This paper presents a method of detecting periodicities in data that exploits a series of projections onto “periodic subspaces.” The algorithm finds its own set of nonorthogonal basis elements (based on the data), rather than assuming a fixed predetermined basis as in the Fourier, Gabor, and wavelet transforms. A major strength of the approach is that it is linearin-period rather than linear-in...

Thu periodicity of the fever in infections with \ \ Filaria bancrofti in this country is not strictly periodic or regular. The parturition cycles of different adult female worms may fail to be simultaneous, whilst some parturition cycles may fail to produce fever or other symptoms. Every attack does not always mean fever, nor is every filarial attack of fever followed by lymphatic manifestation...

In this paper, we investigated the problem of discovering periodicity of a certain event in a binary data series and a new method basing on cross entropy is proposed. First, a series of rational partition methods for binary data series are introduced, which can divide the data series into different segments (partition). Then, we use cross entropy to calculate the partition periodicity, which co...

We contribute to combinatorics and algorithmics of words by introducing new types of periodicities in words. A tiling period of a word w is partial word u such that w can be decomposed into several disjoint parallel copies of u, e.g. a b is a tiling period of aabb. We investigate properties of tiling periodicities and design an algorithm working in O(n log(n) log log(n)) time which finds a tili...

He pointed out the coincidence of the time of biting of the mosquito Culex jatigans, with that of the crowding of the filarial embryos in the peripheral circulation. McKenzie (1881) was able to demonstrate the reversibility of the periodicity of the microfilariae by reversing the sleeping and the waking habits of the infected human host. He also noted the coincidence of the biting hours of the ...

DNA periodicity and its relationship to the formation of nucleosomes has been investigated extensively using autocorrelation and Fourier transform methods. We provide a precise treatment of the mathematical foundation for this type of analysis, and we apply the resulting method to quantify dinucleotide periodicity in several datasets. We begin by demonstrating, via simulation, the sensitivity o...

1 Description The Periodicity Theorem was proved by Raoul Bott over fifty years ago (cf. survey [3], [4], [9]) and quickly became one of the strongest tools in homotopy theory, topology of manifolds and global analysis. The original theorem asserted that homotopy groups of the linear groups GL(n,F) where F is the field of real, complex or quaternion numbers are periodic i.e. πi(GL(k,F) ' πi+nF(...