Accurate and Inaccurate Conceptions About Osmosis That Accompanied Meaningful Problem Solving

This study focused on the knowledge of six outstanding science students who solved an osmosis problem meaningfully. That is, they used appropriate and substantially accurate conceptual knowledge to generate an answer. Three generated a correct answer; three, an incorrect answer. This paper identifies both the accurate and inaccurate conceptions about osmosis of each correct and incorrect solver. The investigation consisted of a presolving clinical interview, think-aloud solving of the problem, and retrospective report of the solving. Of the 12 accurate conceptions identified here, two were especially important in enabling these solvers to generate a correct answer. Of the 8 inaccurate conceptions, either of 2 blocked a correct answer. Four, however, accompanied (and could therefore be concealed by) a correct answer. Teachers could use this information to make a meaningful solving of this problem accessible to more students and to identify more effectively students' inaccurate conceptions about osmosis.     

Scoring to remove guessing in multiple choice examinations

Methods of scoring in multiple choice examinations are outlined in which the examinee's expected change in score because of random guessing must be negative for all situations of partial knowledge. Thus, it can be argued that the guessing component in multiple choice examinations can be completely removed. The examinee is instructed to tick the correct box or, if the correct box is unknown, to cross boxes known to be incorrect, or to leave the question blank. Under the proposed scoring system, it is argued that an examinee will not attempt to demonstrate more knowledge on any particular question than the examinee in fact has. Also, the examiner has quite a degree of freedom as to the size of the rewards for correctly crossed boxes; rewards which need not be equal. There is also quite a range in the possible values of the penalties for incorrect responses and appropriate recommendations are made.     

Determination of the Correct Range of Physical Parameters in the Approximate Analytical Solutions of Nonlinear Equations Using the Adomian Decomposition Method

Physical parameters in dimensionless form in the governing equations of real-life phenomena naturally occur. How to control them by determining their range of validity is in general a big issue. In this paper, a mathematical approach is presented to identify the correct range of physical parameters adopting the recently popular analytic approximate Adomian decomposition method (ADM). Having found the approximate analytical Adomian series solution up to a specified truncation order, the squared residual error formula is employed to work out the threshold and the existence domain of certain physical parameters satisfying a preassigned tolerance. If the current procedure is not closely pursued, the presented results with the ADM may not be up to the desired level of accuracy (the worst is the divergent physically meaningless solutions), or much more ADM series terms need to be computed to satisfy certain accuracy. Examples reveal the necessity of the present approach to make sure that the results embark the correct range of physical parameters in the study of a physical problem containing several dominating parameters.     

IDES: influence diagram based expert system

Influence diagrams have been used effectively in applied decision analysis to model complex systems, identify probabilistic dependence and characterize the flow of information. Their graphical representation and intuitive framework are particularly effective in representing knowledge from experts with diverse backgrounds and varying degrees of technical proficiency. They allow both a symbolic representation of the system interrelationships and a quantitative measure that can be of discrete or continuous functional form. By exploiting this abstraction hierarchy, successive degrees of specification can be made by several individuals, each encoding his or her expert knowledge of the problem and bounds on critical parameters. It is proposed that an interactive computer program that automates this influence diagram technology would provide an excellent tool for building expert systems. This paper describes such a modeling tool: the IDES (Influence Diagram Based Expert System) developed at the University of California at Berkeley as a modeling tool for building expert systems requiring reasoning with uncertain or incomplete information. The Diagnostician's Problem is presented as a tutorial for describing the IDES solution procedure.     

Naturally biased? In search for reaction time evidence for a natural number bias in adults

A major source of errors in rational number tasks is the inappropriate application of natural number rules. We hypothesized that this is an instance of intuitive reasoning and thus can persist in adults, even when they respond correctly. This was tested by means of a reaction time method, relying on a dual process perspective that differentiates between intuitive and analytic reasoning. We measured fifty-eight educated adults’ accuracies and reaction times in a variety of rational number tasks. In half of the items (congruent), the correct response was compatible with natural number properties (thus intuitive reasoning led to a correct answer). In contrast, in the incongruent items, intuitive reasoning would lead to an incorrect answer. In comparing two numbers, there were hardly any natural-number-based errors but correct responses to incongruent items took longer. Regarding the effect of operations, more mistakes were made in incongruent items, and correct responses required longer reaction time. Incongruent items about density elicited considerably more errors than congruent items. These findings can be considered as evidence that the natural number bias is an instance of intuitive reasoning.     

“I can name that Bayesian network in two matrixes!”

For a number of situations, a Bayesian network can be split into a core network consisting of a set of latent variables describing the status of a system, and a set of fragments relating the status variables to observable evidence that could be collected about the system state. This situation arises frequently in educational testing, where the status variables represent the student proficiency and the evidence models (graph fragments linking competency variables to observable outcomes) relate to assessment tasks that can be used to assess that proficiency. The traditional approach to knowledge engineering in this situation would be to maintain a library of fragments, where the graphical structure is specified using a graphical editor and then the probabilities are entered using a separate spreadsheet for each node. If many evidence model fragments employ the same design pattern, a lot of repetitive data entry is required. As the parameter values that determine the strength of the evidence can be buried on interior screens of an interface, it can be difficult for a design team to get an impression of the total evidence provided by a collection of evidence models for the system variables, and to identify holes in the data collection scheme. A Q-matrix - an incidence matrix whose rows represent observable outcomes from assessment tasks and whose columns represent competency variables - provides the graphical structure of the evidence models. The Q-matrix can be augmented to provide details of relationship strengths and provide a high level overview of the kind of evidence available. The relationships among the status variables can be represented with an inverse covariance matrix; this is particularly useful in models from the social sciences as often the domain experts’ knowledge about the system states comes from factor analyses and similar procedures that naturally produce covariance matrixes. The representation of the model using matrixes means that the bulk of the specification work can be done using a desktop spreadsheet program and does not require specialized software, facilitating collaboration with external experts. The design idea is illustrated with some examples from prior assessment design projects.     

Identification of mechanical properties of arteries with certification of global optimality

In this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.

     

Asymptotic behavior of posterior distributions for random processes under incorrect models

In this paper, the asymptotic behavior of posterior distributions on parameters contained in random processes is examined when the specified model for the densities is not necessarily correct. Uniform convergence of likelihood functions in some way is shown to be a sufficient condition for the posterior distributions to be asymptotically confined to a set (Theorem 1). For ergodic stationary Markov processes uniform convergence of likelihood functions is established by the ergodic theorem for Banach-valued stationary processes (Proposition 1). A sufficient condition for the uniform convergence is also shown for general random processes (Proposition 2). These results are used to analyze the asymptotic behavior of posterior distributions on parameters contained in linear systems under incorrect models (Example 1 and 2).     

Full predictivistic modeling of stock market data: Application to change point problems

In change point problems in general we should answer three questions: how many changes are there? Where are they? And, what is the distribution of the data within the blocks? In this paper, we develop a new full predictivistic approach for modeling observations within the same block of observation and consider the product partition model (PPM) for treating the change point problem. The PPM brings more flexibility into the change point problem because it considers the number of changes and the instants when the changes occurred as random variables. A full predictivistic characterization of the model can provide a more tractable way to elicit the prior distribution of the parameters of interest, once prior opinions will be required only about observable quantities. We also present an application to the problem of identifying multiple change points in the mean and variance of a stock market return time series.     

Error noted in a case study on fund allocation using goal programming

In a recent volume of European Journal of Operational Research a Case Study concerning fund allocation using goal programming was reported. However, the goal program model given was incomplete and the solution provided incorrect. In this short communication we propose a more correct formulation. The correctly formulated problem has multiple solutions. It is demonstrated that at least one solution is better than the solution reported in the original paper.     

ARMMS: Analogical reasoning model management system for multicriteria vehicle scheduling

The transportation industry problem of scheduling vehicles combines the spatial characteristics of routing with time domain considerations of activity schedules. The problem is complex because of the numerous interacting constraints in the spatial and time domains. Further, some of the constraints are flexible and some arise in real-time. The scheduling problem is often presented with multiple objectives that are not all economic in nature and which can be contradictory to one another. In response to these needs, this paper describes an analogical reasoning model management system, called ARMMS, designed in the domain of vehicle scheduling. ARMMS consists of knowledge bases and data bases, a truth maintenance system, a user interface, an inference engine, a learning mechanism, and a model library. Given a scheduling problem, ARMMS searches its memory for solutions. If no solution is available, ARMMS falls back on an analogical problem solving approach in which similar experience can be recalled, and solutions to new, but similar, problems can be constructed. If no similar experience exists, ARMMS intelligently selects an appropriate algorithmic model from its model library, based on the input parameters and problem type, to solve the given problem. By combining experts' knowledge, analogical problem-solving approaches, and algorithmic methods, ARMMS provides an efficient problem-solving approach for vehicle scheduling and routing. ARMMS is also a feasible base for the development of intelligent model management systems.     

A production system model of hunter-gatherer resource scheduling adaptations

Flannery has suggested that the shift from a hunter-gatherer economy to one based upon incipient agriculture requires a gradual rescheduling of the groups' resource acquisition activities. Here, concepts from Artificial Intelligence and Adaptive Systems are used to develop a model of prehistoric hunter-gatherer decision-making in the valley of Oaxaca, Mexico. This decision-making system was then used to answer the following questions:

1. 1. Given randomly specified strategies and no initial knowledge of what available rescheduling decisions will improve performance, can the system produce changes that lead to a mix of strategies that correspond to those used by hunter-gatherers in the valley prior to the introduction of incipient agriculture?

2. 2. How would the system adjust its' resource acquisition strategies in response to the introduction of techniques for incipient agriculture?

It is suggested that this basic model is able to explain a significant percentage of the changes in resource use seen in the archaeological record for the site.     

On some inverse problems for elliptic equations and systems

Under study are the inverse problems of determining the right-hand side of a particular form and the solution for elliptic systems, including a series of elasticity systems. (On the boundary of the domain the solution satisfies either the Dirichlet conditions or mixed Dirichlet-Neumann conditions.) We assume that on a system of planes the normal derivatives of the solution can have discontinuities of the first kind. The conjugating boundary conditions on the discontinuity surface are analogous to the continuity conditions for the fields of displacements and stresses for a horizontally laminated medium. The overdetermination conditions are integral (the average of the solution over some domain is specified) or local (the values of the solution on some lines are specified). We study the solvability conditions for these problems and their Fredholm property.     

Quantile regression metamodeling: Toward improved responsiveness in the high-tech electronics manufacturing industry

Both technology and market demands within the high-tech electronics manufacturing industry change rapidly. Accurate and efficient estimation of cycle-time (CT) distribution remains a critical driver of on-time delivery and associated customer satisfaction metrics in these complex manufacturing systems. Simulation models are often used to emulate these systems in order to estimate parameters of the CT distribution. However, execution time of such simulation models can be excessively long limiting the number of simulation runs that can be executed for quantifying the impact of potential future operational changes. One solution is the use of simulation metamodeling which is to build a closed-form mathematical expression to approximate the input–output relationship implied by the simulation model based on simulation experiments run at selected design points in advance. Metamodels can be easily evaluated in a spreadsheet environment “on demand” to answer what-if questions without needing to run lengthy simulations. The majority of previous simulation metamodeling approaches have focused on estimating mean CT as a function of a single input variable (i.e., throughput). In this paper, we demonstrate the feasibility of a quantile regression based metamodeling approach. This method allows estimation of CT quantiles as a function of multiple input variables (e.g., throughput, product mix, and various distributional parameters of time-between-failures, repair time, setup time, loading and unloading times). Empirical results are provided to demonstrate the efficacy of the approach in a realistic simulation model representative of a semiconductor manufacturing system.     

Use of Inappropriate and Inaccurate Conceptual Knowledge to Solve an Osmosis Problem

Two outstanding high school science students each generated a correct answer to an osmosis problem. The solution processes are noteworthy because the problem solvers did not blindly use algorithms. They relied, instead, on conceptual knowledge which was inaccurate and inappropriate to the problem. They thought the osmosis problem was about air pressure, and some of their knowledge about air pressure was inaccurate. Thus, even when students rely on conceptual knowledge to solve a problem, correct answers need not indicate adequate understanding. Characteristics of the problem solvers, salient properties of the problem that could contribute to the problem misrepresentation, and spurious correct answers are identified. Finally, some instructional recommendations and research questions are presented.     

The estimate of the time of motion of certain dynamical systems

An estimate of the time necessary for the phase points of a dynamical system to reach a specified finite domain, containing an asymptotically stable solution, from any initial position belonging to the specified domain is obtained with the sole assumption that the derivative of the Lyapunov function for autonomous second-order systems and for certain higher-order systems has a negative sign.     

Info-gap forecasting and the advantage of sub-optimal models

We consider forecasting in systems whose underlying laws are uncertain, while contextual information suggests that future system properties will differ from the past. We consider linear discrete-time systems, and use a non-probabilistic info-gap model to represent uncertainty in the future transition matrix. The forecaster desires the average forecast of a specific state variable to be within a specified interval around the correct value. Traditionally, forecasting uses a model with optimal fidelity to historical data. However, since structural changes are anticipated, this is a poor strategy. Our first theorem asserts the existence, and indicates the construction, of forecasting models with sub-optimal-fidelity to historical data which are more robust to model error than the historically optimal model. Our second theorem identifies conditions in which the probability of forecast success increases with increasing robustness to model error. The proposed methodology identifies reliable forecasting models for systems whose trajectories evolve with Knightian uncertainty for structural change over time. We consider various examples, including forecasting European Central Bank interest rates following 9/11.     

A research on the grey prediction model GM(1,n)

The grey theory can be applied in the research of prediction, decision-making and control, especially in prediction. The primary characteristic of a grey system is the incompleteness of information. A grey system could be whitened by way of inserting more messages in itself and its accuracy of prediction could be raised. The solution to the existing grey prediction model GM(1,n) is inaccurate and then its prediction accuracy cannot be expected. To solve the existing GM(1,n) by assuming step by step the first order accumulated generating operation data of the associated series to be constants is incorrect. The existing model GM(1,n) is seriously wrong even for a system having a nonnegative associated series with constant entries. There are currently only a few wrong papers based on the existing GM(1,n) model to be published. Almost all the improved prediction models based on the existing GM(1,n) model are correct. For example, the improved models are correct by convolution integral or fitting their forcing terms by several elementary functions. The algorithm of GMC(1,n) is applied to explain why the existing GM(1,n) model is incorrect in this article.     

A parametric GP model dealing with incomplete information for group decision-making

We consider a group decision-making problem where preferences given by the experts are articulated into the form of pairwise comparison matrices. In many cases, experts are not able to efficiently provide their preferences on some aspects of the problem because of a large number of alternatives, limited expertise related to some problem domain, unavailable data, etc., resulting in incomplete pairwise comparison matrices. Our goal is to develop a computational method to retrieve a group priority vector of the considered alternatives dealing with incomplete information. For that purpose, we have established an optimization problem in which a similarity function and a parametric compromise function are defined. Associated to this problem, a logarithmic goal programming formulation is considered to provide an effective procedure to compute the solution. Moreover, the parameters involved in the method have a clear meaning in the context of group problems.     

Mixed-integer minimax dynamic optimization for structure identification of glycerol metabolic network

Cell metabolism is a dynamic regulation process, in which its network structure and/or regulatory mechanisms can change constantly over time due to internal and external perturbations. This paper models glycerol metabolism in continuous fermentation as a nonlinear mixed-integer dynamic system by defining the time-varying metabolic network structure as an integer-valued function. To identify the dynamic network structure and kinetic parameters, we establish a mixed-integer minimax dynamic optimization problem with concentration robustness as its objective functional. By direct multiple shooting strategy and a decomposition approach consisting of convexification, relaxation and rounding strategy, the optimization problem is transformed into a large-scale approximate multistage parameter optimization problem. It is then solved using a competitive particle swarm optimization algorithm. We also show that the relaxation problem yields the best lower bound for the optimization problem, and its solution can be arbitrarily approximated by the solution obtained from rounding strategy. Numerical results indicate that the proposed mixed-integer dynamic system can better describe cellular self-regulation and response to intermediate metabolite inhibitions in continuous fermentation of glycerol. These numerical results show that the proposed numerical methods are effective in solving the large-scale mixed-integer dynamic optimization problems.