2,486 research outputs found
Generalization of One-Sided Concept Lattices
We provide a generalization of one-sided (crisp-fuzzy) concept lattices, based on Galois connections. Our approach allows analysis of object-attribute models with different structures for truth values of attributes. Moreover, we prove that this method of creating one-sided concept lattices is the most general one, i.e., with respect to the set of admissible formal contexts, it produces all Galois connections between power sets and the products of complete lattices. Some possible applications of this approach are also included
Interpretation of Fuzzy Attribute Subsets in Generalized One-Sided Concept Lattices
In this paper we describe possible interpretation and reduction of fuzzy attributes in Generalized One-sided Concept Lattices (GOSCL). This type of concept lattices represent generalization of Formal Concept Analysis (FCA) suitable for analysis of datatables with different types of attributes. FCA as well as generalized one-sided concept lattices represent conceptual data miningmethods. With growing number of attributes the interpretation of fuzzy subsets may become unclear, hence another interpretation of this fuzzy attribute subsets can be valuable. The originality of the presented method is based on the usage of one-sided concept lattices derived from submodels of former object-attribute model by grouping attributes with the same truth value structure. This leads to new method for attribute reduction in GOSCL environment
Representation fields for commutative orders
A representation field for a non-maximal order \Ha in a central simple
algebra is a subfield of the spinor class field of maximal orders which
determines the set of spinor genera of maximal orders containing a copy of
\Ha. Not every non-maximal order has a representation field. In this work we
prove that every commutative order has a representation field and give a
formula for it. The main result is proved for central simple algebras over
arbitrary global fields.Comment: Annales de l'institut Fourier, vol 61, 201
Characterizing rings in terms of the extent of injectivity and projectivity of their modules
Given a ring R, we define its right i-profile (resp. right p-profile) to be
the collection of injectivity domains (resp. projectivity domains) of its right
R-modules. We study the lattice theoretic properties of these profiles and
consider ways in which properties of the profiles may determine the structure
of rings and viceversa. We show that the i-profile is isomorphic to an interval
of the lattice of linear filters of right ideals of R, and is therefore modular
and coatomic. In particular, we give a practical characterization of the
i-profile of a right artinian ring. We show through an example that the
p-profile is not necessarily a set, and also characterize the right p-profile
of a right perfect ring. The study of rings in terms of their (i- or p-)profile
was inspired by the study of rings with no (i- or p-) middle class, initiated
in recent papers by Er, L\'opez-Permouth and S\"okmez, and by Holston,
L\'opez-Permouth and Orhan-Ertas. In this paper, we obtain further results
about these rings and we also use our results to provide a characterization of
a special class of QF-rings in which the injectivity and projectivity domains
of any module coincide.Comment: 19 pages, examples and propositions added. Title change
Reducing facet nucleation during algorithmic self-assembly
Algorithmic self-assembly, a generalization of crystal growth, has been proposed as a mechanism for bottom-up fabrication of complex
nanostructures and autonomous DNA computation. In principle, growth can be programmed by designing a set of molecular tiles with binding
interactions that enforce assembly rules. In practice, however, errors during assembly cause undesired products, drastically reducing yields.
Here we provide experimental evidence that assembly can be made more robust to errors by adding redundant tiles that "proofread" assembly.
We construct DNA tile sets for two methods, uniform and snaked proofreading. While both tile sets are predicted to reduce errors during
growth, the snaked proofreading tile set is also designed to reduce nucleation errors on crystal facets. Using atomic force microscopy to
image growth of proofreading tiles on ribbon-like crystals presenting long facets, we show that under the physical conditions we studied the
rate of facet nucleation is 4-fold smaller for snaked proofreading tile sets than for uniform proofreading tile sets
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