Structural centrality in communications networks

This paper examines the concept of centrality with respect to small-group communication experiments. An index of centrality is presented which is based on the incidence matrix of actual communications rather than on the deviation matrix of possible communications, as in the Bavelas Index of Centrality. The index takes the value of zero for the homogeneous all-channel graph and the value of unity for the homogeneous wheel graph. The index can be computed for individuals as well as groups. Three examples are computed.     

König's Infinity Lemma and Beth's Tree Theorem

König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected (undirected) graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite (undirected) tree with a root has a infinite branch. This tree lemma can be traced to [Beth, E. W. 1955. ‘Semantic entailment and formal derivability’, Mededelingen der Kon. Ned. Akad. v. Wet., new series 18, 13, 309–42]. It is argued that Beth independently discovered the tree lemma in the early 1950s and that it was later recognized among logicians that Beth's result was a consequence of the infinity lemma. The equivalence of these lemmas is an easy consequence of a well known result in graph theory: every connected, locally finite graph has among its partial subgraphs a spanning tree.     

On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood

This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon previous methods because it provides an omnibus test of the entire hierarchy of cancellation axioms, beyond double cancellation. It does so while accounting for the posterior uncertainty that is inherent in the empirical orderings that are implied by these axioms, together. The new method is illustrated through a test of the cancellation axioms on a classic survey data set, and through the analysis of simulated data.     

Model Existence in Non-Compact Modal Logic

Predicate modal logics based on Kwith non-compact extra axioms are discussed and a sufficient condition for the model existence theorem is presented. We deal with various axioms in a general way by an algebraic method, instead of discussing concrete non-compact axioms one by one.     

Decomposable Models: A New Look at Interdependence and Dependence Structures in Psychological Research

Decomposable models represent interdependence structures for observable variables. Each model is fully characterized by a set of conditional independence restrictions, and can be visualized with an undirected as well as a special type of a directed graph. As a consequence each decomposable model can be interpreted either in terms of interdependencies only or as a particular kind of dependence structure, as a recursive system or path analysis model. Under the assumption of normally distributed variables, decomposable models determine the structure of correlation matrices, and maximum-likelihood estimates of these can be calculated with the help of ordinary least squares estimation. Using several examples from psychological research, we discuss the interpretation of decomposable models. Furthermore, it is demonstrated how recursive dependence structures can be specified with the help of decomposable models in a hypothesis generating (exploratory) as well as in a hypothesis testing (confirmatory) manner.     

A Virtue-Based Defense of Mathematical Apriorism

Mathematical apriorists usually defend their view by contending that axioms are knowable a priori, and that the rules of inference in mathematics preserve this apriority for derived statements—so that by following the proof of a statement, we can trace the apriority being inherited. The empiricist Philip Kitcher attacked this claim by arguing there is no satisfactory theory that explains how mathematical axioms could be known a priori. I propose that in analyzing Ernest Sosa’s model of intuition as an intellectual virtue, we can construct an “intuition–virtue” that could supply the missing explanation for the apriority of axioms. I first argue that this intuition–virtue qualifies as an a priori warrant according to Kitcher’s account, and then show that it could produce beliefs about mathematical axioms independent of experience. If my argument stands, this paper could provide insight on how virtue epistemology could help defend mathematical apriorism on a larger scale.     

An Elementary System of Axioms for Euclidean Geometry Based on Symmetry Principles

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us (the homogeneity of space), all directions are the same to us (the isotropy of space) and all units of length we use to create geometric figures are the same to us (the scale invariance of space). On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: (1) it supports the thesis that Euclidean geometry is a priori, (2) it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, (3) it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics.     

Fundamental axioms for preference relations

Summary The basic theory of preference relations contains a trivial part reflected by axioms A1 and A2, which say that preference relations are preorders. The next step is to find other axims which carry the theory beyond the level of the trivial. This paper is to a great part a critical survey of such suggested axioms. The results are much in the negative — many proposed axioms imply too strange theorems to be acceptable as axioms in a general theory of preference. This does not exclude, of course, that they may well be reasonable axioms for special calculi of preference. I believe that many axioms which are rejected here may be plausible if their range of application is restricted by conditions which are possible to formulate only in a language richer than that of the propositional calculus, e.g. in one containing modal operators or probabilistic concepts.     

The information theoretic entropy function as a total expected participation index for communication network experiments

This paper shows how the concept of an incidence matrix of communications can be used to define the entropy of a finite scheme. The properties of the entropy function are examined and the function is found to be best interpreted as a total expected participation index. Data is presented showing the relationship between structural centrality and the new total expected participation index. In general, as the network becomes more centralized the smaller the value of the participation index and as the network becomes more structurally decentralized the greater the participation index.This research was supported in part by Ford Foundation Grant 1-40055 to the Graduate School of Industrial Administration at Carnegie Institute of Technology for Research in Organizational Behavior.The author wishes to acknowledge the aid of Terry B. Marbach in the preparation of data.     

A System of Axioms for Minkowski Spacetime

Journal of Philosophical Logic - We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the...     

Centrality of women's multiple roles: beneficial and detrimental consequences for psychological well-being

Theorists have proposed that greater centrality (personal importance) of a social role is associated with better psychological well-being but that role centrality exacerbates the negative effects of stress in that same social role on well-being. The present study found evidence to support both hypotheses in a sample of 296 women who simultaneously occupied the roles of parent care provider, mother, wife, and employee. Greater centrality of all four roles was related to better psychological well-being. As predicted, wife centrality exacerbated the effects of wife stress on life satisfaction, and employee centrality exacerbated the effects of employee stress on depressive symptoms. Contrary to prediction, centrality of the mother role buffered women from the negative effects of mother stress on depressive symptoms. These findings point to an aspect of role identity that can benefit well-being but that has complex effects in the context of role stress.     

A two-stage algorithm for assessing violations of additivity via axiomatic and numerical conjoint analysis

An algorithm for assessing additivity conjunctively via both axiomatic conjoint analysis and numerical conjoint scaling is described. The algorithm first assesses the degree of individual differences among sets of rankings of stimuli, and subsequently examines either individual or averaged data for violations of axioms necessary for an additive model. The axioms are examined at a more detailed level than has been previously done. Violations of the axioms are broken down into different types. Finally, a nonmetric scaling of the data can be done based on either or both of two different badness-of-fit scaling measures. The advantages of combining all of these features into one algorithm for improving the diagnostic value of axiomatic conjoint measurement in evaluating additivity are discussed.     

社会通则及其有关研究

长期以来,心理学对文化差异的研究以价值观为主导。2002年Leung等人提出了社会通则概念（Social Axiom）,使得对文化差异的研究有了新载体。社会通则区别于价值观、社会态度、人格特质等概念,它是个体对于他人、社会、物质和精神世界的一般化信念,特指个体对两个概念或者两个实体关系的一般性认识。研究者编制的社会通则问卷具有良好的信效度。该问卷在40多个国家的应用表明,社会通则在不同文化和社会背景下具有共同的5个维度,即愤世嫉俗、社会多样性、付出有回报、宗教性和命运控制。社会通则的研究从新视角探讨了文化差异以及心理机制和行为表现的关系,为社会心理学提供了新的研究方向。     

Social network ties and organizational citizenship behavior: evidence of a curvilinear relationship

ABSTRACT

We examine the relationships between employee friendship and advice network centrality and organizational citizenship behavior (OCB). Using social exchange theory as a basis, we argue that centrality within the workplace friendship network will be positively and linearly related to employee OCB. Further, we draw on conservation of resources theory and role theory to predict a curvilinear (inverse U) relationship between employees’ advice network centrality and OCB such that employees will engage in higher levels of OCB at moderate levels of advice centrality than at low and high levels. We test the theoretical model in an academic setting (using other reports of network ties and employee ratings of OCB) and a US-based organization (using other reports of network ties and supervisor ratings of OCB). The results support the idea of a curvilinear relationship between advice network centrality and OCB in both studies and a linear relationship between friendship centrality and OCB in Study 2. Practical implications and directions for future research are addressed.     

Centrality in children's best friend networks: The role of social behaviour

Centrality is an indicator of an individual's relative importance within a social group. Predictors of centrality in best friendship networks were examined in 146 children (70 boys and 76 girls, M_age = 9.95). Children completed measures of social confidence, social desirability, friendship quality, school liking, and loneliness and nominated their best friends from within their class at two time points, 3 months apart. Multigroup path analysis revealed gender differences in the antecedents of centrality. Social confidence, social desirability, and friendship quality predicted changes in the indicators of centrality in best friend networks over time. Boys' social behaviour positively predicted changes in centrality, whereas girls' social behaviour negatively predicted changes in centrality. Together, these findings suggest that some aspects of social behaviour are influential for centrality in best friend groups.     

“Minimax length links” of a dissimilarity matrix and minimum spanning trees

A theorem is proved stating that the set of all minimax links, defined as links minimizing, over paths, the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph, comprise the union of all minimum spanning trees of that graph. This theorem is related to methods of fitting network models to dissimilarity data, particularly a method called Pathfinder due to Schvaneveldt and his colleagues, as well as to single linkage clustering, and results concerning the relationship between minimum spanning trees and single linkage hierarchical trees.Acknowledgments: The author thanks Phipps Arabie, Lawrence J. Hubert, and K. Christoph Klauer for a number of helpful suggestions and comments on various aspects of this paper.     

EEG microstates during different phases of Transcendental Meditation practice

Two phases of Transcendental Meditation (TM)—transcending and undirected mentation—were compared to each other and to task-free resting using multichannel EEG recorded from 20 TM practitioners. An EEG microstate analysis identified four classes of microstates which were labeled A, B, C and D, based on their similarity to previously published classes. For each class of microstates, mean duration, coverage and occurrence were computed. Resting and transcending differed from undirected mentation with decreased prominence of Class A and increased prominence of Class D microstates. In addition, transcending showed decreased prominence of Class C microstates compared to undirected mentation. Based on previous findings on the functional significance of the microstate classes, the results indicate an increased reference to reality and decreased visualization during resting and transcending compared to undirected mentation. Also, our results indicate decreased saliency of internally generated mentations during transcending compared to undirected mentation reflecting a more detached and less evaluative processing. It is proposed that the continuous cycling through these two phases of meditation during a TM session might facilitate and train the flexible modulation of the parameters of these microstates of these particular classes which are known to be altered in psychiatric disorders. This might promote beneficial stabilizing effects for the practitioner of TM.     

On axiomatizations of public announcement logic

In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL  without additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the core set. Moreover, we also propose and advocate an alternative yet meaningful axiomatization of PAL  without the reduction axioms. The completeness is proved directly by a detour method using the canonical model where announcements are treated as merely labels for modalities as in normal modal logics. This new axiomatization and its completeness proof may sharpen our understanding of PAL  and can be adapted to other dynamic epistemic logics.     

On extremal axioms

In the paper translated here, Carnap and Bachmann shows that the apparently metalinguistic ‘extremal' axioms that are added to some axiom systems to the effect that the foregoing axioms are to apply as broadly, or as narrowly, as possible may be formulated directly as proper axioms. They analyze such axioms into four fundamental types, with the help of a concept of ‘complete’ isomorphism.