title:
Chaos synchronization in networks of coupled maps with time-varying
  topologies

abstract:
  Complexity of dynamical networks can arise not only from the complexity of
the topological structure but also from the time evolution of the topology. In
this paper, we study the synchronous motion of coupled maps in time-varying
complex networks both analytically and numerically. The temporal variation is
rather general and formalized as being driven by a metric dynamical system.
Four network models are discussed in detail in which the interconnections
between vertices vary through time randomly. These models are 1) i.i.d.
sequences of random graphs with fixed wiring probability, 2) groups of graphs
with random switches between the individual graphs, 3) graphs with temporary
random failures of nodes, and 4) the meet-for-dinner model where the vertices
are randomly grouped. We show that the temporal variation and randomness of the
connection topology can enhance synchronizability in many cases; however, there
are also instances where they reduce synchronizability. In analytical terms,
the Hajnal diameter of the coupling matrix sequence is presented as a measure
for the synchronizability of the graph topology. In topological terms, the
decisive criterion for synchronization of coupled chaotic maps is that the
union of the time-varying graphs contains a spanning tree.


title:
Generalization of the "Stark unit" for abelian L-functions with multiple
  zeros

abstract:
  For an abelian extension of number fields we show that the Stark conjecture
for all Artin L-functions with zero of order r is equivalent to existence of a
special element in the rational span of the r-th exterior power of the Galois
module of units of the bigger field.


title: Molecular Dynamics Simulation of Shear Moduli for Coulomb Crystals

abstract:
  Torsional (shear) oscillations of neutron stars may have been observed in
quasiperiodic oscillations of Magnetar Giant Flares. The frequencies of these
modes depend on the shear modulus of neutron star crust. We calculate the shear
modulus of Coulomb crystals from molecular dynamics simulations. We find that
electron screening reduces the shear modulus by about 10% compared to previous
Ogata et al. results. Our MD simulations can be extended to calculate the
effects of impurities and or polycrystalline structures on the shear modulus.


title:
Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit
  QED

abstract:
  We present an ideal realization of the Tavis-Cummings model in the absence of
atom number and coupling fluctuations by embedding a discrete number of fully
controllable superconducting qubits at fixed positions into a transmission line
resonator. Measuring the vacuum Rabi mode splitting with one, two and three
qubits strongly coupled to the cavity field, we explore both bright and dark
dressed collective multi-qubit states and observe the discrete square root of N
scaling of the collective dipole coupling strength. Our experiments demonstrate
a novel approach to explore collective states, such as the W-state, in a fully
globally and locally controllable quantum system. Our scalable approach is
interesting for solid-state quantum information processing and for fundamental
multi-atom quantum optics experiments with fixed atom numbers.


title:
A wave effect enabling universal frequency scaling, monostatic passive
  radar, incoherent aperture synthesis, and general immunity to jamming and
  interference

abstract:
  A fundamental Doppler-like but asymmetric wave effect that shifts received
signals in frequency in proportion to their respective source distances, was
recently described as means for a whole new generation of communication
technology using angle and distance, potentially replacing TDM, FDM or CDMA,
for multiplexing. It is equivalent to wave packet compression by scaling of
time at the receiver, converting path-dependent phase into distance-dependent
shifts, and can multiply the capacity of physical channels. The effect was
hitherto unsuspected in physics, appears to be responsible for both the
cosmological acceleration and the Pioneer 10/11 anomaly, and is exhibited in
audio data. This paper discusses how it may be exploited for instant, passive
ranging of signal sources, for verification, rescue and navigation; incoherent
aperture synthesis for smaller, yet more accurate radars; universal immunity to
jamming or interference; and precision frequency scaling of radiant energy in
general.


title: PCAC and coherent pion production by low energy neutrinos

abstract:
  Coherent pi^+ and pi^0 production in low energy neutrino reactions is
discussed in the framework of the partially conserved axial vector current
theory (PCAC). The role of lepton mass effects in suppressing the pi^+
production is emphasized. Instead of using models of pion nucleus scattering,
the available data on pion Carbon scattering are implemented for an analysis of
the PCAC prediction. Our results agree well with the published upper limits for
pi^+ production but are much below the recent MiniBooNE result for pi^0
production.


title:
Three-coloring statistical model with domain wall boundary conditions.
  II. Trigonometric limit

abstract:
  A nontrivial trigonometric limit of the three-coloring statistical model with
the domain wall boundary conditions is considered. In this limit the functional
equations, constructed in the previous paper, are solved and a new determinant
representation for the partial partition functions is found.


title:
Invariant Differential Operators for Non-Compact Lie Groups: the
  $E_{6(-14)}$ case

abstract:
  In the present paper we continue the project of systematic explicit
construction of invariant differential operators. On the example of the
non-compact exceptional group $E_{6(-14)}$ we give the multiplets of
indecomposable elementary representations. This includes the data for all
relevant invariant differential operators.


title: Sparse graphs: metrics and random models

abstract:
  Recently, Bollob\'as, Janson and Riordan introduced a family of random graph
models producing inhomogeneous graphs with $n$ vertices and $\Theta(n)$ edges
whose distribution is characterized by a kernel, i.e., a symmetric measurable
function $\ka:[0,1]^2 \to [0,\infty)$. To understand these models, we should
like to know when different kernels $\ka$ give rise to `similar' graphs, and,
given a real-world network, how `similar' is it to a typical graph $G(n,\ka)$
derived from a given kernel $\ka$.
  The analogous questions for dense graphs, with $\Theta(n^2)$ edges, are
answered by recent results of Borgs, Chayes, Lov\'asz, S\'os, Szegedy and
Vesztergombi, who showed that several natural metrics on graphs are equivalent,
and moreover that any sequence of graphs converges in each metric to a graphon,
i.e., a kernel taking values in $[0,1]$.
  Possible generalizations of these results to graphs with $o(n^2)$ but
$\omega(n)$ edges are discussed in a companion paper [arXiv:0708.1919]; here we
focus only on graphs with $\Theta(n)$ edges, which turn out to be much harder
to handle. Many new phenomena occur, and there are a host of plausible metrics
to consider; many of these metrics suggest new random graph models, and vice
versa.


title: On the complexity of Putinar's Positivstellensatz

abstract:
  We prove an upper bound on the degree complexity of Putinar's
Positivstellensatz. This bound is much worse than the one obtained previously
for Schm\"udgen's Positivstellensatz but it depends on the same parameters. As
a consequence, we get information about the convergence rate of Lasserre's
procedure for optimization of a polynomial subject to polynomial constraints.


title: Vanishing theorems for Dolbeault cohomology of log homogeneous varieties

abstract:
  We consider a complete nonsingular variety $X$ over $\bC$, having a normal
crossing divisor $D$ such that the associated logarithmic tangent bundle is
generated by its global sections. We show that $H^i\big(X, L^{-1} \otimes
\Omega_X^j(\log D)\big) = 0$ for any nef line bundle $L$ on $X$ and all $i < j
- c$, where $c$ is an explicit function of $(X,D,L)$. This implies e.g. the
vanishing of $H^i(X, L \otimes \Omega_X^j)$ for $L$ ample and $i > j$, and
gives back a vanishing theorem of Broer when $X$ is a flag variety.


title: Extreme lattices and vexillar designs

abstract:
  We define a notion of vexillar design for the flag variety in the spirit of
the spherical designs introduced by Delsarte, Goethals and Seidel. For a finite
subgroup of the orthogonal group, we explain how conditions on the group have
the orbits of any flag under the group action be a design and point out why the
minima of a lattice in the sense of the general Hermite constant forming a
4-design implies being extreme. The reasoning proves useful to show the
extremality of many new expected examples ($E_8$, $\La_{24}$, Barnes-Wall
lattices, Thompson-Smith lattice for instance) that were out of reach until
now.


title: Bieri-Neumann-Strebel-Renz invariants and homology jumping loci

abstract:
  We investigate the relationship between the geometric
Bieri-Neumann-Strebel-Renz invariants of a space (or of a group), and the jump
loci for homology with coefficients in rank 1 local systems over a field. We
give computable upper bounds for the geometric invariants, in terms of the
exponential tangent cones to the jump loci over the complex numbers. Under
suitable hypotheses, these bounds can be expressed in terms of simpler data,
for instance, the resonance varieties associated to the cohomology ring. These
techniques yield information on the homological finiteness properties of free
abelian covers of a given space, and of normal subgroups with abelian quotients
of a given group. We illustrate our results in a variety of geometric and
topological contexts, such as toric complexes and Artin kernels, as well as
K\"ahler and quasi-K\"ahler manifolds.


title: Electromagnetically induced spatial light modulation

abstract:
  We theoretically report that, utilizing electromagnetically induced
transparency (EIT), the transverse spatial properties of weak probe fields can
be fast modulated by using optical patterns (e.g. images) with desired
intensity distributions in the coupling fields. Consequently, EIT systems can
function as high-speed optically addressed spatial light modulators. To
exemplify our proposal, we indicate the generation and manipulation of
Laguerre-Gaussian beams based on either phase or amplitude modulation in hot
vapor EIT systems.


title: Equivariant Lie-Rinehart cohomology

abstract:
  In this paper, we study Lie-Rinehart cohomology for quotients of
singularities by finite groups, and interpret these cohomology groups in terms
of integrable connection on modules.


title:
One-particle properties of deformed N $\approx$ 28 odd-N nuclei with
  weakly-bound or resonant neutrons

abstract:
  Possible deformation of odd-N nuclei with N $\approx$ 28 towards the neutron
drip line is investigated using the Nilsson diagram based on deformed
Woods-Saxon potentials. Both weakly-bound and resonant one-particle levels are
properly obtained by directly solving the Schr\"{o}dinger equation in mesh of
space coordinate with the correct boundary condition. If we use the same
diffuseness of the potential as that of $\beta$-stable nuclei, the energy
difference between the neutron 2p$_{3/2}$ and 1f$_{7/2}$ levels becomes very
small or the N=28 energy gap almost disappears, as the binding energies of
those levels approach zero. This suggests that the ground states of those
neutron drip line nuclei are likely to be deformed. In particular, the
spin-parity and the magnetic moment of the ground state of odd-N nuclei,
$^{43}_{16}$S$_{27}$ and $^{45}_{16}$S$_{29}$, are examined. Moreover, it is
suggested that in $^{39}_{12}$Mg$_{27}$ lying outside the drip line the lowest
resonant state may have 5/2$^{-}$, if the N=28 energy gap almost vanishes.


title:
Evidence for the Gompertz Curve in the Income Distribution of Brazil
  1978-2005

abstract:
  This work presents an empirical study of the evolution of the personal income
distribution in Brazil. Yearly samples available from 1978 to 2005 were studied
and evidence was found that the complementary cumulative distribution of
personal income for 99% of the economically less favorable population is well
represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where
$x$ is the normalized individual income. The complementary cumulative
distribution of the remaining 1% richest part of the population is well
represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This
result means that similarly to other countries, Brazil's income distribution is
characterized by a well defined two class system. The parameters $A$, $B$,
$\alpha$, $\beta$ were determined by a mixture of boundary conditions,
normalization and fitting methods for every year in the time span of this
study. Since the Gompertz curve is characteristic of growth models, its
presence here suggests that these patterns in income distribution could be a
consequence of the growth dynamics of the underlying economic system. In
addition, we found out that the percentage share of both the Gompertzian and
Paretian components relative to the total income shows an approximate cycling
pattern with periods of about 4 years and whose maximum and minimum peaks in
each component alternate at about every 2 years. This finding suggests that the
growth dynamics of Brazil's economic system might possibly follow a
Goodwin-type class model dynamics based on the application of the
Lotka-Volterra equation to economic growth and cycle.

categories: q-fin.GN cond-mat.stat-mech nlin.AO physics.soc-ph q-fin.ST


title:
Low-x QCD studies with forward jets in proton-proton collisions at
  sqrt{s} = 14 TeV in CMS

abstract:
  Forward (di)jet measurements are a useful tool to constrain the Parton
Distribution Functions (PDFs) at low values of parton momentum fraction x, and
to study the possible onset of BFKL or gluon saturation QCD evolutions in the
proton. We present studies of jet reconstruction capabilities in the CMS Hadron
Forward (HF) calorimeter (3<|eta|<5). The expected sensitivity of the inclusive
forward jet p_T spectrum to the proton PDF, as well as the azimuthal
decorrelation of Mueller-Navelet jets with a large rapidity separation are
presented for p-p collisions at sqrt{s} = 14 TeV.


title:
Exploring meson correlators in the model with four-quark interaction
  Lagrangian

abstract:
  Meson correlation functions are studied in the model with four-fermion
interaction Lagrangian. We demonstrate that despite the singular character of
system mean energy and corresponding quark condensate found out the meson
observables are finite, quite well identified and compatible with experimental
energy scale. It allows one to use the similar model Hamiltonians for
describing the nonequilibrium features of quark/hadron systems which reveal
themselves in studying ultrarelativistic heavy ion collisions. The analytical
results for meson correlation functions in the Keldysh model are given.


title: Upper Triangular Operator Matrices, SVEP and Browder. Weyl Theorems

abstract:
  A Banach space operator $T\in B({\cal X})$ is polaroid if points
$\lambda\in\iso\sigma\sigma(T)$ are poles of the resolvent of $T$. Let
$\sigma_a(T)$, $\sigma_w(T)$, $\sigma_{aw}(T)$, $\sigma_{SF_+}(T)$ and
$\sigma_{SF_-}(T)$ denote, respectively, the approximate point, the Weyl, the
Weyl essential approximate, the upper semi--Fredholm and lower semi--Fredholm
spectrum of $T$. For $A$, $B$ and $C\in B({\cal X})$, let $M_C$ denote the
operator matrix $(A & C 0 & B)$. If $A$ is polaroid on
$\pi_0(M_C)=\{\lambda\in\iso\sigma(M_C) 0<\dim(M_C-\lambda)^{-1}(0)<\infty\}$,
$M_0$ satisfies Weyl's theorem, and $A$ and $B$ satisfy either of the
hypotheses (i) $A$ has SVEP at points
$\lambda\in\sigma_w(M_0)\setminus\sigma_{SF_+}(A)$ and $B$ has SVEP at points
$\mu\in\sigma_w(M_0)\setminus\sigma_{SF_-}(B)$, or, (ii) both $A$ and $A^*$
have SVEP at points $\lambda\in\sigma_w(M_0)\setminus\sigma_{SF_+}(A)$, or,
(iii) $A^*$ has SVEP at points
$\lambda\in\sigma_w(M_0)\setminus\sigma_{SF_+}(A)$ and $B^*$ has SVEP at points
$\mu\in\sigma_w(M_0)\setminus\sigma_{SF_-}(B)$, then
$\sigma(M_C)\setminus\sigma_w(M_C)=\pi_0(M_C)$. Here the hypothesis that
$\lambda\in\pi_0(M_C)$ are poles of the resolvent of $A$ can not be replaced by
the hypothesis $\lambda\in\pi_0(A)$ are poles of the resolvent of $A$.
  For an operator $T\in B(\X)$, let
$\pi_0^a(T)=\{\lambda:\lambda\in\iso\sigma_a(T),
0<\dim(T-\lambda)^{-1}(0)<\infty\}$. We prove that if $A^*$ and $B^*$ have
SVEP, $A$ is polaroid on $\pi_0^a(\M)$ and $B$ is polaroid on $\pi_0^a(B)$,
then $\sigma_a(\M)\setminus\sigma_{aw}(\M)=\pi_0^a(\M)$.


title: Generalizations of Pauli channels

abstract:
  The Pauli channel acting on 2 x 2 matrices is generalized to an n-level
quantum system. When the full matrix algebra M is decomposed into pairwise
complementary subalgebras, then trace-preserving linear mappings from M to M
are constructed such that the restriction to the subalgebras are depolarizing
channels. The result is the necessary and sufficient condition of complete
positivity. The main examples appear on bipartite systems


title:
Heat-kernel estimates for random walk among random conductances with
  heavy tail

abstract:
  We study models of discrete-time, symmetric, $\Z^{d}$-valued random walks in
random environments, driven by a field of i.i.d. random nearest-neighbor
conductances $\omega_{xy}\in[0,1]$, with polynomial tail near 0 with exponent
$\gamma>0$. We first prove for all $d\geq5$ that the return probability shows
an anomalous decay (non-Gaussian) that approches (up to sub-polynomial terms) a
random constant times $n^{-2}$ when we push the power $\gamma$ to zero. In
contrast, we prove that the heat-kernel decay is as close as we want, in a
logarithmic sense, to the standard decay $n^{-d/2}$ for large values of the
parameter $\gamma$.


title: Theoretical study of HfF$^+$ for the electron EDM search

abstract:
  We report ab initio relativistic correlation calculations of potential curves
and electric dipole transition moments for ten low-lying electronic states,
effective electric field on the electron, hyperfine constants and radiative
lifetimes for the $^3\Delta_1$ state of cation of the heavy transition metal
fluoride HfF$^+$, which it is suggested to be used in experiments to search for
the electric dipole moment of the electron. It is obtained that HfF$^+$ has
deeply bound $^1\Sigma^+$ ground state; its dissociation energy is $D_e=6.4$
eV. The $^3\Delta_1$ state is obtained as the relatively long-lived, with
lifetime equal to about 0.4 s.,first excited state lying about 0.2 eV higher.
The calculated effective electric field, $E_{eff}=W_d|\Omega|$, acting on an
electron in this state is $5.84*10^{24} Hz/{e*cm}$. The obtained hyperfine
constants are $A_{\parallel}= -1239$ MHz for the $^{177}$Hf nucleus and
$A_{\parallel}= -58.1$ MHz for the $^{19}$F nucleus.


title:
Injectivity radius and optimal regularity of Lorentzian manifolds with
  bounded curvature

abstract:
  We review recent work on the local geometry and optimal regularity of
Lorentzian manifolds with bounded curvature. Our main results provide an
estimate of the injectivity radius of an observer, and a local canonical
foliations by CMC (Constant Mean Curvature) hypersurfaces, together with
spatially harmonic coordinates. In contrast with earlier results based on a
global bound for derivatives of the curvature, our method requires only a
sup-norm bound on the curvature near the given observer.


title:
Motivically functorial coniveau spectral sequences; direct summands of
  cohomology of function fields

abstract:
  We construct a 'triangulated analogue' of coniveau spectral sequences: the
motif of a variety over a countable field is 'decomposed' (in the sense of
Postnikov towers) into the twisted (co)motives of its points; this is
generalized to arbitrary Voevodsky's motives. To this end we construct a
'Gersten' weight structure for a certain triangulated category of 'comotives':
the latter is defined to contain comotives for all projective limits of smooth
varieties; the definition of a weight structure was introduced in a preceding
paper. The corresponding weight spectral sequences are essentially coniveau
one; they are $DM^{eff}_{gm}$-functorial (starting from $E_2$) and can be
computed in terms of the homotopy $t$-structure for the category $DM^-_{eff}$
(similarly to the case of smooth varieties). This extends to motives the
seminal coniveau spectral sequence computations of Bloch and Ogus. We also
obtain that the cohomology of a smooth semi-local scheme is a direct summand of
the cohomology of its generic fibre; cohomology of function fields contain
twisted cohomology of their residue fields (for all geometric valuations).
  We also develop further the general theory of weight structures for
triangulated categories (independently from the 'motivic' part of the paper).
Besides, we develop a certain theory of 'nice' pairings of triangulated
categories; this subject seems to be new.


title: Brody curves omitting hyperplanes

abstract:
  A Brody curve, a.k.a. normal curve, is a holomorphic map from the complex
line to the complex projective space of dimension n, such that the family of
its translations is normal. We prove that Brody curves omitting n hyperplanes
in general position have growth order at most one, normal type. This
generalizes a result of Clunie and Hayman who proved it for n=1.


title: Degenerate quantum codes and the quantum Hamming bound

abstract:
  The parameters of a nondegenerate quantum code must obey the Hamming bound.
An important open problem in quantum coding theory is whether or not the
parameters of a degenerate quantum code can violate this bound for
nondegenerate quantum codes. In this paper we show that Calderbank-Shor-Steane
(CSS) codes with alphabet $q\geq 5$ cannot beat the quantum Hamming bound. We
prove a quantum version of the Griesmer bound for the CSS codes which allows us
to strengthen the Rains' bound that an $[[n,k,d]]_2$ code cannot correct more
than $\floor{(n+1)/6}$ errors to $\floor{(n-k+1)/6}$. Additionally, we also
show that the general quantum codes $[[n,k,d]]_q$ with $k+d\leq
{(1-2eq^{-2})n}$ cannot beat the quantum Hamming bound.


title:
On the distance observable in the Moyal plane and in a novel
  two-dimensional space with string-theory pregeometry

abstract:
  Motivation for the study of spacetime noncommutativity comes primarily from
its possible use in investigations of (Planck-scale) spacetime fuzziness, but
most work focuses on S-matrix/field-theory observables and still very little
has been established for geometric observables. We argue that it might be
useful to exploit the "pregeometric" formulation of spacetime noncommutativity,
which in particular describes the coordinates of the Moyal plane in terms of
the phase-space coordinates of a point particle "living" in a
auxiliary/fictitious spacetime ($\{x_1,x_2\}_{Moyal} \equiv
\{q,p\}_{particle}$). This leads us straightforwardly to a distance operator
for the Moyal plane, and allows us to expose some limitations of a previous
attempt to describe the "area of a disc" in the Moyal plane. We also observe
that from our pregeometric perspective it is rather natural to contemplate a
spacetime whose pregeometric picture is based on the phase-space coordinates
(fields) of a string. The fact that such "stringspaces" essentially provide
spacetime points with extendedness is relevant for the fuzziness of geometric
spacetime observables in ways that we preliminarily characterize through an
analysis of the distance observable on a two-dimensional stringspace and
through the observation that by implementing the
Amati-Ciafaloni-Veneziano/Gross-Mende uncertainty relation in the phase space
of the pregeometric string one could have stringspaces with a novel type of
fuzzy coordinates.


title:
Equipartition of energy for the wave equation associated to the
  Dunkl-Cherednik Laplacian

abstract:
  This paper is concerned with energy properties of the wave equation
associated to the Dunkl-Cherednik Laplacian. We establish the conservation of
the total energy, the strict equipartition of energy under suitable assumptions
and the asymptotic equipartition in the general case.


title: Leaf superposition property for integer rectifiable currents

abstract:
  We consider the class of integer rectifiable currents without boundary
satisfying a positivity condition. We establish that these currents can be
written as a linear superposition of graphs of finitely many functions with
bounded variation.


title:
Using Sideband Transitions for Two-Qubit Operations in Superconducting
  Circuits

abstract:
  We demonstrate time resolved driving of two-photon blue sideband transitions
between superconducting qubits and a transmission line resonator. Using the
sidebands, we implement a pulse sequence that first entangles one qubit with
the resonator, and subsequently distributes the entanglement between two
qubits. We show generation of 75% fidelity Bell states by this method. The full
density matrix of the two qubit system is extracted using joint measurement and
quantum state tomography, and shows close agreement with numerical simulation.
The scheme is potentially extendable to a scalable universal gate for quantum
computation.


title: The Angular Momentum Structure of the Nucleon

abstract:
  The proton spin budget is discussed. Results are presented from inclusive and
semi-inclusive deep inelastic scattering and from deeply virtual Compton
scattering. They permit interpretations towards the determination of various
contributions to the proton spin.


title:
Singular limits for the Riemann problem. General diffusion, relaxation,
  and boundary conditions

abstract:
  We consider self-similar approximations of nonlinear hyperbolic systems in
one space dimension with Riemann initial data and general diffusion matrix. We
assume that the matrix of the system is strictly hyperbolic and the diffusion
matrix is close to the identity. No genuine nonlinearity assumption is
required. We show the existence of a smooth, self-similar solution which has
bounded total variation, uniformly in the diffusion parameter. In the
zero-diffusion limit, the solutions converge to a solution of the Riemann
problem associated with the hyperbolic system. A similar result is established
for the relaxation approximation and the boundary-value problem in a half-space
for the same regularizations.


title: Preparation of many-body states for quantum simulation

abstract:
  While quantum computers are capable of simulating many quantum systems
efficiently, the simulation algorithms must begin with the preparation of an
appropriate initial state. We present a method for generating physically
relevant quantum states on a lattice in real space. In particular, the present
algorithm is able to prepare general pure and mixed many-particle states of any
number of particles. It relies on a procedure for converting from a
second-quantized state to its first-quantized counterpart. The algorithm is
efficient in that it operates in time that is polynomial in all the essential
descriptors of the system, such the number of particles, the resolution of the
lattice, and the inverse of the maximum final error. This scaling holds under
the assumption that the wavefunction to be prepared is bounded or its
indefinite integral known and that the Fock operator of the system is
efficiently simulatable.


title:
Quantum integrable systems in three-dimensional magnetic fields: the
  Cartesian case

abstract:
  In this paper we construct integrable three-dimensional quantum-mechanical
systems with magnetic fields, admitting pairs of commuting second-order
integrals of motion. The case of Cartesian coordinates is considered. Most of
the systems obtained are new and not related to the separation of variables in
the corresponding Schr\"odinger equation.


title:
Stability of quantized time-delay nonlinear systems: A
  Lyapunov-Krasowskii-functional approach

abstract:
  Lyapunov-Krasowskii functionals are used to design quantized control laws for
nonlinear continuous-time systems in the presence of constant delays in the
input. The quantized control law is implemented via hysteresis to prevent
chattering. Under appropriate conditions, our analysis applies to stabilizable
nonlinear systems for any value of the quantization density. The resulting
quantized feedback is parametrized with respect to the quantization density.
Moreover, the maximal allowable delay tolerated by the system is characterized
as a function of the quantization density.


title: Discovery of a rapidly pulsating subdwarf B star candidate in omega Cen

abstract:
  We report the discovery of the first variable extreme horizontal branch star
in a globular cluster (omega Cen). The oscillation uncovered has a period of
114 s and an amplitude of 32 mmags. A comparison between horizontal branch
models and observed optical colours indicates an effective temperature of
31,500+-6,300 K for this star, placing it within the instability strip for
rapidly oscillating B subdwarfs. The time scale and amplitude of the pulsation
detected are also in line with what is expected for this type of variable, thus
strengthening the case for the discovery of a new subdwarf B pulsator.


title:
Haar method, averaged matrix, wave cancellations, and L1 stability for
  hyperbolic systems

abstract:
  We develop a version of Haar and Holmgren methods which applies to
discontinuous solutions of nonlinear hyperbolic systems and allows us to
control the L1 distance between two entropy solutions. The main difficulty is
to cope with linear hyperbolic systems with discontinuous coefficients. Our
main observation is that, while entropy solutions contain compressive shocks
only, the averaged matrix associated with two such solutions has compressive or
undercompressive shocks, but no rarefaction-shocks -- which are recognized as a
source for non-uniqueness and instability. Our Haar-Holmgren-type method rests
on the geometry associated with the averaged matrix and takes into account
adjoint problems and wave cancellations along generalized characteristics. It
extends the method proposed earlier by LeFloch et al. for genuinely nonlinear
systems. In the present paper, we cover solutions with small total variation
and a class of systems with general flux that need not be genuinely nonlinear
and includes for instance fluid dynamics equations. We prove that solutions
generated by Glimm or front tracking schemes depend continuously in the L1 norm
upon their initial data, by exhibiting an L1 functional controling the distance
between two solutions.


title: Wave-corpuscle mechanics for elementary charges

abstract:
  It is well known that a concept of point charge interacting with
electromagnetic (EM) field has a problem. To address that problem we introduce
a concept of wave-corpuscle to describe spinless elementary charges interacting
with the classical EM field. Every charge interacts only with the EM field and
is described by a complex valued wave function over 4-dimensional space time
continuum. A system of many charges interacting with the EM field is defined by
a local, gauge and Lorentz invariant Lagrangian with a key ingredient - a
nonlinear self-interaction term providing for a cohesive force assigned to
every charge. An ideal wave-corpuscle is an exact solution to the
Euler-Lagrange equations describing both free or accelerated motion. It carries
explicitly features of a point charge and the de Broglie wave. A system of well
separated charges moving with nonrelativistic velocities are represented
accurately as wave-corpuscles governed by the Newton motion equations for point
charges interacting with the Lorentz forces. In this regime the nonlinearities
are "stealthy" and don't show explicitly anywhere, but they provide for binding
forces that keep localized every individual charge.


title: On the NonKoszulity of (2p+1)-ary partially associative Operads

abstract:
  We present a study of quadratic operads for n-ary algebras and their dual for
n odd. We will focus on the ternary case (i.e n=3). The aim is to underline the
problem of computing the dual operad and the fact that this last is in general
defined in the graded differential operad framework. We prove that the operad
associated to 3-ary partially associative algebra is not Koszul. Recall that,
if n is even, the operad of n-ary partially associative algebras is Koszul.


title:
Finite energy solutions to the isentropic Euler equations with geometric
  effects

abstract:
  Considering the isentropic Euler equations of compressible fluid dynamics
with geometric effects included, we establish the existence of entropy
solutions for a large class of initial data. We cover fluid flows in a nozzle
or in spherical symmetry when the origin r=0 is included. These partial
differential equations are hyperbolic, but fail to be strictly hyperbolic when
the fluid mass density vanishes and vacuum is reached. Furthermore, when
geometric effects are taken into account, the sup-norm of solutions can not be
controlled since there exist no invariant regions. To overcome these
difficulties and to establish an existence theory for solutions with
arbitrarily large amplitude, we search for solutions with finite mass and total
energy. Our strategy of proof takes advantage of the particular structure of
the Euler equations, and leads to a versatile framework covering general
compressible fluid problems. We establish first higher-integrability estimates
for the mass density and the total energy. Next, we use arguments from the
theory of compensated compactness and Young measures, extended here to
sequences of solutions with finite mass and total energy. The third ingredient
of the proof is a characterization of the unbounded support of entropy
admissible Young measures. This requires the study of singular products
involving measures and principal values.


title: Phase dynamics of ferromagnetic Josephson junctions

abstract:
  We have investigated the classical phase dynamics of underdamped
ferromagnetic Josephson junctions by measuring the switching probability in
both the stationary and nonstationary regimes down to 350 mK. We found the
escape temperature to be the bath temperature, with no evidence of additional
spin noise. In the nonstationary regime, we have performed a pump-probe
experiment on the Josephson phase by increasing the frequency of the junction
current bias. We show that an incomplete energy relaxation leads to dynamical
phase bifurcation. Bifurcation manifests itself as premature switching,
resulting in a bimodal switching distribution. We directly measure the phase
relaxation time by following the evolution of the bimodal switching
distribution when varying the bias frequency. Numerical simulations account for
the experimental values of the phase relaxation time.


title:
Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant
  Differential Operators)

abstract:
  In the present paper we continue the project of systematic construction of
invariant differential operators on the example of the non-compact exceptional
algebra $E_{7(-25)}$. Our choice of this particular algebra is motivated by the
fact that it belongs to a narrow class of algebras, which we call 'conformal
Lie algebras', which have very similar properties to the conformal algebras of
$n$-dimensional Minkowski space-time. This class of algebras is identified and
summarized in a table. Another motivation is related to the AdS/CFT
correspondence. We give the multiplets of indecomposable elementary
representations, including the necessary data for all relevant invariant
differential operators.


title: The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian

abstract:
  Results from exact diagonalization show that the spin-polarized Coulomb
ground state at nu=5/2 is adiabatically connected with the Moore-Read wave
function for systems with up to Nel = 16 electrons on the surface of a sphere.
Varying the Haldane pseudopotentials v1 and v3, keeping all others at their
value for Coulomb interaction, energy gap and (v1,v3)-dependent ground state
overlap with the Moore-Read state form two ridges whose peak positions and
extent in the (v1,v3)-plane essentially coincide. Thus, the physics of the
Coulomb ground state at nu=5/2 is indeed captured by the Moore-Read state and
that non-Abelian statistics can be expected under experimental conditions. Such
adiabatic connection is not observed at nu=1/2, unless the width of the
interface wave function and/or Landau level mixing effects are sufficiently
large. Varying the width, an excitation gap is found for all system sizes Nel
\le 18 studied. However, its system size dependence casts doubt on the
existence of a Moore-Read-phase at nu=1/2 in the thermodynamic limit.


title: Lepton Flavour Violation in charged leptons within SUSY-seesaw

abstract:
  In this paper we review our main results for Lepton Flavour Violating (LFV)
semileptonic tau decays and muon-electron conversion in nuclei within the
context of two Constrained SUSY-Seesaw Models, the CMSSM and the NUHM. The
relevant spectrum is that of the Minimal Supersymmetric Standard Model extended
by three right handed neutrinos, $\nu_{R_i}$ and their corresponding SUSY
partners, ${\tilde \nu}_{R_i}$, ($i=1,2,3$). We use the seesaw mechanism for
neutrino mass generation and choose a parameterisation of this mechanism that
allows us to incorporate the neutrino data in our analysis of LFV processes. In
addition to the full one-loop results for the rates of these processes, we will
also review the set of simple formulas, valid at large $\tan \beta$, which are
very useful to compare with present experimental bounds. The sensitivity to
SUSY and Higgs sectors in these processes will also be discussed. This is a
very short summary of the works in Refs. \cite{Arganda:2008jj} and
\cite{Arganda:2007jw} to which we refer the reader for more details.


title:
Cosmological consequences of Yukawa-unified SUSY with mixed axion/axino
  cold and warm dark matter

abstract:
  Supersymmetric models with t-b-\tau Yukawa unification at M_{GUT}
qualitatively predict a sparticle mass spectrum including first and second
generation scalars at the 3--15 TeV scale, third generation scalars at the
(few) TeV scale and gluinos in the sub-TeV range. The neutralino relic density
in these models typically turns out to lie far above the measured dark matter
abundance, prompting the suggestion that instead dark matter is composed of an
axion/axino mixture. We explore the axion and thermal and non-thermal axino
dark matter abundance in Yukawa-unified SUSY models. We find in this scenario
that {\it i}). rather large values of Peccei-Quinn symmetry breaking scale
f_a\sim 10^{12} GeV are favored and {\it ii}). rather large values of GUT scale
scalar masses \sim 10-15 TeV allow for the re-heat temperature T_R of the
universe to be T_R\agt 10^6 GeV. This allows in turn a solution to the
gravitino/Big Bang Nucleosynthesis problem while also allowing for baryogenesis
via non-thermal leptogenesis. The large scalar masses for Yukawa-unified models
are also favored by data on b\to s\gamma and B_s\to \mu^+\mu^- decay. Testable
consequences from this scenario include a variety of robust LHC signatures, a
possible axion detection at axion search experiments, but null results from
direct and indirect WIMP search experiments.


title: Luminescence Spectra of Quantum Dots in Microcavities. II. Fermions

abstract:
  We discuss the luminescence spectra of coupled light-matter systems realized
with semiconductor heterostructures in microcavities in the presence of a
continuous, incoherent pumping, when the matter field is Fermionic. The linear
regime--which has been the main topic of investigation both experimentally and
theoretically--converges to the case of coupling to a Bosonic material field,
and has been amply discussed in the first part of this work. We address here
the nonlinear regime, and argue that, counter to intuition, it is better
observed at low pumping intensities. We support our discussion with particular
cases representative of, and beyond, the experimental state of the art. We
explore the transition from the quantum to the classical regime, by decomposing
the total spectrum into individual transitions between the dressed states of
the light-matter coupling Hamiltonian, reducing the problem to the positions
and broadenings of all possible transitions. As the system crosses to the
classical limit, rich multiplet structures mapping the quantized energy levels
melt and turn to cavity lasing and to an incoherent Mollow triplet in the
direct exciton emission for very good structure. Less ideal figures of merit
can still betray the quantum regime, with a proper balance of cavity versus
electronic pumping.


title:
Ground state configurations of vortices in superconducting film with
  magnetic dot

abstract:
  We consider a thin superconducting film with a magnetic dot with permanent
magnetization (normal to the film) placed on it by a method based on
London-Maxwell equations. For sufficiently high dot magnetization a single
vortex appears in the ground state. Further increase of magnetization is
accompanied with the appearance of antivortices and more vortices in the film.
We study analytically conditions for the appearance of a vortex--antivortex
pair for a range of parameters. The phase diagram with diversity of
vortex--antivortex states is calculated numerically. When appear in the ground
state, antivortices are at distances comparable to the dot radius. For not too
large dot radii the total vorticity in the ground state is predominantly zero
or one. Magnetic field due to the dot and vortices everywhere in space is
calculated analytically.


title: Emergent Electroweak Gravity

abstract:
  We show that any massive cosmological relic particle with small
self-interactions is a super-fluid today, due to the broadening of its wave
packet, and lack of any elastic scattering. The WIMP dark matter picture is
only consistent its mass $M \gg M_{\rm Pl}$ in order to maintain classicality.
The dynamics of a super-fluid are given by the excitation spectrum of bound
state quasi-particles, rather than the center of mass motion of constituent
particles. If this relic is a fermion with a repulsive interaction mediated by
a heavy boson, such as neutrinos interacting via the $Z^0$, the condensate has
the same quantum numbers as the vierbein of General Relativity. Because there
exists an enhanced global symmetry $SO(3,1)_{space}\times SO(3,1)_{spin}$ among
the fermion's self-interactions broken only by its kinetic term, the long
wavelength fluctuation around this condensate is a Goldstone graviton. A
gravitational theory exists in the low energy limit of the Standard Model's
Electroweak sector below the weak scale, with a strength that is parametrically
similar to $G_N$.


title: Magnetic resonance in the cuprates -- exciton, plasmon, or \pi-mode

abstract:
  We re-analyzed the issue whether the resonance peak observed in neutron
scattering experiments on the cuprates is an exciton, a \pi-resonance, or a
magnetic plasmon. We considered a toy model with on-cite Hubbard U and
nearest-neighbor interactions in both charge and spin channels. We found that
the resonance is predominantly an exciton, even if magnetic interaction is
absent and d-wave pairing originates from attractive density-density
interaction. Our results indicate that one cannot distinguish between spin and
charge-mediated pairing interactions by just looking at the resonance peak in
the dynamic spin susceptibility.


title: Is Quantum Logic a Logic?

abstract:
  It is shown that quantum logic is a logic in the very same way in which
classical logic is a logic. Soundness and completeness of both quantum and
classical logics have been proved for novel lattice models that are not
orthomodular and therefore cannot be distributive either - as opposed to the
standard lattice models that are orthomodular and distributive for the
respective logics. Hence, we cannot attribute the orthomodularity to quantum
logic itself, and we cannot attribute the distributivity to classical logic
itself. The valuations of logics with respect of novel models turn out to be
non-numerical, and therefore truth values and truth tables cannot in general be
ascribed to the propositions of logics themselves but only to the variables of
some of their models -for example, the two-valued Boolean algebra. Logics are,
first of all, axiomatic deductive systems, and if we stop short of considering
their semantics (models, valuations, etc.), then both quantum and classical
logics will have a completely equal footing in the sense of being two deductive
systems that differ from each other in a few axioms and nothing else. There is
no ground for considering either of the two logics more "proper" than the
other. Semantics of these logics belong to their models, and we show that there
are bigger differences between the two aforementioned classical models than
between two corresponding quantum and classical models.


title:
Gravity in a stabilized brane world model in five-dimensional
  Brans-Dicke theory

abstract:
  Linearized equations of motion for gravitational and scalar fields are found
and solved in a stabilized brane world model in five-dimensional Brans-Dicke
theory. The physical degrees of freedom are isolated, the mass spectrum of
Kaluza-Klein excitations is found and the coupling constants of these
excitations to matter on the negative tension brane are calculated.


title:
Theoretical and experimental analysis of H2 binding in a prototype metal
  organic framework material

abstract:
  Hydrogen adsorption by the metal organic framework (MOF) structure
Zn2(BDC)2(TED) is investigated using a combination of experimental and
theoretical methods. By use of the nonempirical van der Waals
density-functional (vdW-DF) approach, it is found that the locus of deepest H2
binding positions lies within two types of narrow channel. The energies of the
most stable binding sites, as well as the number of such binding sites, are
consistent with the values obtained from experimental adsorption isotherms and
heat of adsorption data. Calculations of the shift of the H-H stretch frequency
when adsorbed in the MOF give a value of approximately -30 cm-1 at the
strongest binding point in each of the two channels. Ambient temperature
infrared absorption spectroscopy measurements give a hydrogen peak centered at
4120 cm-1, implying a shift consistent with the theoretical calculations.


title: Electro-Optical Nanotraps for Neutral Atoms

abstract:
  We propose a new class of nanoscale electro-optical traps for neutral atoms.
A prototype is the toroidal trap created by a suspended, charged carbon
nanotube decorated with a silver nanosphere dimer. An illuminating laser field,
blue detuned from an atomic resonance frequency, is strongly focused by
plasmons induced in the dimer and generates both a repulsive potential barrier
near the nanostructure surface and a large viscous damping force that
facilitates trap loading. Atoms with velocities of several meters per second
may be loaded directly into the trap via spontaneous emission of just two
photons.

categories: physics.atom-ph cond-mat.mes-hall hep-ph physics.optics quant-ph


title: Standard Logics Are Valuation-Nonmonotonic

abstract:
  It has recently been discovered that both quantum and classical propositional
logics can be modelled by classes of non-orthomodular and thus non-distributive
lattices that properly contain standard orthomodular and Boolean classes,
respectively. In this paper we prove that these logics are complete even for
those classes of the former lattices from which the standard orthomodular
lattices and Boolean algebras are excluded. We also show that neither quantum
nor classical computers can be founded on the latter models. It follows that
logics are "valuation-nonmonotonic" in the sense that their possible models
(corresponding to their possible hardware implementations) and the valuations
for them drastically change when we add new conditions to their defining
conditions. These valuations can even be completely separated by putting them
into disjoint lattice classes by a technique presented in the paper.


title: Curvature tensor under the complete non-compact Ricci Flow

abstract:
  We prove that for a solution $(M^n,g(t))$, $t\in[0,T)$, where $T<\infty$, to
the Ricci flow with bounded curvature on a complete non-compact Riemannian
manifold with the Ricci curvature tensor uniformly bounded by some constant $C$
on $M^n\times [0,T)$, the curvature tensor stays uniformly bounded on
$M^n\times [0,T)$. Some other results are also presented.


title: Neutrino mass matrix in triplet Higgs models with $A_4$ symmetry

abstract:
  We consider triplet Higgs model with $A_4$ symmetry to generate the neutrino
mass matrix. The tribimaximal form of the neutrino mixing matrix can be
naturally obtained. Imposing the neutrino oscillation data, we show that 1)
both normal and inverted mass hierarchy are allowed, 2) there is a lower bound
on the lightest neutrino mass and the effective mass for neutrinoless double
beta decay, 3) the non-vanishing $\th_{13}$ can be accommodated by considering
small perturbation, 4) $\th_{\rm atm}$ should be very close to $\pi/4$ even
after perturbation. }


title: Bayesian credible interval construction for Poisson statistics

abstract:
  The construction of the Bayesian credible (confidence) interval for a Poisson
observable including both the signal and background with and without systematic
uncertainties is presented. Introducing the conditional probability satisfying
the requirement of the background not larger than the observed events to
construct the Bayesian credible interval is also discussed. A Fortran routine,
BPOCI, has been developed to implement the calculation.


title:
Synchronization of discrete-time dynamical networks with time-varying
  couplings

abstract:
  We study the local complete synchronization of discrete-time dynamical
networks with time-varying couplings. Our conditions for the temporal variation
of the couplings are rather general and include both variations in the network
structure and in the reaction dynamics; the reactions could, for example, be
driven by a random dynamical system. A basic tool is the concept of Hajnal
diameter which we extend to infinite Jacobian matrix sequences. The Hajnal
diameter can be used to verify synchronization and we show that it is
equivalent to other quantities which have been extended to time-varying cases,
such as the projection radius, projection Lyapunov exponents, and transverse
Lyapunov exponents. Furthermore, these results are used to investigate the
synchronization problem in coupled map networks with time-varying topologies
and possibly directed and weighted edges. In this case, the Hajnal diameter of
the infinite coupling matrices can be used to measure the synchronizability of
the network process. As we show, the network is capable of synchronizing some
chaotic map if and only if there exists an integer T>0 such that for any time
interval of length T, there exists a vertex which can access other vertices by
directed paths in that time interval.


title:
Dynamically dominant excitations of string solutions in the spin-1/2
  antiferromagnetic Heisenberg chain in magnetic fields

abstract:
  Using Bethe-ansatz solutions, we uncover a well-defined continuum in
dynamical structure factor $S^{+-}(k,\omega)$ of the spin-1/2 antiferromagnetic
Heisenberg chain in magnetic fields. It comes from string solutions which
continuously connect the mode of the lowest-energy excitations in the
zero-field limit and that of bound states of overturned spins from the
ferromagnetic state near the saturation field. We confirm the relevance to real
materials through comparisons with experimental results.


title: On Statistical Significance of Signal

abstract:
  A definition for the statistical significance of a signal in an experiment is
proposed by establishing a correlation between the observed p-value and the
normal distribution integral probability, which is suitable for both counting
experiment and continuous test statistics. The explicit expressions to
calculate the statistical significance for both cases are given.


title: Variations on a theme by Schalkwijk and Kailath

abstract:
  Schalkwijk and Kailath (1966) developed a class of block codes for Gaussian
channels with ideal feedback for which the probability of decoding error
decreases as a second-order exponent in block length for rates below capacity.
This well-known but surprising result is explained and simply derived here in
terms of a result by Elias (1956) concerning the minimum mean-square distortion
achievable in transmitting a single Gaussian random variable over multiple uses
of the same Gaussian channel. A simple modification of the Schalkwijk-Kailath
scheme is then shown to have an error probability that decreases with an
exponential order which is linearly increasing with block length. In the
infinite bandwidth limit, this scheme produces zero error probability using
bounded expected energy at all rates below capacity. A lower bound on error
probability for the finite bandwidth case is then derived in which the error
probability decreases with an exponential order which is linearly increasing in
block length at the same rate as the upper bound.


title:
New Limits on Sterile Neutrinos from Suzaku Observations of the Ursa
  Minor Dwarf Spheroidal Galaxy

abstract:
  We present results of our search for X-ray line emission associated with the
radiative decay of the sterile neutrino, a well-motivated dark matter
candidate, in Suzaku Observatory spectra of the Ursa Minor dwarf spheroidal
galaxy. These data represent the first deep observation of one of these extreme
mass-to-light systems and the first dedicated dark matter search using an X-ray
telescope. No such emission line is positively detected, and we place new
constraints on the combination of the sterile neutrino mass and the
active-sterile neutrino oscillation mixing angle. Line flux upper limits are
derived using a maximum-likelihood-based approach that, along with the lack of
intrinsic X-ray emission, enables us to minimize systematics and account for
those that remain. The limits we derive match or approach the best previous
results over the entire 1--20 keV mass range from a single Suzaku observation.
These are used to place constraints on the existence of sterile neutrinos with
given parameters in the general case and in the case where they are assumed to
constitute all of the dark matter. The range allowed implies that sterile
neutrinos remain a viable candidate to make up some -- or all -- of the dark
matter and also explain pulsar kicks and various other astrophysical phenomena.


title: Bose-Einstein condensation on an atom chip

abstract:
  We report an experiment of creating Bose-Einstein condensate (BEC) on an atom
chip. The chip based Z-wire current and a homogeneous bias magnetic field
create a tight magnetic trap, which allows for a fast production of BEC. After
an 4.17s forced radio frequency evaporative cooling, a condensate with about
3000 atoms appears. And the transition temperature is about 300nK. This compact
system is quite robust, allowing for versatile extensions and further studying
of BEC.


title: Sequential multiple hypothesis testing in presence of control variables

abstract:
  Suppose that at any stage of a statistical experiment a control variable $X$
that affects the distribution of the observed data $Y$ at this stage can be
used. The distribution of $Y$ depends on some unknown parameter $\theta$, and
we consider the problem of testing multiple hypotheses $H_1: \theta=\theta_1$,
$H_2: \theta=\theta_2, ...$, $H_k: \theta=\theta_k$ allowing the data to be
controlled by $X$, in the following sequential context.
  The experiment starts with assigning a value $X_1$ to the control variable
and observing $Y_1$ as a response. After some analysis, another value $X_2$ for
the control variable is chosen, and $Y_2$ as a response is observed, etc. It is
supposed that the experiment eventually stops, and at that moment a final
decision in favor of one of the hypotheses $H_1,...$, $H_k$ is to be taken. In
this article, our aim is to characterize the structure of optimal sequential
testing procedures based on data obtained from an experiment of this type in
the case when the observations $Y_1, Y_2,..., Y_n$ are independent, given
controls $X_1,X_2,..., X_n$, $n=1,2,...$.


title:
Applying Bayesian Neural Network to Determine Neutrino Incoming
  Direction in Reactor Neutrino Experiments and Supernova Explosion Location by
  Scintillator Detectors

abstract:
  In the paper, it is discussed by using Monte-Carlo simulation that the
Bayesian Neural Network(BNN) is applied to determine neutrino incoming
direction in reactor neutrino experiments and supernova explosion location by
scintillator detectors. As a result, compared to the method in
Ref.\cite{key-1}, the uncertainty on the measurement of the neutrino direction
using BNN is significantly improved. The uncertainty on the measurement of the
reactor neutrino direction is about 1.0$^\circ$ at the 68.3% C.L., and the one
in the case of supernova neutrino is about 0.6$^\circ$ at the 68.3% C.L..
Compared to the method in Ref.\cite{key-1}, the uncertainty attainable by using
BNN reduces by a factor of about 20. And compared to the Super-Kamiokande
experiment(SK), it reduces by a factor of about 8.


title:
Characteristic foliation on a hypersurface of general type in a
  projective symplectic manifold

abstract:
  Given a projective symplectic manifold $M$ and a non-singular hypersurface $X
\subset M$, the symplectic form of $M$ induces a foliation of rank 1 on $X$,
called the characteristic foliation. We study the question when the
characteristic foliation is algebraic, namely, all the leaves are algebraic
curves. Our main result is that the characteristic foliation of $X$ is not
algebraic if $X$ is of general type. For the proof, we first establish an
\'etale version of Reeb stability theorem in foliation theory and then combine
it with the positivity of the direct image sheaves associated to families of
curves.


title:
New Limits on the Ultra-high Energy Cosmic Neutrino Flux from the ANITA
  Experiment

abstract:
  We report initial results of the first flight of the Antarctic Impulsive
Transient Antenna (ANITA-1) 2006-2007 Long Duration Balloon flight, which
searched for evidence of a diffuse flux of cosmic neutrinos above energies of 3
EeV. ANITA-1 flew for 35 days looking for radio impulses due to the Askaryan
effect in neutrino-induced electromagnetic showers within the Antarctic ice
sheets. We report here on our initial analysis, which was performed as a blind
search of the data. No neutrino candidates are seen, with no detected physics
background. We set model-independent limits based on this result. Upper limits
derived from our analysis rule out the highest cosmogenic neutrino models. In a
background horizontal-polarization channel, we also detect six events
consistent with radio impulses from ultra-high energy extensive air showers.


title:
De Vries Behavior in Smectics near a Biaxiality Induced Smectic A -
  Smectic C Tricritical Point

abstract:
  We show that a generalized Landau theory for the smectic A and C phases
exhibits a biaxiality induced AC tricritical point. Proximity to this
tricritical point depends on the degree of orientational order in the system;
for sufficiently large orientational order the AC transition is 3D XY-like,
while for sufficiently small orientational order, it is either tricritical or
1st order. We investigate each of the three types of AC transitions near
tricriticality and show that for each type of transition, small orientational
order implies de Vries behavior in the layer spacing, an unusually small layer
contraction. This result is consistent with, and can be understood in terms of,
the "diffuse cone" model of de Vries. Additionally, we show that birefringence
grows upon entry to the C phase. For a continuous transition, this growth is
more rapid the closer the transition is to tricriticality. Our model also
predicts the possibility of a nonmontonic temperature dependence of
birefringence.


title: Negative Group Velocity from Quadrupole Resonance of Plasmonic Spheres

abstract:
  We study the dispersions of plasmonic bands that arise from the coupling of
electric quadrupole resonances in three dimensional photonic crystals (PCs)
consisting of plasmonic spheres. Through analytical derivation, we show that
two branches of quadrupole bands in simple cubic PCs with a small lattice
constant possess negative group velocities. Distinct from double negative media
in which the negative responses originates from the coupling of electric and
magnetic responses (P and M), the negative dispersion induced by quadrupole
resonance is an intrinsic property of quadrupole that does not require coupling
to another degree of freedom. In addition, there is no simple effective medium
description. In plasmonic systems composed of metallic nanoparticle clusters,
the coupled quadrupole resonance may be tuned to lower optical frequencies, and
the coupling strength between this quadrupole resonance and external
electromagnetic (EM) waves are in the same order of the magnetic dipole M.


title: Weak isomorphisms between Bernoulli shifts

abstract:
  In this note, we prove that if G is a countable group that contains a
nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G
are weakly isomorphic.


title: Secret Sharing over Fast-Fading MIMO Wiretap Channels

abstract:
  Secret sharing over the fast-fading MIMO wiretap channel is considered. A
source and a destination try to share secret information over a fast-fading
MIMO channel in the presence of a wiretapper who also makes channel
observations that are different from but correlated to those made by the
destination. An interactive authenticated unrestricted public channel is also
available for use by the source and destination in the secret sharing process.
This falls under the "channel-type model with wiretapper" considered by
Ahlswede and Csiszar. A minor extension of their result (to continuous channel
alphabets) is employed to evaluate the key capacity of the fast-fading MIMO
wiretap channel. The effects of spatial dimensionality provided by the use of
multiple antennas at the source, destination, and wiretapper are then
investigated.


title:
Chandra Cluster Cosmology Project III: Cosmological Parameter
  Constraints

abstract:
  Chandra observations of large samples of galaxy clusters detected in X-rays
by ROSAT provide a new, robust determination of the cluster mass functions at
low and high redshifts. Statistical and systematic errors are now sufficiently
small, and the redshift leverage sufficiently large for the mass function
evolution to be used as a useful growth of structure based dark energy probe.
In this paper, we present cosmological parameter constraints obtained from
Chandra observations of 36 clusters with <z>=0.55 derived from 400deg^2 ROSAT
serendipitous survey and 49 brightest z=~0.05 clusters detected in the All-Sky
Survey. Evolution of the mass function between these redshifts requires
Omega_Lambda>0 with a ~5sigma significance, and constrains the dark energy
equation of state parameter to w0=-1.14+-0.21, assuming constant w and flat
universe. Cluster information also significantly improves constraints when
combined with other methods. Fitting our cluster data jointly with the latest
supernovae, WMAP, and baryonic acoustic oscillations measurements, we obtain
w0=-0.991+-0.045 (stat) +-0.039 (sys), a factor of 1.5 reduction in statistical
uncertainties, and nearly a factor of 2 improvement in systematics compared to
constraints that can be obtained without clusters. The joint analysis of these
four datasets puts a conservative upper limit on the masses of light neutrinos,
Sum m_nu<0.33 eV at 95% CL. We also present updated measurements of Omega_M*h
and sigma_8 from the low-redshift cluster mass function.


title:
Gravitational wave detection using pulsars: status of the Parkes Pulsar
  Timing Array project

abstract:
  The first direct detection of gravitational waves may be made through
observations of pulsars. The principal aim of pulsar timing array projects
being carried out worldwide is to detect ultra-low frequency gravitational
waves (f ~ 10^-9 to 10^-8 Hz). Such waves are expected to be caused by
coalescing supermassive binary black holes in the cores of merged galaxies. It
is also possible that a detectable signal could have been produced in the
inflationary era or by cosmic strings. In this paper we review the current
status of the Parkes Pulsar Timing Array project (the only such project in the
Southern hemisphere) and compare the pulsar timing technique with other forms
of gravitational-wave detection such as ground- and space-based interferometer
systems.


title: Polaron Exchange Model for Ferromagnetic Ordering in Manganite Films

abstract:
  In doped manganites, the strong electron-phonon coupling due to the
Jahn-Teller effect localizes the conduction-band electrons as polarons. This
results in polarons are carriers responsible for transport and ferromagnetic
ordering rather than the bare eg electrons, and sequentially polaron exchange
model is emerged for describing ferromagnetic ordering. In
Pr0.7(Sr1-xCax)0.3MnO3(x=0.3-0.6) epitaxial thin films, for higher-temperature
paramagnetic state and lower-temperature ferromagnetic state, both the
temperature dependent transports present behaviors of small polaron; for
paramagnetic-ferromagnetic transition, the experimental data of Curie
temperature are well described by an energy balance expression induced by
polaron exchange model. These results demonstrate that the polaron models are
proper ways to describe the strongly correlated electrons in the doped
manganites.


title: Hadronic Interactions with Lattice QCD

abstract:
  I discuss recent results of the NPLQCD Collaboration regarding the
calculation of hadronic interactions with lattice QCD. A particular emphasis
will be spent on pi-pi scattering and other meson interactions.


title: Commuting birth-and-death processes

abstract:
  We use methods from combinatorics and algebraic statistics to study analogues
of birth-and-death processes that have as their state space a finite subset of
the $m$-dimensional lattice and for which the $m$ matrices that record the
transition probabilities in each of the lattice directions commute pairwise.
One reason such processes are of interest is that the transition matrix is
straightforward to diagonalize, and hence it is easy to compute $n$ step
transition probabilities. The set of commuting birth-and-death processes
decomposes as a union of toric varieties, with the main component being the
closure of all processes whose nearest neighbor transition probabilities are
positive. We exhibit an explicit monomial parametrization for this main
component, and we explore the boundary components using primary decomposition.


title: $k$-distant crossings and nestings of matchings and partitions

abstract:
  We define and consider k-distant crossings and nestings for matchings and set
partitions, which are a variation of crossings and nestings in which the
distance between vertices is important. By modifying an involution of Kasraoui
and Zeng (Electronic J. Combinatorics 2006, research paper 33), we show that
the joint distribution of k-distant crossings and nestings is symmetric. We
also study the numbers of k-distant noncrossing matchings and partitions for
small k, which are counted by well-known sequences, as well as the orthogonal
polynomials related to k-distant noncrossing matchings and partitions. We
extend Chen et al.'s r-crossings and enhanced r-crossings.


title:
Universal Behavior in Large-scale Aggregation of Independent Noisy
  Observations

abstract:
  Aggregation of noisy observations involves a difficult tradeoff between
observation quality, which can be increased by increasing the number of
observations, and aggregation quality which decreases if the number of
observations is too large. We clarify this behavior for a protypical system in
which arbitrarily large numbers of observations exceeding the system capacity
can be aggregated using lossy data compression. We show the existence of a
scaling relation between the collective error and the system capacity, and show
that large scale lossy aggregation can outperform lossless aggregation above a
critical level of observation noise. Further, we show that universal results
for scaling and critical value of noise which are independent of system
capacity can be obtained by considering asymptotic behavior when the system
capacity increases toward infinity.


title: Unbounded Multi-Magnon and Spike

abstract:
  We generalize the one magnon solution in R X S^2 to unbounded M magnon and
find the corresponding solitonic string configuration in the string sigma
model. This configuration gives rise to the expected dispersion relation
obtained from the spin chain model in the large 't Hooft coupling limit. After
considering (M,M) multi-magnon or spike on R X S^2 X S^2 as a subspace of
AdS(5)XS^5 or AdS(4)XCP^3, we investigate the dispersion relation and the
finite size effect for (M,M) multi-magnon or spike.


title:
Nanomechanical detection of antibiotic-mucopeptide binding in a model
  for superbug drug resistance

abstract:
  The alarming growth of the antibiotic-resistant superbugs
methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant
Enterococcus (VRE) is driving the development of new technologies to
investigate antibiotics and their modes of action. We report the label-free
detection of vancomycin binding to bacterial cell wall precursor analogues
(mucopeptides) on cantilever arrays, with 10 nM sensitivity and at clinically
relevant concentrations in blood serum. Differential measurements quantified
binding constants for vancomycin-sensitive and vancomycin-resistant mucopeptide
analogues. Moreover, by systematically modifying the mucopeptide density we
gain new insights into the origin of surface stress. We propose that stress is
a product of a local chemical binding factor and a geometrical factor
describing the mechanical connectivity of regions affected by local binding in
terms of a percolation process. Our findings place BioMEMS devices in a new
class of percolative systems. The percolation concept will underpin the design
of devices and coatings to significantly lower the drug detection limit and may
also impact on our understanding of antibiotic drug action in bacteria.


title: The effective action in Einstein-Maxwell theory

abstract:
  Considerable work has been done on the one-loop effective action in combined
electromagnetic and gravitational fields, particularly as a tool for
determining the properties of light propagation in curved space. After a short
review of previous work, I present some recent results obtained using the
worldline formalism. In particular, I will discuss various ways of generalizing
the QED Euler-Heisenberg Lagrangian to the Einstein-Maxwell case.


title: Quantum Nernst effect in a bismuth single crystal

abstract:
  We report a theoretical calculation explaining the quantum Nernst effect
observed experimentally in a bismuth single crystal. Generalizing the
edge-current picture in two dimensions, we show that the peaks of the Nernst
coefficient survive in three dimensions due to a van Hove singularity. We also
evaluate the phonon-drag effect on the Nernst coefficient numerically. Our
result agrees with the experimental result for a bismuth single crystal.


title: Super Hilltop Inflation

abstract:
  In this paper, we consider logarithmic radiative corrections and higher order
terms to the supersymmetric hilltop F- and D-term hybrid inflation models.
Conventional F- and D-term hybrid inflation only predicts $n_s \gae 0.98$. We
show that via a positive quadratic and a negative quartic correction the
spectral index can be reduced to $n_s=0.96$ suggested from latest WMAP result
and also cosmic string problem appeared in SUSY hybrid inflation can be solved
with mild tuning of the parameters if $\kappa \lae 0.01$ for F-term inflation
and $g \lae 0.05$ for D-term inflation.


title: Comment on three-point function in AdS(3)/CFT(2)

abstract:
  Recently, exact agreement has been found between bulk and boundary
three-point functions in AdS_3 x S^3 x T^4 with NSNS fluxes. This represents a
non-trivial check of AdS/CFT correspondence beyond the supergravity
approximation as it corresponds to an exact worldsheet computation. When taking
a closer look at this computation, one notices that a crucial point for the
bulk-boundary agreement to hold is an intriguing mutual cancellation between
worldsheet contributions corresponding to the AdS_3 and to the S^3 pieces of
the geometry, what results in a simple factorized form for the final
three-point function. In this note we review this cancellation and clarify some
points about the analytic relation between the SU(2) and the SL(2,R) structure
constants. In particular, we dicuss the connection to the Coulomb gas
representation. We also make some comments on the four-point function.


title: Square function and heat flow estimates on domains

abstract:
  The first purpose of this note is to provide a proof of the usual square
function estimate on Lp (?). It turns out to follow directly from a generic
Mikhlin multiplier theorem obtained by Alexopoulos, which mostly relies on
Gaussian bounds on the heat kernel. We also provide a simple proof of a weaker
version of the square function estimate, which is enough in most instances
involving dispersive PDEs. Moreover, we obtain, by a relatively simple
integration by parts, several useful Lp (?; H) bounds for the derivatives of
the heat ?ow with values in a given Hilbert space H.


title: Asteroids in rooted and directed path graphs

abstract:
  An asteroidal triple is a stable set of three vertices such that each pair is
connected by a path avoiding the neighborhood of the third vertex. Asteroidal
triples play a central role in a classical characterization of interval graphs
by Lekkerkerker and Boland. Their result says that a chordal graph is an
interval graph if and only if it contains no asteroidal triple. In this paper,
we prove an analogous theorem for directed path graphs which are the
intersection graphs of directed paths in a directed tree. For this purpose, we
introduce the notion of a strong path. Two non-adjacent vertices are linked by
a strong path if either they have a common neighbor or they are the endpoints
of two vertex-disjoint chordless paths satisfying certain conditions. A strong
asteroidal triple is an asteroidal triple such that each pair is linked by a
strong path. We prove that a chordal graph is a directed path graph if and only
if it contains no strong asteroidal triple. We also introduce a related notion
of asteroidal quadruple, and conjecture a characterization of rooted path
graphs which are the intersection graphs of directed paths in a rooted tree.


title:
The Cauchy-Crofton formula and the Whitney arc property for definable
  sets

abstract:
  We use the Cauchy-Crofton formula to show that every definable cell (bounded
by a ball with rational radius) in an O-minimal expansion of a field extension
of the real numbers satisfies the Whitney arc property.


title: Skyrmion in spinor condensates and its stability in trap potentials

abstract:
  A necessary condition for the existence of a skyrmion in two-component
Bose-Einstein condensates with $\mathrm{SU(2)}$ symmetry was recently provided
by two of the authors [Phys. Rev. Lett. {\bf 97}, 080403 (2006)], by mapping
the problem to a classical particle in a potential subject to time-dependent
dissipation. Here we further elaborate this approach. For two classes of
models, we demonstrate the existence of the critical dissipation strength above
which the skyrmion solution does not exist. Furthermore, we discuss the local
stability of the skyrmion solution by considering the second-order variation. A
sufficient condition for the local stability is given in terms of the
ground-state energy of a one-dimensional quantum-mechanical Hamiltonian. This
condition requires a minimum number of bosons, for a certain class of the trap
potential. In the optimal case, the minimum number of bosons can be as small
$\sim 10^4$.


title:
Electromagnetic field quantization in an anisotropic magnetodielectric
  medium with spatial-temporal dispersion

abstract:
  By modeling a linear, anisotropic and inhomogeneous magnetodielectric medium
with two independent set of harmonic oscillators, electromagnetic field is
quantized in such a medium. The electric and magnetic polarizations of the
medium are expressed as linear combinations of the ladder operators describing
the magnetodielectric medium. The Maxwell and the constitutive equations of the
medium are obtained as the Heisenberg equations of the total system. The
electric and magnetic susceptibilities of the medium are obtained in terms of
the tensors coupling the medium with the electromagnetic field. The explicit
forms of the electromagnetic field operators are obtained in terms of the
ladder operators of the medium.


title: Props in model categories and homotopy invariance of structures

abstract:
  We prove that any category of props in a symmetric monoidal model category
inherits a model structure. We devote an appendix, about half the size of the
paper, to the proof of the model category axioms in a general setting. We need
the general argument to address the case of props in topological spaces and
dg-modules over an arbitrary ring, but we give a less technical proof which
applies to the category of props in simplicial sets, simplicial modules, and
dg-modules over a ring of characteristic 0.
  We apply the model structure of props to the homotopical study of algebras
over a prop. Our goal is to prove that an object X homotopy equivalent to an
algebra A over a cofibrant prop P inherits a P-algebra structure so that X
defines a model of A in the homotopy category of P-algebras. In the
differential graded context, this result leads to a generalization of
Kadeishvili's minimal model of A-infinity algebras.


title: On a connectedness theorem of Debarre

abstract:
  Under a slightly stronger hypothesis, one improves a connectedness result of
Debarre [D] for a product of two projective spaces in terms of the extension
problem of formal-rational functions (see Theorems 1.3 and 1.4 of the
introduction)


title:
The quintic NLS as the mean field limit of a Boson gas with three-body
  interactions

abstract:
  We investigate the dynamics of a boson gas with three-body interactions in
dimensions $d=1,2$. We prove that in the limit of infinite particle number, the
BBGKY hierarchy of $k$-particle marginals converges to a limiting
(Gross-Pitaevskii (GP)) hierarchy for which we prove existence and uniqueness
of solutions. Factorized solutions of the GP hierarchy are shown to be
determined by solutions of a quintic nonlinear Schr\"odinger equation. Our
proof is based on, and extends, methods of Erd\"os-Schlein-Yau,
Klainerman-Machedon, and Kirkpatrick-Schlein-Staffilani.


title: Some remarks about the second Leibniz cohomology group for Lie algebras

abstract:
  We compare by a very elementary approach the second adjoint and trivial
Leibniz cohomology spaces of a Lie algebra to the usual ones. Examples are
given of coupled cocycles. Some properties are deduced as to Leibniz
deformations. We also consider the class of Lie algebras for which the Koszul
3-form is zero, and prove that it contains all quotients of Borel subalgebras,
or of their nilradicals, of finite dimensional semisimple Lie algebras.
Finally, a list of Kac-Moody types for indecomposable nilpotent Lie algebras of
dimension $\leqslant 7$ is given.


title:
Search for Redshifted 2.2 MeV Neutron Capture Line From A0535+262 in
  Outburst

abstract:
  The Be/X-ray binary system A0535+262 underwent a giant outburst in May-June
2005, followed by a dimmer outburst in August-September 2005. This increased
intensity provided an opportunity to search for redshifted neutron-capture
lines from the surface of the neutron star. If discovered, such lines would
constrain the neutron star equation of state, providing the motivation of this
search. The spectrometer (SPI) on board the INTEGRAL satellite observed the
dimmer outburst and provided the data for this research. We have not detected a
line with enough significance, with the width-dependent upper limits on the
broadened and redshifted neutron capture line in the range of (2 - 11) x
10^(-4) photons cm^(-2) s^(-1). To our knowledge, these are the strongest upper
limits on the redshifted 2.2 MeV emission from an accreting neutron star. Our
analysis of the transparency of the neutron star surface for 2.2 MeV photons
shows that photons have a small but finite chance of leaving the atmosphere
unscattered, which diminishes the possibility of detection.


title: Geometric Realizations of Hermitian curvature models

abstract:
  We show that a Hermitian algebraic curvature model satisfies the Gray
identity if and only if it is geometrically realizable by a Hermitian manifold.
Furthermore, such a curvature model can in fact be realized by a Hermitian
manifold of constant scalar curvature and constant *-scalar curvature which
satisfies the Kaehler condition at the point in question.


title: On $T_{2n-1}^\perp$ spaces

abstract:
  This paper is devoted to the inequalities for mean values of functions from
$T_{2n-1}^\perp$. The simple proof of the classical Jackson inequality in the
case of the second modulus of continuity may be considered as the consequence
of our estimates. The problems of the sharp constants in classical Stechkin's
inequality are also discussed.


title: Aspects of confinement from QCD correlation functions

abstract:
  We discuss the properties of ghost and gluon propagators in Landau gauge
Yang-Mills theory and their relation to the confinement problem. In general two
types of infrared behavior of these functions are allowed from their functional
equations: scaling and decoupling. Both solutions show positivity violations in
the gluon propagator and lead to a confining Polyakov loop potential. However,
only the scaling solution agrees with the Kugo-Ojima confinement scenario and
the related formulation of a physical Hilbert space of Yang-Mills theory. Our
numerical results for the gluon dressing function agree almost pointwise with
the lattice results at all physical momenta.


title: Conformal two-boundary loop model on the annulus

abstract:
  We study the two-boundary extension of a loop model - corresponding to the
dense phase of the O(n) model, or to the Q=n^2 state Potts model - in the
critical regime -2 < n < 2. This model is defined on an annulus of aspect ratio
\tau. Loops touching the left, right, or both rims of the annulus are
distinguished by arbitrary (real) weights which moreover depend on whether they
wrap the periodic direction. Any value of these weights corresponds to a
conformally invariant boundary condition. We obtain the exact seven-parameter
partition function in the continuum limit, as a function of \tau, by a
combination of algebraic and field theoretical arguments. As a specific
application we derive some new crossing formulae for percolation clusters.


title:
High-temperature oxygen non-stoichiometry, conductivity and structure in
  strontium-rich nickelates La2-xSrxNiO4-\delta (x = 1 and 1.4)

abstract:
  Oxygen nonstoichiometry, electrical conductivity and thermal expansion of La2
xSrxNiO4-\delta phases with high levels of strontium substitution (1 =< x =<
1.4) have been investigated in air and oxygen atmosphere in the temperature
range 20-1050 degrees C. These phases retain the K2NiF4-type structure of
La2NiO4 (tetragonal, space group I4/mmm). The oxygen vacancy fraction was
determined independently from thermogravimetric and neutron diffraction
experiments, and is found to increase considerably on heating. The electrical
resistivity, thermal expansion and cell parameters with temperature show
peculiar variations with temperature, and differ notably from
La2NiO4$\pm$\delta in this respect. These variations are tentatively correlated
with the evolution of nickel oxidation state, which crosses from a Ni3+/Ni4+ to
a Ni2+/Ni3+ equilibrium on heating.


title:
Observation of Superfluidity of Polaritons in Semiconductor
  Microcavities

abstract:
  One of the most striking manifestations of quantum coherence in interacting
boson systems is superfluidity. Exciton-polaritons in semiconductor
microcavities are two-dimensional composite bosons predicted to behave as
particular quantum fluids. We report the observation of superfluid motion of
polaritons created by a laser in a semiconductor microcavity. Superfluidity is
investigated in terms of the Landau criterion and manifests itself as the
suppression of scattering from defects when the flow velocity is slower than
the speed of sound in the fluid. On the other hand, a Cerenkov-like wake
pattern is clearly observed when the flow velocity exceeds the speed of sound.
The experimental findings are in excellent quantitative agreement with the
predictions based on a generalized Gross-Pitaevskii theory, showing that
polaritons in microcavities constitute a very rich system for exploring the
physics of non-equilibrium quantum fluids.


title:
Nonparametric estimation of a trend based upon sampled continuous
  processes

abstract:
  Let X be a second order random process indexed by a compact interval [0,T].
Assume that n independent realizations of X are observed on a fixed grid of p
time points. Under mild regularity assumptions on the sample paths of X, we
show the asymptotic normality of suitable nonparametric estimators of the trend
function mu = EX in the space C([0,T]) as n, p go to infinity and, using
Gaussian process theory, we derive approximate simultaneous confidence bands
for mu.


title: Mean field frozen percolation

abstract:
  We define a modification of the Erdos-Renyi random graph process which can be
regarded as the mean field frozen percolation process. We describe the behavior
of the process using differential equations and investigate their solutions in
order to show the self-organized critical and extremum properties of the
critical frozen percolation model. We prove two limit theorems about the
distribution of the size of the component of a typical frozen vertex.


title: On jet bundles and generalized Verma modules

abstract:
  The aim of this paper is to initiate a study of the jet bundles on the
grassmannian $X$ over a field of characteristic zero using higher direct images
of $G$-linearized sheaves, Lie theoretic methods, enveloping algebra theoretic
methods and generalized Verma modules. We calculate the $P$-module of the dual
jet bundle $J^l(L)^*$ and prove it equals the $l$'th piece of the canonical
filtration for $H^0(X,L)^*$. We use the results obtained to prove the
discriminant of any linear system on any grassmannian is irreducible.


title: Cone structure of $L^2$-Wasserstein spaces

abstract:
  The purpose of this paper is to understand the geometric structure of the
$L^2$-Wasserstein space $\pp$ over the Euclidean space.For this sake, we focus
on its cone structure.One of our main results is that the $L^2$-Wasserstein
space over a Polish space has a cone structure if and only if so does the
underlying space.In particular, $\pp$ turns out to have a cone structure.It is
also shown that $\pp$ splits $\R^d$ isometrically but not $\R^{d+1}$.


title: Note on the Fenchel transform in the Heisenberg group

abstract:
  Given a real-valued function defined on the Heisenberg group, we provide a
definition of abstract convexity and Fenchel transform that takes into account
the sub-Riemannian structure of the group. In our main result, we prove that,
likewise the Euclidean case, a convex function can be characterized via its
iterated Fenchel transform; the properties of the H-subdifferential play a
crucial role.


title: Volumes, Traces and Zeta Functions

abstract:
  Let $Q(x)$ be a quadratic form over $\mathbb{R}^n$. The Epstein zeta function
associated to $Q(x)$ is a well known function in number theory. We generalize
the construction of the Epstein zeta function to a class of function $\phi(x)$
defined in $\mathbb{R}^n$ that we call $A-$homogeneous, where $A$ is a real
aquare matrix of order $n$ having each eigenvalue in the left hal space
$\Re\lambda>0$. Such a class includes all the homogeneous polynomials (positive
outside the origin) and all the norms on $\mathbb{R}^n$ which are smooth
outside the origin. As in the classical (i.e. quadratic) case we prove that
such zeta functions are obtained from the Mellin transforms of theta function
of Jacobi type associated to the $A-$homogeneous function $\phi(x)$. We prove
that the zeta function associated to a $A-$homogeneous function $\phi(x)$ which
is positive and smooth outside the origin is an entire meromorphic function
having a unique simple pole at $s=\alpha$ the trace of the matrix $A$ with
residue given by the product of the trace $\alpha$ and the Lebesgue volume of
the unit ball associated to $\phi(x)$, that is the volume of the set $x\in\R^n$
satisfying $\phi(x)<1$. We also prove that the theta funtion associated to
$\phi(x)$ has an asymptotic expansion near the origin. We find that the
coefficients of such expansion depend on the values that the zeta function
associated to $\phi(x)$ assumes at the negative integers.


title:
A simple derivation of Kepler's laws without solving differential
  equations

abstract:
  Proceeding like Newton with a discrete time approach of motion and a
geometrical representation of velocity and acceleration, we obtain Kepler's
laws without solving differential equations. The difficult part of Newton's
work, when it calls for non trivial properties of ellipses, is avoided by the
introduction of polar coordinates. Then a simple reconsideration of Newton's
figure naturally leads to en explicit expression of the velocity and to the
equation of the trajectory. This derivation, which can be fully apprehended by
beginners at university (or even before) can be considered as a first
application of mechanical concepts to a physical problem of great historical
and pedagogical interest.


title: Binary Black Hole Merger in Galactic Nuclei: Post-Newtonian Simulations

abstract:
  This paper studies the formation and evolution of binary supermassive black
holes (SMBHs) in rotating galactic nuclei, focusing on the role of stellar
dynamics. We present the first N-body simulations that follow the evolution of
the SMBHs from kiloparsec separations all the way to their final relativistic
coalescence, and that can robustly be scaled to real galaxies. The N-body code
includes post-Newtonian (PN) corrections to the binary equations of motion up
to order 2.5; we show that the evolution of the massive binary is only
correctly reproduced if the conservative 1PN and 2PN terms are included. The
orbital eccentricities of the massive binaries in our simulations are often
found to remain large until shortly before coalescence. This directly affects
not only their orbital evolution rates, but has important consequences as well
for the gravitational waveforms emitted during the relativistic inspiral. We
estimate gravitational wave amplitudes when the frequencies fall inside the
band of the (planned) Laser Interferometer Space Antennae (LISA). We find
significant contributions -- well above the LISA sensitivity curve -- from the
higher-order harmonics.


title: A simple model for Carnot heat engines

abstract:
  We present a (random) mechanical model consisting of two lottery-like
reservoirs at altitude $E_h$ and $E_l<E_h$, respectively, in the earth's
gravitational field. Both reservoirs consist of $N$ possible ball locations.
The upper reservoir contains initially $n_h\le N$ weight-1 balls and the lower
reservoir contains initially $n_l\le N$ weight-1 balls. Empty locations are
treated as weight-0 balls. These reservoirs are being shaken up so that all
possible ball configurations are equally likely to occur. A cycle consists of
exchanging a ball randomly picked from the higher reservoir and a ball randomly
picked from the lower reservoir. It is straightforward to show that the
efficiency, defined as the ratio of the average work produced to the average
energy lost by the higher reservoir is $\eta=1-E_l/E_h$. We then relate this
system to a heat engine. This thermal interpretation is applicable only when
the number of balls is large. We define the entropy as the logarithm of the
number of ball configurations in a reservoir, namely $S(n)=\ln[N!/n!(N-n)!]$,
with subscripts $h,l$ appended to $S$ and to $n$. When $n_l$ does not differ
much from $n_h$, the system efficiency quoted above is found to coincide with
the maximum efficiency $\eta=1-T_l/T_h$, where the $T$ are absolute
temperatures defined from the above expression of $S$. Fluctuations are
evaluated in Appendix A, and the history of the Carnot discovery (1824) is
recalled in Appendix B. Only elementary physical and mathematical concepts are
employed.


title:
Synthesis and structure of new pyrochlore-type oxides Ln2ScNbO7 (Ln =
  Pr, Nd, Eu, Gd, Dy)

abstract:
  We report the synthesis and structural study of mixed oxides in the Ln2ScNbO7
series. New phases with Ln = Pr, Eu, Gd and Dy are obtained. All crystallize in
the cubic pyrochlore structure type, space group F-d3m, with no Sc-Nb ordering
on the B-site. The structures are determined by Rietveld refinement. The
evolution of cell parameters, interatomic distances and angles as a function of
lanthanide cation size is discussed. Magnetic measurements show the absence of
ordering down to 2 K, in agreement with the presence of strong geometric
frustration in the lanthanide sublattice. The europium phase shows a peculiar
magnetic behaviour; its magnetic susceptibility becomes constant below ca 50 K.
This feature confirms the behaviour observed previously on Eu2Ti2O7 and is
ascribed to crystal field effects.


title:
Structural and magnetic properties of the (Bi2-xPrx)Ru2O7 pyrochlore
  solid solution (0 <= x <= 2)

abstract:
  We report a detailed study of structural and magnetic properties of the
pyrochlore-type (Bi2-xPrx)Ru2O7 series. Eleven compositions with 0 <= x <= 2
were prepared by solid state reaction at 1050 degrees C and found to form a
solid solution in the whole range of compositions. Structural refinements from
X-ray powder diffraction data by the Rietveld method show that the main
variation concerns the ruthenium site. Ru-O distances increase and the Ru-O-Ru
angle (bridging corner-sharing Ru-O octahedra) decreases with increasing
praseodymium content, in agreement with the metal-semiconductor transition
observed previously in this system. Magnetic measurements show that the
metallic Pauli paramagnetism of Ru in Bi2Ru2O7 evolves to a magnetism of
localized low spin moments coexisting with the magnetism of Pr3+ cations
moments. Strong magnetic correlations are present at high Pr content, as
illustrated by a N\'eel temperature of -224 K for Pr2Ru2O7. However no evidence
of a magnetic ordering was found, suggesting that the end compound Pr2Ru2O7 of
the series might stabilize a spin liquid phase.


title:
Topotactic synthesis, structure and magnetic properties of a new
  hexagonal polytype of silver cobaltate(III) AgCoO2+\delta

abstract:
  A new form of delafossite-type AgCoO2+\delta was prepared using ion exchange
from Na0.75CoO2 in molten AgNO3-NH4NO3 at 175 degrees C. Its structure was
determined by Rietveld refinement from XRD data; it is hexagonal, space group
P63/mmc, a = 2.871 and c = 12.222 {\AA}. Its structure differs from previously
reported AgCoO2 (R-3m, 3R polytype) by the stacking of Co-O layers; in the new
phase the 2H stacking of the precursor Na0.75CoO2, consistent with a topotactic
ion exchange of Na by Ag. The new phase is found to contain a slight oxygen
excess (\delta = 0.06). Magnetic susceptibility measurements show the absence
of magnetic transition and a weak Curie term, consistent with the non-magnetic
character of Co3+ ions.


title: Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory

abstract:
  For SU(2) lattice gauge theory we study numerically the infrared behavior of
the Landau gauge ghost and gluon propagators with the special accent on the
Gribov copy dependence. Applying a very efficient gauge fixing procedure and
generating up to 80 gauge copies we find that the Gribov copy effect for both
propagators is essential in the infrared. In particular, our best copy dressing
function of the ghost propagator approaches a plateau in the infrared, while
for the random first copy it still grows. Our best copy zero-momentum gluon
propagator shows a tendency to decrease with growing lattice size which
excludes singular solutions. Our results look compatible with the so-called
decoupling solution with a non-singular gluon propagator. However, we do not
yet consider the Gribov copy problem to be finally resolved.


title: Shear viscosity and out of equilibrium dynamics

abstract:
  Using Grad's method, we calculate the entropy production and derive a formula
for the second-order shear viscosity coefficient in a one-dimensionally
expanding particle system, which can also be considered out of chemical
equilibrium. For a one-dimensional expansion of gluon matter with Bjorken boost
invariance, the shear tensor and the shear viscosity to entropy density ratio
$\eta/s$ are numerically calculated by an iterative and self-consistent
prescription within the second-order Israel-Stewart hydrodynamics and by a
microscopic parton cascade transport theory. Compared with $\eta/s$ obtained
using the Navier-Stokes approximation, the present result is about 20% larger
at a QCD coupling $\alpha_s \sim 0.3$(with $\eta/s\approx 0.18$) and is a
factor of 2-3 larger at a small coupling $\alpha_s \sim 0.01$. We demonstrate
an agreement between the viscous hydrodynamic calculations and the microscopic
transport results on $\eta/s$, except when employing a small $\alpha_s$. On the
other hand, we demonstrate that for such small $\alpha_s$, the gluon system is
far from kinetic and chemical equilibrium, which indicates the break down of
second-order hydrodynamics because of the strong noneqilibrium evolution. In
addition, for large $\alpha_s$ ($0.3-0.6$), the Israel-Stewart hydrodynamics
formally breaks down at large momentum $p_T\gtrsim 3$ GeV but is still a
reasonably good approximation.