To model or not to model

Summary Self-improving control systems may belong to either of two categories, according to whether or not they embody an explicit model of the part of their environment with which they interact. The two forms of operation are discussed and compared, and it is shown that the two may be mathematically equivalent. The treatment also gives theoretical justification for a particular mode of operation for nonmodel-forming controllers.     

Application of the functional-form model to the culture of seaweeds

Selecting the most appropriate species or strains is an important first step in the development of most algal cultivation systems and is usually a tedious, time-consuming, and expensive step. The functional-form model, first developed to synthesize the adaptive significance of easily assessed thallus-form attributes relative to the productivity and survival of benthic macroalgae, is applicable to the culture of seaweeds and can expedite species or strain selection. The production ecology aspects of the model are useful particularly for applications where the desired product is not species-specific, e.g., systems in which the emphasis is on algal production, such as algal biomass farms and wastewater treatment. A thallus-form with a high surface area: volume ratio is more suited for rapid production and nutrient uptake. The utility of this model to strain selection is demonstrated with the red alga Gracilaria tikvahiae, a species that has been considered a maricultural candidate for a number of utilizations. A continuum of surface area: volume ratios for eight clones of G. tikvahiae showed that this ratio decreased as morphological complexity increased and was a good predictor of both short-term photosynthesis and long-term growth rate. Clones near opposite ends of the surface area: volume ratio spectrum had significant differences for both photosynthesis and growth. Each clone of G. tikvahiae possesses concomitant combinations of benefits as well as costs, which should be carefully evaluated for the cultivation application of interest. Knowledge of functional-form relationships in seaweeds can significantly expedite their successful cultivation.     

An ecologist's guide to the animal model

1. Efforts to understand the links between evolutionary and ecological dynamics hinge on our ability to measure and understand how genes influence phenotypes, fitness and population dynamics. Quantitative genetics provides a range of theoretical and empirical tools with which to achieve this when the relatedness between individuals within a population is known.
2. A number of recent studies have used a type of mixed-effects model, known as the animal model, to estimate the genetic component of phenotypic variation using data collected in the field. Here, we provide a practical guide for ecologists interested in exploring the potential to apply this quantitative genetic method in their research.
3. We begin by outlining, in simple terms, key concepts in quantitative genetics and how an animal model estimates relevant quantitative genetic parameters, such as heritabilities or genetic correlations.
4. We then provide three detailed example tutorials, for implementation in a variety of software packages, for some basic applications of the animal model. We discuss several important statistical issues relating to best practice when fitting different kinds of mixed models.
5. We conclude by briefly summarizing more complex applications of the animal model, and by highlighting key pitfalls and dangers for the researcher wanting to begin using quantitative genetic tools to address ecological and evolutionary questions.     

Insights to the minimal model of insulin secretion through a mean-field beta cell model

The present work introduces an extension of the original minimal model of second phase insulin secretion during the intravenous glucose tolerance test (IVGTT), which can provide both physiological and mathematical insights to the minimal model. The extension is named the mean-field beta cell model since it returns the average response of a large number of nonlinear secretory entities. Several secretion models have been proposed for the IVGTT, and we shall identify two fundamentally different theoretical features of these models. Both features can play a central role during the IVGTT, including the one presented in the mean-field beta cell model.     

A model to describe the performance of the UASB reactor

A dynamic model to describe the performance of the Upflow Anaerobic Sludge Blanket (UASB) reactor was developed. It includes dispersion, advection, and reaction terms, as well as the resistances through which the substrate passes before its biotransformation. The UASB reactor is viewed as several continuous stirred tank reactors connected in series. The good agreement between experimental and simulated results shows that the model is able to predict the performance of the UASB reactor (i.e. substrate concentration, biomass concentration, granule size, and height of the sludge bed).     

Two-intermediate model to characterize the structure of fast-folding proteins

This paper introduces a new model that enables researchers to conduct protein folding simulations. A two-step in silico process is used in the course of structural analysis of a set of fast-folding proteins. The model assumes an early stage (ES) that depends solely on the backbone conformation, as described by its geometrical properties—specifically, by the V-angle between two sequential peptide bond planes (which determines the radius of curvature, also called R-radius, according to a second-degree polynomial form). The agreement between the structure under consideration and the assumed model is measured in terms of the magnitude of dispersion of both parameters with respect to idealized values. The second step, called late-stage folding (LS), is based on the “fuzzy oil drop” model, which involves an external hydrophobic force field described by a three-dimensional Gauss function. The degree of conformance between the structure under consideration and its idealized model is expressed quantitatively by means of the Kullback-Leibler entropy, which is a measure of disparity between the observed and expected hydrophobicity distributions. A set of proteins, representative of the fast-folding group - specifically, cold shock proteins - is shown to agree with the proposed model.     

A stochastic model of oncogene expression and the relevance of this model to cancer therapy

Background  

Ablation of an oncogene or of the activity of the protein it encodes can result in apoptosis and/or inhibit tumor cell proliferation. Therefore, if the oncogene or set of oncogenes contributing maximally to a tumor cell's survival can be identified, such oncogene(s) are the most appropriate target(s) for maximizing tumor cell kill.     

Extension of the Haseman-Elston regression model to longitudinal data

We propose an extension to longitudinal data of the Haseman and Elston regression method for linkage analysis. The proposed model is a mixed model having several random effects. As response variable, we investigate the sibship sample mean corrected cross-product (smHE) and the BLUP-mean corrected cross product (pmHE), comparing them with the original squared difference (oHE), the overall mean corrected cross-product (rHE), and the weighted average of the squared difference and the squared mean-corrected sum (wHE). The proposed model allows for the correlation structure of longitudinal data. Also, the model can test for gene x time interaction to discover genetic variation over time. The model was applied in an analysis of the Genetic Analysis Workshop 13 (GAW13) simulated dataset for a quantitative trait simulating systolic blood pressure. Independence models did not preserve the test sizes, while the mixed models with both family and sibpair random effects tended to preserve size well.     

Metal bioavailability to phytoplankton--applicability of the biotic ligand model

To elicit a biological response from a target organism and/or to accumulate within this organism, a metal must first interact with a cell membrane. For hydrophilic metal species, this interaction with the cell surface can be represented in terms of the formation of M-X-cell surface complexes, e.g. M(z+)+(-)X-cell<-->M-X-cell, where -X-cell is a cellular ligand present at the cell surface. According to the free-ion model, or its derivative the biotic ligand model (BLM), the biological response elicited by the metal will be proportional to [M-X-cell]. In this paper, using freshwater algae as our test species, we examine some of the key assumptions that underlie the BLM, namely that metal internalization is slow relative to the other steps involved in metal uptake (i.e. the M-X-cell complex is in equilibrium with metal species in solution), that internalization occurs via cation transport, and that internalization must occur for toxicity to appear. Recent experiments with freshwater algae are described, demonstrating anomalously high metal accumulation and/or toxicity in the presence of a common low molecular weight metabolite (alanine), or in the presence of an assimilable inorganic anion (thiosulfate). The possible implications of these findings for the application of the BLM to higher organisms are discussed.     

Sensitivity to initial conditions in the route-finder model

A model of stimulus generalization [Staddon, J.E.R., Reid, A.K., 1990. On the dynamics of generalization. Psychol. Rev. 97, 576-578] was extended by Reid and Staddon [Reid, A.K., Staddon, J.E.R., 1998. A dynamic route finder for the cognitive map. Psychol. Rev. 105, 585-601] to account for the route-finder issue in the Tolman-Guthrie discussion about cognitive maps. This deterministic model has been described as sensitive to initial conditions in terms of the parameters of a diffusion equation [Reid, A.K., Staddon, J.E.R., 1998. A dynamic route finder for the cognitive map. Psychol. Rev. 105, 585-601]. A simulation study was carried out to test this assertion, evaluating whether the pattern of variation in the model output resembled a chaotic pattern. Results indicate that the model is sensitive to initial conditions, suggesting that the spatial navigation task addressed by this model involves non-linear relationships and complexity beyond the apparent simplicity of the stimulus generalization process.     

Physical model of the plant tissue response to exposure to the microwave electromagnetic field

A hypothesis was suggested to explain the effect of biostimulation of seeds exposed to microwave electromagnetic field. It was shown that the assumption on the determining influence of the microwave field on the transport properties of the conducting system of a plant satisfactorily explains the phenomena observed in germinating seeds and growing plants. A physical model of the response of a plant cell to a microwave field is presented, which served as a basis for the method of calculating the maximum possible time of exposure of plant tissue.     

A new approach to the human muscle model

Hill's (1938) two component muscle model is used as basis for digital computer simulation of human muscular contraction by means of an iterative process. The contractile (CC) and series elastic (SEC) components are lumped components of structures which produce and transmit torque to the external environment. The CC is described in angular terms along four dimensions as a series of non-planar torque-angle-angular velocity surfaces stacked on top of each other, each surface being appropriate to a given level of muscular activation. The SEC is described similarly along dimensions of torque, angular stretch, overall muscle angular displacement and activation. The iterative process introduces negligible error and allows the mechanical outcome of a variety of normal muscular contractions to be evaluated parsimoniously. The model allows analysis of many aspects of muscle behaviour as well as optimization studies. Definition of relevant relations should also allow reproduction and prediction of the outcome of contractions in individuals.     

An introduction to the Mumford-Shah segmentation model.

Some papers of this special issue concern recent results on mathematical models of segmentation. As they are rather technical we propose here a pedagogical introduction for the non-mathematical reader. We briefly present the variational model of image segmentation proposed by David Mumford and we summarize some fundamental results of De Giorgi's school.