Energy Estimates in Hierarchical Plate Theories

Hierarchical error estimates for the energy functional in obstacle problems

We present a hierarchical a posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the energy of the exact solution is, up to oscillation terms, equivalent to an appropriate hierarchical estimator. The proof does not invoke any saturation assumption. Moreover, we prove an a posteriori error estimate indicating that the es...

Empirical estimates for various correlations in longitudinal-dynamic heteroscedastic hierarchical normal models

In this paper, we first define longitudinal-dynamic heteroscedastic hierarchical  normal  models. These models can be used to fit longitudinal data in which the dependency structure is constructed through a dynamic model rather than observations. We discuss different methods for estimating the hyper-parameters. Then the corresponding estimates for the hyper-parameter that causes the association...

Hierarchical Mean-field Theories

Hierarchical Combination of Intruder Theories

Recently automated deduction tools have proved to be very effective for detecting attacks on cryptographic protocols. These analysis can be improved, for finding more subtle weaknesses, by a more accurate modelling of operators employed by protocols. Several works have shown how to handle a single algebraic operator (associated with a fixed intruder theory) or how to combine several operators s...

Asymptotic Estimates of Hierarchical Modeling

In this paper we propose a way to analyze certain classes of dimension reduction models for elliptic problems in thin domains. We develop asymptotic expansions for the exact and model solutions, having the thickness as small parameter. The modeling error is then estimated by comparing the respective expansions, and the upper bounds obtained make clear the influence of the order of the model and...