Let us assume we are given a pairwise Maxwell, quasi-simply r-tangential functional z. Recent developments in Galois analysis [3] have raised the question of whether ζ is partially stochastic. We show that every pairwise contra-Fermat polytope is non-locally abelian. Is it possible to extend everywhere irreducible, Kronecker rings? It was Poisson who first asked whether almost surely Kronecker ...

Even though the logratio methodology provides a range of both generic, mostly exploratory, and purpose-built coordinate representations compositional data, simple pairwise logratios are preferred by many for multivariate analysis in geochemical practice, principally because their simpler interpretation. However, systems that incorporate them predominantly oblique, resulting conceptual practical...

We discuss property-driven non-numerical ranking by rough set partial order approximations and present property-consistency driven algorithm for the non-numerical ranking based on the pairwise comparisons.

A number of space-time codes have been recently proposed for the quasi-static, flat-fading, multipleantenna wireless channel with coherent receiver. In this paper we will focus on design of space-time codes that are linear in the scalar input symbols. We provide design criteria that take into account both the error probability and the channel capacity. We consider the error probability via the ...

We give a new asymptotic upper bound on the size of a code in the Grassmannian space. The bound is better than the upper bounds known previously in the entire range of distances except very large values. the problem of estimating the number of planes whose pairwise distances are bounded below by some given value δ, for a suitably defined distance function d(p, q). This problem has attracted att...

SVM-Pairwise was a major breakthrough in remote homology detection techniques, significantly outperforming previous approaches. This approach has been extensively evaluated and cited by later works, and is frequently taken as a benchmark. No known work however, has examined the gap penalty model employed by SVM-Pairwise. In this paper, we study in depth the relevance and effectiveness of SVM-Pa...

The area under the ROC curve (AUC) is a widely used performance measure in machine learning, and has been widely studied in recent years particularly in the context of bipartite ranking. A dominant theoretical and algorithmic framework for AUC optimization/bipartite ranking has been to reduce the problem to pairwise classification; in particular, it is well known that the AUC regret can be form...

We present a PTAS for computing the maximum a posteriori assignment on Pairwise Markov Random Fields with non-negative weights in planar graphs. This algorithm is practical and not far behind state-of-the-art techniques in image processing. MAP on Pairwise Markov Random Fields with (possibly) negative weights cannot be approximated unless P = NP, even on planar graphs. We also show via reductio...