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We provide an elementary proof of an important theorem by G. V. Epifanov, according to which every two-terminal planar graph satisfying certain connectivity restrictions can by some sequence of series/parallel reductions and delta-wye exchanges be reduced to the graph consisting of the two terminals and just one edge.

Purpose The purpose of the study was to determine whether distinct subgroups of preschool children with speech sound disorders (SSD) could be identified using a subgroup discovery algorithm (SUBgroup discovery via Alternate Random Processes, or SUBARP). Of specific interest was finding evidence of a subgroup of SSD exhibiting performance consistent with atypical speech motor control. Method Ninety-seven preschool children with SSD completed speech and nonspeech tasks. Fifty-three kinematic, acoustic, and behavioral measures from these tasks were input to SUBARP. Results Two distinct subgroups were identified from the larger sample. The 1st subgroup (76%; population prevalence estimate = 67.8%–84.8%) did not have characteristics that would suggest atypical speech motor control. The 2nd subgroup (10.3%; population prevalence estimate = 4.3%– 16.5%) exhibited significantly higher variability in measures of articulatory kinematics and poor ability to imitate iambic lexical stress, suggesting atypical speech motor control. Both subgroups were consistent with classes of SSD in the Speech Disorders Classification System (SDCS; Shriberg et al., 2010a). Conclusion Characteristics of children in the larger subgroup were consistent with the proportionally large SDCS class termed speech delay; characteristics of children in the smaller subgroup were consistent with the SDCS subtype termed motor speech disorder—not otherwise specified. The authors identified candidate measures to identify children in each of these groups.

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This paper describes a method for learning logic relationships that correctly classify a given data set. The method derives from given logic data certain minimum cost satisfiability problems, solves these problems, and deduces from the solutions the desired logic relationships. Uses of the method include data mining, learning logic in expert systems, and identification of critical characteristics for recognition systems. Computational tests have proved that the method is fast and effective.