Data Envelopment Analysis (DEA) is known as a nonparametric mathematical programming approach to productive efficiency analysis. In this paper we show that DEA can be alternatively interpreted as nonparametric least squares regression subject to shape constraints on frontier and sign constraints on residuals. This reinterpretation reveals the classic parametric programming model by Aigner and C...

We are interested in evaluating the state of drivers to determine whether they attentive road or not by using motion sensor data collected from car driving experiments. That is, our goal is design a predictive model that can estimate given sensors. For purpose, we leverage recent developments topological analysis (TDA) analyze and transform coming time series build machine learning based on fea...

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis.

Persistent homology is a relatively new tool from topological data analysis that has transformed, for many, the way data sets (and the information contained in those sets) are viewed. It is derived directly from techniques in computational homology but has the added feature that it is able to capture structure at multiple scales. One way that this multi-scale information can be presented is thr...

Abstract We use methods from computational algebraic topology to study functional brain networks in which nodes represent regions and weighted edges encode the similarity of magnetic resonance imaging (fMRI) time series each region. With these tools, allow one characterize topological invariants such as loops high-dimensional data, we are able gain understanding low-dimensional structures a way...

PROTEIN STABILITY Taylor Dispersion Analysis (TDA) is a microcapillary flow-based technique whereby a nanoliter-scale sample pulse is injected into the laminar flow of run buffer, which then spreads out axially due to the combined actions of convection and radial diffusion. Detection of the equilibrium concentration profile (or Taylorgram) of the dispersed sample pulse allows the molecular diff...