Ladislav Mišík

Adaptive population-based search: Application to estimation of nonlinear regression parameters

Algorithms for the estimation of nonlinear regression parameters are considered. Adaptive population-based search algorithms are proposed and implemented in deriving reliable estimates at a reasonable time with default setting of their controlling parameters. The algorithms are tested on the NIST collection of data sets containing 27 nonlinear regression tasks of various level of difficulty. The experimental results show that both algorithms with competing heuristics are significantly more reliable as compared with the algorithm based on Levenberg-Marquardt optimizing procedure.

Gleason's theorem and completeness of inner product spaces

We generalize the result of Hamhalter and Pták showing that an inner product space whose dimension is either a nonmeasurable cardinal or an arbitrary cardinal is complete iff its lattice of strongly closed subspaces possesses at least one state or one completely additive state, respectively. Moreover, we show that this lattice of any separable space possesses manyσ-finite measures, and we give the Gleason analogue for them.

Cluster points of sequences of fuzzy real numbers

Properties of cluster points of sequences of fuzzy real numbers are investigated in the paper. It is shown that some similar theorems like in the case of real sequences hold. On the other hand, some differences from real case are discussed.

Distribution functions of ratio sequences, IV

AbstractIn this paper we continue our study of distribution functions g(x) of the sequence of blocks

Extreme points of the set of density measures

X_n = (\tfrac{{x_1 }} {{x_n }},\tfrac{{x_2 }} {{x_n }},...,\tfrac{{x_n }} {{x_n }})

Open Problems on Densities II

, n = 1, 2, …, where xn is an increasing sequence of positive integers. Applying a special algorithm we find a lower bound of g(x) also for xn with lower asymptotic density

Evolutionary Algorithms with Competing Heuristics in Computational Statistics

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On Small Sets of Distribution Functions of Ratio Block Sequences

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On Hausdorff Dimensions Related to Sets with Given Asymptotic and Gap Densities

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Some generalizations of Olivier's theorem

= 0. This extends the lower bound of g(x) for xn with