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We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor.
The two most widely used neural models, multilayer perceptron (MLP) and radial basis function network (RBFN), are presented in the framework of system identification and control. The main steps for building such nonlinear black box models are regressor choice, selection of internal architecture, and parameter estimation. The advantages of neural network models are summarized: universal approximation capabilities, flexibility, and parsimony. Two applications are described in steel industry and water treatment, respectively, the control of alloying process in a hot dipped galvanizing line and the control of a coagulation process in a drinking water treatment plant. These examples highlight the interest of neural techniques, when complex nonlinear phenomena are involved, but the empirical knowledge of control operators can be learned.
Type 2 diabetes mellitus is the consequence of both insulin resistance and impaired insulin secretion. In the progression from normal glucose tolerance to diabetes, postprandial glucose (PPG) levels often rise before fasting plasma glucose (FPG) levels increase above 126 mg/dL (7.0 mmol/L). Numerous epidemiologic studies have shown that impaired glucose tolerance is associated with increased risk for macrovascular disease and that isolated postchallenge hyperglycemia is an independent factor for increased mortality. Reducing the risk for microvascular complications by improving glycosylated hemoglobin (HbA(1c)) levels is well documented. Emerging data now support the relationship between glycemic control and macrovascular disease. Epidemiologic studies documenting postprandial hyperglycemia and the risk for increased mortality suggest that lowering PPG levels might be beneficial. Optimizing both FPG and PPG is important in achieving normal/near-normal glucose levels. Many patients with type 2 diabetes have difficulty attaining the recommended HbA(1c) goal despite normal/near-normal FPG levels; thus, pharmacologic treatment targeting PPG levels may prove beneficial.
True ab initio prediction of protein 3D structure requires only the protein primary structure, a physicochemical free energy model, and a search method for identifying the free energy global minimum. Various characteristics of evolutionary algorithms (EAs) mean they are in principle well suited to the latter. Studies to date have been less than encouraging, however. This is because of the limited consideration given to EA design and control parameter issues. A comprehensive study of these issues was, therefore, undertaken for ab initio protein fold prediction using a full atomistic protein model. The performance and optimal control parameter settings of twelve EA designs where first established using a 15-residue polyalanine molecule-design aspects varied include the encoding alphabet, crossover operator, and replacement strategy. It can be concluded that real encoding and multipoint crossover are superior, while both generational and steady-state replacement strategies have merits. The scaling between the optimal control parameter settings and polyalanine size was also identified for both generational and steady-state designs based on real encoding and multipoint crossover. Application of the steady-state design to met-enkephalin indicated that these scalings are potentially transferable to real proteins. Comparison of the performance of the steady state design for met-enkephalin with other ab initio methods indicates that EAs can be competitive provided the correct design and control parameter values are used.
The paper deals with optimal control in a linear integral age-dependent model of population dynamics. A problem for maximizing the harvesting return on a finite time horizon is formulated and analyzed. The optimal controls are the harvesting age and the rate of population removal by harvesting. The gradient and necessary condition for an extremum are derived. A qualitative analysis of the problem is provided. The model shows the presence of a zero-investment period. A preliminary asymptotic analysis indicates possible turnpike properties of the optimal harvesting age. Biological interpretation of all results is provided.
One objective of this study was to investigate whether neuromuscular quantities were associated with preferred pedaling rate selection during submaximal steady-state cycling from a theoretical perspective using a musculoskeletal model with an optimal control analysis. Specific neuromuscular quantities of interest were the individual muscle activation, force, stress and endurance. To achieve this objective, a forward dynamic model of cycling and optimization framework were used to simulate pedaling at three different rates of 75, 90 and 105 rpm at 265 W. The pedaling simulations were produced by optimizing the individual muscle excitation timing and magnitude to reproduce experimentally collected data. The results from these pedaling simulations indicated that all neuromuscular quantities were minimized at 90 rpm when summed across muscles. In the context of endurance cycling, these results suggest that minimizing neuromuscular fatigue is an important mechanism in pedaling rate selection. A second objective was to determine whether any of these quantities could be used to predict the preferred pedaling rate. By using the quantities with the strongest quadratic trends as the performance criterion to be minimized in an optimal control analysis, these quantities were analyzed to assess whether they could be further minimized at 90 rpm and produce normal pedaling mechanics. The results showed that both the integrated muscle activation and average endurance summed across all muscles could be further minimized at 90 rpm indicating that these quantities cannot be used individually to predict preferred pedaling rates.
Heart failure is a disorder that disproportionately affects the elderly, and over 50% of heart failure hospitalizations in the United States occur in persons over 75 years of age. Moreover, despite recent advances in heart failure therapy, optimal treatment of elderly patients remains undefined. In addition, heart failure management in older persons is often complicated by the presence of multiple comorbid conditions, polypharmacy, psychosocial and behavioral concerns, dietary issues, and economic considerations. As a result, management of heart failure in the elderly requires a coordinated, multidisciplinary approach, and a series of recent studies have documented the efficacy of heart failure disease management programs in reducing readmissions, enhancing medication and dietary compliance, and lowering cost of care. Ongoing studies will provide insights into the feasibility and effectiveness of implementing heart failure disease management programs on a population-wide basis, and on the effects of such programs on long-term clinical outcomes and costs.
Recently, budget-conscious policymakers have shifted their attention to the physician services market and have begun to consider a wide variety of price regulatory schemes for moderating expenditures in this market. In a recent article in this journal, Feldman and Sloan warned that price controls on physician services may cause undesirable declines in service quality, independent of their budgetary ramifications. Our aim in this article is to reconsider the effects of price controls in the broader context of insurance coverage and moral hazard. Our ultimate goal is to assess the benefits of price controls independent of specific assumptions about the controversial issues of demand inducement and income targeting. Using a simple extension of the Feldman/Sloan model, we find that price controls can be and almost certainly are welfare-improving as long as consumers are sufficiently well insured, regardless of where one stands on the inducement issue. The salutary effects of price controls, on the other hand, can be compromised by income-targeting behavior on the part of physicians. We also introduce evidence from Medicare's recent fee freeze to evaluate the possibility of income-targeting behavior empirically. While formal studies of income targeting suggest that its magnitude is small in cross-section, we warn that its effects may be larger over time; this is what our descriptive evidence suggests. We conclude that more dramatic short-term progress on physician fee inflation will require stronger measures, such as putting physicians at risk for consumer expenditures.
OBJECTIVE: To assess the degree of control of modifiable cardiovascular risk factors (CRFs) in type 2 diabetic patients. STUDY DESIGN AND METHODS: Cross-sectional study in 501 patients with type 2 diabetes mellitus. The following parameters were used to define optimal control: glycated haemoglobin (HbA(1C)) <7.0%, fasting plasma glucose (FPG) <7.2 mmol/l, postprandial capillary glucose (PCG) <10.0 mmol/l, high-density lipoprotein cholesterol (HDL-C) >1.1 mmol/l, low-density lipoprotein cholesterol (LDL-C) <2.6 mmol/l, triglyceride levels (TG) <1.7 mmol/l, systolic blood pressure (SBP) <130 mmHg, diastolic blood pressure (DBP) <80 mmHg, body mass index (BMI) <25 kg/m2, waist circumference (WC) <88 cm in women and <102 cm in men, and current non-smoking status. The use of various cardioprotective medications was also evaluated. RESULTS: Mean (+/-S.D.) age was 65.4 +/- 11.9 years, 218 (44%) were male. Ninety-six (19%) met coronary artery disease (CAD). Two hundred seven patients (41%) had an HbA(1C) <7.0%, 134 (27%) a FPG <7.2 mmol/l and 231 of 353 (65%) a PCG <10.0 mmol/l. Only 206 (41%) achieved an LDL-C <2.6 mmol/l, but 370 (74%) and 308 (62%) reached an HDL-C >1.1 mmol/l and a TG levels <1.7 mmol/l, respectively. In 359 (72%) patients DBP was <80 mmHg, but in only 136 (27%) was SBP <130 mmHg. Sixty four (13%) achieved a BMI <25 kg/m2, and 420 (84%) were non-smokers. Forty three (15%) women and 104 (48%) men had a WC <88 or <102 cm, respectively. None of the patients had optimal control of all CRFs. CONCLUSIONS: These data demonstrate poor control of modifiable CRFs in the population studied, and support the need for great effort to achieve the recommended goals.
RATIONALE: Dopamine neurotransmission has long been known to exert a powerful influence over the vigor, strength, or rate of responding. However, there exists no clear understanding of the computational foundation for this effect; predominant accounts of dopamine's computational function focus on a role for phasic dopamine in controlling the discrete selection between different actions and have nothing to say about response vigor or indeed the free-operant tasks in which it is typically measured. OBJECTIVES: We seek to accommodate free-operant behavioral tasks within the realm of models of optimal control and thereby capture how dopaminergic and motivational manipulations affect response vigor. METHODS: We construct an average reward reinforcement learning model in which subjects choose both which action to perform and also the latency with which to perform it. Optimal control balances the costs of acting quickly against the benefits of getting reward earlier and thereby chooses a best response latency. RESULTS: In this framework, the long-run average rate of reward plays a key role as an opportunity cost and mediates motivational influences on rates and vigor of responding. We review evidence suggesting that the average reward rate is reported by tonic levels of dopamine putatively in the nucleus accumbens. CONCLUSIONS: Our extension of reinforcement learning models to free-operant tasks unites psychologically and computationally inspired ideas about the role of tonic dopamine in striatum, explaining from a normative point of view why higher levels of dopamine might be associated with more vigorous responding.
Five hundred seventy-four patients with prostate cancer treated by external beam radiation therapy in the United States in 1973 to 1975 have been analyzed comparing radiation dose with in-field recurrence. Dose-response effects are observed for all cases (p = less than .05) and T-2 and T-3 tumors, but not for T-0, T-1 and T-4 tumors. For doses calculated at the center of the prostate, these observations suggest optimal control is obtained at no more than 6000 rad for T-0 and T-1 tumors; 6000-6500 rad for T-2 tumors; 6500-7000 rad for T-3 tumors; and that greater than 7000 rad is required only for T-4 tumors. The paraprostatic dose calculated at a point 4 cm lateral to the center of the prostate also shows a correlation of dose with infield failure for all cases (p = .01). Observations in individual T states suggest optimal control is obtained at no more than 6000 rad for T-0, T-1 and T-2 tumors, 6500-6999 rad for T-3 and greater than or equal to 7000 rad for T-4. These data suggest that for T-2 and T-3 cancers, extension in the periprostatic region must be treated. A comparison of central dose vs. stage indicates institutional policy rather than cancer volume determines the radiation dose used in treating prostate cancer. A change in institutional policies to treat with optimal doses as indicated by this study would result in an overall increase in local control and a decrease in complications.
Based on an existing model for calcium homeostatis (dynamics) and taking the help of feedback linearization philosophy of nonlinear control theory, two control design (medication) strategies are presented for automatic treatment of parturient paresis (milk fever) disease of cows. An important advantage of the new approach is that it results in a simple and straightforward method and eliminates the necessity of a significantly more complex neural network based nonlinear optimal control technique, as proposed by the author earlier. As an added advantage, unlike the neural network technique, the new approach leads to 'closed form solution' for the nonlinear controller. Moreover, global asymptotic stability of the closed loop system is always guaranteed. Besides theoretical justifications, the resulting controllers (medication strategies) are validated from numerical simulation studies of the nonlinear system as well. Moreover, from a numerical study about the robustness of the algorithms with respect to parametric uncertainty, it was observed that the optimal control formulation is a better option over the dynamic inversion formulation.
The authors propose guidelines for the use of retained patient specimens for the quality control of multichannel hematology analyzers. They demonstrate that control limits for patient specimen replicates may be derived from the long-term standard deviations (s) of commercial whole blood controls. They then use computer stimulation of the Coulter multichannel hematology instrument to determine power functions of various procedures using retained specimens. These power functions show that the use of three patient specimens and +/- 2 s limits are optimal for the detection of systematic error. They recommend that three different, previously analyzed normal range specimens be periodically analyzed, e.g., at eight-hour intervals. The differences between the current and original measurements should then be calculated and compared with their +/- 2 s limits. If at least two of the three differences for any directly measured parameter exceed the +/- 2 s limits, there will be a high probability of significant analytic error. Because the power functions of the derived red blood cell parameters, hematocrit, mean corpuscular hemoglobin, and mean corpuscular hemoglobin concentration demonstrate relatively low error detection capabilities, the authors recommend that these parameters not be monitored with the retained patient specimen procedure.
The dynamic optimization (open loop optimal control) of non-linear bioprocesses is considered in this contribution. These processes can be described by sets of non-linear differential and algebraic equations (DAEs), usually subject to constraints in the state and control variables. A review of the available solution techniques for this class of problems is presented, highlighting the numerical difficulties arising from the non-linear, constrained and often discontinuous nature of these systems. In order to surmount these difficulties, we present several alternative stochastic and hybrid techniques based on the control vector parameterization (CVP) approach. The CVP approach is a direct method which transforms the original problem into a non-linear programming (NLP) problem, which must be solved by a suitable (efficient and robust) solver. In particular, a hybrid technique uses a first global optimization phase followed by a fast second phase based on a local deterministic method, so it can handle the nonconvexity of many of these NLPs. The efficiency and robustness of these techniques is illustrated by solving several challenging case studies regarding the optimal control of fed-batch bioreactors and other bioprocesses. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the two-phase hybrid approach presents the best compromise between robustness and efficiency.
An implantable computerized electrical stimulation system designed to induce bladder evacuation in animal models (dogs) after spinal cord transection has been realized and evaluated. This fully programmable system is based on a handheld device and generates a wide range of stimuli through multichannel implantable miniaturized stimulator. Using the new bladder stimulator and inducing reversible fatigue to the external sphincter via the pudendal nerve enables us to reduce the bladder outlet resistance, resulting in the proper emptying of the bladder during stimulation without the need for sacral nerve rhizotomies and the pudendal nerve neurectomies. Four chronically affected dogs were studied to determine the optimal stimulation parameters for inducing a sphincter fatigue that would reliably empty the bladder for the duration of the experiment. These parameters were: maximum amplitude of 1.5 mA +/- 0.5 SD, stimuli composed of a high frequency signal of 200 Hz +/- 50 SD modulated by a low frequency signal of 10 Hz +/- 5 SD, pulse width controlled by a duty-cycle of 20% +/- 10 SD, sacral nerve stimulation of 50 s +/- 25 SD and fatiguing duration of 20 s +/- 5 SD.
Software is presented for automatic generation of first-order ordinary differential equations (ODE) that arise from lumped parameter representations of metabolic and pharmacokinetic systems. The definition of system structures is accomplished by fractional transfer rates between state variables, together with input/output equations and initial conditions of state variables. General non-linear mathematical expressions can be assigned to all structure definition items. The software parses and interprets the system definitions and generates symbolically the mathematical expression of the model's set of ODE. In addition, symbolic derivatives of state equations are determined with respect to model parameters, state variables and external inputs. These derivatives represent the constituents of systems of sensitivity-differential and adjoint-differential equations that arise in identification and optimal control problems. Finally, output routines generate source code that, once compiled and linked to simulation programs, allows efficient numerical integration of the system of ODE. This software has been developed in PROLOG on Macintosh computers and has been extensively used with the programming environment MATLAB. Possible applications of this software include model building, sensitivity analysis, identification, optimal experiment design and numerical solution of optimal control problems.
CD8 T-cell or cytotoxic T-lymphocyte responses develop through an antigen-independent proliferation and differentiation program. This is in contrast to the previous thinking, which was that continuous antigenic stimulation was required. This Opinion discusses why nature has chosen the proliferation program and how it compares to continuous stimulation. Although the two mechanisms should not lead to significantly different dynamics during chronic infection, they do make a difference in acute infection. We argue that programmed proliferation is better at clearance, whereas continuous stimulation is better at limiting acute symptoms. The 7-10 programmed cell divisions observed in vivo might be an optimization of this trade-off. We also discuss the conditions under which the program does or does not require CD4 T-cell help for clearance.
BACKGROUND: Glycaemic control in women with diabetes is critical to satisfactory pregnancy outcome. A systematic review of two randomised trials concluded that there was no clear evidence of benefit from very tight versus tight glycaemic control for pregnant women with diabetes. METHODS: A systematic review of observational studies addressing miscarriage, congenital malformations and perinatal mortality among pregnant women with type 1 and type 2 diabetes was carried out. Literature searches were performed in MEDLINE, EMBASE, CINAHL and Cochrane Library. Observational studies with data on glycated haemoglobin (HbA1c) levels categorised into poor and optimal control (as defined by the study investigators) were selected. Relative risks and odds ratios were calculated for HbA1c and pregnancy outcomes. Adjusted relative risk estimates per 1-percent decrease in HbA1c were calculated for studies which contained information on mean and standard deviations of HbA1c. RESULTS: The review identified thirteen studies which compared poor versus optimal glycaemic control in relation to maternal, fetal and neonatal outcomes. Twelve of these studies reported the outcome of congenital malformations and showed an increased risk with poor glycaemic control, pooled odds ratio 3.44 (95%CI, 2.30 to 5.15). For four of the twelve studies, it was also possible to calculate a relative risk reduction of congenital malformation for each 1-percent decrease in HbA1c, these varied from 0.39 to 0.59. The risk of miscarriage was reported in four studies and was associated with poor glycaemic control, pooled odds ratio 3.23 (95%CI, 1.64 to 6.36). Increased perinatal mortality was also associated with poor glycaemic control, pooled odds ratio 3.03 (95%CI, 1.87 to 4.92) from four studies. CONCLUSION: This analysis quantifies the increase in adverse pregnancy outcomes in women with diabetes who have poor glycaemic control. Relating percentage risk reduction in HbA1c to relative risk of adverse pregnancy events may be useful in motivating women to achieve optimal control prior to conception.