Joint-space tracking of workspace trajectories in continuous time

We present a controller for a class of robotics manipulators which provides exponential convergence to a desired end-effector trajectory using gains specified in joint-space. This is accomplished without appeal to the use of discrete inverse-kinematics algorithms, allowing the controller to be posed entirely in continuous time

Control for an Autonomous Bicycle

The control of nonholonomic and underactuated systems with symmetry is illustrated by the problem of controlling a bicycle. We derive a controller which, using steering and rear-wheel torque, causes a model of a riderless bicycle to recover its balance from a near fall as well as converge to a time parameterized path in the ground plane. Our construction utilizes new results for both the derivation of equations of motion for nonholonomic systems with symmetry, as well as the control of underactuated robotic systems

Dynamic inversion and polar decomposition of matrices

Using the recently introduced concept of a "dynamic inverse" of a map, along with its associated analog computational paradigm. we construct continuous-time nonlinear dynamical systems which produce both regular and generalized inverses of time-varying and fixed matrices, as well as polar decompositions

Tracking implicit trajectories

Output tracking of implcitly defined reference trajectories is examined. A continuous-time nonlinear dynamical system is constructed that produces explicit estimates of time-varying implicit trajectories. We prove that incorporation of this "dynamic inverter" into a tracking controller provides exponential output tracking of the implicitly defined trajectory for nonlinear control systems having vector relative degree and well-behaved internal dynanmics

A dynamic inverse for nonlinear maps

We consider the problem of estimating the time-varying root of a time-dependent nonlinear map. We introduce a "dynamic inverse" of a map, another generally time-dependent map which one composes with the original map to form a nonlinear vector-field. The flow of this vector field decays exponentially to the root. We then show how a dynamic inverse may be determined dynamically while being used simultaneously to find a root. We construct a continuous-time analog computational paradigm around the dynamic inverse

Dynamical methods for polar decomposition and inversion of matrices

AbstractWe show how to obtain polar decomposition as well as inversion of fixed and time-varying matrices using a class of nonlinear continuous-time dynamical systems. First we construct a dynamical system that causes an initial approximation of the inverse of a time-varying matrix to flow exponentially toward the true time-varying inverse. Using a time-parametrized homotopy from the identity matrix to a fixed matrix with unknown inverse, and applying our result on the inversion of time-varying matrices, we show how any positive definite fixed matrix may be dynamically inverted by a prescribed time without an initial guess at the inverse. We then construct a dynamical system that solves for the polar decomposition factors of a time-varying matrix given an initial approximation for the inverse of the positive definite symmetric part of the polar decomposition. As a by-product, this method gives another method of inverting time-varying matrices. Finally, using homotopy again, we show how dynamic polar decomposition may be applied to fixed matrices with the added benefit that this allows us to dynamically invert any fixed matrix by a prescribed time

Integrated Analyses of microRNAs Demonstrate Their Widespread Influence on Gene Expression in High-Grade Serous Ovarian Carcinoma

The Cancer Genome Atlas (TCGA) Network recently comprehensively catalogued the molecular aberrations in 487 high-grade serous ovarian cancers, with much remaining to be elucidated regarding the microRNAs (miRNAs). Here, using TCGA ovarian data, we surveyed the miRNAs, in the context of their predicted gene targets.Integration of miRNA and gene patterns yielded evidence that proximal pairs of miRNAs are processed from polycistronic primary transcripts, and that intronic miRNAs and their host gene mRNAs derive from common transcripts. Patterns of miRNA expression revealed multiple tumor subtypes and a set of 34 miRNAs predictive of overall patient survival. In a global analysis, miRNA:mRNA pairs anti-correlated in expression across tumors showed a higher frequency of in silico predicted target sites in the mRNA 3'-untranslated region (with less frequency observed for coding sequence and 5'-untranslated regions). The miR-29 family and predicted target genes were among the most strongly anti-correlated miRNA:mRNA pairs; over-expression of miR-29a in vitro repressed several anti-correlated genes (including DNMT3A and DNMT3B) and substantially decreased ovarian cancer cell viability.This study establishes miRNAs as having a widespread impact on gene expression programs in ovarian cancer, further strengthening our understanding of miRNA biology as it applies to human cancer. As with gene transcripts, miRNAs exhibit high diversity reflecting the genomic heterogeneity within a clinically homogeneous disease population. Putative miRNA:mRNA interactions, as identified using integrative analysis, can be validated. TCGA data are a valuable resource for the identification of novel tumor suppressive miRNAs in ovarian as well as other cancers

Query Large Scale Microarray Compendium Datasets Using a Model-Based Bayesian Approach with Variable Selection

In microarray gene expression data analysis, it is often of interest to identify genes that share similar expression profiles with a particular gene such as a key regulatory protein. Multiple studies have been conducted using various correlation measures to identify co-expressed genes. While working well for small datasets, the heterogeneity introduced from increased sample size inevitably reduces the sensitivity and specificity of these approaches. This is because most co-expression relationships do not extend to all experimental conditions. With the rapid increase in the size of microarray datasets, identifying functionally related genes from large and diverse microarray gene expression datasets is a key challenge. We develop a model-based gene expression query algorithm built under the Bayesian model selection framework. It is capable of detecting co-expression profiles under a subset of samples/experimental conditions. In addition, it allows linearly transformed expression patterns to be recognized and is robust against sporadic outliers in the data. Both features are critically important for increasing the power of identifying co-expressed genes in large scale gene expression datasets. Our simulation studies suggest that this method outperforms existing correlation coefficients or mutual information-based query tools. When we apply this new method to the Escherichia coli microarray compendium data, it identifies a majority of known regulons as well as novel potential target genes of numerous key transcription factors

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts