Letter from James M. Beck to William F. Bade, 1910 Jul 27.

JOHN W. STERLING.JOHN A. GARVER,JAMES M. BECK,CORTLAND BETTS,CARL A. MEADCABLE ADDRESS NUMLATUS LAW OFFICESSHEARMAN & STERLING55 WALL STREET, NEW YORKNATIONAL CITY BANK BUILDINGJuly 27, 1910.William F. Bade, Esq.,My dear Mr. Bade:I am much interested in your editorial, which is strongly expressed.It is possible that I may not be at the office to-morrow (Thursday) but I fully expect to be here on Friday.Yours very truly,[illegible]0629

Bayesian Updating and Model Class Selection of Deteriorating Hysteretic Structural Models using Seismic Response Data

Identification of structural models from measured earthquake response can play a key role in structural health monitoring, structural control and improving performance-based design. System identification using data from strong seismic shaking is complicated by the nonlinear hysteretic response of structures where the restoring forces depend on the previous time history of the structural response rather than on an instantaneous finite-dimensional state. Furthermore, this inverse problem is ill-conditioned because even if some components in the structure show substantial yielding, others will exhibit nearly elastic response, producing no information about their yielding behavior. Classical least-squares or maximum likelihood estimation will not work with a realistic class of hysteretic models because it will be unidentifiable based on the data. On the other hand, Bayesian updating and model class selection provide a powerful and rigorous approach to tackle this problem when implemented using Markov Chain Monte Carlo simulation methods such as the Metropolis-Hastings, Gibbs Sampler and Hybrid Monte Carlo algorithms. The emergence of these stochastic simulation methods in recent years has led to a renaissance in Bayesian methods across all disciplines in science and engineering because the high-dimensional integrations that are involved can now be readily evaluated. The power of these methods to handle ill-conditioned or unidentifiable system identification problems is demonstrated by using a recently-developed stochastic simulation algorithm, Transitional Markov Chain Monte Carlo, to perform Bayesian updating and model class selection on a class of Masing hysteretic structural models that are relatively simple yet can give realistic responses to seismic loading. Examples will be given using deteriorating hysteretic building models with simulated seismic response data

Lateral cephalometric analysis of asymptomatic volunteers and symptomatic patients with and without bilateral temporomandibular joint disk displacement

Few studies of dentofacial and orthodontic structural relationships relative to temporomandibular joint (TMJ) dysfunction have been reported. We undertook this investigation to determine any correlation of orthodontic and dentofacial characteristics with TMJ bilateral disc displacement. The population of patients was selected from a TMJ clinic where a control group of asymptomatic volunteers had been previously established and standardized. Differences in skeletal structural features were determined among three study groups: (1) asymptomatic volunteers with no TMJ disk displacement, (2) symptomatic patients with no TMJ disc displacement, and (3) symptomatic patients with bilateral TMJ disk displacement. Thirty-two asymptomatic volunteers without disk displacement (25 female, 7 male) were compared with the same number each of symptomatic patients without TMJ disk displacement and symptomatic patients with bilateral TMJ disk displacement. All subjects had undergone a standardized clinical examination, bilateral TMJ magnetic resonance imaging, and lateral cephalometric radiographic analysis. The groups were matched according to sex, TMJ status, age, and Angle classification of malocclusion. Seventeen lateral cephalometric radiographic cranial base, maxillomandibular, and vertical dimension variables were evaluated and compared among the study groups. The mean angle of SNB, or the intersection of the sella-nasion plane and the nasion–point B line (indicating mandibular retrognathism relative to cranial base), of the symptomatic patients-with-displacement group was significantly smaller than that in the asymptomatic volunteers and symptomatic patients without bilateral disk displacement (p \u3c 0.05). Female subjects showed smaller linear measurements of mandibular length, lower facial height, and total anterior facial height than male subjects in all three groups (p \u3c 0.05). The mean angle of ANB, or the intersection of the nasion–point A and nasion–point B planes (indicating retrognathism of mandible relative to maxilla), was significantly greater in female than in male subjects, in all groups (p \u3c 0.05). Symptomatic patients with bilateral disk displacement had a retropositioned mandible, indicated by a smaller mean SNB angle compared with that in asymptomatic volunteers and symptomatic patients with no disk displacement on either side. Lateral cephalometric radiographic assessment may improve predictability of TMJ disk displacement in orthodontic patients but is not diagnostic; nor does the assessment explain any cause-and-effect relationship. (Am J Orthod Dentofacial Orthop 1998;114:248-55.