53,209 research outputs found
Characterization of order-like dependencies with formal concept analysis
Functional Dependencies (FDs) play a key role in many fields
of the relational database model, one of the most widely used database
systems. FDs have also been applied in data analysis, data quality, knowl-
edge discovery and the like, but in a very limited scope, because of their
fixed semantics. To overcome this limitation, many generalizations have
been defined to relax the crisp definition of FDs. FDs and a few of their
generalizations have been characterized with Formal Concept Analysis
which reveals itself to be an interesting unified framework for charac-
terizing dependencies, that is, understanding and computing them in a
formal way. In this paper, we extend this work by taking into account
order-like dependencies. Such dependencies, well defined in the database
field, consider an ordering on the domain of each attribute, and not sim-
ply an equality relation as with standard FDs.Peer ReviewedPostprint (published version
characterization of order-like dependencies with formal concept analysis
Functional Dependencies (FDs) play a key role in many fields of the relational database model, one of the most widely used database systems. FDs have also been applied in data analysis, data quality, knowledge discovery and the like, but in a very limited scope, because of their fixed semantics. To overcome this limitation, many generalizations have been defined to relax the crisp definition of FDs. FDs and a few of their generalizations have been characterized with Formal Concept Analysis which reveals itself to be an interesting unified framework for characterizing dependencies, that is, understanding and computing them in a formal way. In this paper, we extend this work by taking into account order-like dependencies. Such dependencies, well defined in the database
field, consider an ordering on the domain of each attribute, and not simply an equality relation as with standard FDsPostprint (published version
Complexity, BioComplexity, the Connectionist Conjecture and Ontology of Complexity\ud
This paper develops and integrates major ideas and concepts on complexity and biocomplexity - the connectionist conjecture, universal ontology of complexity, irreducible complexity of totality & inherent randomness, perpetual evolution of information, emergence of criticality and equivalence of symmetry & complexity. This paper introduces the Connectionist Conjecture which states that the one and only representation of Totality is the connectionist one i.e. in terms of nodes and edges. This paper also introduces an idea of Universal Ontology of Complexity and develops concepts in that direction. The paper also develops ideas and concepts on the perpetual evolution of information, irreducibility and computability of totality, all in the context of the Connectionist Conjecture. The paper indicates that the control and communication are the prime functionals that are responsible for the symmetry and complexity of complex phenomenon. The paper takes the stand that the phenomenon of life (including its evolution) is probably the nearest to what we can describe with the term “complexity”. The paper also assumes that signaling and communication within the living world and of the living world with the environment creates the connectionist structure of the biocomplexity. With life and its evolution as the substrate, the paper develops ideas towards the ontology of complexity. The paper introduces new complexity theoretic interpretations of fundamental biomolecular parameters. The paper also develops ideas on the methodology to determine the complexity of “true” complex phenomena.\u
Topological inference for EEG and MEG
Neuroimaging produces data that are continuous in one or more dimensions.
This calls for an inference framework that can handle data that approximate
functions of space, for example, anatomical images, time--frequency maps and
distributed source reconstructions of electromagnetic recordings over time.
Statistical parametric mapping (SPM) is the standard framework for whole-brain
inference in neuroimaging: SPM uses random field theory to furnish -values
that are adjusted to control family-wise error or false discovery rates, when
making topological inferences over large volumes of space. Random field theory
regards data as realizations of a continuous process in one or more dimensions.
This contrasts with classical approaches like the Bonferroni correction, which
consider images as collections of discrete samples with no continuity
properties (i.e., the probabilistic behavior at one point in the image does not
depend on other points). Here, we illustrate how random field theory can be
applied to data that vary as a function of time, space or frequency. We
emphasize how topological inference of this sort is invariant to the geometry
of the manifolds on which data are sampled. This is particularly useful in
electromagnetic studies that often deal with very smooth data on scalp or
cortical meshes. This application illustrates the versatility and simplicity of
random field theory and the seminal contributions of Keith Worsley
(1951--2009), a key architect of topological inference.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS337 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Characterization of Order-like Dependencies with Formal Concept Analysis
Abstract. Functional Dependencies (FDs) play a key role in many fields of the relational database model, one of the most widely used database systems. FDs have also been applied in data analysis, data quality, knowledge discovery and the like, but in a very limited scope, because of their fixed semantics. To overcome this limitation, many generalizations have been defined to relax the crisp definition of FDs. FDs and a few of their generalizations have been characterized with Formal Concept Analysis which reveals itself to be an interesting unified framework for characterizing dependencies, that is, understanding and computing them in a formal way. In this paper, we extend this work by taking into account order-like dependencies. Such dependencies, well defined in the database field, consider an ordering on the domain of each attribute, and not simply an equality relation as with standard FDs
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