A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics

Sample pathwise numerical integration of noise-driven engineering dynamical systems cannot generally be performed beyond a limited level of accuracy, especially when the noise processes are modelled using (filtered) white noises. Recently, a locally transversal linearization (LTL) strategy has been proposed by the author (Proc Roy Soc London A 2001; 457 :539–566) for direct integration of deterministic and stochastic non-linear dynamical systems. The present effort is focussed on a host of extensions along with detailed theoretical error analyses of the linearization approach, especially as applied to problems in non-linear stochastic engineering dynamics. Thus, to begin with, estimates of local and global error orders in the basic LTL scheme are obtained separately for the displacement and velocity vectors when the system is driven either by a set of additive noises or by an arbitrary combination of (independently evolving) additive and multiplicative noises. Following this, a new family of higher-order LTL schemes is proposed in order to improve upon the basic LTL method and the associated error orders are established. A stepwise implementation of the lower- and higher-order versions of the LTL method, along with certain computational aspects, is also outlined. The proposed schemes are numerically illustrated, to a limited extent, for a single degree-of-freedom (SDOF) and a two degree-of-freedom (TDOF) non-linear engineering systems under additive and/or multiplicative white noise excitations. Copyright © 2004 John Wiley & Sons, Ltd.     

A dynamic programming method for building free algebras

We are interested in deciding if a given nonassociative polynomial h is an identity for a variety of nonassociative algebras. We present an algorithm for constructing a certain homomorphic image of a free nonassociative algebra which is sufficient to answer the question. The algorithm resembles dynamic programming in that the algebra is built by constructing a sequence of subspaces; the basis of each subspace is determined by the basis of previous subspaces. The number of arithmetic operations required to construct the algebra is bounded by a polynomial in the degree of h and the dimension of the resulting algebra.     

Mechanism of the skeletal isomerisation of linear butenes over ferrierite: analysis of side reactions

An investigation of the effect of reaction conditions on product distribution in the skeletal isomerisation reaction of linear butenes has been carried out. The main reaction routes over ferrierite have been identified. Beside the main product isobutene, major by-product formation occurs. The unwanted reactions include dimerisation of butene to form octenes, hydrogen transfer yielding small amounts of saturated C₃ and C₄ hydrocarbons and disproportionation producing propene and pentenes. The most abundant by-products were pentene and propene, though these were not formed in equimolar amounts as could be expected. Oligomerisation experiments of propene over ferrierite produced large amounts of butene and pentene, revealing the presence of adsorbed nonene. The cracking of this surface species to hexene and propene is the most likely reaction route for the excess propene formation. This additional path to propene formation operates mainly at temperatures above 623 K.     

Simplified method for the measurement of segmental colonic transit time

Segmental colonic transit has been measured in 101 patients. Two MBq of 111Indium absorbed on resin pellets and encapsulated in an enteric coated capsule was given at 7 00 am. Hourly images during the first day, and three images during each subsequent day were acquired for up to three days. Using all scan and patient data the scans were categorised in one of the five patterns of colonic transit: normal, rapid, right delay, left delay, or generalised delay. The geometric centres and per cent activity at each time point was compared between the five groups of colonic transit patients to find the best time for imaging and so to distinguish the five groups. During the first day, early images did not help in diagnosis of patterns of transit, however, in the later images (six hours onwards after the ingestion of the activity) the rapid transit groups could be identified. Images at 27 and 51 hours were both required to distinguish all five groups of patients from each other. Only in the 'normal' transit patients was there some excretion of the activity during the course of the second day, otherwise there was no difference in the images taken in the course of a day (second or third day). A simplified protocol requires a minimum of three images to distinguish all five patterns of colonic transit. The activity should be ingested in the morning (7 00 am) and the first image taken at the end of the working day (8-10 hours after ingestion), the second image on the morning of the second day, and the third image during the course of the third day. This simple protocol would provide all the clinically relevant information necessary for correct classification of the colonic transit.     

Morphology of amorphous layers ballistically deposited on a planar substrate

Identification of a specific biomolecular target appropriately sensitive to a wide array of anesthetics has been elusive. At concentrations close to their respective ED50's for anesthesia in man or other species, 18 compounds, differing in potencies up to 66,000 fold, inhibited cytochrome P450 mediated metabolism of aminopyrine, a synthetic substrate, and arachidonic acid (AA), an endogenous substrate, in isolated liver microsomes. There was a highly significant correlation for both substrates between the absolute concentrations required for anesthesia (EC50) and for inhibition of P450 activity (Ki or IC50). The mean Ki/EC50 ratio was 0.97 for inhibition of aminopyrine demethylase. The mean IC50/EC50 ratios were 0.42 and 0.64 for inhibition of two AA-derived products and 2.8 for a third; a mean ratio of 1.4 for inhibition of overall AA metabolism suggests interaction of general anesthetics with a composite of P450 isozymes. The universal cytochrome P450 monooxygenases, in conjunction with other lipid oxygenases (cyclooxygenases and lipoxygenases) participate in the second messenger AA cascade. In nerve cells the sensitivity of these enzymes to hydrophobic neurodepressant drugs may underlie the state of general anesthesia: reversible disruption of intracellular and intercellular signalling without impairment of enzymes vital to cell respiration.     

Distributed memory systems for simulating artificial neural networks

In executing tasks involving intelligent information processing, the human brain performs better than the digital computer. The human brain derives its power from a large number [O(10¹¹)] of neurons which are interconnected by a dense interconnection network [O(10⁵) connections per neuron]. Artificial neural network (ANN) paradigms adopt the structure of the brain to try to emulate the intelligent information processing methods of the brain. ANN techniques are being employed to solve problems in areas such as pattern recognition, and robotic processing. Simulation of ANNs involves implementation of large number of neurons and a massive interconnection network. In this paper, we discuss various simulation models of ANNs and their implementation on distributed memory systems. Our investigations reveal that communication-efficient networks of distributed memory systems perform better than other topologies in implementing ANNs.