Charles R. Tolle

Lacunarity Definition For Ramified Data Sets Based On Optimal Cover

Lacunarity is a measure of how data fills space. It complements fractal dimension, which measures how much space is filled. This paper discusses the limitations of the standard gliding box algorithm for calculating lacunarity, which leads to a re-examination of what lacunarity is meant to describe. Two new lacunarity measures for ramified data sets are then presented that more directly measure the gaps in a ramified data set. These measures are rigorously defined. An algorithm for estimating the new lacunarity measure, using Fuzzy-C means clustering algorithm, is developed. The lacunarity estimation algorithm is used to analyze two- and three-dimensional Cantor dusts. Applications for these measures include biological modeling and target detection within ramified data sets.

Do dynamical systems follow Benford's law?

Data compiled from a variety of sources follow Benfords law, which gives a monotonically decreasing distribution of the first digit (1 through 9). We examine the frequency of the first digit of the coordinates of the trajectories generated by some common dynamical systems. One-dimensional cellular automata fulfill the expectation that the frequency of the first digit is uniform. The molecular dynamics of fluids, on the other hand, provides trajectories that follow Benfords law. Finally, three chaotic systems are considered: Lorenz, Henon, and Rossler. The Lorenz system generates trajectories that follow Benfords law. The Henon system generates trajectories that resemble neither the uniform distribution nor Benfords law. Finally, the Rossler system generates trajectories that follow the uniform distribution for some parameters choices, and Benfords law for others. (c) 2000 American Institute of Physics.

Suboptimal minimum cluster volume cover-based method for measuring fractal dimension

A new method for calculating fractal dimension is developed in this paper. The method is based on the box dimension concept; however, it involves direct estimation of a suboptimal covering of the data set of interest. By finding a suboptimal cover, this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm. Moreover, any decrease in the error of the covering element count directly increases the accuracy of the fractal dimension estimation. In general, our method represents a mathematical dual to the standard box counting algorithm by not solving for the number of boxes used to cover a data set given the size of the box. Instead, the method chooses the number of covering elements and then proceeds to find the placement of smallest hyperellipsoids that fully covers the data set. This method involves a variant of the Fuzzy-C Means clustering algorithm, as well as the use of the Minimum Cluster Volume clustering algorithm. A variety of fractal dimension estimators using this suboptimal covering method are discussed. Finally, these methods are compared to the standard box counting algorithm and wavelet-decomposition methods for calculating fractal dimension by using one-dimensional cantor dust sets and a set of standard Brownian random fractal images.

A highly stretchable strain sensor based on electrospun carbon nanofibers for human motion monitoring

Highly stretchable and sensitive strain sensors are in great demand for human motion monitoring. This work reports a strain sensor based on electrospun carbon nanofibers (CNFs) embedded in a polyurethane (PU) matrix. The piezoresistive properties and the strain sensing mechanism of the CNFs/PU sensor were investigated. The results showed that the CNFs/PU sensor had high stretchability of strain up to 300%, a high sensitivity of gauge factor as large as 72, and superior stability and reproducibility during the 8000 stretch/release cycles. Furthermore, bending of finger, wrist, or elbow was recorded by the resistance change of the sensor, demonstrating that the strain sensor based on CNFs/PU could have promising applications in flexible and wearable devices for human motion monitoring.

Flexible and Compressible PEDOT:PSS@Melamine Conductive Sponge Prepared via One-Step Dip Coating as Piezoresistive Pressure Sensor for Human Motion Detection

Flexible and wearable pressure sensor may offer convenient, timely, and portable solutions to human motion detection, yet it is a challenge to develop cost-effective materials for pressure sensor with high compressibility and sensitivity. Herein, a cost-efficient and scalable approach is reported to prepare a highly flexible and compressible conductive sponge for piezoresistive pressure sensor. The conductive sponge, poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS)@melamine sponge (MS), is prepared by one-step dip coating the commercial melamine sponge (MS) in an aqueous dispersion of poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS). Due to the interconnected porous structure of MS, the conductive PEDOT:PSS@MS has a high compressibility and a stable piezoresistive response at the compressive strain up to 80%, as well as good reproducibility over 1000 cycles. Thereafter, versatile pressure sensors fabricated using the conductive PEDOT:PSS@MS sponges are attached to the different parts of human body; the capabilities of these devices to detect a variety of human motions including speaking, finger bending, elbow bending, and walking are evaluated. Furthermore, prototype tactile sensory array based on these pressure sensors is demonstrated.

Musings on persistent excitation prompts new weighted least squares SysID method for nonlinear differential equation based systems

The Control community relies heavily on good System Identification (SysID) for finding the plant models needed to develop a good controller. However over time the SysID process and controller development process have remained generally separate activities. One reason for this is that SysID and Control are disparate in their fundamental nature. For good SysID, one is faced with the challenge of persistently exciting plant dynamics; while a good control system attempts to constrain or suppress much of a plants natural dynamics with desired dynamics. It is this inherent conflict that separates the two practices. But for many plants, their inherent instabilities makes trajectory collection difficult, thus there is a desire to perform data collection while under some simple form of control. Nevertheless, in order to perform solid SysID one must sample the very dynamics one might need to suppress; how then can this be achieved? This paper will explore the notation of persistent excitation, its relationship to phase space trajectories, and how one might recover the most nonlinear dynamics information for SysID while remaining under the linearizing based control region - the very place that those dynamics are most suppressed.

Observations on Characterization of Defects in Coiled Tubing From Magnetic-Flux-Leakage Data

This paper presents observations on the sizing of automatically detected artificial flaws in coiled tubing samples using magnetic-flux-leakage data. Sixty-six artificial flaws of various shapes and types, ranging from 0.30 mm deep pits to slots with length of 9.5 mm, in 44.45 mm outer diameter pipe were analyzed. The detection algorithm and the information automatically extracted from the data are described. Observations on the capabilities and limitations for determining the size and shape of the flaws are discussed.