Inners and biocontrol models

Techniques of modelling and simulation are discussed as they relate to bioengineering systems. The advantages and disadvantages of different analytical engineering methods utilized to gather information concerning the behavior of complex physiological and neuromuscular control mechanisms are explained. An Inners Criterion is developed to determine if the roots of a model lie within a certain “biologically realistic region” Γ_B, in the complex plane which contains the roots of linearized models for a large variety of neuromuscular systems. Several algorithmic methods based on the Jury Inners Test are described which specify whether the model roots lie within the desired region, thereby providing an indication as to the validity of the proposed model. This technique can help to eliminate tedious simulation on an unrealistic model with roots lying far outside this region. An exemplary model for control of vergence eye movements is presented and shown to satisfy the Γ_B criterion; several counter-examples are also discussed. The Inners approach can be adapted to other classes of bioengineering systems by specifying the region based on models that are contained in the class of interest.     

Discriminant function implementation of a minimum risk classifier

The paper discusses the possibility of implementing a minimum risk classifier using the learning machine approach. Necessary conditions on the choice of pairwise classification costs are imposed so that the minimum risk classifier can be implemented using pairwise class separating functions. Parameters of these functions are obtained using a two stage algorithm which minimizes a modified least squares criterion of class separation. In comparison to normal least squares objective function, this criterion increases the sensitivity of the learning scheme near the class separating surface and, consequently, allows for an improvement in the performance of the discriminant function decision making processor. Simplicity of the design procedure is achieved by partitioning the multimodal classes into unimodal subsets, since discriminant functions of unimodal classes can usually be implemented simply and with sufficient accuracy as low order polynomials. The proposed design approach is tested experimentally on an artificial pattern recognition problem.     

Neural hierarchical models of ecological populations

Neural networks are increasingly being used in science to infer hidden dynamics of natural systems from noisy observations, a task typically handled by hierarchical models in ecology. This article describes a class of hierarchical models parameterised by neural networks – neural hierarchical models. The derivation of such models analogises the relationship between regression and neural networks. A case study is developed for a neural dynamic occupancy model of North American bird populations, trained on millions of detection/non‐detection time series for hundreds of species, providing insights into colonisation and extinction at a continental scale. Flexible models are increasingly needed that scale to large data and represent ecological processes. Neural hierarchical models satisfy this need, providing a bridge between deep learning and ecological modelling that combines the function representation power of neural networks with the inferential capacity of hierarchical models.     

Adjusted geometric-mean: a novel performance measure for imbalanced bioinformatics datasets learning

One common and challenging problem faced by many bioinformatics applications, such as promoter recognition, splice site prediction, RNA gene prediction, drug discovery and protein classification, is the imbalance of the available datasets. In most of these applications, the positive data examples are largely outnumbered by the negative data examples, which often leads to the development of sub-optimal prediction models having high negative recognition rate (Specificity = SP) and low positive recognition rate (Sensitivity = SE). When class imbalance learning methods are applied, usually, the SE is increased at the expense of reducing some amount of the SP. In this paper, we point out that in these data-imbalanced bioinformatics applications, the goal of applying class imbalance learning methods would be to increase the SE as high as possible by keeping the reduction of SP as low as possible. We explain that the existing performance measures used in class imbalance learning can still produce sub-optimal models with respect to this classification goal. In order to overcome these problems, we introduce a new performance measure called Adjusted Geometric-mean (AGm). The experimental results obtained on ten real-world imbalanced bioinformatics datasets demonstrates that the AGm metric can achieve a lower rate of reduction of SP than the existing performance metrics, when increasing the SE through class imbalance learning methods. This characteristic of AGm metric makes it more suitable for achieving the proposed classification goal in imbalanced bioinformatics datasets learning.     

Sociobiology and the structural stability of behavior patterns

A structural stability approach to population-genetic systems and to dynamic evolutionary games is attempted in order to examine the theoretical significance of sociobiological selection models. A criterion of weak selection is derived that is not restricted to differential reproduction in polymorphic systems but describes possible directions of evolutionary change in time scales governed by genetic mutation rates. The criterion applies to the problems of how the initial mutational basis of an adaptive trait may be established and how this may happen, for analogous traits, independently in different species. Two basic sociobiological concepts are reconsidered with reference to the criterion. It is shown that W. D. Hamilton's condition of increases in inclusive fitness due to altruistic interactions among kin expresses the structural instability of populations against the evolution of altruistic behavior. Using the dynamic approach to evolutionary game theory, it is demonstrated that if a behavioral phenotype is an evolutionarily stable strategy, it is structurally stable against perturbations of the fitness payoffs, provided selection is weak. These results are applied to material problems of the evolution of animal social behavior.     

Dynamic population epidemic models.

Most multipopulation epidemic models are of the contact distribution type, in which the locations of successive contacts are chosen independently from appropriate contact distributions. This paper is concerned with an alternative class of models, termed dynamic population epidemic models, in which infectives move among the populations and can infect only within their current population. Both the stochastic and deterministic versions of such models are considered. Their threshold behavior is analyzed in some depth, as are their final outcomes. Velocities of spread of infection are considered when the populations have a spatial structure. A criterion for finding the equivalent contact distribution epidemic for any given dynamic population epidemic is provided, enabling comparisons to be made for the velocities and final outcomes displayed by the two classes of models. The relationship between deterministic and stochastic epidemic models is also discussed briefly.     

Bayesian Model Selection for Incomplete Data Using the Posterior Predictive Distribution

Summary We explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data. We begin by identifying a property that most model selection criteria for incomplete data should consider. We then show that a straightforward extension of the Gelfand and Ghosh (1998, Biometrika, 85 , 1–11) criterion to incomplete data has two problems. First, it introduces an extra term (in addition to the goodness of fit and penalty terms) that compromises the criterion. Second, it does not satisfy the aforementioned property. We propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion (DIC). In general, the DIC outperforms the posterior predictive criterion, but the latter criterion appears to work well overall and is very easy to compute unlike the DIC in certain classes of models for missing data.     

Plant intelligence: Why,why not or where?

The concept of plant intelligence, as proposed by Anthony Trewavas, has raised considerable discussion. However, plant intelligence remains loosely defined; often it is either perceived as practically synonymous to Darwinian fitness, or reduced to a mere decorative metaphor. A more strict view can be taken, emphasizing necessary prerequisites such as memory and learning, which requires clarifying the definition of memory itself. To qualify as memories, traces of past events have to be not only stored, but also actively accessed. We propose a criterion for eliminating false candidates of possible plant intelligence phenomena in this stricter sense: an “intelligent” behavior must involve a component that can be approximated by a plausible algorithmic model involving recourse to stored information about past states of the individual or its environment. Re-evaluation of previously presented examples of plant intelligence shows that only some of them pass our test.

“You were hurt?” Kumiko said, looking at the scar.Sally looked down. “Yeah.”“Why didn''t you have it removed?”“Sometimes it''s good to remember.”“Being hurt?”“Being stupid.”—(W. Gibson: Mona Lisa Overdrive)

Key words: intelligence, memory, learning, plant development, mathematical models, plant neurobiology, definition of terms     

Single species models with logistic growth and dissymmetric impulse dispersal

In this paper, two classes of single-species models with logistic growth and impulse dispersal (or migration) are studied: one model class describes dissymmetric impulsive bi-directional dispersal between two heterogeneous patches; and the other presents a new way of characterizing the aggregate migration of a natural population between two heterogeneous habitat patches, which alternates in direction periodically. In this theoretical study, some very general, weak conditions for the permanence, extinction of these systems, existence, uniqueness and global stability of positive periodic solutions are established by using analysis based on the theory of discrete dynamical systems. From this study, we observe that the dynamical behavior of populations with impulsive dispersal differs greatly from the behavior of models with continuous dispersal. Unlike models where the dispersal is continuous in time, in which the travel losses associated with dispersal make it difficult for such dispersal to evolve e.g., [25], [26], [28], in the present study it was relatively easy for impulsive dispersal to positively affect populations when realistic parameter values were used, and a rich variety of behaviors were possible. From our results, we found impulsive dispersal seems to more nicely model natural dispersal behavior of populations and may be more relevant to the investigation of such behavior in real ecological systems.     

Dynamic versus instantaneous models of diet choice

We investigate the dynamics of a series of two-prey-one-predator models in which the predator exhibits adaptive diet choice based on the different energy contents and/or handling times of the two prey species. The predator is efficient at exploiting its prey and has a saturating functional response; these two features combine to produce sustained population cycles over a wide range of parameter values. Two types of models of behavioral change are compared. In one class of models ("instantaneous choice"), the probability of acceptance of the poorer prey by the predator instantaneously approximates the optimal choice, given current prey densities. In the second class of models ("dynamic choice"), the probability of acceptance of the poorer prey is a dynamic variable, which begins to change in an adaptive direction when prey densities change but which requires a finite amount of time to approach the new optimal behavior. The two types of models frequently predict qualitatively different population dynamics of the three-species system, with chaotic dynamics and complex cycles being a common outcome only in the dynamic choice models. In dynamic choice models, factors that reduce the rate of behavioral change when the probability of accepting the poorer prey approaches extreme values often produce complex population dynamics. Instantaneous and dynamic models often predict different average population densities and different indirect interactions between prey species. Alternative dynamic models of behavior are analyzed and suggest, first, that instantaneous choice models may be good approximations in some circumstances and, second, that different types of dynamic choice models often lead to significantly different population dynamics. The results suggest possible behavioral mechanisms leading to complex population dynamics and highlight the need for more empirical study of the dynamics of behavioral change.     

“A stochastic solution of the 3-body problem in chemical kinetics. The termolecular stochastic process I”

It appears to be axiomatic that termolecular and higher order reactions occur relatively rarely. The basis for this judgment seems to lie in the supposition that successful 3-Body collisions of 3 interactive species of molecules cannot occur frequently enought to account for chemical or biochemical transformation. In order to provide a more complete mathematical framework than now exists for examining this hypothesis the probability of effective termolecular “δ-collisions” as a function of time is derived. This amounts to adding to the class of reactions for which stochastic models are now available the termolecular reaction. In common with the unimolecular and bimolecular cases this process is seen to satisfy the criterion of consistency-in-the-mean with respect to deterministic formulations. It is planned next to use the termolecular process and the lower order processes in computer-assistedin numero experimental studies aimed at comparing alternative mechanisms of reaction.     

Function-valued adaptive dynamics and optimal control theory

In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function of the strategy value at that argument value only. For this type of models of direct effect, singular strategies can be found using the calculus of variations, with singular strategies needing to satisfy Euler’s equation with environmental feedback. In a broader, more mechanistically oriented class of models, the function-valued strategy affects a process described by differential equations, and fitness can be expressed as an integral in which the integrand for each argument value depends both on the strategy and on process variables at that argument value. In general, the calculus of variations cannot help analyzing this much broader class of models. Here we explain how to find singular strategies in this class of process-mediated models using optimal control theory. In particular, we show that singular strategies need to satisfy Pontryagin’s maximum principle with environmental feedback. We demonstrate the utility of this approach by studying the evolution of strategies determining seasonal flowering schedules.     

Two wrongs don't make a right: the initial viability of different assessment rules in the evolution of indirect reciprocity

Indirect reciprocity models are meant to correspond to simple moral systems, in which individuals assess the interactions of third parties in order to condition their cooperative behavior. Despite the staggering number of possible assessment rules in even the simplest of these models, previous research suggests that only a handful are evolutionarily stable against invasion by free riders. These successful assessment rules fall into two categories, one which positively judges miscreants when they refuse to help other miscreants, the other which does not. Previous research has not, however, demonstrated that all of these rules can invade an asocial population—a requirement for a complete theory of social evolution. Here, I present a general analytical model of indirect reciprocity and show that the class of assessment rules which positively judges a refusal to help scofflaws cannot invade a population of defectors, whereas the other class can. When rare, assessment rules which positively judge a refusal to help bad people produce a poor correlation between reputation and behavior. It is this correlation that generates the assortment crucial in sustaining cooperation through indirect reciprocity. Only assessment rules that require good deeds to achieve a good reputation guarantee a strong correlation between behavior and reputation.     

Path planning versus cue responding: a bio-inspired model of switching between navigation strategies

In this article, we describe a new computational model of switching between path-planning and cue-guided navigation strategies. It is based on three main assumptions: (i) the strategies are mediated by separate memory systems that learn independently and in parallel; (ii) the learning algorithms are different in the two memory systems—the cue-guided strategy uses a temporal-difference (TD) learning rule to approach a visible goal, whereas the path-planning strategy relies on a place-cell-based graph-search algorithm to learn the location of a hidden goal; (iii) a strategy selection mechanism uses TD-learning rule to choose the most successful strategy based on past experience. We propose a novel criterion for strategy selection based on the directions of goal-oriented movements suggested by the different strategies. We show that the selection criterion based on this “common currency” is capable of choosing the best among TD-learning and planning strategies and can be used to solve navigational tasks in continuous state and action spaces. The model has been successfully applied to reproduce rat behavior in two water-maze tasks in which the two strategies were shown to interact. The model was used to analyze competitive and cooperative interactions between different strategies during these tasks as well as relative influence of different types of sensory cues.     

Integration of multiple types of genetic markers for neuroblastoma may contribute to improved prediction of the overall survival

Background

Modern experimental techniques deliver data sets containing profiles of tens of thousands of potential molecular and genetic markers that can be used to improve medical diagnostics. Previous studies performed with three different experimental methods for the same set of neuroblastoma patients create opportunity to examine whether augmenting gene expression profiles with information on copy number variation can lead to improved predictions of patients survival. We propose methodology based on comprehensive cross-validation protocol, that includes feature selection within cross-validation loop and classification using machine learning. We also test dependence of results on the feature selection process using four different feature selection methods.

Results

The models utilising features selected based on information entropy are slightly, but significantly, better than those using features obtained with t-test. The synergy between data on genetic variation and gene expression is possible, but not confirmed. A slight, but statistically significant, increase of the predictive power of machine learning models has been observed for models built on combined data sets. It was found while using both out of bag estimate and in cross-validation performed on a single set of variables. However, the improvement was smaller and non-significant when models were built within full cross-validation procedure that included feature selection within cross-validation loop. Good correlation between performance of the models in the internal and external cross-validation was observed, confirming the robustness of the proposed protocol and results.

Conclusions

We have developed a protocol for building predictive machine learning models. The protocol can provide robust estimates of the model performance on unseen data. It is particularly well-suited for small data sets. We have applied this protocol to develop prognostic models for neuroblastoma, using data on copy number variation and gene expression. We have shown that combining these two sources of information may increase the quality of the models. Nevertheless, the increase is small and larger samples are required to reduce noise and bias arising due to overfitting.

Reviewers

This article was reviewed by Lan Hu, Tim Beissbarth and Dimitar Vassilev.

     

Prediction Models in Configural Frequency Analysis

Configural frequency analysis models are presented for predicting a discrete criterion variable from combining 2 or more discrete predictor variables nonparametrically. Predictions are made via so-called prediction types which allow to predict a criterion class from combined predictor classes. Prediction types are implicitely defined as cells of a 2-dimensional contingeney table with rows as predictor combinations and columns as criterion classes. The CFA is extended for two criteria, and for stratified sampling.     

EMG-Driven Forward-Dynamic Estimation of Muscle Force and Joint Moment about Multiple Degrees of Freedom in the Human Lower Extremity

This work examined if currently available electromyography (EMG) driven models, that are calibrated to satisfy joint moments about one single degree of freedom (DOF), could provide the same musculotendon unit (MTU) force solution, when driven by the same input data, but calibrated about a different DOF. We then developed a novel and comprehensive EMG-driven model of the human lower extremity that used EMG signals from 16 muscle groups to drive 34 MTUs and satisfy the resulting joint moments simultaneously produced about four DOFs during different motor tasks. This also led to the development of a calibration procedure that allowed identifying a set of subject-specific parameters that ensured physiological behavior for the 34 MTUs. Results showed that currently available single-DOF models did not provide the same unique MTU force solution for the same input data. On the other hand, the MTU force solution predicted by our proposed multi-DOF model satisfied joint moments about multiple DOFs without loss of accuracy compared to single-DOF models corresponding to each of the four DOFs. The predicted MTU force solution was (1) a function of experimentally measured EMGs, (2) the result of physiological MTU excitation, (3) reflected different MTU contraction strategies associated to different motor tasks, (4) coordinated a greater number of MTUs with respect to currently available single-DOF models, and (5) was not specific to an individual DOF dynamics. Therefore, our proposed methodology has the potential of producing a more dynamically consistent and generalizable MTU force solution than was possible using single-DOF EMG-driven models. This will help better address the important scientific questions previously approached using single-DOF EMG-driven modeling. Furthermore, it might have applications in the development of human-machine interfaces for assistive devices.