1. INTRODUCTION. It has become a truism, at least among statisticians, that while statistics is a mathematical science, it is not a subfield of mathematics. We even have apho-risms to express some ways in which our science differs from mathematics. George Box: " All models are wrong, but some are useful. " George Cobb: " In mathematics, context obscures structure. In data analysis, context prov...

A popular approach to significance testing proposes to decide whether the given hypothesized statistical model is likely to be true (or false). Statistical decision theory provides a basis for this approach by requiring every significance test to make a decision about the truth of the hypothesis/model under consideration. Unfortunately, many interesting and useful models are obviously false (th...

For 1 ≤ d ≤ ` < k, we give a new lower bound for the minimum d-degree threshold that guarantees a Hamilton `-cycle in k-uniform hypergraphs. When k ≥ 4 and d < ` = k − 1, this bound is larger than the conjectured minimum d-degree threshold for perfect matchings and thus disproves a wellknown conjecture of Rödl and Ruciński. Our (simple) construction generalizes a construction of Katona and Kier...

Forbidding-enforcing systems (fe-systems) define classes of languages (fe-families) based on boundary conditions. We characterize f -families having not necessarily finite forbidders and prove that none of the Chomsky families of languages can be defined with an fe-system, hence, fe-systems provide a completely new way of defining classes of languages. We show that f -families map to f -familie...

Motivated by biomolecular computing, forbidding-enforcing systems (fe-systems) were first used to define classes of languages (fefamilies) based on boundary conditions. This paper presents a new model of fe-systems in which fe-systems define single languages (fe-languages) based on forbidden and enforced subwords. The paper characterizes wellknown languages by fe-systems, investigates the relat...

This paper introduces a new way of modeling classes of physical and biochemical processes and structures based on boundary conditions that are called ‘‘forbidden’’ and ‘‘enforced’’. The model of forbidding–enforcing systems (fe-systems) is presented in a general categorical sense and we use three specific examples of categories to illustrate three different phenomena. The hydrogen and covalent ...

This paper introduces FE0L (forbidding context-free L systems) and FET0L (FE0L systems with tables) systems with permitting conditions and the algorithm for reducing the number of the nonterminal symbols in FE0L (FET0L) systems. The productions of FE0L (FET0L) systems (grammars) do not have only the forbidding conditions but also other attached strings, called permitting conditions. The derivat...