The Predictive Power of Transition Matrices

When working with Markov chains, especially if they are of order greater than one, it is often necessary to evaluate the respective contribution of each lag of the variable under study on the present. This is particularly true when using the Mixture Transition Distribution model to approximate the true fully parameterized Markov chain. Even if it is possible to evaluate each transition matrix using a standard association measure, these measures do not allow taking into account all the available information. Therefore, in this paper, we introduce a new class of so-called "predictive power" measures for transition matrices. These measures address the shortcomings of traditional association measures, so as to allow better estimation of high-order models.

Simulation of electrothermal characteristics of MEMS energy changer under different current excitation

The simulation model of MEMS energy changer is established by using the finite element analysis software ANSYS. The electrothermal performance of MEMS energy changer under the action of different currents was simulated and analyzed. The bridge area is made of NiCr, and the shape of the bridge area is two different chamfering rectangles. The temperature distribution diagram of MEMS energy changers, the temperature change curve and the phase transition distribution diagram of the bridge region were obtained when the four current values acted on each other. The simulation results are analyzed and discussed.

Optimization of the Mixture Transition Distribution Model Using the March Package for R

Optimization of mixture models such as the mixture transition distribution (MTD) model is notoriously difficult because of the high complexity of their solution space. The best approach comprises combining features of two types of algorithms: an algorithm that can explore as completely as possible the whole solution space (e.g., an evolutionary algorithm), and another that can quickly identify an optimum starting from a set of initial conditions (for instance, an EM algorithm). The march package for the R environment is a library dedicated to the computation of Markovian models for categorical variables. It includes different algorithms that can manage the complexity of the MTD model, including an ad hoc hill-climbing procedure. In this article, we first discuss the problems related to the optimization of the MTD model, and then we show how march can be used to solve these problems; further, we provide different syntaxes for the computation of other models, including homogeneous Markov chains, hidden Markov models, and double chain Markov models.

Extraction of ALUsin(ϕ) moments from the hard exclusive π+ channel in a wide range of kinematics with CLAS

The beam-spin asymmetry (BSA) has been measured for the hard exclusive e p → e n π+ reaction over a wide range of kinematics in the deep inelastic regime. The measurements were performed with the CEBAF Large Acceptance Spectrometer (CLAS) using a 5.5 GeV polarized electron beam at Jefferson Lab (JLAB). The ϕ dependence of the BSA as well as the −t, Q 2 and xB dependence of the extracted ALU sin(ϕ) moment will be presented. For ALU sin(ϕ) a clear sign change can be observed between pions emitted in forward and backward direction with a smooth transition around 90° in CM. The results will be discussed in the context of formalisms depending on generalized parton distributions (GPDs) and transition distribution amplitudes (TDAs), which can be used to describe complementary kinematic regimes.

The Use of a Hidden Mixture Transition Distribution Model in Clustering Few but Long Continuous Sequences: An Illustration with Cognitive Skills Data

In accordance with the theme of this special issue, we present a model that indirectly discovers symmetries and asymmetries between past and present assessments within continuous sequences. More specifically, we present an alternative use of a latent variable version of the Mixture Transition Distribution (MTD) model, which allows for clustering of continuous longitudinal data, called the Hidden MTD (HMTD) model. We compare the HMTD and its clustering performance to the popular Growth Mixture Model (GMM), as well as to the recently introduced GMM based on individual case residuals (ICR-GMM). The GMM and the ICR-GMM contrast with HMTD, because they are based on an explicit change function describing the individual sequences on the dependent variable (here, we implement a non-linear exponential change function). This paper has three objectives. First, it introduces the HMTD. Second, we present the GMM and the ICR-GMM and compare them to the HMTD. Finally, we apply the three models and comment on how the conclusions differ depending on the clustering model, when using a specific dataset in psychology, which is characterized by a small number of sequences (n = 102), but that are relatively long (for the domains of psychology and social sciences: t = 20). We use data from a learning experiment, in which healthy adults (19–80 years old) were asked to perform a perceptual–motor skills over 20 trials.