In the present paper, we study frames for finite-dimensional vector spaces over an arbitrary field. We develop a theory of dual in order to obtain and different representations elements space provided by frame. relate introduced with classical one Hilbert apply it three types spaces: conjugate closed subfields complex numbers (in particular, cyclotomic fields), metric spaces, ultrametric normed...

In 1970 Friedman proved completeness of beta eta conversion in the simply-typed lambda calculus for the set-theoretical model. Recently Krishnaswami and Benton have captured the essence of Hudak’s reactive programs in an extension of simply typed lambda calculus with causal streams and a temporal modality and provided this typed lambda calculus for reactive programs with a sound ultrametric sem...

Partitioning of graphs has many practical applications namely in cluster analysis and in automated design of VLSI circuits. Using l-l correspondence between ultrametric partitions of a weighted complete graph K(w) on a finite set X and ultrametrics on X, the computational complexity of the approximation of w by means of an ultrametric u is investigated and systematized. As a main result. a poly...

We mathematically model Ignacio Matte Blanco’s principles of symmetric and asymmetric being through use of an ultrametric topology. We use for this the highly regarded 1975 book of this Chilean psychiatrist and pyschoanalyst (born 1908, died 1995). Such an ultrametric model corresponds to hierarchical clustering in the empirical data, e.g. text. We show how an ultrametric topology can be used a...

This paper presents a new procedure called TREEFAM for estimating ultrametric tree structures from proximity data confounded by differential stimulus familiarity. The objective of the proposed TREEFAM procedure is to quantitatively "filter out" the effects of stimulus unfamiliarity in the estimation of an ultrametric tree. A conditional, alternating maximum likelihood procedure is formulated to...

We show how to decompose all separable ultrametric spaces into a “Lego” combinations of scaled versions full simplices. To do this we introduce metric resolutions spaces, which describe space can be broken up roughly independent pieces. use these define the coarse disjoint union provides way attaching large scale each other in “coarsely way”. notions construct universal categories and proper as...

A hierarchical clustering method is stable if small perturbations on the data set produce small perturbations in the result. This perturbations are measured using the Gromov-Hausdorff metric. We study the problem of stability on linkage-based hierarchical clustering methods. We obtain that, under some basic conditions, standard linkage-based methods are semi-stable. This means that they are sta...

The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free ...