title:
Notes on BPS Wilson Loops and the Cusp Anomalous Dimension in ABJM
  theory

abstract:
  We introduce a new purely bosonic, $\frac{1}{6}$ BPS Wilson loop for ABJM
theory on $S^3$ that couples scalar fields to a latitude at an angle $\theta$
on $S^2\in\mathbb{C}P^3$. Through localization of this operator, we relate the
expansion of the cusp anomalous dimension at small cusp angles to the
logarithmic derivative of the ABJM Wilson loop. This defines,
non-perturbatively in the 't Hooft coupling, the bremsstrahlung function
$B(\lambda)$ describing in three dimensions the soft radiation of a $W$-boson
undergoing a sudden change in trajectory. We compare our results for
$B(\lambda)$ to the known weak/strong coupling expansions of the function
$h(\lambda)$ that enters integrability. At weak coupling we precisely match the
previously known two-loop result. At strong coupling we find agreement at
leading order in $\sqrt{\lambda}$, but a mismatch of the constant coefficient.
We comment on the striking similarity that we observe between these two, in
principle, unrelated functions.


title: On the $\kappa$-Dirac Oscillator revisited

abstract:
  This Letter is based on the $\kappa$-Dirac equation, derived from the
$\kappa$-Poincar\'{e}-Hopf algebra. It is shown that the $\kappa$-Dirac
equation preserves parity while breaks charge conjugation and time reversal
symmetries. Introducing the Dirac oscillator prescription,
$\mathbf{p}\to\mathbf{p}-im\omega\beta\mathbf{r}$, in the $\kappa$-Dirac
equation, one obtains the $\kappa$-Dirac oscillator. Using a decomposition in
terms of spin angular functions, one achieves the deformed radial equations,
with the associated deformed energy eigenvalues and eigenfunctions. The
deformation parameter breaks the infinite degeneracy of the Dirac oscillator.
In the case where $\varepsilon=0$, one recovers the energy eigenvalues and
eigenfunctions of the Dirac oscillator.


title:
A path-integral approach to Bayesian inference for inverse problems
  using the semiclassical approximation

abstract:
  We demonstrate how path integrals often used in problems of theoretical
physics can be adapted to provide a machinery for performing Bayesian inference
in function spaces. Such inference comes about naturally in the study of
inverse problems of recovering continuous (infinite dimensional) coefficient
functions from ordinary or partial differential equations (ODE, PDE), a problem
which is typically ill-posed. Regularization of these problems using $L^2$
function spaces (Tikhonov regularization) is equivalent to Bayesian
probabilistic inference, using a Gaussian prior. The Bayesian interpretation of
inverse problem regularization is useful since it allows one to quantify and
characterize error and degree of precision in the solution of inverse problems,
as well as examine assumptions made in solving the problem -- namely whether
the subjective choice of regularization is compatible with prior knowledge.
Using path-integral formalism, Bayesian inference can be explored through
various perturbative techniques, such as the semiclassical approximation, which
we use in this manuscript. Perturbative path-integral approaches, while
offering alternatives to computational approaches like Markov-Chain-Monte-Carlo
(MCMC), also provide natural starting points for MCMC methods that can be used
to refine approximations.
  In this manuscript, we illustrate a path-integral formulation for inverse
problems and demonstrate it on an inverse problem in membrane biophysics as
well as inverse problems in potential theories involving the Poisson equation.

categories: physics.data-an hep-th math.OC math.ST q-bio.QM stat.TH


title:
Half-integral conservative post-Newtonian approximations in the redshift
  factor of black hole binaries

abstract:
  Recent perturbative self-force computations (Shah, Friedman & Whiting,
submitted to Phys. Rev. {\bf D}, arXiv:1312.1952 [gr-qc]), both numerical and
analytical, have determined that half-integral post-Newtonian terms arise in
the conservative dynamics of black-hole binaries moving on exactly circular
orbits. We look at the possible origin of these terms within the post-Newtonian
approximation, find that they essentially originate from non-linear
"tail-of-tail" integrals and show that, as demonstrated in the previous paper,
their first occurrence is at the 5.5PN order. The post-Newtonian method we use
is based on a multipolar-post-Minkowskian treatment of the field outside a
general matter source, which is re-expanded in the near zone and extended
inside the source thanks to a matching argument. Applying the formula obtained
for generic sources to compact binaries, we obtain the redshift factor of
circular black hole binaries (without spins) at 5.5PN order in the extreme mass
ratio limit. Our result fully agrees with the determination of the 5.5PN
coefficient by means of perturbative self-force computations reported in the
previously cited paper.


title: A Survey of Network-On-Chip Tools

abstract:
  Nowadays System-On-Chips (SoCs) have evolved considerably in term of
performances, reliability and integration capacity. The last advantage has
induced the growth of the number of cores or Intellectual Properties (IPs) in a
same chip. Unfortunately, this important number of IPs has caused a new issue
which is the intra-communication between the elements of a same chip. To
resolve this problem, a new paradigm has been introduced which is the
Network-On-Chip (NoC). Since the introduction of the NoC paradigm in the last
decade, new methodologies and approaches have been presented by research
community and many of them have been adopted by industrials. The literature
contains many relevant studies and surveys discussing NoC proposals and
contributions. However, few of them have discussed or proposed a comparative
study of NoC tools. The objective of this work is to establish a reliable
survey about available design, simulation or implementation NoC tools. We
collected an important amount of information and characteristics about NoC
dedicated tools that we will present throughout this survey. This study is
built around a respectable amount of references and we hope it will help
scientists.


title:
Bose-Einstein Condensates with Derivative and Long-Range Interactions as
  Set-Ups for Analog Black Holes

abstract:
  General types of Bose-Einstein condensates are considered. The formation of
black-hole analogues is examined for both short- and long-range interactions
for arbitrary spatial dimensions greater than two. The former case includes
non-linear derivative terms plus an inevitable external potential, while the
latter one consists solely of gravity-like self-interactions for which
intrinsic formation of analogue Schwarzschild-type background space-times is
possible. The corresponding geometries are studied, and it is shown how they
can be made stable. Their Hawking temperature is estimated, and it is found
that in certain set-ups it can be significantly increased, thus providing
better detectability.


title:
Alternative methods for top-quark mass determination at the Tevatron and
  LHC

abstract:
  I am summarizing here the determination of the top-quark mass from the CDF
and D0 Collaborations at the Tevatron and the ATLAS and CMS Collaborations at
the LHC using non-conventional methods. I am concentrating on the extraction of
the top-quark mass from the top-antitop cross-section, on the mass measurement
using the so-called endpoint method and on the top-quark mass determination
from the b-lifetime. Other alternative methods are described in another article


title: Spectral networks and Fenchel-Nielsen coordinates

abstract:
  We explain that spectral networks are a unifying framework that incorporates
both shear (Fock-Goncharov) and length-twist (Fenchel-Nielsen) coordinate
systems on moduli spaces of flat SL(2,C) connections, in the following sense.
Given a spectral network W on a punctured Riemann surface C, we explain the
process of "abelianization" which relates flat SL(2)-connections (with an
additional structure called "W-framing") to flat C*-connections on a covering.
For any W, abelianization gives a construction of a local Darboux coordinate
system on the moduli space of W-framed flat connections. There are two special
types of spectral network, combinatorially dual to ideal triangulations and
pants decompositions; these two types of network lead to Fock-Goncharov and
Fenchel-Nielsen coordinates respectively.


title:
Transience of the vacant set for near-critical random interlacements in
  high dimensions

abstract:
  The model of random interlacements is a one-parameter family $\mathcal I^u,$
$u \ge 0,$ of random subsets of $\mathbb{Z}^d,$ which locally describes the
trace of simple random walk on a $d$-dimensional torus run up to time $u$ times
its volume. Its complement, the so-called vacant set $\mathcal V^u$, has been
shown to undergo a non-trivial percolation phase-transition in $u;$ i.e., there
exists $u_*(d) \in (0, \infty)$ such that for $u \in [0, u_*(d))$ the vacant
set $\mathcal V^u$ contains a unique infinite connected component $\mathcal
V_\infty^u,$ while for $u > u_*(d)$ it consists of finite connected components.
Sznitman \cite{SZ11,SZ11B} showed that $u_*(d) \sim \log d,$ and in this
article we show the existence of $u(d) > 0$ with $\frac{u(d)}{u_*(d)} \to 1$ as
$d \to \infty$ such that $\mathcal V_\infty^{u}$ is transient for all $u \in
[0, u(d)).$


title: Amplification of Angular Rotations Using Weak Measurements

abstract:
  We present a weak measurement protocol that permits a sensitive estimation of
angular rotations based on the concept of weak-value amplification. The shift
in the state of a pointer, in both angular position and the conjugate orbital
angular momentum bases, is used to estimate angular rotations. This is done by
an amplification of both the real and imaginary parts of the weak-value of a
polarization operator that has been coupled to the pointer, which is a spatial
mode, via a spin-orbit coupling. Our experiment demonstrates the first
realization of weak-value amplification in the azimuthal degree of freedom. We
have achieved effective amplification factors as large as 100, providing a
sensitivity that is on par with more complicated methods that employ quantum
states of light or extremely large values of orbital angular momentum.


title:
Singular solutions, repeated roots and completeness for higher-spin
  chains

abstract:
  We investigate the completeness of the solutions of the Bethe equations for
the integrable spin-s isotropic (XXX) spin chain with periodic boundary
conditions. Solutions containing the exact string i s, i (s-1), ..., -i(s-1),
-is are singular. For s>1/2, there exist also "strange" solutions with repeated
roots, which nevertheless are physical (i.e., correspond to eigenstates of the
Hamiltonian). We derive conditions for the singular solutions and the solutions
with repeated roots to be physical. We formulate a conjecture for the number of
solutions with pairwise distinct roots in terms of the numbers of singular and
strange solutions. Using homotopy continuation, we solve the Bethe equations
numerically for s=1 and s=3/2 up to 8 sites, and find some support for the
conjecture. We also exhibit several examples of strange solutions.


title:
An Efficient Clustering Algorithm for Device-to-Device Assisted Virtual
  MIMO

abstract:
  In this paper, the utilization of mobile devices (MDs) as decode-and-forward
relays in a device-to-device assisted virtual MIMO (VMIMO) system is studied.
Single antenna MDs are randomly distributed on a 2D plane according to a
Poisson point process, and only a subset of them are sources leaving other idle
MDs available to assist them (relays). Our goal is to develop an efficient
algorithm to cluster each source with a subset of available relays to form a
VMIMO system under a limited feedback assumption. We first show that the NP-
hard optimization problem of precoding in our scenario can be approximately
solved by semidefinite relaxation. We investigate a special case with a single
source and analytically derive an upper bound on the average spectral
efficiency of the VMIMO system. Then, we propose an optimal greedy algorithm
that achieves this bound. We further exploit these results to obtain a
polynomial time clustering algorithm for the general case with multiple
sources. Finally, numerical simulations are performed to compare the
performance of our algorithm with that of an exhaustive clustering algorithm,
and it shown that these numerical results corroborate the efficiency of our
algorithm.


title:
Synchrophasor monitoring of single line outages via area angle and
  susceptance

abstract:
  The area angle is a scalar measure of power system area stress that responds
to line outages within the area and is a combination of synchrophasor
measurements of voltage angles around the border of the area. Both idealized
and practical examples are given to show that the variation of the area angle
for single line outages can be approximately related to changes in the overall
susceptance of the area and the line outage severity.


title:
Electronic structure of Zr-Ni-Sn systems: role of clustering and
  nanostructures in Half-Heusler and Heusler limits

abstract:
  Half-Heusler and Heusler compounds have been of great interest for several
decades for thermoelectric, magnetic, half-metallic and many other interesting
properties. Among these systems, Zr-Ni-Sn compounds are interesting
thermoelectrics which can go from semiconducting half-Heusler (HH) limit,
ZrNiSn, to metallic Heusler (FH) limit, ZrNi$_2$Sn. Recently Makogo et al. [J.
Am. Chem. Soc. 133, 18843 (2011)] found that dramatic improvement in the
thermoelectric power factor of HH can be achieved by putting excess Ni into the
system. This was attributed to an energy filtering mechanism due to the
formation of FH nanostructures in the HH matrix. Using density functional
theory we have investigated clustering and nanostructure formation in
HH$_{1-x}$FH$_x$ systems near the HH and FH ends and found that excess Ni atoms
in HH tend to stay close to each other and form nanoclusters of FH. On the
other hand, there is competing interaction between Ni-vacancies in FH which
prevent them from forming HH nano clusters. Effects of nano inclusions on the
electronic structure at both HH and FH ends will be discussed.


title: Notes on discrepancy in the pairwise comparisons method

abstract:
  The pairwise comparisons method is a convenient tool used when the relative
order among different concepts (alternatives) needs to be determined. One
popular implementation of the method is based on solving an eigenvalue problem
for the pairwise comparisons matrix. In such cases the ranking result the
principal eigenvector of the pairwise comparison matrix is adopted, whilst the
eigenvalue is used to determine the index of inconsistency. A lot of research
has been devoted to the critical analysis of the eigenvalue based approach. One
of them is the work (Bana e Costa and Vansnick, 2008). In their work authors
define the conditions of order preservation (COP) and show that even for a
sufficiently consistent pairwise comparisons matrices, this condition can not
be met. The present work defines a more precise criteria for determining when
the COP is met. To formulate the criteria a discrepancy factor is used
describing how far the input to the ranking procedure is from the ranking
result.


title: Multinets in $\mathbb P^2$

abstract:
  Multinets are certain configurations of lines and points with multiplicities
in the complex projective plane P2. They are used in the studies of resonance
and characteristic varieties of complex hyperplane arrangement complements and
cohomology of Milnor fibers. From combinatorics viewpoint they can be
considered as generalizations of Latin squares. Very few exam- ples of
multinets with non-trivial multiplicities are known. In this paper, we present
new examples of multinets. These are obtained by using an analogue of nets in
P3 and intersecting them by planes.


title:
Protein Contact Prediction by Integrating Joint Evolutionary Coupling
  Analysis and Supervised Learning

abstract:
  Protein contacts contain important information for protein structure and
functional study, but contact prediction from sequence remains very
challenging. Both evolutionary coupling (EC) analysis and supervised machine
learning methods are developed to predict contacts, making use of different
types of information, respectively. This paper presents a group graphical lasso
(GGL) method for contact prediction that integrates joint multi-family EC
analysis and supervised learning. Different from existing single-family EC
analysis that uses residue co-evolution information in only the target protein
family, our joint EC analysis uses residue co-evolution in both the target
family and its related families, which may have divergent sequences but similar
folds. To implement joint EC analysis, we model a set of related protein
families using Gaussian graphical models (GGM) and then co-estimate their
precision matrices by maximum-likelihood, subject to the constraint that the
precision matrices shall share similar residue co-evolution patterns. To
further improve the accuracy of the estimated precision matrices, we employ a
supervised learning method to predict contact probability from a variety of
evolutionary and non-evolutionary information and then incorporate the
predicted probability as prior into our GGL framework. Experiments show that
our method can predict contacts much more accurately than existing methods, and
that our method performs better on both conserved and family-specific contacts.


title:
Absolute continuity of the periodic Schr\"odinger operator in
  transversal geometry

abstract:
  We show that the spectrum of a Schr\"odinger operator on $\mathbb{R}^n$,
$n\ge 3$, with a periodic smooth Riemannian metric, whose conformal multiple
has a product structure with one Euclidean direction, and with a periodic
electric potential in $L^{n/2}_{\text{loc}}(\mathbb{R}^n)$, is purely
absolutely continuous. Previously known results in the case of a general metric
are obtained in [12], see also [8], under the assumption that the metric, as
well as the potential, are reflection symmetric.


title: Efficient Lineage for SUM Aggregate Queries

abstract:
  AI systems typically make decisions and find patterns in data based on the
computation of aggregate and specifically sum functions, expressed as queries,
on data's attributes. This computation can become costly or even inefficient
when these queries concern the whole or big parts of the data and especially
when we are dealing with big data. New types of intelligent analytics require
also the explanation of why something happened. In this paper we present a
randomised algorithm that constructs a small summary of the data, called
Aggregate Lineage, which can approximate well and explain all sums with large
values in time that depends only on its size. The size of Aggregate Lineage is
practically independent on the size of the original data. Our algorithm does
not assume any knowledge on the set of sum queries to be approximated.


title: Equivariant functions and vector-valued modular forms

abstract:
  For any discrete group $\Gamma$ and any 2-dimensional complex representation
$\rho$ of $\Gamma$, we introduce the notion of $\rho-$equivariant functions,
and we show that they are parameterized by vector-valued modular forms. We also
provide examples arising from the monodromy of differential equations.


title: Vector-valued automorphic forms and vector bundles

abstract:
  While vector-valued automorphic forms can be defined for an arbitrary
Fuchsian group $\Gamma$ and an arbitrary representation $R$ of $\Gamma$ in
GL$(n,{\mathbb C})$, their existence has been established in the literature
only when restrictions are imposed on both $\Gamma$ and $R$. In this paper, we
prove the existence of $n$ linearly independent vector-valued automorphic forms
for any Fuchsian group $\Gamma$ and any $n$-dimensional complex representation
$R$ of $\Gamma$. To this end, we realize these automorphic forms as global
sections of a special rank $n$ vector bundle built using solutions to the
Riemann-Hilbert problem over various noncompact Riemann surfaces and Kodaira's
vanishing theorem.


title: Contact perturbations of Reebless foliations are universally tight

abstract:
  We give a complete proof of the fact that a contact structure that is
sufficiently close to a Reebless foliation is universally tight.


title: A counterexample to sparse removal

abstract:
  The Tur\'{a}n number of a graph $H$, denoted $\mbox{ex}(n,H)$, is the maximum
number of edges in an $n$-vertex graph with no subgraph isomorphic to $H$.
Solymosi conjectured that if $H$ is any graph and $\mbox{ex}(n,H) =
O(n^{\alpha})$ where $\alpha > 1$, then any $n$-vertex graph with the property
that each edge lies in exactly one copy of $H$ has $o(n^{\alpha})$ edges. This
can be viewed as conjecturing a possible extension of the removal lemma to
sparse graphs, and is well-known to be true when $H$ is a non-bipartite graph,
in particular when $H$ is a triangle, due to Ruzsa and Szemer\'{e}di. Using
Sidon sets we exhibit infinitely many bipartite graphs $H$ for which the
conjecture is false.


title: The quivers of the hereditary algebras of type $\tilde{A}_n$

abstract:
  This is a translation of the diploma thesis of Thomas Br\"ustle,
Darstellungsk\"ocher der erblichen Algebren vom Typ $\tilde{A}_n$, written in
German, at the University of Zurich, August 1990. Supervisor: P. Gabriel.
Translated by K. Baur, May 2013


title: Theoretical Modeling of Internal Hydraulic Jump in Density Currents

abstract:
  In this paper, we propose an analytical framework for internal hydraulic
jumps. Density jumps or internal hydraulic jumps occur when a supper critical
flow of water discharges into a stagnant layer of water with slightly different
density. The approach used here is control volume method which is also used to
analyze ordinary hydraulic jumps. The important difference here is that
entrainment is taken into account. Using conservation equations with the aid of
some simplifying assumptions we come to an equation that gives jump downstream
height as function of jump upstream characteristics and the entrainment. To
determine the magnitude of downstream height we use an experimental equation
for calculating the entrainment. Finally we verify our framework by comparing
the height that we gain from the derived equation with some experimental data.


title: Optical signatures of silicon-vacancy spins in diamond

abstract:
  Colour centres in diamond have emerged as versatile tools for solid-state
quantum technologies ranging from quantum information to metrology, where the
nitrogen-vacancy centre is the most studied to-date. Recently, this toolbox has
expanded to include different materials for their nanofabrication
opportunities, and novel colour centres to realize more efficient spin-photon
quantum interfaces. Of these, the silicon-vacancy centre stands out with
ultrabright single photon emission predominantly into the desirable zero-phonon
line. The challenge for utilizing this centre is to realise the hitherto
elusive optical access to its electronic spin. Here, we report spin-tagged
resonance fluorescence from the negatively charged silicon-vacancy centre. In
low-strain bulk diamond spin-selective excitation under finite magnetic field
reveals a spin-state purity approaching unity in the excited state. We also
investigate the effect of strain on the centres in nanodiamonds and discuss how
spin selectivity in the excited state remains accessible in this regime.


title: An Auction-driven Self-organizing Cloud Delivery Model

abstract:
  The three traditional cloud delivery models -- IaaS, PaaS, and SaaS --
constrain access to cloud resources by hiding their raw functionality and
forcing us to use them indirectly via a restricted set of actions. Can we
introduce a new delivery model, and, at the same time, support improved
security, a higher degree of assurance, find relatively simple solutions to the
hard cloud resource management problems, eliminate some of the inefficiencies
related to resource virtualization, allow the assembly of clouds of clouds,
and, last but not least, minimize the number of interoperability standards?
  We sketch a self-organizing architecture for very large compute clouds
composed of many-core processors and heterogeneous coprocessors. We discuss how
self-organization will address each of the challenges described above. The
approach is {\em bid-centric}. The system of heterogeneous cloud resources is
dynamically, and autonomically, configured to bid to meet the needs identified
in a high-level task or service specification. When the task is completed, or
the service is retired, the resources are released for subsequent reuse.
  Our approach mimics the process followed by individual researchers who, in
response to a call for proposals released by a funding agency, organize
themselves in groups of various sizes and specialities. If the bid is
successful, then the group carries out the proposed work and releases the
results. After the work is completed, individual researchers in the group
disperse, possibly joining other groups or submitting individual bids in
response to other proposals. Similar protocols are common to other human
activities such as procurement management.


title:
A Robust Mathematical Model for Clauser-Horne Experiments, With
  Implications for Rigorous Statistical Analysis

abstract:
  Recent experiments have reached detection efficiencies sufficient to close
the detection loophole, testing the Clauser-Horne (CH) version of Bell's
inequality. For a similar future experiment to be completely loophole-free, it
will be important to have discrete experimental trials with randomized
measurement settings for each trial, and the statistical analysis should not
overlook the possibility of a local state varying over time with possible
dependence on earlier trials (the "memory loophole"). In this paper, a
mathematical model for such a CH experiment is presented, and a method for
statistical analysis that is robust to memory effects is introduced.
Additionally, a new method for calculating exact p-values for martingale-based
statistics is described; previously, only non-sharp upper bounds derived from
the Azuma-Hoeffding inequality have been available for such statistics. This
improvement decreases the required number of experimental trials to demonstrate
non-locality. The statistical techniques are applied to the data of recent
experiments and found to perform well.


title:
Pairing Symmetry, Phase diagram and Edge Modes in Topological
  Fulde-Ferrell-Larkin-Ovchinnikov Phase

abstract:
  The realizations of spin-orbit coupling in cold atoms lead to a burst of
research activities in the searching of topological matters in ultracold atom
systems. The very recent theoretical predictions show that topological
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids can be realized with proper
spin-orbit coupling and Zeeman fields. In this work, a comprehensive
understanding of the pairing symmetry, phase diagram and the edge modes in this
new topological matter are presented. The momentum of the Cooper pairs plays
the role of renormalizing the in-plane Zeeman field and chemical potential. The
in-plane Zeeman field and finite momentum pairing induce asymmetry to the
effective $p$-wave pairing, apart from a small fraction of higher orbital
components. The phase diagram is composed by different phases, which are
determined by the topology and band gap nature of the superfluids. Especially,
the gapped and gapless topological FFLO phase have totally different finite
size effect. These novel features show that the spin-orbit coupled cold atoms
provides an important platform in realizing topological matters which may not
be materialized with solids.


title:
On the amplitude of External Perturbation and the Chaos via Devil's
  Staircase -Stability of Attractors -

abstract:
  We made the chaotic circuit proposed by Chua and the memristic circuit
proposed by Muthuswamy and Chua, and analyzed the behavior of the voltage of
the capacitor, electric current in the inductor and the voltage of the
memristor by adding an external sinusoidal oscillation ${\dot y}(t)\simeq {\dot
i_L}(t)$ of a type $\gamma\omega \cos\omega t$, while the ${\dot x}(t)\simeq
{\dot v_C}(t)$ is given by $y(t)/C$, and studied the Devil's staircase route to
chaos.
  We compared the frequency of the driving oscillation $f_s$ and the frequency
of the response $f_d$ in the window and assigned $W=f_s/f_d$ to each window.
When capacitor $C=1.0$, we observe stable attractors of Farey sequences
$\displaystyle W=\{\frac{1}{2}, \frac{2}{3},\frac{3}{4},\frac{4}{5}, \cdots
,\frac{14}{15},\frac{1}{1}\}$, which can be interpreted as hidden attractors,
while when $C=1.2$, we observe unstable attractors.
  Possible role of octonions in quantum mechanics and Cartan's supersymmetry is
discussed.


title:
On Elementary Theories of Ordinal Notation Systems based on Reflection
  Principles

abstract:
  We consider the constructive ordinal notation system for the ordinal
${\epsilon_0}$ that were introduced by L.D. Beklemishev. There are fragments of
this system that are ordinal notation systems for the smaller ordinals
${\omega_n}$ (towers of ${\omega}$-exponentiations of the height $n$). This
systems are based on Japaridze's provability logic $\mathbf{GLP}$. They are
closely related with the technique of ordinal analysis of $\mathbf{PA}$ and
fragments of $\mathbf{PA}$ based on iterated reflection principles. We consider
this notation system and it's fragments as structures with the signatures
selected in a natural way. We prove that the full notation system and it's
fragments, for ordinals ${\ge\omega_4}$, have undecidable elementary theories.
We also prove that the fragments of the full system, for ordinals
${\le\omega_3}$, have decidable elementary theories. We obtain some results
about decidability of elementary theory, for the ordinal notation systems with
weaker signatures.


title: Decision Trees, Protocols, and the Fourier Entropy-Influence Conjecture

abstract:
  Given $f:\{-1, 1\}^n \rightarrow \{-1, 1\}$, define the \emph{spectral
distribution} of $f$ to be the distribution on subsets of $[n]$ in which the
set $S$ is sampled with probability $\widehat{f}(S)^2$. Then the Fourier
Entropy-Influence (FEI) conjecture of Friedgut and Kalai (1996) states that
there is some absolute constant $C$ such that $\operatorname{H}[\widehat{f}^2]
\leq C\cdot\operatorname{Inf}[f]$. Here, $\operatorname{H}[\widehat{f}^2]$
denotes the Shannon entropy of $f$'s spectral distribution, and
$\operatorname{Inf}[f]$ is the total influence of $f$. This conjecture is one
of the major open problems in the analysis of Boolean functions, and settling
it would have several interesting consequences.
  Previous results on the FEI conjecture have been largely through direct
calculation. In this paper we study a natural interpretation of the conjecture,
which states that there exists a communication protocol which, given subset $S$
of $[n]$ distributed as $\widehat{f}^2$, can communicate the value of $S$ using
at most $C\cdot\operatorname{Inf}[f]$ bits in expectation.
  Using this interpretation, we are able show the following results:
  1. First, if $f$ is computable by a read-$k$ decision tree, then
$\operatorname{H}[\widehat{f}^2] \leq 9k\cdot \operatorname{Inf}[f]$.
  2. Next, if $f$ has $\operatorname{Inf}[f] \geq 1$ and is computable by a
decision tree with expected depth $d$, then $\operatorname{H}[\widehat{f}^2]
\leq 12d\cdot \operatorname{Inf}[f]$.
  3. Finally, we give a new proof of the main theorem of O'Donnell and Tan
(ICALP 2013), i.e. that their FEI$^+$ conjecture composes.
  In addition, we show that natural improvements to our decision tree results
would be sufficient to prove the FEI conjecture in its entirety. We believe
that our methods give more illuminating proofs than previous results about the
FEI conjecture.


title:
Exploring new frontiers in statistical physics with a new, parallel
  Wang-Landau framework

abstract:
  Combining traditional Wang-Landau sampling for multiple replica systems with
an exchange of densities of states between replicas, we describe a general
framework for simulations on massively parallel Petaflop supercomputers. The
advantages and general applicability of the method for simulations of complex
systems are demonstrated for the classical 2D Potts spin model featuring a
strong first-order transition and the self-assembly of lipid bilayers in
amphiphilic solutions in a continuous model.


title:
One Billion Word Benchmark for Measuring Progress in Statistical
  Language Modeling

abstract:
  We propose a new benchmark corpus to be used for measuring progress in
statistical language modeling. With almost one billion words of training data,
we hope this benchmark will be useful to quickly evaluate novel language
modeling techniques, and to compare their contribution when combined with other
advanced techniques. We show performance of several well-known types of
language models, with the best results achieved with a recurrent neural network
based language model. The baseline unpruned Kneser-Ney 5-gram model achieves
perplexity 67.6; a combination of techniques leads to 35% reduction in
perplexity, or 10% reduction in cross-entropy (bits), over that baseline.
  The benchmark is available as a code.google.com project; besides the scripts
needed to rebuild the training/held-out data, it also makes available
log-probability values for each word in each of ten held-out data sets, for
each of the baseline n-gram models.


title: Non-Linear Resonance in Relativistic Preheating

abstract:
  Inflation in the early Universe can be followed by a brief period of
preheating, resulting in rapid and non-equilibrium particle production through
the dynamics of parametric resonance. However, the parametric resonance effect
is very sensitive to the linearity of the reheating sector. Additional
self-interactions in the reheating sector, such as non-canonical kinetic terms
like the DBI Lagrangian, may enhance or frustrate the parametric resonance
effect of preheating. In the case of a DBI reheating sector, preheating is
described by parametric resonance of a damped relativistic harmonic oscillator.
In this paper, we illustrate how the non-linear terms in the relativistic
oscillator shut down the parametric resonance effect. This limits the
effectiveness of preheating when there are non-linear self-interactions.


title:
The puzzling chemical composition of GJ 436b's atmosphere: influence of
  tidal heating on the chemistry

abstract:
  The dissipation of the tidal energy deposited on eccentric planets may induce
a heating of the planet that affects its atmospheric thermal structure. Here we
study the influence of tidal heating on the atmospheric composition of the
eccentric (e = 0.16) "hot Neptune" GJ 436b, for which inconclusive chemical
abundances are retrieved from multiwavelength photometric observations carried
out during primary transit and secondary eclipse. We build up a one-dimensional
model of GJ 436b's atmosphere in the vertical direction and compute the
pressure-temperature and molecular abundances profiles for various plausible
internal temperatures of the planet (up to 560 K) and metallicities (from solar
to 100 times solar), using a radiative-convective model and a chemical model
which includes thermochemical kinetics, vertical mixing, and photochemistry. We
find that the CO/CH4 abundance ratio increases with metallicity and tidal
heating, and ranges from 1/20 to 1000 within the ranges of metallicity and
internal temperature explored. Water vapour locks most of the oxygen and
reaches a very high abundance, whatever the metallicity and internal
temperature of the planet. The CO2/H2O abundance ratio increases dramatically
with metallicity, and takes values between 1e-5-1e-4 with solar elemental
abundances and 0.1 for a metallicity 100 times solar. None of the atmospheric
models based on solid physical and chemical grounds provide a fully
satisfactory agreement with available observational data, although the
comparison of calculated spectra and observations seem to point to models with
a high metallicity and efficient tidal heating, in which high CO/CH4 abundance
ratios and warm temperatures in the dayside atmosphere are favoured.


title:
A geometric realization of the ultradiscrete periodic Toda lattice via
  tropical plane curves

abstract:
  This is a review article on a tropical geometric realization of the
ultradiscrete periodic Toda lattice (UD-pTL). Time evolution of the UD-pTL is
translated into an addition on the Picard group of its spectral curve, which is
a tropical hyperelliptic curve of arbitrary genus depending on the system size.
The addition on the Picard group can be realized by using intersection of
several tropical plane curves, one of which is the spectral curve. In addition,
the tropical eigenvector map, which maps a point in the phase space of the
UD-pTL into a set of points on the spectral curve, can also be realized by
using intersection of tropical curves. Thus, if the initial values are given
then the time evolution of the UD-pTL is completely translated into a motion of
intersection points of tropical plane curves. Moreover, all tropical plane
curves appearing in the curve intersection are explicitly given in terms of the
conserved quantities of the UD-pTL.


title: Large Galois groups with applications to Zariski density

abstract:
  We introduce the first provably efficient algorithm to check if a finitely
generated subgroup of an almost simple semi-simple group over the rationals is
Zariski-dense. We reduce this question to one of computing Galois groups, and
to this end we describe efficient algorithms to check if the Galois group of a
polynomial $p$ with integer coefficients is "generic" (which, for arbitrary
polynomials of degree $n$ means the full symmetric group $S_n,$ while for
reciprocal polynomials of degree $2n$ it means the hyperoctahedral group $C_2
\wr S_n.$). We give efficient algorithms to verify that a polynomial has Galois
group $S_n,$ and that a reciprocal polynomial has Galois group $C_2 \wr S_n.$
We show how these algorithms give efficient algorithms to check if a set of
matrices $\mathcal{G}$ in $\mathop{SL}(n, \mathbb{Z})$ or $\mathop{Sp}(2n,
\mathbb{Z})$ generate a \emph{Zariski dense} subgroup.
  The complexity of doing this in$\mathop{SL}(n, \mathbb{Z})$ is of order
$O(n^4 \log n \log \|\mathcal{G}\|)\log \epsilon$ and in $\mathop{Sp}(2n,
\mathbb{Z})$ the complexity is of order $O(n^8 \log n\log \|\mathcal{G}\|)\log
\epsilon$ In general semisimple groups we show that Zariski density can be
confirmed or denied in time of order $O(n^14 \log \|\mathcal{G}\|\log
\epsilon),$ where $\epsilon$ is the probability of a wrong "NO" answer, while
$\|\mathcal{G}\|$ is the measure of complexity of the input (the maximum of the
Frobenius norms of the generating matrices). The algorithms work essentially
without change over algebraic number fields, and in other semi-simple groups.
However, we restrict to the case of the special linear and symplectic groups
and rational coefficients in the interest of clarity.


title:
Global simulations of magnetorotational turbulence II: turbulent
  energetics

abstract:
  Magnetorotational turbulence draws its energy from gravity and ultimately
releases it via dissipation. However, the quantitative details of this energy
flow have not been assessed for global disk models. In this work we examine the
energetics of a well-resolved, three-dimensional, global magnetohydrodynamic
accretion disk simulation by evaluating statistically-averaged mean-field
equations for magnetic, kinetic, and internal energy using simulation data. The
results reveal that turbulent magnetic (kinetic) energy is primarily injected
by the correlation between Maxwell (Reynolds) stresses and shear in the (almost
Keplerian) mean flow, and removed by dissipation. This finding differs from
previous work using local (shearing-box) models, which indicated that turbulent
kinetic energy was primarily sourced from the magnetic energy reservoir.
Lorentz forces provide the bridge between the magnetic and kinetic energy
reservoirs, converting ~ 1/5 of the total turbulent magnetic power input into
turbulent kinetic energy. The turbulent energies (both magnetic and kinetic)
are mainly driven by terms associated with the turbulent fields, with only a
minor influence from mean magnetic fields. The interaction between mean and
turbulent fields is most evident in the induction equation, with the mean
radial magnetic field being strongly influenced by the turbulent electromotive
force (EMF). During the quasi-steady turbulent state roughly 2/3 of the
Poynting flux travels into the corona, with the remainder transporting magnetic
energy in the radial direction. In contrast to previous studies, the
stress-related part of the Poynting flux is found to dominate, which may have
important implications for "reflection" models of Seyfert galaxy coronae that
typically invoke a picture of buoyant rising of magnetic flux tubes via
advection.


title: Unveiling the MSSM Neutral Higgs Bosons with Leptons and a Bottom Quark

abstract:
  We investigate the prospects for the discovery of neutral Higgs bosons
produced with a bottom quark where the Higgs decays into a pair of tau leptons
and the taus decay into an electron-muon pair, i.e. $bg \to b\phi^0 \to
b\tau^+\tau^- \to be^\pm\mu^\mp + E\!\!\!/_T$, $\phi^0 = h^0, H^0, A^0$. Our
study has been done within the framework of the Minimal Supersymmetric Standard
Model. We consider the dominant physics backgrounds including the production of
Drell-Yan processes ($b\tau^+\tau^-$ and $j\tau^+\tau^-, j = q, g$), top quark
pair ($t\bar{t}$), $tW$ and $jWW$ with realistic acceptance cuts and
efficiencies. We present $5\sigma$ discovery contours for the neutral Higgs
bosons in the ($M_A,\tan\beta$) plane as well as the region with a favored
light Higgs mass (123 GeV $\le m_h\le$ 129 GeV). Promising results are found
for the CP-odd pseudoscalar ($A^0$) and the heavier CP-even scalar ($H^0$)
Higgs bosons with masses up to 800 GeV and $\tan\beta \simeq 50$ at the LHC
with a center of mass energy ($\sqrt{s}$) of 14 TeV and an integrated
luminosity ($L$) of 300 fb$^{-1}$. With $\sqrt{s} =$ 14 TeV and $L =$ 3000
fb$^{-1}$, LHC will be able to discover the Higgs pseudoscalar and the heavier
Higgs scalar beyond $M_A = 1000$ GeV.


title: Improving Fast Dual Ascent for MPC - Part I: The Distributed Case

abstract:
  In dual decomposition, the dual to an optimization problem with a specific
structure is solved in distributed fashion using (sub)gradient and recently
also fast gradient methods. The traditional dual decomposition suffers from two
main short-comings. The first is that the convergence is often slow, although
fast gradient methods have significantly improved the situation. The second is
that computation of the optimal step-size requires centralized computations,
which hinders a fully distributed implementation of the algorithm. In this
paper, the first issue is addressed by providing a tighter characterization of
the dual function than what has previously been reported in the literature.
Then a distributed and a parallel algorithm are presented in which the provided
dual function approximation is minimized in each step. Since the approximation
is more accurate than the approximation used in standard and fast dual
decomposition, the convergence properties are improved. For the second issue,
we extend a recent result to allow for a fully distributed parameter selection
in the algorithm. Further, we show how to apply the proposed algorithms to
optimization problems arising in distributed model predictive control (DMPC)
and show that the proposed distributed algorithm enjoys distributed
reconfiguration, i.e. plug-and-play, in the DMPC context.


title: Improving Fast Dual Ascent for MPC - Part II: The Embedded Case

abstract:
  Recently, several authors have suggested the use of first order methods, such
as fast dual ascent and the alternating direction method of multipliers, for
embedded model predictive control. The main reason is that they can be
implemented using simple arithmetic operations only. However, a known
limitation of gradient-based methods is that they are sensitive to
ill-conditioning of the problem data. In this paper, we present a fast dual
gradient method for which the sensitivity to ill-conditioning is greatly
reduced. This is achieved by approximating the negative dual function with a
quadratic upper bound with different curvature in different directions in the
algorithm, as opposed to having the same curvature in all directions as in
standard fast gradient methods. The main contribution of this paper is a
characterization of the set of matrices that can be used to form such a
quadratic upper bound to the negative dual function. We also describe how to
choose a matrix from this set to get an improved approximation of the dual
function, especially if it is ill-conditioned, compared to the approximation
used in standard fast dual gradient methods. This can give a significantly
improved performance as illustrated by a numerical evaluation on an
ill-conditioned AFTI-16 aircraft model.


title: Cs2NaAl1-xCrxF6: A family of compounds presenting magnetocaloric effect

abstract:
  In this paper we explore the magnetocaloric effect (MCE) of chromium-doped
elpasolite Cs$_2$NaAl$_{1-x}$Cr$_x$F$_6$ (x = 0.01 and 0.62) single crystals.
Our magnetization and heat capacity data show the magnetocaloric potentials to
be comparable to those of garnets, perovskites and other fluorides, producing
magnetic entropy changes of 0.5 J/kg$\cdot$K (x = 0.01) and 11 J/kg$\cdot$K (x
= 0.62), and corresponding adiabatic temperature changes of 4 K and 8 K,
respectively. These values are for a magnetic field change of 5 T at a
temperature around 3 K. A clear Schottky anomaly below 10 K, which becomes more
apparent when an external magnetic field is applied, was observed and related
to the splitting of the Cr$^{3+}$ energy levels. These results hint at a new
family of materials with potential wide use in cryorefrigeration.


title:
Measurement of Galaxy Cluster Integrated Comptonization and Mass Scaling
  Relations with the South Pole Telescope

abstract:
  We describe a method for measuring the integrated Comptonization (YSZ) of
clusters of galaxies from measurements of the Sunyaev-Zel'dovich (SZ) effect in
multiple frequency bands and use this method to characterize a sample of galaxy
clusters detected in South Pole Telescope (SPT) data. We test this method on
simulated cluster observations and verify that it can accurately recover
cluster parameters with negligible bias. In realistic simulations of an
SPT-like survey, with realizations of cosmic microwave background anisotropy,
point sources, and atmosphere and instrumental noise at typical SPT-SZ survey
levels, we find that YSZ is most accurately determined in an aperture
comparable to the SPT beam size. We demonstrate the utility of this method to
measure YSZ and to constrain mass scaling relations using X-ray mass estimates
for a sample of 18 galaxy clusters from the SPT-SZ survey. Measuring YSZ within
a 0.75' radius aperture, we find an intrinsic log-normal scatter of 21+/-11% in
YSZ at a fixed mass. Measuring YSZ within a 0.3 Mpc projected radius
(equivalent to 0.75' at the survey median redshift z = 0.6), we find a scatter
of 26+/-9%. Prior to this study, the SPT observable found to have the lowest
scatter with mass was cluster detection significance. We demonstrate, from both
simulations and SPT observed clusters, that YSZ measured within an aperture
comparable to the SPT beam size is equivalent, in terms of scatter with cluster
mass, to SPT cluster detection significance.


title: Basic Properties of Coherent-Squeezed States Revisited

abstract:
  In this paper we treat coherent-squeezed states of Fock space once more and
study some basic properties of them from a geometrical point of view.
  Since the set of coherent-squeezed states $\{\ket{\alpha, \beta}\ |\ \alpha,
\beta \in \fukuso\}$ makes a real 4-dimensional surface in the Fock space
${\cal F}$ (which is of course not flat), we can calculate its metric.
  On the other hand, we know that coherent-squeezed states satisfy the minimal
uncertainty of Heisenberg under some condition imposed on the parameter space
$\{\alpha, \beta\}$, so that we can study the metric from the view point of
uncertainty principle. Then we obtain a surprising simple form (at least to
us).
  We also make a brief review on Holonomic Quantum Computation by use of a
simple model based on nonlinear Kerr effect and coherent-squeezed operators.


title: Measuring Dark Matter Distribution in Directional Direct Detection

abstract:
  Direct detection of dark matter with directional sensitivity offers not only
measurement of both recoil energy and direction of dark matter, but also a way
to understand dark matter distribution in the Galaxy. Maxwell distribution is
usually supposed as the distribution near the Earth, however, deviation from
that, caused by tidal streams in the Galaxy, has been suggested. We explore the
possibility of distinguishing the distribution by direct detection using
nuclear emulsions.


title: Efficient Large-Scale Graph Processing on Hybrid CPU and GPU Systems

abstract:
  The increasing scale and wealth of inter-connected data, such as those
accrued by social network applications, demand the design of new techniques and
platforms to efficiently derive actionable knowledge from large-scale graphs.
However, real-world graphs are famously difficult to process efficiently. Not
only they have a large memory footprint, but also most graph algorithms entail
memory access patterns with poor locality, data-dependent parallelism and a low
compute-to-memory access ratio. Moreover, most real-world graphs have a highly
heterogeneous node degree distribution, hence partitioning these graphs for
parallel processing and simultaneously achieving access locality and
load-balancing is difficult.
  This work starts from the hypothesis that hybrid platforms (e.g.,
GPU-accelerated systems) have both the potential to cope with the heterogeneous
structure of real graphs and to offer a cost-effective platform for
high-performance graph processing. This work assesses this hypothesis and
presents an extensive exploration of the opportunity to harness hybrid systems
to process large-scale graphs efficiently. In particular, (i) we present a
performance model that estimates the achievable performance on hybrid
platforms; (ii) informed by the performance model, we design and develop TOTEM
- a processing engine that provides a convenient environment to implement graph
algorithms on hybrid platforms; (iii) we show that further performance gains
can be extracted using partitioning strategies that aim to produce partitions
that each matches the strengths of the processing element it is allocated to,
finally, (iv) we demonstrate the performance advantages of the hybrid system
through a comprehensive evaluation that uses real and synthetic workloads (as
large as 16 billion edges), multiple graph algorithms that stress the system in
various ways, and a variety of hardware configurations.


title: A Landau de Gennes theory of liquid crystal elastomers

abstract:
  In this article, we study minimization of the Landau-de Gennes energy for
liquid crystal elastomer.The total energy, is of the sum of the Lagrangian
elastic stored energy function of the elastomer and the Eulerian Landau-de
Gennes energy of the liquid crystal. Our model consider two sources of
anisotropy represented by the traceless nematic order tensor $Q$ (rigid units),
and the positive definite step-length tensor $L$ (network). This work is
motivated by the study of cytoskeletal networks which can be regarded as
consisting of rigid rod units crosslinked into a polymeric-type network.
  Due to the mixed Eulerian-Lagrangian structure of the energy, it is essential
that the deformation maps $\varphi$ be invertible. We require sufficient
regularity of the fields $(\varphi, Q)$ of the problem, and that the
deformation map satisfies the Ciarlet-Necas condition. These, in turn,
determine what boundary conditions are admissible, which include the case of
Dirichlet conditions on both fields. The approach of including the
Rapini-Papoular surface energy for the pull-back tensor $\tilde Q$ is also
discussed. The regularity requirements lead us to consider powers of the
gradient of the order tensor $Q$ higher than quadratic in the energy.
  We assume polyconvexity of the stored energy function with respect to the
effective deformation tensor and apply methods from isotropic nonlinear
elasticity. We formulate a necessary and sufficient condition to guarantee this
invertibility property in terms of the growth to infinity of the bulk liquid
crystal energy $f(Q)$, as the minimum eigenvalue of $Q$ approaches the singular
limit of $-\frac{1}{3}$. $L$ becomes singular as the minimum eigenvalue of $Q$
reaches $-\frac{1}{3}$. Lower bounds on the eigenvalues of $Q$ are needed to
ensure compatibility between the theories of Landau-de Gennes and Maier-Saupe
of nematics (see Ball 2010).


title: Sparse Allreduce: Efficient Scalable Communication for Power-Law Data

abstract:
  Many large datasets exhibit power-law statistics: The web graph, social
networks, text data, click through data etc. Their adjacency graphs are termed
natural graphs, and are known to be difficult to partition. As a consequence
most distributed algorithms on these graphs are communication intensive. Many
algorithms on natural graphs involve an Allreduce: a sum or average of
partitioned data which is then shared back to the cluster nodes. Examples
include PageRank, spectral partitioning, and many machine learning algorithms
including regression, factor (topic) models, and clustering. In this paper we
describe an efficient and scalable Allreduce primitive for power-law data. We
point out scaling problems with existing butterfly and round-robin networks for
Sparse Allreduce, and show that a hybrid approach improves on both.
Furthermore, we show that Sparse Allreduce stages should be nested instead of
cascaded (as in the dense case). And that the optimum throughput Allreduce
network should be a butterfly of heterogeneous degree where degree decreases
with depth into the network. Finally, a simple replication scheme is introduced
to deal with node failures. We present experiments showing significant
improvements over existing systems such as PowerGraph and Hadoop.


title: Coxeter's frieze patterns and discretization of the Virasoro orbit

abstract:
  We show that the space of classical Coxeter's frieze patterns can be viewed
as a discrete version of a coadjoint orbit of the Virasoro algebra. The
canonical (cluster) (pre)symplectic form on the space of frieze patterns is a
discretization of the Kirillov symplectic form. We relate a continuous version
of frieze patterns to conformal metrics of constant curvature in dimension 2.


title:
Possible generation of anomalously soft quark excitations at nonzero
  temperature: Nonhyperbolic dispersion of parapion and van Hove singularity

abstract:
  We study the quark spectrum at finite temperature near and above the
pseudocritical temperature of the chiral phase transition incorporating the
effects of the collective modes with the quantum number of the sigma
(parasigma) and pion (parapion) in a chiral effective model with a nonzero
current quark mass. Below the pion zero-binding temperature where the pionic
modes are bound, the quark self-energy has van Hove singularity induced by the
scattering of quarks with the composite bound pions with a nonhyperbolic
dispersion curve. This singularity is found to cause a drastic change in the
quark spectrum from that in the mean field picture near the pseudocritical
temperature: The quark spectrum has an unexpected sharp peak at an energy
considerably lower than the constituent quark mass, while the spectrum
approaches the mean field one at high temperatures. We clarify that the
emergence of this anomalous structure of the quark spectral function originates
from the composite nature of the pionic modes with a non-Lorentz invariant
dispersion relation in the medium at finite temperature.


title:
Mathematical Model of Colorectal Cancer with Monoclonal Antibody
  Treatments

abstract:
  We present a new mathematical model of colorectal cancer growth and its
response to monoclonal-antibody (mAb) therapy. Although promising, most mAb
drugs are still in trial phases, and the possible variations in the dosing
schedules of those currently approved for use have not yet been thoroughly
explored. To investigate the effectiveness of current mAb treatment schedules,
and to test hypothetical treatment strategies, we have created a system of
nonlinear ordinary differential equations (ODE) to model colorectal cancer
growth and treatment. The model includes tumor cells, elements of the host's
immune response, and treatments. Model treatments include the chemotherapy
agent irinotecan and one of two monoclonal antibodies - cetuximab, which is
FDA-approved for colorectal cancer, and panitumumab, which is still being
evaluated in clinical trials. The model incorporates patient-specific
parameters to account for individual variations in immune system strength and
in medication efficacy against the tumor. We have simulated outcomes for groups
of virtual patients on treatment protocols for which clinical trial data are
available, using a range of biologically reasonable patient-specific parameter
values. Our results closely match clinical trial results for these protocols.
We also simulated experimental dosing schedules, and have found new schedules
which, in our simulations, reduce tumor size more effectively than current
treatment schedules. Additionally, we examined the system's equilibria and
sensitivity to parameter values. In the absence of treatment, tumor evolution
is most affected by the intrinsic tumor growth rate and carrying capacity. When
treatment is introduced, tumor growth is most affected by drug-specific PK/PD
parameters.


title:
Rounding Lasserre SDPs using column selection and spectrum-based
  approximation schemes for graph partitioning and Quadratic IPs

abstract:
  We present an approximation scheme for minimizing certain Quadratic Integer
Programming problems with positive semidefinite objective functions and global
linear constraints. This framework includes well known graph problems such as
Minimum graph bisection, Edge expansion, Sparsest Cut, and Small Set expansion,
as well as the Unique Games problem. These problems are notorious for the
existence of huge gaps between the known algorithmic results and NP-hardness
results. Our algorithm is based on rounding semidefinite programs from the
Lasserre hierarchy, and the analysis uses bounds for low-rank approximations of
a matrix in Frobenius norm using columns of the matrix.
  For all the above graph problems, we give an algorithm running in time
$n^{O(r/\epsilon^2)}$ with approximation ratio
$\frac{1+\epsilon}{\min\{1,\lambda_r\}}$, where $\lambda_r$ is the $r$'th
smallest eigenvalue of the normalized graph Laplacian $\mathcal{L}$. In the
case of graph bisection and small set expansion, the number of vertices in the
cut is within lower-order terms of the stipulated bound. Our results imply
$(1+O(\epsilon))$ factor approximation in time $n^{O(r^\ast/\epsilon^2)}$ where
is the number of eigenvalues of $\mathcal{L}$ smaller than $1-\epsilon$ (for
variants of sparsest cut, $\lambda_{r^\ast} \ge \mathrm{OPT}/\epsilon$ also
suffices, and as $\mathrm{OPT}$ is usually $o(1)$ on interesting instances of
these problems, this requirement on $r^\ast$ is typically weaker). For Unique
Games, we give a factor $(1+\frac{2+\epsilon}{\lambda_r})$ approximation for
minimizing the number of unsatisfied constraints in $n^{O(r/\epsilon)}$ time,
improving upon an earlier bound for solving Unique Games on expanders. We also
give an algorithm for independent sets in graphs that performs well when the
Laplacian does not have too many eigenvalues bigger than $1+o(1)$.


title:
Order on the Fixed Points of the Gieseker Variety With Respect to the
  Torus Action

abstract:
  In this paper I consider three families of orders on the set of r-
multipartitions of n, depending on r rational parameters. The one we are
interested in is a geometric order on the set of fixed points for a torus
action on the Gieseker variety. The other two serve as bounds for the geometric
one, providing an almost accurate description.


title:
Spherical tilings by congruent quadrangles over pseudo-double wheels
  (III) - the essential uniqueness in case of convex tiles

abstract:
  In [B.Gruenbaum, G.C. Shephard, Spherical tilings with transitivity
properties, in: The geometric vein, Springer, New York, 1981, pp. 65-98], they
proved "for every spherical normal tiling by congruent tiles, if it is
isohedral, then the graph is a Platonic solid, an Archimedean dual, an n-gonal
bipyramid (n>2), or an n-gonal trapezohedron (i.e., the pseudo-double wheel of
2n faces)". In the classification of spherical monohedral tilings, one
naturally asks an "inverse problem" of their result: For a spherical monohedral
tiling of the above mentioned topologies, when is the tiling isohedral? We
prove that for any spherical monohedral quadrangular tiling being topologically
a trapezohedron, if the number of faces is 6, or 8, if the tile is a kite, a
dart or a rhombi, or if the tile is convex, then the tiling is isohedral.


title: Rare-event Probability Estimation via Empirical Likelihood Maximization

abstract:
  We explore past and recent developments in rare-event probability estimation
with a particular focus on a novel Monte Carlo technique Empirical Likelihood
Maximization (ELM). This is a versatile method that involves sampling from a
sequence of densities using MCMC and maximizing an empirical likelihood. The
quantity of interest, the probability of a given rare-event, is estimated by
solving a convex optimization program related to likelihood maximization.
Numerical experiments are performed using this new technique and benchmarks are
given against existing robust algorithms and estimators.


title:
Response to a population bottleneck can be used to infer recessive
  selection

abstract:
  Here we present the first genome wide statistical test for recessive
selection. This test uses explicitly non-equilibrium demographic differences
between populations to infer the mode of selection. By analyzing the transient
response to a population bottleneck and subsequent re-expansion, we
qualitatively distinguish between alleles under additive and recessive
selection. We analyze the response of the average number of deleterious
mutations per haploid individual and describe time dependence of this quantity.
We introduce a statistic, $B_R$, to compare the number of mutations in
different populations and detail its functional dependence on the strength of
selection and the intensity of the population bottleneck. This test can be used
to detect the predominant mode of selection on the genome wide or regional
level, as well as among a sufficiently large set of medically or functionally
relevant alleles.


title:
An Atlas of Galaxy Spectral Energy Distributions from the Ultraviolet to
  the Mid-Infrared

abstract:
  We present an atlas of 129 spectral energy distributions for nearby galaxies,
with wavelength coverage spanning from the UV to the mid-infrared. Our atlas
spans a broad range of galaxy types, including ellipticals, spirals, merging
galaxies, blue compact dwarfs and luminous infrared galaxies. We have combined
ground-based optical drift-scan spectrophotometry with infrared spectroscopy
from Spitzer and Akari, with gaps in spectral coverage being filled using
MAGPHYS spectral energy distribution models. The spectroscopy and models were
normalized, constrained and verified with matched-aperture photometry measured
from Swift, GALEX, SDSS, 2MASS, Spitzer and WISE images. The availability of 26
photometric bands allowed us to identify and mitigate systematic errors present
in the data. Comparison of our spectral energy distributions with other
template libraries and the observed colors of galaxies indicates that we have
smaller systematic errors than existing atlases, while spanning a broader range
of galaxy types. Relative to the prior literature, our atlas will provide
improved K-corrections, photometric redshifts and star-formation rate
calibrations.


title: BPS $M2$-branes in $AdS_4\times Q^{1, 1, 1}$ Dual to Loop Operators

abstract:
  In this paper, we first compute the Killing spinors of $AdS_4\times Q^{1, 1,
1}$ and its certain orbifolds. Based on this, two classes of $M2$-brane
solutions are found. The first class of solutions includes $M2$-branes dual to
Wilson loops in the fundamental representation as special cases. The second
class includes the candidates of the holographic description of vortex loops in
the dual field theories.


title: Muon spin spectroscopy in multiferroic (Cu,Zn)$_{3}$Mo$_{2}$O$_{9}$

abstract:
  We present the muon spin relaxation/rotation spectra in the multiferroic
compound (Cu,Zn)$_{3}$Mo$_{2}$O$_{9}$. The parent material
Cu$_{3}$Mo$_{2}$O$_{9}$ has a multiferroic phase below $T_{\rm N}$ = 8.0 K,
where the canted antiferromagnetism and the ferroelectricity coexist. The
asymmetry time spectra taken at RIKEN-RAL pulsed muon facility show a drastic
change at $T_{\rm N}$. At low temperatures the weakly beating oscillation
caused by the static internal magnetic fields in the antiferromagnetic phase
was observed in Cu$_{3}$Mo$_{2}$O$_{9}$ and the lightly ($0.5\%$) Zn-doped
sample. From the fitting of the oscillating term, we obtain the order parameter
in these samples: ferromagnetic moment in two sublattices of antiferromagnet.
In the heavily ($5.0\%$) Zn-doped sample, the muon-spin oscillation is rapidly
damped. The frequency-domain spectrum of this sample suggests a formation of
magnetic superstructure.


title:
Noncommutative information is revealed from Hawking radiation as
  tunneling

abstract:
  We revisit the tunneling process from a Schwarzschild black hole in the
noncommutative spacetime and obtain the non-thermal tunneling probability. In
such non-thermal spectrum, the correlations are discovered, which can carry the
information about the noncommutativity. Thus this enlightens a way to find the
noncommutative information in the Hawking radiation. The entropy is also shown
to be conserved in the whole radiation process, which implies that the
unitarity is held even for the Hawking radiation from noncommutative black
holes.


title: Geometry of Defects in Solids

abstract:
  The appealing connection between non-Euclidean geometries and defects in
solids is brought forth in this article. Drawing a correspondence between the
nature of a defect and a specific geometric property of the material space not
only illuminates the underlying structure of defects in solids but also
provides an unambiguous way to represent defect densities within a physical
theory. We present a rigorous background of the relevant concepts from
classical differential geometry, as well as illustrations of isolated defects
in a lattice, to motivate the relationship between continuous defect densities
and various tensor fields in differential geometry. We identify the
Riemann-Christoffel tensor (or curvature tensor), the Cartan tensor (or torsion
tensor), and the nonmetricity tensor (obtained from the covariant derivative of
the metric tensor), associated with the material space, with the density of
disclinations, dislocations, and point-defects (vacancies, interstitials,
substitutional), respectively. We end our discussion with remarks on the
elastic stress field associated with defect distribution and on the analogy
between the present theory and the general theory of relativity.


title:
On Motzkin-Straus Type of Results and Frankl-F\"uredi Conjecture for
  Hypergraphs

abstract:
  A remarkable connection between the order of a maximum clique and the
Graph-Lagrangian of a graph was established by Motzkin and Straus in 1965. This
connection and its extension were useful in both combinatorics and
optimization. Since then, Graph-Lagrangian has been a useful tool in extremal
combinatorics. In this paper, we give a parametrized Graph-Lagrangian for
non-uniform hypergraphs and provide several Motzkin-Straus type results for
nonuniform hypergraphs which generalize results from [1] and [2]. Another part
of the paper concerns a long-standing conjecture of Frankl-F\"uredi on
Graph-Lagrangians of hypergraphs. We show the connection between the
Graph-Lagrangian of $\{1, r_1, r_2, \cdots, r_l\}$-hypergraphs and $\{ r_1,
r_2, \cdots, r_l\}$-hypergraphs. Some of our results provide solutions to the
maximum value of a class of polynomial functions over the standard simplex of
the Euclidean space.


title: Heat kernel coupling for multiple graph analysis

abstract:
  In this paper, we introduce heat kernel coupling (HKC) as a method of
constructing multimodal spectral geometry on weighted graphs of different size
without vertex-wise bijective correspondence. We show that Laplacian averaging
can be derived as a limit case of HKC, and demonstrate its applications on
several problems from the manifold learning and pattern recognition domain.


title: Weak value as an indicator of back-action

abstract:
  In this study we critically examine some important papers on weak measurement
and weak values. We find some insufficiency and mistakes in these papers, and
we demonstrate that the real parts of weak values provide the back-action to
the post-selection, which is caused by weak measurement. Two examples, a
counterfactual statement of Hardy's paradox and experiments that determine the
average trajectory of photons passing through double slits, are investigated
from our view point.


title: Periodic optical rogue waves

abstract:
  Random excitation of intense periodic highly-localized single-cycle light
pulses in a stochastic background by continuous-wave stimulated Brillouin
scattering in long optical fibers with weak feedback is found experimentally.
Events with low period numbers are dominant and the optical feedback is crucial
for the phenomenon. A three-wave coupling model for the phenomenon is proposed.
The results are in good qualitative agreement with the observed phenomenon. The
latter should be relevant to the understanding of similar rogue wave events in
other nonlinear dissipative systems.


title:
Parametric density-based optimization of partition in cluster analysis,
  with applications

abstract:
  We developed an optimal in the natural sense algorithm of partition in
cluster analysis based on the densities of observations in the different
hypotheses. These densities may be characterized, for instance, as the
multivariate so-called "quasi-Gaussian distribution".
  We describe also the possible applications in technical diagnosis, demography
and philology.


title:
Conic Optimization via Operator Splitting and Homogeneous Self-Dual
  Embedding

abstract:
  We introduce a first order method for solving very large convex cone
programs. The method uses an operator splitting method, the alternating
directions method of multipliers, to solve the homogeneous self-dual embedding,
an equivalent feasibility problem involving finding a nonzero point in the
intersection of a subspace and a cone. This approach has several favorable
properties. Compared to interior-point methods, first-order methods scale to
very large problems, at the cost of requiring more time to reach very high
accuracy. Compared to other first-order methods for cone programs, our approach
finds both primal and dual solutions when available or a certificate of
infeasibility or unboundedness otherwise, is parameter-free, and the
per-iteration cost of the method is the same as applying a splitting method to
the primal or dual alone. We discuss efficient implementation of the method in
detail, including direct and indirect methods for computing projection onto the
subspace, scaling the original problem data, and stopping criteria. We describe
an open-source implementation, which handles the usual (symmetric)
non-negative, second-order, and semidefinite cones as well as the
(non-self-dual) exponential and power cones and their duals. We report
numerical results that show speedups over interior-point cone solvers for large
problems, and scaling to very large general cone programs.


title: Parallel Multi-Block ADMM with o(1/k) Convergence

abstract:
  This paper introduces a parallel and distributed extension to the alternating
direction method of multipliers (ADMM) for solving convex problem: minimize
$\sum_{i=1}^N f_i(x_i)$ subject to $\sum_{i=1}^N A_i x_i=c, x_i\in
\mathcal{X}_i$. The algorithm decomposes the original problem into N smaller
subproblems and solves them in parallel at each iteration. This Jacobian-type
algorithm is well suited for distributed computing and is particularly
attractive for solving certain large-scale problems.
  This paper introduces a few novel results. Firstly, it shows that extending
ADMM straightforwardly from the classic Gauss-Seidel setting to the Jacobian
setting, from 2 blocks to N blocks, will preserve convergence if matrices $A_i$
are mutually near-orthogonal and have full column-rank. Secondly, for general
matrices $A_i$, this paper proposes to add proximal terms of different kinds to
the N subproblems so that the subproblems can be solved in flexible and
efficient ways and the algorithm converges globally at a rate of o(1/k).
Thirdly, a simple technique is introduced to improve some existing convergence
rates from O(1/k) to o(1/k).
  In practice, some conditions in our convergence theorems are conservative.
Therefore, we introduce a strategy for dynamically tuning the parameters in the
algorithm, leading to substantial acceleration of the convergence in practice.
Numerical results are presented to demonstrate the efficiency of the proposed
method in comparison with several existing parallel algorithms.
  We implemented our algorithm on Amazon EC2, an on-demand public computing
cloud, and report its performance on very large-scale basis pursuit problems
with distributed data.


title:
Cross-Layer MIMO Transceiver Optimization for Multimedia Streaming in
  Interference Networks

abstract:
  In this paper, we consider dynamic precoder/decorrelator optimization for
multimedia streaming in MIMO interference networks. We propose a truly
cross-layer framework in the sense that the optimization objective is the
application level performance metrics for multimedia streaming, namely the
playback interruption and buffer overflow probabilities. The optimization
variables are the MIMO precoders/decorrelators at the transmitters and the
receivers, which are adaptive to both the instantaneous channel condition and
the playback queue length. The problem is a challenging multi-dimensional
stochastic optimization problem and brute-force solution has exponential
complexity. By exploiting the underlying timescale separation and special
structure in the problem, we derive a closed-form approximation of the value
function based on continuous time perturbation. Using this approximation, we
propose a low complexity dynamic MIMO precoder/decorrelator control algorithm
by solving an equivalent weighted MMSE problem. We also establish the technical
conditions for asymptotic optimality of the low complexity control algorithm.
Finally, the proposed scheme is compared with various baselines through
simulations and it is shown that significant performance gain can be achieved.


title: Perturbation of Browder Spectrum of Upper-triangular Operator Matrices

abstract:
  Let $M_{C}=\left(\begin{array}{cc}A&C\\0&B\\\end{array} \right)$ is a 2-by-2
upper triangular operator matrix acting on the Banach space $X\oplus Y$ or
Hilbert space $H\oplus K$. For the most import spectra such as spectrum,
essential spectrum and Weyl spectrum, the characterizations of the
perturbations of $M_{C}$ on Banach space have been presented. However, the
characterization for the Browder spectrum on the Banach space is still unknown.
The goal of this paper is to present some necessary and sufficient conditions
for $M_C$ to be Browder for some $C\in B(Y,X)$ by using an alternative approach
based on matrix representation of operators and the ghost index theorem.
Moreover, in the Hilbert space case the characterizations of the Fredholm and
invertible perturbations of Browder spectrum are also given.


title: On the Lyapunov function for complex-balanced mass-action systems

abstract:
  We present a new proof, using the log-sum inequality, that the
pseudo-Helmholtz free energy function is a Lyapunov function for
complex-balanced mass-action systems. This proof is shorter and simpler than
previous proofs.


title:
Magnonic Band Structure, Complete Bandgap and Collective Spin Wave
  Excitation in Nanoscale Two--Dimensional Magnonic Crystals

abstract:
  We present the observation of a complete bandgap and collective spin wave
excitation in two-dimensional magnonic crystals comprised of arrays of
nanoscale antidots and nanodots, respectively. Considering that the frequencies
dealt with here fall in the microwave band, these findings can be used for the
development of suitable magnonic metamaterials and spin wave based signal
processing. We also present the application of a numerical procedure, to
compute the dispersion relations of spin waves for any high symmetry direction
in the first Brillouin zone. The results obtained from this procedure has been
reproduced and verified by the well established plane wave method for an
antidot lattice, when magnetization dynamics at antidot boundaries is pinned.
The micromagnetic simulation based method can also be used to obtain
iso--frequency countours of spin waves. Iso--frequency contours are analougous
of the Fermi surfaces and hence, they have the potential to radicalize our
understanding of spin wave dynamics. The physical origin of bands, partial and
full magnonic bandgaps has been explained by plotting the spatial distribution
of spin wave energy spectral density. Although, unfettered by rigid assumptions
and approximations, which afflict most analytical methods used in the study of
spin wave dynamics, micromagnetic simulations tend to be computationally
demanding. Thus, the observation of collective spin wave excitation in the case
of nanodot arrays, which can obviate the need to perform simulations may also
prove to be valuable.


title:
A Decision Model for Supporting Task Allocation Processes in Global
  Software Development

abstract:
  Today, software-intensive systems are increasingly being developed in a
globally distributed way. However, besides its benefit, global development also
bears a set of risks and problems. One critical factor for successful project
management of distributed software development is the allocation of tasks to
sites, as this is assumed to have a major influence on the benefits and risks.
We introduce a model that aims at improving management processes in globally
distributed projects by giving decision support for task allocation that
systematically regards multiple criteria. The criteria and causal relationships
were identified in a literature study and refined in a qualitative interview
study. The model uses existing approaches from distributed systems and
statistical modeling. The article gives an overview of the problem and related
work, introduces the empirical and theoretical foundations of the model, and
shows the use of the model in an example scenario.


title: Optimal variance estimation without estimating the mean function

abstract:
  We study the least squares estimator in the residual variance estimation
context. We show that the mean squared differences of paired observations are
asymptotically normally distributed. We further establish that, by regressing
the mean squared differences of these paired observations on the squared
distances between paired covariates via a simple least squares procedure, the
resulting variance estimator is not only asymptotically normal and root-$n$
consistent, but also reaches the optimal bound in terms of estimation variance.
We also demonstrate the advantage of the least squares estimator in comparison
with existing methods in terms of the second order asymptotic properties.


title:
Measurement of pretzelosity asymmetry of charged pion production in
  Semi-Inclusive Deep Inelastic Scattering on a polarized $^3$He target

abstract:
  An experiment to measure single-spin asymmetries in semi-inclusive production
of charged pions in deep-inelastic scattering on a transversely polarized
$^3$He target was performed at Jefferson Lab in the kinematic region of
$0.16<x<0.35$ and $1.4<Q^2<2.7$ ${\rm GeV^2}$. The pretzelosity asymmetries on
$^3$He, which can be expressed as the convolution of the $h^\perp_{1T}$
transverse momentum dependent distribution functions and the Collins
fragmentation functions in the leading order, were measured for the first time.
Using the effective polarization approximation, we extracted the corresponding
neutron asymmetries from the measured $^3$He asymmetries and cross-section
ratios between the proton and $^3$He. Our results show that for both
$\pi^{\pm}$ on $^3$He and on the neutron the pretzelosity asymmetries are
consistent with zero within experimental uncertainties.


title:
Deterministic and stochastic analysis of distributed order systems using
  operational matrix

abstract:
  The fractional order system, which is described by the fractional order
derivative and integral, has been studied in many engineering areas. Recently,
the concept of fractional order has been generalized to the distributed order
concept, which is a parallel connection of fractional order integrals and
derivatives taken to the infinitesimal limit in delta order. On the other hand,
there are very few numerical methods available for the analysis of distributed
order systems, particularly under stochastic forcing. This paper first proposes
a numerical scheme for analyzing the behavior of a SISO linear system with a
single term distributed order differentiator/integrator using an operational
matrix in the time domain under both deterministic and random forcing. To
assess the stochastic distributed order system, the existing Monte-Carlo,
polynomial chaos and frequency methods are first adopted to the stochastic
distributed order system for comparison. The numerical examples demonstrate the
accuracy and computational efficiency of the proposed method for analyzing
stochastic distributed order systems.


title:
Interpreting the Spin-down Evolutions of Isolated Neutron Stars with
  Hall Effects

abstract:
  The observed long-term spin-down evolution of isolated radio pulsars cannot
be explained by the standard magnetic dipole radiation with a constant braking
torque. However, how and why the torque varies still remains controversial,
which is a major issue in understanding neutron stars. Many pulsars have been
observed with significant long-term changes of their spin-down rates modulated
by quasi-periodic oscillations. Applying the phenomenological model of pulsar
timing noise we developed recently to the observed precise pulsar timing data
of isolated neutron stars, here we show that the observed long-term evolutions
of their spin-down rates and quasi-periodic modulations can be explained by
Hall effects in their crusts. Therefore the evolution of their crustal magnetic
fields, rather than that in their cores, dominates the observed long term
spin-down evolution of these young pulsars. Understanding of the nature of
pulsar timing noise not only reveals the interior physics of neutron stars, but
also allows physical modeling of pulsar spin-down and thus improves the
sensitivity of gravitational wave detections with pulsars.


title: Hadron spectra from overlap fermions on HISQ gauge configurations

abstract:
  Adopting a mixed action approach, we report here results on hadron spectra
containing one or more charm quarks. We use overlap valence quarks on a
background of 2+1+1 flavor HISQ gauge configurations generated by the MILC
collaboration. We also study the ratio of leptonic decay constants, f_Ds*/f_Ds.
Results are obtained at two lattice spacings.


title: Deformations of box complexes

abstract:
  Box complex is a $\mathbb{Z}_2$-space associated to a graph, and it is known
that a certain $\mathbb{Z}_2$-homotopy invariant of it, called the
$\mathbb{Z}_2$-index, gives an effective lower bound for the chromatic number.
On the other hand, we show that any $\mathbb{Z}_2$-homotopy invariant of the
box complex is not equivalent to the chromatic number. Namely, we construct a
graph homomorphism $f:X \rightarrow Y$ such that it gives rise to a
$\mathbb{Z}_2$-homotopy equivalence between their box complexes, but $X$ and
$Y$ have different chromatic numbers. To see this, we show that some
deformations of graphs do not change the $\mathbb{Z}_2$-simple homotopy types
of box complexes.


title:
Completeness of one two-interval boundary value problem with
  transmission conditions

abstract:
  This paper presents a new approach to the two-interval Sturm-Liouville
eigenfunction expansions, based essentially on the method of integral
equations. We consider the Sturm-Liouville problem together with two
supplementary transmission conditions at one interior point. Further we develop
Green's function method for spectral analysis of the considered problem in
modified Hilbert space.


title: Proper Biconservative immersions into the Euclidean space

abstract:
  In this paper, using the framework of equivariant differential geometry, we
study proper $SO(p+1) \times SO(q+1)$-invariant biconservative hypersurfaces
into the Euclidean space ${\mathbb R}^n$ ($n=p+q+2$) and proper
$SO(p+1)$-invariant biconservative hypersurfaces into the Euclidean space
${\mathbb R}^n$ ($n=p+2$). Moreover, we show that, in these two classes of
invariant families, there exists no proper biharmonic immersion.


title: Superfluid light in propagating geometries

abstract:
  We review how the paraxial approximation naturally leads to a hydrodynamic
description of light propagation in a Kerr nonlinear medium analogous to the
Gross-Pitaevskii equation for the temporal evolution of the order parameter of
a superfluid. The main features of the many-body collective dynamics of these
fluids of light in a propagating geometry are discussed: Generation and
observation of Bogoliubov sound waves on top of the fluid is first described.
Experimentally accessible manifestations of superfluidity are then highlighted.
Perspectives in view of realizing analog models of gravity are finally given.


title: Geometry and percolation on half planar triangulations

abstract:
  We analyze the geometry of domain Markov half planar triangulations. In
\cite{AR13} it is shown that there exists a one-parameter family of measures
supported on half planar triangulations satisfying translation invariance and
domain Markov property. We study the geometry of these maps and show that they
exhibit a sharp phase-transition in view of their geometry at $\alpha = 2/3$.
For $\alpha<2/3$, the maps form a tree-like stricture with infinitely many
small cut-sets. For $\alpha > 2/3$, we obtain maps of hyperbolic nature with
exponential growth and anchored expansion. Some results about the geometry of
percolation clusters on such maps and random walk on them are also obtained.


title: Skewon field and cosmic wave propagation

abstract:
  For the study of the gravitational coupling of electromagnetism and the
equivalence principle, we have used the spacetime constitutive tensor density
{chi}ijkl, and discovered the nonmetric (axion) part (A){chi}ijkl (equal to
{phi}eijkl) of {chi}ijkl worthy investigation. Since we have used Lagrangian
formalism, {chi}ijkl is effectively symmetric under the interchange of index
pairs, ij and kl, and has 21 independent degrees of freedom. Hehl, Obukhov and
Rubilar have started from charge-flux formalism to study electromagnetism,
discovered the antisymmetric part (Sk){chi}ijkl (15 degrees of freedom) of
{chi}ijkl under the interchange of index pairs ij and kl worthy investigation,
and called it skewon field. In this paper, we study the propagation of the
Hehl-Obukhov-Rubilar skewon field in weak gravity field/dilute matter or with
weak violation of the Einstein Equivalence Principle (EEP), and further
classify it into Type I and Type II skewons. From the dispersion relation we
show that no dissipation/no amplification condition implies that the additional
skewon field must be of Type II. For Type I skewon field, the
dissipation/amplification is proportional to the frequency and the CMB spectrum
would deviate from Planck spectrum. From the high precision agreement of the
CMB spectrum to 2.755 K Planck spectrum, we constrain the Type I cosmic skewon
field (SkI){chi}ijkl to less than a few x 10-35. The skewon part of
constitutive tensor constructed from asymmetric metric is of Type II, hence is
allowed. This study may also find applications in macroscopic electrodynamics
in the case of laser pumped medium or dissipative medium.


title:
The Entropy Relations of Black Holes with Multihorizons in Higher
  Dimensions

abstract:
  We study the entropy relations of multi-horizons black holes in higher
dimensional (A)dS spacetime with maximal symmetries, including Einstein-Maxwell
gravity and $f(R)$(-Maxwell) gravity. These additional equalities in
thermodynamics are expected to be useful to understanding the origin of black
hole entropy at the microscopic level. Revisiting the entropy product
introduced by Cvetic etc, in our case, it has an unexpected behavior. It is
shown that this electric charge $Q$ plays an important role in this entropy
product. The entropy product of charged black holes only depends on the
electric charge $Q$ and is mass independence. When $Q$ vanishes in the
solution, it turns to mass dependence, even when including the effect of the
un-physical ``virtual'' horizons. In this sense, the ``universal relation'' of
this entropy product is destroyed. Then we introduce another kind of
``universal'' entropy relation, which only depends on the cosmological constant
$\Lambda$ and the background topology $k$, and which does not depend on the
conserved charges $Q$, nor even the mass $M$.


title:
Improved estimators in simple random sampling when study variable is an
  attribute

abstract:
  This article addresses the problem of estimating the population mean in the
presence of auxiliary information when study variable itself is qualitative in
nature. Bias and mean squared error (MSE) expressions of the class of
estimators are derived up to the first order of approximation. The suggested
estimators have been compared with the traditional estimator and several other
estimators considered by Singh (2010). In addition, we support this theoretical
result by an empirical study to show the superiority of the constructed
estimator over others.


title:
A polynomial time complete disjunction property in intuitionistic
  propositional logic

abstract:
  We extend the polynomial time algorithms due to Buss and Mints(APAL 1999) and
Ferrari, Fiorentini and Fiorino(LPAR 2002) to yield a polynomial time complete
disjunction property in intuitionistic propositional logic.


title:
Representing Knowledge Base into Database for WAP and Web-based Expert
  System

abstract:
  Expert System is developed as consulting service for users spread or public
requires affordable access. The Internet has become a medium for such services,
but presence of mobile devices make the access becomes more widespread by
utilizing mobile web and WAP (Wireless Application Protocol). Applying expert
systems applications over the web and WAP requires a knowledge base
representation that can be accessed simultaneously. This paper proposes single
database to accommodate the knowledge representation with decision tree mapping
approach. Because of the database exist, consulting application through both
web and WAP can access it to provide expert system services options for more
affordable for public.


title: Fast Approximate $K$-Means via Cluster Closures

abstract:
  $K$-means, a simple and effective clustering algorithm, is one of the most
widely used algorithms in multimedia and computer vision community. Traditional
$k$-means is an iterative algorithm---in each iteration new cluster centers are
computed and each data point is re-assigned to its nearest center. The cluster
re-assignment step becomes prohibitively expensive when the number of data
points and cluster centers are large.
  In this paper, we propose a novel approximate $k$-means algorithm to greatly
reduce the computational complexity in the assignment step. Our approach is
motivated by the observation that most active points changing their cluster
assignments at each iteration are located on or near cluster boundaries. The
idea is to efficiently identify those active points by pre-assembling the data
into groups of neighboring points using multiple random spatial partition
trees, and to use the neighborhood information to construct a closure for each
cluster, in such a way only a small number of cluster candidates need to be
considered when assigning a data point to its nearest cluster. Using complexity
analysis, image data clustering, and applications to image retrieval, we show
that our approach out-performs state-of-the-art approximate $k$-means
algorithms in terms of clustering quality and efficiency.


title: Fast Neighborhood Graph Search using Cartesian Concatenation

abstract:
  In this paper, we propose a new data structure for approximate nearest
neighbor search. This structure augments the neighborhood graph with a bridge
graph. We propose to exploit Cartesian concatenation to produce a large set of
vectors, called bridge vectors, from several small sets of subvectors. Each
bridge vector is connected with a few reference vectors near to it, forming a
bridge graph. Our approach finds nearest neighbors by simultaneously traversing
the neighborhood graph and the bridge graph in the best-first strategy. The
success of our approach stems from two factors: the exact nearest neighbor
search over a large number of bridge vectors can be done quickly, and the
reference vectors connected to a bridge (reference) vector near the query are
also likely to be near the query. Experimental results on searching over large
scale datasets (SIFT, GIST and HOG) show that our approach outperforms
state-of-the-art ANN search algorithms in terms of efficiency and accuracy. The
combination of our approach with the IVFADC system also shows superior
performance over the BIGANN dataset of $1$ billion SIFT features compared with
the best previously published result.


title: Some monodromy groups of finite index in $Sp_4(\mathbb{Z})$

abstract:
  We determine the index of five of the $7$ hypergeometric Calabi-Yau operators
that have finite index in $Sp_4(\mathbb{Z})$ and in two cases give a complete
description of the monodromy group. Furthermore we found six non-hypergeometric
Calabi-Yau operators with finite index in $Sp_4(\mathbb{Z})$, most notably a
case where the index is one.


title:
Acoustoelectric effects in very high-mobility $p$-SiGe/Ge/SiGe
  heterostructure at low temperatures in high magnetic fields

abstract:
  The contactless Surface Acoustic Wave (SAW) technique was implemented to
probe the high-frequency (ac) conductivity in a high-mobility $p$-SiGe/Ge/SiGe
structure in the integer quantum Hall (IQHE) regime. The structure was grown by
low-energy plasma-enhanced chemical vapor deposition and comprised a
two-dimensional channel formed in a compressively strained Ge layer. It was
investigated at temperatures of 0.3 - 5.8 K and magnetic fields up to 18 T at
various SAW intensities. In the IQHE regime, in minima of the conductivity
oscillations with small filling factors, holes are localized. The ac
conductivity is of the hopping nature and can be described within the
"two-site" model. Furthermore, the dependence of the ac conductivity on the
electric field of the SAW was determined. The manifestation of non-linear
effects is interpreted in terms of nonlinear percolation-based conductivity.


title:
Impurity effects in a two-dimensional topological superconductor: A link
  of Tc-robustness with a topological number

abstract:
  Impurity effects are probes for revealing an unconventional property in
superconductivity. We study effects of non-magnetic impurities, in a 2D
topological superconductor with s-wave pairing, the Rashba spin-orbit coupling,
and the Zeeman term. Using a self-consistent T-matrix approach, we calculate a
phenomenological formula for the Thouless-Kohmoto-Nightingale-Nijs (TKNN)
invariant in interacting systems, as well as density of states, with different
magnetic fields. This quantity weakly depends on the magnetic field, when a
spectral gap opens, whereas this changes drastically, when in-gap states
occurs. Furthermore, in the latter case, we find that the Anderson's theorem
(robustness of s-wave superconductivity against non-magnetic impurities) breaks
down. We discuss the origin, from the viewpoints of both unconventional
superconductivity and the TKNN invariant.


title: Ultrafast atomic transport in recrystallizing ultrafine grained Ni

abstract:
  We studied tracer self-diffusion in ultrafine grained Ni prepared by high
pressure torsion. Two Ni materials of low (99.6 wt. %) and high (99.99 wt. %)
purity levels were investigated. While the ultrafine grained structure of less
pure Ni remained stable during diffusion annealing, recrystallization and
subsequent grain growth occurred in high purity Ni at the same annealing
conditions. Nevertheless, qualitatively similar ultrafast diffusion rates were
measured in the samples of both purity levels. In high purity Ni, the kinetics
of recrystallization was found to deviate strongly from the predictions of the
Johnson-Mehl-Avrami-Kolmogorov theory. Moreover, the ultrafast diffusion paths
withstood the recrystallization process. A model which accounts for solute
redistribution in front of the moving boundary is suggested. Retaining of
deformation-induced ultrafast diffusion paths in recrystallized Ni is explained
by a specific mechanism of enhanced stability of the residual ultrafine grained
fraction against recrystallization.