Power-law Distributions in Information Science - Making the Case for Logarithmic Binning

We suggest partial logarithmic binning as the method of choice for uncovering the nature of many distributions encountered in information science (IS). Logarithmic binning retrieves information and trends "not visible" in noisy power-law tails. We also argue that obtaining the exponent from logarithmically binned data using a simple least square method is in some cases warranted in addition to methods such as the maximum likelihood. We also show why often used cumulative distributions can make it difficult to distinguish noise from genuine features, and make it difficult to obtain an accurate power-law exponent of the underlying distribution. The treatment is non-technical, aimed at IS researchers with little or no background in mathematics.Comment: Accepted for publication in JASIS

Describing a craniofacial anomaly: Finite elements and the biometrics of landmark locations

An intergroup comparison of cephalometric landmark configurations by the finite-element method elegantly depicts the algebra of some of the size and shape change measures that one may define by reference to those landmarks. In studies of mean differences between groups, the statistical analysis of these finite elements is equivalent to competent statistical analysis of the same data using any other geometric metaphor, such as properly standardized vector descriptions of landmark “movement” or scalar measures, size and shape variables, taken in sufficient variety. In applications to landmark data, the reality of finite-element depictions is purely statistical rather than phenomenological. In the absence of additional evidence, they should not be held either more or less biologically meaningful than other descriptions of the same landmark changes to which they lead. These propositions are exemplified using landmark data from 13 cases of Apert syndrome.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37643/1/1330740408_ftp.pd

The Morphometric Synthesis for landmarks and edge-elements in images

Over the last decade, techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry, and computer graphics have been combined in a coherent new system of tools for the biometric analysis of landmarks , or labelled points, along with the biological images in which they are seen. Multivariate analyses of samples for all the usual scientific purposes - description of mean shapes, of shape variation, and of the covariation of shape with size, group, or other causes or effects - may be carried out very effectively in the tangent space to David Kendall's shape space at the Procrustes average shape. For biometric interpretation of such analyses, we need a basis for the tangent space that is Procrustes-orthonormal, and we need graphics for visualizing mean shape differences and other segments and vectors there; both of these needs are managed by the thin-plate spline. The spline also links the biometrics of landmarks to deformation analysis of curves in the images from which the landmarks originally arose. This article reviews the principal tools of this synthesis in a typical study design involving landmarks and edge information from a microfossil.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75091/1/j.1365-3121.1995.tb00535.x.pd

Beyond words, yes, but also beyond numbers

Safina’s fascinating series of fifty separate feuilletons tries to bridge a painful Methodenstreit in contemporary ethology mainly by an accumulation of anecdotes. Some deal with his own dogs, but most derive from reading or conversing with observers of a wider range of social mammals including elephants, wolves, apes, and whales. In spite of the many interruptions by travesties of the academic lifestyle and its literature, there is a point to be made, concerning the centrality of evidence about cooperative behavior styles, especially aspects of child-rearing, for the understanding of “what animals think and feel.” But Safina’s argument would be a lot more persuasive, at least to this outsider, if he were more aware of his own methodological preferences and the restraints they impose on the rhetoric of scientific persuasion. In spite of my skepticism, I sketch a possible application of his ideas to human neuroteratology

Allometry and developmental integration of body growth in a piranha, Pygocentrus nattereri (Teleostei: Ostariophysi)

Piranhas, like many teleosts, change their diets on both ontogenetic and phylogenetic time scales. Prior studies have suggested that pervasive morphological changes in body form on a phylogenetic time scale may be related to changes in diet, but previous reports have found little shape change in piranhas on an ontogenetic time scale. We re-examine the post-transformational allometry of body form in one piranha, Pygocentrus nattereri (Kner), using the method of thin-plate splines decomposed by their partial warps. We find substantial evidence of allometry, primarily elongation of the mid-body relative to the more anterior and posterior regions, elongation of the postorbital and nape regions relative to the more anterior head and posterior body, and deepening of the head relative to the body. In addition to these pervasive changes throughout the body, there are some that are more localized, especially elongation of the postorbital region relative to eye diameter and snout, and an even more localized elongation of the snout relative to eye diameter. Initial dietary transitions are associated with changes in head and jaw proportions, but rates of shape change decelerate through growth, so that the final transition to a diet increasingly dominated by small whole fish appears associated with change largely in overall body size. © 1995 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50288/1/1052230309_ftp.pd

The inappropriateness of conventional cephalometrics

1. 1. Cephalometric conventions today may have little basis in either biology or biometrics.2. 2. There is no theory of cephalometrics, only conventions which involve landmarks and straight lines only. These fail to capture the curving of form and its changes, exclude proper measures of size for bent structures, and misrepresent growth, portraying it as vector displacement rather than a generalized distortion.3. 3. Conventional cephalometric procedures misinform by fabrication of misleading geometric quantities, by camouflage, particularly of remodeling, by confusion about what is happening (analysis of rotations, treating shape separately from size, and registering angles on landmarks as vertices), and by subtraction as a representation of growth.4. 4. We suggest that the present systems offer little real hope of improvement sufficient to meet our needs in craniofacial growth research. We call attention to three possible techniques to be included in future cephalometric conventions: (1) tangents and curvatures, (2) Blum's medial axis ("skeleton"), and (3) biorthogonal grids.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23746/1/0000718.pd

Craniofacial dysmorphology in 22q11.2 deletion syndrome by 3D laser surface imaging and geometric morphometrics: illuminating the developmental relationship to risk for psychosis

Persons with 22q11.2 deletion syndrome (22q11.2DS) are characterized inter alia by facial dysmorphology and greatly increased risk for psychotic illness. Recent studies indicate facial dysmorphology in adults with schizophrenia. This study evaluates the extent to which the facial dysmorphology of 22q11.2DS is similar to or different from that evident in schizophrenia. Twenty-one 22q11.2DS-sibling control pairs were assessed using 3D laser surface imaging. Geometric morphometrics was applied to 30 anatomical landmarks, 480 geometrically homologous semi-landmarks on curves and 1720 semi-landmarks interpolated on each 3D facial surface. Principal component (PC) analysis of overall shape space indicated PC2 to strongly distinguish 22q11.2DS from controls. Visualization of PC2 indicated 22q11.2DS and schizophrenia to be similar in terms of overall widening of the upper face, lateral displacement of the eyes/orbits, prominence of the cheeks, narrowing of the lower face, narrowing of nasal prominences and posterior displacement of the chin; they differed in terms of facial length (increased in 22q11.2DS, decreased in schizophrenia), mid-face and nasal prominences (displaced upwards and outwards in 22q11.2DS, less prominent in schizophrenia); lips (more prominent in 22q11.2DS; less prominent in schizophrenia) and mouth (open mouth posture in 22q11.2DS; closed mouth posture in schizophrenia). These findings directly implicate dysmorphogenesis in a cerebral-craniofacial domain that is common to 22q11.2DS and schizophrenia and which may repay further clinical and genetic interrogation in relation to the developmental origins of psychotic illness