Scoring Divergent Thinking Tests by Computer With a Semantics-Based Algorithm

Divergent thinking (DT) tests are useful for the assessment of creative potentials. This article reports the semantics-based algorithmic (SBA) method for assessing DT. This algorithm is fully automated: Examinees receive DT questions on a computer or mobile device and their ideas are immediately compared with norms and semantic networks. This investigation compared the scores generated by the SBA method with the traditional methods of scoring DT (i.e., fluency, originality, and flexibility). Data were collected from 250 examinees using the “Many Uses Test” of DT. The most important finding involved the flexibility scores from both scoring methods. This was critical because semantic networks are based on conceptual structures, and thus a high SBA score should be highly correlated with the traditional flexibility score from DT tests. Results confirmed this correlation (r = .74). This supports the use of algorithmic scoring of DT. The nearly-immediate computation time required by SBA method may make it the method of choice, especially when it comes to moderate- and large-scale DT assessment investigations. Correlations between SBA scores and GPA were insignificant, providing evidence of the discriminant and construct validity of SBA scores. Limitations of the present study and directions for future research are offered

Heat transfer enhancement of a periodic array of isothermal pipes

We address the problem of two-dimensional heat conduction in a solid slab whose upper and lower surfaces are subjected to uniform convection. In the midsection of the slab there is a periodic array of isothermal pipes of general cross section. The main objective of this work is to find the optimum shapes of the pipes that maximize the Shape Factor (heat transport rate). The Shape Factor is obtained by transforming the periodic array of pipes into a periodic array of strips, using the generalized Schwarz- Christoffel transformation, and applying the collocation boundary element method on the transformed domain. Subsequently we pose the inverse problem, i.e. finding the shape that maximizes the Shape factor given the perimeter of the pipes. For large Biot number the optimum shapes are in agreement with the isothermal case, i.e. circular for sufficiently small perimeters/heat transfer, and elongated towards the surfaces of the slab for larger perimeters/heat transfer. Furthermore, for the isothermal case, we were able to discover a new family of optimum shapes for large thickness of the slab and large perimeters, which do not have their maximum width on the horizontal axis of symmetry. For small Biot number the optimum pipes are flatter than the isothermal ones for a given perimeter. The flatness becomes more apparent for larger perimeters. Most important, for large perimeters there exists a critical thickness which is characterized by maximum heat transfer rate. This is further investigated using the finite element method to obtain the critical thickness of a slab and the critical depth of the periodic array of circular pipe

Visualization of topology of transformation pathways in complex chemical systems

Studying transformation in a chemical system by considering its energy as a function of coordinates of the system's components provides insight and changes our understanding of this process. Currently, a lack of effective visualization techniques for high-dimensional energy functions limits chemists to plot energy with respect to one or two coordinates at a time. In some complex systems, developing a comprehensive understanding requires new visualization techniques that show relationships between all coordinates at the same time. We propose a new visualization technique that combines concepts from topological analysis, multi-dimensional scaling, and graph layout to enable the analysis of energy functions for a wide range of molecular structures. We demonstrate our technique by studying the energy function of a dimer of formic and acetic acids and a LTA zeolite structure, in which we consider diffusion of methane

Extracting and visualizing topological information from large high-dimensional data sets

This doctoral dissertation explores and advances topology-based data analysis and visualization, a field that concerns itself with creating tools for gaining insights from scientific data, thus supporting the process of scientific knowledge discovery. In particular, the study proposes two novel analytical techniques, inspired by domain-specific problems and presents a study of error of approximation for these techniques. The first part of the dissertation focuses on a specific problem that arises in computational chemistry. Analysis of transformation pathways is a well-known tool for the investigation of chemical systems and has implications for the design of chemical reactions and materials. However, existing techniques for analyzing transformation pathways either lack the required level of detail for such analyses, or they are limited to low-dimensional data. These issues, complicated by the noise in data and by issues of handling periodic boundaries, are addressed by a novel technique, which involves the extraction of a topological structure, the ``Morse complex,'' and visualizing it as a graph, augmented with additional information, enabling the desired end-user analysis. The technique is then successfully applied to the analyses of two different types of chemical data, which demonstrates its utility. The second part of the dissertation concentrates on the problem of enabling the comparison of data sets in terms of their topologies. In particular, the focus is on enabling the comparison between different instances of the same topological structure, namely a contour tree. One possible solution to this problem is to correlate contour trees in terms of the geometric proximity of their critical points. In order to visualize this correlation, a novel technique combines the extraction of the contour trees, dimensionality reduction, graph drawing, and contours construction. The technique produces a visual metaphor called a ``geometry-preserving topological landscape.'' The utility of the technique is demonstrated through a comparative analysis of data sets based on their corresponding landscapes. The remainder of the dissertation is dedicated to studying the problem of error quantification for the proposed techniques, as well as for more general settings. In particular, the focus is on approximation methods used to reconstruct a domain. For example, by studying the ability of these techniques to preserve topological information, one can derive method selection recommendations, which are potentially generalizable to various topological data analysis techniques. To address this problem, a novel definition of a difference measure for topological abstraction, the ''merge tree,'' is presented and subsequently used to evaluate the previously mentioned approximation methods. The resulting recommendations are found to support the selection of approximation methods for the two proposed techniques

Visualization of topology of transformation pathways in complex chemical systems

Studying transformation in a chemical system by considering its energy as a function of coordinates of the system's components provides insight and changes our understanding of this process. Currently, a lack of effective visualization techniques for high-dimensional energy functions limits chemists to plot energy with respect to one or two coordinates at a time. In some complex systems, developing a comprehensive understanding requires new visualization techniques that show relationships between all coordinates at the same time. We propose a new visualization technique that combines concepts from topological analysis, multi-dimensional scaling, and graph layout to enable the analysis of energy functions for a wide range of molecular structures. We demonstrate our technique by studying the energy function of a dimer of formic and acetic acids and a LTA zeolite structure, in which we consider diffusion of methane