Detailed box counting analysis was conducted of (1) fractures observed in exposures of the Devonian Shale in the central Appalachians Valley and Ridge Province of West Virginia, (2) several fracture patterns presented in the literature, and (3) active faults mapped throughout the main island (Honshu) of Japan. Box curves reveal, with few exceptions, that most naturally occurring fracture patter...

We present a novel technique for analyzing the geometry of streamlines representing large scale flow fields produced in scientific simulations. We introduce the box counting ratio, a metric related to the Kolmogorov capacity or box counting dimension, for quantifying geometric complexity of streamlines (or streamline segments). We utilize this metric to drive a visual analytic framework for ext...

By employing an embedding result due to Mañé, and its recent strengthening due to Foias & Olson it is shown that a global attractor with finite fractal (box counting) dimension d lies within an arbitrarily small neighbourhood of a smooth graph over the space spanned by the first [[2d+1]] Fourier-Galerkin modes. The proof is, however, non-constructive.

In this session we want to review the basic concepts introduced in class for convolution in continuous-time. It has been proved that in order to determine the characteristics of a linear, time-invariant (LTI) system we need to know the impulse response of the system. When we apply an input x(t) to a system that has h(t) as its impulse response, we obtain an output y(t) (see Figure 1). One of th...

Using box-counting and spatial regression, this paper analyzes the morphological characteristics of coastal settlement patterns and their spatial determinants, with a case of the Wen-Tai region on the Chinese eastern coast. Coastal settlement patterns, which reflect the interactions between people and the surrounding environment, can indicate the anthropogenic pressure sustained in the coastal ...

We refer to the point p′ satisfying (1) as an -approximate solution. Clearly, approximation to a prescribed absolute error is also possible. We refer to a point p′ satisfying (2) as witness. This condition holds if and only if p 6∈ conv(S). This is because in this case we can prove the Voronoi cell of p′ with respect to the two point set {p, p′} contains conv(S) (see Figure 1). Equivalently, th...

1. Data collection High resolution aerial photography was taken in Aberfoyle in September 2002. We selected 12 plots representing mature Sitka spruce stands between 30 and 40 years in age that were surveyed at the beginning of 2003. The aim of this field data collection was the validation of the results of the image processing analysis in the tree counting and LiDAR analysis projects. The propo...

Language production comprises conceptual, grammatical, and word form encoding as well as articulation. This paper focuses on word form or phonological encoding. Phonological encoding in speech production can be subdivided into a number of sub-processes such as segmental, metrical, and syllabic encoding. Each of these processes is briefly described and illustrated with examples from my own resea...

A robot is free to move in a non-convex polygonal region, starting against an edge on the boundary. Ahead of the robot at one unit of distance is a corner, i.e. a reflex vertex (see Figure 1). The angle θ is unknown to the robot. The robot’s task is to look at the region around the corner, which it initially cannot see. We let φ = π − θ. If φ ≥ π/2, the robot is best off moving straight to the ...

Candle stick bars contain only the first, highest, lowest, and last value of a time series of dozens or thousands of data (see Figure 1). Therefore candle sticks bars are a data compression tool. Mr. Homma in Sakata, Japan, introduced candle stick bars for trading rice around 1850 [1]. The Western version of the candle stick bar is the Open-High-Low-Close bar (OHLC bar). It is commonly used to ...