13,203 research outputs found
Approximations from Anywhere and General Rough Sets
Not all approximations arise from information systems. The problem of fitting
approximations, subjected to some rules (and related data), to information
systems in a rough scheme of things is known as the \emph{inverse problem}. The
inverse problem is more general than the duality (or abstract representation)
problems and was introduced by the present author in her earlier papers. From
the practical perspective, a few (as opposed to one) theoretical frameworks may
be suitable for formulating the problem itself. \emph{Granular operator spaces}
have been recently introduced and investigated by the present author in her
recent work in the context of antichain based and dialectical semantics for
general rough sets. The nature of the inverse problem is examined from
number-theoretic and combinatorial perspectives in a higher order variant of
granular operator spaces and some necessary conditions are proved. The results
and the novel approach would be useful in a number of unsupervised and semi
supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings,
Springe
On chemisorption of polymers to solid surfaces
The irreversible adsorption of polymers to a two-dimensional solid surface is
studied. An operator formalism is introduced for chemisorption from a
polydisperse solution of polymers which transforms the analysis of the
adsorption process to a set of combinatorial problems on a two-dimensional
lattice. The time evolution of the number of polymers attached and the surface
area covered are calculated via a series expansion. The dependence of the final
coverage on the parameters of the model (i.e. the parameters of the
distribution of polymer lengths in the solution) is studied. Various methods
for accelerating the convergence of the resulting infinite series are
considered. To demonstrate the accuracy of the truncated series approach, the
series expansion results are compared with the results of stochastic
simulation.Comment: 20 pages, submitted to Journal of Statistical Physic
The zeta function on the critical line: Numerical evidence for moments and random matrix theory models
Results of extensive computations of moments of the Riemann zeta function on
the critical line are presented. Calculated values are compared with
predictions motivated by random matrix theory. The results can help in deciding
between those and competing predictions. It is shown that for high moments and
at large heights, the variability of moment values over adjacent intervals is
substantial, even when those intervals are long, as long as a block containing
10^9 zeros near zero number 10^23. More than anything else, the variability
illustrates the limits of what one can learn about the zeta function from
numerical evidence.
It is shown the rate of decline of extreme values of the moments is modelled
relatively well by power laws. Also, some long range correlations in the values
of the second moment, as well as asymptotic oscillations in the values of the
shifted fourth moment, are found.
The computations described here relied on several representations of the zeta
function. The numerical comparison of their effectiveness that is presented is
of independent interest, for future large scale computations.Comment: 31 pages, 10 figures, 19 table
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