21,547 research outputs found

### Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time

For critical bond-percolation on high-dimensional torus, this paper proves
sharp lower bounds on the size of the largest cluster, removing a logarithmic
correction in the lower bound in Heydenreich and van der Hofstad (2007). This
improvement finally settles a conjecture by Aizenman (1997) about the role of
boundary conditions in critical high-dimensional percolation, and it is a key
step in deriving further properties of critical percolation on the torus.
Indeed, a criterion of Nachmias and Peres (2008) implies appropriate bounds on
diameter and mixing time of the largest clusters. We further prove that the
volume bounds apply also to any finite number of the largest clusters. The main
conclusion of the paper is that the behavior of critical percolation on the
high-dimensional torus is the same as for critical Erdos-Renyi random graphs.
In this updated version we incorporate an erratum to be published in a
forthcoming issue of Probab. Theory Relat. Fields. This results in a
modification of Theorem 1.2 as well as Proposition 3.1.Comment: 16 pages. v4 incorporates an erratum to be published in a forthcoming
issue of Probab. Theory Relat. Field

### Perturbed Self-Similar Massless Scalar Field in Spherically Symmetric Spaceimes

In this paper, we investigate the linear perturbations of the spherically
symmetric spacetimes with kinematic self-similarity of the second kind. The
massless scalar field equations are solved which yield the background and an
exact solutions for the perturbed equations. We discuss the boundary conditions
of the resulting perturbed solutions. The possible perturbation modes turn out
to be stable as well as unstable. The analysis leads to the conclusion that
there does not exist any critical solution.Comment: 15 pages, accepted for publication Int. J. Mod. Phys.

### Pattern Matching and Discourse Processing in Information Extraction from Japanese Text

Information extraction is the task of automatically picking up information of
interest from an unconstrained text. Information of interest is usually
extracted in two steps. First, sentence level processing locates relevant
pieces of information scattered throughout the text; second, discourse
processing merges coreferential information to generate the output. In the
first step, pieces of information are locally identified without recognizing
any relationships among them. A key word search or simple pattern search can
achieve this purpose. The second step requires deeper knowledge in order to
understand relationships among separately identified pieces of information.
Previous information extraction systems focused on the first step, partly
because they were not required to link up each piece of information with other
pieces. To link the extracted pieces of information and map them onto a
structured output format, complex discourse processing is essential. This paper
reports on a Japanese information extraction system that merges information
using a pattern matcher and discourse processor. Evaluation results show a high
level of system performance which approaches human performance.Comment: See http://www.jair.org/ for any accompanying file

### The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

For independent nearest-neighbour bond percolation on Z^d with d >> 6, we
prove that the incipient infinite cluster's two-point function and three-point
function converge to those of integrated super-Brownian excursion (ISE) in the
scaling limit. The proof is based on an extension of the new expansion for
percolation derived in a previous paper, and involves treating the magnetic
field as a complex variable. A special case of our result for the two-point
function implies that the probability that the cluster of the origin consists
of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an
error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong
statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic,
and xr package

### Relation between fundamental estimation limit and stability in linear quantum systems with imperfect measurement

From the noncommutative nature of quantum mechanics, estimation of canonical
observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its
performance by the Heisenberg uncertainty relation, \mean{\Delta
\hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4. This fundamental lower-bound
may become bigger when taking the structure and quality of a specific
measurement apparatus into account. In this paper, we consider a particle
subjected to a linear dynamics that is continuously monitored with efficiency
$\eta\in(0,1]$. It is then clarified that the above Heisenberg uncertainty
relation is replaced by \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq
\hbar^2/4\eta if the monitored system is unstable, while there exists a stable
quantum system for which the Heisenberg limit is reached.Comment: 4 page

### Anomalous Crossing Frequency in Odd Proton Nuclei

A generic explanation for the recently observed anomalous crossing
frequencies in odd proton rare earth nuclei is given. As an example, the proton
${1\over 2} [541]$ band in $^{175}$Ta is discussed in detail by using the
angular momentum projection theory. It is shown that the quadrupole pairing
interaction is decisive in delaying the crossing point and the changes in
crossing frequency along the isotope chain are due to the different neutron
shell fillings

### Quantitative and qualitative characteristics of greenery in suburban residential districts of Metro Manila

This case study was conducted to better understand the present situation of urban greenery in Marikina City, in the suburbs of metropolitan Manila, a typical large Asian city. A vegetation survey was conducted in residential districts of Marikina City, and the quantitative and qualitative characteristics of trees were analyzed. Lot size had some influence on the quantity of greenery in residential lots. In smaller lots, however, quantity did not increase in proportion to lot size. It appears, then, that the land-use controls for individual lots did not function effectively. Quantitative differences of greenery were related to qualitative differences, depending on the year or period of development of the residential area. In the newly developed residential lots, the greenery is comprised mostly of ornamental trees. Under the present circumstances, there is no assurance of sustaining the desired quantity of greenery in smaller residential lots. From these results, we proposed that regulations on lot size/coverage and promotion of tree planting involving local residents are needed to sustain urban greenery in residential districts

### On the Backbending Mechanism of $^{48}$Cr

The mechanism of backbending in $^{48}$Cr is investigated in terms of the
Projected Shell Model and the Generator Coordinate Method. It is shown that
both methods are reasonable shell model truncation schemes. These two quite
different quantum mechanical approaches lead to a similar conclusion that the
backbending is due to a band crossing involving an excited band which is built
on simultaneously broken neutron and proton pairs in the ``intruder'' subshell
$f_{7/2}$. It is pointed out that this type of band crossing is usually known
to cause the second backbending in rare-earth nuclei.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

### On the Formation Age of the First Planetary System

Recently, it has been observed the extreme metal-poor stars in the Galactic
halo, which must be formed just after Pop III objects. On the other hand, the
first gas clouds of mass $\sim 10^6 M_{\odot}$ are supposed to be formed at $z
\sim$ 10, 20, and 30 for the $1\sigma$, $2\sigma$ and $3\sigma$, where the
density perturbations are assumed of the standard $\Lambda$CDM cosmology. If we
could apply this gaussian distribution to the extreme small probability, the
gas clouds would be formed at $z \sim$40, 60, and 80 for the $4\sigma$,
$6\sigma$, and $8\sigma$. The first gas clouds within our galaxy must be formed
around $z\sim 40$. Even if the gas cloud is metal poor, there is a lot of
possibility to form the planets around such stars. The first planetary systems
could be formed within $\sim 6\times 10^7$ years after the Big Bang in the
universe. Even in our galaxies, it could be formed within $\sim 1.7\times 10^8$
years. It is interesting to wait the observations of planets around metal-poor
stars. For the panspermia theory, the origin of life could be expected in such
systems.Comment: 5 pages,Proceedings IAU Symposium No. 249, 2007, Exoplanets:Y-S. Sun,
S. Ferraz-Mello and J.-L, Zhou, eds. (p325

- …