In a given graph G = (V, E), a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G, if there exists a unique extension of the colors of S to a c ≥ χ(G) coloring of the vertices of G. A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number, denoted by d(G, c). The d(G = Cm × Kn...

The (2, F) generalized Fibonacci sequences were defined in [1] and [2]. In [3] K. Atanassov extended the definition to the case of three sequences and listed thirty-six systems defining the (3, F) generalized Fibonacci sequences. Ten of these thirty-six systems were discarded as trivial and the remaining twenty-six were placed in seven classes termed "groups." In this paper the structure of the...

Some researchers argue that task switching involves task-set reconfiguration--that is, changing the existing task set to perform a different task. Although this idea is intriguing, it is often unclear what is reconfigured and which processes are involved in reconfiguration. We addressed these issues by defining task sets, identifying differences between them, and obtaining evidence that was dia...

BACKGROUND Gene set enrichment analysis (GSEA) is an analytic approach which simultaneously reduces the dimensionality of microarray data and enables ready inference of the biological meaning of observed gene expression patterns. Here we invert the GSEA process to identify class-specific gene signatures. Because our approach uses the Kolmogorov-Smirnov approach both to define class specific sig...

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperp...

Over the last several years there have been consistent calls for a consensus definition and classification system for the syndrome now known as acute kidney injury (AKI) [1,2]. The major aim of such a system, it was argued, would be to bring this major intensive care syndrome to a standard of definition and a level of classification similar to that achieved by other common ICU syndromes (e.g. s...