Higher-dimensional tree structures

AbstractVarious generalizations of tree-characterization theorems are developed for n-dimensional complexes. In particular, generalizations of three conditions satisfied by trees T are studied: T is connected, T is acyclic, |V(T)| − |E(T)| = 1, where V(T) and E(T) denote the vertex and edge sets of T, respectively.Earlier work by Beineke and Pippert is extended in generalizing these conditions and studying which combinations of such conditions yield characterizations of the n-dimensional trees treated here

Measurement in biological systems from the self-organisation point of view

Measurement in biological systems became a subject of concern as a consequence of numerous reports on limited reproducibility of experimental results. To reveal origins of this inconsistency, we have examined general features of biological systems as dynamical systems far from not only their chemical equilibrium, but, in most cases, also of their Lyapunov stable states. Thus, in biological experiments, we do not observe states, but distinct trajectories followed by the examined organism. If one of the possible sequences is selected, a minute sub-section of the whole problem is obtained, sometimes in a seemingly highly reproducible manner. But the state of the organism is known only if a complete set of possible trajectories is known. And this is often practically impossible. Therefore, we propose a different framework for reporting and analysis of biological experiments, respecting the view of non-linear mathematics. This view should be used to avoid overoptimistic results, which have to be consequently retracted or largely complemented. An increase of specification of experimental procedures is the way for better understanding of the scope of paths, which the biological system may be evolving. And it is hidden in the evolution of experimental protocols.Comment: 13 pages, 5 figure

The Magic machine: a handbook of computer sorcery

xviii+357hlm.;23c