We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from Goeritz matrix that link. Further, we show how Jones polynomial can be recovered when corresponding checkerboard surface is orientable, or more information known about its Gordon–Litherland form. In process develop theory matrices cographic matroids, which extends to any symmetric integer matrix. place thi...

Two-dimensional depth-resolved Jones-matrix images of scattering biological tissues were measured with novel double-source double-detector polarization-sensitive optical coherence tomography (OCT). The Jones matrix can be determined in a single scan with this OCT system. The experimental results show that this system can be effectively applied to the measurement of soft tissues, which are less ...

Modern digital crosscorrelators permit the simultaneous measurement of all four Stokes parameters. However, the results must be calibrated to correct for the polarization transfer function of the receiving system. The transfer function for any device can be expressed by its Mueller matrix. We express the matrix elements in terms of fundamental system parameters that describe the voltage transfe...

The polarization-transforming properties of rotational prisms are analyzed with polarized light by using the Jones calculus and the exact ray-trace. A general expression of the Jones matrix for a rotational prism is derived, incorporating an explicit dependence on the image-rotation angle or the wave-front-rotation angle. The Jones matrix for the Pechan, Dove, Reversion, and Delta prisms is der...

We carry out a statistical characterization of Jones matrix eigenvalues and eigenmodes to gain deeper insight into recently proposed fiber models based on Jones matrix spectral decomposition. A set of linear dynamic equations for the Pauli coordinates of the Jones matrix is established. Using stochastic calculus, we determine the joint distribution of the retardation angle of the eigenmodes and...

Smit and Frenkel’ have shown that the phase diagram of the two-dimensional Lennard-Jones fluid depends largely on the details of the truncation of the potential. In this Note, Gibbs-ensemble calculations are reported for the three-dimensional Lennard-Jones fluid. As expected, the phase diagram for this system also depends significantly on the details of the truncation. The Lennard-Jones potenti...

Eigenfunction methods for mapping high dimensional data sets into lower dimensional spaces are useful in a broad range of applications. In particular, a recent paper by Jones et al [2] shows that eigenfunctions of the Laplacian operator give a good local coordinate system under very general conditions. Here I outline the proof of the theorem and explore its use in cryo-electron microscopy.