6,294 research outputs found
How regular can maxitive measures be?
We examine domain-valued maxitive measures defined on the Borel subsets of a
topological space. Several characterizations of regularity of maxitive measures
are proved, depending on the structure of the topological space. Since every
regular maxitive measure is completely maxitive, this yields sufficient
conditions for the existence of a cardinal density. We also show that every
outer-continuous maxitive measure can be decomposed as the supremum of a
regular maxitive measure and a maxitive measure that vanishes on compact
subsets under appropriate conditions.Comment: 24 page
Integrated and Differentiated Spaces of Triangular Fuzzy Numbers
Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely
possibility theory, and of a versatile tool for both linguistic and numerical
modeling. Numerous works now combine fuzzy concepts with other scientific
disciplines as well as modern technologies. In mathematics, fuzzy sets have
triggered new research topics in connection with category theory, topology,
algebra, analysis. In this paper, we use the triangular fuzzy numbers for
matrix domains of sequence spaces with infinite matrices. We construct the new
space with triangular fuzzy numbers and investigate to structural, topological
and algebraic properties of these spaces.Comment: 10 pages, 17 reference
Toward a multilevel representation of protein molecules: comparative approaches to the aggregation/folding propensity problem
This paper builds upon the fundamental work of Niwa et al. [34], which
provides the unique possibility to analyze the relative aggregation/folding
propensity of the elements of the entire Escherichia coli (E. coli) proteome in
a cell-free standardized microenvironment. The hardness of the problem comes
from the superposition between the driving forces of intra- and inter-molecule
interactions and it is mirrored by the evidences of shift from folding to
aggregation phenotypes by single-point mutations [10]. Here we apply several
state-of-the-art classification methods coming from the field of structural
pattern recognition, with the aim to compare different representations of the
same proteins gathered from the Niwa et al. data base; such representations
include sequences and labeled (contact) graphs enriched with chemico-physical
attributes. By this comparison, we are able to identify also some interesting
general properties of proteins. Notably, (i) we suggest a threshold around 250
residues discriminating "easily foldable" from "hardly foldable" molecules
consistent with other independent experiments, and (ii) we highlight the
relevance of contact graph spectra for folding behavior discrimination and
characterization of the E. coli solubility data. The soundness of the
experimental results presented in this paper is proved by the statistically
relevant relationships discovered among the chemico-physical description of
proteins and the developed cost matrix of substitution used in the various
discrimination systems.Comment: 17 pages, 3 figures, 46 reference
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
Covariant fuzzy observables and coarse-graining
A fuzzy observable is regarded as a smearing of a sharp observable, and the
structure of covariant fuzzy observables is studied. It is shown that the
covariant coarse-grainings of sharp observables are exactly the covariant fuzzy
observables. A necessary and sufficient condition for a covariant fuzzy
observable to be informationally equivalent to the corresponding sharp
observable is given.Comment: 19 page
Inclusion hyperspaces and capacities on Tychonoff spaces: functors and monads
The inclusion hyperspace functor, the capacity functor and monads for these
functors have been extended from the category of compact Hausdorff spaces to
the category of Tychonoff spaces. Properties of spaces and maps of inclusion
hyperspaces and capacities (non-additive measures) on Tychonoff spaces are
investigated
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