A Multidimensional Array Representation of State-Transition Model Dynamics

Cost-effectiveness analyses often rely on cohort state-transition models (cSTMs). The cohort trace is the primary outcome of cSTMs, which captures the proportion of the cohort in each health state over time (state occupancy). However, the cohort trace is an aggregated measure that does not capture information about the specific transitions among health states (transition dynamics). In practice, these transition dynamics are crucial in many applications, such as incorporating transition rewards or computing various epidemiological outcomes that could be used for model calibration and validation (e.g., disease incidence and lifetime risk). In this article, we propose an alternative approach to compute and store cSTMs outcomes that capture both state occupancy and transition dynamics. This approach produces a multidimensional array from which both the state occupancy and the transition dynamics can be recovered. We highlight the advantages of the multidimensional array over the traditional cohort trace and provide potential applications of the proposed approach with an example coded in R to facilitate the implementation of our method.

COORDINATE SYSTEM FOR REPRESENTATION OF MULTIDIMENSIONAL DATA

Visualization of analyzing multidimensional data is often required in order to improve perception and visibility. The purpose of this research is a multidimensional array of data representation. It is proposed to use a three-dimensional model as a tool. The methods used to represent an array of data with more than three dimensions are presented. The principle of constructing a multidimensional array cell is considered. An example of the constructed hypercube cell is given. The formulas for calculating the number of faces of the figure, the number of triangles that can be built through points, the number of internal triangles are obtained. The approach of visualization of aggregates is described. The use of color gradation to improve the convenience of perception of the cell in the analysis of the cube cells. It is concluded that the proposed model allows us to perceive each cell as an independent data element in the construction of charts for the analyzed indicators.

The Wing Foil: A Novel Compliant Radial Foil Bearing Design

To meet the challenging demands for high performance, affordable compliant foil bearings (CFBs), a novel compliant support element has been developed. This recently patented, novel support element uses a multidimensional array of multiple, formed, cantilever “wing foil” tabs. The wing foil bearing has all the features required to achieve state-of-the-art performance (Gen III for radial bearings). This paper describes two radial foil bearings using the wing foil and the unique design features. Test data for a 31.75 mm diameter bearing operating in air and in steam up to 42 krpm are presented to demonstrate the performance of this bearing. It is shown to have low subsynchronous vibration and reasonable damping through rigid shaft critical speeds.

The Wing Foil: A Novel Compliant Radial Foil Bearing Design

To meet the challenging demands for high performance, affordable compliant foil bearings, a novel compliant support element has been developed. This recently patented, novel support element uses a multidimensional array of multiple, formed, cantilever “wing foil” tabs. The wing foil bearing has all the features required to achieve state of the art performance (Gen III for radial bearings). This paper describes two radial foil beings using the wing foil and the unique design features. Test data for a 31.75 mm diameter bearing operating in air and in steam up to 42 krpm are presented to demonstrate the performance of this bearing. It is shown to have low subsynchronous vibration and reasonable damping through rigid shaft critical speeds.