Different early rearing experiences have long‐term effects on cortical organization in captive chimpanzees (Pan troglodytes)

Consequences of rearing history in chimpanzees (Pan troglodytes) have been explored in relation to behavioral abnormalities and cognition; however, little is known about the effects of rearing conditions on anatomical brain development. Human studies have revealed that experiences of maltreatment and neglect during infancy and childhood can have detrimental effects on brain development and cognition. In this study, we evaluated the effects of early rearing experience on brain morphology in 92 captive chimpanzees (ages 11–43) who were either reared by their mothers (n = 46) or in a nursery (n = 46) with age‐group peers. Magnetic resonance brain images were analyzed with a processing program (BrainVISA) that extracts cortical sulci. We obtained various measurements from 11 sulci located throughout the brain, as well as whole brain gyrification and white and grey matter volumes. We found that mother‐reared chimpanzees have greater global white‐to‐grey matter volume, more cortical folding and thinner grey matter within the cortical folds than nursery‐reared animals. The findings reported here are the first to demonstrate that differences in early rearing conditions have significant consequences on brain morphology in chimpanzees and suggests potential differences in the development of white matter expansion and myelination.     

Circle graphs and monadic second-order logic

This article is part of a project consisting in expressing, whenever possible, graph properties and graph transformations in monadic second-order logic or in its extensions using modulo p cardinality set predicates or auxiliary linear orders. A circle graph is the intersection graph of a set of chords of a circle. Such a set is called a chord diagram. It can also be described by a word with two occurrences of each letter, called a double occurrence word. If a circle graph is prime for the split (or join) decomposition defined by Cunnigham, it has a unique representation by a chord diagram, and this diagram can be defined by monadic second-order formulas with the even cardinality set predicate. By using the (canonical) split decomposition of a circle graph, we define in monadic second-order logic with auxiliary linear orders all its chord diagrams. This construction uses the fact that the canonical split decomposition of a graph can be constructed in monadic second-order logic with help of an arbitrary linear order. We prove that the order of first occurrences of the letters in a double occurrence word w that represents a connected circle graph determines this word in a unique way. The word w can be defined by a monadic second-order formula from the word of first occurrences of letters. We also prove that a set of circle graphs has bounded clique-width if and only if all the associated chord diagrams have bounded tree-width.     

Toward a contemporary quantitative model of punishment

A direct‐suppression, or subtractive, model of punishment has been supported as the qualitatively and quantitatively superior matching law‐based punishment model (Critchfield, Paletz, MacAleese, & Newland, 2003; de Villiers, 1980; Farley, 1980). However, this conclusion was made without testing the model against its predecessors, including the original (Herrnstein, 1961) and generalized (Baum, 1974) matching laws, which have different numbers of parameters. To rectify this issue, we reanalyzed a set of data collected by Critchfield et al. (2003) using information theoretic model selection criteria. We found that the most advanced version of the direct‐suppression model (Critchfield et al., 2003) does not convincingly outperform the generalized matching law, an account that does not include punishment rates in its prediction of behavior allocation. We hypothesize that this failure to outperform the generalized matching law is due to significant theoretical shortcomings in model development. To address these shortcomings, we present a list of requirements that all punishment models should satisfy. The requirements include formal statements of flexibility, efficiency, and adherence to theory. We compare all past punishment models to the items on this list through algebraic arguments and model selection criteria. None of the models presented in the literature thus far meets all of the requirements.     

A discriminated rapid-acquisition laboratory procedure for human continuous choice

Previous continuous choice laboratory procedures for human participants are either prohibitively time-intensive or result in inadequate fits of the generalized matching law (GML). We developed a rapid-acquisition laboratory procedure (Procedure for Rapidly Establishing Steady-State Behavior, or PRESS-B) for studying human continuous choice that reduces participant burden and produces data that is well-described by the GML. To test the procedure, 27 human participants were exposed to 9 independent concurrent random-interval random-interval reinforcement schedules over the course of a single, 37-min session. Fits of the GML to the participants' data accounted for large proportions of variance (median R²: 0.94), with parameter estimates that were similar to those previously found in human continuous choice studies [median a: 0.67; median log(b): -0.02]. In summary, PRESS-B generates human continuous choice behavior in the laboratory that conforms to the GML with limited experimental duration.     

Coding responses and the generalization of matching to sample in children.

Two experiments studied the conditions of stimulus control necessary for the generalization of relational matching to sample. Matching required the selection of comparison shapes rotated 90 degrees clockwise from the orientation of the corresponding sample. In Experiment 1, five children were taught to: (a) code the orientations of samples, (b) transform sample codings to account for the 90 degree rotation, and (c) repeat the transformed sample coding response to a comparison. High levels of generalization occurred with a set of novel stimuli for which stable sample-coding responses were initially available. In another novel set, where stable sample-coding responses were not initially available, low levels of generalized matching were recorded. Matching performance improved after stable coding responses were trained. In Experiment 2, two children and three adults were trained in a form of the matching task that produced poor generalization despite the presence of stable sample-coding responses. Retraining to modify the stimulus control exerted by these coding responses produced an immediate improvement in generalized matching to sample. Results suggest that the generalization of matching is dependent on structure of stimulus control that the component responses exert on each other.     

The monadic second-order logic of graphs XV: On a conjecture by D. Seese

A conjecture by D. Seese states that if a set of graphs has a decidable monadic second-order theory, then it is the image of a set of trees under a transformation of relational structures defined by monadic second-order formulas, or equivalently, has bounded clique-width. We prove that this conjecture is true if and only if it is true for the particular cases of bipartite undirected graphs, of directed graphs, of partial orders and of comparability graphs. We also prove that it is true for line graphs, for interval graphs and for partial orders of dimension 2. Our treatment of certain countably infinite graphs uses a representation of countable linear orders by binary trees that can be constructed by monadic second-order formulas. By using a counting argument, we show the intrinsic limits of the methods used here to handle this conjecture.     

Contingency and choice: The implications of matching theory for classroom instruction

This paper describes a mathematical account of behavior known as matching theory. Matching theory evolved out of basic operant research and assumes that individuals can engage in a variety of behaviors at any moment, but they choose one to the exclusion of others. According to the matching equation, choices in behavior match the relative amount of reinforcement provided for each alternative. Although the principles of matching theory have proven useful in developing novel treatment strategies, few data exist validating the matching equation in natural human environments. Recent applications of matching theory to children's classroom behavior are described, and the implications of matching theory for classroom management and effective teaching are discussed.     

Experimental evaluation of matching via a commercially available basketball video game

Many recent nonlaboratory-based quantitative analyses of behavior have relied on archival competitive sporting data. However, the ratio-based reinforcement schedules in most athletic competitions and the correlational nature of archival data analyses raise concern over the contributions of such findings to the behavior analytic literature. The current experiment evaluated whether matching in a human operant paradigm would approximate matching observed in nonlaboratory-based sports data. To this end, we used in-game attributes to parametrically manipulate 2- and 3-point shooting in a commercially available basketball video game. The behavior of 6 of 9 participants conformed to the generalized matching equation. These results suggest matching in sporting contexts may be a product of restricted nonindependent concurrent random-ratio schedules. Implications of this experiment, including those in applied behavior analysis and potential influence on gamification, are discussed.     

Matrix operations and the properties of networks and directed graphs

Matrix multiplication is frequently used to derive properties and quantitative features of directed graphs and networks from their adjacency or value matrices. In many cases, a “modified” matrix multiplication is employed, where other binary operations replace ordinary addition and multiplication. In this paper, a set of conditions for permissible value domains, “addition” and “multiplication” operations, and value matrices is developed under which generalized matrix multiplication directly yields properties of a digraph or network. An additional condition ensures that the properties are related to paths of the structure rather than sequences in general. Finally, a number of applications of generalized matrix multiplication are discussed.     

Children's identity matching and oddity: assessing control by specific and general sample-comparison relations.

After children in Experiments 1 and 2 learned identity matching or oddity, control by sample-comparison relations was assessed. Tests for generalized control displayed novel samples and two comparison stimuli, one identical to the sample. Specific relations were tested with identical or nonidentical sample-comparison stimuli from one set of stimuli and substitute comparisons from either the other training set or from a novel set. When tests displayed identical stimuli, patterns of comparison selection suggested control by generalized identity and oddity. However, selection patterns varied when stimuli were nonidentical and familiar or novel substitute comparisons were used. Therefore, control by specific relations is not a precondition for generalized identity and oddity. One set of training stimuli was used in Experiment 3, and generalized performances occurred again. Moreover, control by specific relations was shown by the oddity subjects and 2 of 6 identity subjects. Generalized and specific control may therefore exist simultaneously. In Experiment 4, selections were irregular on tests displaying substitute comparisons and samples and familiar comparison stimuli; this finding supported the relational account of specific sample-comparison control found in Experiment 3.     

The generalized matching law as a description of multiple-schedule responding

The literature was examined to determine how well the generalized matching law (Baum, 1974) describes multiple-schedule responding. In general, it describes the data well, accounting for a median of 91% of the variance. The median size of the undermatching parameter was 0.46; the median bias parameter was 1.00. The size of the undermatching parameter, and the proportion of the variance accounted for by the equation, varied inversely with the number of schedules conducted, with the number of sessions conducted per schedule, and with the time within a component. The undermatching parameter also varied with the operanda used to produce reinforcers and with the reinforcer used. The undermatching parameter did not vary consistently with component duration or with several other variables. Bias was greater when fewer rather than more schedules were conducted, when two rather than one operanda were used, and when White Carneaux rather than homing pigeons served as subjects. These results imply that the generalized matching law may describe both concurrent and multiple-schedule responding, but that the same variables do not always influence the bias and undermatching parameters in the same way for the two types of schedules.     

Graph‐Framing Effects in Decision Making

This study manipulated the graphical representation of options by framing the physical characters in figures and found that preferences could be affected even when the words and numbers of the problem were constant. Based on attribute substitution theory and an equate‐to‐differentiate approach, we proposed a two‐process model of graph‐framing effects. In the first mental process, the graph‐editing process, the physical features (e.g., distance, size) represented in the graph are visually edited, and the perceived numerical difference between the options is judged based on its physical features. The second mental process, the preferential choice process, occurs by an equate‐to‐differentiate approach in which people seek to equate the difference between options on the dimension on which the difference is smaller, thus leaving the greater other‐dimensional difference to be the determinant of the final choice. Four experiments were tested for graph‐framing effects. Experiment 1 found a graph‐framing effect in coordinate graphs resting on the (de)compression of the scales employed in the figures. Experiment 2 revealed additional graph‐framing effects in other question scenarios and showed that preference changes were mediated by perceived numerical distances. Experiment 3 further confirmed the presence of graph‐framing effects in sector graphs similar to those found in coordinate ones. Experiment 4 suggested that such graph‐framing effects could be eliminated when logical processing (e.g., introducing a mathematical operation before a choice task) was encouraged. This paper discusses related research and a possible substrate basis for graph‐framing effects. Copyright © 2011 John Wiley & Sons, Ltd.     

USING MICROSOFT OFFICE EXCEL® 2007 TO CONDUCT GENERALIZED MATCHING ANALYSES

The generalized matching equation is a robust and empirically supported means of analyzing relations between reinforcement and behavior. Unfortunately, no simple task analysis is available to behavior analysts interested in using the matching equation to evaluate data in clinical or applied settings. This technical article presents a task analysis for the use of Microsoft Excel to analyze and plot the generalized matching equation. Using a data‐based case example and a step‐by‐step guide for completing the analysis, these instructions are intended to promote the use of quantitative analyses by researchers with little to no experience in quantitative analyses or the matching law.     

CREATING SINGLE-SUBJECT DESIGN GRAPHS WITH MICROSOFT EXCEL™

Because single-subject design methodology is the cornerstone of behavior-analytic research, behavior analysts are often engaged in the practice of graph production. There are a variety of computer software packages on the market that can be used to create graphs; however, not all of them are suitable for producing single-subject design line graphs. Microsoft Excel 97 for Windows 95/NT and MacOS operating systems contains a variety of features that are conducive to producing reversal, multiple baseline, and multielement graphs (among others) that conform to many of the technical recommendations for publication in the Journal of Applied Behavior Analysis. We present detailed instructions on creating these graphs using Microsoft Excel.     

On the exponent in the "generalized" matching equation

A power function equation between ratios of behavior and ratios of reinforcement rates has been called a generalized form of Herrnstein's (1961) matching law, even without a formal relationship having been shown between the two equations. The present work uses a functional relationship to prove that when ratios of reinforcement are not equivalent to ratios of behavior, and the transform leading to this inequality is consistent for every pair of reinforcement rates, the result is a power function relationship between response and reinforcement ratios. The label “generalized matching equation” for the power function equation is thus validated formally.     

Planarity and segmentation in stereoscopic matching

The matching of stereograms which contain periodic patterns suggests ways in which the stereo correspondence problem may be solved in human vision. The stereograms seem to be segmented by coarse-scale features. Within each segment a set of matches approximating a plane is chosen. In regions with periodic patterns there may be many such planar sets, and the disparity of coarse-scale features seems to guide the choice of a particular set. This emphasis on planarity may reflect the occurrence of correlation-like operations in cortical neurons. An attractive possibility is that segmentation effectively delimits areas of the visual field within which disparities are likely to be slow changing (eg local tangent planes to surfaces) so that the correlation sums evaluated in a segment can give the best estimate of depth. A mechanism of this kind cannot account for all of stereo matching, since not all visual objects are well described by ensembles of planes. But it is likely to be a component of the matching system which is particularly important where images are 'noisy' and averaging is needed to extract reliable disparities.     

A mathematical analysis of a natural class of partitions of a graph

Any finite graph (nondirected, no loops) can be coupled with its complementary graph producing what we term a completed graph. This paper studies completed graphs in the context of a structural concept called stratification that is motivated by theoretical work in social psychology and sociology. A completed graph is stratified in case its node (vertex) set can be divided into two nonempty subsets with exactly one of the two types of ties holding between every pair of nodes from distinct sets. A completed graph is totally stratified in case every one of its nontrivial completed subgraphs is stratified. The first part of the paper relates the concept of stratification to the familiar graph property of connectedness. In particular, a completed graph is totally stratified if and only if it does not have a four point completed subgraph that is connected in both the original graph relation and its complementary relation. Using the concept of stratification, completed graphs can be decomposed uniquely into taxonomic structures, that is, nested sets of partitions. An algorithm for the decomposition based on the work with the concept of stratification is developed. The relationship between the notion of stratification and the ideas in balance theory is examined, and stratification is viewed as a generalization of Davis' notion of clustering. It turns out that the concepts of clique, status, and structural equivalence used throughout the social networks literature can be defined in an interesting way for completed graphs. Cliques are sets of nodes with similar internal links and statuses are sets of nodes with similar external links. Structurally equivalent sets are both cliques and statuses. The concepts of status and structural equivalence are closely related to the decomposition algorithm. In particular, for any totally stratified completed graph, the set of all statuses and the set of all maximal structurally equivalent sets can be generated by mathematical operations performed on the taxonomic decomposition of the completed graph. Finally some of our resuls are informally related to the blockmodeling approach to analyzing social network data discussed in several previous Journal of Mathematical Psychology articles.