Statistical analysis of shape through triangulation of landmarks: A study of sexual dimorphism in hominids

Two objects with homologous landmarks are said to be of the same shape if the configuration of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. In an earlier paper, the authors proposed statistical analysis of shape by considering logarithmic differences of all possible Euclidean distances between landmarks. Tests of significance for differences in the shape of objects and methods of discrimination between populations were developed with such data. In the present paper, the corresponding statistical methodology is developed by triangulation of the landmarks and by considering the angles as natural measurements of shape. This method is applied to the study of sexual dimorphism in hominids.

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

A thymidine triphosphate shape analog lacking Watson–Crick pairing ability is replicated with high sequence selectivity

Compound 1 (F), a nonpolar nucleoside analog that is isosteric with thymidine, has been proposed as a probe for the importance of hydrogen bonds in biological systems. Consistent with its lack of strong H-bond donors or acceptors, F is shown here by thermal denaturation studies to pair very poorly and with no significant selectivity among natural bases in DNA oligonucleotides. We report the synthesis of the 5′-triphosphate derivative of 1 and the study of its ability to be inserted into replicating DNA strands by the Klenow fragment (KF, exo− mutant) of Escherichia coli DNA polymerase I. We find that this nucleotide derivative (dFTP) is a surprisingly good substrate for KF; steady-state measurements indicate it is inserted into a template opposite adenine with efficiency (Vmax/Km) only 40-fold lower than dTTP. Moreover, it is inserted opposite A (relative to C, G, or T) with selectivity nearly as high as that observed for dTTP. Elongation of the strand past F in an F–A pair is associated with a brief pause, whereas that beyond A in the inverted A–F pair is not. Combined with data from studies with F in the template strand, the results show that KF can efficiently replicate a base pair (A–F/F–A) that is inherently very unstable, and the replication occurs with very high fidelity despite a lack of inherent base-pairing selectivity. The results suggest that hydrogen bonds may be less important in the fidelity of replication than commonly believed and that nucleotide/template shape complementarity may play a more important role than previously believed.

Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

Positron-emission tomography imaging of long-term shape recognition challenges

Long-term visual memory performance was impaired by two types of challenges: a diazepam challenge on acquisition and a sensory challenge on recognition. Using positron-emission tomography regional cerebral blood flow imaging, we studied the effect of these challenges on regional brain activation during the delayed recognition of abstract visual shapes as compared with a baseline fixation task. Both challenges induced a significant decrease in differential activation in the left fusiform gyrus, suggesting that this region is involved in the automatic or volitional comparison of incoming and stored stimuli. In contrast, thalamic differential activation increased in response to memory challenges. This increase might reflect enhanced retrieval attempts as a compensatory mechanism for restoring recognition performance.

Control of Cyclin D1, p27Kip1, and Cell Cycle Progression in Human Capillary Endothelial Cells by Cell Shape and Cytoskeletal Tension

The extracellular matrix (ECM) plays an essential role in the regulation of cell proliferation during angiogenesis. Cell adhesion to ECM is mediated by binding of cell surface integrin receptors, which both activate intracellular signaling cascades and mediate tension-dependent changes in cell shape and cytoskeletal structure. Although the growth control field has focused on early integrin and growth factor signaling events, recent studies suggest that cell shape may play an equally critical role in control of cell cycle progression. Studies were carried out to determine when cell shape exerts its regulatory effects during the cell cycle and to analyze the molecular basis for shape-dependent growth control. The shape of human capillary endothelial cells was controlled by culturing cells on microfabricated substrates containing ECM-coated adhesive islands with defined shape and size on the micrometer scale or on plastic dishes coated with defined ECM molecular coating densities. Cells that were prevented from spreading in medium containing soluble growth factors exhibited normal activation of the mitogen-activated kinase (erk1/erk2) growth signaling pathway. However, in contrast to spread cells, these cells failed to progress through G1 and enter S phase. This shape-dependent block in cell cycle progression correlated with a failure to increase cyclin D1 protein levels, down-regulate the cell cycle inhibitor p27Kip1, and phosphorylate the retinoblastoma protein in late G1. A similar block in cell cycle progression was induced before this same shape-sensitive restriction point by disrupting the actin network using cytochalasin or by inhibiting cytoskeletal tension generation using an inhibitor of actomyosin interactions. In contrast, neither modifications of cell shape, cytoskeletal structure, nor mechanical tension had any effect on S phase entry when added at later times. These findings demonstrate that although early growth factor and integrin signaling events are required for growth, they alone are not sufficient. Subsequent cell cycle progression and, hence, cell proliferation are controlled by tension-dependent changes in cell shape and cytoskeletal structure that act by subjugating the molecular machinery that regulates the G1/S transition.