A dynamic mathematical model for sequential leach bed anaerobic digestion of organic fraction of municipal solid waste

A mathematical model that describes the operation of a sequential leach bed process for anaerobic digestion of organic fraction of municipal solid waste (MSW) is developed and validated. This model assumes that ultimate mineralisation of the organic component of the waste occurs in three steps, namely solubilisation of particulate matter, fermentation to volatile organic acids (modelled as acetic acid) along with liberation of carbon dioxide and hydrogen, and methanogenesis from acetate and hydrogen. The model incorporates the ionic equilibrium equations arising due to dissolution of carbon dioxide, generation of alkalinity from breakdown of solids and dissociation of acetic acid. Rather than a charge balance, a mass balance on the hydronium and hydroxide ions is used to calculate pH. The flow of liquid through the bed is modelled as occurring through two zones-a permeable zone with high flushing rates and the other more stagnant. Some of the kinetic parameters for the biological processes were obtained from batch MSW digestion experiments. The parameters for flow model were obtained from residence time distribution studies conducted using tritium as a tracer. The model was validated using data from leach bed digestion experiments in which a leachate volume equal to 10% of the fresh waste bed volume was sequenced. The model was then tested, without altering any kinetic or flow parameters, by varying volume of leachate that is sequenced between the beds. Simulations for sequencing/recirculating 5 and 30% of the bed volume are presented and compared with experimental results. (C) 2002 Elsevier Science B.V. All rights reserved.

The LFA-1-associated molecule PTA-1 (CD226) on T cells forms a dynamic molecular complex with protein 4.1G and human discs large

Clustering of the T cell integrin, LFA-1, at specialized regions of intercellular contact initiates integrin-mediated adhesion and downstream signaling, events that are necessary for a successful immunological response. But how clustering is achieved and sustained is not known. Here we establish that an LFA-1-associated molecule, PTA-1, is localized to membrane rafts and binds the carboxyl-terminal domain of isoforms of the actin-binding protein 4.1G. Protein 4.1 is known to associate with the membrane-associated guanylate kinase homologue, human discs large. We show that the carboxyl-terminal peptide of PTA-1 also can bind human discs large and that the presence or absence of this peptide greatly influences binding between PTA-1 and different isoforms of 4.1G. T cell stimulation with phorbol ester or PTA-1 cross-linking induces PTA-1 and 4.1G to associate tightly with the cytoskeleton, and the PTA-1 from such activated cells now can bind to the amino-terminal region of 4.1G. We propose that these dynamic associations provide the structural basis for a regulated molecular adhesive complex that serves to cluster and transport LFA-1 and associated molecules.

Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as (1)/(p)integral(Omega)[sigma(u)dA(p) + (1)/(2)delu(2p)]dx, where u is a map from a domain Omega is an element of R-n into the m-dimensional unit sphere of Rm+1 and A is a differential one-form in Omega.

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

Functional analysis of a real-time protocol for networked control systems

Traditional real-time control systems are tightly integrated into the industrial processes they govern. Now, however, there is increasing interest in networked control systems. These provide greater flexibility and cost savings by allowing real-time controllers to interact with industrial processes over existing communications networks. New data packet queuing protocols are currently being developed to enable precise real-time control over a network with variable propagation delays. We show how one such protocol was formally modelled using timed automata, and how model checking was used to reveal subtle aspects of the control system's dynamic behaviour.

Intake rates and the functional response in shorebirds (Charadriiformes) eating macro-invertebrates

As field determinations take much effort, it would be useful to be able to predict easily the coefficients describing the functional response of free-living predators, the function relating food intake rate to the abundance of food organisms in the environment. As a means easily to parameterise an individual-based model of shorebird Charadriiformes populations, we attempted this for shorebirds eating macro-invertebrates. Intake rate is measured as the ash-free dry mass (AFDM) per second of active foraging; i.e. excluding time spent on digestive pauses and other activities, such as preening. The present and previous studies show that the general shape of the functional response in shorebirds eating approximately the same size of prey across the full range of prey density is a decelerating rise to a plateau, thus approximating the Holling type 11 ('disc equation') formulation. But field studies confirmed that the asymptote was not set by handling time, as assumed by the disc equation, because only about half the foraging time was spent in successfully or unsuccessfully attacking and handling prey, the rest being devoted to searching. A review of 30 functional responses showed that intake rate in free-living shorebirds varied independently of prey density over a wide range, with the asymptote being reached at very low prey densities (< 150/m(-2)). Accordingly, most of the many studies of shorebird intake rate have probably been conducted at or near the asymptote of the functional response, suggesting that equations that predict intake rate should also predict the asymptote. A multivariate analysis of 468 'spot' estimates of intake rates from 26 shorebirds identified ten variables, representing prey and shorebird characteristics, that accounted for 81 % of the variance in logarithm-transformed intake rate. But four-variables accounted for almost as much (77.3 %), these being bird size, prey size, whether the bird was an oystercatcher Haematopus ostralegus eating mussels Mytilus edulis, or breeding. The four variable equation under-predicted, on average, the observed 30 estimates of the asymptote by 11.6%, but this discrepancy was reduced to 0.2% when two suspect estimates from one early study in the 1960s were removed. The equation therefore predicted the observed asymptote very successfully in 93 % of cases. We conclude that the asymptote can be reliably predicted from just four easily measured variables. Indeed, if the birds are not breeding and are not oystercatchers eating mussels, reliable predictions can be obtained using just two variables, bird and prey sizes. A multivariate analysis of 23 estimates of the half-asymptote constant suggested they were smaller when prey were small but greater when the birds were large, especially in oystercatchers. The resulting equation could be used to predict the half-asymptote constant, but its predictive power has yet to be tested. As well as predicting the asymptote of the functional response, the equations will enable research workers engaged in many areas of shorebird ecology and behaviour to estimate intake rate without the need for conventional time-consuming field studies, including species for which it has not yet proved possible to measure intake rate in the field.

Prediction of functional capacity in chronic heart failure patients using myocardial tissue Doppler

Background. Exercise therapy improves functional capacity in CHF, but selection and individualization of training would be helped by a simple non-invasive marker of peak VO2. Peak VO2 in these pts is difficult to predict without direct measurement, and LV ejection fraction is a poor predictor. Myocardial tissue velocities are less load-dependent, and may be predictive of the exercise response in CHF pts. We sought to use tissue velocity as a predictor of peak VO2 in CHF pts. Methods. Resting 2D-echocardiography and tissue Doppler imaging were performed in 182 CHF pts (159 male, age 62±10 years) before and after metabolic exercise testing. The majority of these patients (129, 71%) had an ischemic cardiomyopathy, with resting EF of 35±13% and a peak VO2 of 13.5±4.7 ml/kg/min. Results. Neither resting EF (r=0.15) nor peak EF (r=0.18, both p=NS) were correlated with peak VO2. However, peak VO2 correlated with peak systolic velocity in septal (Vss, r=0.31) and lateral walls (Vsl, r=0.26, both p=0.01). In a general linear model (r2 = 0.25), peak VO2 was calculated from the following equation: 9.6 + 0.68*Vss - 0.09*age + 0.06*maximum HR. This model proved to be a superior predictor of peak VO2 (r=0.51, p=0.01) than the standard prediction equations of Wasserman (r= -0.12, p=0.01). Conclusions. Resting tissue Doppler, age and maximum heart rate may be used to predict functional capacity in CHF patients. This may be of use in selecting and following the response to therapy, including for exercise training.

Integrating runtime assertions with dynamic types: Structuring a derivation from an incomputable specification

An inherent incomputability in the specification of a functional language extension that combines assertions with dynamic type checking is isolated in an explicit derivation from mathematical specifications. The combination of types and assertions (into "dynamic assertion-types" - DATs) is a significant issue since, because the two are congruent means for program correctness, benefit arises from their better integration in contrast to the harm resulting from their unnecessary separation. However, projecting the "set membership" view of assertion-checking into dynamic types results in some incomputable combinations. Refinement of the specification of DAT checking into an implementation by rigorous application of mathematical identities becomes feasible through the addition of a "best-approximate" pseudo-equality that isolates the incomputable component of the specification. This formal treatment leads to an improved, more maintainable outcome with further development potential.