Exotic phase separation in one-dimensional hard-core boson system with two- and three-body interactions

We investigate the ground state phase diagram of hard-core boson system with repulsive two-body and attractive three-body interactions in one-dimensional optic lattice. When these two interactions are comparable and increasing the hopping rate, physically intuitive analysis indicates that there exists an exotic phase separation regime between the solid phase with charge density wave order and superfluid phase. We identify these phases and phase transitions by numerically analyzing the density distribution, structure factor of density-density correlation function, three-body correlation function and von Neumann entropy estimator obtained by density matrix renormalization group method. These exotic phases and phase transitions are expected to be observed in the ultra-cold polar molecule experiments by properly tuning interaction parameters, which is constructive to understand the physics of ubiquitous insulating-superconducting phase transitions in condensed matter systems

Statistical tools for assessment of spatial properties of mutations observed under the microarray platform

Mutations are alterations of the DNA nucleotide sequence of the genome. Analyses of spatial properties of mutations are critical for understanding certain mutational mechanisms relevant to genetic disease, diversity, and evolution. The studies in this thesis focus on two types of mutations: point mutations, i.e., single nucleotide polymorphism (SNP) genotype differences, and mutations in segments, i.e., copy number variations (CNVs). The microarray platform, such as the Mouse Diversity Genotyping Array (MDGA), detects these mutations genome-wide with lower cost compared to whole genome sequencing, and thus is considered for suitability as a screening tool for large populations. Yet it provides observation of mutations with high degree of missingness across the genome due to its design, which thus leads to challenges for statistical analyses. Three topics are studied in this thesis: the development of formal statistical tools for detecting the existence of point mutation clusters under the microarray platform; the evaluation of the performance of test statistics developed while accounting for various probe designs, in terms of the capabilities of detecting mutation clusters; the development of formal statistical tools for testing the existence of spatial association between point mutations and mutations in segments. Statistical models such as Poisson point processes and Neyman-Scott processes are used for the distributions of the locations of point mutations under null and alternative hypotheses. Monte Carlo frameworks are established for statistical inference and the evaluation of power performance of the proposed test statistics. Tests with desirable performance are identified and recommended as screening tools. These statistical tools can be used for the study of other genomic events in the form of point events and events in segments, as well as with other microarray platforms than the MDGA which is utilized here. Simulated probe sets based on a window-based probe design mimicing the design of the MDGA are used to study the effect of various factors in probe design on the performance of test statistics. Insights are offered for determining key features in such design, such as probe intensity, when designing a new microarray platform, in order to achieve desired power for the purpose of mutation cluster detection

PIXOR: Real-time 3D Object Detection from Point Clouds

We address the problem of real-time 3D object detection from point clouds in the context of autonomous driving. Computation speed is critical as detection is a necessary component for safety. Existing approaches are, however, expensive in computation due to high dimensionality of point clouds. We utilize the 3D data more efficiently by representing the scene from the Bird's Eye View (BEV), and propose PIXOR, a proposal-free, single-stage detector that outputs oriented 3D object estimates decoded from pixel-wise neural network predictions. The input representation, network architecture, and model optimization are especially designed to balance high accuracy and real-time efficiency. We validate PIXOR on two datasets: the KITTI BEV object detection benchmark, and a large-scale 3D vehicle detection benchmark. In both datasets we show that the proposed detector surpasses other state-of-the-art methods notably in terms of Average Precision (AP), while still runs at >28 FPS.Comment: Update of CVPR2018 paper: correct timing, fix typos, add acknowledgemen