Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g. through a measurement, by connecting it to Bayes's theorem. The unknown quantity is modelled as a (may be high-dimensional) random variable. Such a description has two constituents, the measurable function and the measure. One group of methods is identified as updating the measure, the other group changes the measurable function. We connect both groups with the relatively recent methods of functional approximation of stochastic problems, and introduce especially in combination with the second group of methods a new procedure which does not need any sampling, hence works completely deterministically. It also seems to be the fastest and more reliable when compared with other methods. We show by example that it also works for highly nonlinear non-smooth problems with non-Gaussian measures.
Abstract-The paper addresses a Hierarchical Decode and Forward (HDF) strategy in the wireless 2-Way Relay Channel (2-WRC). This strategy uses a Hierarchical eXclusive Code (HXC) that allows full decoding of the hierarchical symbols at the relay. The HXC represents two data sources only through the exclusive law and requires side information on the complementary data at the destination (which naturally holds for the 2-WRC). The HDF strategy has the advantage over classical MAC stage relaying with joint decoding that its rate region extends beyond the classical MAC region. We present a layered design of the HXC codebook which uses an arbitrary outer state-of-the-art capacity approaching code (e.g. LDPC) and an inner layer with an exclusive symbol alphabet. We provide basic theorems showing that this scheme forms an HXC and we also evaluate its alphabet constrained rate regions. The rate regions depend on the relative channel phase parameters. Some channel rotation leads to catastrophic violation of the exclusive law. However these values appear only in a limited range of phases and have only mild impact on the mean capacity for some component symbol constellations.
A fully coupled transient heat and moisture transport in a masonry structure is examined in this paper. Supported by several successful applications in civil engineering the nonlinear diffusion model proposed by Künzel [1] is adopted in the present study. A strong material heterogeneity together with a significant dependence of the model parameters on initial conditions as well as the gradients of heat and moisture fields vindicates the use of a hierarchical modeling strategy to solve the problem of this kind. Attention is limited to the classical first order homogenization in a spatial domain developed here in the framework of a two step (meso-macro) multi-scale computational scheme (FE 2 problem). Several illustrative examples are presented to investigate the influence of transient flow at the level of constituents (meso-scale) on the macroscopic response including the effect of macro-scale boundary conditions. A two-dimensional section of Charles Bridge subjected to actual climatic conditions is analyzed next to confirm the suitability of algorithmic format of FE 2 scheme for the parallel computing.
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