In recent years, with the development of automated microscopy technologies, the volume and complexity of image data on gene expression have increased tremendously. The only way to analyze quantitatively and comprehensively such biological data is by developing and applying new sophisticated mathematical approaches. Here, we present extensions of 2D singular spectrum analysis (2D-SSA) for applic...

Let A be a set of trivariate irreducible integral polynomials and let D be an A-invariant cylindrical algebraic decomposition (cad) of three-dimensional space. This paper presents a new algorithm for determining the interstack adjacencies in D over a given non-nullifying (for A) 0-cell, 1-cell adjacency in the cad D 0 of the plane induced by D. We show that this new adjacency algorithm for thre...

To overcome the Courant limit on the time step size of the conventional finite-difference time-domain (FDTD) method, some weakly conditionally stable and unconditionally stable FDTD methods have been developed recently. To analyze the relations between these methods theoretically, they are all viewed as approximations of the conventional FDTD scheme in present discussion. The errors between the...

The time-to-frequency-domain conversion is often required in many applications of the finite-difference time-domain (FDTD) method. This paper presents a new FDTD time-to-frequencydomain conversion algorithm based on the optimization of nonuniform fast Fourier transform (NUFFT) with several redundancy-reduction techniques. The proposed algorithm can perform the FDTD conversion at multiple desire...

Wave propagation in a double negative (DNG) medium, i.e., a medium having negative permittivity and negative permeability, is studied both analytically and numerically. The choices of the square root that leads to the index of refraction and the wave impedance in a DNG medium are determined by imposing analyticity in the complex frequency domain, and the corresponding wave properties associated...

This paper presents an unconditionally stable leapfrog alternating-direction-implicit finite-difference time-domain (ADIFDTD) method for lossy media. Conductivity terms of lossy media are incorporated into the leapfrog ADI-FDTD method in an analogous manner as the conventional explicit FDTD method since the leapfrog ADI-FDTD method is a perturbation of the conventional explicit FDTD method. Imp...

Traditional finite difference time domain (FDTD) is classic numerical method for solving wave propagation problems such as electromagnetic wave, seismic wave and acoustic wave. As for airborne GPR simulation, modeling space is so large that memory consuming is pretty huge; on the other hand, the area between source antenna and ground surface is homogenous medium – air, where analytic solution c...