To distinguish continuous from discontinuous evolutionary change, a relation of nearness between phenotypes is needed. Such a relation is based on the probability of one phenotype being accessible from another through changes in the genotype. This nearness relation is exemplified by calculating the shape neighborhood of a transfer RNA secondary structure and provides a characterization of disco...

Conditioning of a nonsingular matrix subspace is addressed in terms of its best conditioned elements. Computationally the problem is seemingly challenging. By associating with the task an intersection problem with unitary matrices leads to a more accessible approach. A resulting matrix nearness problem can be viewed to generalize the so-called Löwdin problem in quantum chemistry. For critical p...

An axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for topology.

The nearness diagram (ND) navigation method is a reactive navigation method used for obstacle avoidance in which five different robot-environment states are defined and five corresponding actions are designed carefully. In the ND+ navigation method, one more robot-environment state is added and all action equations are reformed to both achieve smoother robot motions and reduce manual parameter ...

Finding concepts that are similar to a given concept can prove useful in constructing user-friendly interfaces for querying DLontologies—the concrete use case being a query answering system with an enhanced user interface that suggests semantically relevant keywords (based on concept similarity) during query formulation. Most investigations on the similarity of concepts rely on ad-hoc and non-r...

This paper discusses a new class of matrix nearness problems that measure approximation error using a directed distance measure called a Bregman divergence. Bregman divergences offer an important generalization of the squared Frobenius norm and relative entropy, and they all share fundamental geometric properties. In addition, these divergences are intimately connected with exponential families...