Some properties of transition matrices for chain binomial models

A chain binomial model is a Markov chain with a transition matrix whose rows are binomial probabilities. Two such chains are presented and illustrated with possible applications. The paper will focus in particular on some interesting properties of the transition matrices

Testing two cognitive theories of insight

Insight in problem solving occurs when the problem solver fails to see how to solve a problem and then-"aha!"-there is a sudden realization how to solve it. Two contemporary theories have been proposed to explain insight. The representational change theory (e.g., G. Knoblich, S. Ohlsson, & G. E. Rainey, 2001) proposes that insight occurs through relaxing self-imposed constraints on a problem and by decomposing chunked items in the problem. The progress monitoring theory (e.g., J. N. MacGregor, T. C. Ormerod, & E. P. Chronicle, 2001) proposes that insight is only sought once it becomes apparent that the distance to the goal is unachievable in the moves remaining. These 2 theories are tested in an unlimited move problem, to which neither theory has previously been applied. The results lend support to both, but experimental manipulations to the problem suggest that the representational change theory is the better indicator of performance. The findings suggest that testable opposing predictions can be made to examine theories of insight and that the use of eye movement data is a fruitful method of both examining insight and testing theories of insight

Failings in the Treatment of Electronic Signatures

Original article can be found at: http://www.herts.ac.uk/courses/schools-of-study/law/hertfordshire-law-journal/home.cfmPeer reviewe

The influence of bulk particulate properties on pneumatic conveying performance

Interest in the use of dense phase conveying has grown considerably in recent years. However, not all products are capable of being conveyed in dense phase and it is often difficult to predict which products have dense phase capability without carrying out pilot conveying trials. The main objective of this work was to investigate the effect of bulk particular properties on pneumatic conveying performance. To achieve this, an extensive programme of conveying trials was carried out and each product tested was subjected to a series of bench scale tests to evaluate the bulk properties of the material. A phase diagram is proposed, based on the aeration properties of a material, which groups together products of similar conveying potential. The phase diagram gives a first indication on the basis of a small sample of material whether or not a product is capable of dense phase conveying. Further, it will predict the most appropriate mode of flow. For products capable of dense phase in a moving bed type flow regime, a further correlation is proposed which predicts the likely conveying performance in the pipeline in terms of mass throughput of product for given conditions based on the air retention characteristics of a product. The correlation has been generalised to extend its applicability to a range of pipeline configurations. The combination of the phase diagram and the correlation for dense phase moving bed type flow (the most commonly used form of dense phase conveying) provides a powerful design tool which will reduce the need for full conveying trials. In addition, the effect of material bulk properties on blow tank performance has also been investigated and a correlation between aeration properties and blow tank discharge characteristics is proposed

Thin spray film thickness measuring technique

Thin spray film application depths, in the 0.0002 cm to 0.002 cm range, are measured by portable, commercially available, light density measuring device used in conjunction with glass plate or photographic film. Method is automated by using mechanical/electrical control for shutting off film applicator at desired densitometer reading

Periodic Motions in Banach Space and Applications to Functional-Differential Equations

In establishing the existence of periodic solutions for nonautonomous differential equations of the form x = g(x, t), where g is periodic in t of period for fixed x, it is often convenient to consider the translation operator T(x(t)) = x(t + ). If corresponding to each initial vector chosen in an appropriate region there corresponds a unique solution of our equation, then periodicity may be established by proving the existence of a fixed point under T. This same technique is also useful for more general functional equations and can be extended in a number of interesting ways. In this paper we shall consider a variable type of translation operator which is useful in investigating periodicity for autonomous differential and functional equations where the period involved is less obvious

Insight and search in Katona’s five-square problem

Insights are often productive outcomes of human thinking. We provide a cognitive model that explains insight problem solving by the interplay of problem space search and representational change, whereby the problem space is constrained or relaxed based on the problem representation. By introducing different experimental conditions that either constrained the initial search space or helped solvers to initiate a representational change, we investigated the interplay of problem space search and representational change in Katona’s five-square problem. Testing 168 participants, we demonstrated that independent hints relating to the initial search space and to representational change had little effect on solution rates. However, providing both hints caused a significant increase in solution rates. Our results show the interplay between problem space search and representational change in insight problem solving: The initial problem space can be so large that people fail to encounter impasse, but even when representational change is achieved the resulting problem space can still provide a major obstacle to finding the solution

The dynamics of search, impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem

The nine-dot problem is often used to demonstrate and explain mental impasse, creativity, and out of the box thinking. The present study investigated the interplay of a restricted initial search space, the likelihood of invoking a representational change, and the subsequent constraining of an unrestricted search space. In three experimental conditions, participants worked on different versions of the nine-dot problem that hinted at removing particular sources of difficulty from the standard problem. The hints were incremental such that the first suggested a possible route for a solution attempt; the second additionally indicated the dot at which lines meet on the solution path; and the final condition also provided non-dot locations that appear in the solution path. The results showed that in the experimental conditions, representational change is encountered more quickly and problems are solved more often than for the control group. We propose a cognitive model that focuses on general problem solving heuristics and representational change to explain problem difficulty

Heuristics and representational change in two-move matchstick tasks

Insight problems are problems where the problem solver struggles to find a solution until * aha! * the solution suddenly appears. Two contemporary theories suggest that insight problems are difficult either because problem solvers begin with an incorrect representation of the problem, or that problem solvers apply inappropriate heuristics to the problem. The relative contributions of representational change and inappropriate heuristics on the process of insight problem solving was studied with a task that required the problem solver to move two matchsticks in order to transform an incorrect arithmetic statement into a correct one. Problem solvers (N = 120) worked on two different types of two-move matchstick arithmetic problems that both varied with respect to the effectiveness of heuristics and to the degree of a necessary representational change of the problem representation. A strong influence of representational change on solution rates was found whereas the influence of heuristics had minimal effects on solution rates. That is, the difficulty of insight problems within the two-move matchstick arithmetic domain is governed by the degree of representational change required. A model is presented that details representational change as the necessary condition for ensuring that appropriate heuristics can be applied on the proper problem representation