Christopher W. Kulp

Using forbidden ordinal patterns to detect determinism in irregularly sampled time series

It is known that when symbolizing a time series into ordinal patterns using the Bandt-Pompe (BP) methodology, there will be ordinal patterns called forbidden patterns that do not occur in a deterministic series. The existence of forbidden patterns can be used to identify deterministic dynamics. In this paper, the ability to use forbidden patterns to detect determinism in irregularly sampled time series is tested on data generated from a continuous model system. The study is done in three parts. First, the effects of sampling time on the number of forbidden patterns are studied on regularly sampled time series. The next two parts focus on two types of irregular-sampling, missing data and timing jitter. It is shown that forbidden patterns can be used to detect determinism in irregularly sampled time series for low degrees of sampling irregularity (as defined in the paper). In addition, comments are made about the appropriateness of using the BP methodology to symbolize irregularly sampled time series.

Quantum tunneling recombination in a system of randomly distributed trapped electrons and positive ions

During the past 10 years, quantum tunneling has been established as one of the dominant mechanisms for recombination in random distributions of electrons and positive ions, and in many dosimetric materials. Specifically quantum tunneling has been shown to be closely associated with two important effects in luminescence materials, namely long term afterglow luminescence and anomalous fading. Two of the common assumptions of quantum tunneling models based on random distributions of electrons and positive ions are: (a) An electron tunnels from a donor to the nearest acceptor, and (b) the concentration of electrons is much lower than that of positive ions at all times during the tunneling process. This paper presents theoretical studies for arbitrary relative concentrations of electrons and positive ions in the solid. Two new differential equations are derived which describe the loss of charge in the solid by tunneling, and they are solved analytically. The analytical solution compares well with the results of Monte Carlo simulations carried out in a random distribution of electrons and positive ions. Possible experimental implications of the model are discussed for tunneling phenomena in long term afterglow signals, and also for anomalous fading studies in feldspars and apatite samples.

Using ordinal partition transition networks to analyze ECG data

Electrocardiogram (ECG) data from patients with a variety of heart conditions are studied using ordinal pattern partition networks. The ordinal pattern partition networks are formed from the ECG time series by symbolizing the data into ordinal patterns. The ordinal patterns form the nodes of the network and edges are defined through the time ordering of the ordinal patterns in the symbolized time series. A network measure, called the mean degree, is computed from each time series-generated network. In addition, the entropy and number of non-occurring ordinal patterns (NFP) is computed for each series. The distribution of mean degrees, entropies, and NFPs for each heart condition studied is compared. A statistically significant difference between healthy patients and several groups of unhealthy patients with varying heart conditions is found for the distributions of the mean degrees, unlike for any of the distributions of the entropies or NFPs.

Using missing ordinal patterns to detect nonlinearity in time series data

The number of missing ordinal patterns (NMP) is the number of ordinal patterns that do not appear in a series after it has been symbolized using the Bandt and Pompe methodology. In this paper, the NMP is demonstrated as a test for nonlinearity using a surrogate framework in order to see if the NMP for a series is statistically different from the NMP of iterative amplitude adjusted Fourier transform (IAAFT) surrogates. It is found that the NMP works well as a test statistic for nonlinearity, even in the cases of very short time series. Both model and experimental time series are used to demonstrate the efficacy of the NMP as a test for nonlinearity.

Simulations of isothermal processes in the semilocalized transition (SLT) model of thermoluminescence (TL)

Semilocalized transition (SLT) kinetic models for thermoluminescence (TL) contain characteristics of both a localized transition (LT) and of a single trap model. TL glow curves within SLT models typically contain contain two TL peaks; the first peak corresponds to the intra-pair luminescence due to LTs and the second TL peak corresponds to delocalized transitions involving the conduction band (CB). The latter delocalized TL peak has also been found to exhibit non-typical double-peak structure, in which the main TL peak is accompanied by a smaller peak called the displacement peak. This paper describes the simulation of isothermal luminescence signals using a previously published SLT model. It is found that these simulated isothermal signals exhibit several unusual time characteristics. Isothermal signals associated with the LTs follow first order kinetics and are therefore described by single decaying exponentials. However, isothermal signals associated with delocalized transitions show a non-typical complex structure characterized by several time regions with different decay characteristics. For certain values of the parameters in the SLT model the isothermal signals can also exhibit non-monotonic behaviour as a function of time. Another notable result from the simulations is that isothermal currents (which are proportional to the concentration of electrons in the CB) can persist for very long periods of time, even after the apparent termination of the isothermal luminescence signals. It is concluded that isothermal processes described by the SLT model depend strongly on the presence of SLTs, in contrast to previous studies using Monte Carlo simulations, which showed a weak interdependence of these phenomena. The simulations in this paper suggest that isothermal experiments offer a sensitive method for detecting the presence of SLTs in a dosimetric material.

Using Mathematica to Compose Music and Analyze Music with Information Theory

In this paper we present two case studies for the application of the technical computing software Mathematica in the domain of music creation and music research. The first section describes an experimental interface for the usage of random points, parametric curves and other mathematical objects in the role of three-dimensional musical scores. Similar to the technology of the old-fashioned player piano roles which encode any arbitrary piece for mechanical player piano in three basic dimensions (onset, pitch, duration) we provide an interface where a 3-dimensional score is created, visualized and played. With this software the scores can be created with the assistance of a rich arsenal of mathematical functions and also the sound of each single note can be controlled in terms of mathematical functions. The aim of this software is the creation of experimental musical pieces which explore the musical potential of certain mathematical functions. In this paper we restrict ourselves to sketch the interface. The more interesting aspects, namely the ‘musicality’ of concrete sonifications of certain mathematical objects, are subject to our live demonstrations in Berlin.

When Two Balls Are Just One.

A camcorder can be a powerful tool in pedagogical settings, such as in an introductory physics course or in introducing undergraduates to data collection. In this paper, we discuss our experience using a Panasonic PV-GS150 digital camcorder to analyze the motion of a falling steel ball, with the goal of determining the acceleration due to gravity, g = 9.80 m/s2. When performing this simple experiment, an interesting technical issue arose that led to an excellent teaching opportunity that is based on an unexpected and intriguing method of computing g.