An absolute interval scale of order for point patterns

Human observers readily make judgements about the degree of order in planar arrangements of points (point patterns). Here, based on pairwise ranking of 20 point patterns by degree of order, we have been able to show that judgements of order are highly consistent across individuals and the dimension of order has an interval scale structure spanning roughly 10 just-notable-differences (jnd) between disorder and order. We describe a geometric algorithm that estimates order to an accuracy of half a jnd by quantifying the variability of the size and shape of spaces between points. The algorithm is 70% more accurate than the best available measures. By anchoring the output of the algorithm so that Poisson point processes score on average 0, perfect lattices score 10 and unit steps correspond closely to jnds, we construct an absolute interval scale of order. We demonstrate its utility in biology by using this scale to quantify order during the development of the pattern of bristles on the dorsal thorax of the fruit fly.     

Mathematical approximation techniques in biophysical models

The mathematical characterization of biophysical problems often leads to certain transcendental functions which must be evaluated to fully appreciate the significance of the mathematical model. In illustration, many mathematical models concerned with wave propagation and transmission of fluids through elastic tubes require treatment of the various kinds of Bessel functions and their ratios. In my recent work (The Special Functions and Their Approximations, Volumes 1 and 2, Academic Press, 1969) polynomial, rational and infinite series expansions in series of Chebyshev polynomials are developed for a wide class of transcendental functions which include Bessel functions as special cases. In numerous instances, tables of coefficients are presented. In the present paper, we show how these ideas can be exploited to yield economic methods for the evaluation of Bessel functions arising in the problems cited. As the approximations can be given in closed form, they can be easily applied to further simplify available closed form analyses.     

Development of SDT sensor based eddy current probe for detection of deep fatigue cracks in multi-layer structure

The detection and characterization of deeply buried fatigue damage in thick, multi-layer airframe components pose significant technical challenges to the aviation safety community. Currently, no nondestructive evaluation technique is available to reliably detect such potential damage from the exterior of the airframe, which is highly desirable in light of inspection cost as well as avoidance of structure damage. Recent technological advances in high-sensitivity magnetic sensors, i.e., spin-dependent tunneling (SDT) sensors, make it feasible to employ electromagnetic inspection techniques for deep fatigue crack inspection. In this work, we report on the development and fabrication of a low frequency eddy current probe based on a magnetically shielded SDT pickup sensor concentrically located in the interior of an induction drive coil to enable localized deep diffusion of the electromagnetic field into the part under test. Simulation studies were conducted to demonstrate the deep penetration capability of this probe configuration and to understand inspection sensitivity based on magnetic field perturbation due to subsurface cracking. Experimental results obtained using this SDT sensor on samples with induced flaws demonstrate its potential for practical application.     

The importance of structured noise in the generation of self-organizing tissue patterns through contact-mediated cell�Ccell signalling

Lateral inhibition provides the basis for a self-organizing patterning system in which distinct cell states emerge from an otherwise uniform field of cells. The development of the microchaete bristle pattern on the notum of the fruitfly, Drosophila melanogaster, has long served as a popular model of this process. We recently showed that this bristle pattern depends upon a population of dynamic, basal actin-based filopodia, which span multiple cell diameters. These protrusions establish transient signalling contacts between non-neighbouring cells, generating a type of structured noise that helps to yield a well-ordered and spaced pattern of bristles. Here, we develop a general model of protrusion-based patterning to analyse the role of noise in this process. Using a simple asynchronous cellular automata rule-based model we show that this type of structured noise drives the gradual refinement of lateral inhibition-mediated patterning, as the system moves towards a stable configuration in which cells expressing the inhibitory signal are near-optimally packed. By analysing the effects of introducing thresholds required for signal detection in this model of lateral inhibition, our study shows how filopodia-mediated cell–cell communication can generate complex patterns of spots and stripes, which, in the presence of signalling noise, align themselves across a patterning field. Thus, intermittent protrusion-based signalling has the potential to yield robust self-organizing tissue-wide patterns without the need to invoke diffusion-mediated signalling.     

On the error in Padé approximations for functions defined by Stieltjes integrals

Consdier I(z) = ∫^b_a w(t)f(t, z) dt, f(t, z) = (1 + t/z)⁻¹. It is known that generalized Gaussian quadrature of I(z) leads to approximations which occupy the (n, n + r − 1) positions of the Padé matrix table for I(z). Here r is a positive integer or zero. In a previous paper the author developed a series representation for the error in Gaussian quadrature. This approach is now used to study the error in the Padé approximations noted. Three important examples are treated. Two of the examples are generalized to the case where f(t, z) = (1 + t/z)^−v.     

Free-space optical communications link budget estimation

This paper describes a new methodology of estimating free-space optical communications link budgets to be expected in conditions of severe turbulence. The approach is derived from observing that the ability of an adaptive optics (AO) system to compensate turbulence along a path is limited by the transmitter and receiver Rayleigh range, proportional to the diameter of the optics squared and inverse of the wavelength of light utilized. The method uses the Fried parameter computed over the range outside of the transmitter and receiver Rayleigh ranges, to calculate the Strehl ratios that yield a reasonable prediction of the light impinging on the receiving telescope aperture and the power coupling into the fiber. Comparisons will be given between theory and field measurements. These comparisons show that AO is most effective within the Rayleigh ranges, or when an atmospheric gradient is present, and lesser so when the total range is much greater than the sum of the Rayleigh ranges.     

圣·莫尼卡公共图书馆

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