Abstract Context The F-measure has been widely used as a performance metric when selecting binary classifiers for prediction, but it also criticized, especially given the availability of alternatives such ϕ (also known Matthews Correlation Coefficient). Objectives Our goals are to (1) investigate possible issues related in depth and show how can address them, (2) explore relationships between ....

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

On a Lebesgue measure space with measure element do, and total measure finite or infinite, we consider the complex-valued measurable functions f, y, so, ., each determined only a.e., and each belonging to all L,-classes simultaneously, 1<r< a. We donote (i) by F = {f} a ring of functions with complex constants and ordinary multiplication and closed under the involution: if f -= f + if2 e F then...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

Let (AZ, F ) be a bipermutative algebraic cellular automaton. We present conditions which force a probability measure which is invariant for the N×Z-action of F and the shift map σ to be the Haar measure on Σ, a closed shift-invariant subgroup of the Abelian compact group AZ. This generalizes simultaneously results of B. Host, A. Maass and S. Mart́ınez [7] and M. Pivato [14]. This result is appl...

SpatialML is an annotation scheme for marking up references to places in natural language. It covers both named and nominal references to places, grounding them where possible with geo-coordinates, including both relative and absolute locations, and characterizes relationships among places in terms of a region calculus. A freely available annotation editor has been developed for SpatialML, alon...

If f is a measurable transformation of a Lebesgue measure space (X,A, λ) to itself, that does not preserve the measure λ, one can study the invariant measures of f and compare them to λ. A especially interesting case is when f is non-singular with respect to λ (in the sense thatλ(A) = 0 iff λ( f(A)) = 0), but nevertheless there exist no σ-finite invariant measure which is absolutely continuous ...