244 research outputs found
Face-to-face vs. computerized conferences : a controlled experiment. Volume I: Findings
This is a report on the first controlled experiment conducted as part of a four year effort to explore the feasibility and effectiveness of using the computer to structure the communication for various types of group tasks. It uses a language called INTERACT, developed as part of this grant effort, to administer all instructions and conduct a group problem solving discussion in a computer conference. The experiment compares the process and outcome of face to face vs. computer mediated group problem solving discussions.
The objectives of this experiment are the following basic research questions: To gain quantified and detailed knowledge about the consequences and characteristics of computerized conferencing as a communications mode, as compared to the usual face-to-face discussion mode. To lay the foundation for a subsequent experiment which will seek to alter the process of group communication via computer, in order to improve group performance. To assess the feasibility of using a high level language to conduct automated experiments on group communication and problem solving
Face-to-face vs. computerized conferences : a controlled experiment, Volume II: Methodological Appendices
This is volume II of research report 12. It is comprised of the methodoligical appendices that support volume I
The Statistics of the Points Where Nodal Lines Intersect a Reference Curve
We study the intersection points of a fixed planar curve with the
nodal set of a translationally invariant and isotropic Gaussian random field
\Psi(\bi{r}) and the zeros of its normal derivative across the curve. The
intersection points form a discrete random process which is the object of this
study. The field probability distribution function is completely specified by
the correlation G(|\bi{r}-\bi{r}'|) = .
Given an arbitrary G(|\bi{r}-\bi{r}'|), we compute the two point
correlation function of the point process on the line, and derive other
statistical measures (repulsion, rigidity) which characterize the short and
long range correlations of the intersection points. We use these statistical
measures to quantitatively characterize the complex patterns displayed by
various kinds of nodal networks. We apply these statistics in particular to
nodal patterns of random waves and of eigenfunctions of chaotic billiards. Of
special interest is the observation that for monochromatic random waves, the
number variance of the intersections with long straight segments grows like , as opposed to the linear growth predicted by the percolation model,
which was successfully used to predict other long range nodal properties of
that field.Comment: 33 pages, 13 figures, 1 tabl
On the Nodal Count Statistics for Separable Systems in any Dimension
We consider the statistics of the number of nodal domains aka nodal counts
for eigenfunctions of separable wave equations in arbitrary dimension. We give
an explicit expression for the limiting distribution of normalised nodal counts
and analyse some of its universal properties. Our results are illustrated by
detailed discussion of simple examples and numerical nodal count distributions.Comment: 21 pages, 4 figure
Short and Long Range Screening of Optical Singularities
Screening of topological charges (singularities) is discussed for paraxial
optical fields with short and with long range correlations. For short range
screening the charge variance in a circular region with radius grows
linearly with , instead of with as expected in the absence of
screening; for long range screening it grows faster than : for a field whose
autocorrelation function is the zero order Bessel function J_{0}, the charge
variance grows as R ln R$. A J_{0} correlation function is not attainable in
practice, but we show how to generate an optical field whose correlation
function closely approximates this form. The charge variance can be measured by
counting positive and negative singularities inside the region A, or more
easily by counting signed zero crossings on the perimeter of A. \For the first
method the charge variance is calculated by integration over the charge
correlation function C(r), for the second by integration over the zero crossing
correlation function Gamma(r). Using the explicit forms of C(r) and of Gamma(r)
we show that both methods of calculation yield the same result. We show that
for short range screening the zero crossings can be counted along a straight
line whose length equals P, but that for long range screening this
simplification no longer holds. We also show that for realizable optical
fields, for sufficiently small R, the charge variance goes as R^2, whereas for
sufficiently large R, it grows as R. These universal laws are applicable to
both short and pseudo-long range correlation functions
Counting nodal domains on surfaces of revolution
We consider eigenfunctions of the Laplace-Beltrami operator on special
surfaces of revolution. For this separable system, the nodal domains of the
(real) eigenfunctions form a checker-board pattern, and their number is
proportional to the product of the angular and the "surface" quantum numbers.
Arranging the wave functions by increasing values of the Laplace-Beltrami
spectrum, we obtain the nodal sequence, whose statistical properties we study.
In particular we investigate the distribution of the normalized counts
for sequences of eigenfunctions with where . We show that the distribution approaches
a limit as (the classical limit), and study the leading
corrections in the semi-classical limit. With this information, we derive the
central result of this work: the nodal sequence of a mirror-symmetric surface
is sufficient to uniquely determine its shape (modulo scaling).Comment: 36 pages, 8 figure
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