Guiding Data Analysts with Visual Statistical Strategies

Abstract

The concept of statistical strategy is introduced and used to develop a structured graphical user interface for guiding data analysis. The interface visually represents statistical strategies that are designed by expert data analysts to guide novices. The representation is an abstraction of the expert's concepts of the essence of a data analysis. We argue that an environment that visually guides and structures data analysis will improve data analysis productivity, accuracy, accessibility, and satisfaction in comparison to an environment without such aids, especially for novice data analysts. Our concepts are based on notions from cognitive science, and can be empirically evaluated. The interface consists of two interacting windows—the guidemap and the workmap. Each window contains a graph that has nodes and edges. The guidemap graph represents the statistical strategy for a specific statistical task (such as describing data). Nodes represent potential data analysis actions that can be taken by the system. Edges represent potential actions that can be taken by the analyst. The guidemap graph exists prior to the data analysis session, having been created by an expert. The workmap graph represents the complete history of all steps taken by the data analyst. It is constructed during the data analysis session as a result of the analyst's actions. Workmap nodes represent data sets, data models, or data analysis procedures that have been created or used by the analyst. Workmap edges represent the chronological sequence of the analyst's actions. One workmap node is highlighted to indicate which statistical object is the focus of the strategy. We illustrate our concepts with ViSta, the Visual Statistics system that we have developed.     

On the hybrid projection method for fixed point and equilibrium problems

In this paper, fixed point and equilibrium problems are considered based on a hybrid projection method. Strong convergence theorems of common elements are established in the framework of real Hilbert spaces.     

Empirical Modeling of a Hydraulic Actuator in a Vehicle Control System

The pressure information of a hydraulic actuator plays a key role in modern vehicle control and fault diagnosis. The difficulty in measuring pressure directly naturally motivates such an indirect approach as an observer whose accuracy depends heavily upon the availability of a high fidelity model of a hydraulic actuator. Notwithstanding its success in understanding the dynamics of the first principle model of a hydraulic actuator, it is not suited to controller/observer design due to its complexity. This paper presents an alternative to the first principle modeling methodology: an empirical approach to hydraulic actuator modeling. Linear and nonlinear system identification techniques are applied to obtain low-order models of a hydraulic actuator. Experimental results show how the empirical models reproduce the key features of a hydraulic actuator with sufficient accuracy.     

Real Hypersurfaces in Complex Two-plane Grassmannians with {\mathfrak{D}^{\bot}}-Parallel Shape Operator

In this paper we consider a new notion of ${\mathfrak{D}^{\bot}}$ -parallel shape operator for real hypersurfaces in complex two-plane Grassmannians ${G_2(\mathbb{C}^{m+2})}$ and give a non-existence theorem for a Hopf hypersurface in ${G_2(\mathbb{C}^{m+2})}$ with ${\mathfrak{D}^{\bot}}$ -parallel shape operator.     

A Note on Quasi-paranormal Operators

Let T be a bounded linear operator on an infinite dimensional complex Hilbert space. In this paper, we introduce the new class, denoted ${{\mathcal{QP}}}$ , of operators satisfying ${{\|T^{2}x\|^{2}\leq \|T^{3}x\|\|Tx\|}}$ for all ${{x \in \mathcal{H}}}$ . This class includes the classes of paranormal operators and quasi-class A operators. We prove basic structural properties of these operators. Using these results, we also prove that if E is the Riesz idempotent for a nonzero isolated point λ₀ of the spectrum of ${{T \in \mathcal{QP}}}$ , then E is self-adjoint if and only if ${{N(T-\lambda_{0}) \subseteq N(T^{*}-\overline{\lambda}_{0})}}$ .     

Maximal commutative subalgebras of matrix algebras

Maximal commutative subalgebras of the algebra of n by n matrices over a field k very rarely have dimension smaller than n. There is a (B, N)-construction which yields subalgebras of this kind. The Courter's algebra that is of this kind was shown a (B, N)-construction where B is the Schur algebra of size 4 and N = k ⁴. That is, the Courter's algebra is isomorphic to B ? (k ⁴)², the idealization of (k ⁴)². It was questioned how many isomorphism classes can be produced by varying the finitely generated faithful B-module N. In this paper, we will show that the set of all algebras B ? N ² fall into a single isomorphism class, where B is the Schur algebra of size 4 and N a finitely generated faithful B-module.     

Analysis of subspace migrations in limited-view inverse scattering problems

An analysis of subspace migration that occurs in the limited-view inverse scattering problem is considered herein. Based on the structure of singular vectors associated with the nonzero singular values of the multi-static response matrix, we establish a relationship between the subspace migration imaging function and Bessel functions of integer order of the first kind. The revealed structure and numerical examples show why subspace migration is applicable for imaging of small scatterers in limited-view inverse scattering problems.     

Significant decrease in interfacial energy of grain boundary through serrated grain boundary transition

The mechanism of serrated grain boundary formation and its effect on liquation behaviour have been studied in a wrought nickel-based superalloy – Alloy 263. It was newly discovered that grain boundaries are considerably serrated in the absence of γ?′-phase or M₂₃C₆ at the grain boundaries. An electron energy-loss spectroscopy study suggests that serration is triggered by the discontinuous segregation of C and Cr atoms at grain boundaries for the purpose of relieving the excessive elastic strain energy. The grain boundaries serrate to have specific segments approaching one {111} low-index plane at a boundary so that the interfacial free energy of the grain boundary can be decreased, which may be responsible for the driving force of the serration. The serrated grain boundaries effectively suppress grain coarsening and are highly resistant to liquation due to their lower wettability resulting from a lower interfacial energy of the grain boundary.     

Influence of SiNx:H film properties according to gas mixture ratios for crystalline silicon solar cells

The Hydrogenated silicon nitride (SiN_x:H) using plasma enhanced chemical vapor deposition is widely used in photovoltaic industry as an antireflection coating and passivation layer. In the high temperature firing process, the SiN_x:H film should not change the properties for its use as high quality surface layer in crystalline silicon solar cells. For optimizing surface layer in crystalline silicon solar cells, by varying gas mixture ratios (SiH₄ + NH₃ + N₂, SiH₄ + NH₃, SiH₄ + N₂), the hydrogenated silicon nitride films were analyzed for its antireflection and surface passivation (electrical and chemical) properties. The film deposited with the gas mixture of SiH₄ + NH₃ + N₂ showed the best properties in before and after firing process conditions.The single crystalline silicon solar cells fabricated according to optimized gas mixture condition (SiH₄ + NH₃ + N₂) on large area substrate of size 156 mm × 156 mm (Pseudo square) was found to have the conversion efficiency as high as 17.2%. The reason for the high efficiency using SiH₄ + NH₃ + N₂ is because of the good optical transmittance and passivation properties. Optimized hydrogenated silicon nitride surface layer and high efficiency crystalline silicon solar cells fabrication sequence has also been explained in this study.     

Band gap tunable and improved microstructure characteristics of Cu2ZnSn(S1−x,Sex)4 thin films by annealing under atmosphere containing S and Se

Cu₂ZnSn(S_xS_1?x)₄ (CZTSSe) thin films were prepared by annealing a stacked precursor prepared on Mo coated glass substrates by the sputtering technique. The stacked precursor thin films were prepared from Cu, SnS₂, and ZnS targets at room temperature with stacking orders of Cu/SnS₂/ZnS. The stacked precursor thin films were annealed using a tubular two zone furnace system under a mixed N₂ (95%) + H₂S (5%) + Se vaporization atmosphere at 580 °C for 2 h. The effects of different Se vaporization temperature from 250 °C to 500 °C on the structural, morphological, chemical, and optical properties of the CZTSSe thin films were investigated. X-ray diffraction patterns, Raman spectroscopy, and X-ray photoelectron spectroscopy results showed that the annealed thin films had a single kesterite crystal structure without a secondary phase. The 2θ angle position for the peaks from the (112) plane in the annealed thin films decreased with increasing Se vaporization temperature. Energy dispersive X-ray results showed that the presence of Se in annealed thin films increased from 0 at% to 42.7 at% with increasing Se vaporization temperatures. UV–VIS spectroscopy results showed that the absorption coefficient of all the annealed thin films was over 10⁴ cm^?1 and that the optical band gap energy decreased from 1.5 eV to 1.05 eV with increasing Se vaporization temperature.