Factorial comparison of working memory models.

Three questions have been prominent in the study of visual working memory limitations: (a) What is the nature of mnemonic precision (e.g., quantized or continuous)? (b) How many items are remembered? (c) To what extent do spatial binding errors account for working memory failures? Modeling studies have typically focused on comparing possible answers to a single one of these questions, even though the result of such a comparison might depend on the assumed answers to both others. Here, we consider every possible combination of previously proposed answers to the individual questions. Each model is then a point in a 3-factor model space containing a total of 32 models, of which only 6 have been tested previously. We compare all models on data from 10 delayed-estimation experiments from 6 laboratories (for a total of 164 subjects and 131,452 trials). Consistently across experiments, we find that (a) mnemonic precision is not quantized but continuous and not equal but variable across items and trials; (b) the number of remembered items is likely to be variable across trials, with a mean of 6.4 in the best model (median across subjects); (c) spatial binding errors occur but explain only a small fraction of responses (16.5% at set size 8 in the best model). We find strong evidence against all 6 documented models. Our results demonstrate the value of factorial model comparison in working memory.

A matrix-calculation-based algorithm for numerical change propagation analysis

Engineering changes (ECs) are raised throughout the lifecycle of engineering products. A single change to one component produces knock-on effects on others necessitating additional changes. This change propagation significantly affects the development time and cost and determines the product's success. Predicting and managing such ECs is, thus, essential to companies. Some prediction tools model change propagation by algorithms, whereof a subgroup is numerical. Current numerical change propagation algorithms either do not account for the exclusion of cyclic propagation paths or are based on exhaustive searching methods. This paper presents a new matrix-calculation-based algorithm which can be applied directly to a numerical product model to analyze change propagation and support change prediction. The algorithm applies matrix multiplications on mutations of a given design structure matrix accounting for the exclusion of self-dependences and cyclic propagation paths and delivers the same results as the exhaustive search-based Trail Counting algorithm. Despite its factorial time complexity, the algorithm proves advantageous because of its straightforward matrix-based calculations which avoid exhaustive searching. Thereby, the algorithm can be implemented in established numerical programs such as Microsoft Excel which promise a wider application of the tools within and across companies along with better familiarity, usability, practicality, security, and robustness. © 1988-2012 IEEE.

State estimation schemes for independent component coupled hidden Markov models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results. © Taylor & Francis Group, LLC.