The changes in chemical composition during development of the bovine nuchal ligament

Whole bovine nuchal ligaments, or portions thereof (in the case of commercially valuable animals), were obtained from 45 animals (28 fetal and 17 postnatal) ranging in age from 110 days of gestation to 10 yr. Insoluble elastin was quantitatively prepared from the fresh ligaments by extraction with hot alkali and by a combination of multiple extractions with alkaline buffer and then repeated autoclaving. When adult samples were examined, the yields of insoluble residue by these two methods were very similar, but with young fetal samples the second method gave significantly higher values, because of incomplete purification of the elastin residue. The changes in the concentration of collagen, alkali-insoluble elastin, and DNA have been examined. DNA concentration, and, thus, cell population density, fell progressively during the fetal period of development, to reach a steady value soon after birth. Collagen appeared in appreciable quantities before elastin, but its concentration was rapidly halved at about the time of birth. Insoluble elastin concentration was low until the end of the 7th fetal month, at which time it began to rise rapidly. The rate of increase in elastin concentration remained high throughout the next 10–12 wk, by which time the adult value had been reached. Quantitative studies, on the basis of the whole ligament, showed that the total cell content rises to a maximum at birth, but falls soon after to a level about half that at birth. Total collagen production and elastin deposition continue at a steady, maximal rate over the interval from 235 days of gestation to the end of the 1st postnatal month. It is concluded that the immediate postnatal period would be the most favorable phase in which to attempt the isolation of the soluble precursor elastin

Finitely generated ideal languages and synchronizing automata

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2^n states, where n is the maximal length of words in L. Our constructions are based on the De Bruijn graph.Comment: Submitted to WORDS 201

Multiple Loop Self-Triggered Model Predictive Control for Network Scheduling and Control

We present an algorithm for controlling and scheduling multiple linear time-invariant processes on a shared bandwidth limited communication network using adaptive sampling intervals. The controller is centralized and computes at every sampling instant not only the new control command for a process, but also decides the time interval to wait until taking the next sample. The approach relies on model predictive control ideas, where the cost function penalizes the state and control effort as well as the time interval until the next sample is taken. The latter is introduced in order to generate an adaptive sampling scheme for the overall system such that the sampling time increases as the norm of the system state goes to zero. The paper presents a method for synthesizing such a predictive controller and gives explicit sufficient conditions for when it is stabilizing. Further explicit conditions are given which guarantee conflict free transmissions on the network. It is shown that the optimization problem may be solved off-line and that the controller can be implemented as a lookup table of state feedback gains. Simulation studies which compare the proposed algorithm to periodic sampling illustrate potential performance gains.Comment: Accepted for publication in IEEE Transactions on Control Systems Technolog

Synchronizing automata with random inputs

We study the problem of synchronization of automata with random inputs. We present a series of automata such that the expected number of steps until synchronization is exponential in the number of states. At the same time, we show that the expected number of letters to synchronize any pair of the famous Cerny automata is at most cubic in the number of states

Complexity of checking whether two automata are synchronized by the same language

A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.Comment: 12 pages, 4 figure