27,900 research outputs found
Coevolutionary Dynamics in a Minimal Substrate
One of the central difficulties of coevolutionary methods arises from 'intransitive superiority' - in a two-player game, for example, the fact that A beats B, and B beats C, does not exclude the possibility that C beats A. Such cyclic superiority in a coevolutionary substrate is hypothesized to cause cycles in the dynamics of the population such that it 'chases its own tail' - traveling through some part of strategy space more than once despite apparent improvement with each step. It is often difficult to know whether an application domain contains such difficulties and to verify this hypothesis in the failure of a given coevolutionary set-up. In this paper we wish to elucidate some of the issues and concepts in an abstract domain where the dynamics of coevolution can be studied simply and directly. We define three simple 'number games' that illustrate intransitive superiority and resultant oscillatory dynamics, as well as some other relevant concepts. These include the distinction between a player's perceived performance and performance with respect to an external metric, and the significance of strategies with a multi-dimensional nature. These features alone can also cause oscillatory behavior and coevolutionary failure
Nonlinear sigma Model Treatment of Quantum Antiferromagnets in a Magnetic Field
We present a theoretical analysis of the properties of low-dimensional
quantum antiferromagnets in applied magnetic fields. In a nonlinear sigma model
description, we use a spin stiffness analysis, a 1/N expansion, and a
renormalization group approach to describe the broken-symmetry regimes of
finite magnetization, and, in cases of most interest, a low-field regime where
symmetry is restored by quantum fluctuations. We compute the magnetization,
critical fields, spin correlation functions, and decay exponents accessible by
nuclear magnetic resonance experiments. The model is relevant to many systems
exhibiting Haldane physics, and provides good agreement with data for the
two-chain spin ladder compound CuHpCl.Comment: 14 pages, 6 figures, full paper to accompany cond-mat/980415
On the Plutinos and Twotinos of the Kuiper Belt
We illuminate dynamical properties of Kuiper Belt Objects (KBOs) in the 3:2
(``Plutino'') and 2:1 (``Twotino'') Neptunian resonances within the model of
resonant capture and migration. We analyze a series of numerical integrations,
each involving the 4 migratory giant planets and 400 test particles distributed
throughout trans-Neptunian space, to measure efficiencies of capture as
functions of migration speed. Snapshots of the spatial distribution of resonant
KBOs reveal that Twotinos cluster +/- 75 degrees away from Neptune's longitude,
while Plutinos cluster +/- 90 degrees away. Longitudinal clustering persists
even for surveys that are not volume-limited in their ability to detect
resonant KBOs. Remarkably, between -90 degrees and -60 degrees of Neptune's
longitude, we find the sky density of Twotinos to nearly equal that of
Plutinos, despite the greater average distance of Twotinos. We couple our
findings to observations to crudely estimate that the intrinsic Twotino
population is within a factor of 3 of the Plutino population. Most strikingly,
the migration model predicts that more Twotinos may lie at longitudes behind
that of Neptune than ahead of it. The magnitude of the asymmetry amplifies
dramatically with faster rates of migration and can be as large as 300%. A
differential measurement of the sky density of 2:1 resonant objects behind of
and in front of Neptune's longitude would powerfully constrain the migration
history of that planet.Comment: AJ, in press, to appear in December 2002 issue. For version with
higher resolution figures, see
http://astron.berkeley.edu/~echiang/ppp/ppp.htm
A random hierarchical lattice: the series-parallel graph and its properties
We consider a sequence of random graphs constructed by a hierarchical procedure. The construction replaces existing edges by pairs of edges in series or parallel with probability and respectively. We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. In each case we find a phase transition at
An efficient algorithm for calculation of the Luenberger canonical form
An algorithm is suggested to obtain the Luenberger canonical form for multivariable systems. The method computes the canonical form directly without having to compute the transformation matrix. In addition, there is a large reduction in the number of calculations. The reduced computations along with Gaussian techniques lend to greater inherent accuracy and the ability to refine the solution with additional computations
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The Secondary School Writing Center: A Place to Build Confident, Competent Writers
The three of us led an International Writing Centers Association-sponsored allday
workshop on secondary school writing centers at the NCTE Convention.
Writing centers at all levels follow the theoretical background of Bruffee,
Murray, Elbow, and North, to name a few. They are not remedial facilities, as
some schools would like them to be, or ESL facilities to improve basic writing in
English. No, a secondary school writing center is primarily a place where we
work with all students, regardless of their innate talent, to build their
confidence and competency as writers. Whether we are talking about students
who need to fine-tune excellent papers or students who need to discover what
they really want to say, a writing center can be a safe harbor within the
sometimes stormy seas of the school day. We can think of no better way to
reform writing instruction.University Writing Cente
Magnetic white dwarfs in the Early Data Release of the Sloan Digital Sky Survey
We have identified 7 new magnetic DA white dwarfs in the Early Data Release
of the Sloan Digital Sky Survey. Our selection strategy has also recovered all
the previously known magnetic white dwarfs contained in the SDSS EDR,
KUV03292+0035 and HE0330-0002. Analysing the SDSS fibre spectroscopy of the
magnetic DA white dwarfs with our state-of-the-art model spectra, we find
dipole field strengths 1.5<=B_d<=63MG and effective temperatures
8500<=Teff<=39000K. As a conservative estimate, we expect that the complete
SDSS will increase the number of known magnetic white dwarfs by a factor 3.Comment: 7 pages, 4 figures, accepted for publication in Astronomy &
Astrophysic
Assumptions that imply quantum dynamics is linear
A basic linearity of quantum dynamics, that density matrices are mapped
linearly to density matrices, is proved very simply for a system that does not
interact with anything else. It is assumed that at each time the physical
quantities and states are described by the usual linear structures of quantum
mechanics. Beyond that, the proof assumes only that the dynamics does not
depend on anything outside the system but must allow the system to be described
as part of a larger system. The basic linearity is linked with previously
established results to complete a simple derivation of the linear Schrodinger
equation. For this it is assumed that density matrices are mapped one-to-one
onto density matrices. An alternative is to assume that pure states are mapped
one-to-one onto pure states and that entropy does not decrease.Comment: 10 pages. Added references. Improved discussion of equations of
motion for mean values. Expanded Introductio
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