Dual Time-Stepping Using Second Derivatives

First and Second Derivatives in Time Series Classification Using DTW

In our previous work [2] we developed some new distance function based on a derivative and showed that our algorithm is efficient. In contrast to well-known measures from the literature, our approach considers the general shape of a time series rather than point-to-point function comparison. The new distance was used in classification with the nearest neighbor rule. Now, we improve on our previ...

Option Valuation using Fourier Space Time Stepping

It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jumpdiffusion and Lévy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the resulting pricing problem requires solving a more difficult partial-integro differential equation (PIDE) and although several approaches for solving the PIDE have...

Pricing using Fourier Space Time - stepping Framework

First Derivatives versus Second Derivatives

Suppose we continue to consider our two systems, and ask what happens if we allow them to exchange volume as well as energy? (We’re placing them in mechanical as well as thermal contact.) Again, the total entropy must be a maximum with respect to exchanges of energy and exchanges of volume. Working through similar mathematics, we find an expression for the change in total entropy and insist tha...

Analysis of Human Stepping Time Intervals Using Acceleration Sensors

Gait analysis plays an important role in characterizing individuals and each condition and gait analysis systems have been developed using various devices or instruments. However, most systems do not catch synchronous stepping actions between right foot and left foot. For obtaining a precise gait pattern, a synchronous walking sensing system is developed, in which a pair of acceleration and ang...