The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Field manual 3-24 and the heritage of counterinsurgency theory

The Counterinsurgency Manual FM 3-24 has been accused of being over-dependent on the counterinsurgency 'classics' Galula and Thompson. But comparison reveals that it is different in spirit. Galula and Thompson seek practical control; the Manual seeks to build 'legitimacy'. Its concept of legitimacy is superficially Weberian, but owes more to the writings of the American Max Manwaring. The Manual presupposes that a rights-based legal order can (other things being equal) be made to be cross-culturally attractive; 'effective governance' by itself can build legitimacy. The fusion of its methods with an ideology creates unrealistic criteria for success. Its weaknesses suggest a level of incapacity to think politically that will, in time, result in further failures.

Markov models of aging: theory and practice

We review and structure some of the mathematical and statistical models that have been developed over the past half century to grapple with theoretical and experimental questions about the stochastic development of aging over the life course. We suggest that the mathematical models are in large part addressing the problem of partitioning the randomness in aging: How does aging vary between individuals, and within an individual over the lifecourse? How much of the variation is inherently related to some qualities of the individual, and how much is entirely random? How much of the randomness is cumulative, and how much is merely short-term flutter? We propose that recent lines of statistical inquiry in survival analysis could usefully grapple with these questions, all the more so if they were more explicitly linked to the relevant mathematical and biological models of aging. To this end, we describe points of contact among the various lines of mathematical and statistical research. We suggest some directions for future work, including the exploration of information-theoretic measures for evaluating components of stochastic models as the basis for analyzing experiments and anchoring theoretical discussions of aging.

The Natural History of Slapton Ley Nature Reserve XVIII: nitrogen and phosphorus losses from the catchment - an export coefficient modelling approach

Nitrogen and phosphorus losses from the catchment of Slapton Ley, a small coastal lake in SW England, were calculated using an adaptation of a model developed by Jorgensen (1980). A detailed survey of the catchment revealed that its land use is dominated by both permanent and temporary grassland (respectively 38 and 32% of its total area), and that the remainder is made up of the cultivation of cereals and field vegetables, and market gardening. Livestock numbers in the catchment constitute ca. 6600 head of cattle, 10,000 sheep, 590 pigs, 1700 poultry and 58 horses. The permanent human population of the area is ca. 2000, served by two small gravity-fed sewage treatment works (STWs). Inputs to, and losses from, farmland in the catchment were computed using Jorgensen’s model, and coefficients derived from the data of Cooke (1976), Gostick (1982), Rast and Lee (1983) and Vollenweider (1968). Allowing for outputs from STWs, the total annual external load of N and P upon Slapton Ley is 160 t (35 kg ha-1) a-1 N, and 4.8 t (1.05 kg ha-1) a-1 P. Accordingly to Vollenweider (1968, 1975), such loadings exceed OECD permissible level by a factor of ca. 50 in the case of N, and ca. 5 in that of P. In order to reduce nutrient loads, attention would need to be paid to both STW and agricultural sources.

Determination of tube theory parameters using a simple grid model as an example

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slipsprings model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes.

Hippurate: the natural history of a mammalian-microbial co-metabolite

Hippurate, the glycine conjugate of benzoic acid, is a normal constituent of the endogenous urinary metabolite profile and has long been associated with the microbial degradation of certain dietary components, hepatic function and toluene exposure, and is also commonly used as a measure of renal clearance. Here we discuss the potential relevance of hippurate excretion with regards to normal endogenous metabolism and trends in excretion relating to gender, age, and the intestinal microbiota. Additionally, the significance of hippurate excretion with regards to disease states including obesity, diabetes, gastrointestinal diseases, impaired renal function, psychological disorders and autism, as well as toxicity and parasitic infection, are considered.

The processing of number and gender agreement in Spanish: an event related potential investigation of the effects of structural distance

Previous research suggests that the processing of agreement is affected by the distance between the agreeing elements. However, the unique contribution of structural distance (number of intervening syntactic phrases) to the processing of agreement remains an open question, since previous investigations do not tease apart structural and linear distance (number of intervening words). We used event related potentials (ERPs) to examine the extent to which structural distance impacts the processing of Spanish number and gender agreement. Violations were realized both within the phrase and across the phrase. Across both levels of structural distance, linear distance was kept constant, as was the syntactic category of the agreeing elements. Number and gender agreement violations elicited a robust P600 between 400 and 900ms, a component associated with morphosyntactic processing. No amplitude differences were observed between number and gender violations, suggesting that the two features are processed similarly at the brain level. Within-phrase agreement yielded more positive waveforms than across-phrase agreement, both for agreement violations and for grammatical sentences (no agreement by distance interaction). These effects can be interpreted as evidence that structural distance impacts the establishment of agreement overall, consistent with sentence processing models which predict that hierarchical structure impacts the processing of syntactic dependencies. However, due to the lack of an agreement by distance interaction, the possibility cannot be ruled out that these effects are driven by differences in syntactic predictability between the within-phrase and across-phrase configurations, notably the fact that the syntactic category of the critical word was more predictable in the within-phrase conditions.