[Mathematical formulation of a problem and an algorhythm for determination of the components of an evoked potential].
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Brain↗
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Results for “Problem Formulation”
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[Problems posed by formulation of dry forms with delayed action administered orally].
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Administration, Oral↗
[Surgical aspects of liver substitution (functional and anatomic substitution). I: Formulation of the problem].
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Humans↗
[Third etiological factor of food poisoning--literature review and formulation of the problem].
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Bacterial Toxins↗
[Altered mental states during physiological labor (the formulation of the problem)].
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Adolescent↗
[Retrospective estimation of the frequency of heterozygous beta-thalassemia in the Crimean Tartar population. Formulation of the problem. Estimation of the gametic contribution to a mixed population from frequencies of the ABO blood group genes].
Polymorphism of the beta-thalassemia gene frequency in non-indigenous populations of Central Asia, especially Crimean Tartars, is often explained by inter-ethnic marriages. The frequencies of these marriages, however, are not sufficient to produce the observed gene frequencies. Because of this, an estimation of the extent of Uzbek gametic contribution to the ethnic group of Crimean Tartar origin was conducted using data on the frequencies of ABO blood group genes. The maximum-likelihood estimate obtained (0.325) was used to determine the heterozygous beta-thalassemia frequency of the ancestral Crimean Tartar population.
ABO Blood-Group System↗
The application of pinch analysis to water, reagent and effluent management in a chlor-alkali facility.
South African industry is coming under increasing pressure to reduce the amount of freshwater it uses and the amount of effluent it produces. Water pinch is a cleaner production technique aimed at reducing the freshwater consumption and effluent production within a chemical complex. The design of water-reuse or water pinch networks as applied to the case study of a chlor-alkali complex is considered. Insights are provided into the analysis and formulation of problems for large-scale industrial systems and the application of present techniques and tools to the formulated problem is illustrated. The features of the problem posed by the chlor-alkali facility are discussed and the limitations of the present theory in dealing with this problem highlighted. The concepts of utility-waterpinch analysis and process-water pinch analysis are introduced.
Chemical Industry↗
Optimal reconstruction of historical water supply to a distribution system: A. Methodology.
The New Jersey Department of Health and Senior Services (NJDHSS), with support from the Agency for Toxic Substances and Disease Registry (ATSDR) conducted an epidemiological study of childhood leukaemia and nervous system cancers that occurred in the period 1979 through 1996 in Dover Township, Ocean County, New Jersey. The epidemiological study explored a wide variety of possible risk factors, including environmental exposures. ATSDR and NJDHSS determined that completed human exposure pathways to groundwater contaminants occurred in the past through private and community water supplies (i.e. the water distribution system serving the area). To investigate this exposure, a model of the water distribution system was developed and calibrated through an extensive field investigation. The components of this water distribution system, such as number of pipes, number of tanks, and number of supply wells in the network, changed significantly over a 35-year period (1962--1996), the time frame established for the epidemiological study. Data on the historical management of this system was limited. Thus, it was necessary to investigate alternative ways to reconstruct the operation of the system and test the sensitivity of the system to various alternative operations. Manual reconstruction of the historical water supply to the system in order to provide this sensitivity analysis was time-consuming and labour intensive, given the complexity of the system and the time constraints imposed on the study. To address these issues, the problem was formulated as an optimization problem, where it was assumed that the water distribution system was operated in an optimum manner at all times to satisfy the constraints in the system. The solution to the optimization problem provided the historical water supply strategy in a consistent manner for each month of the study period. The non-uniqueness of the selected historical water supply strategy was addressed by the formulation of a second model, which was based on the first solution. Numerous other sensitivity analyses were also conducted using these two models. Both models are solved using a two-stage progressive optimality algorithm along with genetic algorithms (GAs) and the EPANET2 water distribution network solver. This process reduced the required solution time and generated a historically consistent water supply strategy for the water distribution system.
Algorithms↗
Well-posed formulation of the inverse problem of electrocardiography.
It has long been speculated that incorporation of available time constraints into the inverse electrocardiography problem could improve the accuracy of maps of epicardial potential or activation reconstructed from body surface potential measurements. However, all prior formulations of this problem have remained ill-posed, and the best way to utilize these constraints has been unclear. By making proper use of the timing information, we show that the inverse electrocardiography problem (for calculation of ventricular surface activation isochrones) is formally well-posed under anisotropic bidomain conditions and the assumption that ventricular muscle action potential phase 0 is a step discontinuity. In practical terms, this implies that non-regularized stable activation map solutions are possible if correlates of derived body surface potential derivative discontinuity times can be identified from the noisy analog signals, and only a small number of ventricular surface activation function extrema occur during a unit of time resolution defined by phase zero duration over the spatial extent of a bidomain point. We include a quasi-realistic numerical example illustrating the ease with which the extrema of the endocardial and epicardial activation maps are computed via Jump Maps derived from body surface potentials (this being the crucial step in rendering images of ventricular surface activation in this approach). The efficient signal processing algorithm used to accomplish this task is well suited to the setting of multiple extrema occurring during overlapping phase zero time intervals.
Algorithms↗
Temporally unconstrained space-time treatment of linear formulations of the inverse problem of electroencephalography.
This paper provides an optimal mechanism for the introduction of temporal constraints into linear imaging formulations of the inverse electroencephalography problem. The method is based on derivation of a "virtual-SVD," an extension of generalized singular value decomposition to the setting of random matrices. Surprisingly, the formalism is superior, in principle, to standard regularization methods even in the absence of known temporal constraints. Investigation of this basic temporally unconstrained setting was undertaken to illustrate the application of the method, and as a necessary first step in its systematic evaluation. Although abstract simulations demonstrate superior accuracy for the virtual-SVD method as compared with standard methods, investigation of a particular realistic simulation involving spatiotemporally distributed temporal lobe interictal spikes indicates that significant improvement in solution estimate quality under temporally unconstrained conditions may be limited to a very narrow range of the signal-to-noise ratio (particularly in the context of a markedly row-deficient transfer matrix). These results underline the prospective importance of investigation of the efficacy and feasibility of application of temporal constraints (such as those resulting from knowledge of the general time series format of epilepsy associated wave forms, evoked potentials, etc.) within the derived formalism.
Biomedical Engineering↗
Improved parameter estimation for systems with an experimentally located Hopf bifurcation.
When performing system identification, we have two sources of information: experimental data and prior knowledge. Many cell-biological systems are oscillating, and sometimes we know an input where the system reaches a Hopf bifurcation. This is the case, for example, for glycolysis in yeast cells and for the Belousov-Zhabotinsky reaction, and for both of these systems there exist significant numbers of quenching data, ideal for system identification. We present a method that includes prior knowledge of the location of a Hopf bifurcation in estimation based on time-series. The main contribution is a reformulation of the prior knowledge into the standard formulation of a constrained optimisation problem. This formulation allows for any of the standard methods to be applied, including all the theories regarding the method's properties. The reformulation is carried out through an over-parametrisation of the original problem. The over-parametrisation allows for extra constraints to be formed, and the net effect is a reduction of the search space. A method that can solve the new formulation of the problem is presented, and the advantage of adding the prior knowledge is demonstrated on the Brusselator.
Algorithms↗
Unsteady processes in machines.
Couplings in machines and mechanisms always have play and friction. While under loading, stick-slip phenomena and impact events can take place. Such processes are modeled as multibody systems whose structure is time variant or unsteady. The time-variant number of degrees of freedom is due to stick-slip contacts. The coupling characteristics become unsteady, for instance there exist jumps in the loads, if impacts occur. For establishing a uniform theory for such phenomena we use a Lagrangian approach connecting the additional constraint equations and the equations of motion by Lagrange multipliers, which are proportional to the constraint forces. Stick-slip and impact events are evaluated by indicator functions leading to special numerical algorithms for the search of switching points. Contact problems are formulated as a complementarity problem which can be solved by efficient algorithms. The theory is applied to rattling in gears, impact drilling machines, turbine blade dampers, and a woodpecker toy. In some of these applications, chaos as a result of bifurcations is possible, which results from variations in the parameters. (c) 1994 American Institute of Physics.
Journal Article↗
Missile guidance law design using adaptive cerebellar model articulation controller.
An adaptive cerebellar model articulation controller (CMAC) is proposed for command to line-of-sight (CLOS) missile guidance law design. In this design, the three-dimensional (3-D) CLOS guidance problem is formulated as a tracking problem of a time-varying nonlinear system. The adaptive CMAC control system is comprised of a CMAC and a compensation controller. The CMAC control is used to imitate a feedback linearization control law and the compensation controller is utilized to compensate the difference between the feedback linearization control law and the CMAC control. The online adaptive law is derived based on the Lyapunov stability theorem to learn the weights of receptive-field basis functions in CMAC control. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. Then the adaptive CMAC control system is designed to achieve satisfactory tracking performance. Simulation results for different engagement scenarios illustrate the validity of the proposed adaptive CMAC-based guidance law.
Algorithms↗
Inverse calculation of material parameters for a thin-layer system using transient elastic waves.
The inverse calculation of material parameters of a thin-layer system is investigated using transient elastic waves. The inverse problem is formulated as an optimization problem in which the norm of the discrepancies between the calculated and measured normal surface displacements is minimized through the simplex algorithm. The theoretical result is first solved using the Laplace transform and the transient response is then implemented analytically by Cagniard's method. In the experiment, the source time function is generated by the brittle fracture of a pencil lead on the surface of the thin-layer system, and a National Bureau of Standards (NBS) conical transducer is used to record the surface responses. To obtain reliable inverse results for material parameters, a two-step inverse calculation procedure is proposed. The recovered material parameters of the specimens agree well with the theoretical values and experimental results.
Journal Article↗
Utility measurement in healthcare: the things I never got to.
The present article provides a brief historical background on the development of utility measurement and cost-utility analysis in healthcare. It then outlines a number of research ideas in this field that the author never got to. The first idea is extremely fundamental. Why is health economics the only application of economics that does not use the discipline of economics? And, more importantly, what discipline should it use? Research ideas are discussed to investigate precisely the underlying theory and axiom systems of both Paretian welfare economics and the decision-theoretical utility approach. Can the two approaches be integrated or modified in some appropriate way so that they better reflect the needs of the health field? The investigation is described both for the individual and societal levels. Constructing a 'Robinson Crusoe' society of only a few individuals with different health needs, preferences and willingness to pay is suggested as a method for gaining insight into the problem. The second idea concerns the interval property of utilities and, therefore, QALYs. It specifically concerns the important requirement that changes of equal magnitude anywhere on the utility scale, or alternatively on the QALY scale, should be equally desirable. Unfortunately, one of the original restrictions on utility theory states that such comparisons are not permitted by the theory. It is shown, in an important new finding, that while this restriction applies in a world of certainty, it does not in a world of uncertainty, such as healthcare. Further research is suggested to investigate this property under both certainty and uncertainty. Other research ideas that are described include: the development of a precise axiomatic basis for the time trade-off method; the investigation of chaining as a method of preference measurement with the standard gamble or time trade-off; the development and training of a representative panel of the general public to improve the completeness, coherence and consistency of measured preferences; and the investigation, using a model of a very small society, of the conflict between the patient perspective and the societal perspective regarding preferences. Finally, it is suggested that an important area of research, which the author never got to, would be to work closely with specific decision makers on specific decision problems, to help them formulate the problem, provide useful analyses, and to publish these as case studies to give the field a better understanding of the problems and the needs of decision makers.
Consumer Behavior↗
RAPTOR: optimal protein threading by linear programming.
This paper presents a novel linear programming approach to do protein 3-dimensional (3D) structure prediction via threading. Based on the contact map graph of the protein 3D structure template, the protein threading problem is formulated as a large scale integer programming (IP) problem. The IP formulation is then relaxed to a linear programming (LP) problem, and then solved by the canonical branch-and-bound method. The final solution is globally optimal with respect to energy functions. In particular, our energy function includes pairwise interaction preferences and allowing variable gaps which are two key factors in making the protein threading problem NP-hard. A surprising result is that, most of the time, the relaxed linear programs generate integral solutions directly. Our algorithm has been implemented as a software package RAPTOR-RApid Protein Threading by Operation Research technique. Large scale benchmark test for fold recognition shows that RAPTOR significantly outperforms other programs at the fold similarity level. The CAFASP3 evaluation, a blind and public test by the protein structure prediction community, ranks RAPTOR as top 1, among individual prediction servers, in terms of the recognition capability and alignment accuracy for Fold Recognition (FR) family targets. RAPTOR also performs very well in recognizing the hard Homology Modeling (HM) targets. RAPTOR was implemented at the University of Waterloo and it can be accessed at http://www.cs.uwaterloo.ca/~j3xu/RAPTOR_form.htm.
Algorithms↗
Piezoelectric transducer design via multiobjective optimization.
The design of piezoelectric transducers is usually based on single-objective optimization only. In most practical applications of piezoelectric transducers, however, there exist multiple design objectives that often are contradictory to each other by their very nature. It is impossible to find a solution at which each objective function gets its optimal value simultaneously. Our design approach is to first find a set of Pareto-optimal solutions, which can be considered to be best compromises among multiple design objectives. Among these Pareto-optimal solutions, the designer can then select the one solution which he considers to be the best one. In this paper we investigate the optimal design of a Langevin transducer. The design problem is formulated mathematically as a constrained multiobjective optimization problem. The maximum vibration amplitude and the minimum electrical input power are considered as optimization objectives. Design variables involve continuous variables (dimensions of the transducer) and discrete variables (the number of piezoelectric rings and material types). In order to formulate the optimization problem, the behavior of piezoelectric transducers is modeled using the transfer matrix method based on analytical models. Multiobjective evolutionary algorithms are applied in the optimization process and a set of Pareto-optimal designs is calculated. The optimized results are analyzed and the preferred design is determined.
Journal Article↗
A contact model with ingrowth control for bone remodelling around cementless stems.
This work presents a computational model for bone remodelling around cementless stems. The problem is formulated as a material optimisation problem considering the bone and stem surfaces to be in contact. To emphasise the behaviour of the bone/stem interface, the computer model detects the existence of bone ingrowth during the remodelling; consequently, the contact conditions are changed for a better interface simulation. The trabecular bone is modelled as a strictly orthotropic material with equivalent properties computed by homogenisation. The distribution of bone relative density is obtained by the minimisation of a function that considers both the bone structural stiffness and the biological cost associated with metabolic maintenance of bone tissue. The situation of multiple load conditions is considered. The remodelling law, obtained from the necessary conditions for an optimum, is derived analytically from the optimisation problem and solved numerically using a suitable finite element mesh. The formulation is applied to an implanted femur. Results of bone density and ingrowth distribution are obtained for different coating conditions. Bone ingrowth does not occur over the entire coated surfaces. Indeed, we observed regions where separation or high relative displacement occurs that preclude bone ingrowth attachment. This prediction of the model is consistent with clinical observations of bone ingrowth. Thus, this model, which detect bone ingrowth and allow modification of the interface conditions, are useful for analysis of existing stems as well as design optimisation of coating extent and location on such stems.
Animals↗