A study was made of seasonality in twin birth rate in Denmark between 1977 and 1984. We studied all twin births (N = 45,550) in all deliveries (N = 3,679,932) during that period. Statistical analysis using a simple harmonic sinusoidal model provided no evidence for seasonality. However, sequential polynomial analysis disclosed a significant fit to a fifth order polynomial curve with peaks in tw...

For every polynomial f of degree n with no double roots, there is an associated family C(f) of harmonic algebraic curves, fibred over the circle, with at most n−1 singular fibres. We study the combinatorial topology of C(f) in the generic case when there are exactly n − 1 singular fibres. In this case, the topology of C(f) is determined by the data of an n-tuple of noncrossing matchings on the ...

We give a method of decomposing bundle-valued polynomials compatible with the action of the Lie group Spin(n), where important tools are Spin(n)-equivariant operators and their spectral decompositions. In particular, the top irreducible component is realized as an intersection of kernels of these operators. 0 Introduction Spherical harmonic polynomials or spherical harmonics are polynomial solu...

this paper presents a new control methodology for active power filters that provide an adaptive online harmonic estimation with partial and selective harmonic reduction schemes, which has been implemented within an integrated controller. the proposed approach is to provide partial and selective reduction of those individual harmonics which exceed the recommended levels as set by regulatory bodi...

We demonstrate an algebraic construction of all the simultaneous eigenfunctions of the conserved operators for distinguishable particles governed by the Calogero Hamiltonian. Our construction is completely parallel to the construction of the Fock space for decoupled quantum harmonic oscillators. The simultaneous eigenfunction does not coincide with the non-symmetric Hi-Jack polynomial, which sh...

This paper presents an innovative approach to investigate the information encoding taking place in the visual pathway, particularly the retinal pathway. Gabor time-frequency (TF) transformation is applied to the spatio-temporal spike trains from the layers of the retinal pathway, corresponding to input object stimuli varying in shape, orientation & distance. These spike trains are generated by ...

We present a 2D high-order and easily accessible immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method to solve fully nonlinear wave-structure interaction problems in marine hydrodynamics using potential-flow theory. To reduce the total number of cells without losing accuracy, quad-tree refinements are employed close free-surface structure boundaries. The is simpler implement tha...

We study the class of polynomial threshold functions using harmonic analysis and apply the results to derive lower bounds related to ACo functions. A Boolean function is polynomial threshold if it can be represented as a sign function of a sparse polynomial (one that consists of a polynomial number of terms). Our main result is that the class of polynomial threshold functions can be characteriz...