Application of Complexity Theory to an Information Processing Model in Science Education

The current work examines the role of working-memory capacity in problem solving in science education. It treats an information-processing model with tools of complexity theory. Nonlinear methods are used to correlate the subjects' achievement scores with working-memory capacity. Data have been taken from the achievement scores in simple organic-synthesis chemical problems. The subjects (N = 319) were in grade twelve (age 17–18). Problems of various Z-demands (that is the number of steps needed to solve the problem) from two to eight were used. Rank-order sequences of the subjects, according to their scores, were generated, and each score was then replaced by the value of subject's working memory capacity measured by the digit backward span test. Then the sequences were mapped onto a one-dimensional random walk model and when treated as dynamic flows were found to possess fractal geometry with characteristics depending on the Z-demand of the problem. The findings were interpreted using concepts from complexity theory, such as correlation exponents, fractal dimensions and entropy. The null hypothesis was tested with surrogate data.     

Application of possibility theory to investment decisions

Carlson and Fuller (2001, Fuzzy Sets and Systems, 122, 315–326) introduced the concept of possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see Bodjanova (2005, Information Science, 172, 73–89) for detail). We then discuss the application of these results to decision making problems in which the parameters may involve uncertainty and vagueness. As an application, we develop expression for fuzzy net present value (FNPV) of future cash flows involving adaptive fuzzy numbers by using their possibilistic moments. An illustrative numerical example is given to illustrate the results.     

Banach空间中N阶脉冲积分-微分方程边值问题的解

运用Monch不动点定理，获得了Banach空间中一类N阶非线性混合型脉冲积分-微分方程边值问题解的存在性．最后给出一个三阶无穷脉冲积分-微分方程边值问题的例子来说明文中所给的条件是合理的．     

Scission induced by circular shear and heat conduction in an elastomeric cylinder

Constitutive equations for the thermo-mechanics of elastomeric materials generally assume that they do not undergo microstructural change. A constitutive theory is discussed here which accounts for such changes arising from continuous scission of macromolecular junctions of elastomeric networks due to deformation and high temperatures and the subsequent cross-linking of molecules into new networks with new reference states. The total stress is the superposition of the stresses in the remainder of the original network and in each subsequently formed network. Each network acts as a temperature-dependent non-linear elastic material. The interaction of this material response with inhomogeneous deformation and temperature fields is studied for finite circular shear of a cylinder. Numerical results illustrate how the mechanical response of the cylinder depends on the temperature dependence of both the scission–cross-linking process and the properties of the elastic networks.     

Riemann问题的间断有限元

用时空全离散间断零次有限元对Riemarm问题进行了数值求解，没有出现振荡，很好的模拟了稀疏波的逐渐稀疏化和激波的剧烈变化。     

Inverse problems of aggregation processes

The coagulation frequency is the key ingredient in the population balance (Smoluchowski) equation of coagulation kinetics. An inverse problem is formulated to extract the coagulation frequency from transient size distributions when these distributions are self-similar. Two numerical examples illustrate the procedure. The first demonstrates the inverse problem for the recovery of singular coagulation frequencies, while the second shows the procedure when self-similarity is approximate. Transient droplet coagulation experiments in a turbulent flow field have been performed. The resulting size distributions are observed to be self-similar. The inverse problem is used to determine the drop coagulation frequency. This frequency shows significant deviation from the coagulation frequencies derived from simple models of drop-drop interactions in a turbulent flow field.     

A variable neighborhood search for the capacitated arc routing problem with intermediate facilities

The capacitated arc routing problem (CARP) focuses on servicing edges of an undirected network graph. A wide spectrum of applications like mail delivery, waste collection or street maintenance outlines the relevance of this problem. A realistic variant of the CARP arises from the need of intermediate facilities (IFs) to load up or unload the service vehicle and from tour length restrictions. The proposed Variable Neighborhood Search (VNS) is a simple and robust solution technique which tackles the basic problem as well as its extensions. The VNS shows excellent results on four different benchmark sets. Particularly, for all 120 instances the best known solution could be found and in 71 cases a new best solution was achieved.     

A complexity approach to sustainability – Stafford Beer revisited

There is wide acceptance of the need for a more holistic approach to sustainability. However, practical solutions remain elusive and tend to exhibit underlying conflicts between different paradigms and their associated methodologies. This paper argues the need to wield analytical tools that themselves embody the principles of systemic, ecological thinking. We present here a theoretical framework based on complexity science – focused on organisational and second order cybernetics – that highlights our understanding of the concept of sustainability. The paper goes on to reflect upon how current practice would benefit from such an approach.     

Chordal bipartite completion of colored graphs

Golumbic, Kaplan, and Shamir [Graph sandwich problems, J. Algorithms 19 (1995) 449-473], in their paper on graph sandwich problems published in 1995, left the status of the sandwich problems for strongly chordal graphs and chordal bipartite graphs open. It was recently shown [C.M.H. de Figueiredo, L. Faria, S. Klein, R. Sritharan, On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs, Theoret. Comput. Sci., accepted for publication] that the sandwich problem for strongly chordal graphs is NP-complete. We show that given graph G with a proper vertex coloring c, determining whether there is a supergraph of G that is chordal bipartite and also is properly colored by c is NP-complete. This implies that the sandwich problem for chordal bipartite graphs is also NP-complete.     

Increasing efficiency of inverse iteration

Inverse iteration is simple but not very efficient method for computing few eigenvalues with minimal absolute values and corresponding eigenvectors of a symmetric matrix. The idea is to increase its efficiency by technique similar to multigrid methods used for solving linear systems. This approach is not new, but until now multigrid was mostly used for solving linear system which appear in Rayleigh quotient iteration, inverse iteration and related iterative methods. Instead of choosing appropriate coordinates (grids), our algorithm performs inverse iteration on a sequence of subspaces with decreasing dimensions (multispace). Block Lanczos method is used for the selection of a smaller subspace. This will produce a banded matrix, which makes inverse iteration even faster in the smaller dimensions.