Phylogenetic systematics of Southeast Asian flying lizards (Iguania: Agamidae: Draco) as inferred from mitochondrial DNA sequence data

Phylogenetic analysis of mitochondrial DNA sequence data using maximum parsimony, minimum evolution (of log-determinant distances), and maximum-likelihood optimality criteria provided a robust estimate of Draco phylogenetic relationships. Although the analyses based on alternative optimality criteria were not entirely congruent, non-parametric bootstrap analyses identified many well-supported clades that were common to the analyses under the three altrenative criteria. Relationships within the major clades are generally well resolved and strongly supported, although this is not the case for the Philippine volans subclade. The hypothesis that a clade composed primarily of Philippine species represents a rapid radiation could not be rejected. A revised taxonomy for Draco is provided.     

On our best behavior: optimality models in human behavioral ecology

This paper discusses problems associated with the use of optimality models in human behavioral ecology. Optimality models are used in both human and non-human animal behavioral ecology to test hypotheses about the conditions generating and maintaining behavioral strategies in populations via natural selection. The way optimality models are currently used in behavioral ecology faces significant problems, which are exacerbated by employing the so-called ‘phenotypic gambit’: that is, the bet that the psychological and inheritance mechanisms responsible for behavioral strategies will be straightforward. I argue that each of several different possible ways we might interpret how optimality models are being used for humans face similar and additional problems. I suggest some ways in which human behavioral ecologists might adjust how they employ optimality models; in particular, I urge the abandonment of the phenotypic gambit in the human case.     

Algorithmic and complexity results for decompositions of biological networks into monotone subsystems

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical results include polynomial-time approximation algorithms as well as constant-ratio inapproximability results. One of the algorithms, which has a worst-case guarantee of 87.9% from optimality, is based on the semidefinite programming relaxation approach of Goemans-Williamson [Goemans, M., Williamson, D., 1995. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42 (6), 1115-1145]. The algorithm was implemented and tested on a Drosophila segmentation network and an Epidermal Growth Factor Receptor pathway model, and it was found to perform close to optimally.     

Genetic details, optimization and phage life histories

Optimality models assume that phenotypes evolve by natural selection largely independently of underlying genetic mechanisms. This neglect of genetic mechanisms is considered an advantage by some evolutionary biologists but a fatal flaw by others. The controversy has gone unresolved, in part, from a lack of complex phenotypes that meet optimality criteria and for which the underlying genetic mechanisms are known. Here, we look at both perspectives for lysis time in bacteriophages. We find that the basic assumptions of the optimality model are compatible with the genetic details, but the optimality model is limited in its ability to accommodate lysis time plasticity because the mechanistic underpinnings of plasticity are poorly known.     

A tractable revenue management model for capacity allocation and overbooking over an airline network

In this paper, we develop a revenue management model to jointly make the capacity allocation and overbooking decisions over an airline network. The crucial observation behind our model is that if the penalty cost of denying boarding to the reservations were given by a separable function, then the optimality equation for the joint capacity allocation and overbooking problem would decompose by the itineraries. We exploit this observation by building an approximation to the penalty cost that is separable by the numbers of reservations for different itineraries. In this case, we can obtain an approximate solution to the optimality equation by plugging the separable approximation into the boundary condition of the optimality equation. Our computational experiments compare our approach with a standard deterministic linear programming formulation, as well as a recent joint capacity allocation and overbooking model. When compared with the standard deterministic linear programming formulation, our approach can provide significant profit improvements. On the other hand, when compared with the recent joint capacity allocation and overbooking model, our approach can provide similar profit performance with substantially shorter runtimes.     

Multi-objective behavioural mechanisms are adopted by foraging animals to achieve several optimality goals simultaneously

1. Animals foraging for resources are under a variety of selective pressures, and separate optimality models have been developed predicting the optimal reproductive strategies they should adopt. 2. In most cases, the proximate behavioural mechanisms adopted to achieve such optimality goals have been identified. This is the case, for example, for optimal patch time and sex allocation in insect parasitoids. However, behaviours modelled within this framework have mainly been studied separately, even though real animals have to optimize some behaviours simultaneously. 3. For this reason, it would be better if proximate behavioural rules were designed to attain several goals simultaneously. Despite their importance, such multi-objective proximate rules remain to be discovered. 4. Based on experiments on insect parasitoids that simultaneously examine their optimal patch time and sex allocation strategies, it is shown here that animals can adopt multi-objective behavioural mechanisms that appear consistent with the two optimal goals simultaneously. 5. Results of computer simulations demonstrate that these behavioural mechanisms are indeed consistent with optimal reproductive strategies and have thus been most likely selected over the course of the evolutionary time.     

MIP formulations for an application of project scheduling in human resource management

In the literature, various discrete-time and continuous-time mixed-integer linear programming (MIP) formulations for project scheduling problems have been proposed. The performance of these formulations has been analyzed based on generic test instances. The objective of this study is to analyze the performance of discrete-time and continuous-time MIP formulations for a real-life application of project scheduling in human resource management. We consider the problem of scheduling assessment centers. In an assessment center, candidates for job positions perform different tasks while being observed and evaluated by assessors. Because these assessors are highly qualified and expensive personnel, the duration of the assessment center should be minimized. Complex rules for assigning assessors to candidates distinguish this problem from other scheduling problems discussed in the literature. We develop two discrete-time and three continuous-time MIP formulations, and we present problem-specific lower bounds. In a comparative study, we analyze the performance of the five MIP formulations on four real-life instances and a set of 240 instances derived from real-life data. The results indicate that good or optimal solutions are obtained for all instances within short computational time. In particular, one of the real-life instances is solved to optimality. Surprisingly, the continuous-time formulations outperform the discrete-time formulations in terms of solution quality.     

Increased taxon sampling greatly reduces phylogenetic error

Several authors have argued recently that extensive taxon sampling has a positive and important effect on the accuracy of phylogenetic estimates. However, other authors have argued that there is little benefit of extensive taxon sampling, and so phylogenetic problems can or should be reduced to a few exemplar taxa as a means of reducing the computational complexity of the phylogenetic analysis. In this paper we examined five aspects of study design that may have led to these different perspectives. First, we considered the measurement of phylogenetic error across a wide range of taxon sample sizes, and conclude that the expected error based on randomly selecting trees (which varies by taxon sample size) must be considered in evaluating error in studies of the effects of taxon sampling. Second, we addressed the scope of the phylogenetic problems defined by different samples of taxa, and argue that phylogenetic scope needs to be considered in evaluating the importance of taxon-sampling strategies. Third, we examined the claim that fast and simple tree searches are as effective as more thorough searches at finding near-optimal trees that minimize error. We show that a more complete search of tree space reduces phylogenetic error, especially as the taxon sample size increases. Fourth, we examined the effects of simple versus complex simulation models on taxonomic sampling studies. Although benefits of taxon sampling are apparent for all models, data generated under more complex models of evolution produce higher overall levels of error and show greater positive effects of increased taxon sampling. Fifth, we asked if different phylogenetic optimality criteria show different effects of taxon sampling. Although we found strong differences in effectiveness of different optimality criteria as a function of taxon sample size, increased taxon sampling improved the results from all the common optimality criteria. Nonetheless, the method that showed the lowest overall performance (minimum evolution) also showed the least improvement from increased taxon sampling. Taking each of these results into account re-enforces the conclusion that increased sampling of taxa is one of the most important ways to increase overall phylogenetic accuracy.     

On areas of endemism,with an example from the African Restionaceae

Areas of endemism are central to cladistic biogeography. The concept has been much debated in the past, and from this has emerged the generally accepted definition as an area to which at least two species are endemic. Protocols for locating areas of endemism have been neglected, and to date no attempt has been made to develop optimality criteria against which to evaluate competing hypotheses of areas of endemism. Here various protocols for finding areas of endemism are evaluated--protocols based on both phonetic and parsimony analyses, on both unweighted data and data weighted by various criteria. The optimality criteria used to compare the performance of the methods include the number of species included in the areas of endemism, the number of areas delimited, and the degree of distributional congruency of the species restricted to each area of endemism. These methods are applied to the African Restionaceae in the Cape Floristic Region. Parsimony methods using weighted data are shown to perform best on the combination of all three optimality criteria. By varying the weighting parameters, the size of the areas of endemism can be varied. This provides a very useful tool for locating areas of endemism that satisfy prespecified scale criteria.     

An economic model of the limits to foraging range in central place foragers with numerical solutions for bumblebees

1. A model is described that evaluates the maximum economic foraging range in central place foragers by using optimality criteria to discriminate between foraging sites at different distances from the forager's central place. 2. The basic model can be varied to suit foragers that optimise either their rate of net energy uptake or their foraging efficiency. 3. The model requires specification of the time and energy budgets of travel and foraging, and of the rewards obtainable at potential foraging sites. 4. The specific case of bumblebees, whose foraging ranges are poorly known, is considered. 5. Numerical solutions of the model for parameter values that represent bumblebees and their forage predict economic foraging ranges exceeding several kilometres. The model demonstrates that economics alone can explain extensive flight ranges in bees.     

Adaptive Dc-optimal designs for dose finding based on a continuous efficacy endpoint

We introduce a new optimal design for dose finding with a continuous efficacy endpoint. This design is studied in the context of a flexible model for the mean of the dose-response. The design incorporates aspects of both D- and c-optimality and can be used when the study goals under consideration include dose-response estimation, followed by identification of the target dose. Different optimality criteria are considered. Simulations are shown with results comparing our adaptive design to the fixed allocation (without adaptations). We show that both the estimation of dose-response and identification of the minimum effective dose are improved using our design.     

A neural network methodology of quadratic optimization.

According to the basic optimization principle of artificial neural networks, a novel kind of neural network model for solving the quadratic programming problem is presented. The methodology is based on the Lagrange multiplier theory in optimization and seeks to provide solutions satisfying the necessary conditions of optimality. The equilibrium point of the network satisfies the Kuhn-Tucker condition for the problem. The stability and convergency of the neural network is investigated and the strategy of the neural optimization is discussed. The feasibility of the neural network method is verified with the computation examples. Results of the simulation of the neural network to solve optimum problems are presented to illustrate the computational power of the neural network method.     

Biological optimality: Comparison of generalized feasibility and optimality conditions for linear,error-minimizing systems

An attempt is made to compare the conditions for the general error-optimality of linear systems developed by Kalman with the conditions for feasibility of linear models of neuromuscular and physiological control systems. Models of three actual physiological systems are tested for both the above criteria. Theoretical analysis presented here shows that there are no simple relationships between the two sets of conditions. Analysis carried out on the physiological systems models suggests the need for a general set of conditions for other optimality criteria, such as time and energy minimization, similar to Kalman's condition for error minimization.     

A model for the resistance of tumor cells to cancer chemotherapeutic agents

A mathematical model of tumor resistance to chemotherapy based on a stochastic process of change is presented. The probability of no resistant cells is utilized as a fundamental quantity of interest, and the effects of various therapeutic strategies on it are explored. Situations where one or two drugs are available are treated in detail and extrapolation made to the n-drug case. The situation where two drugs may not be given simultaneously is examined, and it is found that sequential alternation of drugs satisfies certain optimality criteria when both drugs are equally effective. From this it is inferred that the simultaneous administration of all available active agents is optimal where this is permissible.     

Optimality principles in arterial branching

A comparative study of four optimality principles for the branching geometry of blood arteries is presented. The results offer four different criteria which can be tested by experimental data to establish which of these principles is followed in the cardiovascular system. More significantly, the results suggest the further possibility that the geometry of arterial junctions may be governed by all of these principles simultaneously, to thus achieve a much higher degree of optimality than has hitherto been suspected. This result offers a basis for seeking a correlation between the degree of optimality of a particular junction and the incidence of certain arterial lesions at that junction.     

Optimality under noise: higher memory strategies for the alternating prisoner's dilemma.

The Alternating Prisoner's Dilemma is a variant of the iterated Prisoner's Dilemma in which the players alternate in the roles of actor and recipient. We searched for strategies which are "optimal" in the Alternating Prisoner's Dilemma with noise (a non-zero probability that a player's decision will be transmitted incorrectly). In order to achieve success against a variety of other strategies, a strategy must be "self-cooperating" (able to achieve mutual cooperation with its clone), "C-exploiting" (able to exploit unconditional cooperators), and "D-unexploitable" (able to resist exploitation by defectors). It must also have high evolutionary "dominance", a general measure of evolutionary performance which considers both resistance to invasion and the ability to invade other strategies. A strategy which meets these optimality criteria can evolve cooperation by invading a population of defectors and establishing a stable cooperative society. Most of the strategies commonly discussed in the Alternating Prisoner's Dilemma literature are low-memory strategies such as Tit For Tat, Pavlov, and Firm But Fair, but none of these strategies can simultaneously meet all of the optimality criteria. However, we discovered a class of higher memory "Firm Pavlov" strategies, which not only meet our stringent optimality criteria, but also achieve remarkable success in round-robin tournaments and evolutionary interactions. These higher memory strategies are friendly enough to cooperate with their clone, pragmatic enough to exploit unconditional cooperators, and wary enough to resist exploitation by defectors: they are truly "optimal under noise" in the Alternating Prisoner's Dilemma.     

Automatic identification of structural gene fragments using a set of peptides

A computer program is designed to facilitate the identification of coding gene's fragments using a set of peptides. The program is written on Basic programming language for personal computer "Iskra-226" (USSR). To accelerate some operations, computer code commands are used. Treatment of 50 DNA fragments by means of 10 peptides takes ca. 1 h of computer time. The program outputs list coding gene's fragments and corresponding peptides. The suggested algorithm is based on our finding that the number of false identifications of a coding gene fragments may be predicted by Poisson distribution and minimized using correct criteria. The suggested method enables one to evaluate the reliability of the true identification of DNA fragments in case of mistakes in primary structure of the gene fragments or peptides.     

Optimality criteria for the design of 2-color microarray studies

We discuss the definition and application of design criteria for evaluating the efficiency of 2-color microarray designs. First, we point out that design optimality criteria are defined differently for the regression and block design settings. This has caused some confusion in the literature and warrants clarification. Linear models for microarray data analysis have equivalent formulations as ANOVA or regression models. However, this equivalence does not extend to design criteria. We discuss optimality criterion, and argue against applying regression-style D-optimality to the microarray design problem. We further disfavor E- and D-optimality (as defined in block design) because they are not attuned to scientific questions of interest.     

On the optimal control of fed-batch reactors with substrate-inhibited kinetics

The optimal feed rate profiles, for fed-batch fermentation that maximizes the biomass production and accounts for time, are analyzed. The solution can be found only if the final arc of the optimal control is a batch arc, since in this case the final concentrations of substrate and biomass can be determined by ulterior conditions on the mass balance and on the final growth rate of biomass and thus it is possible to solve the resulting time optimal problem by using Green's theorem. This evidences the "turnpike property" of the solution, which tries to spend the maximum time on or at least near the singular arc along which the substrate concentration is maintained constant. The optimality of the final batch arc is related to the time operational cost in the performance index. The sequence of the control depends on the initial conditions for which six different regions, with the respective patterns, have been identified, in case the performance index allows the control sequence to have a final batch.     

Model-based identification of motion sensor placement for tracking retraction and elongation of the tongue

Electromagnetic articulography (EMA) is designed to track facial and tongue movements. In practice, the EMA sensors for tracking the movement of the tongue’s surface are placed heuristically. No recommendation exists. Within this paper, a model-based approach providing a mathematical analysis and a computational-based recommendation for the placement of sensors, which is based on the tongue’s envelope of movement, is proposed. For this purpose, an anatomically detailed Finite Element (FE) model of the tongue has been employed to determine the envelope of motion for retraction and elongation using a forward simulation. Two optimality criteria have been proposed to identify a set of optimal sensor locations based on the pre-computed envelope of motion. The first one is based on the assumption that locations exhibiting large displacements contain the most information regarding the tongue’s movement and are less susceptible to measurement errors. The second one selects sensors exhibiting each the largest displacements in the anterior-posterior, superior-inferior, medial-lateral and overall direction. The quality of the two optimality criteria is analysed based on their ability to deduce from the respective sensor locations the corresponding muscle activation parameters of the relevant muscle fibre groups during retraction and elongation by solving the corresponding inverse problem. For this purpose, a statistical analysis has been carried out, in which sensor locations for two different modes of deformation have been subjected to typical measurement errors. Then, for tongue retraction and elongation, the expectation value, the standard deviation, the averaged bias and the averaged coefficient of variation have been computed based on 41 different error-afflicted sensor locations. The results show that the first optimality criteria is superior to the second one and that the averaged bias and averaged coefficient of variation decrease when the number of sensors is increased from 2, 4 to 6 deployable sensors.