Effects of Palatal Expansion on Speech Production

Introduction: Rapid palatal expanders (RPEs) are a commonly used orthodontic adjunct for the treatment of posterior crossbites. RPEs are cemented to bilateral posterior teeth across the palate and thus may interfere with proper tongue movement and linguopalatal contact. The purpose of this study was to identify what specific role RPEs have on speech sound production for the child and early adolescent orthodontic patient. Materials and Methods: RPEs were treatment planned for patients seeking orthodontics at Marquette University. Speech recordings were made using a phonetically balanced reading passage (“The Caterpillar”) at 3 time points: 1) before RPE placement; 2) immediately after cementation; and 3) 10-14 days post appliance delivery. Measures of vocal tract resonance (formant center frequencies) were obtained for vowels and measures of noise distribution (spectral moments) were obtained for consonants. Two-way repeated measures (ANOVA) was used along with post-hoc tests for statistical analysis. Results: For the vowel /i/, the first formant increased and the second formant decreased indicating a more inferior and posterior tongue position. For /e/, only the second formant decreased resulting in a more posterior tongue position. The formants did not return to baseline within the two-week study period. For the fricatives /s/, //, /t/, and /k/, a significant shift from high to low frequencies indicated distortion upon appliance placement. Of these, only /t/ fully returned to baseline during the study period. Conclusion: Numerous phonemes were distorted upon RPE placement which indicated altered speech sound production. For most phonemes, it takes longer than two weeks for speech to return to baseline, if at all. Clinically, the results of this study will help with pre-treatment and interdisciplinary counseling for orthodontic patients receiving palatal expanders

The Incorrect Usage of Propositional Logic in Game Theory: The Case of Disproving Oneself

Recently, we had to realize that more and more game theoretical articles have been published in peer-reviewed journals with severe logical deficiencies. In particular, we observed that the indirect proof was not applied correctly. These authors confuse between statements of propositional logic. They apply an indirect proof while assuming a prerequisite in order to get a contradiction. For instance, to find out that "if A then B" is valid, they suppose that the assumptions "A and not B" are valid to derive a contradiction in order to deduce "if A then B". Hence, they want to establish the equivalent proposition "A and not B implies A and not A" to conclude that "if A then B" is valid. In fact, they prove that a truth implies a falsehood, which is a wrong statement. As a consequence, "if A then B" is invalid, disproving their own results. We present and discuss some selected cases from the literature with severe logical flaws, invalidating the articles.Comment: 16 pages, 2 table

On the Single-Valuedness of the Pre-Kernel

Based on results given in the recent book by Meinhardt (2013), which presents a dual characterization of the pre-kernel by a finite union of solution sets of a family of quadratic and convex objective functions, we could derive some results related to the uniqueness of the pre-kernel. Rather than extending the knowledge of game classes for which the pre-kernel consists of a single point, we apply a different approach. We select a game from an arbitrary game class with a single pre-kernel element satisfying the non-empty interior condition of a payoff equivalence class, and then establish that the set of related and linear independent games which are derived from this pre-kernel point of the default game replicates this point also as its sole pre-kernel element. In the proof we apply results and techniques employed in the above work. Namely, we prove in a first step that the linear mapping of a pre-kernel element into a specific vector subspace of balanced excesses is a singleton. Secondly, that there cannot exist a different and non-transversal vector subspace of balanced excesses in which a linear transformation of a pre-kernel element can be mapped. Furthermore, we establish that on the restricted subset on the game space that is constituted by the convex hull of the default and the set of related games, the pre-kernel correspondence is single-valued, and therefore continuous. Finally, we provide sufficient conditions that preserve the pre-nucleolus property for related games even when the default game has not a single pre-kernel point.Comment: 24 pages, 2 table

(Average-) convexity of common pool and oligopoly TU-games

The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexity, however, fails whenever cost functions are arbitrary. We present sufficient conditions involving the cost functions (like weakly decreasing marginal costs as well as weakly decreasing average costs) and the average joint production function in order to guarantee the convexity of the common pool game. A similar approach is effective to investigate a relaxation of the convexity property known as the average-convexity property for a cooperative game. An example illustrates that oligopoly games are a special case of common pool games whenever the average joint production function represents an inverse demand function