Explore the vast range of titles available.

Stimulus equivalence paradigm has been used to investigate symbolic behavior over the last 50 years. Still, little attention has been directed in the study of equivalence classes maintenance. This bibliographic review, based on the PRISMA Protocol, provides an overview of the effects of different variables on the stability of equivalence classes over time. Searches were conducted on four databases (PsychINFO, Elsevier Scopus, Web of Science, and SciELO) and returned 95 results. Excluding the duplicated papers and applying the inclusion and exclusion criteria resulted in 14 papers. The references of each paper were examined for papers about maintenance of equivalence relations that were not found in the database search and 10 more articles were included. Therefore, 24 papers were selected in this bibliographic review. The papers were categorized considering the variable investigated, that is: class size, training and testing parameters, nature of stimuli, generalized relations, and equivalence based instruction. Future studies should focus on the study of variables that affect the maintenance of equivalence classes, considering the small number of papers in this field and the importance of this knowledge in both experimental and applied settings.

This study aimed to verify the role of three parameters on the formation of equivalence classes between Black faces and a positive symbol, in children who demonstrated negative bias toward Black faces in a pretest. Maintenance was also verified 6 weeks after equivalence tests. Forty-six children (11 Black; 27 girls) who demonstrated racial bias in a pretest were divided into four groups. All groups first learned AB relations (A1 and A2 were, respectively, a positive and a negative symbol, and B were abstract stimuli) and then BC relations (C1 was a Black face and C2 was an abstract stimulus). The Control Group then advanced immediately to equivalence tests (AC, and CA, without differential consequences). For the Mixed Training Group, a block of trials mixing AB and BC relations, with differential consequences, preceded equivalence tests. For the Feedback Reduction Group, equivalence tests were preceded by a trial block mixing AB and BC relations, but with feedback in 50% of trials. The Symmetry Group received symmetry tests after training of each baseline relation. Thirty-three children showed class formation relating Black faces and the positive symbol, and 27 maintained at least one of the equivalence relations after 6 weeks. Average biases toward Black faces were positive in a posttest, for participants who formed equivalence classes, and remained negative for those that did not form classes. The Control Group showed less pronounced bias reduction and maintenance of relations after 6 weeks, suggesting that these outcomes may be affected by training parameters.

“Yield,” the percentage of participants in a group who form a set of equivalence classes, has been used very broadly to identify the effect of different training protocols on class formation and expansion, identify variables that enhance the immediate emergence of these classes, and characterize the differential relatedness of class members. In addition, yield is now being used to document the formation of educationally relevant equivalence classes. To further understand the value of using yield, we considered six possible criticisms of its use to study equivalence classes. Upon analysis, each criticism was supported; instead, each disclosed a nonyield factor that could play a critical role in the measurement of class formation but has not yet been explored experimentally. Finally, yield cannot be replaced with trial-based measures of responding or vice versa; rather, both types of measures are needed to obtain a comprehensive understanding of equivalence class formation.

Thirty college students attempted to form three 3‐node 5‐member equivalence classes under the simultaneous protocol. After concurrent training of AB, BC, CD, and DE relations, all probes used to assess the emergence of symmetrical, transitive, and equivalence relations were presented for two test blocks. When the A‐E stimuli were all shapes, none of 10 participants formed classes. When the A, B, D, and E stimuli were shapes and the C stimuli were meaningful pictures, 8 of 10 participants formed classes. This high yield may reflect the expansion of existing classes that consist of the associates of the meaningful stimuli, rather than the formation of the ABCDE classes, per se. When the A‐E stimuli were shapes and the C stimuli became SDs prior to class formation, 5 out of 10 participants formed classes. Thus, the discriminative functions served by the meaningful stimuli can account for some of the enhancement of class formation produced by the inclusion of a meaningful stimulus as a class member. A sorting task, which provided a secondary measure of class formation, indicated the formation of all three classes when the emergent relations probes indicated the same outcome. In contrast, the sorting test indicated “partial” class formation when the emergent relations test indicated no class formation. Finally, the effects of nodal distance on the relatedness of stimuli in the equivalence classes were not influenced by the functions served by the C stimuli in the equivalence classes.

Two three-member equivalence classes were formed with abstract three-dimensional objects that were observed by touch only by use of matching-to-sample (MTS) trials and the simple-to-complex protocol. Classes emerged immediately for one participant and with a delay in transitivity for the other. For all relational types, reaction time (RT) duration and observing-response (OR) frequency decreased with trial repetition to the very low asymptotes. For the derived relations, error-free decrements implied “learning” without feedback. The highly correlated ORs and RTs suggested that OR frequency accounted for RT duration. Also, information-gathering efficiency per OR increased with trial repetition. Thus, RT duration reflected OR frequency and cognitive processing. Initial RTs were long for baseline trials, much shorter for symmetry probes, intermediate for transitivity probes, and shortest for equivalence probes. More ORs occurred to samples than comparisons and the positive and negative comparisons produced similar OR frequencies. In addition, transitivity performances were predicted by frequency of sample-observing in previously administered baseline and symmetry probes. All findings were based on single-trial data. Finally, observing behavior may also influence the emergence of fluency.

This experiment presents a manual-observing procedure as an inexpensive alternative for investigating stimulus control and establishing equivalence classes in a matching-to-sample task (MTS). To illustrate the procedure, we evaluated the effects of different MTS training structures on observing responses and equivalence class formation. Participants had to press a button below each covered sample and comparison stimuli to reveal the stimulus. Four participants were exposed to two different sequences of the many-to-one (MTO) and one-to-many (OTM) procedures, using the manual-observing procedure during training and testing. The results showed that the manual-observing procedure allowed participants to acquire conditional discriminations and form equivalence classes, suggesting that the use of manual-observing responses in an MTS procedure is a useful procedure to evaluate stimulus control in an MTS task.

The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among other material, some remarkable improvements on Brown's classical representability theorem. In addition, the author introduces a class of triangulated categories\"--the \"well generated triangulated categories\"--and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated, and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra, algebraic geometry, homotopy theory, and mathematical physics.

Two experiments used post‐class formation within‐class relational assessment test performances to evaluate whether participants demonstrated preference for certain members of an equivalence class based on the type of relation that existed between class members. In Experiment 1, two 5‐node 7‐member equivalence classes, consisting entirely of nonsense syllables, were established using the simultaneous protocol. Only 1 of the 6 participants in Experiment 1 formed classes. After class formation, the effects of the different relations between stimuli were evaluated using within‐class relational assessment tests, and the 1 participant showed an absolute preference for transitive over equivalence relations, and for baseline over symmetrical relations. Experiment 2 was identical to Experiment 1, except that one of the nonsense syllable stimuli in each class was replaced by a pictorial stimulus. Under these conditions, classes were formed by 5 of 13 participants. During the relational assessment tests, the 5 participants who formed classes demonstrated almost exclusive preferences for transitive relations over equivalence relations and for trained baseline relations over symmetrical relations. Thus, this research demonstrates that the members of equivalence classes are differentially related to each other based on relational type.

A descent sequence is a word π = π₁π₂ ··· π n over the set of nonnegative integers such that π₁ = 0 and π i ≤ 1 + des(π₁π₂ ··· π i−1) for i = 2, 3, ..., n, where des(π₁π₂ ··· π m ) is the number of descents in the word π₁π₂ ··· π m , that is, the number of two entry factors π j π j+1 such that π j > π j+1. In this paper, we obtain some enumerative results for descent sequences avoiding patterns of length 3 and 4. In particular, we determine the number of Wilf equivalence classes among single patterns of length 3 and among pairs of patterns of length 3, and state the corresponding result for a set of k patterns of length 3 when 3 ≤ k ≤ 13. We also consider single patterns of length 4. The main tool is the use of generating trees.

Peirce is the father of semiotics. However, his theory was developed long before the developments in information theory. The codification procedures studied by the latter turn out to be crucial also for biology. At the root of both information and semiosis there are equivalence classes. In the case of biological systems, we speak of functional equivalence classes. Equivalence classes represent the grid that organism impose on biochemical processes and signals of the external or internal environment. The whole feedback circuit that is built in this way allows information control. Symbolic systems represent another kind of dealing-with-information as far as they deal with the matching of our concepts with the world.