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.     

Experimental study of the optimal time for tenolysis

We have attempted to define the optimal time for tenolysis by evaluating the blood supply, the rupture rate, and the tensile strength of tenolysed and control tendons. In 128 chickens tenolysis was performed 1, 3, 6, 12, 16, and 24 weeks after primary tendon repair. Tenolysis at 1 and 3 weeks resulted in devascularization, weak tendons, and high rupture rates. Tenolysis at 6 weeks after the primary repair had mixed effects on the blood supply but weakened the tendon. Tenolysis at 12 weeks after the tendon repair did not weaken the tendon and resulted in an increased blood supply. Tenolysis at 16 and 24 weeks did not weaken the tendon, but had varied effects on the blood supply. We recommend an interval of 12 weeks between primary tendon repair and tenolysis.     

Rabies in raccoons: optimal control for a discrete time model on a spatial grid

An epidemic model for rabies in raccoons is formulated with discrete time and spatial features. The goal is to analyze the strategies for optimal distribution of vaccine baits to minimize the spread of the disease and the cost of implementing the control. Discrete optimal control techniques are used to derive the optimality system, which is then solved numerically to illustrate various scenarios.     

Clinical effects of 2-DG drug restraining SARS-CoV-2 infection: A fractional order optimal control study

Fractional calculus is very convenient tool in modeling of an emergent infectious disease system comprising previous disease states, memory of disease patterns, profile of genetic variation etc. Significant complex behaviors of a disease system could be calibrated in a proficient manner through fractional order derivatives making the disease system more realistic than integer order model. In this study, a fractional order differential equation model is developed in micro level to gain perceptions regarding the effects of host immunological memory in dynamics of SARS-CoV-2 infection. Additionally, the possible optimal control of the infection with the help of an antiviral drug, viz. 2-DG, has been exemplified here. The fractional order optimal control would enable to employ the proper administration of the drug minimizing its systematic cost which will assist the health policy makers in generating better therapeutic measures against SARS-CoV-2 infection. Numerical simulations have advantages to visualize the dynamical effects of the immunological memory and optimal control inputs in the epidemic system.     

Computational models of signalling networks for non-linear control

Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.     

Computational mechanisms of sensorimotor control

In order to generate skilled and efficient actions, the motor system must find solutions to several problems inherent in sensorimotor control, including nonlinearity, nonstationarity, delays, redundancy, uncertainty, and noise. We review these problems and five computational mechanisms that the brain may use to limit their deleterious effects: optimal feedback control, impedance control, predictive control, Bayesian decision theory, and sensorimotor learning. Together, these computational mechanisms allow skilled and fluent sensorimotor behavior.     

Computational approaches to motor control

New concepts and computational models that integrate behavioral and neurophysiological observations have addressed several of the most fundamental long-standing problems in motor control. These problems include the selection of particular trajectories among the large number of possibilities, the solution of inverse kinematics and dynamics problems, motor adaptation and the learning of sequential behaviors.     

An optimal time control problem for the administration of 2′,3′-dideoxycytidine by using red blood cells as bioreactors

The problem of optimal dosage is studied for the administration of ddCyd using erythrocytes as carriers and bioreactors. The volume of erythrocytes and the initial amount of drug to be loaded have to be determined in such a way that the duration of the therapeutic effect is maximized without exceeding the toxic threshold. It is found that the optimal control is unique and it is at the upper vertex of the set of the admissible controls. A more general case is also briefly discussed.     

External optimal control of self-organisation dynamics in a chemotaxis reaction diffusion system

Detailed quantitative understanding and specific external control of cellular behaviour are general long-term goals of modem bioscience research activities in systems biology. Pattern formation and self-organisation processes both in single cells and in distributed cell populations are phenomena which are highly significant for the functionality of life, because life requires to maintain a highly organised spatiotemporal system structure. In particular chemotaxis is crucial for various biological aspects of intercellular signalling and cell aggregation. As an example for model based control of self-organising biological systems, we describe numerical optimal control of E. coli bacterial chemotaxis based on a 1-D two-component partial differential equation (PDE) model of reaction diffusion type. We present a numerical scheme to force cell aggregation patterns to particular desired results by applying a boundary influx control of chemoattractant without interfering with the system itself. Optimal controls are numerically computed by using a specially tailored interior point optimisation technique applied to a direct collocation discretisation of the control function and the PDE constraint. The objective to be minimised is the deviation of a desired cell distribution from the cell density, which results from the dynamics of the controlled system.     

An optimal control model for maximum-height human jumping

To understand how intermuscular control, inertial interactions among body segments, and musculotendon dynamics coordinate human movement, we have chosen to study maximum-height jumping. Because this activity presents a relatively unambiguous performance criterion, it fits well into the framework of optimal control theory. The human body is modeled as a four-segment, planar, articulated linkage, with adjacent links joined together by frictionless revolutes. Driving the skeletal system are eight musculotendon actuators, each muscle modeled as a three-element, lumped-parameter entity, in series with tendon. Tendon is assumed to be elastic, and its properties are defined by a stress-strain curve. The mechanical behavior of muscle is described by a Hill-type contractile element, including both series and parallel elasticity. Driving the musculotendon model is a first-order representation of excitation-contraction (activation) dynamics. The optimal control problem is to maximize the height reached by the center of mass of the body subject to body-segmental, musculotendon, and activation dynamics, a zero vertical ground reaction force at lift-off, and constraints which limit the magnitude of the incoming neural control signals to lie between zero (no excitation) and one (full excitation). A computational solution to this problem was found on the basis of a Mayne-Polak dynamic optimization algorithm. Qualitative comparisons between the predictions of the model and previously reported experimental findings indicate that the model reproduces the major features of a maximum-height squat jump (i.e. limb-segmental angular displacements, vertical and horizontal ground reaction forces, sequence of muscular activity, overall jump height, and final lift-off time).     

Construction of optimal quality control for oligo arrays

MOTIVATION: Oligo arrays are important experimental tools for the high throughput measurement of gene expression levels. During production of oligo arrays, it is important to identify any faulty manufacturing step. RESULTS: We describe a practical algorithm for the construction of optimal quality control designs that identify any faulty manufacturing step. The algorithm uses hillclimbing, a search technique from combinatorial optimization. We also present the results of using this algorithm on all practical quality control design sizes. AVAILABILITY: On request from the authors.     

杜氏盐藻电击转化方法的系统优化

本研究系统分析了盐藻生长状态、电击条件、电击缓冲液成分和质粒浓度等条件对电击转化效率的影响。实验结果表明:正常接种后培养7d对数生长中期的盐藻细胞,在25μF、0.8kV的电击条件下加入终浓度为10μg/mL的质粒可使盐藻电击转化效率达到1.85‰;电击缓冲液中加入0.4mol/L的甘油可使转化效率显著提高至2.03‰(P<0.05)。在上述优化电击体系下,运用3种不同质粒分别转化盐藻细胞后获得的转化效率无显著差异。通过对电击转化中相关因素的优化,本研究建立了一种适用于杜氏盐藻的高效稳定的电击转化体系,为杜氏盐藻的转基因研究提供有效方法。     

The optimal allocation of time during the diving cycle

Previous research has used a "marginal value" approach to determinehow long a diver should spend on the surface obtaining oxygenif it is to maximize the proportion of time in the foragingarea. In this paper we develop an explicit and general versionof this model and show how it results in predictions about bothtime on the surface and time under water. We also extend theanalysis to include the maximization of the net rate of energeticgain and the maximization of energetic efficiency. We show thatthe various currencies can be distinguished qualitatively interms of the way in which their predictions depend on the parametersthat characterize the animal and its environment. A generalfeature of the results is that the time in the foraging areashould first increase and then decrease as round-trip traveltime, , from the surface to the foraging area and back againincreases.     

An optimal control problem for ovine brucellosis with culling

A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnseba et al. [A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2–11. Available at http://www.math.u-bordeaux1.fr/～pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost.     

Computational modeling of the EGF-receptor system: a paradigm for systems biology

Computational models have rarely been used as tools by biologists but, when models provide experimentally testable predictions, they can be extremely useful. The epidermal growth factor receptor (EGFR) is probably the best-understood receptor system, and computational models have played a significant part in its elucidation. For many years, models have been used to analyze EGFR dynamics and to interpret mutational studies, and are now being used to understand processes including signal transduction, autocrine loops and developmental patterning. The success of EGFR modeling can be a guide to combining models and experiments productively to understand complex biological processes as integrated systems.     

On optimal propagule size and developmental time

A negative relationship between propagule size and development time is often imposed as a constraint on the evolution of optimal propagule size. Here I argue that when mortality is size-dependent, the optimisation of propagule size is in fact independent of the length of the ensuing developmental period. Furthermore, I show that whether larger or smaller propagules are favoured in response to factors that affect growth and mortality rates will depend on which of these variables scale more sharply with size. I use marine fish to exemplify some of the points raised in this note.     

Computational simulations on the fish-type-II antifreeze protein-ice-solvent system

Based on the computational simulation with the vacuum environment for the fish-type-II antifreeze proteinice-solvent (water) system, the multi-complex system of the antifreeze protein-ice-water has been constructed and calculated. We have studied the interaction of such proteinice system with water solvent through the dynamics simulation with 350 ps. By employing the Molecular Dynamics simulation and semi-empirical method calculation, we have further investigated the interface properties of the antifreeze protein and ice crystal combined system. Consequently, a water solvent affects significantly the properties of this combined system. __________ Translated from Journal of Beijing Normal University (Natural Science), 2006, 42(1): 74–77 [译自: 北京师范大学学报]