Let S be a closed convex set of matrices and C be a given matrix. The matrix nearness problem considered in this paper is to find a matrix X in the set S at which max {|xij − cij |} reaches its minimum value. In order to solve the matrix nearness problem, the problem is reformulated to a min-max problem firstly, then the relationship between the min-max problem and a monotone linear variational...

The development of cognitively plausible models of human spatial reasoning may ultimately result in computational systems that are better equipped to meet human needs. This paper explores how human subjects perceive the qualitative spatial relation nearness within an environmental space. Based on experimental data, a three-valued nearness relation is analysed in two stages. First, the results a...

An important step in the solution of a matrix nearness problem that arises in certain machine learning 3 applications is finding the zero of f(α) = z exp(logX + αzz )z − b. The matrix valued exponential and logarithm 4 in f(α) arises from the use of the von Neumann matrix divergence tr(X logX − X log Y − X + Y ) to measure the 5 nearness between the positive definite matrices X and Y . A key st...

To avoid the false results of deterministic identification methods induced by uncertainties, a fuzzy nearness-based method is proposed for the damage identification of bridge. An improved index based on ratios of modal shape components is used as identification measurements. The knowledge base for damage identification is established through corresponding relationship between fuzzified measurem...

The theory of formal spaces and the more recent theory of apartness spaces have a priori not much more in common than that each of them was initiated as a constructive approach to general topology. We nonetheless try to do the first steps in relating these competing theories to each other. Formal topology was put forward in the mid 1980s by Sambin [8] in order to make available to Martin–Löf’s ...

Smart spaces of the future will consist of a large number of computing devices intelligently communicating with each other to perform various day-to-day tasks. Selforganization of these devices to form task-oriented clusters is a necessity as these devices grow in number. Given a rich collection of mobile tetherless smart-devices, it is important to investigate schemes for task-based self-organ...

Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high dimensional spaces. We consider the case where data is drawn from sampling a probability distribution that has support on or near a submanifold of Euclidean space. We show how to “learn” the homology of the submanifold with high confidence. We discuss an algorithm to do this and provide lear...