An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling

A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [_?1¹₁^?1]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White (White, Boorman & Breiger, 1976). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.     

Complexity Results for Modal Dependence Logic

Modal dependence logic was introduced recently by Väänänen. It enhances the basic modal language by an operator = (). For propositional variables p ₁, . . . , p _n , = (p ₁, . . . , p _n-1, p _n ) intuitively states that the value of p _n is determined by those of p ₁, . . . , p _n-1. Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time. In this paper we consider fragments of modal dependence logic obtained by restricting the set of allowed propositional connectives. We show that satisfiability for poor man’s dependence logic, the language consisting of formulas built from literals and dependence atoms using ${\wedge, \square, \lozenge}$ (i. e., disallowing disjunction), remains NEXPTIME-complete. If we only allow monotone formulas (without negation, but with disjunction), the complexity drops to PSPACE-completeness. We also extend Väänänen’s language by allowing classical disjunction besides dependence disjunction and show that the satisfiability problem remains NEXPTIME-complete. If we then disallow both negation and dependence disjunction, satisfiability is complete for the second level of the polynomial hierarchy. Additionally we consider the restriction of modal dependence logic where the length of each single dependence atom is bounded by a number that is fixed for the whole logic. We show that the satisfiability problem for this bounded arity dependence logic is PSPACE-complete and that the complexity drops to the third level of the polynomial hierarchy if we then disallow disjunction. In this way we completely classify the computational complexity of the satisfiability problem for all restrictions of propositional and dependence operators considered by Väänänen and Sevenster.     

Recognizing group cognition

In this paper, we approach the idea of group cognition from the perspective of the “extended mind” thesis, as a special case of the more general claim that systems larger than the individual human, but containing that human, are capable of cognition (Clark, 2008, Clark and Chalmers, 1998). Instead of deliberating about “the mark of the cognitive” (Adams & Aizawa, 2008), our discussion of group cognition is tied to particular cognitive capacities. We review recent studies of group problem solving and group memory which reveal that specific cognitive capacities that are commonly ascribed to individuals are also aptly ascribed at the level of groups. These case studies show how dense interactions among people within a group lead to both similarity-inducing and differentiating dynamics that affect the group’s ability to solve problems. This supports our claim that groups have organization-dependent cognitive capacities that go beyond the simple aggregation of the cognitive capacities of individuals. Group cognition is thus an emergent phenomenon in the sense of Wimsatt (1986). We further argue that anybody who rejects our strategy for showing that cognitive properties can be instantiated at multiple levels in the organizational hierarchy on a priori grounds is a “demergentist,” and thus incurs the burden of proof for explaining why cognitive properties are “stuck” at a certain level of organizational structure. Finally, we show that our analysis of group cognition escapes the “coupling-constitution” charge that has been leveled against the extended mind thesis (Adams & Aizawa, 2008).     

Problem representation: The effects of spatial arrays

Two studies examined how characteristics of spatial arrays contribute to efficient problem representation. Thirty-two adults were presented with information about family relationships in one of two arrays: a hierarchy or a matrix. Their answers to two different sets of questions were timed. The matrix format was superior to the hierarchy for one set of questions only; no differences between the arrays emerged for the other set. The data were interpreted in terms of how the family relationships were mapped onto the arrays; the mapping differences between the arrays affected the number of mental steps needed to solve some questions, but not others. In a second experiment (N=32), the same problem information was remapped onto the arrays, with the mapping relations reversed. As predicted, the pattern of response times exactly reflected the change in mapping. It is proposed that, for spatial arrays, efficiency of problem representation is best understood in terms of the number of mental steps in the problem solution.     

A statistical approach to Saaty's scaling method for priorities

This paper investigates the logarithmic least squares (LLSM) approach to Saaty's (Journal of Mathematical Psychology, 1977, 5, 234–281) scaling method for priorities in hierarchical structures. It is argued that statistical criteria are important in deciding the scaling method controversy. It is shown that LLSM is statistically optimal under a number of realistic and practical models. Variances and covariances of parameter estimates are derived. The covariance matrix associated with overall priority differences is also developed. These results allow for a significance analysis of apparent priority differences.     

An Alternate Method of Deriving Priorities and Related Inferences for Group Decision Making in Analytic Hierarchy Process

Some work has been carried out in the past on statistically deriving priorities in Analytic Hierarchy Process (AHP). In AHP, the aggregated worths of the alternatives, when compared with respect to several criteria, are estimated in a hierarchical comparisons model introduced by Saaty. In this setup, statistical models are used for Saaty's method of scaling in paired comparisons experiments in any level of the hierarchy. At the end, the final priority weights of the alternatives and related inferences are developed with appropriate statistical methods. Existing statistical methods in the literature assume independence of the entries of the paired comparison matrix. However, these entries are highly dependent among themselves. In this article, we propose a statistical method that allows for the dependence among the entries of the pairwise comparisons matrix. The proposed method is then illustrated with a numerical example. Copyright © 2011 John Wiley & Sons, Ltd.     

A Type Hierarchy of Selection Processes for the Evaluation of Evolutionary Analogies

In this paper I propose a type-hierarchy approach to provide an intersubjective framework for the evaluation of evolutionary analogies. This approach develops David Hull’s and others’ attempts to provide full generalisation for selection processes, in order to show that sociocultural development and, particularly, scientific change can be considered as an instance of Darwinian selection. I argue that the recent work by Eileen Cornell Way on type hierarchies can offer the kind of generalisation needed to solve the main problems that still affect Hull’s theory and to show that the evolutionary analogy is, after all, only a particular way of grouping phenomena together. If Hull’s main objective is a unified theory of selection, which supports the idea that science selection and natural selection obey the same laws, I also argue that the type hierarchy approach to models shows that this objective is unsustainable as it stands, and is in need of further development. I will firstly introduce the general outline of the type hierarchy approach to models. Then, after a brief recapitulation of Hull’s main points and difficulties, I will try and construct a hierarchy for a general abstraction of selection processes. Finally I will introduce the main criticisms that Hull’s work has faced from philosophers and scientists, and show how they compare with my proposal.     

说谎者悖论的一个新解决方案的纲要(英文)

首先,本文在第二节中提出了谎者悖论所包含的一些问题,比如加强的说谎者悖论,Curry悖论,Yablo悖论,偶然的说谎者悖论,以及塔尔斯基的真不可定义性定理。其次,在第三节简单介绍了塔尔斯基的分层理论,并且指出了他方案的一个最大不足之处就是把一个真谓词分成了很多个个真谓词,这和我们的直观很不符合。之后在第四节介绍了我的一个解悖方案,并讨论了它的一些性质,比如可靠性,完全性,以及我的方案和塔尔斯基方案的区别。第五节说明了第二节中提到的一些问题在我的这个方案下如何处理。     

An alternative scaling method for priorities in hierarchical structures

The early contributions of Saaty have spawned a multitude of applications of principal right (PR) eigenvector “scaling” of a dominance matrix [R]. Prior to Saaty's work (1977–1984) scaling of dominance matrices received little attention in multidimensional scaling, e.g., see Shepard (1972, pp. 26–27). This eigenvector method (EM) of scaling [R] yields u_i scores (weights) popularly used at each branching of the Analytic Hierarchy Process (AHP) technique that has been increasingly applied in multiple criterion analysis of utility, preference, probability, and performance. In this paper, it is proposed that an alternate least squares method (LSM) scaling technique yielding least squares optimal scores (weights) provides $\text{w}{}_{\mathrm{i}}{}^1$ values having a number of important advantages over u_i scores popularly utilized to date.     

Unification and Revolution: A Paradigm for Paradigms

Incommensurability was Kuhn’s worst mistake. If it is to be found anywhere in science, it would be in physics. But revolutions in theoretical physics all embody theoretical unification. Far from obliterating the idea that there is a persisting theoretical idea in physics, revolutions do just the opposite: they all actually exemplify the persisting idea of underlying unity. Furthermore, persistent acceptance of unifying theories in physics when empirically more successful disunified rivals can always be concocted means that physics makes a persistent implicit assumption concerning unity. To put it in Kuhnian terms, underlying unity is a paradigm for paradigms. We need a conception of science which represents problematic assumptions concerning the physical comprehensibility and knowability of the universe in the form of a hierarchy, these assumptions becoming less and less substantial and more and more such that their truth is required for science, or the pursuit of knowledge, to be possible at all, as one goes up the hierarchy. This hierarchical conception of science has important Kuhnian features, but also differs dramatically from the view Kuhn expounds in his The Structure of Scientific Revolutions. In this paper, I compare and contrast these two views in a much more detailed way than has been done hitherto. I show how the hierarchical view can be construed to emerge from Kuhn’s view as it is modified to overcome objections. I argue that the hierarchical conception of science is to be preferred to Kuhn’s view.     

Memory for target height is scaled to observer height

According to the embodied approach to visual perception, individuals scale the environment to their bodies. This approach highlights the central role of the body for immediate, situated action. The present experiments addressed whether body scaling—specifically, eye-height scaling—occurs in memory when action is not immediate. Participants viewed standard targets that were either the same height as, taller than, or shorter than themselves. Participants then viewed a comparison target and judged whether the comparison was taller or shorter than the standard target. Participants were most accurate when the standard target height matched their own heights, taking into account postural changes. Participants were biased to underestimate standard target height, in general, and to push standard target height away from their own heights. These results are consistent with the literature on eye-height scaling in visual perception and suggest that body scaling is not only a useful metric for perception and action, but is also preserved in memory.     

Disfluencies, language comprehension, and Tree Adjoining Grammars

Disfluencies include editing terms such as uh and um as well as repeats and revisions. Little is known about how disfluencies are processed, and there has been next to no research focused on the way that disfluencies affect structure-building operations during comprehension. We review major findings from both computational linguistics and psycholinguistics, and then we summarize the results of our own work which centers on how the parser behaves when it encounters a disfluency. We describe some new research showing that information associated with misarticulated verbs lingers, and which adds to the large body of data on the critical influence of verb argument structures on sentence comprehension. The paper also presents a model of disfluency processing. The parser uses a Tree Adjoining Grammar to build phrase structure. In this approach, filled and unfilled pauses affect the timing of Substitution operations. Repairs and corrections are handled by a mechanism we term “Overlay,” which allows the parser to overwrite an undesired tree with the appropriate, correct tree. This model of disfluency processing highlights the need for the parser to sometimes coordinate the mechanisms that perform garden-path reanalysis with those that do disfluency repair. The research program as a whole demonstrates that it is possible to study disfluencies systematically and to learn how the parser handles filler material and mistakes. It also showcases the power of Tree Adjoining Grammars, a formalism developed by Aravind Joshi which has yielded results in many different areas of linguistics and cognitive science.     

The Chief Inducement? The Idea of Marriage as Friendship

A combination of social forces has thrown marriage into question in westernised societies at the end of the millennium. This uncertainty creates space for new ways of thinking about marriage. In this context, we examine the idea of marriage as friendship. We trace its genealogy in the work of Mary Wollstonecraft, John Stuart Mill and Harriet Taylor and then subject it to critical scrutiny using some of Michel de Montaigne's ideas. We ask how applicable the ideal of higher friendship is to marriage and what might be gained and lost by a synthesis of marriage and friendship. Grounding the discussion in historical sources is valuable because the topic is so little explored in the contemporary philosophical literature. This approach also allows any enduring value in these historical texts to be elicited     

Multilinear representations for ordinal utility functions

An ordinal utility function u over two attributes X₁, X₂ is additive if there exists a strictly monotonic function ϕ such that ϕ(u) = v₁(x₂) + v₂(x₂) for some functions v₁, v₂. Here we consider the class of ordinal utility functions over n attributes for which each pair of attributes is additive, but not necessarily separable, for any fixed levels of the remaining attributes. We show that while this class is more general than those that are ordinally additive, the assessment task is of the same order of difficulty, and involves a hierarchy of multilinear rather than additive decompositions.     

Intersectionality in Clinical Medicine: The Need for a Conceptual Framework

Intersectionality has become a significant intellectual approach for those thinking about the ways that race, gender, and other social identities converge in order to create unique forms of oppression. Although the initial work on intersectionality addressed the unique position of black women relative to both black men and white women, the concept has since been expanded to address a range of social identities. Here we consider how to apply some of the theoretical tools provided by intersectionality to the clinical context. We begin with a brief discussion of intersectionality and how it might be useful in a clinical context. We then discuss two clinical scenarios that highlight how we think considering intersectionality could lead to more successful patient–clinician interactions. Finally, we extrapolate general strategies for applying intersectionality to the clinical context before considering objections and replies.     

Measurement scales and scale independence in the analytic hierarchy process

One approach to evaluate the relative performance of decision alternatives with respect to multiple criteria is provided by the analytic hierarchy process. The method is based on pairwise comparisons between attributes, and several numerical measurement scales for the ratio statements have been proposed. The choice of measurement scale is re‐examined, and new arguments supporting the measurement scale of geometric progression are derived. Separately from the measurement scale considerations, the effects of the scale parameter in geometric measurement scale are also studied. By using a regression model for pairwise comparisons data, it is shown that the statistical inference does not depend on the value of the scale parameter in the case of a single pairwise comparison matrix. It is also shown when the scale independence of statistical inference can be achieved in a decision hierarchy. This requires the use of the geometric‐mean aggregation rule instead of the traditional arithmetic‐mean aggregation. The results of the case study demonstrate that the measurement scale and the aggregation rule have potentially large impacts on decision support. Copyright © 2000 John Wiley & Sons, Ltd.     

Further considerations of a general d′ in multidimensional space

Thomas (Psychonom. Bull. Rev. 6 (1999) 224) proposed a generalization of d′,d_g′ for multidimensional distributions and demonstrated that it is not equivalent to Euclidean distance as had been assumed in some previous studies. In this note, it is further shown not to be a metric in the general sense as it fails the triangle inequality. Also, a rigorous proof is offered of the claim (found in Thomas, Psychonom. Bull. Rev. 6 (1999) 224) that in order for the definition of d_g′ to correspond to the quantity that is estimated from data in the traditional way (using hits and false alarms) one must assume a distance classifier (proved in the case of equal covariance matrices). If one assumes optimal responding instead, then the estimated d′ corresponds to (the square root of) Mahalanobis distance. This latter observation clears up an apparent paradox between the fact that d_g′ is not a metric and Ashby and Perrin's (Psychol. Rev. 95 (1988) 124) statement relating the weighted Euclidean scaling model and a signal detection model of similarity that would yield a distance classifier.     

A dynamic constructivist approach to culture: Lessons learned from personality psychology

The comparison of differences between cultural groups has been a dominant approach in cross-cultural psychology. This approach assumes behavioral influence of a relatively static, monolithic culture on members in a cultural group. This paper, however, calls for a dynamic constructivist approach to the study of culture. We begin by drawing a parallel between past research in cultural and personality psychology. We then highlight recent findings that attest to the value of a social-cognitive model of culture. Specifically, we discuss studies that have demonstrated how well established cross-cultural differences may appear or disappear depending on the availability, accessibility, and applicability of cultural theories. We present evidence that situational characteristics may render cultural theories more or less accessible and applicable, and propose a culture × situation interaction model for understanding inter- and intra-cultural variations.     

The origins of the phenomenology of pain: Brentano,Stumpf and Husserl

The following investigation aims to determine the historical origins of the phenomenology of pain. According to my central thesis, these origins can be traced back to an enthralling discussion between Husserl and two of his most important teachers, Brentano and Stumpf. According to my reconstruction of this discussion, while Brentano defended the view that all feelings, including pain, are intentional experiences, and while Stumpf argued that pain is a non-intentional feeling-sensation, Husserl of the Logical Investigations provides compelling resources to resolve the polemic between his teachers by showing how pain can be conceived as a pre-intentional experience. According to my argument, this largely forgotten discussion is of significance not only because it enriches our understanding of pain, but also because it modifies the phenomenological conception of consciousness. Thus in the concluding section, I show why the Husserlian resolution of the controversy between Brentano and Stumpf is of importance for our understanding of the central phenomenological theme—intentionality.