By Stephen Slade
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Braid teams have been brought into the mathematical literature in 1925 in a seminar paper via E. Artin, even if the belief was once implicit in Hurwitz's 1891 manuscript. within the years due to the fact that, and especially within the final 5-10 years, they've got performed a job in various and unforeseen methods in greatly diversified parts of arithmetic, together with knot thought, homotopy thought, singularity conception, dynamical structures, and such a lot lately operator algebras, the place intriguing new discoveries are last the distance by means of having remarkable purposes to knots and hyperlinks.
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Coo • WO • •• . • · · • · ·•··. · coo ·· ,. · •- .. · . · · o 800 0 0 0 ~OO Timeoftloy •• COO Fig. 2. Variability of eosinophil counts in samples of blood from individual animals. Data from mice of two inbred strains, C 57 Black Subline 4 (B4 ), on top; C57 Bladl: Subline 1 (B1 ), at the bottom. Each dot represents eosinophil blood cell count from a different animal. Animals are of comparable sex and age (cf. ) Furthermore, on a time plot the shape of a given curve representing biologic data need not necessarily be a sinusoidal one, even if this shape should be determined solely by physiologic factors resulting in a circadian rhythm.
28 F. HALBERG, Y. L. TONG, and E. A. , these rhythms are largely, if not fully, "synchronized-inphase" in most of the data. As to parameter estimation, the cosinor provides concurrent estimates of the amplitude as well as the phase of a given rhythm in the sample investigated, quite apart from providing for the often desirable weighting of rp by C and vice versa. It should be added that the estimation of the phase, per se, of a given rhythm often can be appropriately carried out by other procedures previously outlined by STEPHENS  and BATSCHELET , notably when the original data consist of angles that are directly determined or when for some other reason the weighting of the rp is not desirable.
HALBERG, Y. L. TONG, /1ale polienls and E. A. J 80s01 cell corcinomq/o cCTf'Cilloma/a Fig. 11. Summary of serial mitotic counts originally published by TAHTI  analyzed by cosinor (d. also ). Note that the cosinors summarizing subsets of series from male or female patients or from patients with squamous cell carcinomata or basal cell carcinomata all yield error ellipses that cover the pole-a circadian rhythm is not detected. ) malignancy-the error ellipse does not cover the pole. The diversity of microscopic structure in various tumors may find a counterpart in different kinds of rhythm alteration in different cancers  Circadian System Phase - An Aspect of Temporal Morphology 47 to appropriately sampled data-in order to better approximate the non-sinusoidal shape of such a rhythm and to estimate more properly the amplitude as well as the phase.