Modeling and inverse simulation of somersaults on the trampoline

This paper describes a biomechanical model for numerical simulation of front and back somersaults, without twist, performed on the trampoline. The developed mathematical formulation is used to solve an inverse dynamics problem, in which the moments of muscle forces at the joints that result in a given (measured) motion are determined. The nature of the stunts and the way the human body is maneuvered and controlled can be studied. The calculated torques can then be used as control signals for a dynamic simulation. This provides a way to check the inverse dynamics procedures, and influence of typical control errors on somersault performance can be studied. To achieve these goals, the nonlinear dynamical model of the trampolinist and the interacting trampoline bed has been identified, and a methodology for recording the actual somersault performances was proposed. Some results of numerical simulations are reported.     

The influence of touchdown conditions and contact phase technique on post-flight height in the straight handspring somersault vault

In vaulting the gymnast must generate sufficient linear and angular momentum during the approach and table contact in order to complete the rotational requirements in the post-flight phase. This study investigated the effects of touchdown conditions and contact technique on peak post-flight height of a straight handspring somersault vault. A planar seven-segment torque-driven computer simulation model of the contact phase in vaulting was evaluated by varying joint torque activation time histories to match three performances of a straight handspring somersault vault by an elite gymnast. The closest matching simulation was used as a starting point to optimise peak post-flight height of the mass centre for a straight handspring somersault. It was found that optimising either the touchdown conditions or the contact technique increased post-flight height by 0.1 m whereas optimising both together increased post-flight height by 0.4 m above that of a simulation matching the recorded performance. Thus touchdown technique and contact technique make similar contributions to post-flight height in the straight handspring somersault vault. Increasing touchdown velocity and angular momentum lead to additional post-flight height although there was a critical value of vertical touchdown velocity beyond which post-flight height decreased.     

Stable oscillations in mathematical models of biological control systems

Summary Oscillations in a class of piecewise linear (PL) equations which have been proposed to model biological control systems are considered. The flows in phase space determined by the PL equations can be classified by a directed graph, called a state transition diagram, on anN-cube. Each vertex of theN-cube corresponds to an orthant in phase space and each edge corresponds to an open boundary between neighboring orthants. If the state transition diagram contains a certain configuration called a cyclic attractor, then we prove that for the associated PL equation, all trajectories in the regions of phase space corresponding to the cyclic attractor either (i) approach a unique stable limit cycle attractor, or (ii) approach the origin, in the limitt→∞. An algebraic criterion is given to distinguish the two cases. Equations which can be used to model feedback inhibition are introduced to illustrate the techniques.     

Unstable steady state operations of substrate inhibited cultures by dissolved oxygen control

Microorganism kinetic growth characterized by substrate inhibition was investigated by means of a continuous stirred tank reactor equipped with a feedback controller of the medium feeding flow rate. The aerobic growth of Pseudomonas sp. OX1 with phenol as carbon/energy source was adopted as a case study to test a new control strategy using dissolved oxygen concentration as a state variable. The controller was successful in steadily operating bioconversion under intrinsically unstable conditions. A simple model of the controlled system was proposed to set the feedback controller.The specific growth rate of Pseudomonas sp. OX1 was successfully described by means of the Haldane model. The regression of the experimental data yielded μ_M = 0.26 h⁻¹, K_Ph = 5 × 10⁻³ g/L and K_I = 0.2 g/L. The biomass-to-substrate fractional yield as a function of the specific growth rate did not change moving from substrate-inhibited to substrate-deficient state. The data was modelled according to the Pirt model: m = 1.7 × 10⁻² g/(g h), . The specific growth rates calculated for batch and continuous growth were compared.     

Nonlinear control of HIV-1 infection with a singular perturbation model

Using a singular perturbation approximation, a nonlinear state-space model of HIV-1 infection, having as state variables the number of healthy and infected CD4+T cells and the number of virion particles, is simplified and used to design a control law. The control law comprises an inner block that performs feedback linearizing of the virus dynamics and an outer block implementing an LQ regulator that drives the number of virion particles to a number below the specification. A sensitivity analysis of the resulting law is performed with respect to the model parameter to the infection rate, showing that the controlled system remains stable in the presence of significant changes of this parameter with respect to the nominal value.     

Dynamics and control of the two-pulse protocol in electroporation: numerical exploration

Externally applied voltages can create transient, non-selective pores in a cell’s membrane, a phenomenon known as electroporation. Electroporation has reduced toxicity, is easy to perform, and does not induce the immune system. Therefore, the technique has a wide range of biological and medical applications. Previous experiments show that a two-pulse protocol, which consists of a fast, large-magnitude pulse and a slow, small-magnitude pulse, can increase the efficiency of drug delivery such as gene electrotransfer. In this work, we investigate the dynamics and control of the two-pulse protocol using a macroscopic model of electroporation. Numerical simulations show that there exists a range of pore radii that cannot be sustained using the conventional, open-loop, two-pulse protocol. As a result, one may need to use pores that are significantly larger than the sizes of the targeted molecules. Moreover, it is not possible to know the rate of delivery a priori. To ensure accurate drug delivery and avoid potential damage to the cell’s membrane, we explore feedback mechanisms to eliminate the gap in sustainable pore radii and thus to precisely control the electroporation process. Numerical simulations show that a straightforward feedback algorithm can achieve robust control effects. Moreover, the control algorithm is effective without knowledge of the model and thus has the potential to be implemented in experiments.     

The Integrated Aerobiology Modeling System applied to the spread of soybean rust into the Ohio River valley during September 2006

Soybean rust (Phakopsora pachyrhizi) has recently invaded North America and has the potential to be the most destructive foliar disease of soybean. As part of the response to this threat, the Integrated Aerobiology Modeling System (IAMS) was constructed to forecast the aerial movement of this pathogen from subtropical to middle latitude portions of the continent. IAMS simulations have been conducted daily for the past two growing seasons and integrated with information from a nationwide observation network into a decision support system for soybean farmers. After the 2005 season, the United States Department of Agriculture reported that many millions of United States (U.S.) soybean hectares that would have been treated for soybean rust in 2005 were not due to this decision support system. In 2006, soybean rust appeared for the first time in the major U.S. soybean production region over 1000 km from known areas of inoculum production. IAMS predictions of the geographical extent and timing of disease symptom expression were well matched with subsequent observations of the disease in the field.     

A mathematical modelling framework for elucidating the role of feedback control in translation termination

Translation is the final stage of gene expression where messenger RNA is used as a template for protein polymerization from appropriate amino acids. Release of the completed protein requires a release factor protein acting at the termination/stop codon to liberate it. In this paper we focus on a complex feedback control mechanism involved in the translation and synthesis of release factor proteins, which has been observed in different systems. These release factor proteins are involved in the termination stage of their own translation. Further, mutations in the release factor gene can result in a premature stop codon. In this case translation can result either in early termination and the production of a truncated protein or readthrough of the premature stop codon and production of the complete release factor protein. Thus during translation of the release factor mRNA containing a premature stop codon, the full length protein negatively regulates its production by its action on a premature stop codon, while positively regulating its production by its action on the regular stop codon. This paper develops a mathematical modelling framework to investigate this complex feedback control system involved in translation. A series of models is established to carefully investigate the role of individual mechanisms and how they work together. The steady state and dynamic behaviour of the resulting models are examined both analytically and numerically.     

Data acquisition and control of a continuous fermentation unit

Summary Data acquisition and computer control ofZymomonas mobilis fermentation for ethanol production has been studied. An HP 200 series microcomputer system was used in conjunction with an HP 3497A data acquisition unit. On-line ethanol, glucose and cell mass were measured for use as possible control variables. Dilution rate was used as the manipulative variable. A versatile, user-friendly data acquisition program was written to gather, control and analyze data from the continuous fermentation. The program allows user-given control and calibration algorithms so that sophisticated control policies, e.g., self-tuning regulator (STR) and instrumentation, can be implemented with relative ease.     

Feedback-induced gain control in stochastic spiking networks

The joint influence of recurrent feedback and noise on gain control in a network of globally coupled spiking leaky integrate-and-fire neurons is studied theoretically and numerically. The context of our work is the origin of divisive versus subtractive gain control, as mixtures of these effects are seen in a variety of experimental systems. We focus on changes in the slope of the mean firing frequency-versus-input bias (f –I) curve when the gain control signal to the cells comes from the cells’ output spikes. Feedback spikes are modeled as alpha functions that produce an additive current in the current balance equation. For generality, they occur after a fixed minimum delay. We show that purely divisive gain control, i.e. changes in the slope of the f –I curve, arises naturally with this additive negative or positive feedback, due to a linearizing actions of feedback. Negative feedback alone lowers the gain, accounting in particular for gain changes in weakly electric fish upon pharmacological opening of the feedback loop as reported by Bastian (J Neurosci 6:553–562, 1986). When negative feedback is sufficiently strong it further causes oscillatory firing patterns which produce irregularities in the f –I curve. Small positive feedback alone increases the gain, but larger amounts cause abrupt jumps to higher firing frequencies. On the other hand, noise alone in open loop linearizes the f –I curve around threshold, and produces mixtures of divisive and subtractive gain control. With both noise and feedback, the combined gain control schemes produce a primarily divisive gain control shift, indicating the robustness of feedback gain control in stochastic networks. Similar results are found when the “input” parameter is the contrast of a time-varying signal rather than the bias current. Theoretical results are derived relating the slope of the f –I curve to feedback gain and noise strength. Good agreement with simulation results are found for inhibitory and excitatory feedback. Finally, divisive feedback is also found for conductance-based feedback (shunting or excitatory) with and without noise. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Rapidly optimizing an aptamer based BoNT sensor by feedback system control (FSC) scheme

The sensitivity and detection time of an aptamer based biosensor for detecting botulinum neurotoxin (BoNT) depend upon the formation of proper tertiary architecture of aptamer, which closely correlates with the combinatorial effects of multiple types of ions and their concentrations presented in the buffer. Finding the optimal conditions for four different ions at 12 different concentrations, 20,736 possible combinations, by brute force is an extremely laborious and time-consuming task. Here, we introduce a feedback system control (FSC) scheme that can rapidly identify the best combination of components to form the optimal aptamer structure binding to a target molecule. In this study, rapid identification of optimized ionic combinations for electrochemical aptasensor of BoNT type A (BoNT/A) detection has been achieved. Only about 10 iterations with about 50 tests in each iteration are needed to identify the optimal ionic concentration out of the 20,736 possibilities. The most exciting finding was that a very short detection time and high sensitivity could be achieved with the optimized combinational ion buffer. Only a 5-min detection time, compared with hours or even days, was needed for aptamer-based BoNT/A detection with a limit of detection of 40 pg/ml. The methodologies described here can be applied to other multi-parameter chemical systems, which should significantly improve the rate of parameter optimization.     

IPM计算机决策技术简述

害虫综合管理的对象是一个复杂的生态系统。计算机已成为操纵这种复杂系统的有效决策工具。ＩＰＭ统计分析,模型生成,生态过程模拟和数据管理是计算机辅助决策的初级形式。在此基础上,ＩＰＭ决策过程的计算机化在近几年达到了很高的程度,出现了ＩＰＭ决策支持和专家系统。这标志着ＩＰＭ科学决策时代的到来。在某种意义上,计算机软硬件的技术进步改变了ＩＰＭ的过去,影响着ＩＰＭ的现在,决定着ＩＰＭ的未来。     

The overshoot phenomenon in cotransport

Based on simplified equations, the overshoot curve experimentally observed with Na⁺-linked cotransport of neutral substrate (sugars or amino acids) has been simulated by computer. The approach is in principle similar to that of previous approaches (Weiss, S.D., McNamara, P.D. and Segal, S. (1981) J. Theor. Biol. 91, 597–608), but more general; in particular, it includes the effect of electrical membrane potential difference, and the quantitative relationship between height of peak and certain transport parameters, such as maximum rate, dissociation constant of ternary complex, electric charge of translocator, respectively. In addition, it tests two alternative models with respect to the rate-determining step: the translocation, on the one hand, and the association/dissociation of the ligands at the translocator site, on the other. The major findings are the following: (1) An overshoot can be obtained similar to that usually found experimentally, provided that maximum rate and affinity between translocator and transport of solute exceed certain minimum values. (2) The overshoot effect with Na-linked cotransport is enhanced by a negative membrane potential (inside relative to outside) and decreased by a positive potential. In the first case, the peak is higher and occurs faster. In the latter case, the peak is lower and delayed. (3) The effect of an electric potential difference on the overshoot curve does not depend appreciably on the charge of the empty translocator, except if the translocation of the latter is strongly rate-limiting. (4) To obtain an overshoot curve, it is not necessary that the translocation step be rate-limiting, contrary to what has been postulated previously (Läuger, P. (1980) J. Membrane Biol. 57, 163–178).     

The Bearing of the Sandwich Course on the University Education of Biologists

A practical course for postgraduate students is described in which the drawing techniques used to observe, report, and explain biological structures and developments were taught and practised.     

Periodic solution of a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control

In this paper, a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control is considered. We obtain sufficient conditions of the global asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.     

Flight style optimization in ski jumping on normal,large, and ski flying hills

In V-style ski jumping, aerodynamic forces are predominant performance factors and athletes have to solve difficult optimization problems in parts of a second in order to obtain their jump length maximum and to keep the flight stable. Here, a comprehensive set of wind tunnel data was used for optimization studies based on Pontryagin′s minimum principle with both the angle of attack α and the body-ski angle β as controls. Various combinations of the constraints α_max and β_min(t) were analyzed in order to compare different optimization strategies. For the computer simulation studies, the Olympic hill profiles in Esto-Sadok, Russia (HS 106 m, HS 140 m), and in Harrachov, Czech Republic, host of the Ski Flying World Championships 2014 (HS 205 m) were used. It is of high importance for ski jumping practice that various aerodynamic strategies, i.e. combinations of α- and β-time courses, can lead to similar jump lengths which enables athletes to win competitions using individual aerodynamic strategies. Optimization results also show that aerodynamic behavior has to be different at different hill sizes (HS). Optimized time courses of α and β using reduced drag and lift areas in order to mimic recent equipment regulations differed only in a negligible way. This indicates that optimization results presented here are not very sensitive to minor changes of the aerodynamic equipment features when similar jump length are obtained by using adequately higher in-run velocities. However, wind tunnel measurements with athletes including take-off and transition to stabilized flight, flight, and landing behavior would enable a more detailed understanding of individual flight style optimization.     

Properties of 3D rotations and their relation to eye movement control

Rotations of the eye are generated by the torques that the eye muscles apply to the eye. The relationship between eye orientation and the direction of the torques generated by the extraocular muscles is therefore central to any understanding of the control of three-dimensional eye movements of any type. We review the geometrical properties that dictate the relationship between muscle pulling direction and 3D eye orientation. We then show how this relation can be used to test the validity of oculomotor control hypotheses. We test the common modeling assumption that the extraocular muscle pairs can be treated as single bidirectional muscles. Finally, we investigate the consequences of assuming fixed muscle pulley locations when modeling the control of eye movements.     

Fully implicit parallel simulation of single neurons

When a multi-compartment neuron is divided into subtrees such that no subtree has more than two connection points to other subtrees, the subtrees can be on different processors and the entire system remains amenable to direct Gaussian elimination with only a modest increase in complexity. Accuracy is the same as with standard Gaussian elimination on a single processor. It is often feasible to divide a 3-D reconstructed neuron model onto a dozen or so processors and experience almost linear speedup. We have also used the method for purposes of load balance in network simulations when some cells are so large that their individual computation time is much longer than the average processor computation time or when there are many more processors than cells. The method is available in the standard distribution of the NEURON simulation program.