Linear and Geometric Mixtures - Analysis

Linear and geometric mixtures are two methods to combine arbitrary models in data compression. Geometric mixtures generalize the empirically well-performing PAQ7 mixture. Both mixture schemes rely on weight vectors, which heavily determine their performance. Typically weight vectors are identified via Online Gradient Descent. In this work we show that one can obtain strong code length bounds for such a weight estimation scheme. These bounds hold for arbitrary input sequences. For this purpose we introduce the class of nice mixtures and analyze how Online Gradient Descent with a fixed step size combined with a nice mixture performs. These results translate to linear and geometric mixtures, which are nice, as we show. The results hold for PAQ7 mixtures as well, thus we provide the first theoretical analysis of PAQ7.Comment: Data Compression Conference (DCC) 201

Mixing Strategies in Data Compression

We propose geometric weighting as a novel method to combine multiple models in data compression. Our results reveal the rationale behind PAQ-weighting and generalize it to a non-binary alphabet. Based on a similar technique we present a new, generic linear mixture technique. All novel mixture techniques rely on given weight vectors. We consider the problem of finding optimal weights and show that the weight optimization leads to a strictly convex (and thus, good-natured) optimization problem. Finally, an experimental evaluation compares the two presented mixture techniques for a binary alphabet. The results indicate that geometric weighting is superior to linear weighting.Comment: Data Compression Conference (DCC) 201

Partial-volume Bayesian classification of material mixtures in MR volume data using voxel histograms

The authors present a new algorithm for identifying the distribution of different material types in volumetric datasets such as those produced with magnetic resonance imaging (MRI) or computed tomography (CT). Because the authors allow for mixtures of materials and treat voxels as regions, their technique reduces errors that other classification techniques can create along boundaries between materials and is particularly useful for creating accurate geometric models and renderings from volume data. It also has the potential to make volume measurements more accurately and classifies noisy, low-resolution data well. There are two unusual aspects to the authors' approach. First, they assume that, due to partial-volume effects, or blurring, voxels can contain more than one material, e.g., both muscle and fat; the authors compute the relative proportion of each material in the voxels. Second, they incorporate information from neighboring voxels into the classification process by reconstructing a continuous function, ρ(x), from the samples and then looking at the distribution of values that ρ(x) takes on within the region of a voxel. This distribution of values is represented by a histogram taken over the region of the voxel; the mixture of materials that those values measure is identified within the voxel using a probabilistic Bayesian approach that matches the histogram by finding the mixture of materials within each voxel most likely to have created the histogram. The size of regions that the authors classify is chosen to match the sparing of the samples because the spacing is intrinsically related to the minimum feature size that the reconstructed continuous function can represent

Covariant Balance Laws in Continua with Microstructure

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas

Laboratory study on the effects of hydraulic and granulometric parameters on the response of granular soil to internal erosion

Erosion is a major environmental problem to agricultural land as well as to civil engineering infrastructures. Rainwater infiltration into granular soils can lead to the migration of fine particles by suffusion. This experimental study is conducted to evaluate the susceptibility to erosion of cohesionless soils. The soil under investigation was collected from the coastal region of Mostaganem (West of Algeria) where erosion has recently caused several damages. To assess soil instability to erosion, two approaches have been proposed in the literature: the geometric approach and the hydraulic approach. Few studies have examined the combination of the two methods. The objective of our study is the combination of the two approaches by determining the critical hydraulic load responsible for triggering erosion as a function of soil characteristics. An experimental parametric study was conducted to determine the influence of initial amount of fines, hydraulic gradient and axial stress on the initiation and evolution of suffusion. A combination of the interactions between these parameters allowed us to express the critical hydraulic gradient and to identify the hydraulic behavior of the soil according to the studied parameters. This approach can better estimate the erodibility of cohesionless soils. It can be used in future development studies at this site to reduce the risk of erosion