Identity,Indiscernibility, and Philosophical Claims

The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.     

Visual Perception in Japanese Rock Garden Design

We present an investigation into the relation between design principles in Japanese gardens, and their associated perceptual effects. This leads to the realization that a set of design principles described in a Japanese gardening text by Shingen (1466), shows many parallels to the visual effects of perceptual grouping, studied by the Gestalt school of psychology. Guidelines for composition of rock clusters closely relate to perception of visual figure. Garden design elements are arranged into patterns that simplify figure-ground segmentation, while seemingly balancing the visual salience of subparts and the global arrangement. Visual ‘ground’ is analyzed via medial axis transformation (MAT), often associated with shape perception in humans. MAT analysis reveals implicit structure in the visual ground of a quintessential rock garden design. The MAT structure enables formal comparison of structure of figure and ground. They share some aesthetic qualities, with interesting differences. Both contain naturalistic asymmetric, self-similar, branching structures. While the branching pattern of the ground converges towards the viewer, that of the figure converges in the opposite direction.     

Worlds within Worlds: Kabbalah and the New Scientific Paradigm

Beginning with relativity and quantum theory, the deterministic view that has dominated and shaped Western culture for more than 2,500 years has begun to unravel, leading to the emergence of a new paradigm. This new paradigm effectively reformulates the project of science, conceiving of existence as an interpenetrating web of coevolving, cocreative relationships. By exploring Kabbalah and the new scientific paradigm within the context of shared evolutionary principles, I seek to demonstrate a viable alternative to the prevailing deterministic worldview. By going beyond the limits of determinism and re–visioning existence as an evolutionary, emergent phenomenon, we can establish a new basis for an authentic dialogue between science and religion.     

The CHIC Model: A Global Model for Coupled Binary Data

Often problems result in the collection of coupled data, which consist of different N-way N-mode data blocks that have one or more modes in common. To reveal the structure underlying such data, an integrated modeling strategy, with a single set of parameters for the common mode(s), that is estimated based on the information in all data blocks, may be most appropriate. Such a strategy implies a global model, consisting of different N-way N-mode submodels, and a global loss function that is a (weighted) sum of the partial loss functions associated with the different submodels. In this paper, such a global model for an integrated analysis of a three-way three-mode binary data array and a two-way two-mode binary data matrix that have one mode in common is presented. A simulated annealing algorithm to estimate the model parameters is described and evaluated in a simulation study. An application of the model to real psychological data is discussed. T. Wilderjans is a Research Assistant of the Fund for Scientific Research—Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2005/04). We are grateful to Kristof Vansteelandt for providing us with an interesting data set. We also thank three anonymous reviewers for their useful comments.     

Structural Realism, Scientific Change, and Partial Structures

Scientific change has two important dimensions: conceptual change and structural change. In this paper, I argue that the existence of conceptual change brings serious difficulties for scientific realism, and the existence of structural change makes structural realism look quite implausible. I then sketch an alternative account of scientific change, in terms of partial structures, that accommodates both conceptual and structural changes. The proposal, however, is not realist, and supports a structuralist version of van Fraassen’s constructive empiricism (structural empiricism).     

A context-free language for binary multinomial processing tree models

This paper provides a new formalization for the class of binary multinomial processing tree (BMPT) models, and theorems for the class are developed using the formalism. MPT models are a popular class of information processing models for categorical data in specific cognitive paradigms. They have a recursive structure that is productively described with the tools of formal language and computation theory. We provide an axiomatization that characterizes BMPT models as strings in a context-free language, and then we add model-theoretic axioms and definitions to interpret the strings as parameterized probabilistic models for categorical data. The language for BMPT models is related to the Full Binary Tree language, a well-studied context-free language. Once BMPT models are viewed from the perspective of the Full Binary Tree language, a number of theoretical and computational results can be developed. In particular, we have a number of results concerning the enumerations of BMPT models as well as the identifiability of subclasses of these models.     

The repetition-break plot structure: a cognitive influence on selection in the marketplace of ideas

Using research into learning from sequences of examples, we generate predictions about what cultural products become widely distributed in the social marketplace of ideas. We investigate what we term the Repetition-Break plot structure: the use of repetition among obviously similar items to establish a pattern, and then a final contrasting item that breaks with the pattern to generate surprise. Two corpus studies show that this structure arises in about a third of folktales and story jokes. An experiment shows that jokes with this structure are more interesting than those without the initial repetition. Thus, we document evidence for how a cognitive factor influences the cultural products that are selected in the marketplace of ideas.     

Recovering a Probabilistic Knowledge Structure by Constraining its Parameter Space

In the Basic Local Independence Model (BLIM) of Doignon and Falmagne (Knowledge Spaces, Springer, Berlin, 1999), the probabilistic relationship between the latent knowledge states and the observable response patterns is established by the introduction of a pair of parameters for each of the problems: a lucky guess probability and a careless error probability. In estimating the parameters of the BLIM with an empirical data set, it is desirable that such probabilities remain reasonably small. A special case of the BLIM is proposed where the parameter space of such probabilities is constrained. A simulation study shows that the constrained BLIM is more effective than the unconstrained one, in recovering a probabilistic knowledge structure.     

The Local Minima Problem in Hierarchical Classes Analysis: An Evaluation of a Simulated Annealing Algorithm and Various Multistart Procedures

Hierarchical classes models are quasi-order retaining Boolean decomposition models for N-way N-mode binary data. To fit these models to data, rationally started alternating least squares (or, equivalently, alternating least absolute deviations) algorithms have been proposed. Extensive simulation studies showed that these algorithms succeed quite well in recovering the underlying truth but frequently end in a local minimum. In this paper we evaluate whether or not this local minimum problem can be mitigated by means of two common strategies for avoiding local minima in combinatorial data analysis: simulated annealing (SA) and use of a multistart procedure. In particular, we propose a generic SA algorithm for hierarchical classes analysis and three different types of random starts. The effectiveness of the SA algorithm and the random starts is evaluated by reanalyzing data sets of previous simulation studies. The reported results support the use of the proposed SA algorithm in combination with a random multistart procedure, regardless of the properties of the data set under study. Eva Ceulemans is a post-doctoral fellow of the Fund for Scientific Research Flanders (Belgium). Iwin Leenen is a post-doctoral researcher of the Spanish Ministerio de Educación y Ciencia (programa Ramón y Cajal). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/05/04).