Wyniki wyszukiwania - BazTech

1

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks

Klęsk P.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 3

525-544

EN

Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic probabilities of discrepancy between these minima for given for given conditions of an experiment. The probabilities are calculated in terms of all relevant constants: the sample size, the number of cross-validation folds, the capacity of the set of approximating functions and bounds on this set. We report experiments carried out to validate the results.

2

Information dynamics. Premises, Challenges and Results

Sobczyk K.

Prace Instytutu Podstawowych Problemów Techniki PAN

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2000

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nr 2

1-32

EN

In various fields of contemporary research information and dynamics are becoming the key terms. Theoretic information reasoning is well known in physics, especially in thermodynamics where the relationship between the statistical (or, informational) entropy of the system and its thermodynamical entropy has been studied since a long time. Information theory is especially relevant to data processing and statistical inference. Generally speaking, the apparatus of information theory is applicable to any probabilistic system of observations since whenever we make statistical observations (or design and conduct statistical experiments) we seek information. When the language of information theory (the concepts of enropy, mutual information between random variables and processes, information rate, maximum entropy formalism, information flow etc.) is used in connection with system dynamics we come to the notion of information dynamics. The objective of this report is to show a potential of the basic information theoretic methodology for the analysis of various problems of system dynamics. In particular, we wish to indicate some challenges and expound our recent results on the maximum information entropy approach to the analysis of stochastic dynamical systems.

3

Statistical modelling of rough surfaces and finite element contact analysis

Buczkowski R.

Prace Instytutu Podstawowych Problemów Techniki PAN

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1999

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nr 3

3-118

EN

In the present work statistical aspects of the micromechanics of normal and tangential models between metallic rough surfaces are described. A detailed statistical analysis of rough surfaces is performed in terms of asperity (peak or summit) distribution and the distribution of curvature at the asperities. A random surface model of asperities with the Gaussian height distribution combined with mechanical description of a single peak based on the Hertz theory coupled with the Mindlin friction theory is investigated. The complete description of anisotropic random surfaces is restricted here to strongly rough surfaces; for such surfaces the summits are represented by highly eccentric elliptic paraboloids having their semimajor axes oriented in the derection of the grain. Some of the limitations of early contact models have been successively overcome by more generalized model in order to incorporate the deformation of asperities to be assumed elasto-plastic. Because the 20-node solid element of serendipity family does not fulfill the physical contact requirements properly (the equivalent nodal forces include negative values) an original 21-node three-dimensional transient element for contact problem was developed. The quadratic line and plane zero-thickness diagonal joint elements obtained by Lobatto integration scheme have been implemented for simulation of the displacement discontinuity at the contact syrface (separation, slip along the interface). Essentially most of the study is devoted to the three-dimensional contact analysis taking into account the anisotropic properties between two contacting bodies in presence of the unilateral contact conditions and non-linear friction coefficients in both the principal tangential directions. The statistical contact algorithms have been coded into both workstation Sun Ultra 1 and supercomputer SGI Power Challenge XL finite element programs for static 2D- and 3D- dimensional elasto-plastic contact analysis. Some examples have been selected to demonstrate applicability of the proposed method.