title: Sharp Bounds in Stochastic Network Calculus

abstract:
  The practicality of the stochastic network calculus (SNC) is often questioned
on grounds of potential looseness of its performance bounds. In this paper it
is uncovered that for bursty arrival processes (specifically Markov-Modulated
On-Off (MMOO)), whose amenability to \textit{per-flow} analysis is typically
proclaimed as a highlight of SNC, the bounds can unfortunately indeed be very
loose (e.g., by several orders of magnitude off). In response to this uncovered
weakness of SNC, the (Standard) per-flow bounds are herein improved by deriving
a general sample-path bound, using martingale based techniques, which
accommodates FIFO, SP, EDF, and GPS scheduling. The obtained (Martingale)
bounds gain an exponential decay factor of ${\mathcal{O}}(e^{-\alpha n})$ in
the number of flows $n$. Moreover, numerical comparisons against simulations
show that the Martingale bounds are remarkably accurate for FIFO, SP, and EDF
scheduling; for GPS scheduling, although the Martingale bounds substantially
improve the Standard bounds, they are numerically loose, demanding for
improvements in the core SNC analysis of GPS.


title:
On quasi-linear PDAEs with convection: applications, indices, numerical
  solution

abstract:
  For a class of partial differential algebraic equations (PDAEs) of
quasi-linear type which include nonlinear terms of convection type a
possibility to determine a time and spatial index is considered. As a typical
example we investigate an application from plasma physics. Especially we
discuss the numerical solution of initial boundary value problems by means of a
corresponding finite difference splitting procedure which is a modification of
a well known fractional step method coupled with a matrix factorization. The
convergence of the numerical solution towards the exact solution of the
corresponding initial boundary value problem is investigated. Some results of a
numerical solution of the plasma PDAE are given.


title:
Convergence of Runge-Kutta Methods Applied to Linear Partial
  Differential-Algebraic Equations

abstract:
  We apply Runge-Kutta methods to linear partial differential-algebraic
equations of the form $Au_t(t,x) + B(u_{xx}(t,x)+ru_x(t,x))+Cu(t,x) = f(t,x)$,
where $A,B,C\in\R^{n,n}$ and the matrix $A$ is singular. We prove that under
certain conditions the temporal convergence order of the fully discrete scheme
depends on the time index of the partial differential-algebraic equation. In
particular, fractional orders of convergence in time are encountered.
Furthermore we show that the fully discrete scheme suffers an order reduction
caused by the boundary conditions. Numerical examples confirm the theoretical
results.


title: Minimal symmetric differences of lines in projective planes

abstract:
  Let q be an odd prime power and let f(r) be the minimum size of the symmetric
difference of r lines in the Desarguesian projective plane PG(2,q). We prove
some results about the function f(r), in particular showing that there exists a
constant C>0 such that f(r)=O(q) for Cq^{3/2}<r<q^2 - Cq^{3/2}.


title: Double cosets in free groups

abstract:
  In this paper we study double cosets of finite rank free groups. We focus our
attention on cancellation types in double cosets and their formal language
properties.


title:
Far-Ultraviolet Spectroscopy of the Nova-Like Variable KQ Monocerotis: A
  New SW Sextantis Star?

abstract:
  New optical spectra obtained with the SMARTS 1.5m telescope and archival IUE
far-ultraviolet spectra of the nova-like variable KQ Mon are discussed. The
optical spectra reveal Balmer lines in absorption as well as He I absorption
superposed on a blue continuum. The 2011 optical spectrum is similar to the
KPNO 2.1m IIDS spectrum we obtained 33 years earlier, except that the Balmer
and He I absorption is stronger in 2011. Far-ultraviolet IUE spectra reveal
deep absorption lines due to C II, Si III, Si IV, C IV, and He II, but no P
Cygni profiles indicative of wind outflow. We present the results of the first
synthetic spectral analysis of the IUE archival spectra of KQ Mon with
realistic optically thick, steady-state, viscous accretion-disk models with
vertical structure and high-gravity photosphere models. We find that the
photosphere of the white dwarf (WD) contributes very little FUV flux to the
spectrum and is overwhelmed by the accretion light of a steady disk. Disk
models corresponding to a WD mass of ~0.6 Msun, with an accretion rate of order
10^{-9} Msun/yr and disk inclinations between 60 and 75 deg, yield distances
from the normalization in the range of 144 to 165 pc. KQ Mon is discussed with
respect to other nova-like variables. Its spectroscopic similarity to the FUV
spectra of three definite SW Sex stars suggests that it is likely a member of
the SW Sex class and lends support to the possibility that the WD is magnetic.


title:
Adaptive Randomized Distributed Space-Time Coding in Cooperative MIMO
  Relay Systems

abstract:
  An adaptive randomized distributed space-time coding (DSTC) scheme and
algorithms are proposed for two-hop cooperative MIMO networks. Linear minimum
mean square error (MMSE) receivers and an amplify-and-forward (AF) cooperation
strategy are considered. In the proposed DSTC scheme, a randomized matrix
obtained by a feedback channel is employed to transform the space-time coded
matrix at the relay node. Linear MMSE expressions are devised to compute the
parameters of the adaptive randomized matrix and the linear receive filter. A
stochastic gradient algorithm is also developed to compute the parameters of
the adaptive randomized matrix with reduced computational complexity. We also
derive the upper bound of the error probability of a cooperative MIMO system
employing the randomized space-time coding scheme first. The simulation results
show that the proposed algorithms obtain significant performance gains as
compared to existing DSTC schemes.


title: Probit transformation for kernel density estimation on the unit interval

abstract:
  Kernel estimation of a probability density function supported on the unit
interval has proved difficult, because of the well known boundary bias issues a
conventional kernel density estimator would necessarily face in this situation.
Transforming the variable of interest into a variable whose density has
unconstrained support, estimating that density, and obtaining an estimate of
the density of the original variable through back-transformation, seems a
natural idea to easily get rid of the boundary problems. In practice, however,
a simple and efficient implementation of this methodology is far from
immediate, and the few attempts found in the literature have been reported not
to perform well. In this paper, the main reasons for this failure are
identified and an easy way to correct them is suggested. It turns out that
combining the transformation idea with local likelihood density estimation
produces viable density estimators, mostly free from boundary issues. Their
asymptotic properties are derived, and a practical cross-validation bandwidth
selection rule is devised. Extensive simulations demonstrate the excellent
performance of these estimators compared to their main competitors for a wide
range of density shapes. In fact, they turn out to be the best choice overall.
Finally, they are used to successfully estimate a density of non-standard shape
supported on $[0,1]$ from a small-size real data sample.


title: On the p-adic Second Main Theorem

abstract:
  We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving
an improvement to the non-archimedean Second Main Theorems of Ru and An in the
case where all the hypersurfaces have degree greater than one and all
intersections are transverse. In particular, under a transversality assumption,
if f is a nonconstant non-archimedean analytic map to P^n and D_1,..,D_q are
hypersurfaces of degree d, we prove the defect relation
\sum_{i=1}^q\delta_f(D_i)\leq n-1+1/d, which is sharp for all positive integers
n and d.


title:
Extending the Planetary Mass Function to Earth Mass by Microlensing at
  Moderately High Magnification

abstract:
  A measurement by microlensing of the planetary mass function of planets with
masses ranging from 5M_E to 10M_J and orbital radii from 0.5 to 10 AU was
reported recently. A strategy for extending the mass range down to (1-3)M_E is
proposed here. This entails monitoring the peaks of a few tens of microlensing
events with moderately high magnifications with 1-2m class telescopes. Planets
of a few Earth masses are found to produce deviations of ~ 5% to the peaks of
microlensing light curves with durations ~ (0.7-3)hr in events with
magnification ~ 100 if the projected separation of the planet lies in the
annular region (0.85-1.2)r_E. Similar deviations are produced by Earth mass
planets in the annular region (0.95-1.05)r_E. It is possible that sub-Earths
could be detected very close to the Einstein ring if they are sufficiently
abundant, and also planetary systems with more than one low mass planet.


title:
Phase space factors for $\beta^+\beta^+$ decay and competing modes of
  double-$\beta$ decay

abstract:
  A complete and improved calculation of phase space factors (PSF) for
$2\nu\beta^+\beta^+$ and $0\nu\beta^+\beta^+$ decay, as well as for the
competing modes $2\nu EC\beta^+$, $0\nu EC\beta^+$, and $2\nu ECEC$, is
presented. The calculation makes use of exact Dirac wave functions with finite
nuclear size and electron screening and includes life-times, single and summed
positron spectra, and angular positron correlations.


title:
Linear forms in logarithms and integral points on higher-dimensional
  varieties

abstract:
  We apply inequalities from the theory of linear forms in logarithms to deduce
effective results on S-integral points on certain higher-dimensional varieties
when the cardinality of S is sufficiently small. These results may be viewed as
a higher-dimensional version of an effective result of Bilu on integral points
on curves. In particular, we prove a completely explicit result for integral
points on certain affine subsets of the projective plane. As an application, we
generalize an effective result of Vojta on the three-variable unit equation by
giving an effective solution of the polynomial unit equation f(u,v)=w, where
u,v, and w are S-units, |S|\leq 3, and f is a polynomial satisfying certain
conditions (which are generically satisfied). Finally, we compare our results
to a higher-dimensional version of Runge's method, which has some
characteristics in common with the results here.


title:
Jack polynomials as fractional quantum Hall states and the Betti numbers
  of the (k+1)-equals ideal

abstract:
  We show that for Jack parameter \alpha = -(k+1)/(r-1), certain Jack
polynomials studied by Feigin-Jimbo-Miwa-Mukhin vanish to order r when k+1 of
the coordinates coincide. This result was conjectured by Bernevig and Haldane,
who proposed that these Jack polynomials are model wavefunctions for fractional
quantum Hall states. Special cases of these Jack polynomials include the
wavefunctions of Laughlin and Read-Rezayi. In fact, along these lines we prove
several vanishing theorems known as clustering properties for Jack polynomials
in the mathematical physics literature, special cases of which had previously
been conjectured by Bernevig and Haldane. Motivated by the method of proof,
which in case r = 2 identifies the span of the relevant Jack polynomials with
the S_n-invariant part of a unitary representation of the rational Cherednik
algebra, we conjecture that unitary representations of the type A Cherednik
algebra have graded minimal free resolutions of Bernstein-Gelfand-Gelfand type;
we prove this for the ideal of the (k+1)-equals arrangement in the case when
the number of coordinates n is at most 2k+1. In general, our conjecture
predicts the graded S_n-equivariant Betti numbers of the ideal of the
(k+1)-equals arrangement with no restriction on the number of ambient
dimensions.

categories: math-ph cond-mat.mes-hall math.AC math.MP math.RT


title: Quantum Search on the Spatial Grid

abstract:
  This paper explores Quantum Search on the two dimensional spatial grid.
Recent exploration into the topic has devised a solution that runs in
O(sqrt(n*ln(n))). This paper explores a new algorithm that gives promise for
the O(sqrt(n)) result that is the lower bound off of the grid.


title: Sparse Phase Retrieval: Convex Algorithms and Limitations

abstract:
  We consider the problem of recovering signals from their power spectral
density. This is a classical problem referred to in literature as the phase
retrieval problem, and is of paramount importance in many fields of applied
sciences. In general, additional prior information about the signal is required
to guarantee unique recovery as the mapping from signals to power spectral
density is not one-to-one. In this paper, we assume that the underlying signals
are sparse. Recently, semidefinite programming (SDP) based approaches were
explored by various researchers. Simulations of these algorithms strongly
suggest that signals upto $o(\sqrt{n})$ sparsity can be recovered by this
technique. In this work, we develop a tractable algorithm based on reweighted
$l_1$-minimization that recovers a sparse signal from its power spectral
density for significantly higher sparsities, which is unprecedented.
  We discuss the square-root bottleneck of the existing convex algorithms and
show that a $k$-sparse signal can be efficiently recovered using $O(k^2logn)$
phaseless Fourier measurements. We also show that a $k$-sparse signal can be
recovered using only $O(k log n)$ phaseless measurements if we are allowed to
design the measurement matrices.


title:
Relativistic effects in the tidal interaction between a white dwarf and
  a massive black hole in Fermi normal coordinates

abstract:
  We consider tidal encounters between a white dwarf and an intermediate mass
black hole. Both weak encounters and those at the threshold of disruption are
modeled. The numerical code combines mesh-based hydrodynamics, a spectral
method solution of the self-gravity, and a general relativistic Fermi normal
coordinate system that follows the star and debris. Fermi normal coordinates
provide an expansion of the black hole tidal field that includes quadrupole and
higher multipole moments and relativistic corrections. We compute the mass loss
from the white dwarf that occurs in weak tidal encounters. Secondly, we compute
carefully the energy deposition onto the star, examining the effects of
nonradial and radial mode excitation, surface layer heating, mass loss, and
relativistic orbital motion. We find evidence of a slight relativistic
suppression in tidal energy transfer. Tidal energy deposition is compared to
orbital energy loss due to gravitational bremsstrahlung and the combined losses
are used to estimate tidal capture orbits. Heating and partial mass stripping
will lead to an expansion of the white dwarf, making it easier for the star to
be tidally disrupted on the next passage. Finally, we examine angular momentum
deposition. By including the octupole tide, we are able for the first time to
calculate deflection of the center of mass of the star and debris. With this
observed deflection, and taking into account orbital relativistic effects, we
compute directly the change in orbital angular momentum and show its balance
with computed spin angular momentum deposition.


title:
On the Support of Solar Prominence Material by the Dips of a Coronal
  Flux Tube

abstract:
  The dense prominence material is believed to be supported against gravity
through the magnetic tension of dipped coronal magnetic field. For quiescent
prominences, which exhibit many gravity-driven flows, hydrodynamic forces are
likely to play an important role in the determination of both the large and
small scale magnetic field distributions. In this study, we present the first
steps toward creating three-dimensional magneto-hydrostatic prominence model
where the prominence is formed in the dips of a coronal flux tube. Here 2.5D
equilibria are created by adding mass to an initially force-free magnetic
field, then performing a secondary magnetohydrodynamic relaxation. Two inverse
polarity magnetic field configurations are studied in detail, a simple o-point
configuration with a ratio of the horizontal field (B_x) to the axial field
(B_y) of 1:2 and a more complex model that also has an x-point with a ratio of
1:11. The models show that support against gravity is either by total pressure
or tension, with only tension support resembling observed quiescent
prominences. The o-point of the coronal flux tube was pulled down by the
prominence material, leading to compression of the magnetic field at the base
of the prominence. Therefore tension support comes from the small curvature of
the compressed magnetic field at the bottom and the larger curvature of the
stretched magnetic field at the top of the prominence. It was found that this
method does not guarantee convergence to a prominence-like equilibrium in the
case where an x-point exists below the prominence flux tube. The results imply
that a plasma beta of ~ 0.1 is necessary to support prominences through
magnetic tension.


title: Noise in electromigrated nanojunctions

abstract:
  Noise measurements are a probe beyond simple electronic transport that can
reveal additional information about electronic correlations and inelastic
processes. Here we report noise measurements in individual electromigrated
nanojunctions, examining the evolution from the many channel regime to the
tunneling regime, using a radio frequency technique. While we generally observe
the dependence of noise on bias expected for shot noise, in approximately 12%
of junction configurations we find discrete changes in the bias dependence at
threshold values of the bias, consistent with electronic excitation of local
vibrational modes. Moreover, with some regularity we find significant
mesoscopic variation in the magnitude of the noise in particular junctions even
with small changes in the accompanying conductance. In another $\sim$17% of
junctions we observe pronounced asymmetries in the inferred noise magnitude as
a function of bias polarity, suggesting that investigators should be concerned
about current-driven ionic motion in the electrodes even at biases well below
those used for deliberate electromigration.


title: Hadronic Parity Violation

abstract:
  The history and phenomenology of hadronic parity nonconservation (PNC) is
reviewed. We discuss the current status of the experimental tests and theory.
We describe a re-analysis of the asymmetry for polarized proton-proton
scattering that, when combined with other experimental constraints and with a
recent lattice QCD calculation of the weak pion-nucleon coupling, reveals a
much more consistent pattern of PNC couplings. In particular, isoscalar
coupling strengths are similar to but somewhat larger than the "best value"
estimate of Donoghue, Desplanques, and Holstein, while both lattice QCD and
experiment indicate a suppressed parity-nonconserving pion-nucleon coupling. We
discuss the relationship between meson-exchange models of hadronic PNC and
formulations based on effective theory, stressing their general compatibility
as well as the challenge presented to theory by experiment, as several of the
most precise measurements involve significant momentum scales. Future
directions are proposed.


title: Non-connective K-theory of relative exact categories

abstract:
  The main objective of this paper is to propose a definition of non-connective
K-theory for a wide class of relative exact categories which, in general, do
not satisfy the factorization axiom and confirm that it agrees with the
non-connective K-theory for exact categories and complicial exact categories
with weak equivalences. The main application is to study the topological
filtrations of non-connective K-theory of a noetherian commutative ring with
unit in terms of Koszul cubes.


title: Charge carrier relaxation model in hopping system

abstract:
  The relaxation phenomena of charge carriers in hopping system have been
demonstrated and investigated theoretically. An analytical model describing the
charge carrier relaxation is proposed based on the hopping transport theory.
The relation between the material disorder, electric field and temperature and
the relaxation phenomena has been discussed in detail, respectively. The
calculated results reveal that the increase of electric field and temperature
can promote the relaxation effect in disordered systems, while the increase of
material disorder will weaken the relaxation. The proposed model can explain
well the stretched-exponential law by adopting the appropriate parameters. The
calculation shows a good agreement with the experimental data for organic
semiconductors.


title:
Absence of a static in-plane magnetic moment in the "hidden-order" phase
  of URu$_2$Si$_2$

abstract:
  We have carried out a careful magnetic neutron scattering study of the heavy
fermion compound \URuSi\ to probe the possible existence of a small magnetic
moment parallel to tetragonal basal plane in the "hidden-order" phase. This
small in-plane component of the magnetic moment on the uranium sites
$S_\parallel$ has been postulated by two recent models (rank-5
superspin/hastatic order) aiming to explain the hidden-order phase, in addition
to the well-known out-of-plane component $S_\perp ~ \approx~0.01-0.04
$\mu_B$/U. In order to separate $S_\parallel$ and $S_\perp$ we take advantage
of the condition that for magnetic neutron scattering only the components of
the magnetic structure that are perpendicular to the scattering vector $Q$
contribute to the magnetic scattering. We find no evidence for an in-plane
magnetic moment $S_\parallel$. Based on the statistics of our measurement, we
establish that the upper experimental limit for the size of any possible
in-plane component is $S^{\rm{max}}_\parallel ~ \leq~1\cdot 10^{-3} ~\mu_B$/U.


title:
BCS-BEC crossover at finite temperature in spin-orbit coupled Fermi
  gases

abstract:
  By adopting a $T$-matrix-based method within the $G_0G$ approximation for the
pair susceptibility, we study the effects of the pairing fluctuation on the
three-dimensional spin-orbit coupled Fermi gases at finite temperature. The
critical temperatures of the superfluid/normal phase transition are determined
for three different types of spin-orbit coupling (SOC): (1) the extreme oblate
(EO) or Rashba SOC, (2) the extreme prolate (EP) or equal Rashba-Dresselhaus
SOC, and (3) the spherical (S) SOC. For EO- and S-type SOC, the SOC dependence
of the critical temperature signals a crossover from BCS to BEC state; at
strong SOC limit, the critical temperature recover those of ideal BEC of
rashbons. The pairing fluctuation induces a pseudogap in the fermionic
excitation spectrum in both superfluid and normal phases. We find that, for EO-
and S-type SOC, even at weak coupling, sufficiently strong SOC can induce
sizable pseudogap. Our research suggests that the spin-orbit coupled Fermi
gases may open new means to the study of the pseudogap formation in fermionic
systems.


title: Lattice points in rotated convex domains

abstract:
  If $\mathcal{B}\subset \mathbb{R}^d$ ($d\geqslant 2$) is a compact convex
domain with a smooth boundary of finite type, we prove that for almost every
rotation $\theta\in SO(d)$ the remainder of the lattice point problem,
$P_{\theta \mathcal{B}}(t)$, is of order $O_{\theta}(t^{d-2+2/(d+1)-\zeta_d})$
with a positive number $\zeta_d$. Furthermore we extend the estimate of the
above type, in the planar case, to general compact convex domains.


title: An active asteroid belt causing the UX Ori phenomenon in RZ Psc

abstract:
  We report the discovery of mid-infrared excess emission in the young object
RZ Psc. The excess constitutes ~8% of its Lbol, and is well fit by a single
500K black-body implying a dust free region within 0.7AU for optically thick
dust. The object displays dust obscuration events (UXOR behaviour) with a
time-scale that suggests dusty material on orbits of 0.5AU. We also report a
12.4 year cyclical photometric variability which can be interpreted as due to
perturbations in the dust distribution. The system is characterized by a high
inclination, marginal extinction (during bright photometric states), a single
temperature for the warm dust, and an age estimate which puts the star beyond
the formation stage. We propose that the dust occultation events present a
dynamical view of an active asteroid belt whose collisional products
sporadically obscure the central star.


title:
Monotonicity of the optimal perimeter in isoperimetric problems on
  ${\mathbb{Z}}^{k} \times {\mathbb{N}}^{d}$

abstract:
  We prove general theorems for isoperimetric problems on lattices of the form
${\mathbb{Z}}^{k} \times {\mathbb{N}}^{d}$ which state that the perimeter of
the optimal set is a monotonically increasing function of the volume under
certain natural assumptions, such as local symmetry or being induced by an
$\ell_p$-norm. The proved monotonicity property is surprising considering that
solutions are not always nested (and consequently standard techniques such as
compressions do not apply). The monotonicity results of this note apply in
particular to vertex- and edge-isoperimetric problems in the $\ell_p$ distances
and can be used as a tool to elucidate properties of optimal sets. As an
application, we consider the edge-isoperimetric inequality on the graph
${\N}^2$ in the $\ell_\infty$-distance. We show that there exist arbitrarily
long consecutive values of the volume for which the minimum boundary is the
same.


title: A Study of P-wave Heavy Meson Interactions in A Chiral Quark Model

abstract:
  The analytical forms of the interaction potentials between one S-wave and one
P-wave heavy mesons as well as the potentials between two P-wave heavy mesons
are deduced based on a chiral quark model. Our results explicitly show the
attractive property between two heavy mesons. Consequently, a series of
possible molecular states are obtained. It is expected that our study might
shed some light on the popular discussions of the newly observed XYZ states.


title: Quantum phase transitions in heavy fermion metals and Kondo insulators

abstract:
  Strongly correlated electron systems at the border of magnetism are of active
current interest, particularly because the accompanying quantum criticality
provides a route towards both strange-metal non-Fermi liquid behavior and
unconventional superconductivity. Among the many important questions is whether
the magnetism acts simply as a source of fluctuations in the textbook Landau
framework, or instead serves as a proxy for some unexpected new physics. We put
into this general context the recent developments on quantum phase transitions
in antiferromagnetic heavy fermion metals. Among these are the extensive recent
theoretical and experimental studies on the physics of Kondo destruction in a
class of beyond-Landau quantum critical points. Also discussed are the
theoretical basis for a global phase diagram of antiferromagnetic heavy fermion
metals, and the recent surge of materials suitable for studying this phase
diagram. Furthermore, we address the generalization of this global phase
diagram to the case of Kondo insulators, and consider the future prospect to
study the interplay among Kondo coherence, magnetism and topological states.
Finally, we touch upon related issues beyond the antiferromagnetic settings,
arising in mixed valent, ferromagnetic, quadrupolar, or spin glass f-electron
systems, as well as some general issues on emergent phases near quantum
critical points.


title: Exact temporal evolution of the two-species Bose-Einstein condensates

abstract:
  We construct exact stationary solutions to the one-dimensional coupled
Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with
equal intraspecies and interspecies interaction constants. Three types of
complex solutions as well as their soliton limits are derived. By making use of
the SU(2) unitary symmetry, we further obtain analytical time-evolving
solutions. These solutions exhibit spatiotemporal periodicity.


title:
Primordial power spectrum: a complete analysis with the WMAP nine-year
  data

abstract:
  We have improved further the error sensitive Richardson-Lucy deconvolution
algorithm making it applicable directly on the un-binned measured angular power
spectrum of Cosmic Microwave Background observations to reconstruct the form of
the primordial power spectrum. This improvement makes the application of the
method significantly more straight forward by removing some intermediate stages
of analysis allowing a reconstruction of the primordial spectrum with higher
efficiency and precision and with lower computational expenses. Applying the
modified algorithm we fit the WMAP 9 year data using the optimized
reconstructed form of the primordial spectrum with more than 300 improvement in
\chi^2 with respect to the best fit power-law. This is clearly beyond the reach
of other alternative approaches and reflects the efficiency of the proposed
method in the reconstruction process and allow us to look for any possible
feature in the primordial spectrum projected in the CMB data. Though the
proposed method allow us to look at various possibilities for the form of the
primordial spectrum, all having good fit to the data, proper error-analysis is
needed to test for consistency of theoretical models since, along with possible
physical artefacts, most of the features in the reconstructed spectrum might be
arising from fitting noises in the CMB data. Reconstructed error-band for the
form of the primordial spectrum using many realizations of the data, all
bootstrapped and based on WMAP 9 year data, shows proper consistency of
power-law form of the primordial spectrum with the WMAP 9 data at all wave
numbers. Including WMAP polarization data in to the analysis have not improved
much our results due to its low quality but we expect Planck data will allow us
to make a full analysis on CMB observations on both temperature and
polarization separately and in combination.


title: Topological Mirror Superconductivity

abstract:
  We demonstrate the existence of topological superconductors (SC) protected by
mirror and time reversal (TR) symmetries. D-dimensional (D=1,2,3) crystalline
SCs are characterized by 2^(D-1) independent integer topological invariants,
which take the form of mirror Berry phases. These invariants determine the
distribution of Majorana modes on a mirror symmetric boundary. The parity of
total mirror Berry phase is the Z_2 index of a class DIII SC, implying that a
DIII topological SC with a mirror line must also be a topological mirror SC but
not vice versa, and that a DIII SC with a mirror plane is always TR trivial but
can be mirror topological. We introduce representative models and suggest
experimental signatures in feasible systems. Advances in quantum computing, the
case for nodal SCs, the case for class D, and topological SCs protected by
rotational symmetries are pointed out.

categories: cond-mat.supr-con cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.str-el


title:
Finite Morse index solutions and asymptotics of weighted nonlinear
  elliptic equations

abstract:
  By introducing a suitable setting, we study the behavior of finite Morse
index solutions of the equation
  \[ -\{div} (|x|^\theta \nabla v)=|x|^l |v|^{p-1}v \;\;\; \{in $\Omega \subset
\R^N \; (N \geq 2)$}, \leqno(1) \] where $p>1$, $\theta, l\in\R^1$ with
$N+\theta>2$, $l-\theta>-2$, and $\Omega$ is a bounded or unbounded domain.
Through a suitable transformation of the form $v(x)=|x|^\sigma u(x)$, equation
(1) can be rewritten as a nonlinear Schr\"odinger equation with Hardy potential
  $$-\Delta u=|x|^\alpha |u|^{p-1}u+\frac{\ell}{|x|^2} u \;\; \{in $\Omega
\subset \R^N \;\; (N \geq 2)$}, \leqno{(2)}$$ where $p>1$, $\alpha \in
(-\infty, \infty)$ and $\ell \in (-\infty,(N-2)^2/4)$.
  We show that under our chosen setting for the finite Morse index theory of
(1), the stability of a solution to (1) is unchanged under various natural
transformations. This enables us to reveal two critical values of the exponent
$p$ in (1) that divide the behavior of finite Morse index solutions of (1),
which in turn yields two critical powers for (2) through the transformation.
The latter appear difficult to obtain by working directly with (2).


title:
Next-to-leading order perturbative contributions in the QCD sum rules
  for mesonic two-point correlation functions with unequal quark masses

abstract:
  In this article, we assume that the two quarks have unequal masses and
calculate the next-to-leading order contributions to the spectral densities of
the mesonic two-point correlation functions of the vector, axialvector, scalar
and pseudoscalar currents. We take dimensional regularization to regularize
both the ultraviolet and infrared divergences, and use optical theorem to
obtain the spectral densities directly, furthermore, we present some necessary
technical details for readers convenience. The analytical expressions are
applicable in many phenomenological analysis besides the QCD sum rules.


title:
Hamiltonian cycles in Cayley graphs of imprimitive complex reflection
  groups

abstract:
  Generalizing a result of Conway, Sloane, and Wilkes for real reflection
groups, we show the Cayley graph of an imprimitive complex reflection group
with respect to standard generating reflections has a Hamiltonian cycle. This
is consistent with the long-standing conjecture that for every finite group, G,
and every set of generators, S, of G the undirected Cayley graph of G with
respect to S has a Hamiltonian cycle.


title:
The IMACS Cluster Building Survey: V. Further Evidence for Starburst
  Recycling from Quantitative Galaxy Morphologies

abstract:
  Using $J$ and $K_s$ band imaging obtained as part of the IMACS Cluster
Building Survey (ICBS) we measure S\'ersic indices for 2160 field and cluster
galaxies at $0.31 < z < 0.54$. Using both mass- and magnitude-limited samples,
we compare the distributions for spectroscopically determined passive,
continuously starforming, starburst, and poststarburst systems and show that
previously established spatial and statistical connections between these types
extend to their gross morphologies. Outside of cluster cores, we find close
structural ties between starburst and continuously starforming, as well as
poststarburst and passive types, but not between starbursts and poststarbursts.
These results independently support two conclusions presented in Paper II of
this ICBS series (Dressler et al.): 1) most starbursts are the product of a
non-disruptive triggering mechanism that is insensitive to global environment,
such as minor-mergers; 2) starbursts and poststarbursts generally represent
transient phases in the lives of "normal" starforming and quiescent galaxies,
respectively, originating from and returning to these systems in closed
"recycling" loops. In this picture, spectroscopically identified poststarbursts
constitute a minority of all recently terminated starbursts, largely ruling-out
the typical starburst as a quenching event in all but the densest environments.


title: Spin resonance in Luttinger liquid with spin-orbit interaction

abstract:
  Spin-orbit interaction in quantum wires leads to a spin resonance at low
temperatures, even in the absence of an external dc magnetic field. We study
the effect of electron-electron interaction on the resonance. This interaction
is strong in quantum wires. We show that the electron-electron interaction
changes the shape of the resonance curve and produces an additional cusp at the
plasmon frequency. However, except for very strong electron-electron
interaction these changes are weak since this interaction by itself does not
break the spin-rotation symmetry that is violated weakly by the spin-orbit
interaction and external magnetic field.


title: Non-Uniqueness of Minimal Superpermutations

abstract:
  We examine the open problem of finding the shortest string that contains each
of the n! permutations of n symbols as contiguous substrings (i.e., the
shortest superpermutation on n symbols). It has been conjectured that the
shortest superpermutation has length $\sum_{k=1}^n k!$ and that this string is
unique up to relabelling of the symbols. We provide a construction of short
superpermutations that shows that, if the conjectured minimal length is true,
then uniqueness fails for all n >= 5. Furthermore, uniqueness fails
spectacularly; we construct more than doubly-exponentially many distinct
superpermutations of the conjectured minimal length.


title:
HST Spectral Mapping of L/T Transition Brown Dwarfs Reveals Cloud
  Thickness Variations

abstract:
  Most directly imaged giant exoplanets are fainter than brown dwarfs with
similar spectra. To explain their relative underluminosity unusually cloudy
atmospheres have been proposed. However, with multiple parameters varying
between any two objects, it remained difficult to observationally test this
idea. We present a new method, sensitive time-resolved Hubble Space Telescope
near-infrared spectroscopy, to study two rotating L/T transition brown dwarfs
(2M2139 and SIMP0136). The observations provide spatially and spectrally
resolved mapping of the cloud decks of the brown dwarfs. The data allow the
study of cloud structure variations while other parameters are unchanged. We
find that both brown dwarfs display variations of identical nature: J- and
H-band brightness variations with minimal color and spectral changes. Our light
curve models show that even the simplest surface brightness distributions
require at least three elliptical spots. We show that for each source the
spectral changes can be reproduced with a linear combination of only two
different spectra, i.e. the entire surface is covered by two distinct types of
regions. Modeling the color changes and spectral variations together reveal
patchy cloud covers consisting of a spatially heterogenous mix of
low-brightness, low-temperature thick clouds and brighter, thin and warm
clouds. We show that the same thick cloud patches seen in our varying brown
dwarf targets, if extended to the entire photosphere, predict near-infrared
colors/magnitudes matching the range occupied by the directly imaged exoplanets
that are cooler and less luminous than brown dwarfs with similar spectral
types. This supports the models in which thick clouds are responsible for the
near infrared properties of these underluminous exoplanets.


title:
Neutrino-induced meson productions off nucleon at forward limit in
  nucleon resonance region

abstract:
  We study forward neutrino-induced meson production off the nucleon in the
resonance region. Our calculation is based on a dynamical coupled-channels
(DCC) model that reasonably describes pi (gamma) N -> pi N, eta N, K Lambda, K
Sigma data in the resonance region. We apply the PCAC hypothesis to the DCC
model to relate the pi N reaction amplitude to the forward neutrino reaction
amplitude. In this way, we give a prediction for nu N -> pi N, pi pi N, eta N,
K Lambda, K Sigma reaction cross sections. The predicted nu N -> pi pi N, eta
N, K Lambda, K Sigma cross sections are, for the first time, based on a model
extensively tested by data. We compare our results with those from the
Rein-Sehgal model that has been very often used in the existing Monte Carlo
simulators for neutrino experiments. We find a significant difference between
them.


title:
Robust Decentralized State Estimation and Tracking for Power Systems via
  Network Gossiping

abstract:
  This paper proposes a fully decentralized adaptive re-weighted state
estimation (DARSE) scheme for power systems via network gossiping. The enabling
technique is the proposed Gossip-based Gauss-Newton (GGN) algorithm, which
allows to harness the computation capability of each area (i.e. a database
server that accrues data from local sensors) to collaboratively solve for an
accurate global state. The DARSE scheme mitigates the influence of bad data by
updating their error variances online and re-weighting their contributions
adaptively for state estimation. Thus, the global state can be estimated and
tracked robustly using near-neighbor communications in each area. Compared to
other distributed state estimation techniques, our communication model is
flexible with respect to reconfigurations and resilient to random failures as
long as the communication network is connected. Furthermore, we prove that the
Jacobian of the power flow equations satisfies the Lipschitz condition that is
essential for the GGN algorithm to converge to the desired solution.
Simulations of the IEEE-118 system show that the DARSE scheme can estimate and
track online the global power system state accurately, and degrades gracefully
when there are random failures and bad data.


title: Nonlinear stability of cosmological solutions in massive gravity

abstract:
  We investigate nonlinear stability of two classes of cosmological solutions
in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW)
solutions and anisotropic FLRW solutions. For this purpose we construct the
linear cosmological perturbation theory around axisymmetric Bianchi type--I
backgrounds. We then expand the background around the two classes of solutions,
which are fixed points of the background evolution equation, and analyze linear
perturbations on top of it. This provides a consistent truncation of nonlinear
perturbations around these fixed point solutions and allows us to analyze
nonlinear stability in a simple way. In particular, it is shown that isotropic
FLRW solutions exhibit nonlinear ghost instability. On the other hand,
anisotropic FLRW solutions are shown to be ghost-free for a range of parameters
and initial conditions.


title:
Bootstrapping Trust in Online Dating: Social Verification of Online
  Dating Profiles

abstract:
  Online dating is an increasingly thriving business which boasts
billion-dollar revenues and attracts users in the tens of millions.
Notwithstanding its popularity, online dating is not impervious to worrisome
trust and privacy concerns raised by the disclosure of potentially sensitive
data as well as the exposure to self-reported (and thus potentially
misrepresented) information. Nonetheless, little research has, thus far,
focused on how to enhance privacy and trustworthiness. In this paper, we report
on a series of semi-structured interviews involving 20 participants, and show
that users are significantly concerned with the veracity of online dating
profiles. To address some of these concerns, we present the user-centered
design of an interface, called Certifeye, which aims to bootstrap trust in
online dating profiles using existing social network data. Certifeye verifies
that the information users report on their online dating profile (e.g., age,
relationship status, and/or photos) matches that displayed on their own
Facebook profile. Finally, we present the results of a 161-user Mechanical Turk
study assessing whether our veracity-enhancing interface successfully reduced
concerns in online dating users and find a statistically significant trust
increase.


title:
Modulation of electron carrier density at the n-type LaAlO3/SrTiO3
  interface by water adsorption

abstract:
  We investigate energetic stability and dissociation dynamics of water
adsorption at the LaAlO3 surface of the n-type LaAlO3/SrTiO3 (LAO/STO)
interface and its effect on electronic properties of the interface by carrying
out first-principles electronic structure calculations. In an ambient
atmosphere at room temperature the configuration of 1 monolayer (ML) of water
molecules including 3/4 ML of dissociated water molecules adsorbed at the
surface is found to be most stable, the configuration of 1 ML of dissociated
water molecules is metastable. Water molecule dissociation induces a shift-up
of the valence band maximum (VBM) of the LAO surface, reducing the gap between
the VBM of the LAO surface and the conduction band minimum of the STO. For the
LAO/STO interface with three LAO unit-cell layers, once the coverage of
dissociated water molecules reaches 1/2 ML the gap is closed, the interface
becomes metallic and the carrier density at the LAO/STO interface increases
with increasing the coverage of dissociated water molecules. Our findings
suggest two ways to control the conductivity at the LAO/STO interface: (I)
insulator-metal transition by adsorbing a mount of water at the bare surface;
(II) carrier density change by the transition between the most stable and the
metastable adsorption configurations for 1 ML coverage in an ambient atmosphere
at room temperature.


title:
A finite-volume matrix Hamiltonian model for a Delta -> nucleon-pion
  system

abstract:
  A matrix Hamiltonian model is developed to address the finite-volume effects
appearing in studies of baryon resonances in lattice QCD. The Hamiltonian model
includes interaction terms in a transparent way, and can be readily generalized
to address multi-channel problems. The eigenvalue equation of the model is
exactly solvable, and can be matched onto chiral effective field theory. The
model is investigated in the case of Delta -> nucleon-pion scattering. A robust
method for determining the resonance parameters from lattice QCD is developed.
It involves constraining the free parameters of the model based on the lattice
spectrum in question. The method is tested in the context of a set of
pseudodata, and a picture of the model-dependence is obtained by examining a
variety of regularization schemes in the model. A comparison is made with the
Luescher method, and it is found that the matrix Hamiltonian method is equally
robust. Both methods are tested in a more realistic scenario, where a
background interaction corresponding to direct nucleon-pion scattering is
incorporated into the pseudodata. The resulting extraction of the resonance
parameters associated with the Delta baryon resonance provides evidence that an
effective field theory style of approach yields a successful realization of
finite-volume effects in the context of baryon resonances.


title: A Construction of Subshifts and a Class of Semigroups

abstract:
  Subshifts with property $(A)$ are constructed from a class of directed
graphs. As special cases the Markov-Dyck shifts are shown to have property
$(A)$. The semigroups, that are associated to $\mathcal R$-graph shifts with
Property (A), are determined. Also results on the reconstruction of $\mathcal
R$-graphs from their $\mathcal R$-graph shifts are obtained.


title: Anisotropic non-gaussianity with noncommutative spacetime

abstract:
  We study single field inflation in noncommutative spacetime and compute
two-point and three-point correlation functions for the curvature perturbation.
We find that both power spectrum and bispectrum for comoving curvature
perturbation are statistically anisotropic and the bispectrum is also modified
by a phase factor depending upon the noncommutative parameters. The
non-linearity parameter $f_{NL}$ is small for small statistical anisotropic
corrections to the bispectrum coming from the noncommutative geometry and is
consistent with the recent PLANCK bounds. There is a scale dependence of
$f_{NL}$ due to the noncommutative spacetime which is different from the
standard single field inflation models and statistically anisotropic vector
field inflation models. Deviations from statistical isotropy of CMB, observed
by PLANCK can tightly constraint the effects due to noncommutative geometry on
power spectrum and bispectrum.


title:
Improved Foreground Detection via Block-based Classifier Cascade with
  Probabilistic Decision Integration

abstract:
  Background subtraction is a fundamental low-level processing task in numerous
computer vision applications. The vast majority of algorithms process images on
a pixel-by-pixel basis, where an independent decision is made for each pixel. A
general limitation of such processing is that rich contextual information is
not taken into account. We propose a block-based method capable of dealing with
noise, illumination variations and dynamic backgrounds, while still obtaining
smooth contours of foreground objects. Specifically, image sequences are
analysed on an overlapping block-by-block basis. A low-dimensional texture
descriptor obtained from each block is passed through an adaptive classifier
cascade, where each stage handles a distinct problem. A probabilistic
foreground mask generation approach then exploits block overlaps to integrate
interim block-level decisions into final pixel-level foreground segmentation.
Unlike many pixel-based methods, ad-hoc post-processing of foreground masks is
not required. Experiments on the difficult Wallflower and I2R datasets show
that the proposed approach obtains on average better results (both
qualitatively and quantitatively) than several prominent methods. We
furthermore propose the use of tracking performance as an unbiased approach for
assessing the practical usefulness of foreground segmentation methods, and show
that the proposed approach leads to considerable improvements in tracking
accuracy on the CAVIAR dataset.


title: Square-summable variation and absolutely continuous spectrum

abstract:
  Recent results of Denisov and Kaluzhny-Shamis describe the absolutely
continuous spectrum of Jacobi matrices with coefficients that obey an l^2
bounded variation condition with step p and are asymptotically periodic. We
extend these results to orthogonal polynomials on the unit circle. We also
replace the asymptotic periodicity condition by the weaker condition of
convergence to an isospectral torus and, for p=1 and p=2, we remove even that
condition.


title: Single point potentials with total resonant tunneling

abstract:
  Two rectangular models described by the one-dimensional Schroedinger equation
with sharply localized potentials are suggested. The potentials have a
multi-layer thin structure being composed from adjacent barriers and wells.
Their peculiar tunneling properties are studied in considerable detail.
Particularly, in the zero-range limit when the potentials are squeezed to a
single point, sharp peaks with total transmission are observed at certain
(positive and negative) quantized values of the potential strength constant
forming infinite discrete sets. Beyond these sets, the barrier-well structures
behave as a perfectly reflecting wall. The transcendental equations with
respect to potential strengths, the solutions of which determine transmission
(resonance) sets, are derived. In this regard, both the models are exactly
solvable. The energy dependence of an incident particle is shown to reveal a
resonance behavior, being completely different from that observed in a typical
double barrier structure.


title:
Transition Temperature and Upper Critical Field in SmFeAsO1-xFx
  Synthesized at Low Heating Temperatures

abstract:
  Low-temperature synthesis is a promising and potentially effective method for
improving superconducting properties. We report on the fabrication of
polycrystalline samples of SmFeAsO1-xFx with nominal x content varying in a
wide range of x = 0-0.35 synthesized at 900 deg C. This synthesis temperature
is around 300 deg C lower than the conventional synthesis temperature. The
variation in the lattice parameters and transition temperature (Tc) of various
F-doped samples indicates that reduction of the unit cell volume (V) seems to
be the main reason for the rise of Tc up to 57.8 K. Magnetoresistance
measurements showed that the upper critical field slope (dHc2/dT) increased
with increasing F concentration up to x = 0.2, where it reached a maximum value
of -8 T/K corresponding to a coherence length of 10 angstrom. At still higher F
doping levels, dHc2/dT and the low field Jc decreased; above 0.5 T, however, Jc
had almost the same value. Compared with previous reports, the present
synthesis route with low synthesis temperatures and commonly available FeF2 as
the source of F is more effective at introducing F into the SmFeAsO system and
thereby resulting in improved superconducting properties for the system. In
addition, this new sample preparation method also reduces unnecessary problems
such as the evaporation of F and reaction between the crucible and
superconductor during the solid-state reaction.


title: Neurally Implementable Semantic Networks

abstract:
  We propose general principles for semantic networks allowing them to be
implemented as dynamical neural networks. Major features of our scheme include:
(a) the interpretation that each node in a network stands for a bound
integration of the meanings of all nodes and external events the node links
with; (b) the systematic use of nodes that stand for categories or types, with
separate nodes for instances of these types; (c) an implementation of
relationships that does not use intrinsically typed links between nodes.


title:
Cauchy Problem for a Darboux Integrable Wave Map System and Equations of
  Lie Type

abstract:
  The Cauchy problem for harmonic maps from Minkowski space with its standard
flat metric to a certain non-constant curvature Lorentzian 2-metric is studied.
The target manifold is distinguished by the fact that the Euler-Lagrange
equation for the energy functional is Darboux integrable. The time evolution of
the Cauchy data is reduced to an ordinary differential equation of Lie type
associated to SL(2) acting on a manifold of dimension 4. This is further
reduced to the simplest Lie system: the Riccati equation. Lie reduction permits
explicit representation formulas for various initial value problems.
Additionally, a concise (hyperbolic) Weierstrass-type representation formula is
derived. Finally, a number of open problems are framed.


title:
Vortical light bullets in second-harmonic-generating media supported by
  a trapping potential

abstract:
  We introduce a three-dimensional (3D) model of optical media with the
quadratic ($\chi ^{(2)}$) nonlinearity and an effective 2D isotropic
harmonic-oscillator (HO) potential. While it is well known that 3D \chi^2
solitons with embedded vorticity ("vortical light bullets") are unstable in the
free space, we demonstrate that they have a broad stability region in the
present model, being supported by the HO potential against the splitting
instability. The shape of the vortical solitons may be accurately predicted by
the variational approximation (VA). They exist above a threshold value of the
total energy (norm) and below another critical value, which determines a
stability boundary. The existence threshold vanishes is a part of the parameter
space, depending on the mismatch parameter, which is explained by means of the
comparison with the 2D counterpart of the system. Above the stability boundary,
the vortex features shape oscillations, periodically breaking its axisymmetric
form and restoring it. Collisions between vortices moving in the longitudinal
direction are studied too. The collision is strongly inelastic at relatively
small values of the velocities, breaking the two colliding vortices into three,
with the same vorticity. The results suggest a possibility of the creation of
stable 3D optical solitons with the intrinsic vorticity.


title: Classification of blowup limits for SU(3) singular Toda systems

abstract:
  For singular $SU(3)$ Toda systems, we prove that the limit of energy
concentration is a finite set. In addition, for fully bubbling solutions we use
Pohozaev identity to prove a uniform estimate. Our results extend previous
results of Jost-Lin-Wang on regular $SU(3)$ Toda systems.


title:
CN Anomalies in the Halo System and the Origin of Globular Clusters in
  the Milky Way

abstract:
  We explore the kinematics and orbital properties of a sample of red giants in
the halo system of the Milky Way that are thought to have formed in globular
clusters, based on their anomalously strong UV/blue CN bands. The orbital
parameters of the CN-strong halo stars are compared to those of the inner- and
outer-halo populations as described by Carollo et al., and to the orbital
parameters of globular clusters with well-studied Galactic orbits. The
CN-strong field stars and the globular clusters both exhibit kinematics and
orbital properties similar to the inner-halo population, indicating that
stripped or destroyed globular clusters could be a significant source of
inner-halo field stars, and suggesting that both the CN-strong stars and the
majority of globular clusters are primarily associated with this population.


title:
Markov Chain Monte Carlo for Arrangement of Hyperplanes in
  Locality-Sensitive Hashing

abstract:
  Since Hamming distances can be calculated by bitwise computations, they can
be calculated with less computational load than L2 distances. Similarity
searches can therefore be performed faster in Hamming distance space. The
elements of Hamming distance space are bit strings. On the other hand, the
arrangement of hyperplanes induce the transformation from the feature vectors
into feature bit strings. This transformation method is a type of
locality-sensitive hashing that has been attracting attention as a way of
performing approximate similarity searches at high speed. Supervised learning
of hyperplane arrangements allows us to obtain a method that transforms them
into feature bit strings reflecting the information of labels applied to
higher-dimensional feature vectors. In this p aper, we propose a supervised
learning method for hyperplane arrangements in feature space that uses a Markov
chain Monte Carlo (MCMC) method. We consider the probability density functions
used during learning, and evaluate their performance. We also consider the
sampling method for learning data pairs needed in learning, and we evaluate its
performance. We confirm that the accuracy of this learning method when using a
suitable probability density function and sampling method is greater than the
accuracy of existing learning methods.


title:
Wave modes of collective vortex gyration in dipolar-coupled-dot-array
  magnonic crystals

abstract:
  Lattice vibration modes are collective excitations in periodic arrays of
atoms or molecules. These modes determine novel transport properties in solid
crystals. Analogously, in periodical arrangements of magnetic vortex-state
disks, collective vortex motions have been predicted. Here, we experimentally
observe wave modes of collective vortex gyration in one-dimensional (1D) chains
of periodic disks using time-resolved scanning transmission x-ray microscopy.
The observed modes are interpreted based on micromagnetic simulation and
numerical calculation of coupled Thiele equations. Dispersion of the modes is
found to be strongly affected by both vortex polarization and chirality
ordering, as revealed by the explicit analytical form of 1D infinite chains. A
thorough understanding thereof is fundamental both for lattice vibrations and
vortex dynamics, which we demonstrate for 1D magnonic crystals. Such magnetic
disk arrays with vortex-state ordering, referred to as magnetic metastructure,
offer potential implementation into information processing devices.


title: Socle filtrations of the standard Whittaker (g,K)-modules of Spin(r,1)

abstract:
  Studied are the composition series of the standard Whittaker (g,K)-modules.
For a generic infinitesimal character, the structures of these modules are
completely understood, but if the infinitesimal character is integral, then
there are not so many cases in which the structures of them are known. In this
paper, as an example of the integral case, we determine the socle filtrations
of the standard Whittaker (g,K)-modules when G is the group Spin(r,1) and the
infinitesimal character is regular integral.


title: Margins, Shrinkage, and Boosting

abstract:
  This manuscript shows that AdaBoost and its immediate variants can produce
approximate maximum margin classifiers simply by scaling step size choices with
a fixed small constant. In this way, when the unscaled step size is an optimal
choice, these results provide guarantees for Friedman's empirically successful
"shrinkage" procedure for gradient boosting (Friedman, 2000). Guarantees are
also provided for a variety of other step sizes, affirming the intuition that
increasingly regularized line searches provide improved margin guarantees. The
results hold for the exponential loss and similar losses, most notably the
logistic loss.


title:
Combinatorial expressions of the solutions to initial value problems of
  the discrete and ultradiscrete Toda molecules

abstract:
  Combinatorial expressions are presented to the solutions to initial value
problems of the discrete and ultradiscrete Toda molecules. For the discrete
Toda molecule, a subtraction-free expression of the solution is derived in
terms of non-intersecting paths, for which two results in combinatorics,
Flajolet's interpretation of continued fractions and Gessel--Viennot's lemma on
determinants, are applied. By ultradiscretizing the subtraction-free
expression, the solution to the ultradiscrete Toda molecule is obtained. It is
finally shown that the initial value problem of the ultradiscrete Toda molecule
is exactly solved in terms of shortest paths on a specific graph.


title:
Dynamics of ultra-intense circularly polarized solitons under
  inhomogeneous plasmas

abstract:
  The dynamics of the ultra-intense circularly polarized solitons under
inhomogeneous plasmas are examined. The interaction is modeled by the Maxwell
and relativistic hydrodynamic equations and is solved with fully implicit
energy-conserving numerical scheme. It is shown that a propagating weak soliton
can be decreased and reflected by increasing plasma background, which is
consistent with the existing studies based on hypothesis of weak density
response. However it is found that ultra-intense soliton is well trapped and
kept still when encountering increasing background. Probably, this founding can
be applied for trapping and amplifying high-intensity laser-fields.


title:
Stable Nonlinear Identification From Noisy Repeated Experiments via
  Convex Optimization

abstract:
  This paper introduces new techniques for using convex optimization to fit
input-output data to a class of stable nonlinear dynamical models. We present
an algorithm that guarantees consistent estimates of models in this class when
a small set of repeated experiments with suitably independent measurement noise
is available. Stability of the estimated models is guaranteed without any
assumptions on the input-output data. We first present a convex optimization
scheme for identifying stable state-space models from empirical moments. Next,
we provide a method for using repeated experiments to remove the effect of
noise on these moment and model estimates. The technique is demonstrated on a
simple simulated example.


title: On the asymptotic behavior of the hyperbolic Brownian motion

abstract:
  The main results in this paper concern large and moderate deviations for the
radial component of a $n$-dimensional hyperbolic Brownian motion (for $n\geq
2$) on the Poincar\'{e} half-space. We also investigate the asymptotic behavior
of the hitting probability $P_\eta(T_{\eta_1}^{(n)}<\infty)$ of a ball of
radius $\eta_1$, as the distance $\eta$ of the starting point of the hyperbolic
Brownian motion goes to infinity.


title:
A relation between additive and multiplicative complexity of Boolean
  functions

abstract:
  In the present note we prove an asymptotically tight relation between
additive and multiplicative complexity of Boolean functions with respect to
implementation by circuits over the basis {+,*,1}.


title: Rational cuspidal curves with four cusps on Hirzebruch surfaces

abstract:
  The purpose of this article is to shed light on the question of how many and
what kind of cusps a rational cuspidal curve on a Hirzebruch surface can have.
We use birational transformations to construct rational cuspidal curves with
four cusps on the Hirzebruch surfaces and find associated results for these
curves.


title: Additive inverse regression models with convolution-type operators

abstract:
  In a recent paper Birke and Bissantz (2008) considered the problem of
nonparametric estimation in inverse regression models with convolution-type
operators. For multivariate predictors nonparametric methods suffer from the
curse of dimensionality and we consider inverse regression models with the
additional qualitative assumption of additivity. In these models several
additive estimators are studied. In particular, we investigate estimators under
the random design assumption which are applicable when observations are not
available on a grid. Finally, we compare this estimator with the marginal
integration and the non-additive estimator by means of a simulation study. It
is demonstrated that the new method yields a substantial improvement of the
currently available procedures.


title: Diffusion Effects in Gradient Echo Memory

abstract:
  We study the effects of diffusion on a $\Lambda$-gradient echo memory, which
is a coherent optical quantum memory using thermal gases. The efficiency of
this memory is high for short storage time, but decreases exponentially due to
decoherence as the storage time is increased. We study the effects of both
longitudinal and transverse diffusion in this memory system, and give both
analytical and numerical results that are in good agreement. Our results show
that diffusion has a significant effect on the efficiency. Further, we suggest
ways to reduce these effects to improve storage efficiency.


title: A super Ornstein-Uhlenbeck process interacting with its center of mass

abstract:
  We construct a supercritical interacting measure-valued diffusion with
representative particles that are attracted to, or repelled from, the center of
mass. Using the historical stochastic calculus of Perkins, we modify a super
Ornstein-Uhlenbeck process with attraction to its origin, and prove continuum
analogues of results of Englander [Electron. J. Probab. 15 (2010) 1938-1970]
for binary branching Brownian motion. It is shown, on the survival set, that in
the attractive case the mass normalized interacting measure-valued process
converges almost surely to the stationary distribution of the
Ornstein-Uhlenbeck process, centered at the limiting value of its center of
mass. In the same setting, it is proven that the normalized super
Ornstein-Uhlenbeck process converges a.s. to a Gaussian random variable, which
strengthens a theorem of Englander and Winter [Ann. Inst. Henri Poincare
Probab. Stat. 42 (2006) 171-185] in this particular case. In the repelling
setting, we show that the center of mass converges a.s., provided the repulsion
is not too strong and then give a conjecture. This contrasts with the center of
mass of an ordinary super Ornstein-Uhlenbeck process with repulsion, which is
shown to diverge a.s. A version of a result of Tribe [Ann. Probab. 20 (1992)
286-311] is proven on the extinction set; that is, as it approaches the
extinction time, the normalized process in both the attractive and repelling
cases converges to a random point a.s.


title:
Pressure suppression of spin-density-wave gap in the optical
  conductivity of SrFe2As2

abstract:
  Optical reflectance R(w) of a pressure-induced superconductor SrFe2As2 has
been measured under external pressure to 6 GPa and at temperatures to 8 K.
Optical conductivity s(w) has been derived from the measured R(w). At ambient
pressure, in the antiferromagnetic state below T_N=198 K, a pronounced feature
develops in s(w) due to the opening of a spin density wave (SDW) gap, as
already reported in the literature. With increasing pressure, the SDW gap
feature in s(w) is progressively suppressed. At 4 GPa, where the sample is
superconducting, the SDW gap feature in s(w) is strongly reduced than that at
ambient pressure, but is still clearly observed. At 6 GPa, the SDW gap is
completely suppressed. The pressure evolutions of the SDW gap magnitude and the
spectral weight closely follow the pressure evolution of T_N.


title:
Generating extrema approximation of analytically incomputable functions
  through usage of parallel computer aided genetic algorithms

abstract:
  This paper presents capabilities of using genetic algorithms to find
approximations of function extrema, which cannot be found using analytic ways.
To enhance effectiveness of calculations, algorithm has been parallelized using
OpenMP library. We gained much increase in speed on platforms using
multithreaded processors with shared memory free access. During analysis we
used different modifications of genetic operator, using them we obtained varied
evolution process of potential solutions. Results allow to choose best methods
among many applied in genetic algorithms and observation of acceleration on
Yorkfield, Bloomfield, Westmere-EX and most recent Sandy Bridge cores.


title:
Theory of spin pumping through an interacting quantum dot tunnel coupled
  to a ferromagnet with time-dependent magnetization

abstract:
  We investigate two schemes for pumping spin adiabatically from a ferromagnet
through an interacting quantum dot into a normal lead, which exploit the
possibility to vary in time the ferromagnet's magnetization, either its
amplitude or its direction. For this purpose, we extend a diagrammatic
real-time technique for pumping to situations in which the leads' properties
are time dependent. In the first scheme, the time-dependent magnetization
amplitude is combined with a time-dependent level position of the quantum dot
to establish both a charge and a spin current. The second scheme uses a uniform
rotation of the ferromagnet's magnetization direction to generate a pure spin
current without a charge current. We discuss the influence of an
interaction-induced exchange field on the pumping characteristics.


title:
On 1-cocycles induced by a positive definite function on a locally
  compact abelian group

abstract:
  For $\varphi$ a normalized positive definite function on a locally compact
abelian group $G$, we consider on the one hand the unitary representation
$\pi_\varphi$ associated to $\varphi$ by the GNS construction, on the other
hand the probability measure $\mu_\varphi$ on the Pontryagin dual $\hat{G}$
provided by Bochner's theorem. We give necessary and sufficient conditions for
the vanishing of 1-cohomology $H^1(G,\pi_\varphi)$ and reduced 1-cohomology
$\bar{H}^1(G,\pi_\varphi)$. For example, $\bar{H}^1(G,\pi_\varphi)=0$ if and
only if either $Hom(G,\mathbb{C})=0$ or $\mu_\varphi(1_G)=0$, where $1_G$ is
the trivial character of $G$.


title: The polarized Gamma-Ray Burst GRB 061122

abstract:
  We report on the polarization measure, obtained with IBIS on board INTEGRAL,
of the prompt emission of GRB 061122. Over an 8 s interval containing the
brightest part of the Gamma-Ray Burst we put a lower limit on its polarization
fraction of 60% at 68% c.l. and of 33% at 90% c.l. on the 250-800 keV energy
range.
  We performed late time optical and near infra-red imaging observations of the
GRB field using the Telescopio Nazionale Galileo (TNG), and the
Canada-France-Hawaii Telescope (CFHT). Our multi-band (ugrizYJHK) photometry
allowed us to identify the host galaxy of GRB 061122 and to build its SED.
Using a photometric redshift code we fitted these data, and derived the basic
properties of the galaxy, including its type and redshift, that we could
constrain to the interval [0.57, 2.10] at a 90% c.l., with a best fit value of
z=1.33.
  The polarization measurement in different energy bands, together with the
distance determination, allowed us to put the most stringent limit (xi <
3.4x10-16) to date to a possible Lorentz Invariance Violation based on the
vacuum birefringence effect, predicted by some quantum-gravity theories.


title: Frictional anisotropy of metal nanoparticles adsorbed on graphene

abstract:
  Friction force acting on silver and nickel nanoparticles sheared on a
graphene sheet in different lateral directions is investigated using classical
molecular dynamics simulations. The results reveal the existence of frictional
anisotropy for both metals. In most cases, the maximum value of the friction
force is about two times larger than the minimum one. The form of dependencies
of instantaneous values of the friction force components on the corresponding
lateral components of the position of the centre of mass of the nanoislands
strongly depends on sliding direction, varying between the sawtooth and the
irregular one. A qualitative explanation of the results based on the "patch"
model is proposed.


title: Back action cancellation in resolved sideband regime

abstract:
  We consider the simple model of measurement of mechanical oscillator position
via Fabry-Pero cavity pumped by detuned laser (end mirror of cavity is mass of
oscillator) in resolved sideband regime when laser is detuned from cavity's
frequency by frequency of mechanical oscillator $\pm\omega_m$ and relaxation
rate $\gamma$ of cavity is small: $\gamma\ll \omega_m$. We demonstrate
fluctuation back action cancellation in reflected wave. However, it does not
allow to circumvent Standard Quantum Limit, the reason of it is the dynamic
back action.


title:
Analytical scattering matrix of subwavelength infinitely conducting
  metallic gratings in TM polarization

abstract:
  We obtain in TM polarization an analytical expression of the scattering
matrix of one infinitely conducting metallic lamellar grating with
subwavelength slits. The theory is based on the Monomode Modal Method which
consists in considering only one propagative mode in grating slits. Two
expressions are exposed. The first one comes directly from the theory equations
and the second one clearly reveals the Airy-like form of the scattering matrix
terms. The theory is validated on a multi-grating object and the stability of
the numerical results are shown at the same time. This work provides a basic
and very efficient theoretical tool to calculate the diffraction by a stack of
subwavelength metallic gratings.


title: Symmetry Protected Quantum State Renormalization

abstract:
  Symmetry protected topological (SPT) phases with gapless edge excitations
have been shown to exist in principle in strongly interacting bosonic/fermionic
systems and it is highly desirable to find practical systems to realize such
phases through numerical calculation. A central question to be addressed is how
to determine the SPT order in the system given the numerical simulation result
while no local order parameter can be measured to distinguish the phases from a
trivial one. In the tensor network approach to simulate strongly interacting
systems, the quantum state renormalization algorithm has been demonstrated to
be effective in identifying the intrinsic topological orders. Here we show that
a modified algorithm can identify SPT orders by extracting the fixed point
entanglement pattern in the ground state wave function which is essential for
the existence of SPT order. The key to this approach is to add symmetry
protection to the quantum state renormalization process and we demonstrate the
effectiveness of this algorithm with the example of AKLT states in both 1D and
2D.


title: Parallel Search with Extended Fibonacci Primitive

abstract:
  Search pattern experienced by the processor to search an element in secondary
storage devices follows a random sequence. Formally, it is a random walk and
its modeling is crucial in studying performance metrics like memory access
time. In this paper, we first model the random walk using extended Fibonacci
series. Our simulation is done on a parallel computing model (PRAM) with EREW
strategy. Three search primitives are proposed under parallel computing model
and each primitive is thoroughly tested on an array of size $10^7$ with the
size of random walk being $10^4$. Our findings reveal that search primitive
with pointer jumping is better than the other two primitives. Our key
contribution lies in modeling random walk as an extended Fibonacci series
generator and simulating the same with various search primitives.


title:
Hanle effect in (In,Ga)As quantum dots: Role of nuclear spin
  fluctuations

abstract:
  The role of nuclear spin fluctuations in the dynamic polarization of nuclear
spins by electrons is investigated in (In,Ga)As quantum dots. The
photoluminescence polarization under circularly polarized optical pumping in
transverse magnetic fields (Hanle effect) is studied. A weak additional
magnetic field parallel to the optical axis is used to control the efficiency
of nuclear spin cooling and the sign of nuclear spin temperature. The shape of
the Hanle curve is drastically modified with changing this control field, as
observed earlier in bulk semiconductors and quantum wells. However, the
standard nuclear spin cooling theory, operating with the mean nuclear magnetic
field (Overhauser field), fails to describe the experimental Hanle curves in a
certain range of control fields. This controversy is resolved by taking into
account the nuclear spin fluctuations owed to the finite number of nuclei in
the quantum dot. We propose a model describing cooling of the nuclear spin
system by electron spins experiencing fast vector precession in the random
Overhauser fields of nuclear spin fluctuations. The model allows us to
accurately describe the measured Hanle curves and to determine the parameters
of the electron-nuclear spin system of the studied quantum dots.


title:
A Qualitative Comparison of the Suitability of Four Theorem Provers for
  Basic Auction Theory

abstract:
  Novel auction schemes are constantly being designed. Their design has
significant consequences for the allocation of goods and the revenues
generated. But how to tell whether a new design has the desired properties,
such as efficiency, i.e. allocating goods to those bidders who value them most?
We say: by formal, machine-checked proofs. We investigated the suitability of
the Isabelle, Theorema, Mizar, and Hets/CASL/TPTP theorem provers for
reproducing a key result of auction theory: Vickrey's 1961 theorem on the
properties of second-price auctions. Based on our formalisation experience,
taking an auction designer's perspective, we give recommendations on what
system to use for formalising auctions, and outline further steps towards a
complete auction theory toolbox.


title: The ForMaRE Project - Formal Mathematical Reasoning in Economics

abstract:
  The ForMaRE project applies formal mathematical reasoning to economics. We
seek to increase confidence in economics' theoretical results, to aid in
discovering new results, and to foster interest in formal methods, i.e.
computer-aided reasoning, within economics. To formal methods, we seek to
contribute user experience feedback from new audiences, as well as new
challenge problems. In the first project year, we continued earlier game theory
studies but then focused on auctions, where we are building a toolbox of
formalisations, and have started to study matching and financial risk.
  In parallel to conducting research that connects economics and formal
methods, we organise events and provide infrastructure to connect both
communities, from fostering mutual awareness to targeted matchmaking. These
efforts extend beyond economics, towards generally enabling domain experts to
use mechanised reasoning.


title:
First-principles study of metal-induced gap states in metal/oxide
  interfaces and their relation with the complex band structure

abstract:
  We develop a simple model to compute the energy-dependent decay factors of
metal-induced gap states in metal/insulator interfaces considering the
collective behaviour of all the bulk complex bands in the gap of the insulator.
The agreement between the penetration length obtained from the model
(considering only bulk properties) and full first-principles simulations of the
interface (including explicitly the interfaces) is good. The influence of the
electrodes and the polarization of the insulator is analyzed. The method
simplifies the process of screening materials to be used in Schootky barriers
or in the design of giant tunneling electroresistance and magnetoresistance
devices.


title:
Detection of self-oscillations of the transport current in a doubly
  connected superconductor

abstract:
  It has been found experimentally that when dc current is passed through a
circuit consisting of two superconductors connected in parallel and reaches its
critical value in one of the circuit branches the current in the branches
undergoes quasi-harmonic undamped oscillations. The mechanism resulting in the
appearance of the self-oscillations is discussed. The characteristics of
magnetic field freezing in a circuit with self-oscillating current are
examined.


title: From Symplectic Measurements to the Mahler Conjecture

abstract:
  In this note we link symplectic and convex geometry by relating two seemingly
different open conjectures: a symplectic isoperimetric-type inequality for
convex domains, and Mahler's conjecture on the volume product of centrally
symmetric convex bodies. More precisely, we show that if for convex bodies of
fixed volume in the classical phase space the Hofer-Zehnder capacity is
maximized by the Euclidean ball, then a hypercube is a minimizer for the volume
product among centrally symmetric convex bodies.


title: QCD with Two Light Dynamical Chirally Improved Quarks

abstract:
  Results for the excited meson and baryon spectrum with two flavors of
Chirally Improved sea quarks are presented. We simulate several ensembles with
pion masses ranging from 250 to 600 MeV and extrapolate to the physical pion
mass. Strange quarks are treated within the partially quenched approximation.
Using the variational method, we investigate the content of the states. Among
others, we discuss the flavor singlet/octet content of Lambda states. In
general, our results compare well with experiment, in particular we get very
good agreement with the Lambda(1405) and confirm its flavor singlet nature.


title: Network Non-Neutrality through Preferential Signaling

abstract:
  One of the central issues in the debate on network neutrality has been
whether one should allow or prevent preferential treatment by an internet
service provider (ISP) of traffic according to its origin. This raised the
question of whether to allow an ISP to have exclusive agreement with a content
provider (CP). In this paper we consider discrimination in the opposite
direction. We study the impact that a CP can have on the benefits of several
competing ISPs by sharing private information concerning the demand for its
content. More precisely, we consider ISPs that compete over access to one
common CP. Each ISP selects the price that it charges its subscribers for
accessing the content. The CP is assumed to have private information about
demand for its content, and in particular, about the inverse demand function
corresponding to the content. The competing ISPs are assumed to have knowledge
on only the statistical distribution of these functions. We derive in this
paper models for studying the impact that the CP can have on the utilities of
the ISPs by favoring one of them by exclusively revealing its private
information. We also consider the case where CP can charge ISPs for providing
such information. We propose two mechanisms based on {\em weighted proportional
fairness} for payment between ISPs and CP. Finally, we compare the social
utility resulting from these mechanisms with the optimal social utility by
introducing a performance metric termed as {\em price of partial bargaining}


title: 3D Smoothed Particle Hydrodynamics Models of Betelgeuse's Bow Shock

abstract:
  Betelgeuse, the bright red supergiant (RSG) in Orion, is a runaway star. Its
supersonic motion through the interstellar medium has resulted in the formation
of a bow shock, a cometary structure pointing in the direction of motion. We
present the first 3D hydrodynamic simulations of the formation and evolution of
Betelgeuse's bow shock. We show that the bow shock morphology depends
substantially on the growth timescale for Rayleigh-Taylor versus
Kelvin-Helmholtz instabilities. We discuss our models in light of the recent
Herschel, GALEX and VLA observations. If the mass in the bow shock shell is low
(~few x 0.001 Msun), as seems to be implied by the AKARI and Herschel
observations, then Betelgeuse's bow shock is very young and is unlikely to have
reached a steady state. The circular, smooth bow shock shell is consistent with
this conclusion. We further discuss the implications of our results, in
particular, the possibility that Betelgeuse may have only recently entered the
RSG phase.


title:
The rate of convergence to early asymptotic behaviour in age-structured
  epidemic models

abstract:
  Age structure is incorporated in many types of epidemic model. Often it is
convenient to assume that such models converge to early asymptotic behaviour
quickly, before the susceptible population has been appreciably depleted. We
make use of dynamical systems theory to show that for some reasonable parameter
values, this convergence can be slow. Such a possibility should therefore be
considered when parameterising age-structured epidemic models.


title: Derivations on triangular Banach algebras of order three

abstract:
  In this paper, we define some new notions of triangular Banach algebras and
we investigate the derivations on these algebras.


title:
Exploring Morphology-Activity Relationships: Ab Initio Wulff
  Construction for RuO2 Nanoparticles under Oxidizing Conditions

abstract:
  We present a density-functional theory based Wulff construction of the
equilibrium shape of RuO2 particles in an oxygen environment. The obtained
intricate variations of the crystal habit with the oxygen chemical potential
allow for a detailed discussion of the dependence on the oxidizing pretreatment
observed in recent powder catalyst studies. The analysis specifically indicates
an incomplete particle shape equilibration in previously employed low
temperature calcination. Equilibrated particles could be active CO oxidation
catalysts with long-term stability in oxidizing feed and then represent an
interesting alternative to the previously suggested core-shell concept.


title: Viscosity anomaly in core-softened liquids

abstract:
  The present article presents a molecular dynamics study of several anomalies
of core-softened systems. It is well known that many core-softened liquids
demonstrate diffusion anomaly. Usual intuition relates the diffusion
coefficient to shear viscosity via Stockes-Einstein relation. However, it can
break down at low temperature. In this respect it is important to see if
viscosity also demonstrates anomalous behavior.


title:
Freezing and quantization of current passing through a doubly connected
  superconductor with a point contact

abstract:
  The particulars of dc current passage through a structure consisting of a
doubly connected superconductor (DCS) with branches that are asymmetric with
respect to length and critical current have been investigated experimentally.
The short branch, which has the lowest critical current, was a clamping
niobium-niobium point contact with length comparable to the coherence length of
the superconductor. In contrast to a previously studied DCS with a short branch
much longer than the coherence length, it was found that when the short-branch
current reaches the critical value the currents in the branches of the DCS do
not undergo self-excited oscillations; a current exceeding the critical value
enters the long branch when this current is increased in portions (is
quantized), and when it is subsequently decreased it freezes partially or
completely in the DCS circuit.


title:
Current states of a doubly connected superconductor with two point
  contacts

abstract:
  The distribution of the transport current in branches of a doubly connected
superconductor (DCS) with two clamping point contacts is investigated
experimentally when the contacts are in the different states: (a) one or both
contacts are in the critical state, (b) both are in the supercritical
(resistive) state. In the state (a) the transport current frozen in the DCS and
injected through one of the contacts can be increased or decreased by tuning
the value and polarity of the current passing through the other contact. In the
state (b), the current self-oscillations the amplitude and the frequency of
which depend on the value of the injected transport current appear in the
branches of the DCS. A role of the parametric Josephson inductance and
resistivity of the contact in formation of its critical state and in
distribution of the current in the branches of the DCS is discussed.


title:
Improving CUR Matrix Decomposition and the Nystr\"{o}m Approximation via
  Adaptive Sampling

abstract:
  The CUR matrix decomposition and the Nystr\"{o}m approximation are two
important low-rank matrix approximation techniques. The Nystr\"{o}m method
approximates a symmetric positive semidefinite matrix in terms of a small
number of its columns, while CUR approximates an arbitrary data matrix by a
small number of its columns and rows. Thus, CUR decomposition can be regarded
as an extension of the Nystr\"{o}m approximation.
  In this paper we establish a more general error bound for the adaptive
column/row sampling algorithm, based on which we propose more accurate CUR and
Nystr\"{o}m algorithms with expected relative-error bounds. The proposed CUR
and Nystr\"{o}m algorithms also have low time complexity and can avoid
maintaining the whole data matrix in RAM. In addition, we give theoretical
analysis for the lower error bounds of the standard Nystr\"{o}m method and the
ensemble Nystr\"{o}m method. The main theoretical results established in this
paper are novel, and our analysis makes no special assumption on the data
matrices.


title:
Quantization of diamagnetic current in a superconducting ring with the
  Josephson point contact

abstract:
  It was established experimentally that a critical value of the diamagnetic
current, excited by an external magnetic field in a superconducting ring (with
an inductance of about ~ 10^-6 H) with a Nb-Nb clamping point contact having
the Josephson contact properties is a strictly periodic function of field
strength, despite the complex microstructure of the clamping contact. The
reasons of the periodic dependence are discussed on a basis of the interference
model of diamagnetic current and quantized values of the circulating current in
the microinterferometer formed by the clamping contact.


title: Typical Entanglement

abstract:
  Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space,
and consider the reduced density matrix \rho of an N-dimensional subsystem. The
bipartite entanglement properties of \psi are encoded in the spectrum of \rho.
By means of a saddle point method and using a "Coulomb gas" model for the
eigenvalues, we obtain the typical spectrum of reduced density matrices. We
consider the cases of an unbiased ensemble of pure states and of a fixed value
of the purity. We finally obtain the eigenvalue distribution by using a
statistical mechanics approach based on the introduction of a partition
function.


title:
A study of volatile compounds in the breath of children with type 1
  diabetes

abstract:
  A pilot study of exhaled volatile compounds and their correlation with blood
glucose levels in eight children with type 1 diabetes is reported. Five paired
blood and breath samples were obtained from each child over a 6 hour period.
The blood glucose concentration ranged from 41.4 to 435.6 mg/dL. Breath samples
were collected in Tedlar bags and immediately evacuated through thermal
desorption tubes packed with Carbopack B and C. The VOCs were later recovered
by thermal desorption and analysed using gas chromatography mass spectrometry.
The study identified 74 volatile compounds present in at least 10% of the
patient samples. Of these 74 volatiles 36 were found in all patient samples
tested. Further analysis of the 36 compounds found that none showed significant
overall correlation with blood glucose levels. Isoprene showed a weak negative
correlation with blood glucose levels. Acetone was found to have no correlation
with blood glucose levels for the patients studied. Some patients showed
significant individual correlation between the relative peak areas of certain
compounds and blood glucose levels. However, there was no consistent pattern
observed within these results across all 8 patients. Additional breath samples
were collected in Tedlar bags and analysed using SIFTMS for 3 of the patients
and a healthy control. The levels of 24 volatiles are reported and were found
to be generally consistent with previously reported SIFT-MS data. In agreement
with the GCMS data, no compounds exhibited a significant overall correlation
with blood glucose level.


title:
Invertible mappings and the large deviation theory for the $q$-maximum
  entropy principle

abstract:
  The possibility of reconciliation between canonical probability distributions
obtained from the $q$-maximum entropy principle with predictions from the law
of large numbers when empirical samples are held to the same constraints, is
investigated into. Canonical probability distributions are constrained by both:
$(i)$ the additive duality of generalized statistics and $(ii)$ normal averages
expectations. Necessary conditions to establish such a reconciliation are
derived by appealing to a result concerning large deviation properties of
conditional measures. The (dual) $q^*$-maximum entropy principle is shown {\bf
not} to adhere to the large deviation theory. However, the necessary conditions
are proven to constitute an invertible mapping between: $(i)$ a canonical
ensemble satisfying the $q^*$-maximum entropy principle for energy-eigenvalues
$\varepsilon_i^*$, and, $(ii)$ a canonical ensemble satisfying the
Shannon-Jaynes maximum entropy theory for energy-eigenvalues $\varepsilon_i$.
Such an invertible mapping is demonstrated to facilitate an \emph{implicit}
reconciliation between the $q^*$-maximum entropy principle and the large
deviation theory. Numerical examples for exemplary cases are provided.

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


title: Set-optimization meets variational inequalities

abstract:
  We study necessary and sufficient conditions to attain solutions of
set-optimization problems in therms of variational inequalities of Stampacchia
and Minty type. The notion of a solution we deal with has been introduced Heyde
and Loehne, for convex set-valued objective functions. To define the set-valued
variational inequality, we introduce a set-valued directional derivative and we
relate it to the Dini derivatives of a family of linearly scalarized problems.
The optimality conditions are given by Stampacchia and Minty type Variational
inequalities, defined both by the set valued directional derivative and by the
Dini derivatives of the scalarizations. The main results allow to obtain known
variational characterizations for vector valued optimization problems.


title:
Proof of a conjecture of Thomassen on Hamilton cycles in highly
  connected tournaments

abstract:
  A conjecture of Thomassen from 1982 states that for every k there is an f(k)
so that every strongly f(k)-connected tournament contains k edge-disjoint
Hamilton cycles. A classical theorem of Camion, that every strongly connected
tournament contains a Hamilton cycle, implies that f(1)=1. So far, even the
existence of f(2) was open. In this paper, we prove Thomassen's conjecture by
showing that f(k)=O(k^2*log^2(k)). This is best possible up to the logarithmic
factor. As a tool, we show that every strongly 10^4*k*log(k)-connected
tournament is k-linked (which improves a previous exponential bound). The proof
of the latter is based on a fundamental result of Ajtai, Koml\'os and
Szemer\'edi on asymptotically optimal sorting networks.


title:
Optical Rotation Quasi-Phase-Matching for Circularly Polarized High
  Harmonic Generation

abstract:
  The first scheme for quasi-phase-matching high harmonic generation of
circularly polarized radiation is proposed: optical rotation
quasi-phase-matching (ORQPM). In ORQPM propagation of the driving radiation in
a system exhibiting circular birefringence causes its plane of polarization to
rotate; by appropriately matching the period of rotation to the coherence
length it is possible to avoid destructive interference of the generated
radiation. It is shown that ORQPM is approximately 5 times more efficient than
conventional QPM, and half as efficient as true phase-matching.


title:
Valence-skipping and negative-U in the d-band from repulsive local
  Coulomb interaction

abstract:
  We show that repulsive local Coulomb interaction alone can drive
valence-skipping charge disproportionation in the degenerate d-band, resulting
in effective negative-U. This effect is shown to originate from anisotropic
orbital-multipole scattering, and occurs only for $d^1$, $d^4$, $d^6$ and $d^9$
fillings (and their immediate surroundings). Explicit boundaries for
valence-skipping are derived and the paramagnetic phase diagram for $d^4$ and
$d^6$ is calculated. We also establish that the valence-skipping metal is very
different, in terms of its local valence distribution, compared to the
atomic-like Hund's metal. These findings explains why transition metal
compounds with the aforementioned d-band fillings are more prone to
valence-skipping charge order and anomalous superconductivity.


title: Asymptotic analysis of solutions to a gauged O(3) sigma model

abstract:
  We analyze an elliptic equation arising in the study of the gauged O(3) sigma
model with the Chern-Simons term. In this paper, we study the asymptotic
behavior of solutions and apply it to prove the uniqueness of stable solutions.
However, one of the features of this nonlinear equation is the existence of
stable nontopological solutions in $\RN$, which implies the possibility that a
stable solution which blows up at a vortex point exists. To exclude this kind
of blow up behavior is one of the main difficulties which we have to overcome.


title: SPM Bulletin 35

abstract:
  This issue contains a number of abstracts of papers directly related to
selection principles, some of which presented at the conference SPMC2012, and
the announcement of the solution of Malyhin's Problem.