Singularity of Mean Curvature Flow of Lagrangian Submanifolds

In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold is Lagrangian and almost calibrated by Re\Omega in a Calabi-Yau n-fold (M,\Omega), and T>0 is the first blow-up time of the mean curvature flow, then the tangent cone of the mean curvature flow at a singular point (X,T) is a stationary Lagrangian integer multiplicity current in R\sup 2n with volume density greater than one at X. When n=2, the tangent cone consists of a finite union of more than one 2-planes in R\sup 4 which are complex in a complex structure on R\sup 4

PARALLEL INDEPENDENT COMPONENT ANALYSIS WITH REFERENCE FOR IMAGING GENETICS: A SEMI-BLIND MULTIVARIATE APPROACH

Imaging genetics is an emerging field dedicated to the study of genetic underpinnings of brain structure and function. Over the last decade, brain imaging techniques such as magnetic resonance imaging (MRI) have been increasingly applied to measure morphometry, task-based function and connectivity in living brains. Meanwhile, high-throughput genotyping employing genome-wide techniques has made it feasible to sample the entire genome of a substantial number of individuals. While there is growing interest in image-wide and genome-wide approaches which allow unbiased searches over a large range of variants, one of the most challenging problems is the correction for the huge number of statistical tests used in univariate models. In contrast, a reference-guided multivariate approach shows specific advantage for simultaneously assessing many variables for aggregate effects while leveraging prior information. It can improve the robustness of the results compared to a fully blind approach. In this dissertation we present a semi-blind multivariate approach, parallel independent component analysis with reference (pICA-R), to better reveal relationships between hidden factors of particular attributes. First, a consistency-based order estimation approach is introduced to advance the application of ICA to genotype data. The pICA-R approach is then presented, where independent components are extracted from two modalities in parallel and inter-modality associations are subsequently optimized for pairs of components. In particular, prior information is incorporated to elicit components of particular interests, which helps identify factors carrying small amounts of variance in large complex datasets. The pICA-R approach is further extended to accommodate multiple references whose interrelationships are unknown, allowing the investigation of functional influence on neurobiological traits of potentially related genetic variants implicated in biology. Applied to a schizophrenia study, pICA-R reveals that a complex genetic factor involving multiple pathways underlies schizophrenia-related gray matter deficits in prefrontal and temporal regions. The extended multi-reference approach, when employed to study alcohol dependence, delineates a complex genetic architecture, where the CREB-BDNF pathway plays a key role in the genetic factor underlying a proportion of variation in cue-elicited brain activations, which plays a role in phenotypic symptoms of alcohol dependence. In summary, our work makes several important contributions to advance the application of ICA to imaging genetics studies, which holds the promise to improve our understating of genetics underlying brain structure and function in healthy and disease

Bearing fault diagnosis based on active learning and random forest

Bearing plays an important role in rotating machineries and has received increasing attention in diagnosis of its faults accurately. This paper proposes a fault diagnosis approach exploiting active learning (AL) based on random forest (RF), which can perform accurate bearing fault diagnosis with most valuable samples. First, feature vectors are obtained by empirical mode decomposition (EMD) process for original vibration signals and selected as input of the system. Second, samples with highest uncertainty are selected through AL and added to the training set to train RF classifier. Finally, trained RF is employed to perform classification for bearing faults with testing set. Experimental results demonstrate that the proposed approach can effectively and accurately identify typical bearing faults

A Unified Algorithm Framework for Unsupervised Discovery of Skills based on Determinantal Point Process

Learning rich skills through temporal abstractions without supervision of external rewards is at the frontier of Reinforcement Learning research. Existing works mainly fall into two distinctive categories: variational and Laplacian-based skill (a.k.a., option) discovery. The former maximizes the diversity of the discovered options through a mutual information loss but overlooks coverage of the state space, while the latter focuses on improving the coverage of options by increasing connectivity during exploration, but does not consider diversity. In this paper, we propose a unified framework that quantifies diversity and coverage through a novel use of the Determinantal Point Process (DPP) and enables unsupervised option discovery explicitly optimizing both objectives. Specifically, we define the DPP kernel matrix with the Laplacian spectrum of the state transition graph and use the expected mode number in the trajectories as the objective to capture and enhance both diversity and coverage of the learned options. The proposed option discovery algorithm is extensively evaluated using challenging tasks built with Mujoco and Atari, demonstrating that our proposed algorithm substantially outperforms SOTA baselines from both diversity- and coverage-driven categories. The codes are available at https://github.com/LucasCJYSDL/ODPP