On grammar forms with terminal context

Summary A context-free grammar form G defines a family of context-free grammars {ie397-01}(G). In this paper {ie397-02}(G) is extended to give the family of terminal context grammars {ie397-03}(G), which were introduced by Book [4]. It is shown that the families of languages defined by {ie397-04}(G) and {ie397-05}(G) are equal when G is an -free context-free grammar form. This generalizes the result of Book [4] for context-free grammars and underlines the usefulness of the notion of grammar forms in formal language theory.The work of the second author was carried out partially under a National Research Council of Canada Grant. No. A-7700 and partially under the auspices of the University of Karlsruhe     

On a direct algorithm for the generation of log-normal pseudo-random numbers

The random variable \(\left( {\prod {_{i = 1}^n {{X_i } \mathord{\left/ {\vphantom {{X_i } {X_{i + n} }}} \right. \kern-0em} {X_{i + n} }}} } \right)^{{1 \mathord{\left/ {\vphantom {1 {\sqrt {2n} }}} \right. \kern-0em} {\sqrt {2n} }}}\) is used to generate standard log-normal variables Λ(0, 1), where theX _i are independent uniform variables on [0, 1].     

Polynomoperatoren in C k [a,b]

Some estimations for the relative projection constantP(∏ _n+k ^k ,Csik[a,b]) are given. By constructing an associated polynomial operatorL _n :C ⁰[a,b]→∏ _n ⁰ to a given polynomial operatorH _n+k :C ^k [a,b]→∏ _n+k ^k we get a lower bound for the projection constant. An upper bound forP(∏ _n+k ^k ,C ^k [a,b]) is obtained by the determination of the norms of appropriate polynomial operatorsP _n+k :C ^k [a,b]→∏ _n+k ^k . Further we give a convergence property for the sequence (P _n+k ) _n∈?.     

Einleitung und Abbruch der künstlichen Ernährung beim einwilligungsunfähigen Patienten

Definition of the problem: In Austria the legal discussion on initiating and withdrawing artificial nutrition in incompetent patients has just begun. Arguments and conclusion: Legal regulations are lacking, but there appears to be agreement on accepting advance directives under specific criteria. This would mean that a presumed will and documented refusal of treatment and nutrition has to be respected by physicians. However, there is no consensus with regard to the “supposed will” of an incompetent patient to refuse treatment and nutrition. At present, surrogate decision making with regard to refusing life-sustaining treatment or nutrition is only accepted according to a declared and documented directive of the patient himself. When the patient’s will has to be “surmised” the protection of life has priority. In Austria this concept is based on the national constitution and its duty to protect life.     

Software specification using graph grammars

The following paper demonstrates that programmed sequential graph grammars can be used in a systematic proceeding to specify the changes of high level intermediate data structures arising in a programming support environment, in which all tools work in an incremental and syntax-driven mode. In this paper we lay stress upon the way to get the specification rather than on the result of this process. Therefore, we give here some approach to “specification engineering” using graph grammars. This approach is influenced by the syntactical definition of the underlying language for Programming in the Small, the module concept etc. to be supported on one side but also by the idea of the user interface.     

Hyperinsulinemic Hypoglycemia Associated with a CaV1.2 Variant with Mixed Gain- and Loss-of-Function Effects

The voltage-dependent L-type calcium channel isoform Ca_V1.2 is critically involved in many physiological processes, e.g., in cardiac action potential formation, electromechanical coupling and regulation of insulin secretion by beta cells. Gain-of-function mutations in the calcium voltage-gated channel subunit alpha 1 C (CACNA1C) gene, encoding the Ca_V1.2 α₁-subunit, cause Timothy syndrome (TS), a multisystemic disorder that includes autism spectrum disorders and long QT (LQT) syndrome. Strikingly, TS patients frequently suffer from hypoglycemia of yet unproven origin. Using next-generation sequencing, we identified a novel heterozygous CACNA1C mutation in a patient with congenital hyperinsulinism (CHI) and associated hypoglycemic episodes. We characterized the electrophysiological phenotype of the mutated channel using voltage-clamp recordings and in silico action potential modeling experiments. The identified Ca_V1.2^L566P mutation causes a mixed electrophysiological phenotype of gain- and loss-of-function effects. In silico action potential modeling supports that this mixed electrophysiological phenotype leads to a tissue-specific impact on beta cells compared to cardiomyocytes. Thus, CACNA1C variants may be associated with non-syndromic hyperinsulinemic hypoglycemia without long-QT syndrome, explained by very specific electrophysiological properties of the mutated channel. We discuss different biochemical characteristics and clinical impacts of hypoglycemia in the context of CACNA1C variants and show that these may be associated with significant morbidity for Timothy Syndrome patients. Our findings underline that the potential of hypoglycemia warrants careful attention in patients with CACNA1C variants, and such variants should be included in the differential diagnosis of non-syndromic congenital hyperinsulinism.