This article presents a theorem about the topological conjugacy of a gradient dynamical system with a constant time step and the cascade generated by its Euler method. It is shown that on the two-dimensional sphere S² the gradient dynamical flow is, under some natural assumptions, correctly reproduced by the Euler method for a sufficiently small time step. This means that the time-map of the induced dynamical system is globally topologically conjugate to the discrete dynamical system obtained via the Euler method.
Relations between theory and empirical knowledge belong to basic problemsin philosophy of science and have been undergone detailed philosophical reflection,including epistemological aspects. During last several dozen years,due to development of computer technology, numerical simulations becamea common tool in natural sciences. Their epistemological aspects, however,have not worked out yet. A specific role of computer simulations manifestsin subcellular biology, where possibilities of performing experiments and observationsare limited. Computer simulation is complementary to observationand experiment and comes into complex relations with them. It allows us tocome to a conclusion if experiment or observations are impossible to perform.In particular, simulations allow researchers to estimate the parameters thatcannot be measured.
In this paper the life phenomenon is analysed from cybernetic point of view. The Korzeniewski’s approach is discussed and complemented. The analysis is based on autonomous systems theory and information metabolism theory. Philosophical aspects of the problem are taken into consideration as well.
The trouble of proving the effects of participation lies in the mismatch between three aspects of ownership: physical (possession), legal (ownership proper) and psychological (participation). In our interdisciplinary systemic model of ownership, we propose 10 relationships related to ownership/participation from: „A is a part of B” - greatest involvement to „A does not know about B” - the least involvement. „A” and „B” may take different values of: a person, an institution, a community, a group, an object (material, energetic, informational, purchasing). Once formalized we can view the studies in participation from one, system theory point of view, and formulate hypotheses related to many aspects of ownership. A multilevel analysis with multiple measures of both participation and effectiveness from two data sets has supported the proposed model.
The trouble of proving the effects of participation lies in the mismatch between three aspects of ownership: physical (possession), legal (ownership proper) and psychological (participation). In our interdisciplinary systemic model of ownership, we propose 10 relationships related to ownership/participation from: „A is a part of B” - greatest involvement to „A does not know about B” - the least involvement. „A” and „B” may take different values of: a person, an institution, a community, a group, an object (material, energetic, informational, purchasing). Once formalized we can view the studies in participation from one, system theory point of view, and formulate hypotheses related to many aspects of ownership. A multilevel analysis with multiple measures of both participation and effectiveness from two data sets has supported the proposed model.
In this paper, the concept of structural information is presented. The mathematical foundation of the concept is put forward, and the nature of information encoded in a structure is studied. A method for calculating the amount of structural information is introduced. An application to the analysis of cognitive maps is also presented and discussed.
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