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Statement of Problem:A thorough knowledge of the salient features of malocclusion makes the practitioner to come to a proper diagnosis and to formulate proper mechanotherapy. It also helps to predict the prognosis, prior to the onset of treatment process. Among the various malocclusions, Class II div 2 occurs the least often. The literature review does not clearly describe the classical skeletal and dental features of Angle's Class II div 2 malocclusion.Purpose of Study:The aim of this study is to describe the unique features of Angle's Class II division 2 malocclusion.Materials and Methods:A total of 612 pre-treatment records (study models and cephalograms), with age ranging from 14 to 25 years, were obtained from the hospital records of Drs Sudha and Nageswar Rao Siddhartha Institute of Dental Sciences. Among these samples, 317 were Class II div 1 and 295 were Class II div 2. The lateral cephalograms were analyzed by using Kodak software and the arch width analysis was calculated by using digital vernier calipers.Results:Student's t test was used for the study. On the cephalograms, the vertical skeletal measurements and few of the dental variables showed a significant difference. On the plaster models, the maxillary transverse measurements revealed a notable discrimination between the groups.Conclusion:Angle's Class II div 2 malocclusion has a marked horizontal growth pattern with decreased lower facial thirds, palatally inclined upper anteriors, and remarkably increased transverse maxillary arch dimensions.

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In this paper, we investigate the problem of statistical model checking (SMC) for hyperproperties. To reason about probabilistic hyperproperties, we first propose the temporal logic HyperPCTL * that extends PCTL * and HyperPCTL. We show that HyperPCTL * can express important probabilistic information-flow security policies. Then, we introduce SMC algorithms verifying HyperPCTL * formulas on for discretetime Markov chains, based on sequential probability ratio tests (SPRT) with a new notion of indifference region. Our SMC algorithms can handle both non-nested and nested probability operators for any desired significance level. Finally, we evaluate our SMC algorithms on four case studies: time side-channel vulnerability in encryption, probabilistic anonymity in dining cryptographers, probabilistic noninterference of parallel programs, and the performance of a randomized cache replacement policy.

There is a growing interest on formal methodsbased robotic motion planning for temporal logic objectives. In this work, we extend the scope of existing synthesis methods to hyper-temporal logics. We are motivated by the fact that important planning objectives, such as optimality, robustness, and privacy, (maybe implicitly) involve the interrelation between multiple paths; such objectives are thus hyperproperties, and cannot be expressed with usual temporal logics like the linear temporal logic (LTL). We show that such hyperproperties can be expressed by HyperLTL, an extension of LTL to multiple paths. To handle the complexity of motion planning with HyperLTL specifications, we introduce a symbolic approach for synthesizing planning strategies on discrete transition systems. Our planning method is evaluated on several case studies.