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    Understanding UOP Student Housing Decisions: A Machine Learning Approach

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    Daniel Bernoulli\u27s Observations concerning Recurrent Series

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    Daniel Bernoulli’s article Observations concerning Recurrrent Series is one of the gems of the mathematical literature. It describes a numerical method for solving polynomial equations. This method, now known as “Bernoulli’s method”, is still in use today. The basis of the method is the study of certain sequences of numbers that satisfy what we now call linear recurrence relations. Bernoulli’s article shows how to find solutions of these recurrence relations. A nice application is a now well-known formula for the Fibonacci numbers. Bernoulli also uses his theory of recurrence relations to give a proof of an early form of De Moivre’s Theorem

    Administration and Faculty

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    The History of McGeorge School of Law’s California Victims Resource Center

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    Note from the Chief Articles & Symposium Editor

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    The Bonding Project: Addressing Mental Health Issues in the Older LGBTQ+ Community in Sacramento

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    https://scholarlycommons.pacific.edu/nursing-portfolios/1023/thumbnail.jp

    The Role of Vertical Skeletal Pattern in Predicting Molar Relationship Transitions from the primary to the permanent dentition

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    Introduction:The terminal plane of the primary dentition is a well-established predictor of future occlusion, yet its prognostic value may be influenced by vertical skeletal growth. Hyperdivergence, in particular, has received limited attention in untreated longitudinal samples. Objective:To investigate the influence of vertical skeletal patterns on molar relationship transition from primary to permanent dentition and to identify cephalometric and dental predictors of final molar relationship. Methods: A longitudinal cohort of 58 untreated subjects from the AAOF Legacy Collection was analyzed across three developmental stages: T1 (primary dentition), T2 (early mixed dentition), and T3 (permanent dentition). Subjects were stratified by mandibular plane angle (MPA) at T1 into hyperdivergent, normodivergent, and hypodivergent groups. Cephalometric and digitized dental cast measurements were obtained at each time point. A multivariate L2-regularized logistic regression model was developed to identify predictors associated with Class II molar relationship at T3. Results:Subjects were on average 5.3 years at T1, 7.5 years at T2, and 13.7 years at T3. Baseline molar terminal plane distributions were similar across vertical skeletal groups (P = 0.106). From T1 to T3, mesial steps most often transitioned to Class I, distal steps overwhelmingly ended in Class II, and flush terminal planes showed variable outcomes. Hyperdivergent subjects, particularly those with flush or distal steps, demonstrated a higher tendency to finish in Class II compared with hypo- and normodivergent peers, although differences were not statistically significant (P = 0.513). From T2 to T3, Class II relationships persisted more frequently in hyperdivergent subjects (56% vs. 44%), but again without significance (P = 0.163). Logistic regression identified integrated dento-skeletal predictors of Class II at T3, including terminal plane relationship, overjet, PFH/AFH ratio, and maxillary intermolar width. Predictive models achieved good discrimination (AUC 0.84–0.88). Conclusions:Vertical skeletal pattern alone was not significantly associated with molar classification outcomes. However, children with hyperdivergent growth patterns showed directional trends toward less favorable molar transitions. Predictive models that combined sagittal, vertical, and transverse dento-skeletal features provided good accuracy in identifying risk for Class II outcomes, underscoring the value of integrated diagnostic approaches in the mixed dentition

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