72,837 research outputs found

    Distributions associated with general runs and patterns in hidden Markov models

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    This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general classes of patterns (competing patterns and generalized later patterns), and thus, the theory includes as special cases results for a large class of problems that have wide application. The unobserved state sequence is assumed to be Markovian with a general order of dependence. An auxiliary Markov chain is associated with the state sequence and is used to simplify the computations. Two examples are given to illustrate the use of the methodology. Whereas the first application is more to illustrate the basic steps in applying the theory, the second is a more detailed application to DNA sequences, and shows that the methods can be adapted to include restrictions related to biological knowledge.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS125 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Strain-energy release rate analysis of a laminate with a postbuckled delamination

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    The objectives are to present the derivation of the new virtual crack closure technique, evaluate the accuracy of the technique, and finally to present the results of a limited parametric study of laminates with a postbuckled delamination. Although the new virtual crack closure technique is general, only homogeneous, isotropic laminates were analyzed. This was to eliminate the variation of flexural stiffness with orientation, which occurs even for quasi-isotropic laminates. This made it easier to identify the effect of geometrical parameters on G. The new virtual crack closure technique is derived. Then the specimen configurations are described. Next, the stress analyses is discussed. Finally, the virtual crack closure technique is evaluated and then used to calculate the distribution of G along the delamination front of several laminates with a postbuckled delamination

    The Energy Transfer Process in Planetary Flybys

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    We illustrate the energy transfer during planetary flybys as a function of time using a number of flight mission examples. The energy transfer process is rather more complicated than a monotonic increase (or decrease) of energy with time. It exhibits temporary maxima and minima with time which then partially moderate before the asymptotic condition is obtained. The energy transfer to angular momentum is exhibited by an approximate Jacobi constant for the system. We demonstrate this with flybys that have shown unexplained behaviors: i) the possible onset of the "Pioneer anomaly" with the gravity assist of Pioneer 11 by Saturn to hyperbolic orbit (as well as the Pioneer 10 hyperbolic gravity assist by Jupiter) and ii) the Earth flyby anomalies of small increases in energy {\it in the geocentric system} (Galileo-I, NEAR, and Rosetta, in additioon discussing the Cassini and Messenger flybys). Perhaps some small, as yet unrecognized effect in the energy-transfer process can shed light on these anomalies.Comment: 29 pages, 43 images combined into 13 figures. Additions to answer comments of refere
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