Integer programs for one- and two-mode blockmodeling based on prespecified image matrices for structural and regular equivalence

Establishing blockmodels for one- and two-mode binary network matrices has typically been accomplished using multiple restarts of heuristic algorithms that minimize functions of inconsistency with an ideal block structure. Although these algorithms likely yield exceptional performance, they are not assured to provide blockmodels that optimize the functional indices. In this paper, we present integer programming models that, for a prespecified image matrix, can produce guaranteed optimal solutions for matrices of nontrivial size. Accordingly, analysts performing a confirmatory analysis of a prespecified blockmodel structure can apply our models directly to obtain an optimal solution. In exploratory cases where a blockmodel structure is not prespecified, we recommend a two-stage procedure, where a heuristic method is first used to identify an image matrix and the integer program is subsequently formulated and solved to identify the optimal solution for that image matrix. Although best suited for ideal block structures associated with structural equivalence, the integer programming models have the flexibility to accommodate functional indices pertaining to regular equivalence. Computational results are reported for a variety of one- and two-mode matrices from the blockmodeling literature.     

Some results concerning the quality of vertex solutions found by a method for multiple-objective linear programming

The Zionts-Wallenius algorithm for multiple-objective linear programming terminates with an extreme point solution that is locally but not necessary globally optimal. To find the globally optimal solution, a search along the facets of the solution space polyhedron may be required. In this paper we report the results of an experiment to determine how close the local and global optima are. We discuss the concept of closeness and propose one measure. Computer simulation is used to determine, in general, the quality of the solution found by the Zionts-Wallenius method for two types of non-linear utility functions. The merits of a search procedure are discussed in the context of the results.     

The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability

In theory, the greatest lower bound (g.l.b.) to reliability is the best possible lower bound to the reliability based on single test administration. Yet the practical use of the g.l.b. has been severely hindered by sampling bias problems. It is well known that the g.l.b. based on small samples (even a sample of one thousand subjects is not generally enough) may severely overestimate the population value, and statistical treatment of the bias has been badly missing. The only results obtained so far are concerned with the asymptotic variance of the g.l.b. and of its numerator (the maximum possible error variance of a test), based on first order derivatives and the asumption of multivariate normality. The present paper extends these results by offering explicit expressions for the second order derivatives. This yields a closed form expression for the asymptotic bias of both the g.l.b. and its numerator, under the assumptions that the rank of the reduced covariance matrix is at or above the Ledermann bound, and that the nonnegativity constraints on the diagonal elements of the matrix of unique variances are inactive. It is also shown that, when the reduced rank is at its highest possible value (i.e., the number of variables minus one), the numerator of the g.l.b. is asymptotically unbiased, and the asymptotic bias of the g.l.b. is negative. The latter results are contrary to common belief, but apply only to cases where the number of variables is small. The asymptotic results are illustrated by numerical examples.This research was supported by grant DMI-9713878 from the National Science Foundation.     

The Nature of Physical Reality

This account of the dynamical theory of chaos leads to a metaphysical picture of a world with an open future, in which the laws of physics are emergent-downward approximations to a more subtle and supple reality and in which there is downward causation through information input as well as upward causation through energy input. Such a metaphysical picture can accommodate both human and divine agency.     

Joint production model: A note on a connection between market prices and CP anchor values

This paper focuses on a justification of the assumption ‘In a joint production competitive industry, market prices are inversely proportional to anchor values’. This assumption is important to underpin the property ‘In a competitive industry the maximum profit mix and the best technological mix coincide’.     

Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part II: Category Theoretic Approaches

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets.We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.What we give is a (critical) survey of quite a lot of such approaches which have been offered in the last approximately 35 years.Part I was devoted to model based and to axiomatic approaches; the present Part II is devoted to category theoretic approaches.This paper is a version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005.     

The Logic and Meaning of Plurals. Part I

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, “The logic and meaning of plurals, II”, aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor.     

Optimal or Typical Performance? The Impact of Instructional Set on the Behavioral Assessment of Parent-Child Interactions

The behavioral assessment of parent-child interactions is an important component of treatment planning and evaluation in many evidence-based parent training programs. However, numerous factors unrelated to the parent-child interaction may add error to the assessment. This study investigated the impact of task instructions on parents’ behaviors during the analogue parent-child interaction observation, the Dyadic Parent-Child Interaction Coding System (DPICS). Forty-eight mother-child dyads were randomly assigned to one of two conditions that differed on level of specificity of instructions. Significant differences were observed between groups, with parents who received specific instructions using more praises during the DPICS tasks. Specific instructions may shift parents’ behaviors toward optimal, rather than typical, interaction patterns and should be considered in the context of the assessment goals.     

执行功能与心理理论关系的元分析:抑制控制和灵活转换的作用

心理理论的发展对个体社会化具有重要意义。研究通过元分析的方法,表明执行功能能够有效预测个体心理理论的发展水平(r=0.37,p0.001),且具有跨文化和跨人群的稳定性;同时,在个体的毕生发展中,执行功能均与心理理论存在显著相关,证明了执行功能的表达说;但在不同的发展阶段(Q1=411.75,p10.001,df1=90;Q2=219.49,p20.001,df2=50),心理理论的发展会受到执行功能不同成分的影响:0~3岁时抑制控制起关键作用;3~12岁时,心理理论受到抑制控制和灵活转换的共同影响;青春期阶段,灵活转换的作用明显;而到了成年期,抑制控制与灵活转换均会对心理理论产生积极影响。     

Teaching help‐seeking when lost to individuals with autism spectrum disorder

Deficits in safety skills and communication deficits place individuals with autism spectrum disorder (ASD) at an increased risk of danger. We used a multiple‐probe across‐participants design to evaluate the effects of video modeling and programming common stimuli to teach low‐ and high‐tech help‐seeking responses to children with ASD when lost. Participants acquired answering or making a FaceTime^® call and exchanging an identification card in contrived and natural settings. Responses generalized to novel community settings and maintained during a one‐ and two‐week follow‐up. Social validity measures showed that the procedures and outcomes of the study were acceptable to indirect and direct consumers, and immediate and extended community members. Implications are that children with ASD can effectively be taught both low‐ and high‐tech help‐seeking responses when lost.