Bayesian Learning with Dependency Structures via Latent Factors, Mixtures, and Copulas

Bayesian methods offer a flexible and convenient probabilistic learning framework to extract interpretable knowledge from complex and structured data. Such methods can characterize dependencies among multiple levels of hidden variables and share statistical strength across heterogeneous sources. In the first part of this dissertation, we develop two dependent variational inference methods for full posterior approximation in non-conjugate Bayesian models through hierarchical mixture- and copula-based variational proposals, respectively. The proposed methods move beyond the widely used factorized approximation to the posterior and provide generic applicability to a broad class of probabilistic models with minimal model-specific derivations. In the second part of this dissertation, we design probabilistic graphical models to accommodate multimodal data, describe dynamical behaviors and account for task heterogeneity. In particular, the sparse latent factor model is able to reveal common low-dimensional structures from high-dimensional data. We demonstrate the effectiveness of the proposed statistical learning methods on both synthetic and real-world data.

Vascular structures for volumetric cooling and mechanical strength

When solid material is removed in order to create flow channels in a load carrying structure, the strength of the structure decreases. On the other hand, a structure with channels is lighter and easier to transport as part of a vehicle. Here, we show that this trade off can be used for benefit, to design a vascular mechanical structure. When the total amount of solid is fixed and the sizes, shapes, and positions of the channels can vary, it is possible to morph the flow architecture such that it endows the mechanical structure with maximum strength. The result is a multifunctional structure that offers not only mechanical strength but also new capabilities necessary for volumetric functionalities such as self-healing and self-cooling. We illustrate the generation of such designs for strength and fluid flow for several classes of vasculatures: parallel channels, trees with one, two, and three bifurcation levels. The flow regime in every channel is laminar and fully developed. In each case, we found that it is possible to select not only the channel dimensions but also their positions such that the entire structure offers more strength and less flow resistance when the total volume (or weight) and the total channel volume are fixed. We show that the minimized peak stress is smaller when the channel volume (φ) is smaller and the vasculature is more complex, i.e., with more levels of bifurcation. Diminishing returns are reached in both directions, decreasing φ and increasing complexity. For example, when φ=0.02 the minimized peak stress of a design with one bifurcation level is only 0.2% greater than the peak stress in the optimized vascular design with two levels of bifurcation. © 2010 American Institute of Physics.

Efects of mineral suspension and dissolution on strength and compressibility of soft carbonate rocks

© 2014 Elsevier B.V.Calcarenites are highly porous soft rocks formed of mainly carbonate grains bonded together by calcite bridges. The above characteristics make them prone to water-induced weathering, frequently featuring large caverns and inland natural underground cavities. This study is aimed to determine the main physical processes at the base of the short- and long-term weakening experienced by these rocks when interacting with water. We present the results of microscale experimental investigations performed on calcarenites from four different sites in Southern Italy. SEM, thin sections, X-ray CT observations and related analyses are used for both the interpretation-definition of the structure changes, and the identification-quantification of the degradation mechanisms. Two distinct types of bonding have been identified within the rock: temporary bonding (TB) and persistent bonding (PB). The diverse mechanisms linked to these two types of bonding explain both the observed fast decrease in rock strength when water fills the pores (short-term effect of water), identified with a short-term debonding (STD), and a long-term weakening of the material, when the latter is persistently kept in water-saturated conditions (long-term effect of water), identified with a long-term debonding (LTD). To highlight the micro-hydro-chemo-mechanical processes of formation and annihilation of the TB bonds and their role in the evolution of the mechanical strength of the material, mechanical tests on samples prepared by drying partially saturated calcarenite powder, or a mix of glass ballotini and calcarenite powder were conducted. The long-term debonding processes have also been investigated, using acid solutions in order to accelerate the reaction rates. This paper attempts to identify and quantify differences between the two types of bonds and the relative micro-scale debonding processes leading to the macro-scale material weakening mechanisms.

Silica polymer bonding of stressed silica grains: An early growth of intergranular tensile strength

© 2015 Elsevier Ltd. All rights reserved.Laboratory tests on microscale are reported in which millimeter-sized amorphous silica cubes were kept highly compressed in a liquid environment of de-ionized water solutions with different silica ion concentrations for up to four weeks. Such an arrangement simulates an early evolution of bonds between two sand grains stressed in situ. In-house designed Grain Indenter-Puller apparatus allowed measuring strength of such contacts after 3-4 weeks. Observations reported for the first time confirm a long-existing hypothesis that a stressed contact with microcracks generates silica polymers, forming a bonding structure between the grains on a timescale in the order of a few weeks. Such structure exhibits intergranular tensile force at failure of 1-1.5 mN when aged in solutions containing silica ion concentrations of 200-to 500-ppm. The magnitude of such intergranular force is 2-3 times greater than that of water capillary force between the same grains.