A framework for state-based time-series analysis and prediction

Time-series analysis and prediction play an important role in state-based systems that involve dealing with varying situations in terms of states of the world evolving with time. Generally speaking, the world in the discourse persists in a given state until something occurs to it into another state. This paper introduces a framework for prediction and analysis based on time-series of states. It takes a time theory that addresses both points and intervals as primitive time elements as the temporal basis. A state of the world under consideration is defined as a set of time-varying propositions with Boolean truth-values that are dependent on time, including properties, facts, actions, events and processes, etc. A time-series of states is then formalized as a list of states that are temporally ordered one after another. The framework supports explicit expression of both absolute and relative temporal knowledge. A formal schema for expressing general time-series of states to be incomplete in various ways, while the concept of complete time-series of states is also formally defined. As applications of the formalism in time-series analysis and prediction, we present two illustrating examples.

Parallel implementation of the recurrence method for computing the power-spectral density of thin avalanche photodiodes

A simulation program has been developed to calculate the power-spectral density of thin avalanche photodiodes, which are used in optical networks. The program extends the time-domain analysis of the dead-space multiplication model to compute the autocorrelation function of the APD impulse response. However, the computation requires a large amount of memory space and is very time consuming. We describe our experiences in parallelizing the code using both MPI and OpenMP. Several array partitioning schemes and scheduling policies are implemented and tested Our results show that the OpenMP code is scalable up to 64 processors on an SGI Origin 2000 machine and has small average errors.

Parallel bandwidth characteristics calculations for thin avalanche photodiodes on a SGI Origin 2000 supercomputer

An important factor for high-speed optical communication is the availability of ultrafast and low-noise photodetectors. Among the semiconductor photodetectors that are commonly used in today’s long-haul and metro-area fiber-optic systems, avalanche photodiodes (APDs) are often preferred over p-i-n photodiodes due to their internal gain, which significantly improves the receiver sensitivity and alleviates the need for optical pre-amplification. Unfortunately, the random nature of the very process of carrier impact ionization, which generates the gain, is inherently noisy and results in fluctuations not only in the gain but also in the time response. Recently, a theory characterizing the autocorrelation function of APDs has been developed by us which incorporates the dead-space effect, an effect that is very significant in thin, high-performance APDs. The research extends the time-domain analysis of the dead-space multiplication model to compute the autocorrelation function of the APD impulse response. However, the computation requires a large amount of memory space and is very time consuming. In this research, we describe our experiences in parallelizing the code in MPI and OpenMP using CAPTools. Several array partitioning schemes and scheduling policies are implemented and tested. Our results show that the code is scalable up to 64 processors on a SGI Origin 2000 machine and has small average errors.