Gaussian Multiresolution Models: Exploiting Sparse Markov and Covariance Structure

In this paper, we consider the problem of learning Gaussian multiresolution (MR) models in which data are only available at the finest scale, and the coarser, hidden variables serve to capture long-distance dependencies. Tree-structured MR models have limited modeling capabilities, as variables at one scale are forced to be uncorrelated with each other conditioned on other scales. We propose a new class of Gaussian MR models in which variables at each scale have sparse conditional covariance structure conditioned on other scales. Our goal is to learn a tree-structured graphical model connecting variables across scales (which translates into sparsity in inverse covariance), while at the same time learning sparse structure for the conditional covariance (not its inverse) within each scale conditioned on other scales. This model leads to an efficient, new inference algorithm that is similar to multipole methods in computational physics. We demonstrate the modeling and inference advantages of our approach over methods that use MR tree models and single-scale approximation methods that do not use hidden variables

Learning Latent Tree Graphical Models

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world datasets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups dataset

A selectively reduced degree basis for efficient mixed nonlinear isogeometric beam formulations with extensible directors

The effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu-Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the stress resultants and strains of the beam, which are allowed to be discontinuous across elements. This approach turns out to significantly improve the computational efficiency and the accuracy of the results. We consider a beam formulation with extensible directors, where cross-sectional strains are enriched to avoid Poisson locking by an enhanced assumed strain method. In numerical examples, we show the superior per degree-of-freedom accuracy of IGA over conventional finite element analysis, due to the higher order continuity in the displacement field. We further verify the efficient rotational coupling between beams, as well as the path-independence of the results.Comment: 50 pages, 23 figure

Catechin-capped gold nanoparticles: green synthesis, characterization, and catalytic activity toward 4-nitrophenol reduction

An eco-friendly approach is described for the green synthesis of gold nanoparticles using catechin as a reducing and capping agent. The reaction occurred at room temperature within 1 h without the use of any external energy and an excellent yield (99%) was obtained, as determined by inductively coupled plasma mass spectrometry. Various shapes of gold nanoparticles with an estimated diameter of 16.6 nm were green-synthesized. Notably, the capping of freshly synthesized gold nanoparticles by catechin was clearly visualized with the aid of microscopic techniques, including high-resolution transmission electron microscopy, atomic force microscopy, and field emission scanning electron microscopy. Strong peaks in the X-ray diffraction pattern of the as-prepared gold nanoparticles confirmed their crystalline nature. The catalytic activity of the as-prepared gold nanoparticles was observed in the reduction of 4-nitrophenol to 4-aminophenol in the presence of NaBH(4). The results suggest that the newly prepared gold nanoparticles have potential uses in catalysis

A Tree-Based Context Model for Object Recognition

There has been a growing interest in exploiting contextual information in addition to local features to detect and localize multiple object categories in an image. A context model can rule out some unlikely combinations or locations of objects and guide detectors to produce a semantically coherent interpretation of a scene. However, the performance benefit of context models has been limited because most of the previous methods were tested on datasets with only a few object categories, in which most images contain one or two object categories. In this paper, we introduce a new dataset with images that contain many instances of different object categories, and propose an efficient model that captures the contextual information among more than a hundred object categories using a tree structure. Our model incorporates global image features, dependencies between object categories, and outputs of local detectors into one probabilistic framework. We demonstrate that our context model improves object recognition performance and provides a coherent interpretation of a scene, which enables a reliable image querying system by multiple object categories. In addition, our model can be applied to scene understanding tasks that local detectors alone cannot solve, such as detecting objects out of context or querying for the most typical and the least typicalscenes in a dataset.This research was partially funded by Shell International Exploration and Production Inc., by Army Research Office under award W911NF-06-1-0076, by NSF Career Award (ISI 0747120), and by the Air Force Office of Scientific Research under Award No.FA9550-06-1-0324. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Air Force

An Integrative Approach to Treat Parkinson's Disease: Ukgansan Complements L-Dopa by Ameliorating Dopaminergic Neuronal Damage and L-Dopa-Induced Dyskinesia in Mice

Parkinson's disease (PD) is accompanied by motor impairments due to the loss of dopaminergic neurons in the nigrostriatal pathway. Levodopa (L-dopa) has been the gold standard therapy for PD since the 1960s; however, its neurotoxic features accelerate PD progression through auto-oxidation or the induction of dyskinetic movements. Ukgansan (UGS) is a well-known prescription for treating PD in traditional medicines of East Asia, and its anti-PD function has been experimentally evaluated. The present study investigated whether UGS attenuates (1) motor dysfunction and dopaminergic neuronal damage when co-treated with L-dopa and (2) L-dopa-induced dyskinesia (LID) in 6-hydroxydopamine (6-OHDA)-induced PD mice. Although L-dopa was found to reduce motor dysfunctions, it failed to decrease the dopaminergic neuronal damage and increased the expression of dopamine receptor 1 (D1R) and 2 (D2R) in the 6-OHDA-injected mouse striatum. Co-treatment with UGS resulted in normal striatal histology and ameliorated motor impairments. In addition, UGS suppressed the dyskinesia induced by chronic L-dopa treatment while restoring the dopaminergic neurons in the striatum. For the underlying mechanism, UGS reduced the overexpression of D1R-related signaling proteins, such as phosphorylated extracellular signal-regulated kinase, ΔFosB, and c-fos in the striatum. Overall, the results suggest that the effect of UGS could be complementary to L-dopa by ameliorating motor dysfunction, restoring the dopaminergic neurons, and suppressing the dyskinetic movements in PD

Multiscale Gaussian graphical models and algorithms for large-scale inference

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 119-123).Graphical models provide a powerful framework for stochastic processes by representing dependencies among random variables compactly with graphs. In particular, multiscale tree-structured graphs have attracted much attention for their computational efficiency as well as their ability to capture long-range correlations. However, tree models have limited modeling power that may lead to blocky artifacts. Previous works on extending trees to pyramidal structures resorted to computationally expensive methods to get solutions due to the resulting model complexity. In this thesis, we propose a pyramidal graphical model with rich modeling power for Gaussian processes, and develop efficient inference algorithms to solve large-scale estimation problems. The pyramidal graph has statistical links between pairs of neighboring nodes within each scale as well as between adjacent scales. Although the graph has many cycles, its hierarchical structure enables us to develop a class of fast algorithms in the spirit of multipole methods. The algorithms operate by guiding far-apart nodes to communicate through coarser scales and considering only local interactions at finer scales. The consistent stochastic structure of the pyramidal graph provides great flexibilities in designing and analyzing inference algorithms. Based on emerging techniques for inference on Gaussian graphical models, we propose several different inference algorithms to compute not only the optimal estimates but also approximate error variances as well. In addition, we consider the problem of rapidly updating the estimates based on some new local information, and develop a re-estimation algorithm on the pyramidal graph. Simulation results show that this algorithm can be applied to reconstruct discontinuities blurred during the estimation process or to update the estimates to incorporate a new set of measurements introduced in a local region.by Myung Jin Choi.S.M