title: Primality test for numbers of the form $(2p)^{2^n}+1$

abstract:
  We describe a primality test for number $M=(2p)^{2^n}+1$ with odd prime $p$
and positive integer $n$. And we also give the special primality criteria for
all odd primes $p$ not exceeding 19. All these primality tests run in
polynomial time in log$_{2}(M)$. A certain special $2p$-th reciprocity law is
used to deduce our result.


title: Schr\"odinger operators on periodic discrete graphs

abstract:
  We consider Schr\"odinger operators with periodic potentials on periodic
discrete graphs. The spectrum of the Schr\"odinger operator consists of an
absolutely continuous part (a union of a finite number of non-degenerated
bands) plus a finite number of flat bands, i.e., eigenvalues of infinite
multiplicity. We obtain estimates of the Lebesgue measure of the spectrum in
terms of geometric parameters of the graph and show that they become identities
for some class of graphs. Moreover, we obtain stability estimates and show the
existence and positions of large number of flat bands for specific graphs. The
proof is based on the Floquet theory and the precise representation of fiber
Schr\"odinger operators, constructed in the paper.


title: Liquids more stable than crystals

abstract:
  All liquids (except helium due to quantum effects) crystallize at low
temperatures, forming ordered structures. The competition between disorder,
which stabilizes the liquid phase, and energy, which favors the ordered
crystalline structure, inevitably turns in favor of the latter when temperature
is lowered and the entropic contribution to the free energy becomes
progressively less and less relevant. The "liquid" state survives at low
temperatures only as a glass, an out-of-equilibrium arrested state of matter.
This textbook description holds inevitably for atomic and molecular systems,
where the interaction between particles is set by quantum mechanical laws. The
question remains whether the same physics hold for colloidal particles, where
inter-particle interactions are usually short-ranged and tunable. Here we show
that for patchy colloids with limited valence, conditions can be found for
which the disordered liquid phase is stable all the way down to the
zero-temperature limit. Our results offer interesting cues for understanding
the stability of gels and the glass forming ability of atomic and molecular
network glasses.


title: How well can we guess theoretical uncertainties?

abstract:
  The problem of estimating the effect of missing higher orders in perturbation
theory is analyzed with emphasis in the application to Higgs production in
gluon-gluon fusion. Well-known mathematical methods for an approximated
completion of the perturbative series are applied with the goal to not truncate
the series, but complete it in a well-defined way, so as to increase the
accuracy - if not the precision - of theoretical predictions. The uncertainty
arising from the use of the completion procedure is discussed and a recipe for
constructing a corresponding probability distribution function is proposed.


title: Spectral Singularity in confined PT symmetric optical potential

abstract:
  We present an analytical study for the scattering amplitudes (Reflection
$|R|$ and Transmission $|T|$), of the periodic ${\cal{PT}}$ symmetric optical
potential $ V(x) = \displaystyle W_0 \left( \cos ^2 x + i V_0 \sin 2x \right) $
confined within the region $0 \leq x \leq L$, embedded in a homogeneous medium
having uniform potential $W_0$. The confining length $L$ is considered to be
some integral multiple of the period $ \pi $. We give some new and interesting
results. Scattering is observed to be normal ($|T| ^2 \leq 1, \ |R|^2 \leq 1$)
for $V_0 \leq 0.5 $, when the above potential can be mapped to a Hermitian
potential by a similarity transformation. Beyond this point ($ V_0 > 0.5 $)
scattering is found to be anomalous ($|T| ^2, \ |R|^2 $ not necessarily $ \leq
1 $). Additionally, in this parameter regime of $V_0$, one observes infinite
number of spectral singularities $E_{SS}$ at different values of $V_0$.
Furthermore, for $L= 2 n \pi$, the transition point $V_0 = 0.5$ shows
unidirectional invisibility with zero reflection when the beam is incident from
the absorptive side ($Im [V(x)] < 0$) but finite reflection when the beam is
incident from the emissive side ($Im [V(x)] > 0$), transmission being
identically unity in both cases. Finally, the scattering coefficients $|R|^2$
and $|T|^2 $ always obey the generalized unitarity relation : $ ||T|^2 - 1| =
\sqrt{|R_R|^2 |R_L|^2}$, where subscripts $R$ and $L$ stand for right and left
incidence respectively.


title:
Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic
  Fibrations

abstract:
  We consider elliptic fibrations with arbitrary base dimensions, and
generalise previous work by the second author. In particular, we check
universal closedness for the moduli of semistable objects with respect to a
polynomial stability that reduces to PT-stability on threefolds. We also show
openness of this polynomial stability. On the other hand, we write down
criteria under which certain 2-term polynomial semistable complexes are mapped
to torsion-free semistable sheaves under a Fourier-Mukai transform. As an
application, we construct an open immersion from a moduli of complexes to a
moduli of Gieseker stable sheaves on higher dimensional elliptic fibrations.


title:
Probing the top quark chromoelectric and chromomagnetic dipole moments
  in single top $tW$-channel at the LHC

abstract:
  We study the effects of chromoelectric and chromomagnetic dipole moments
(CEDM and CMDM) on the production cross section of single top $tW$-channel at
the LHC based on the effective Lagrangian approach. We show that the impact of
CEDM and CMDM could be large. Using the experimental measurement of the
$tW$-channel cross section, constraints on CEDM and CMDM are extracted. These
constraints are comparable with the ones obtained from the top pair analysis.


title:
Towards the Chalonge 17th Paris Cosmology Colloquium 2013: highlights
  and conclusions of the Chalonge 16th Paris Cosmology Colloquium 2012

abstract:
  LWDM (Warm Dark Matter) is progressing impressively.The galactic scale crisis
and decline of LCDM+baryons are staggering. The 16th Paris Chalonge Colloquium
2012 combined real cosmological/astrophysical data and hard theory predictive
approach in the LWDM Standard Model. News and reviews from
ACT,WMAP,SPT,QUIET,Planck,Herschel,JWST,UFFO,KATRIN and MARE experiments;
astrophysics, particle and nuclear physics WDM searches, galactic observations,
related theory and simulations, with the aim of synthesis and clarification.
Here highlights by P Biermann, C Burigana, C Conselice, A Cooray, H de Vega, C
Giunti & M Laveder, J Kormendi & K Freeman, E Ma, J Mather, L Page, G Smoot, N
Sanchez. Summary and conclusions by de Vega, Falvella and Sanchez. Data confirm
primordial CMB gaussianity. Effective (Ginsburg-Landau) Inflation theory
predicts r about 0.04-0.05, negligeable running of ns, the inflation energy
scale (GUT scale) and the set of CMB observables in agreement with the data.
WMAP9 and Planck measurements are compatible with one or two Majorana sterile
neutrinos in the eV mass scale. Cored (non cusped) DM halos and keV WDM are
strongly favored by theory and observations, Wimps are strongly disfavoured.
LambdaCDM with baryons do not work at small scales. Inside galaxy cores,
quantum WDM effects are important. Quantum WDM calculations (Thomas-Fermi)
provide galaxy masses, velocity dispersions and cored profiles and their sizes
in agreement with observations. A WDM fermion of about 2 keV naturally
reproduces galaxy, large scale and cosmological observations. WDM keV particles
deserve dedicated astronomical and laboratory searches, theoretical work and
numerical simulations. KATRIN can be adapted to look to keV scale sterile
neutrinos. It will be a fantastic discovery to detect dark matter in beta
decay. Photos of the Colloquium are included


title: Local Conformal Symmetry in Physics and Cosmology

abstract:
  We show how to lift a generic non-scale invariant action in Einstein frame
into a locally conformally-invariant (or Weyl-invariant) theory and present a
new general form for Lagrangians consistent with Weyl symmetry. Advantages of
such a conformally invariant formulation of particle physics and gravity
include the possibility of constructing geodesically complete cosmologies. We
present a conformal-invariant version of the standard model coupled to gravity,
and show how Weyl symmetry may be used to obtain unprecedented analytic control
over its cosmological solutions. Within this new framework, generic FRW
cosmologies are geodesically complete through a series of big crunch - big bang
transitions. We discuss a new scenario of cosmic evolution driven by the Higgs
field in a \textquotedblleft minimal\textquotedblright% \ conformal standard
model, in which there is no new physics beyond the standard model at low
energies, and the current Higgs vacuum is metastable as indicated by the latest
LHC data.


title: Sojourn measures of Student and Fisher-Snedecor random fields

abstract:
  Limit theorems for the volumes of excursion sets of weakly and strongly
dependent heavy-tailed random fields are proved. Some generalizations to
sojourn measures above moving levels and for cross-correlated scenarios are
presented. Special attention is paid to Student and Fisher-Snedecor random
fields. Some simulation results are also presented.


title:
Towards Synthetic Descriptive Set Theory: An instantiation with
  represented spaces

abstract:
  Using ideas from synthetic topology, a new approach to descriptive set theory
is suggested. Synthetic descriptive set theory promises elegant explanations
for various phenomena in both classic and effective descriptive set theory.
Presently, we mainly focus on developing the ideas in the category of
represented spaces.


title:
Attempt at Perfecting Non-Relativistic Quantum Mechanics Based on
  Interaction

abstract:
  Many wave phenomena are related to interactions. Considering once neglected
interactions in some cases, states of large objects and Newton's idea about
measurement, we attempt to modify some concepts and principles of
non-relativistic quantum mechanics. Our modifications may help one to
understand some typical quantum phenomena with near classical and intuitive
ideas without changing past correct results, may mediate some contradictions
logically, and then may partially perfect non-relativistic quantum mechanics.
We also give a review of the argument between Einstein and Bohr about
non-relativistic quantum mechanics simply based on interaction.


title: Homogenization of unbounded integrals with quasiconvex growth

abstract:
  We study homogenization by $\Gamma$-convergence of periodic nonconvex
integrals when the integrand has quasiconvex growth with convex effective
domain.


title: The Majorana spinor representation of the Poincare group

abstract:
  There are Poincare group representations on complex Hilbert spaces, like the
Dirac spinor field, or real Hilbert spaces, like the electromagnetic field
tensor. The Majorana spinor is an element of a 4 dimensional real vector space.
The Majorana spinor field is a space-time dependent Majorana spinor, solution
of the free Dirac equation.
  The Majorana-Fourier and Majorana-Hankel transforms of Majorana spinor fields
are defined and related to the linear and angular momenta of a spin one-half
representation of the Poincare group. We show that the Majorana spinor field
with finite mass is an unitary irreducible projective representation of the
Poincare group on a real Hilbert space.
  Since the Bargmann-Wigner equations are valid for all spins and are based on
the free Dirac equation, these results open the possibility to study Poincare
group representations with arbitrary spins on real Hilbert spaces.


title: Families of generalized Kloosterman sums

abstract:
  We construct p-adic relative cohomology for a family of toric exponential
sums which generalize the classical Kloosterman sums. Under natural hypotheses
such as quasi-homogeneity and nondegeneracy, this cohomology is acyclic except
in the top dimension. Our construction enables sufficiently sharp estimates for
the action of Frobenius on cohomology so that our earlier work may be applied
to the L-functions coming from linear algebra operations on these families to
deduce a number of basic properties.


title: Symmetry breaking in the collisions of double channel BEC solitons

abstract:
  We investigate an attractive Bose-Einstein condensate in two coupled one
dimensional channels. In this system a stable double channel soliton can be
formed. It is symmetric for small interaction parameters and asymmetric for
large ones. We study this symmetry breaking phenomenon in detail. Next, we
investigate the dynamics of symmetric double channel soliton collisions. For
sufficiently strong interactions we observe spontaneous symmetry breaking
during the collision. Approximate considerations based on two different
methods, Bogoliubov and variational, are used to describe this effect. The
results are compatible.


title: Determinantal Martingales and Correlations of Noncolliding Random Walks

abstract:
  We study the noncolliding random walk (RW), which is a particle system of
one-dimensional, simple and symmetric RWs starting from distinct even sites and
conditioned never to collide with each other. When the number of particles is
finite, $N < \infty$, this discrete process is constructed as an $h$-transform
of absorbing RW in the $N$-dimensional Weyl chamber. We consider Fujita's
polynomial martingales of RW with time-dependent coefficients and express them
by introducing a complex Markov process. It is a complexification of RW, in
which independent increments of its imaginary part are in the hyperbolic secant
distribution, and it gives a discrete-time conformal martingale. The
$h$-transform is represented by a determinant of the matrix, whose entries are
all polynomial martingales. From this determinantal-martingale representation
(DMR) of the process, we prove that the noncolliding RW is determinantal for
any initial configuration with $N < \infty$, and determine the correlation
kernel as a function of initial configuration. We show that noncolliding RWs
started at infinite-particle configurations having equidistant spacing are
well-defined as determinantal processes and give DMRs for them. Tracing the
relaxation phenomena shown by these infinite-particle systems, we obtain a
family of equilibrium processes parameterized by particle density, which are
determinantal with the discrete analogues of the extended sine-kernel of
Dyson's Brownian motion model with $\beta=2$. Following Donsker's invariance
principle, convergence of noncolliding RWs to the Dyson model is also
discussed.


title: Tauberian and Abelian theorems for long-range dependent random fields

abstract:
  This paper surveys Abelian and Tauberian theorems for long-range dependent
random fields. We describe a framework for asymptotic behaviour of covariance
functions or variances of averaged functionals of random fields at infinity and
spectral densities at zero. The use of the theorems and their limitations are
demonstrated through applications to some new and less-known examples of
covariance functions of long-range dependent random fields.


title:
Derivations and central extensions of symmetric modular Lie algebras and
  superalgebras

abstract:
  Over algebraically closed fields of positive characteristic, for simple Lie
(super)algebras, and certain Lie (super)algebras close to simple ones, with
symmetric root systems (such that for each root, there is minus it of the same
multiplicity) and of ranks most needed in an approach to the classification of
simple vectorial Lie superalgebras, we list the outer derivations and
nontrivial central extensions. When the answer is clear for the infinite
series, it is given for any rank.
  We also list the outer derivations and nontrivial central extensions of one
series of nonsymmetric, namely, periplectic Lie superalgebras (of any rank)
preserving the nondegenerate supersymmetric odd bilinear forms, and of the Lie
algebras obtained from periplectic Lie superalgebras by desuperization when the
characteristic of the ground field is equal to 2.
  We also list the outer derivations and nontrivial central extensions of an
analog of the rank 2 exceptional Lie algebra discovered by Shen Guangyu.
  Several results are counterintuitive.


title:
Convergence in $L_p([0,T])$ of wavelet expansions of
  $\varphi$-sub-Gaussian random processes

abstract:
  The article presents new results on convergence in $L_p([0,T])$ of wavelet
expansions of $\varphi$-sub-Gaussian random processes. The convergence rate of
the expansions is obtained. Specifications of the obtained results are
discussed.


title: General Existence of Solutions to Dynamic Programming Principle

abstract:
  We provide an alternative approach to the existence of solutions to dynamic
programming equations arising in the discrete game-theoretic interpretations
for various nonlinear partial differential equations including the infinity
Laplacian, mean curvature flow and Hamilton-Jacobi type. Our general result is
similar to Perron's method but adapted to the discrete situation.


title:
Full superconducting gap in the doped topological crystalline insulator,
  Sn$_{0.6}$In$_{0.4}$Te

abstract:
  The thermal conductivity of the doped topological crystalline insulator,
Sn$_{0.6}$In$_{0.4}$Te superconducting single crystal with $T_c =$ 4.1 K, was
measured down to 50 mK. It is found that the residual linear term $\kappa_0/T$
is negligible in zero magnetic field. The $\kappa_0/T$ shows a slow field
dependence at low magnetic field. These results suggest that the
superconducting gap is nodeless, unless there exist point nodes with directions
perpendicular to the heat current. Due to its high-symmetry fcc crystal
structure of Sn$_{0.6}$In$_{0.4}$Te, however, such point nodes can be excluded.
Therefore we demonstrate that this topological superconductor candidate has a
full superconducting gap in the bulk. It is likely the unconventional
odd-parity $A_{1u}$ state which supports a surface Andreev bound state.


title: Nonextensive Nuclear Liquid-Gas Phase Transition

abstract:
  We study an effective relativistic mean-field model of nuclear matter with
arbitrary proton fraction at finite temperature in the framework of
nonextensive statistical mechanics, characterized by power-law quantum
distributions. We investigate the presence of thermodynamic instability in a
warm and asymmetric nuclear medium and study the consequent nuclear liquid-gas
phase transition by requiring the Gibbs conditions on the global conservation
of baryon number and electric charge fraction. We show that nonextensive
statistical effects play a crucial role in the equation of state and in the
formation of mixed phase also for small deviations from the standard
Boltzmann-Gibbs statistics.


title: Vertex-Coloring Edge-Weighting of Bipartite Graphs with Two Edge Weights

abstract:
  Let $G$ be a graph and $\mathcal {S}$ be a subset of $Z$. A vertex-coloring
$\mathcal {S}$-edge-weighting of $G$ is an assignment of weight $s$ by the
elements of $\mathcal {S}$ to each edge of $G$ so that adjacent vertices have
different sums of incident edges weights.
  It was proved that every 3-connected bipartite graph admits a vertex-coloring
$\{1,2\}$-edge-weighting (Lu, Yu and Zhang, (2011) \cite{LYZ}). In this paper,
we show that the following result: if a 3-edge-connected bipartite graph $G$
with minimum degree $\delta$ contains a vertex $u\in V(G)$ such that
$d_G(u)=\delta$ and $G-u$ is connected, then $G$ admits a vertex-coloring
$\mathcal {S}$-edge-weighting for $\mathcal {S}\in \{\{0,1\},\{1,2\}\}$. In
particular, we show that every 2-connected and 3-edge-connected bipartite graph
admits a vertex-coloring $\mathcal {S}$-edge-weighting for $\mathcal {S}\in
\{\{0,1\},\{1,2\}\}$. The bound is sharp, since there exists a family of
infinite bipartite graphs which are 2-connected and do not admit
vertex-coloring $\{1,2\}$-edge-weightings or vertex-coloring
$\{0,1\}$-edge-weightings.


title:
Combine Umbrella Sampling with Integrated Tempering Method for Efficient
  and Accurate Calculation of Free Energy Changes of Complex Energy Surface

abstract:
  Umbrella sampling is an efficient method for the calculation of free energy
changes of a system along well-defined reaction coordinates. However, when
multiple parallel channels along the reaction coordinate or hidden barriers in
directions perpendicular to the reaction coordinate exist, it is difficult for
conventional umbrella sampling methods to generate sufficient sampling within
limited simulation time. Here we propose an efficient approach to combine
umbrella sampling with the integrated tempering sampling method. The umbrella
sampling method is applied to conformational degrees of freedom which possess
significant barriers and are chemically more relevant. The integrated tempering
sampling method is employed to facilitate the sampling of other degrees of
freedom in which statistically non-negligible barriers may exist. The combined
method is applied to two model systems and show significantly improved sampling
efficiencies as compared to standalone conventional umbrella sampling or
integrated tempering sampling approaches. Therefore, the combined approach will
become a very efficient method in the simulation of biomolecular processes
which often involve sampling of complex rugged energy landscapes.


title: A "Light," Centrally-Concentrated Milky Way Halo?

abstract:
  We discuss a novel approach to "weighing" the Milky Way dark matter halo, one
that combines the latest samples of halo stars selected from the Sloan Digital
Sky Survey (SDSS) with state-of-the-art numerical simulations of Milky Way
analogs. The fully cosmological runs employed in the present study include
"Eris", one of the highest-resolution hydrodynamical simulations of the
formation of a M_vir=8e11 M_sun late-type spiral, and the dark-matter only
M_vir=1.7e12 M_sun "Via Lactea II" simulation. Eris provides an excellent
laboratory for creating mock SDSS samples of tracer halo stars, and we
successfully compare their density, velocity anisotropy, and radial velocity
dispersion profiles with the observational data. Most mock SDSS realizations
show the same "cold veil" recently observed in the distant stellar halo of the
Milky Way, with tracers as cold as sigma_los ~ 50 km/s between 100-150 kpc.
Controlled experiments based on the integration of the spherical Jeans equation
as well as a particle tagging technique applied to Via Lactea II show that a
"heavy" M_vir 2e12 M_sun realistic host produces a poor fit to the kinematic
SDSS data. We argue that these results offer added evidence for a "light,"
centrally-concentrated Milky Way halo.


title: Cosmology with an Effective $\Lambda$-Term in Lyra Manifold

abstract:
  A cosmological model in Lyra's geometry are studied under the assumption that
an effective cosmological term is appeared in the field equations as the result
of interaction between the displacement vector field and an auxiliary $ \Lambda
$ - term. Some exact solutions of the model equations are obtained and
preliminary studied for the simplest cases in order to illustrate how such a
model works


title:
Extreme Current Fluctuations in Lattice Gases: Beyond Nonequilibrium
  Steady States

abstract:
  We use the macroscopic fluctuation theory (MFT) to study large current
fluctuations in non-stationary diffusive lattice gases. We identify two
universality classes of these fluctuations which we call elliptic and
hyperbolic. They emerge in the limit when the deterministic mass flux is small
compared to the mass flux due to the shot noise. The two classes are determined
by the sign of compressibility of \emph{effective fluid}, obtained by mapping
the MFT into an inviscid hydrodynamics. An example of the elliptic class is the
Symmetric Simple Exclusion Process where, for some initial conditions, we can
solve the effective hydrodynamics exactly. This leads to a super-Gaussian
extreme current statistics conjectured by Derrida and Gerschenfeld (2009) and
yields the optimal path of the system. For models of the hyperbolic class the
deterministic mass flux cannot be neglected, leading to a different extreme
current statistics.


title: Inverse effect of magnetostriction in magnetoelectric laminates

abstract:
  We introduce the notion of inverse effect of magnetostriction for
magnetostrictive/piezoelectric heterostructures and study this effect
theoretically and experimentally. It is shown that the inverse effect of
magnetostriction may crucially contribute to the mechanism of magnetoelectric
coupling. It is shown that the studied effect essentially modifies the
saturation magnetostriction of the whole structure as compared to its magnetic
phase bulk and also induces an additional magnetic anisotropy. Our
consideration provides useful insight into the fundamental issue of
strain-mediated magnetoelectric coupling. Understanding this effect may lead to
its utilization in original experimental concepts and the improvement of the ME
coupling.


title: Graphite in Science and Nuclear Technique

abstract:
  The monograph is devoted to the application of graphite and graphite
composites in science and technology. The structure and electrical properties,
the technological aspects of production of high-strength synthetic graphites,
the dynamics of the graphite destruction, traditionally used in the nuclear
industry are discussed. It is focuses on the characteristics of graphitization
and properties of graphite composites based on carbon isotope 13C. The book is
based, generally, on the original results, and concentrated on the actual
problems of application and testing of graphite materials in modern nuclear
physics, in scientific and technical applications. For scientists and engineers
specializing in nuclear physics and engineering, physics of nuclear reactors,
condensed matter, for undergraduate, graduate and post-graduate students of
universities physical specialties.


title:
Crossing the Reality Gap: a Short Introduction to the Transferability
  Approach

abstract:
  In robotics, gradient-free optimization algorithms (e.g. evolutionary
algorithms) are often used only in simulation because they require the
evaluation of many candidate solutions. Nevertheless, solutions obtained in
simulation often do not work well on the real device. The transferability
approach aims at crossing this gap between simulation and reality by
\emph{making the optimization algorithm aware of the limits of the simulation}.
  In the present paper, we first describe the transferability function, that
maps solution descriptors to a score representing how well a simulator matches
the reality. We then show that this function can be learned using a regression
algorithm and a few experiments with the real devices. Our results are
supported by an extensive study of the reality gap for a simple quadruped robot
whose control parameters are optimized. In particular, we mapped the whole
search space in reality and in simulation to understand the differences between
the fitness landscapes.


title:
Existence of Solutions for Nonconvex Differential Inclusions of Monotone
  Type

abstract:
  Differential inclusions with compact, upper semi-continuous, not necessarily
convex right-hand sides in R^n are studied. Under a weakened monotonicity-type
condition the existence of solutions is proved.


title: Intelligent Hybrid Man-Machine Translation Quality Estimation

abstract:
  Inferring evaluation scores based on human judgments is invaluable compared
to using current evaluation metrics which are not suitable for real-time
applications e.g. post-editing. However, these judgments are much more
expensive to collect especially from expert translators, compared to evaluation
based on indicators contrasting source and translation texts. This work
introduces a novel approach for quality estimation by combining learnt
confidence scores from a probabilistic inference model based on human
judgments, with selective linguistic features-based scores, where the proposed
inference model infers the credibility of given human ranks to solve the
scarcity and inconsistency issues of human judgments. Experimental results,
using challenging language-pairs, demonstrate improvement in correlation with
human judgments over traditional evaluation metrics.


title:
On discrete rarefaction waves in a nonlinear Schr\"odinger equation toy
  model for weak turbulence

abstract:
  We explore further the rarefaction wave-like solutions recently discussed in
work of the second author with J. Colliander, T. Oh and G. Simpson for a model
Hamiltonian dynamical system derived by Colliander-Keel-Staffilani-Takaoka-Tao
to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger
equation on the torus.


title:
On purely real surfaces in Kaehler surfaces and Lorentz surfaces in
  Lorentzian Kaehler surfaces

abstract:
  An immersion $\phi \colon M \to \tilde M$ of a manifold $M$ into an
indefinite Kaehler manifold $\tilde M$ is called purely real if the almost
complex structure $J$ on $\tilde M$ carries the tangent bundle of $M$ into a
transversal bundle. In this article we survey some recent results on purely
real surfaces in Kaehler surfaces as well as on Lorentz surfaces in Lorentzian
Kaehler surfaces.


title: Riemannian Submanifolds: A Survey

abstract:
  Submanifold theory is a very active vast research field which plays an
important role in the development of modern differential geometry. This branch
of differential geometry is still so far from being exhausted; only a small
portion of an exceedingly fruitful field has been cultivated, much more remains
to be discovered. In this article, the author provides a broad review of
Riemannian submanifolds in differential geometry.


title:
Submanifolds of warped product manifolds $I\times_f S^{m-1}(k)$}} from a
  $p$-harmonic viewpoint

abstract:
  We study $p$-harmonic maps, $p$-harmonic morphisms, biharmonic maps, and
quasiregular mappings into submanifolds of warped product Riemannian manifolds
${I}\times_f S^{m-1}(k)\, $ of an open interval and a complete
simply-connecteded $(m-1)$-dimensional Riemannian manifold of constant
sectional curvature $k$. We establish an existence theorem for $p$-harmonic
maps and give a classification of complete stable minimal surfaces in certain
three dimensional warped product Riemannian manifolds ${\bf R}\times_f
S^{2}(k)\, ,$ building on our previous work. When $f \equiv\, $ Const. and
$k=0$, we recapture a generalized Bernstein Theorem and hence the Classical
Bernstein Theorem in $R^3$. We then extend the classification to parabolic
stable minimal hypersurfaces in higher dimensions.


title: $\delta$-Invariants, Inequalities of Submanifolds and Their Applications

abstract:
  The famous Nash embedding theorem was aimed for in the hope that if
Riemannian manifolds could be regarded as Riemannian submanifolds, this would
then yield the opportunity to use extrinsic help. However, as late as 1985 (see
\cite{G}) this hope had not been materialized. The main reason for this is due
to the lack of controls of the extrinsic properties of the submanifolds by the
known intrinsic invariants. In order to overcome such difficulties as well as
to provide answers to an open question on minimal immersions, we introduced in
the early 1990's new types of Riemannian invariants, known as the
$\delta$-invariants or the so-called Chen invariants, different in nature from
the "classical" Ricci and scalar curvatures. At the same time we also able to
establish general optimal relations between the new intrinsic invariants and
the main extrinsic invariants for Riemannian submanifolds. Since then many
results concerning these invariants, inequalities, related subjects, and their
applications have been obtained by many geometers.
  The main purpose of this article is thus to provide an extensive and
comprehensive survey of results over this very active field of research done
during the last fifteen years. Several related inequalities and their
applications are presented in this survey article as well.


title: Questions and Remarks to the Langlands Program

abstract:
  A brief survey is given of the classical Langlands correspondence between
n-dimensional representations of Galois groups of local and global fields of
dimension 1 and irreducible representations of the groups GL(n). A
generalization of the Langlands program to fields of dimension 2 is considered
and the corresponding version for 1-dimensional representations is described.
We formulate a conjecture on a direct image (=automorphic induction) of
automorphic forms which links the Langlands correspondences in dimension 2 and
1. The direct image conjecture implies the classical Hasse-Weil conjecture on
the analytical behaviour of the L-functions of curves defined over global
fields of dimension 1.


title:
On Stochastic Subgradient Mirror-Descent Algorithm with Weighted
  Averaging

abstract:
  This paper considers stochastic subgradient mirror-descent method for solving
constrained convex minimization problems. In particular, a stochastic
subgradient mirror-descent method with weighted iterate-averaging is
investigated and its per-iterate convergence rate is analyzed. The novel part
of the approach is in the choice of weights that are used to construct the
averages. Through the use of these weighted averages, we show that the known
optimal rates can be obtained with simpler algorithms than those currently
existing in the literature. Specifically, by suitably choosing the stepsize
values, one can obtain the rate of the order $1/k$ for strongly convex
functions, and the rate $1/\sqrt{k}$ for general convex functions (not
necessarily differentiable). Furthermore, for the latter case, it is shown that
a stochastic subgradient mirror-descent with iterate averaging converges (along
a subsequence) to an optimal solution, almost surely, even with the stepsize of
the form $1/\sqrt{1+k}$, which was not previously known. The stepsize choices
that achieve the best rates are those proposed by Paul Tseng for acceleration
of proximal gradient methods.


title:
Experimental realization of epsilon-near-zero metamaterial slabs with
  metal-dielectric multilayers

abstract:
  Epsilon-near-zero (ENZ) metamaterial slabs at visible frequencies based on
metal-dielectric multilayers are experimentally realized. Transmission,
reflection and absorption spectra are measured and used to determine the
complex refractive indices and the effective permittivities of the ENZ slabs,
which agree with the results obtained from both the numerical simulations and
the optical nonlocalities analysis. Furthermore, light propagation in ENZ slabs
and directional emission from ENZ prisms are also analyzed. The accurate
determination of the ENZ wavelength for metal-dielectric multilayer
metamaterial slabs is important for realizing many unique applications, such as
phase front manipulation and enhancement of photonic density of states.


title:
Existence for weakly coercive nonlinear diffusion equations via a
  variational principle

abstract:
  We are concerned with the study of the well-posedness of a nonlinear
diffusion equation with a monotonically increasing multivalued time-dependent
nonlinearity derived from a convex continuous potential having a superlinear
growth to infinity. The results in this paper state that the solution of the
nonlinear equation can be retrieved as the null minimizer of an appropriate
minimization problem for a convex functional involving the potential and its
conjugate. This approach, inspired by the Brezis-Ekeland variational principle,
provides new existence results under minimal growth and coercivity conditions.


title:
New evolutionary sequences for extremely low mass white dwarfs:
  Homogeneous mass and age determinations, and asteroseismic prospects

abstract:
  We provide a fine and homogeneous grid of evolutionary sequences for He-core
white dwarfs with masses 0.15-0.45 Msun, including the mass range for ELM white
dwarfs (<0.20Msun). The grid is appropriate for mass and age determination, and
to study their pulsational properties. White dwarf sequences have been computed
by performing full evolutionary calculations that consider the main energy
sources and processes of chemical abundance changes during white dwarf
evolution. Initial models for the evolving white dwarfs have been obtained by
computing the non-conservative evolution of a binary system consisting of a
Msun ZAMS star and a 1.4 Msun neutron star for various initial orbital periods.
To derive cooling ages and masses for He-core white dwarf we perform a least
square fitting of the M(Teff, g) and Age(Teff, g) relations provided by our
sequences by using a scheme that takes into account the time spent by models in
different regions of the Teff-g plane. This is useful when multiple solutions
for cooling age and mass determinations are possible in the case of
CNO-flashing sequences. We also explore the adiabatic pulsational properties of
models near the critical mass for the development of CNO flashes (~0.2 Msun).
This is motivated by the discovery of pulsating white dwarfs with stellar
masses near this threshold value. We obtain reliable and homogeneous mass and
cooling age determinations for 58 very low-mass white dwarfs, including 3
pulsating stars. Also, we find substantial differences in the period spacing
distributions of g-modes for models with stellar masses ~ 0.2 Msun, which could
be used as a seismic tool to distinguish stars that have undergone CNO flashes
in their early cooling phase from those that have not. Finally, for an easy
application of our results, we provide a reduced grid of values useful to
obtain masses and ages of He-core white dwarf.


title: Wormhole geometries in Eddington-inspired Born-Infeld gravity

abstract:
  Eddington-inspired Born-Infeld gravity (EiBI) gravity is a recently proposed
modified theory of gravity, based on the classic work of Eddington and on
Born-Infeld nonlinear electrodynamics. In this paper, we consider the
possibility that wormhole geometries are sustained in EiBI gravity. We present
the gravitational field equations for an anisotropic stress-energy tensor and
consider the generic conditions, for the auxiliary metric, at the wormhole
throat. In addition to this, we obtain an exact solution for an asymptotically
flat wormhole.


title:
Do Periodicities in Extinction -- with Possible Astronomical Connections
  -- Survive a Revision of the Geological Timescale?

abstract:
  A major revision of the geological timescale was published in 2012. We
re-examine our past finding of a 27 Myr periodicity in marine extinction rates
by re-assigning dates to the extinction data used previously. We find that the
spectral power at this period is somewhat increased, and persists at a narrow
bandwidth, which supports our previous contention that the Nemesis hypothesis
is untenable as an explanation for the periodicity that was first noted by Raup
and Sepkoski in the 1980s. We enumerate a number of problems in a recent study
comparing extinction rates with time series models.

categories: astro-ph.EP astro-ph.GA physics.bio-ph physics.geo-ph q-bio.PE


title:
Comparing theories: the dynamics of changing vocabulary. A case-study in
  relativity theory

abstract:
  There are several first-order logic (FOL) axiomatizations of special
relativity theory in the literature, all looking essentially different but
claiming to axiomatize the same physical theory. In this paper, we elaborate a
comparison, in the framework of mathematical logic, between these FOL theories
for special relativity. For this comparison, we use a version of mathematical
definability theory in which new entities can also be defined besides new
relations over already available entities. In particular, we build an
interpretation of the reference-frame oriented theory SpecRel into the
observationally oriented Signalling theory of James Ax. This interpretation
provides SpecRel with an operational/experimental semantics. Then we make
precise, "quantitative" comparisons between these two theories via using the
notion of definitional equivalence. This is an application of logic to the
philosophy of science and physics in the spirit of Johan van Benthem's work.


title: Estimates on the number of partially ordered sets

abstract:
  Partially ordered sets of type (k, n) are the sets such that
  a) cardinality of each set is n,
  b) dimension of each set is two,
  c) length of the maximal antichain in each set is k.
  Let \alpha_k(n) be the number of partially ordered sets of type (k, n). We
prove that \alpha_k(n)<min{k^{2n}/((k!)^2), (n-k+1)^{2n}/(((n-k)!)^2)}. Denote
by \xi_k(n) the number of permutations from S_n such that the maximal
decreasing chain of such permutation has length k. We prove that
\xi_k(n)<k^{2n}/(((k-1)!)^2). We survey connections among the pairs of linear
orders, the pairs Young diagrams, two-dimensional arrays of positive integers
and matrices of nonnegative integers. This survey is based on papers of
Schensted and Knuth. We show the generating function of \xi_k(n). It was
obtained by Gessen in 1990.


title: On a parabolic operator of dissipative systems

abstract:
  A parabolic integro differential operator operator L suitable to describe
many phenomena in various physical fields,is considered. By means of
equivalence between L and the third order equation which describe the evolution
inside an exponentially shaped Josephson junction (ESJJ), an asymptotic
analysis for (ESJJ) is achieved, evaluating explicitly boundary contributions
related to the Dirichlet problem.


title:
Cooperative effects in one-dimensional random atomic gases: Absence of
  single atom limit

abstract:
  We study superradiance in a one-dimensional geometry, where N>>1 atoms are
randomly distributed along a line. We present an analytic calculation of the
photon escape rates based on the diagonalization of the N x N coupling matrix
Uij = cos xij, where xij is the dimensionless random distance between any two
atoms. We show that unlike a three-dimensional geometry, for a one- dimensional
atomic gas the single-atom limit is never reached and the photon is always
localized within the atomic ensemble. This localization originates from
long-range cooperative effects and not from disorder as expected on the basis
of the theory of Anderson localization.


title:
Symmetric nuclear matter with chiral three-nucleon forces in the
  self-consistent Green's functions approach

abstract:
  We present calculations for symmetric nuclear matter using chiral nuclear
interactions within the Self-Consistent Green's Functions approach in the
ladder approximation. Three-body forces are included via effective one-body and
two-body interactions, computed from an uncorrelated average over a third
particle. We discuss the effect of the three-body forces on the total energy,
computed with an extended Galitskii-Migdal-Koltun sum-rule, as well as on
single-particle properties. Saturation properties are substantially improved
when three-body forces are included, but there is still some underlying
dependence on the SRG evolution scale.


title:
Solution of Rectangular Fuzzy Games by Principle of Dominance Using
  LR-type Trapezoidal Fuzzy Numbers

abstract:
  Fuzzy Set Theory has been applied in many fields such as Operations Research,
Control Theory, and Management Sciences etc. In particular, an application of
this theory in Managerial Decision Making Problems has a remarkable
significance. In this Paper, we consider a solution of Rectangular Fuzzy game
with pay-off as imprecise numbers instead of crisp numbers viz., interval and
LR-type Trapezoidal Fuzzy Numbers. The solution of such Fuzzy games with pure
strategies by minimax-maximin principle is discussed. The Algebraic Method to
solve Fuzzy games without saddle point by using mixed strategies is also
illustrated. Here, pay-off matrix is reduced to pay-off matrix by Dominance
Method. This fact is illustrated by means of Numerical Example.


title:
A Comparative study of Transportation Problem under Probabilistic and
  Fuzzy Uncertainties

abstract:
  Transportation Problem is an important aspect which has been widely studied
in Operations Research domain. It has been studied to simulate different real
life problems. In particular, application of this Problem in NP- Hard Problems
has a remarkable significance. In this Paper, we present a comparative study of
Transportation Problem through Probabilistic and Fuzzy Uncertainties. Fuzzy
Logic is a computational paradigm that generalizes classical two-valued logic
for reasoning under uncertainty. In order to achieve this, the notation of
membership in a set needs to become a matter of degree. By doing this we
accomplish two things viz., (i) ease of describing human knowledge involving
vague concepts and (ii) enhanced ability to develop cost-effective solution to
real-world problem. The multi-valued nature of Fuzzy Sets allows handling
uncertain and vague information. It is a model-less approach and a clever
disguise of Probability Theory. We give comparative simulation results of both
approaches and discuss the Computational Complexity. To the best of our
knowledge, this is the first work on comparative study of Transportation
Problem using Probabilistic and Fuzzy Uncertainties.


title: Competing Crystal Phases in the Lowest Landau Level

abstract:
  We show that the solid phase between the 1/5 and 2/9 fractional quantum Hall
states arises from an extremely delicate interplay between type-1 and type-2
composite fermion crystals, clearly demonstrating its nontrivial, strongly
correlated character. We also compute the phase diagram of various crystals
occurring over a wide range of filling factors, and demonstrate that the
elastic constants exhibit non-monotonic behavior as a function of the filling
factor, possibly leading to distinctive experimental signatures that can help
mark the phase boundaries separating different kinds of crystals.


title: Trapezoidal Fuzzy Numbers for the Transportation Problem

abstract:
  Transportation Problem is an important problem which has been widely studied
in Operations Research domain. It has been often used to simulate different
real life problems. In particular, application of this Problem in NP Hard
Problems has a remarkable significance. In this Paper, we present the closed,
bounded and non empty feasible region of the transportation problem using fuzzy
trapezoidal numbers which ensures the existence of an optimal solution to the
balanced transportation problem. The multivalued nature of Fuzzy Sets allows
handling of uncertainty and vagueness involved in the cost values of each cells
in the transportation table. For finding the initial solution of the
transportation problem we use the Fuzzy Vogel Approximation Method and for
determining the optimality of the obtained solution Fuzzy Modified Distribution
Method is used. The fuzzification of the cost of the transportation problem is
discussed with the help of a numerical example. Finally, we discuss the
computational complexity involved in the problem. To the best of our knowledge,
this is the first work on obtaining the solution of the transportation problem
using fuzzy trapezoidal numbers.


title:
Impacts of Generalized Uncertainty Principle on Black Hole
  Thermodynamics and Salecker-Wigner Inequalities

abstract:
  We investigate the impacts of Generalized Uncertainty Principle (GUP)
proposed by some approaches to quantum gravity such as String Theory and Doubly
Special Relativity on black hole thermodynamics and Salecker-Wigner
inequalities. Utilizing Heisenberg uncertainty principle, the Hawking
temperature, Bekenstein entropy, specific heat, emission rate and decay time
are calculated. As the evaporation entirely eats up the black hole mass, the
specific heat vanishes and the temperature approaches infinity with an infinite
radiation rate. It is found that the GUP approach prevents the black hole from
the entire evaporation. It implies the existence of remnants at which the
specific heat vanishes. The same role is played by the Heisenberg uncertainty
principle in constructing the hydrogen atom. We discuss how the linear GUP
approach solves the entire-evaporation-problem. Furthermore, the black hole
lifetime can be estimated using another approach; the Salecker-Wigner
inequalities. Assuming that the quantum position uncertainty is limited to the
minimum wavelength of measuring signal, Wigner second inequality can be
obtained. If the spread of quantum clock is limited to some minimum value, then
the modified black hole lifetime can be deduced. Based on linear GUP approach,
the resulting lifetime difference depends on black hole relative mass and the
difference between black hole mass with and without GUP is not negligible.


title:
Discovering Stock Price Prediction Rules of Bombay Stock Exchange Using
  Rough Fuzzy Multi Layer Perception Networks

abstract:
  In India financial markets have existed for many years. A functionally
accented, diverse, efficient and flexible financial system is vital to the
national objective of creating a market driven, productive and competitive
economy. Today markets of varying maturity exist in equity, debt, commodities
and foreign exchange. In this work we attempt to generate prediction rules
scheme for stock price movement at Bombay Stock Exchange using an important
Soft Computing paradigm viz., Rough Fuzzy Multi Layer Perception. The use of
Computational Intelligence Systems such as Neural Networks, Fuzzy Sets, Genetic
Algorithms, etc. for Stock Market Predictions has been widely established. The
process is to extract knowledge in the form of rules from daily stock
movements. These rules can then be used to guide investors. To increase the
efficiency of the prediction process, Rough Sets is used to discretize the
data. The methodology uses a Genetic Algorithm to obtain a structured network
suitable for both classification and rule extraction. The modular concept,
based on divide and conquer strategy, provides accelerated training and a
compact network suitable for generating a minimum number of rules with high
certainty values. The concept of variable mutation operator is introduced for
preserving the localized structure of the constituting Knowledge Based
sub-networks, while they are integrated and evolved. Rough Set Dependency Rules
are generated directly from the real valued attribute table containing Fuzzy
membership values. The paradigm is thus used to develop a rule extraction
algorithm. The extracted rules are compared with some of the related rule
extraction techniques on the basis of some quantitative performance indices.
The proposed methodology extracts rules which are less in number, are accurate,
have high certainty factor and have low confusion with less computation time.


title: Decuplet baryon masses in covariant baryon chiral perturbation theory

abstract:
  We present an analysis of the lowest-lying decuplet baryon masses in the
covariant baryon chiral perturbation theory with the extended-on-mass-shell
scheme up to next-to-next-to-next-to-leading order. In order to determine the
$14$ low-energy constants, we perform a simultaneous fit of the $n_f=2+1$
lattice QCD data from the PACS-CS, QCDSF-UKQCD, and HSC Collaborations, taking
finite-volume corrections into account self-consistently. We show that up to
next-to-next-to-next-to-leading order one can achieve a good description of the
lattice QCD and experimental data. Surprisingly, we note that the current
lattice decuplet baryon masses can be fitted rather well by the next-to-leading
order baryon chiral perturbation theory, which, however, misses the
experimental data a little bit. Furthermore, we predict the pion- and
strangeness-sigma terms of the decuplet baryons by use of the Feynman-Hellmann
theorem.


title: Diversities and Conformities

abstract:
  Diversities have recently been developed as multiway metrics admitting clear
and useful notions of hyperconvexity and tight span. In this note we consider
the analytic properties of diversities, in particular the generalizations of
uniform continuity, uniform convergence, Cauchy sequences and completeness to
diversities. We develop conformities, a diversity analogue of uniform spaces,
which abstract these concepts in the metric case. We show that much of the
theory of uniform spaces admits a natural analogue in this new structure; for
example, conformities can be defined either axiomatically or in terms of
uniformly continuous pseudodiversities.
  Just as diversities can be restricted to metrics, conformities can be
restricted to uniformities. We find that these two notions of restriction,
which are functors in the appropriate categories, are related by a natural
transformation.


title: Bursts of Active Transport in Living Cells

abstract:
  We scrutinize the temporally-resolved speed of active cargo transport in
living cells, and show intermittent bursting motions. These nonlinear
fluctuations follow a scaling law over several decades of time and space, the
statistical regularities displaying a time-averaged shape that we interpret to
reflect stress buildup followed by rapid release. The power law of scaling is
the same as seen in driven jammed colloids, granular, and magnetic systems. The
implied regulation of active transport with environmental obstruction extends
the classical notion of molecular crowding.


title: Light transport and localization in two-dimensional correlated disorder

abstract:
  Structural correlations in disordered media are known to affect significantly
the propagation of waves. In this article, we theoretically investigate the
transport and localization of light in 2D photonic structures with short-range
correlated disorder. The problem is tackled semi-analytically using the
Baus-Colot model for the structure factor of correlated media and a modified
independent scattering approximation. We find that short-range correlations
make it possible to easily tune the transport mean free path by more than a
factor of 2 and the related localization length over several orders of
magnitude. This trend is confirmed by numerical finite-difference time-domain
calculations. This study therefore shows that disorder engineering can offer
fine control over light transport and localization in planar geometries, which
may open new opportunities in both fundamental and applied photonics research.


title:
Fuzzy Integer Linear Programming Mathematical Models for Examination
  Timetable Problem

abstract:
  ETP is NP Hard combinatorial optimization problem. It has received tremendous
research attention during the past few years given its wide use in
universities. In this Paper, we develop three mathematical models for NSOU,
Kolkata, India using FILP technique. To deal with impreciseness and vagueness
we model various allocation variables through fuzzy numbers. The solution to
the problem is obtained using Fuzzy number ranking method. Each feasible
solution has fuzzy number obtained by Fuzzy objective function. The different
FILP technique performance are demonstrated by experimental data generated
through extensive simulation from NSOU, Kolkata, India in terms of its
execution times. The proposed FILP models are compared with commonly used
heuristic viz. ILP approach on experimental data which gives an idea about
quality of heuristic. The techniques are also compared with different
Artificial Intelligence based heuristics for ETP with respect to best and mean
cost as well as execution time measures on Carter benchmark datasets to
illustrate its effectiveness. FILP takes an appreciable amount of time to
generate satisfactory solution in comparison to other heuristics. The
formulation thus serves as good benchmark for other heuristics. The
experimental study presented here focuses on producing a methodology that
generalizes well over spectrum of techniques that generates significant results
for one or more datasets. The performance of FILP model is finally compared to
the best results cited in literature for Carter benchmarks to assess its
potential. The problem can be further reduced by formulating with lesser number
of allocation variables it without affecting optimality of solution obtained.
FLIP model for ETP can also be adapted to solve other ETP as well as
combinatorial optimization problems.


title: Homology of analogues of Heisenberg Lie algebras

abstract:
  We calculate the homology of three families of 2-step nilpotent Lie
(super)algebras associated with the symplectic, orthogonal, and general linear
groups. The symplectic case was considered by Getzler and the main motivation
for this work was to complete the calculations started by him. In all three
cases, these algebras can be realized as the nilpotent radical of a parabolic
subalgebra of a simple Lie algebra, and our first approach relies on a theorem
of Kostant, but is otherwise elementary and involves combinatorics of Weyl
groups and partitions which may be of independent interest. Our second approach
is an application of (un)stable representation theory of the classical groups
in the sense of recent joint work of the author with Snowden, which is shorter
and more conceptual.


title:
Demonstration of improved sensitivity of echo interferometers to
  gravitational acceleration

abstract:
  We have developed two configurations of an echo interferometer that rely on
standing wave excitation of a laser-cooled sample of rubidium atoms that
measures acceleration. For a two-pulse configuration, the interferometer signal
is modulated at the recoil frequency and exhibits a sinusoidal frequency chirp
as a function of pulse spacing. For a three-pulse stimulated echo
configuration, the signal is observed without recoil modulation and exhibits a
modulation at a single frequency. The three-pulse configuration is less
sensitive to effects of vibrations and magnetic field curvature leading to a
longer experimental timescale. For both configurations of the atom
interferometer (AI), we show that a measurement of acceleration with a
statistical precision of 0.5% can be realized by analyzing the shape of the
echo envelope that has a temporal duration of a few microseconds. Using the
two-pulse AI, we obtain measurements of acceleration that are statistically
precise to 6 parts per million (ppm) on a 25 ms timescale. Using the
three-pulse AI, we obtain measurements of acceleration that are statistically
precise to 0.4 ppm on a timescale of 50 ms. A further statistical enhancement
is achieved by analyzing the data across the echo envelope to improve the
statistical precision to 75 parts per billion (ppb). We discuss methods for
reducing prominent systematic effects due to a magnetized vacuum chamber and
improving the signal-to-noise ratio. Simulations of both AI configurations with
a timescale of 300 ms reached in a non-magnetic vacuum chamber suggest that an
optimized experiment with improved vibration isolation and atoms selected in
the mF = 0 state can result in measurements of g statistically precise to 0.3
pbb for the two-pulse AI and 0.6 ppb for the three-pulse AI.


title:
Achieving greater Explanatory Power and Forecasting Accuracy with
  Non-uniform spread Fuzzy Linear Regression

abstract:
  Fuzzy regression models have been applied to several Operations Research
applications viz., forecasting and prediction. Earlier works on fuzzy
regression analysis obtain crisp regression coefficients for eliminating the
problem of increasing spreads for the estimated fuzzy responses as the
magnitude of the independent variable increases. But they cannot deal with the
problem of non-uniform spreads. In this work, a three-phase approach is
discussed to construct the fuzzy regression model with non-uniform spreads to
deal with this problem. The first phase constructs the membership functions of
the least-squares estimates of regression coefficients based on extension
principle to completely conserve the fuzziness of observations. They are then
defuzzified by the centre of area method to obtain crisp regression
coefficients in the second phase. Finally, the error terms of the method are
determined by setting each estimated spread equal to its corresponding observed
spread. The Tagaki-Sugeno inference system is used for improving the accuracy
of forecasts. The simulation example demonstrates the strength of fuzzy linear
regression model in terms of higher explanatory power and forecasting
performance.


title: Dynamical Yukawa Couplings

abstract:
  The matter content of the Standard Model admits a global symmetry due to the
generational structure of the spectrum respected by all interactions except for
fermion couplings to the Higgs doublet. This symmetry is identified as the
largest possible global symmetry of the free theory and extended to the case of
massive neutrinos. The violation of such symmetry is then assumed dynamical and
the value of the Yukawa couplings is fixed by a variational principle. This
ansatz yields compelling results: Quark Yukawas naturally accommodate
hierarchical masses and small mixing whereas Lepton Yukawas exhibit a
hierarchical pattern for charged leptons and simultaneously degeneracy in the
neutrino sector correlated with large mixing and Majorana phases. The
difference in the mixing patterns of Quark and Leptons in this scheme stem from
the Dirac vs Majorana nature of fermions.


title:
A Dynamic Algorithm for the Longest Common Subsequence Problem using Ant
  Colony Optimization Technique

abstract:
  We present a dynamic algorithm for solving the Longest Common Subsequence
Problem using Ant Colony Optimization Technique. The Ant Colony Optimization
Technique has been applied to solve many problems in Optimization Theory,
Machine Learning and Telecommunication Networks etc. In particular, application
of this theory in NP-Hard Problems has a remarkable significance. Given two
strings, the traditional technique for finding Longest Common Subsequence is
based on Dynamic Programming which consists of creating a recurrence relation
and filling a table of size . The proposed algorithm draws analogy with
behavior of ant colonies function and this new computational paradigm is known
as Ant System. It is a viable new approach to Stochastic Combinatorial
Optimization. The main characteristics of this model are positive feedback,
distributed computation, and the use of constructive greedy heuristic. Positive
feedback accounts for rapid discovery of good solutions, distributed
computation avoids premature convergence and greedy heuristic helps find
acceptable solutions in minimum number of stages. We apply the proposed
methodology to Longest Common Subsequence Problem and give the simulation
results. The effectiveness of this approach is demonstrated by efficient
Computational Complexity. To the best of our knowledge, this is the first Ant
Colony Optimization Algorithm for Longest Common Subsequence Problem.


title: On the application of GMRES to oscillatory singular integral equations

abstract:
  We present a new method for the numerical solution of singular integral
equations on the real axis. The method's value stems from an explicit formula
for the Cauchy integral of a complex exponential multiplied by a rational
function. Additionally, the inner product of such functions is computed
explicitly. With these tools, the GMRES algorithm is applied to both
non-oscillatory and oscillatory singular integral equations. Ideas from
Fredholm theory and Riemann--Hilbert problems are used to motivate
preconditioners for these singular integral equations. A dramatic acceleration
in convergence is realized. This presents a strong link between the theory of
singular integral equations and the numerical analysis of such equations.
Furthermore, this method presents a first step towards a solver for the inverse
scattering transform that does not require the deformation of a
Riemann--Hilbert problem.


title:
Determination of the top-quark pole mass and strong coupling constant
  from the t t-bar production cross section in pp collisions at sqrt(s) = 7 TeV

abstract:
  The inclusive cross section for top-quark pair production measured by the CMS
experiment in proton-proton collisions at a center-of-mass energy of 7 TeV is
compared to the QCD prediction at next-to-next-to-leading order with various
parton distribution functions to determine the top-quark pole mass, mtpole, or
the strong coupling constant, alphaS. With the parton distribution function set
NNPDF2.3, a pole mass of 176.7 +3.0 -2.8 GeV is obtained when constraining
alphaS at the scale of the Z boson mass, mZ, to the current world average.
Alternatively, by constraining mtpole to the latest average from direct mass
measurements, a value of alphaS(mZ) = 0.1151 +0.0028 -0.0027 is extracted. This
is the first determination of alphaS using events from top-quark production.


title:
Andreev Reflection Like Enhancement Above Bulk $T_c$ in Electron
  Underdoped Iron Arsenides

abstract:
  We use point contact spectroscopy (PCS) to probe the superconducting
properties of electron doped $\rm{Ba(Fe_{1-x}Co_x)_2As_2}$ ($\rm{x = 0.05,
0.055, 0.07, 0.08}$) and hole doped $\rm{Ba_{0.8}K_{0.2}Fe_2As_2}$. PCS
directly probes the low energy density of states via Andreev reflection,
revealing two distinct superconducting gaps in both compound families. Apart
from the electron underdoped $\rm{Ba(Fe_{1-x}Co_{x})_2As_2}$, the excess
current due to Andreev reflection for the compounds follows the typical BCS
temperature dependence. For underdoped $\rm{Ba(Fe_{1-x}Co_{x})_2As_2}$, the
temperature dependence of the excess current deviates from that of BCS,
developing a tail at higher temperatures and surviving above bulk $T_c$.
Possible explanations for this anomalous behavior are explored.


title:
Systematic of isovector and isoscalar giant quadrupole resonances in
  normal and superfluid spherical nuclei

abstract:
  The isoscalar (IS) and isovector (IV) quadrupole responses of nuclei are
systematically investigated using the time-dependent Skyrme Energy Density
Functional including pairing in the BCS approximation. Using two different
Skyrme functionals, Sly4 and SkM*, respectively 263 and 304 nuclei have been
found to be spherical along the nuclear charts. The time-dependent evolution of
these nuclei has been systematically performed giving access to their
quadrupole responses. It is shown that the mean-energy of the collective high
energy state globally reproduces the experimental IS and IV collective energy
but fails to reproduce their lifetimes. It is found that the mean collective
energy depends rather significantly on the functional used in the mean-field
channel. Pairing by competing with parity effects can slightly affect the
collective response around magic numbers and induces a reduction of the
collective energy compared to the average trend. Low-lying states, that can
only be considered if pairing is included, are investigated. While the approach
provides a fair estimate of the low lying state energy, it strongly
underestimates the transition rate $B(E2)$. Finally, the possibility to access
to the density dependence of the symmetry energy through parallel measurements
of both the IS- and IV-GQR is discussed.


title:
Integrable Scalar Cosmologies I. Foundations and links with String
  Theory

abstract:
  We build a number of integrable one--scalar spatially flat cosmologies, which
play a natural role in inflationary scenarios, examine their behavior in
several cases and draw from them some general lessons on this type of systems,
whose potentials involve combinations of exponential functions, and on similar
non--integrable ones. These include the need for the scalar to emerge from the
initial singularity while climbing up sufficiently steep exponential potentials
("climbing phenomenon") and the inevitable collapse in a big Crunch whenever
the scalar tries to settle at negative extrema of the potential. We also
elaborate on the links between these types of potentials and "brane
supersymmetry breaking", a mechanism that ties together string scale and scale
of supersymmetry breaking in a class of orientifold models. We show that, under
some assumptions that are spelled out in the text, the extended objects of
these vacua can inject inflationary phases with discrete values of the spectral
index that are determined by the number of unwrapped dimensions of the branes
and by the inverse power with which the string coupling $g_s$ enters their
world--volume actions. An NS fivebrane, which is interestingly unstable in this
class of models, when wrapped on a small internal cycle would yield a spectral
index that is amusingly close to the experimentally favored PLANCK value ns ~
0.96.

categories: hep-th gr-qc hep-ph math-ph math.MP nlin.SI


title:
Misalignment of the Jet and the Normal to the Dusty Torus in the Broad
  Absorption Line QSO FIRST\,J155633.8+351758

abstract:
  We performed VLBA observations of the Broad Absorption Line Quasar
FIRST\,J155633.8+351758, "the first radio loud BALQSO". Our observations at
15.3 GHz partially resolved a secondary component at positional angle (PA)
$\approx 35^{\circ}$. We combine this determination of the radio jet projection
on the sky plane, with the constraint that the jet is viewed within
$14.3^{\circ}$ of the line of sight (as implied by the high variability
brightness temperature) and with the position angle (PA) of the optical/UV
continuum polarization in order to study the quasar geometry. Within the
context of the standard model, the data indicates a "dusty torus" (scattering
surface) with a symmetry axis tilted relative to the accretion disk normal and
a polar broad absorption line outflow aligned with the accretion disk normal.
We compare this geometry to that indicated by the higher resolution radio data,
brightness temperature and optical/UV continuum polarization PA of a similar
high optical polarization BALQSO, Mrk\,231. A qualitatively similar geometry is
found in these two polar BALQSOs; the continuum polarization is determined
primarily by the tilt of the dusty torus.


title: Model Independent Electromagnetic corrections in hadronic $\tau$ decays

abstract:
  The long distance correction to the total decay width of the $\tau^{\pm}\to
K^{0}\pi^{\pm}\nu$ decay is calculated in a model independent approach where a
discrimination of photons in the Bremmstrahlung process is assumed. This
correction is completely free of UV and IR singularities and moreover, it
satisfies electromagnetic gauge invariance. The result of this work can be
applied on the tau decays: $\tau^{\pm}\to \pi^{\pm}\pi^{0}\nu,
K^{\pm}\pi^{0}\nu$.


title: Covariant extrinsic gravity and the geometric origin of dark energy

abstract:
  We construct the covariant or model independent induced Einstein-Yang-Mills
field equations on a 4-dimensional brane embedded isometrically in an
D-dimensional bulk space, assuming the matter fields are confined to the brane.
Applying this formalism to cosmology, we derive the generalized Friedmann
equations. We derive the density parameter of dark energy in terms of width of
the brane, normal curvature radii and the number of extra large dimensions. We
show that dark energy could actually be the manifestation of the local
extrinsic shape of the brane. It is shown that the predictions of this model
are in good agreement with observation if we consider an 11-dimensional bulk
space.


title: On the Existence and Utility of Rigid Quasilocal Frames

abstract:
  The notion of a rigid quasilocal frame (RQF) provides a geometrically natural
way to define a system in general relativity, and a new way to analyze the
problem of motion. An RQF is defined as a two-parameter family of timelike
worldlines comprising the boundary (topologically R x S^2) of the history of a
finite spatial volume, with the rigidity conditions that the congruence of
worldlines be expansion- and shear-free. In other words, the size and shape of
the system do not change. In previous work, such systems in Minkowski space
were shown to admit precisely the same six degrees of freedom of rigid body
motion that we are familiar with in Newtonian space-time, without any
constraints, circumventing a century-old theorem due to Herglotz and Noether.
This is a consequence of the fact that a two-sphere of any shape always admits
precisely six conformal Killing vector fields, which generate an action of the
Lorentz group on the sphere. Here we review the previous work in flat spacetime
and extend it in three directions: (1) Using a Fermi normal coordinates
approach, we explicitly construct, to the first few orders in powers of areal
radius, the general solution to the RQF rigidity equations in a generic curved
spacetime, and show that the resulting RQFs possess exactly the same six
motional degrees of freedom as in flat spacetime; (2) We discuss how RQFs
provide a natural context in which to understand the flow of energy, momentum
and angular momentum into and out of a system; in particular, we derive a
simple, exact expression for the flux of gravitational energy (a gravitational
analogue of the Poynting vector) in terms of operationally-defined geometrical
quantities on the boundary; (3) We use this new gravitational (or
"geometrical") energy flux to resolve another apparent paradox, this one
involving electromagnetism in flat spacetime, which we discovered in the course
of this work.


title: Complexity of the FIFO Stack-Up Problem

abstract:
  We study the combinatorial FIFO stack-up problem. In delivery industry, bins
have to be stacked-up from conveyor belts onto pallets with respect to customer
orders. Given k sequences q_1, ..., q_k of labeled bins and a positive integer
p, the aim is to stack-up the bins by iteratively removing the first bin of one
of the k sequences and put it onto an initially empty pallet of unbounded
capacity located at one of p stack-up places. Bins with different pallet labels
have to be placed on different pallets, bins with the same pallet label have to
be placed on the same pallet. After all bins for a pallet have been removed
from the given sequences, the corresponding stack-up place will be cleared and
becomes available for a further pallet. The FIFO stack-up problem is to find a
stack-up sequence such that all pallets can be build-up with the available p
stack-up places. In this paper, we introduce two digraph models for the FIFO
stack-up problem, namely the processing graph and the sequence graph. We show
that there is a processing of some list of sequences with at most p stack-up
places if and only if the sequence graph of this list has directed pathwidth at
most p-1. This connection implies that the FIFO stack-up problem is NP-complete
in general, even if there are at most 6 bins for every pallet and that the
problem can be solved in polynomial time, if the number p of stack-up places is
assumed to be fixed. Further the processing graph allows us to show that the
problem can be solved in polynomial time, if the number k of sequences is
assumed to be fixed.


title:
Minisuperspace model of Machian Resolution of Problem of Time. I.
  Isotropic Case

abstract:
  A local resolution to the Problem of Time that is Machian and was previously
demonstrated for various relational mechanics models is here shown to work for
a more widely studied quantum cosmological model. Namely, closed isotropic
minisuperspace GR with minimally-coupled scalar field matter. This uses work
firstly along the lines of Barbour's at the classical level. Secondly, it uses
a Machianized version of the Semiclassical Approach to Quantum Cosmology.
Finally, it uses a combined Machianized version of a combined Semiclassical
Histories Timeless Records scheme along the lines of Halliwell's work. This
program's goal is the treatment of inhomogeneous perturbations about the
present paper's model, drawing also qualitatively from the relational mechanics
examples since these have nontrivial notions of inhomogeneity/structure
(clumping) as well as nontrivial linear constraints.


title:
Stabilizing spatially structured populations through Adaptive Limiter
  Control

abstract:
  Stabilizing the dynamics of complex, non-linear systems is a major concern
across several scientific disciplines including ecology and conservation
biology. Unfortunately, most methods proposed to reduce the fluctuations in
chaotic systems are not applicable for real, biological populations. This is
because such methods typically require detailed knowledge of system specific
parameters and the ability to manipulate them in real time; conditions often
not met by most real populations. Moreover, real populations are often noisy
and extinction-prone, which can sometimes render such methods ineffective. Here
we investigate a control strategy, which works by perturbing the population
size, and is robust to reasonable amounts of noise and extinction probability.
This strategy, called the Adaptive Limiter Control (ALC), has been previously
shown to increase constancy and persistence of laboratory populations and
metapopulations of Drosophila melanogaster. Here we present a detailed
numerical investigation of the effects of ALC on the fluctuations and
persistence of metapopulations. We show that at high migration rates,
application of ALC does not require a priori information about the population
growth rates. We also show that ALC can stabilize metapopulations even when
applied to as low as one-tenth of the total number of subpopulations. Moreover,
ALC is effective even when the subpopulations have high extinction rates:
conditions under which one other control algorithm has previously failed to
attain stability. Importantly, ALC not only reduces the fluctuation in
metapopulation sizes, but also the global extinction probability. Finally, the
method is robust to moderate levels of noise in the dynamics and the carrying
capacity of the environment. These results, coupled with our earlier empirical
findings, establish ALC to be a strong candidate for stabilizing real
biological metapopulations.


title: The Changing Geometry of a Fitness Landscape Along an Adaptive Walk

abstract:
  It has recently been noted that the relative prevalence of the various kinds
of epistasis varies along an adaptive walk. This has been explained as a result
of mean regression in NK model fitness landscapes. Here we show that this
phenomenon occurs quite generally in fitness landscapes. We propose a simple
and general explanation for this phenomemon, confirming the role of mean
regression. We provide support for this explanation with simulations, and
discuss the empirical relevance of our findings.


title: Systoles and Dehn surgery for hyperbolic 3-manifolds

abstract:
  Given a closed hyperbolic 3-manifold M of volume V, and a link L in M such
that the complement M \ L is hyperbolic, we establish a bound for the systole
length of M \ L in terms of V. This extends a result of Adams and Reid, who
showed that in the case that M is not hyperbolic, there is a universal bound of
7.35534... . As part of the proof, we establish a bound for the systole length
of a non-compact finite volume hyperbolic manifold which grows asymptotically
like (4/3)log(V).


title: Comment on `Wedges, cones, cosmic strings and their vacuum energy'

abstract:
  A recent paper (2012 \emph{J. Phys.\ A} \textbf{45} 374018) is extended by
investigating the behavior of the regularized quantum scalar stress tensor near
the axes of cones and their covering manifold, the Dowker space. A cone is
parametrized by its angle $\theta_1$, where $\theta_1=2\pi$ for flat space. We
find that the tensor components have singularities of the type $r^\gamma$, but
the generic leading $\gamma$ equals ${4\pi \over \theta_1} - 2$, which is
negative if and only if $\theta_1>2\pi$, and is a positive integer if
$\theta_1={2\pi\over N}$. Thus the functions are analytic in those cases that
can be solved by the method of images starting from flat space, and they are
not divergent in the cases that interpolate between those. As a wedge of angle
$\alpha$ can be solved by images starting from a cone of angle $2\alpha$, a
divergent stress can arise in a wedge with $\pi <\alpha \le 2\pi$ but not in a
smaller one.


title:
An approximate analytical solution of free convection problem for
  vertical isothermal plate via transverse coordinate Taylor expansion

abstract:
  The model under consideration is based on approximate analytical solution of
two dimensional stationary Navier-Stokes and Fourier-Kirchhoff equations.
Approximations are based on the typical for natural convection assumptions: the
fluid noncompressibility and Bousinesq approximation. We also assume that
ortogonal to the plate component (x) of velocity is neglectible small. The
solution of the boundary problem is represented as a Taylor Series in $x$
coordinate for velocity and temperature which introduces functions of vertical
coordinate (y), as coefficients of the expansion. The correspondent boundary
problem formulation depends on parameters specific for the problem: Grashoff
number, the plate height (L) and gravity constant. The main result of the paper
is the set of equations for the coefficient functions for example choice of
expansion terms number. The nonzero velocity at the starting point of a flow
appears in such approach as a development of convecntional boundary layer
theory formulation.


title: Random differences in Szemer\'edi's theorem and related results

abstract:
  We introduce a new, elementary method for studying random differences in
arithmetic progressions and convergence phenomena along random sequences of
integers. We apply our method to obtain significant improvements on previously
known results.


title:
Kendall's Shape Statistics as a Classical Realization of Barbour-type
  Timeless Records Theory approach to Quantum Gravity

abstract:
  I previously showed that Kendall's work on shape geometry is in fact also the
geometrical description of Barbour's relational mechanics' reduced
configuration spaces (alias shape spaces). I now describe the extent to which
Kendall's subsequent statistical application to e.g. the `standing stones
problem' realizes further ideas along the lines of Barbour-type timeless
records theories, albeit just at the classical level.


title: Global transformations preserving spectral data

abstract:
  We show the existence of a real analytic isomorphism between a space of
impedance function $\rho$ of the Sturm-Liouville problem
  $- \rho^{-2}(\rho^2f')' + uf$ on $(0,1)$, where $u$ is a function of $\rho,
\rho', \rho''$, and that of potential $p$ of the Schr{\"o}dinger equation $-
y'' + py$ on $(0,1)$, keeping their boundary conditions and spectral data.
  This mapping is associated with the classical Liouville transformation $f \to
\rho f$, and yields a global isomorphism between solutions to inverse problems
for the Sturm-Liouville equations of the impedance form and those to the
Schr{\"o}dinger equations.


title:
Polynomial propagation of moments and global existence for a
  Vlasov-Poisson system with a point charge

abstract:
  In this paper, we extend to the case of initial data constituted of a Dirac
mass plus a bounded density (with finite moments) the theory of Lions and
Perthame [6] for the Vlasov-Poisson equation. Our techniques also provide
polynomially growing in time estimates for moments of the bounded density.


title:
Modeling Human Mobility and its Applications in Routing in
  Delay-Tolerant Networks: a Short Survey

abstract:
  Human mobility patterns are complex and distinct from one person to another.
Nevertheless, motivated by tremendous potential benefits of modeling such
patterns in enabling new mobile services and technologies, researchers have
attempted to capture salient characteristics of human mobility. In this short
survey paper, we review some of the major techniques for modeling humans'
co-location, as well as predicting human location and trajectory. Further, we
review one of the most important application areas of such models, namely,
routing in delay-tolerant networks.


title: Link Based Session Reconstruction: Finding All Maximal Paths

abstract:
  This paper introduces a new method for the session construction problem,
which is the first main step of the web usage mining process. Through
experiments, it is shown that when our new technique is used, it outperforms
previous approaches in web usage mining applications such as next-page
prediction.


title: Implications of PSR J1614-2230 for NJL hybrid star

abstract:
  The recent determination of the mass of the pulsar PSR J1614-2230 with $1.97
\pm 0.04 M_\odot$ by \cite{Demorest}, renewed the discussions about the
possibility of exotic matter being present at the core of neutron stars. Since
the description of matter at densities beyond nuclear saturation is model
dependent, several works have explored different aspects of the fact that the
maximum neutron star mass implied by any equation of state (EoS) must exceed
the mass of PSR J1614-2230. In this article we present an extensive study of
hybrid star masses using several parametrizations of a relativistic mean-field
hadronic EoS together with a typical three-flavor NJL model with scalar, vector
and 't Hooft interactions as realized.


title: The Dynamics of Star Stream Gaps

abstract:
  When a massive object crosses a star stream velocity changes are induced both
along and transverse to the stream which can lead to the development of a
visible gap. For a stream narrow relative to its orbital radius the time of
stream crossing is sufficiently short that the impact approximation can be used
to derive the changes in angular momenta and radial actions along the star
stream. The epicyclic approximation is used to calculate the evolution of the
density of the stream as it orbits around in a galactic potential. Analytic
expressions are available for a point mass, however, the general expressions
are easily numerically evaluated for perturbing objects with arbitrary density
profiles. With a simple allowance for the velocity dispersion of the stream,
moderately warm streams can be modeled. The predicted evolution agrees well
with the outcome of simulations of stellar streams for streams with widths up
to 1% of the orbital radius of the stream. The angular momentum distribution
within the stream shears out gaps with time, further reducing their visibility,
although the size of the shear effect requires more detailed simulations. An
illustrative model indicates that shear will limit the persistent gaps to a
minimum length of a few times the stream width. In general the equations are
useful for dynamical insight into the development of stream gaps and their
measurement.


title: Nonlinear elliptic equations with high order singularities

abstract:
  We study non-variational degenerate elliptic equations with high order
singular structures. No boundary data are imposed and singularities occur along
an {\it a priori} unknown interior region. We prove that positive solutions
have a universal modulus of continuity that does not depend on their infimum
value. We further obtain sharp, quantitative regularity estimates for
non-negative limiting solutions.


title:
Long-range coupling of silicon photonic waveguides using lateral leakage
  and adiabatic passage

abstract:
  We present a new approach to long range coupling based on a combination of
adiabatic passage and lateral leakage in thin shallow ridge waveguides on a
silicon photonic platform. The approach enables transport of light between two
isolated waveguides through a mode of the silicon slab that acts as an optical
bus. Due to the nature of the adiabatic protocol, the bus mode has minimal
population and the transport is highly robust. We prove the concept and examine
the robustness of this approach using rigorous modelling. We further
demonstrate the utility of the approach by coupling power between two
waveguides whilst bypassing an intermediate waveguide. This concept could form
the basis of a new interconnect technology for silicon integrated photonic
chips.


title: The 2-ranks of connected compact Lie groups

abstract:
  The 2-rank of a compact Lie group $G$ is the maximal possible rank of the
elementary 2-subgroup ${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$ of $G$. The
study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was
initiated in 1953 by A. Borel and J.-P. Serre. Since then the 2-ranks of
compact Lie groups have been investigated by many mathematician. The 2-ranks of
compact Lie groups relate closely with several important areas in mathematics.
  In this article, we survey important results concerning 2-ranks of compact
Lie groups. In particular, we present the complete determination of 2-ranks of
compact connected simple Lie groups $G$ via the 2-numbers introduced by B. Y.
Chen and T. Nagano in [Un invariant g\'em\'etrique riemannien, C. R. Acad. Sci.
Paris, 295 (1982), 389--391] and [A Riemannian geometric invariant and its
applications to a problem of Borel and Serre, Trans. Amer. Math. Soc. 308
(1988), 273--297].


title:
Effect of Selenium doping on the superconductivity of
  Nb$_2$Pd(S$_{1-x}$Se$_x$)$_5$

abstract:
  We study the isovalent substitution effect by partially introducing Se on S
site in the newly discovered superconductor Nb$_2$PdS$_5$ ($T_c\sim$6 K) whose
upper critical field is found to be far above its Pauli paramagnetic limit. In
this Nb$_2$Pd(S$_{1-x}$Se$_x$)$_5$ (0$\leq$$x$$\leq$0.8) system,
superconductivity is systematically suppressed by the Se concentration and
ultimately disappears when $x\geq$ 0.5, after which a semiconducting-like
ground state emerges. In spite of the considerably reduced $T_c$ with Se
doping, the ratio of the upper critical field $H_{c2}$ to $T_c$, remains
unaffected. Moreover, the size of the heat capacity jump at $T_c$ is smaller
than that expected for a BCS superconductor, implying that a strong-coupling
theory cannot be the origin of this large upper critical field. In addition,
the low-lying quasiparticle excitations are consistent with a nodeless gap
opening over the Fermi surface. These results combined impose severe
constraints on any theory of exotic superconductivity in this system.


title: RNA secondary structure prediction from multi-aligned sequences

abstract:
  It has been well accepted that the RNA secondary structures of most
functional non-coding RNAs (ncRNAs) are closely related to their functions and
are conserved during evolution. Hence, prediction of conserved secondary
structures from evolutionarily related sequences is one important task in RNA
bioinformatics; the methods are useful not only to further functional analyses
of ncRNAs but also to improve the accuracy of secondary structure predictions
and to find novel functional RNAs from the genome. In this review, I focus on
common secondary structure prediction from a given aligned RNA sequence, in
which one secondary structure whose length is equal to that of the input
alignment is predicted. I systematically review and classify existing tools and
algorithms for the problem, by utilizing the information employed in the tools
and by adopting a unified viewpoint based on maximum expected gain (MEG)
estimators. I believe that this classification will allow a deeper
understanding of each tool and provide users with useful information for
selecting tools for common secondary structure predictions.


title: Strong embeddability and extensions of groups

abstract:
  We introduce the notion of strong embeddability for a metric space. This
property lies between coarse embeddability and property A. A relative version
of strong embeddability is developed in terms of a family of set maps on the
metric space. When restricted to discrete groups, this yields relative coarse
embeddability. We verify that groups acting on a metric space which is strongly
embeddable has this relative strong embeddability, provided the stabilizer
subgroups do. As a corollary, strong embeddability is preserved under group
extensions.


title:
Curvature estimates for minimal hypersurfaces via generalized longitude
  function

abstract:
  On some specified convex supporting sets of spheres, we find a generalized
longitude function whose level sets are totally geodesic. Given an arbitrary
(weakly) harmonic map into spheres, the composition of the generalized
longitude function and harmonic map satisfies an elliptic equation of
divergence type. With the aid of corresponding Harnack inequality, we establish
image shrinking property and then the regularity results are followed. Applying
such results to study the Gauss image of minimal hypersurfaces in Euclidean
spaces, we obtain curvature estimates and corresponding Bernstein theorems.


title: Holonomic D-modules on abelian varieties

abstract:
  We study the Fourier-Mukai transform for holonomic D-modules on complex
abelian varieties. Among other things, we show that the cohomology support loci
of a holonomic D-module are finite unions of linear subvarieties, which go
through points of finite order for objects of geometric origin; that the
standard t-structure on the derived category of holonomic complexes
corresponds, under the Fourier-Mukai transform, to a certain perverse coherent
t-structure in the sense of Kashiwara and Arinkin-Bezrukavnikov; and that
Fourier-Mukai transforms of simple holonomic D-modules are intersection
complexes in this t-structure. This supports the conjecture that Fourier-Mukai
transforms of holonomic D-modules are "hyperk\"ahler perverse sheaves".


title: Helioseismology of Pre-Emerging Active Regions III: Statistical Analysis

abstract:
  The subsurface properties of active regions prior to their appearance at the
solar surface may shed light on the process of active region formation.
Helioseismic holography has been applied to samples taken from two populations
of regions on the Sun (pre-emergence and without emergence), each sample having
over 100 members, that were selected to minimize systematic bias, as described
in Paper I (Leka et al., 2012). Paper II (Birch et al., 2012) showed that there
are statistically significant signatures in the average helioseismic properties
that precede the formation of an active region. This paper describes a more
detailed analysis of the samples of pre-emergence regions and regions without
emergence, based on discriminant analysis. The property that is best able to
distinguish the populations is found to be the surface magnetic field, even a
day before the emergence time. However, after accounting for the correlations
between the surface field and the quantities derived from helioseismology,
there is still evidence of a helioseismic precursor to active region emergence
that is present for at least a day prior to emergence.


title:
A useful way to obtain the central charge of entanglement Hamiltonian --
  Nested entanglement entropy

abstract:
  In this paper, we review how to obtain the central charge of a critical
entanglement Hamiltonian through the nested entanglement entropy which was
first introduced in [J. Lou et al. PRB 84, 245128 (2011)]. The critical
phenomena of the entanglement Hamiltonian can be identified by the central
charge obtained by the nested entanglement entropy. We review our previous
studies[J. Lou et al. PRB 84, 245128 (2011), S. Tanaka et al. PRA 87, 214401
(2013)] in which we investigated certain entanglement nature of two-dimensional
valence-bond-solid (VBS) state and quantum hard-square models on square and
triangle ladders using the nested entanglement entropy.


title: Reinforcing Power Grid Transmission with FACTS Devices

abstract:
  We explore optimization methods for planning the placement, sizing and
operations of Flexible Alternating Current Transmission System (FACTS) devices
installed into the grid to relieve congestion created by load growth or
fluctuations of intermittent renewable generation. We limit our selection of
FACTS devices to those that can be represented by modification of the
inductance of the transmission lines. Our master optimization problem minimizes
the $l_1$ norm of the FACTS-associated inductance correction subject to
constraints enforcing that no line of the system exceeds its thermal limit. We
develop off-line heuristics that reduce this non-convex optimization to a
succession of Linear Programs (LP) where at each step the constraints are
linearized analytically around the current operating point. The algorithm is
accelerated further with a version of the cutting plane method greatly reducing
the number of active constraints during the optimization, while checking
feasibility of the non-active constraints post-factum. This hybrid algorithm
solves a typical single-contingency problem over the MathPower Polish Grid
model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard
laptop---a speed up that allows the sizing and placement of a family of FACTS
devices to correct a large set of anticipated contingencies. From testing of
multiple examples, we observe that our algorithm finds feasible solutions that
are always sparse, i.e., FACTS devices are placed on only a few lines. The
optimal FACTS are not always placed on the originally congested lines, however
typically the correction(s) is made at line(s) positioned in a relative
proximity of the overload line(s).


title: The Bergman Shift Operator on Polynomial Lemniscates

abstract:
  We investigate the relationship between the Bergman shift operator and the
support of the corresponding measure. We pay special attention to the situation
when the measure of orthogonality is concentrated on a polynomial lemniscate.
As an application of our new results, we obtain a ratio asymptotic result for a
wide variety of measures supported on polynomial lemniscates.


title: PROOFTOOL: a GUI for the GAPT Framework

abstract:
  This paper introduces PROOFTOOL, the graphical user interface for the General
Architecture for Proof Theory (GAPT) framework. Its features are described with
a focus not only on the visualization but also on the analysis and
transformation of proofs and related tree-like structures, and its
implementation is explained. Finally, PROOFTOOL is compared with three other
graphical interfaces for proofs.


title: Proof in Context -- Web Editing with Rich, Modeless Contextual Feedback

abstract:
  The Agora system is a prototypical Wiki for formal mathematics: a web-based
system for collaborating on formal mathematics, intended to support informal
documentation of formal developments. This system requires a reusable proof
editor component, both for collaborative editing of documents, and for
embedding in the resulting documents. This paper describes the design of
Agora's asynchronous editor, that is generic enough to support different tools
working on editor content and providing contextual information, with
interactive theorem proverss being a special, but important, case described in
detail for the Coq theorem prover.