We present algorithms to count paths and cycles of a given length in a directed graph. The algorithms have time complexity O(2 n poly n) and space complexity O(poly n).

The Finite-Diierence Time Domain (FDTD) method has received considerable attention recently. The popularity of the FDTD method stems from the fact that it is not limited to a speciic geometry and it does not restrict the constitutive parameters of a scatterer. Furthermore, it provides a direct solution to problems with transient illumination, but can also be used for harmonic analysis. However,...

Abstract Inter-vehicle communication system using 720 MHz band to prevent car crashes at an intersection has been proposed in Japan recently. In this paper, the propagation characteristics at an intersection surrounded by concrete block walls in residential area were analyzed by using the FDTD method for the first time. We investigated the influence of wall thickness and source locations on the...

This paper presents time-transient polarimetric analysis for a simplified bridge model on water Surface. We extend our previous 2D time-transient analysis to 3D polarimetric scattering problem. Here the Finite-Difference Time-Domain (FDTD) method is utilized. In addition to the time-transient feature, we focus on the generating mechanism of the volume scattering component with increase of the s...

The influences of the filling rate on the photonic band gap properties of the two dimensional hex photonic crystals are investigated using the finite-difference time-domain method. When the filling rate f varies from 0.227 to 0.735 reminding the refractive index as 5, the number of the photonic band gaps decreases from 5 to 2 bands, the width of the photonic band gap between the transmit peaks ...

We present an improved perfectly matched layer (PML) for the analysis of plasmonic structures, based on the manipulation of PML parameters. Two different types of stretched coordinate PML are employed sequentially in the spatial domain: a real stretched coordinate PML to increase the effective buffer space around plasmonic structures and a complex stretched coordinate PML to absorb outgoing wav...

We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, with complexity in the Counting Hierarchy for Positivity, and in polynomi...

In light of the promising results obtained by driving a lowcomplexity digital waveguide (DW) violin model with synthetic bowing gestures , we currently explore the possibilities of combining DW and finite-difference time-domain (FDTD) frameworks to construct refined, yet efficient physical models of string quartet instruments. We extend previous approaches by combining a finite-width bow-string...

This paper exploits the homogeneity feature of the Singapore private residential condominium market and constructs matched home purchase price and rental price series using the repeated sales method. These matched series allow us to conduct time series analysis to examine the long-term present value relationship in the housing market. Three key findings are obtained. First, we fail to establish...

This paper presents a method for implementing off-grid boundary conditions (BCs) within Yee’s Finite-Difference Time-Domain (FDTD) method, without disturbing the existing uniform mesh or changing the standard FDTD code. Both perfect electric conductor (PEC) and perfect magnetic conductor (PMC) walls are considered. The field values at off-grid virtual boundaries are obtained by extrapolation of...