15,705 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
Quasi-Chemical Theory and Implicit Solvent Models for Simulations
A statistical thermodynamic development is given of a new implicit solvent
model that avoids the traditional system size limitations of computer
simulation of macromolecular solutions with periodic boundary conditions. This
implicit solvent model is based upon the quasi-chemical approach, distinct from
the common integral equation trunk of the theory of liquid solutions. The
physical content of this theory is the hypothesis that a small set of solvent
molecules are decisive for these solvation problems. A detailed derivation of
the quasi-chemical theory escorts the development of this proposal. The
numerical application of the quasi-chemical treatment to Li ion hydration
in liquid water is used to motivate and exemplify the quasi-chemical theory.
Those results underscore the fact that the quasi-chemical approach refines the
path for utilization of ion-water cluster results for the statistical
thermodynamics of solutions.Comment: 30 pages, contribution to Santa Fe Workshop on Treatment of
Electrostatic Interactions in Computer Simulation of Condensed Medi
Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances
A history is given of the applications of the simple expression generalized
from the surmise by Wigner and also by Ibach to extract the strength of the
interaction between steps on a vicinal surface, via the terrace width
distribution (TWD). A concise guide for use with experiments and a summary of
some recent extensions are provided.Comment: 11 pages, 4 figures, reformatted (with revtex) version of refereed
paper for special issue of Applied Physics A entitled "From Surface Science
to Device Physics", in honor of the retirements of Prof. H. Ibach and Prof.
H. L\"ut
Variable Precision Rough Set Approximations in Concept Lattice
The notions of variable precision rough set and concept lattice are can be shared by a basic notion, which is the definability of a set of objects based on a set of properties. The two theories of rough set and concept lattice can be compared, combined and applied to each other based on definability. Based on introducing the definitions of variable precision rough set and concept lattice, this paper shows that any extension of a concept in concept lattice is an equivalence class of variable precision rough set. After that, we present a definition of lower and upper approximations in concept lattice and generate the lower and upper approximations concept of concept lattice. Afterwards, we discuss the properties of the new lower and upper approximations. Finally, an example is given to show the validity of the properties that the lower and upper approximations have
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