Pareto-optimal alignment of biological sequences]

The problem of alignment of two symbol sequences is considered. The validity of the available algorithms for constructing optimal alignment depends on the weighting coefficients which are frequently difficult to choose. A new approach to the problem is proposed, which is based on the use of vector weighting functions (instead of tradionally used scalar ones) and Pareto-optimal alignment (an alignment that is optimal at any choice of weighting coefficient will always be Pareto-optimal). An efficient algorithm for constructing all Pareto-optimal alignments of two sequences is proposed. An approach to choosing a "biologically correct" alignment among all Pareto-optimal alignments is suggested.     

Metabolic Pathfinding Using RPAIR Annotation

Metabolic databases contain information about thousands of small molecules and reactions, which can be represented as networks. In the context of metabolic reconstruction, pathways can be inferred by searching optimal paths in such networks. A recurrent problem is the presence of pool metabolites (e.g., water, energy carriers, and cofactors), which are connected to hundreds of reactions, thus establishing irrelevant shortcuts between nodes of the network. One solution to this problem relies on weighted networks to penalize highly connected compounds. A more refined solution takes the chemical structure of reactants into account in order to differentiate between side and main compounds of a reaction. Thanks to an intensive annotation effort at KEGG, decompositions of reactions into reactant pairs (RPAIR) categorized by their role (main, trans, cofac, ligase, and leave) are now available.The goal of this article is to evaluate the impact of RPAIR data on pathfinding in metabolic networks. To this end, we measure the impact of different parameters concerning the construction of the metabolic network: mapping of reactions and reactant pairs onto a graph, use of selected categories of reactant pairs, weighting schemes for compounds and reactions, removal of highly connected metabolites, and reaction directionality. In total, we tested 104 combinations of parameters and identified their optimal values for pathfinding on the basis of 55 reference pathways from three organisms.The best-performing metabolic network combines the biochemical knowledge encoded by KEGG RPAIR with a weighting scheme penalizing highly connected compounds. With this network, we could recover reference pathways from Escherichia coli with an average accuracy of 93% (32 pathways), from Saccharomyces cerevisiae with an average accuracy of 66% (11 pathways), and from humans with an average accuracy of 70% (12 pathways). Our pathfinding approach is available as part of the Network Analysis Tools.     

Using priced timed automaton to analyse the energy consumption in cloud computing environment

According to the fact that cloud servers have different energy consumption on different running states, as well as the energy waste problem caused by the mismatching between cloud servers and cloud tasks, we carry out researches on the energy optimal method achieved by a priced timed automaton for the cloud computing center in this paper. The priced timed automaton is used to model the running behaviors of the cloud computing system. After introducing the matching matrix of cloud tasks and cloud resources as well as the power matrix of the running states of cloud servers, we design a generation algorithm for the cloud system automaton based on the generation rules and reduction rules given ahead. Then, we propose another algorithm to settle the minimum path energy consumption problem in the cloud system automaton, therefore obtaining an energy optimal solution and an energy optimal value for the cloud system. A case study and repeated experimental analyses manifest that our method is effective and feasible.     

Optimal multiple testing and design in clinical trials

A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper, we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the procedures. This leads us to an explicit optimization problem with objective and constraints that describe its specific desiderata. We present a complete solution for deriving optimal procedures for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal procedures that are identical to existing procedures, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for other cases it yields completely novel and more powerful procedures than existing ones. We demonstrate the nature of our novel procedures and their improved power extensively in a simulation and on the APEX study (Cohen et al., 2016).     

The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model

The paper analyzes optimal harvesting of age-structured populations described by the Lotka-McKendrik model. It is shown that the optimal time- and age-dependent harvesting control involves only one age at natural conditions. This result leads to a new optimization problem with the time-dependent harvesting age as an unknown control. The integral Lotka model is employed to explicitly describe the time-varying age of harvesting. It is proven that in the case of the exponential discounting and infinite horizon the optimal strategy is a stationary solution with a constant harvesting age. A numeric example on optimal forest management illustrates the theoretical findings. Discussion and interpretation of the results are provided.     

An optimizing start-up strategy for a bio-methanator

This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang–bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.     

Using the biomasses of soil nematode taxa as weighting factors for assessing soil food web conditions

We propose the use of nematode generic biomasses as weighting factors for calculation of nematode community indices. Three data sets were used to calculate the indices using guild-based weighting (i.e., fixed weighting of nematode guilds) and genus-based weighting (i.e., weighting based on the nematode generic biomasses). The genus-based weighting factors were quadratically correlated with guild-based weighting factors, but the genus-based weighting factors were highly variable within each nematode guild, indicating that important information was likely missing when guild-based weighting was used. Although variation patterns of in the indices in response to management practices and land use were often similar for the two weighting systems, they sometimes differed substantially, and the specific index values frequently differed depending on which weighting system was used. In addition, the absolute values of the indices were frequently found to be different between the two weighting systems. Based on the comparison of indices from the two systems, we found that the genus-based system was complementary rather than superior to the guild-based system. It was suggested that both weighting systems should be used for the calculation of the nematode community indices in a study in order to better distinguish the treatment effects.     

Chasing and pursuit in the dolichopodid fly Poecilobothrus nobilitatus

1. Male Poecilobothrus nobilitatus show two distinct kinds of pursuit. Females are “shadowed” at a distance of a few cm, using both rotational and lateral movements. Other males are chased, in a pursuit that involves only rotation and fast forward flight. The rotational component of pursuit appears to have the same control system in both types of tracking, and it is best described as a continuous translation of the error angle between the direction of the target and the pursuing fly's body axis into the pursuing fly's angular velocity. The constant of proportionality is 30–40°·s^?1 per degree, and the delay in the system is about 15 ms. Pursuit on the ground is 2–3 times slower than in flight, although the delay seems to be similar.
2. Attempts were made to see whether the aerial pursuits could be modelled effectively by a saccadic or discontinuous control system, as suggested for Musca pursuit (Wagner 1986). It was found that the velocity profiles of the chases could be fitted by an overlapping series of plausible saccade-like events, However, the correlation between visual information (error angle and error angular velocity) available just before each fictive saccade correlated poorly with saccade peak velocity. It is thus concluded that Poedlobothrus pursuit is basically continuous in nature, but it is argued that the two types of mechanism are hard to distinguish in natural behaviour.

     

Motion Control in Saccade and Smooth Pursuit for Bionic Eye Based on Three-dimensional Coordinates

Saccade and smooth pursuit are two important functions of human eye.In order to enable bionic eye to imitate the two functions,a control method that implements saccade and smooth pursuit based on the three-dimensional coordinates of target is proposed.An optimal observation position is defined for bionic eye based on three-dimensional coordinates.A kind of motion planning method with high accuracy is developed.The motion parameters of stepper motor consisting of angle acceleration and turning time are computed according to the position deviation,the target's angular velocity and the stepper motor's current angular velocity in motion planning.The motors are controlled with the motion parameters moving to given position with desired angular velocity in schedule time.The experimental results show that the bionic eye can move to optimal observation positions in 0.6 s from initial location and the accuracy of 3D coordinates is improved.In addition,the bionic eye can track a target within the error of less than 20 pixels based on three-dimensional coordinates.It is verified that saccade and smooth pursuit of bionic eye based on three-dimensional coordinates are feasible.     

A 'cheap' optimal control approach to estimate muscle forces in musculoskeletal systems

This paper shows a new method to estimate the muscle forces in musculoskeletal systems based on the inverse dynamics of a multi-body system associated optimal control. The redundant actuator problem is solved by minimizing a time-integral cost function, augmented with a torque-tracking error function, and muscle dynamics is considered through differential constraints. The method is compared to a previously implemented human posture control problem, solved using a Forward Dynamics Optimal Control approach and to classical static optimization, with two different objective functions. The new method provides very similar muscle force patterns when compared to the forward dynamics solution, but the computational cost is much smaller and the numerical robustness is increased. The results achieved suggest that this method is more accurate for the muscle force predictions when compared to static optimization, and can be used as a numerically 'cheap' alternative to the forward dynamics and optimal control in some applications.     

Hierarchical genetic algorithm for near optimal feedforward neural network design

In this paper, we propose a genetic algorithm based design procedure for a multi layer feed forward neural network. A hierarchical genetic algorithm is used to evolve both the neural networks topology and weighting parameters. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies, including a feasibility check highlighted in literature. A multi objective cost function is used herein to optimize the performance and topology of the evolved neural network simultaneously. In the prediction of Mackey Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to traditional learning algorithms for the multi layer Perceptron networks and radial basis function networks. Based upon the chosen cost function, a linear weight combination decision making approach has been applied to derive an approximated Pareto optimal solution set. Therefore, designing a set of neural networks can be considered as solving a two objective optimization problem.     

Revisiting excitation pattern design for magnetic resonance imaging through optimisation of the signal contrast efficiency

The design of excitation signals for Magnetic Resonance Imaging (MRI) is cast as an optimal control problem. Here, we demonstrate that signals other than pulse excitations, which are ubiquitous in MRI, can provide adequate excitation, thus challenging the optimality and ubiquity of pulsed signals. A class of on-resonance piecewise continuous amplitude modulated signals is introduced. It is shown that despite the bilinear nature of the Bloch equations, the spins system response is largely analytically tractable for this class of signals, using Galerkin approximation methods. To challenge the optimality of the pulse excitation, an appropriate cost criterion, the Signal Contrast Efficiency (SCE), is developed. It is to be optimised subject to dynamics expressed by the Bloch equations. To solve the problem the Bloch equation is transferred to the excitation dependent rotating frame of reference. The numerical solutions to the problem for different tissue types show that for a short period of time, pulse excitations provide the maximum signal contrast. However, the problem should be solved for longer periods of time which may result in a different answer than a pulse. For this purpose, the approximate analytic solution which is derived based on averaging the Bloch equation in the excitation dependent rotating frame of reference will be used to find the optimal excitation pattern. The solution to the optimisation problem is potentially useful for all forms of MRI including structural and functional imaging. The objective of this paper is to show that while classically transient response of pulses have been monitored so far, the optimal excitation pattern may be the steady state response of a non-pulse excitation.     

A parameter optimization approach for the optimal control of large-scale musculoskeletal systems.

This paper describes a computational method for solving optimal control problems involving large-scale, nonlinear, dynamical systems. Central to the approach is the idea that any optimal control problem can be converted into a standard nonlinear programming problem by parameterizing each control history using a set of nodal points, which then become the variables in the resulting parameter optimization problem. A key feature of the method is that it dispenses with the need to solve the two-point, boundary-value problem derived from the necessary conditions of optimal control theory. Gradient-based methods for solving such problems do not always converge due to computational errors introduced by the highly nonlinear characteristics of the costate variables. Instead, by converting the optimal control problem into a parameter optimization problem, any number of well-developed and proven nonlinear programming algorithms can be used to compute the near-optimal control trajectories. The utility of the parameter optimization approach for solving general optimal control problems for human movement is demonstrated by applying it to a detailed optimal control model for maximum-height human jumping. The validity of the near-optimal control solution is established by comparing it to a solution of the two-point, boundary-value problem derived on the basis of a bang-bang optimal control algorithm. Quantitative comparisons between model and experiment further show that the parameter optimization solution reproduces the major features of a maximum-height, countermovement jump (i.e., trajectories of body-segmental displacements, vertical and fore-aft ground reaction forces, displacement, velocity, and acceleration of the whole-body center of mass, pattern of lower-extremity muscular activity, jump height, and total ground contact time).     

An integrated scheduling and control model for multi-mode projects

In today’s highly competitive uncertain project environments, it is of crucial importance to develop analytical models and algorithms to schedule and control project activities so that the deviations from the project objectives are minimized. This paper addresses the integrated scheduling and control in multi-mode project environments. We propose an optimization model that models the dynamic behavior of projects and integrates optimal control into a practically relevant project scheduling problem. From the scheduling perspective, we address the discrete time/cost trade-off problem, whereas an optimal control formulation is used to capture the effect of project control. Moreover, we develop a solution algorithm for two particular instances of the optimal project control. This algorithm combines a tabu search strategy and nonlinear programming. It is applied to a large scale test bed and its efficiency is tested by means of computational experiments. To the best of our knowledge, this research is the first application of optimal control theory to multi-mode project networks. The models and algorithms developed in this research are targeted as a support tool for project managers in both scheduling and deciding on the timing and quantity of control activities.     

Weighted least squares in calibration: the problem with using "quality coefficients" to select weighting formulas

The quality coefficient (Q) has frequently been used to select weighting formulae in calibration, and especially so in bioanalytical work, where there has been increasing awareness of the importance of data heteroscedasticity in recent years. However, this quantity is statistically flawed and should not be used for this purpose. The quality coefficient is computed from the differences between the apparent and true concentrations of the calibration samples as obtained from the least-squares calibration fit. Q is defined as the sum of either the squares or the absolute values of these differences, taken directly or as percentage (relative) deviations. It is calculated for several different trial weighting formulae, and the lowest Q value is then deemed to identify the best weighting choice. However, these Qs are predisposed to favor data consistent with their definitions-homoscedastic data for tests employing absolute differences, and data having proportional error (constant coefficient of variance) for tests using relative differences-because the Q in each case closely resembles the quantity actually minimized by the least-squares fit of the calibration data. The problem is examined and illustrated through Monte Carlo computations on data having either constant or proportional uncertainty and subjected to both tests. A modified Q based on the results of both the absolute and relative tests is much more reliable than either test alone but is still not recommended as a solution to the weighting problem, as other, statistically sound approaches are available and readily used.     

The numerical method for the optimal supporting position and related optimal control for the catalytic reaction system

This paper considers the numerical approximation for the optimal supporting position and related optimal control of a catalytic reaction system with some control and state constraints, which is governed by a nonlinear partial differential equations with given initial and boundary conditions. By the Galerkin finite element method, the original problem is projected into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then the control parameterization method is applied to approximate the control and reduce the original system to an optimal parameter selection problem, in which both the position and related control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a particle swarm optimization algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method.     

Distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method

In this paper, we present a distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method. The dynamic model comprises system of three coupled reaction-diffusion models, involving the tumor cells, the normal tissues and the drug concentration. An optimal control problem is formulated with the goal of minimizing the tumor cell density and reducing the side effects of the drug. A distributed parameters method based on the application of variational calculus is used on an integral-Hamiltonian, which is then used to obtain an optimal coupled system of forward state equations and backward co-state equations. The Galerkin finite element method is used to realistically represent the brain structure as well as to facilitate computation. Finally a three-dimensional test case is considered and partitioned into a set of spherical finite elements, using tri-linear basis functions, except for the elements affected by singularities of polar and azimuthal angles, as well as the origin.     

An evolutionary approach to enzyme kinetics: Optimization of ordered mechanisms

A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is based on the assumption that an increase in reaction rates was an important characteristic of the evolution of the kinetic properties of enzymes. The corresponding nonlinear optimization problem is solved taking into account the constraint that the rate constants of the elementary processes do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Generalizations concern ordered uni-uni-reactions involving an arbitrary number of elementary steps. It could be shown that depending on the substrate and product concentrations different types of solutions can be found which are classified according to the number of rate constants assuming in the optimal state submaximal values. A general rule is derived concerning the number of possible solutions of the given optimization problem. For high values of the equilibrium constant one solution always applies to a very large range of the concentrations of the reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. Optimal kinetic parameters of ordered enzymic mechanisms with two substrates and one product (bi-uni-mechanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In all cases studied the model predicts a matching of the concentrations of the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the model can be applied to the calculation of the optimal kinetic design of real enzymes.     

A nonlinear numerical model of percutaneous drug absorption.

A nonlinear mathematical model developed by Chandrasekaran et al. is examined to monitor pharmacokinetic profiles in percutaneous drug absorption and is addressed to several associated problems that could occur in the data analysis of in vitro experiments. The formulation of the model gives rise to a nonlinear partial differential equation (PDE) of parabolic type, and a family of finite-difference methods is developed for the numerical solution of the associated initial/boundary-value problem. The value given to a parameter in this family determines the stability properties of the resulting method and whether the solution is obtained explicitly or implicitly. In the case of implicit members of the family it is seen that the solution of the nonlinear PDE is obtained by solving a linear algebraic system, the coefficient matrix of which is tridiagonal. The behaviors of two methods of the family are examined in a series of numerical experiments. Numerical differentiation and integration procedures are combined to monitor the cumulative amount of drug eliminated into the receptor cell per unit area as time increases. It is found that the use of the equation for the simple membrane model to estimate the permeability coefficient and lag time is warranted even if the system should be described by the dual-sorption model, provided cumulative amount versus time data collected for a sufficiently long time are used. However, being different from the behavior in the simple membrane model, the lag time, which can be estimated in this way, is dose-dependent and decreases with increasing donor cell concentration. On the other hand, the permeability coefficient in the dual-sorption model remains constant irrespective of the donor cell concentrations as in the simple membrane model.