subgroups of totally disconnected locally compact groups

abstract:
  We observe a correspondence between collections of closed subgroups and
normal subgroups in totally disconnected locally compact groups. This
correspondence is applied to prove structure theorems for two classes of
totally disconnected locally compact second countable groups: the class of such
groups with an open solvable subgroup and the class of such groups with a
pro-nilpotent compact open subgroup. As a second application, we give new
proofs and generalizations of results of G. Willis and Y. Barnea, M. Ershov,
and T. Weigel on totally disconnected locally compact groups which are
topologically simple and compactly generated,


title: Some surfaces of general type for which Bloch's conjecture holds

abstract:
  We give many examples of surfaces of general type with $p_g=0$ for which
Bloch's conjecture holds, for all values of $K^2$ except 9. Our surfaces are
equipped with an involution.


title:
Excited-state potential-energy surfaces of metal-adsorbed organic
  molecules from Linear Expansion \Delta-Self-Consistent Field
  Density-Functional Theory (\Delta SCF-DFT)

abstract:
  Accurate and efficient simulation of excited state properties is an important
and much aspired cornerstone in the study of adsorbate dynamics on metal
surfaces. To this end, the recently proposed linear expansion \Delta
Self-Consistent Field (le\Delta SCF) method by Gavnholt et al. [Phys. Rev. B
78, 075441 (2008)] presents an efficient alternative to time consuming
quasi-particle calculations. In this method the standard Kohn-Sham equations of
Density-Functional Theory are solved with the constraint of a non-equilibrium
occupation in a region of Hilbert-space resembling gas-phase orbitals of the
adsorbate. In this work we discuss the applicability of this method for the
excited-state dynamics of metal-surface mounted organic adsorbates,
specifically in the context of molecular switching. We present necessary
advancements to allow for a consistent quality description of excited-state
potential-energy surfaces (PESs), and illustrate the concept with the
application to Azobenzene adsorbed on Ag(111) and Au(111) surfaces. We find
that the explicit inclusion of substrate electronic states modifies the
topologies of intra-molecular excited-state PESs of the molecule due to image
charge and hybridization effects. While the molecule in gas phase shows a clear
energetic separation of resonances that induce isomerization and backreaction,
the surface-adsorbed molecule does not. The concomitant possibly simultaneous
induction of both processes would lead to a significantly reduced switching
efficiency of such a mechanism.


title:
$C^{1,\alpha}$ Interior Regularity for Nonlinear Nonlocal Elliptic
  Equations With Rough Kernels

abstract:
  We prove a $C^{1,\alpha}$ interior regularity theorem for fully nonlinear
uniformly elliptic integro-differential equations without assuming any
regularity of the kernel. We then give some applications to linear theory and
higher regularity of a special class of nonlinear operators.


title: Factorization of integer-valued polynomials with square-free denominator

abstract:
  We describe an algorithm to compute the essentially different factorizations
of a given image primitive integer-valued polynomial $f(X)=g(X)/d\in\Q[X]$,
where $g\in\Z[X]$ and $d\in\N$ is square-free, assuming that the factorization
of $g(X)$ in $\Z[X]$ and $d$ in $\Z$ is known. We translate this problem into a
combinatorial one.


title: Singular superspaces

abstract:
  We introduce a wide category of superspaces, called locally finitely
generated, which properly includes supermanifolds but enjoys much stronger
permanence properties, as are prompted by applications. Namely, it is closed
under taking finite fibre products (i.e. is finitely complete) and thickenings
by spectra of Weil superalgebras. Nevertheless, in this category, morphisms
with values in a supermanifold are still given in terms of coordinates. This
framework gives a natural notion of relative supermanifolds over a locally
finitely generated base. Moreover, the existence of inner homs, whose source is
the spectrum of a Weil superalgebra, is established; they are generalisations
of the Weil functors defined for smooth manifolds.


title: Semi-supervised Eigenvectors for Large-scale Locally-biased Learning

abstract:
  In many applications, one has side information, e.g., labels that are
provided in a semi-supervised manner, about a specific target region of a large
data set, and one wants to perform machine learning and data analysis tasks
"nearby" that prespecified target region. For example, one might be interested
in the clustering structure of a data graph near a prespecified "seed set" of
nodes, or one might be interested in finding partitions in an image that are
near a prespecified "ground truth" set of pixels. Locally-biased problems of
this sort are particularly challenging for popular eigenvector-based machine
learning and data analysis tools. At root, the reason is that eigenvectors are
inherently global quantities, thus limiting the applicability of
eigenvector-based methods in situations where one is interested in very local
properties of the data.
  In this paper, we address this issue by providing a methodology to construct
semi-supervised eigenvectors of a graph Laplacian, and we illustrate how these
locally-biased eigenvectors can be used to perform locally-biased machine
learning. These semi-supervised eigenvectors capture
successively-orthogonalized directions of maximum variance, conditioned on
being well-correlated with an input seed set of nodes that is assumed to be
provided in a semi-supervised manner. We show that these semi-supervised
eigenvectors can be computed quickly as the solution to a system of linear
equations; and we also describe several variants of our basic method that have
improved scaling properties. We provide several empirical examples
demonstrating how these semi-supervised eigenvectors can be used to perform
locally-biased learning; and we discuss the relationship between our results
and recent machine learning algorithms that use global eigenvectors of the
graph Laplacian.


title: Micro and Macro Fractals generated by multi-valued dynamical systems

abstract:
  Given a multi-valued function $\Phi$ on a topological space $X$ we study the
properties of its fixed fractal, which is defined as the closure of the orbit
$\Phi^\omega(Fix(\Phi))=\bigcup_{n\in\omega}\Phi^n(Fix(\Phi))$ of the set
$Fix(\Phi)=\{x\in X:x\in\Phi(x)\}$ of fixed points of $\Phi$. A special
attention is paid to the duality between micro-fractals and macro-fractals,
which are fixed fractals for a contracting compact-valued function $\Phi$ on a
complete metric space $X$ and its inverse multi-function $\Phi^{-1}$. With help
of algorithms (described in this paper) we generate various images of
macro-fractals which are dual to some well-known micro-fractals like the
fractal cross, the Sierpinski triangle, Sierpinski carpet, the Koch curve, or
the fractal snowflakes. The obtained images show that macro-fractals have a
large-scale fractal structure, which becomes clearly visible after a suitable
zooming.


title:
Improved Approximation Algorithms for (Budgeted) Node-weighted Steiner
  Problems

abstract:
  Moss and Rabani[12] study constrained node-weighted Steiner tree problems
with two independent weight values associated with each node, namely, cost and
prize (or penalty). They give an O(log n)-approximation algorithm for the
prize-collecting node-weighted Steiner tree problem (PCST). They use the
algorithm for PCST to obtain a bicriteria (2, O(log n))-approximation algorithm
for the Budgeted node-weighted Steiner tree problem. Their solution may cost up
to twice the budget, but collects a factor Omega(1/log n) of the optimal prize.
We improve these results from at least two aspects.
  Our first main result is a primal-dual O(log h)-approximation algorithm for a
more general problem, prize-collecting node-weighted Steiner forest, where we
have (h) demands each requesting the connectivity of a pair of vertices. Our
algorithm can be seen as a greedy algorithm which reduces the number of demands
by choosing a structure with minimum cost-to-reduction ratio. This natural
style of argument (also used by Klein and Ravi[10] and Guha et al.[8]) leads to
a much simpler algorithm than that of Moss and Rabani[12] for PCST.
  Our second main contribution is for the Budgeted node-weighted Steiner tree
problem, which is also an improvement to [12] and [8]. In the unrooted case, we
improve upon an O(log^2(n))-approximation of [8], and present an O(log
n)-approximation algorithm without any budget violation. For the rooted case,
where a specified vertex has to appear in the solution tree, we improve the
bicriteria result of [12] to a bicriteria approximation ratio of (1+eps, O(log
n)/(eps^2)) for any positive (possibly subconstant) (eps). That is, for any
permissible budget violation (1+eps), we present an algorithm achieving a
tradeoff in the guarantee for prize. Indeed, we show that this is almost tight
for the natural linear-programming relaxation used by us as well as in [12].


title: Nonlinear Hawkes Processes

abstract:
  The Hawkes process is a simple point process that has long memory, clustering
effect, self-exciting property and is in general non-Markovian. The future
evolution of a self-exciting point process is influenced by the timing of the
past events. There are applications in finance, neuroscience, genome analysis,
seismology, sociology, criminology and many other fields. We first survey the
known results about the theory and applications of both linear and nonlinear
Hawkes processes. Then, we obtain the central limit theorem and process-level,
i.e. level-3 large deviations for nonlinear Hawkes processes. The level-1 large
deviation principle holds as a result of the contraction principle. We also
provide an alternative variational formula for the rate function of the level-1
large deviations in the Markovian case. Next, we drop the usual assumptions on
the nonlinear Hawkes process and categorize it into different regimes, i.e.
sublinear, sub-critical, critical, super-critical and explosive regimes. We
show the different time asymptotics in different regimes and obtain other
properties as well. Finally, we study the limit theorems of linear Hawkes
processes with random marks.


title:
Investigating Two Successive Flux Rope Eruptions In A Solar Active
  Region

abstract:
  We investigate two successive flux rope (FR1 and FR2) eruptions resulting in
two coronal mass ejections (CMEs) on 2012 January 23. Both FRs appeared as an
EUV channel structure in the images of high temperature passbands of the
Atmospheric Imaging Assembly prior to the CME eruption. Through fitting their
height evolution with a function consisting of linear and exponential
components, we determine the onset time of the FR impulsive acceleration with
high temporal accuracy for the first time. Using this onset time, we divide the
evolution of the FRs in the low corona into two phases: a slow rise phase and
an impulsive acceleration phase. In the slow rise phase of the FR1, the
appearance of sporadic EUV and UV brightening and the strong shearing along the
polarity inverse line indicates that the quasi-separatrix-layer reconnection
likely initiates the slow rise. On the other hand for the FR2, we mainly
contribute its slow rise to the FR1 eruption, which partially opened the
overlying field and thus decreased the magnetic restriction. At the onset of
the impulsive acceleration phase, the FR1 (FR2) reaches the critical height of
84.4$\pm$11.2 Mm (86.2$\pm$13.0 Mm) where the decline of the overlying field
with height is fast enough to trigger the torus instability. After a very short
interval ($\sim$2 minutes), the flare emission began to enhance. These results
reveal the compound activity involving multiple magnetic FRs and further
suggest that the ideal torus instability probably plays the essential role of
initiating the impulsive acceleration of CMEs.


title: Deriving Derivatives

abstract:
  Quantitative structuring is a rigorous framework for the design of financial
products. We show how it incorporates traditional investment ideas while
supporting a more accurate expression of clients' views. We touch upon adjacent
topics regarding the safety of financial derivatives and the role of pricing
models in product design.


title: Exploration and Trapping of Mortal Random Walkers

abstract:
  Exploration and trapping properties of random walkers that may evanesce at
any time as they walk have seen very little treatment in the literature, and
yet a finite lifetime is a frequent occurrence, and its effects on a number of
random walk properties may be profound. For instance, whereas the average
number of distinct sites visited by an immortal walker grows with time without
bound, that of a mortal walker may, depending on dimensionality and rate of
evanescence, remain finite or keep growing with the passage of time. This
number can in turn be used to calculate other classic quantities such as the
survival probability of a target surrounded by diffusing traps. If the traps
are immortal, the survival probability will vanish with increasing time.
However, if the traps are evanescent, the target may be spared a certain death.
We analytically calculate a number of basic and broadly used quantities for
evanescent random walkers.


title: Elasticity theory of structuring

abstract:
  Financial derivatives have often been criticized as casino-style betting
instruments. It turns out that many naive ways of making them are indeed
equivalent to gambling. Fortunately, this inadvertent effect can be understood
and prevented. We present a theory of product design which achieves that.


title:
Global existence and temporal decay in Keller-Segel models coupled to
  fluid equations

abstract:
  We consider a Keller-Segel model coupled to the incompressible Navier-Stokes
equations in spatial dimensions two and three.
  We establish the local existence of regular solutions and present some
blow-up criteria for both cases that equations of oxygen concentration is of
parabolic or hyperbolic type. We also prove global existence and decay estimate
in time under the some smallness conditions of initial data.


title:
Critical Invariant Circles in Asymmetric and Multiharmonic Generalized
  Standard Maps

abstract:
  Invariant circles play an important role as barriers to transport in the
dynamics of area-preserving maps. KAM theory guarantees the persistence of some
circles for near-integrable maps, but far from the integrable case all circles
can be destroyed. A standard method for determining the existence or
nonexistence of a circle, Greene's residue criterion, requires the computation
of long-period orbits, which can be difficult if the map has no reversing
symmetry. We use de la Llave's quasi-Newton, Fourier-based scheme to
numerically compute the conjugacy of a Diophantine circle conjugate to rigid
rotation, and the singularity of a norm of a derivative of the conjugacy to
predict criticality. We study near-critical conjugacies for families of
rotational invariant circles in generalizations of Chirikov's standard map.
  A first goal is to obtain evidence to support the long-standing conjecture
that when circles breakup they form cantori, as is known for twist maps by
Aubry-Mather theory. The location of the largest gaps is compared to the maxima
of the potential when anti-integrable theory applies. A second goal is to
support the conjecture that locally most robust circles have noble rotation
numbers, even when the map is not reversible. We show that relative robustness
varies inversely with the discriminant for rotation numbers in quadratic
algebraic fields. Finally, we observe that the rotation number of the globally
most robust circle generically appears to be a piecewise-constant function in
two-parameter families of maps.


title: Atomic Hydrogen in a Galactic Center Outflow

abstract:
  We describe a population of small, high velocity, atomic hydrogen clouds,
loops, and filaments found above and below the disk near the Galactic Center.
The objects have a mean radius of 15 pc, velocity widths of $\sim 14$ km/s and
are observed at $|z|$ heights up to 700 pc. The velocity distribution of the
clouds shows no signature of Galactic rotation. We propose a scenario where the
clouds are associated with an outflow from a central star-forming region at the
Galactic Center. We discuss the clouds as entrained material traveling at $\sim
200$ km/s in a Galactic wind.


title: Compressive parameter estimation in AWGN

abstract:
  Compressed sensing is by now well-established as an effective tool for
extracting sparsely distributed information, where sparsity is a discrete
concept, referring to the number of dominant nonzero signal components in some
basis for the signal space. In this paper, we establish a framework for
estimation of continuous-valued parameters based on compressive measurements on
a signal corrupted by additive white Gaussian noise (AWGN). While standard
compressed sensing based on naive discretization has been shown to suffer from
performance loss due to basis mismatch, we demonstrate that this is not an
inherent property of compressive measurements. Our contributions are summarized
as follows: (a) We identify the isometries required to preserve fundamental
estimation-theoretic quantities such as the Ziv-Zakai bound (ZZB) and the
Cramer-Rao bound (CRB). Under such isometries, compressive projections can be
interpreted simply as a reduction in "effective SNR." (b) We show that the
threshold behavior of the ZZB provides a criterion for determining the minimum
number of measurements for "accurate" parameter estimation. (c) We provide
detailed computations of the number of measurements needed for the isometries
in (a) to hold for the problem of frequency estimation in a mixture of
sinusoids. We show via simulations that the design criterion in (b) is accurate
for estimating the frequency of a single sinusoid.


title: Dimension Changing Phase Transitions in Instanton Crystals

abstract:
  We investigate lattices of instantons and the dimension-changing transitions
between them. Our ultimate goal is the 3D->4D transition, which is
holographically dual to the phase transition between the baryonic and the
quarkyonic phases of cold nuclear matter. However, in this paper (just as in
[1]) we focus on lower dimensions -- the 1D lattice of instantons in a harmonic
potential V M_2^2x_2^2+M_3^2x_2^2+M_4^2x_4^2 and the zigzag-shaped lattice as a
first stage of the 1D->2D transition. We prove that in the low- and
moderate-density regimes, interactions between the instantons are dominated by
two-body forces. This drastically simplifies finding the ground state of the
instantons' orientations, so we made a numeric scan of the whole orientation
space instead of assuming any particular ansatz.
  We find that depending on the M_2/M_3/M_4 ratios, the ground state of
instanton orientations can follow a wide variety of patterns. For the straight
1D lattices, we found orientations periodically running over elements of a Z_2,
Klein, prismatic, or dihedral subgroup of the SU(2)/Z_2, as well as irrational
but link-periodic patterns. For the zigzag-shaped lattices, we detected 4
distinct orientation phases -- the anti-ferromagnet, another abelian phase, and
two non-abelian phases. Allowing the zigzag amplitude to vary as a function of
increasing compression force, we obtained the phase diagram for the straight
and zigzag-shaped lattices in the (force, M_3/M_4), (chemical potential,
M_3/M_4), and (density, M_3/M_4) planes. Some of the transitions between these
phases are second-order while others are first-order.
  Our techniques can be applied to other types of non-abelian crystals.


title:
The Symbolic Generic Initial System of Almost Linear Point
  Configurations in P2

abstract:
  Consider an ideal I in K[x,y,z] corresponding to a point configuration in P2
where all but one of the points lies on a single line. In this paper we study
the symbolic generic initial system obtained by taking the reverse
lexicographic generic initial ideals of the corresponding uniform fat point
ideals. We describe the limiting shape of this system of ideals and, in proving
this result, demonstrate that infinitely many of the uniform fat point ideals
are componentwise linear.


title: The Symbolic Generic Initial System of Points on an Irreducible Conic

abstract:
  In this note we study the limiting behaviour of the symbolic generic initial
system of an ideal I in K[x,y,z] corresponding to an arrangement of r points of
P2 lying on an irreducible conic. In particular, we show that the limiting
shape of this system is the subset of R2 such consisting of all points above
the line through (2,0) and (0, r/2) when r is greater than or equal to four.


title: Criteria of valid line sum arrays for multidimensional matrices

abstract:
  Gale and Ryser found a criterion for existence of a binary matrix with given
row and column sums. Mirsky extended the theorem of Gale and Ryser to $q$-ary
matrices. In this paper, we are interested in higher dimensional extension of
these theorems. We first introduce multidimensional matrices as a higher
dimensional generalization of matrices. We next replace the concept of row and
columns in matrices by lines in multidimensional matrices. We finally find a
criterion for existence of a $q$-ary multidimensional matrices with given line
sums.


title:
Monoidify! Monoids as a Design Principle for Efficient MapReduce
  Algorithms

abstract:
  It is well known that since the sort/shuffle stage in MapReduce is costly,
local aggregation is one important principle to designing efficient algorithms.
This short paper represents an attempt to more clearly articulate this design
principle in terms of monoids, which generalizes the use of combiners and the
in-mapper combining pattern.


title: Entropically Patchy Particles: Engineering Valence through Shape Entropy

abstract:
  Patchy particles are a popular paradigm for the design and synthesis of
nanoparticles and colloids for self-assembly. In "traditional" patchy
particles, anisotropic interactions arising from patterned coatings,
functionalized molecules, DNA, and other enthalpic means create the possibility
for directional binding of particles into higher-ordered structures. Although
the anisotropic geometry of non-spherical particles contributes to the
interaction patchiness through van der Waals, electrostatic, and other
interactions, how particle shape contributes entropically to self-assembly is
only now beginning to be understood. It has been recently demonstrated that,
for hard shapes, entropic forces are directional. A newly proposed theoretical
framework that defines and quantifies directional entropic forces demonstrates
the anisotropic--that is, patchy--nature of these emergent, attractive forces.
Here we introduce the notion of entropically patchy particles as the entropic
counterpart to enthalpically patchy particles. Using three example "families"
of shapes, we judiciously modify entropic patchiness by introducing geometric
features to the particles so as to target specific crystal structures, which
then assembled with Monte Carlo simulations. We quantify the emergent entropic
valence via a potential of mean force and torque. We generalize these shape
operations to shape anisotropy dimensions, in analogy with the anisotropy
dimensions introduced for enthalpically patchy particles. Our findings
demonstrate that entropic patchiness and emergent valence provide a way of
engineering directional bonding into nanoparticle systems, whether in the
presence or absence of additional, non-entropic forces.

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


title: The Kirchhoff indices and the matching numbers of unicyclic graphs

abstract:
  The Kirchhoff index of a connected graph is the sum of resistance distances
between all unordered pairs of vertices in the graph. It found considerable
applications in a variety of fields. In this paper, we determine the minimum
Kirchhoff index among the unicyclic graphs with fixed number of vertices and
matching number, and characterize the extremal graphs.


title: Remote Mentoring Young Females in STEM through MAGIC

abstract:
  The limited representation of women in STEM workforce is a concerning
national issue. It has been found that the gender stratification is not due to
the lack of talent amongst young females, but due to the lack of access to
female role models. To this end, "remote mentoring" is an effective way to
offer nation-wide personalized STEM mentoring to young females from all
segments of the society. In this paper, we introduce MAGIC, an organization
dedicated to mentoring young females in STEM through remote methods. We conduct
a retrospective study of MAGIC's formative years and present our experience in
remotely establishing 23 highly tailored mentor-mentee pairs. We provide
several key findings on STEM remote mentoring, such as popular communication
tools, frequently sought STEM skills among girls, and projects that could be
accomplished through remote mentoring. Furthermore, we present key challenges
faced by mentors and mentees, notable outcomes, and lessons learnt about remote
mentoring.


title:
Adaptive Reduced-Rank RLS Algorithms based on Joint Iterative
  Optimization of Filters for Space-Time Interference Suppression

abstract:
  This paper presents novel adaptive reduced-rank filtering algorithms based on
joint iterative optimization of adaptive filters. The novel scheme consists of
a joint iterative optimization of a bank of full-rank adaptive filters that
constitute the projection matrix and an adaptive reduced-rank filter that
operates at the output of the bank of filters. We describe least squares (LS)
expressions for the design of the projection matrix and the reduced-rank filter
and recursive least squares (RLS) adaptive algorithms for its computationally
efficient implementation. Simulations for a space-time interference suppression
in a CDMA system application show that the proposed scheme outperforms in
convergence and tracking the state-of-the-art reduced-rank schemes at about the
same complexity.


title: Strain Solitons and Topological Defects in Bilayer Graphene

abstract:
  Spontaneous symmetry-breaking, where the ground state of a system has lower
symmetry than the underlying Hamiltonian, is ubiquitous in physics. It leads to
multiply-degenerate ground states, each with a different "broken" symmetry
labeled by an order parameter. The variation of this order parameter in space
leads to soliton-like features at the boundaries of different broken-symmetry
regions and also to topological point defects. Bilayer graphene is a
fascinating realization of this physics, with an order parameter given by its
interlayer stacking coordinate. Bilayer graphene has been a subject of intense
study because in the presence of a perpendicular electric field, a band gap
appears in its electronic spectrum [1-3] through a mechanism that is intimately
tied to its broken symmetry. Theorists have further proposed that novel
electronic states exist at the boundaries between broken-symmetry stacking
domains [4-5]. However, very little is known about the structural properties of
these boundaries. Here we use electron microscopy to measure with nanoscale and
atomic resolution the widths, motion, and topological structure of soliton
boundaries and topological defects in bilayer graphene. We find that each
soliton consists of an atomic-scale registry shift between the two graphene
layers occurring over 6-11 nm. We infer the minimal energy barrier to
interlayer translation and observe soliton motion during in-situ heating above
1000 {\deg}C. The abundance of these structures across a variety samples, as
well as their unusual properties, suggests that they will have substantial
effects on the electronic and mechanical properties of bilayer graphene.


title: Does a Quantum Particle Know its Own Energy?

abstract:
  If a wave function does not describe microscopic reality then what does?
Reformulating quantum mechanics in path-integral terms leads to a notion of
"precluded event" and thence to the proposal that quantal reality differs from
classical reality in the same way as a set of worldlines differs from a single
worldline. One can then ask, for example, which sets of electron trajectories
correspond to a Hydrogen atom in its ground state and how they differ from
those of an excited state. We address the analogous questions for simple model
that replaces the electron by a particle hopping (in discrete time) on a
circular lattice.


title: Ring around the colloid

abstract:
  In this work, we show that Janus washers, genus-one colloids with hybrid
anchoring conditions, form topologically required defects in nematic liquid
crystals. Experiments under crossed polarizers reveal the defect structure to
be a rigid disclination loop confined within the colloid, with an accompanying
defect in the liquid crystal. When confined to a homeotropic cell, the
resulting colloid-defect ring pair tilts relative to the far field director, in
contrast to the behavior of toroidal colloids with purely homeotropic
anchoring. We show that this tilting behavior can be reversibly suppressed by
the introduction of a spherical colloid into the center of the toroid, creating
a new kind of multi-shape colloidal assemblage.


title:
Adaptive Decision Feedback Reduced-Rank Equalization Based on Joint
  Iterative Optimization of Adaptive Estimation Algorithms for Multi-Antenna
  Systems

abstract:
  This paper presents a novel adaptive reduced-rank multi-input-multi-output
(MIMO) decision feedback equalization structure based on joint iterative
optimization of adaptive estimators. The novel reduced-rank equalization
structure consists of a joint iterative optimization of two equalization
stages, namely, a projection matrix that performs dimensionality reduction and
a reduced-rank estimator that retrieves the desired transmitted symbol. The
proposed reduced-rank structure is followed by a decision feedback scheme that
is responsible for cancelling the inter-antenna interference caused by the
associated data streams. We describe least squares (LS) expressions for the
design of the projection matrix and the reduced-rank estimator along with
computationally efficient recursive least squares (RLS) adaptive estimation
algorithms. Simulations for a MIMO equalization application show that the
proposed scheme outperforms the state-of-the-art reduced-rank and the
conventional estimation algorithms at about the same complexity.


title:
Quantum Hall Effect of Two-Component Bosons at Fractional and Integral
  Fillings

abstract:
  We investigate the feasibility of many candidate quantum Hall states for
two-component bosons in the lowest Landau level. We identify interactions for
which spin-singlet incompressible states occur at filling factors $\nu=2/3$,
4/5 and 4/3, and spin-partially-polarized states at filling factors 3/4 and
3/2, where "spin" serves as a generic label for the two components. We study
ground states, excitations, edge states and entanglement spectrum for systems
with up to 16 bosons, and construct explicit trial wave functions to clarify
the underlying physics. The composite fermion theory very accurately describes
the ground states as well as excitations at $\nu=2/3$, 4/5 and 3/4, although it
is less satisfactory for the $\nu=3/2$ state. For $\nu=4/3$ a "non-Abelian
spin-singlet" state has been proposed to occur for a 2-body contact
interaction; we find that it is more likely that the actual state here is a
spin-singlet state of reverse-flux-attached composite fermions at filling
$\nu^*=4$. We also consider incompressible states at integral filling factors
$\nu=1$ and 2. The incompressible state at $\nu=1$ is shown to be well
described by the parton-based Jain spin-singlet wave function, and the
incompressible state at $\nu=2$ as the spin-singlet state of
reverse-flux-attached composite fermions at $\nu^*=2$.


title: Exotic symmetric space over a finite field, III

abstract:
  Let X be an exotic symmetric space G/H \times V, where G= GL(V) and H = Sp(V)
for a symplectic vector space V over an algebraically closed field of odd
characteristic. In our previous papers, character sheaves on X were constructed
based on the explicit data. In this paper, we give a conceptual definition of
character sheaves on X based on the idea of Ginzburg in the case of symmetric
spaces, which we call Ginzburg type character sheaves. We prove that Ginzburg
type character sheaves on X actually coincide with those defined in our papers.
This gives a classification of Ginzburg type character sheaves on X.


title:
Double-Pulse Deexcitations in a One-Dimensional Strongly Correlated
  System

abstract:
  We investigate the ultrafast optical response of the one-dimensional
half-filled extended Hubbard model exposed to two successive laser pulses. By
using the time-dependent Lanczos method, we find that following the first
pulse, the excitation and deexcitation process between the ground state and
excitonic states can be precisely controlled by the relative temporal
displacement of the pulses. The underlying physics can be understood in terms
of a modified Rabi model. Our simulations clearly demonstrate the
controllability of ultrafast transition between excited and deexcited phases in
strongly correlated electron systems.


title:
Tensor categories and the mathematics of rational and logarithmic
  conformal field theory

abstract:
  We review the construction of braided tensor categories and modular tensor
categories from representations of vertex operator algebras, which correspond
to chiral algebras in physics. The extensive and general theory underlying this
construction also establishes the operator product expansion for intertwining
operators, which correspond to chiral vertex operators, and more generally, it
establishes the logarithmic operator product expansion for logarithmic
intertwining operators. We review the main ideas in the construction of the
tensor product bifunctors and the associativity isomorphisms. For rational and
logarithmic conformal field theories, we review the precise results that yield
braided tensor categories, and in the rational case, modular tensor categories
as well. In the case of rational conformal field theory, we also briefly
discuss the construction of the modular tensor categories for the
Wess-Zumino-Novikov-Witten models and, especially, a recent discovery
concerning the proof of the fundamental rigidity property of the modular tensor
categories for this important special case. In the case of logarithmic
conformal field theory, we mention suitable categories of modules for the
triplet \mathcal{W}-algebras as an example of the applications of our general
construction of the braided tensor category structure.


title:
Electromagnetic Casimir effect on the boundary of a D-dimensional cavity
  and the high temperature asymptotics

abstract:
  We consider the finite temperature Casimir stress acting on the boundary of a
D>=3 dimensional cavity due to the vacuum fluctuations of electromagnetic
fields. Both perfectly conducting and infinitely permeable boundary conditions
are considered, and it is proved that they correspond mathematically to the
relative and absolute boundary conditions. The divergence terms of the Casimir
free energy are related to the heat kernel coefficients of the Laplace
operator. It is shown that the Casimir stress is free of divergence if and only
if D is exactly three. The high temperature asymptotics of the regularized
Casimir free energy are also found to depend on the heat kernel coefficients.
When D>3, renormalization is required to remove terms of order higher than or
equal to T^2.


title: Exact Weight Subgraphs and the k-Sum Conjecture

abstract:
  We consider the Exact-Weight-H problem of finding a (not necessarily induced)
subgraph H of weight 0 in an edge-weighted graph G. We show that for every H,
the complexity of this problem is strongly related to that of the infamous
k-Sum problem. In particular, we show that under the k-Sum Conjecture, we can
achieve tight upper and lower bounds for the Exact-Weight-H problem for various
subgraphs H such as matching, star, path, and cycle. One interesting
consequence is that improving on the O(n^3) upper bound for Exact-Weight-4-Path
or Exact-Weight-5-Path will imply improved algorithms for 3-Sum, 5-Sum,
All-Pairs Shortest Paths and other fundamental problems. This is in sharp
contrast to the minimum-weight and (unweighted) detection versions, which can
be solved easily in time O(n^2). We also show that a faster algorithm for any
of the following three problems would yield faster algorithms for the others:
3-Sum, Exact-Weight-3-Matching, and Exact-Weight-3-Star.


title: Light stop phenomenology

abstract:
  We consider the discovery potential of light stops in the MSSM at the LHC.
Here, we assume that the lightest neutralino is the LSP and that the lighter
stop is the NLSP. Direct stop pair production is difficult to probe in
scenarios with a small mass splitting between the stop and a neutralino. We
discuss two different search channels: the monojet and the two $b$--flavoured
jets and large missing transverse energy signature. We present the discovery
reach in the stop--neutralino mass plane for both channels. The latter process
is sensitive to the stop--higgsino--$b$ quark coupling. This allows us to test
a supersymmetry relation involving superpotential couplings. We briefly comment
on the possible precision with which the coupling can be measured.


title:
Spatially periodic domain wall pinning potentials: Asymmetric pinning
  and dipolar biasing

abstract:
  Domain wall propagation has been measured in continuous, weakly disordered,
quasi-two-dimensional, Ising-like magnetic layers that are subject to spatially
periodic domain wall pinning potentials. The potentials are generated
non-destructively using the stray magnetic field of ordered arrays of
magnetically hard [Co/Pt]$_m$ nanoplatelets which are patterned above and are
physically separated from the continuous magnetic layer. The effect of the
periodic pinning potentials on thermally activated domain wall creep dynamics
is shown to be equivalent, at first approximation, to that of a uniform,
effective retardation field, $H_{ret}$, which acts against the applied field,
$H$. We show that $H_{ret}$ depends not only on the array geometry but also on
the relative orientation of $H$ and the magnetization of the nanoplatelets. A
result of the latter dependence is that wall-mediated hysteresis loops obtained
for a set nanoplatelet magnetization exhibit many properties that are normally
associated with ferromagnet/antiferromagnet exchange bias systems. These
include a switchable bias, coercivity enhancement and domain wall roughness
that is dependent on the applied field polarity.


title:
On the structure of fundamental groups of conic-line arrangements having
  a cycle in their graph

abstract:
  The fundamental group of the complement of a plane curve is a very important
topological invariant. In particular, it is interesting to find out whether
this group is determined by the combinatorics of the curve or not, and whether
it is a direct sum of free groups and a free abelian group, or it has a
conjugation-free geometric presentation.
  In this paper, we investigate the structure of this fundamental group when
the graph of the conic-line arrangement is a unique cycle of length $n$ and the
conic passes through all the multiple points of the cycle. We show that if n is
odd, then the affine fundamental group is abelian but not conjugation-free. For
the even case, if n>4, then using quotients of the lower central series, we
show that the fundamental group is not even a direct sum of a free abelian
group and free groups.


title:
Balancing small fixed and proportional transaction cost in trading
  strategies

abstract:
  Transaction costs appear in financial markets in more than one form. There
are several results in the literature on small proportional transaction cost
and not that many on fixed transaction cost. In the present work, we
heuristically study the effect of both types of transaction cost by focusing on
a portfolio optimization. Here we assume the presence of fixed transaction cost
and that there is a balance between fixed and proportional transaction cost,
such that none of them dominates the other, asymptotically. We find out that
the deviation of value function, when the fixed transaction cost is
$\varepsilon$, from the Merton value function, without transaction cost, is of
order $\varepsilon^1/2$ which is different from the pure proportional cost of
$\varepsilon^2/3$. Based on this, we propose an expansion for the value
function in terms of powers of $\varepsilon^1/2$.


title: Pricing TARN Using a Finite Difference Method

abstract:
  Typically options with a path dependent payoff, such as Target Accumulation
Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper
describes a finite difference scheme for pricing a TARN option. Key steps in
the proposed scheme involve tracking of multiple one-dimensional finite
difference solutions, application of jump conditions at each cash flow exchange
date, and a cubic spline interpolation of results after each jump. Since a
finite difference scheme for TARN has significantly different features from a
typical finite difference scheme for options with a path independent payoff, we
give a step by step description on the implementation of the scheme, which is
not available in the literature. The advantages of the proposed finite
difference scheme over the Monte Carlo method are illustrated by examples with
three different knockout types. In the case of constant or time dependent
volatility models (where Monte Carlo requires simulation at cash flow dates
only), the finite difference method can be faster by an order of magnitude than
the Monte Carlo method to achieve the same accuracy in price. Finite difference
method can be even more efficient in comparison with Monte Carlo in the case of
local volatility model where Monte Carlo requires significantly larger number
of time steps. In terms of robust and accurate estimation of Greeks, the
advantage of the finite difference method will be even more pronounced.


title: Riemannian manifolds with local symmetry

abstract:
  We give a classification of many closed Riemannian manifolds M whose
universal cover possesses a nontrivial amount of symmetry. More precisely, we
consider closed Riemannian manifolds $M$ such that Isom$(\widetilde{M})$ has
noncompact connected components. We prove that in many cases, such a manifold
is as a fiber bundle over a locally homogeneous space. This is inspired by work
of Eberlein (for nonpositively curved manifolds) and Farb-Weinberger (for
aspherical manifolds), and generalizes work of Frankel (for a semisimple group
action). As an application, we characterize simply-connected Riemannian
manifolds with both compact and finite volume noncompact quotients.


title:
Dynamics of spin-1 bosons in an optical lattice: spin mixing, quantum
  phase revival spectroscopy and effective three-body interactions

abstract:
  We study the dynamics of spin-1 atoms in a periodic optical-lattice potential
and an external magnetic field in a quantum quench scenario where we start from
a superfluid ground state in a shallow lattice potential and suddenly raise the
lattice depth. The time evolution of the non-equilibrium state, thus created,
shows collective collapse-and-revival oscillations of matter-wave coherence as
well as oscillations in the spin populations. We show that the complex pattern
of these two types of oscillations reveals details about the superfluid and
magnetic properties of the initial many-body ground state. Furthermore, we show
that the strengths of the spin-dependent and spin-independent atom-atom
interactions can be deduced from the observations. The Hamiltonian that
describes the physics of the final deep lattice not only contains two-body
interactions but also effective multi-body interactions, which arise due to
virtual excitations to higher bands. We derive these effective spin-dependent
three-body interaction parameters for spin-1 atoms and describe how spin-mixing
is affected. Spinor atoms are unique in the sense that multi-body interactions
are directly evident in the in-situ number densities in addition to the
momentum distributions. We treat both antiferromagnetic (e.g. $^{23}$Na atoms)
and ferromagnetic (e.g. $^{87}$Rb and $^{41}$K) condensates.


title:
Measurement of energy relaxation in quantum Hall edge states utilizing
  quantum point contacts

abstract:
  We demonstrated a method to probe local electronic states and energy
relaxation in quantum Hall edge states utilizing quantum point contacts. We
evaluated relaxation lengths in two cases; first, with electron tunneling, and
second, only with energy exchange without tunneling between edge states. The
results were consistent with previous experiments and validated our method with
quantum point contacts. We applied this method to measure the energy relaxation
length around a hotspot in quantum Hall regimes and revealed the possible
short-distance relaxation process to be the relaxation due to energy exchange
between edge states without electron tunneling.


title:
Integrable model for density-modulated quantum condensates: solitons
  passing through a soliton lattice

abstract:
  An integrable model possessing inhomogeneous ground states is proposed as an
effective model of non-uniform quantum condensates such as supersolids and
Fulde--Ferrell--Larkin--Ovchinnikov superfluids. The model is a higher-order
analog of the nonlinear Schr\"odinger equation. We derive an $n$-soliton
solution via the inverse scattering theory with elliptic-functional background,
and reveal various kinds of soliton dynamics such as dark soliton billiards,
dislocations, gray solitons, and envelope solitons. We also provide the exact
bosonic and fermionic quasiparticle eigenstates and clarify their tunneling
phenomena. The solutions are expressed by a determinant of theta functions.

categories: cond-mat.quant-gas cond-mat.supr-con nlin.PS nlin.SI


title:
Mid-infrared laser phase-locking to a remote near-infrared frequency
  reference for high precision molecular spectroscopy

abstract:
  We present a new method for accurate mid-infrared frequency measurements and
stabilization to a near-infrared ultra-stable frequency reference, transmitted
with a long-distance fibre link and continuously monitored against
state-of-the-art atomic fountain clocks. As a first application, we measure the
frequency of an OsO4 rovibrational molecular line around 10 $\mu$m with a
state-of-the-art uncertainty of 8x10-13. We also demonstrate the frequency
stabilization of a mid-infrared laser with fractional stability better than
4x10-14 at 1 s averaging time and a line-width below 17 Hz. This new
stabilization scheme gives us the ability to transfer frequency stability in
the range of 10-15 or even better, currently accessible in the near-infrared or
in the visible, to mid-infrared lasers in a wide frequency range.


title:
First order global asymptotics for confined particles with singular pair
  repulsion

abstract:
  We study a physical system of $N$ interacting particles in $\mathbb{R}^d$,
$d\geq1$, subject to pair repulsion and confined by an external field. We
establish a large deviations principle for their empirical distribution as $N$
tends to infinity. In the case of Riesz interaction, including Coulomb
interaction in arbitrary dimension $d>2$, the rate function is strictly convex
and admits a unique minimum, the equilibrium measure, characterized via its
potential. It follows that almost surely, the empirical distribution of the
particles tends to this equilibrium measure as $N$ tends to infinity. In the
more specific case of Coulomb interaction in dimension $d>2$, and when the
external field is a convex or increasing function of the radius, then the
equilibrium measure is supported in a ring. With a quadratic external field,
the equilibrium measure is uniform on a ball.


title: The Child-Langmuir law in the quantum domain

abstract:
  It is shown using dimensional analysis that the maximum current density
J_{QCL} transported on application of a voltage V_g across a gap of size D
follows the relation J_{QCL} ~ \hbar^{3 - 2\alpha} V_g^\alpha /D^{5 - 2\alpha}.
The classical Child-Langmuir result is recovered at \alpha = 3/2 on demanding
that the scaling law be independent of \hbar. For a nanogap in the deep quantum
regime, additional inputs in the form of appropriate boundary conditions and
the behaviour of the exchange-correlation potential show that \alpha = 5/14.
This is verified numerically for several nanogaps. It is also argued that in
this regime, the limiting mechanism is quantum reflection from a downhill
potential due to a sharp change in slope seen by the electron on emerging
through the barrier.


title:
Approximating {0,1,2}-Survivable Networks with Minimum Number of Steiner
  Points

abstract:
  We consider low connectivity variants of the Survivable Network with Minimum
Number of Steiner Points (SN-MSP) problem: given a finite set $R$ of terminals
in a metric space (M,d), a subset $B \subseteq R$ of "unstable" terminals, and
connectivity requirements {r_{uv}: u,v \in R}, find a minimum size set $S
\subseteq M$ of additional points such that the unit-disc graph of $R \cup S$
contains $r_{uv}$ pairwise internally edge-disjoint and $(B \cup S)$-disjoint
$uv$-paths for all $u,v \in R$. The case when $r_{uv}=1$ for all $u,v \in R$ is
the {\sf Steiner Tree with Minimum Number of Steiner Points} (ST-MSP) problem,
and the case $r_{uv} \in \{0,1\}$ is the {\sf Steiner Forest with Minimum
Number of Steiner Points} (SF-MSP) problem. Let $\Delta$ be the maximum number
of points in a unit ball such that the distance between any two of them is
larger than 1. It is known that $\Delta=5$ in $\mathbb{R}^2$ The previous known
approximation ratio for {\sf ST-MSP} was $\lfloor (\Delta+1)/2
\rfloor+1+\epsilon$ in an arbitrary normed space \cite{NY}, and $2.5+\epsilon$
in the Euclidean space $\mathbb{R}^2$ \cite{cheng2008relay}. Our approximation
ratio for ST-MSP is $1+\ln(\Delta-1)+\epsilon$ in an arbitrary normed space,
which in $\mathbb{R}^2$ reduces to $1+\ln 4+\epsilon < 2.3863 +\epsilon$. For
SN-MSP with $r_{uv} \in \{0,1,2\}$, we give a simple $\Delta$-approximation
algorithm. In particular, for SF-MSP, this improves the previous ratio
$2\Delta$.


title: Cellular categories

abstract:
  We study locally presentable categories equipped with a cofibrantly generated
weak factorization system. Our main result is that these categories are closed
under 2-limits, in particular under pseudopullbacks. We give applications to
deconstructible classes in Grothendieck categories. We discuss pseudopullbacks
of combinatorial model categories.


title: ISM Processing in the Inner 20 pc in Galactic center

abstract:
  We present the Submillimeter Array (SMA) 157-pointing mosaic in 0.86 mm dust
continuum emission with 5$".1\times4"$.2 angular resolution, and the NRAO Green
Bank 100m Telescope (GBT) observations of the CS/C$^{34}$S/$^{13}$CS 1-0 and
SiO 1-0 emission with $\le20"$$\times18"$ angular resolution. The dust
continuum image marginally resolves at least several tens of 10-10$^{2}$
$M_{\odot}$ dense clumps in the 5$'$ field including the circumnuclear disk
(CND) and the exterior gas streamers. There is very good agreement between the
high resolution dust continuum map of the CND and all previous molecular line
observations. As the dust emission is the most reliable optically thin tracer
of the mass, free from most chemical and excitation effects, we demonstrate the
reality of the abundant localized structures within the CND, and their
connection to external gas structures. From the spectral line data, the
velocity dispersions of the dense clumps and their parent molecular clouds are
$\sim$10-20 times higher than their virial velocity dispersions. This supports
the idea that the CND and its immediate environment may not be stationary or
stable structures. Some of the dense gas clumps are associated with 22 GHz
water masers and 36.2 GHz and 44.1 GHz CH$_{3}$OH masers. However, we do not
find clumps which are bound by the gravity of the enclosed molecular gas.
Hence, the CH$_{3}$OH or H$_{2}$O maser emission may be due to strong
(proto)stellar feedback, which may be dispersing some of the gas clumps.


title: Lattice Paths and Order-preserving Partial Transformations

abstract:
  Let ${\cal PO}_n$ be the semigroup of all order-preserving partial
transformations of a finite chain. It is shown that there exist bijections
between the set of certain lattice paths in the Cartesian plane that start at
$(0,0)$, end at $(n-1,n-1)$, and certain subsemigroups of ${\cal PO}_n$.
Several consequences of these bijections were discussed.


title: Stochastic integration in Banach spaces - a survey

abstract:
  This paper presents a brief survey of the theory of stochastic integration in
Banach spaces. Expositions of the stochastic integrals in martingale type 2
spaces and UMD spaces are presented, as well as some applications of the latter
to vector-valued Malliavin calculus and the stochastic maximal regularity
problem. A new proof of the stochastic maximal regularity theorem is included.


title: Fractal structures in Adversarial Prediction

abstract:
  Fractals are self-similar recursive structures that have been used in
modeling several real world processes. In this work we study how "fractal-like"
processes arise in a prediction game where an adversary is generating a
sequence of bits and an algorithm is trying to predict them. We will see that
under a certain formalization of the predictive payoff for the algorithm it is
most optimal for the adversary to produce a fractal-like sequence to minimize
the algorithm's ability to predict. Indeed it has been suggested before that
financial markets exhibit a fractal-like behavior. We prove that a fractal-like
distribution arises naturally out of an optimization from the adversary's
perspective.
  In addition, we give optimal trade-offs between predictability and expected
deviation (i.e. sum of bits) for our formalization of predictive payoff. This
result is motivated by the observation that several time series data exhibit
higher deviations than expected for a completely random walk.


title: Optimal amortized regret in every interval

abstract:
  Consider the classical problem of predicting the next bit in a sequence of
bits. A standard performance measure is {\em regret} (loss in payoff) with
respect to a set of experts. For example if we measure performance with respect
to two constant experts one that always predicts 0's and another that always
predicts 1's it is well known that one can get regret $O(\sqrt T)$ with respect
to the best expert by using, say, the weighted majority algorithm. But this
algorithm does not provide performance guarantee in any interval. There are
other algorithms that ensure regret $O(\sqrt {x \log T})$ in any interval of
length $x$. In this paper we show a randomized algorithm that in an amortized
sense gets a regret of $O(\sqrt x)$ for any interval when the sequence is
partitioned into intervals arbitrarily. We empirically estimated the constant
in the $O()$ for $T$ upto 2000 and found it to be small -- around 2.1. We also
experimentally evaluate the efficacy of this algorithm in predicting high
frequency stock data.


title:
Novel Network Coding-based Techniques for Multi-layer Video Delivery
  over Multi-hop Wireless testbed

abstract:
  The actual performance of video delivery over wireless networks is best
captured through experimental studies over real testbed, which is crucial to
uncover the technical problems and practical challenges of realizing the
proposed video delivery techniques. Network coding (NC) provides a paradigm
shift to optimize the network resources for enhancing the video quality as a
result of delivery over multi-hop wireless networks. In this paper, we propose
a novel framework for evaluating the performance of NC-based video delivery
over multi-hop wireless networks. Based on an experimental testbed
implementation of inter-layer video coding and delivery, we propose a new
generalized technique for multi-hop interlayer NC in enhancing video delivery
quality. We evaluate the trade-off between complexity of multi-hop NC, and
video quality gain. We provide clear recommendations for best design choices of
NC-based inter-layer video coding and delivery over multi-hop wireless mesh
network considering link conditions and Packet Delivery Ratio (PDR). The
results show that using NC improves the layered video performance in single and
multi-hop network. The average number of decoded layers when using NC in single
hop outperforms that when using NC in multi-hop.


title: Classification of Topological Defects in Abelian Topological States

abstract:
  In this paper we propose the most general classification of point-like and
line-like extrinsic topological defects in (2+1)-dimensional Abelian
topological states. We first map generic extrinsic defects to boundary defects,
and then provide a classification of the latter. Based on this classification,
the most generic point defects can be understood as domain walls between
topologically distinct boundary regions. We show that topologically distinct
boundaries can themselves be classified by certain maximal subgroups of
mutually bosonic quasiparticles, called Lagrangian subgroups. We study the
topological properties of the point defects, including their quantum dimension,
localized zero modes, and projective braiding statistics.


title: Supersymmetry Breaking in Anti-de Sitter spacetime

abstract:
  We study the questions of how supersymmetry is spontaneously broken in Anti
de-Sitter spacetime. We verify that the would-be R-symmetry in $AdS_4$ plays a
central role for the existence of meta-stable supersymmetry breaking. To
illustrate, some well-known models such as Poloyni models and O'Raifeartaigh
models are investigated in detail. Our calculations are reliable in flat
spacetime limit and confirm us that meta-stable vacua are generic even though
quantum corrections are taken into account.


title:
The X-ray spectro-timing properties of a major radio flare episode in
  Cygnus X-3

abstract:
  We have performed a principal component analysis on the X-ray spectra of the
microquasar Cygnus X-3 from RXTE, INTEGRAL and Swift during a major flare
ejection event in 2006 May-July. The analysis showed that there are two main
variability components in play, i.e. two principal components explained almost
all the variability in the X-ray lightcurves. According to the spectral shape
of these components and spectral fits to the original data, the most probable
emission components corresponding to the principal components are
inverse-Compton scattering and bremsstrahlung. We find that these components
form a double-peaked profile when phase-folded with the peaks occurring in
opposite phases. This could be due to an asymmetrical wind around the companion
star with which the compact object is interacting.


title: Generalized Baumslag-Solitar groups: rank and finite index subgroups

abstract:
  A generalized Baumslag-Solitar (GBS) group is a finitely generated group
acting on a tree with infinite cyclic edge and vertex stabilizers. We show how
to determine effectively the rank (minimal cardinality of a generating set) of
a GBS group; as a consequence, one can compute the rank of the mapping torus of
a finite order outer automorphism of a free group $F_n$. We also show that the
rank of a finite index subgroup of a GBS group G cannot be smaller than the
rank of G. We determine which GBS groups are large (some finite index subgroup
maps onto $F_2$), and we solve the commensurability problem (deciding whether
two groups have isomorphic finite index subgroups) in a particular family of
GBS groups.


title:
Inner Fluctuations in Noncommutative Geometry without the first order
  condition

abstract:
  We extend inner fluctuations to spectral triples that do not fulfill the
first-order condition. This involves the addition of a quadratic term to the
usual linear terms. We find a semi-group of inner fluctuations, which only
depends on the involutive algebra A and which extends the unitary group of A.
This has a key application in noncommutative spectral models beyond the
Standard Model, of which we consider here a toy model.