Rumination, post-traumatic growth, and distress : structural equation modelling with cancer survivors

Objective Theoretical models of post-traumatic growth (PTG) have been derived in the general trauma literature to describe the post-trauma experience that facilitates the perception of positive life changes. To develop a statistical model identifying factors that are associated with PTG, structural equation modelling (SEM) was used in the current study to assess the relationships between perception of diagnosis severity, rumination, social support, distress, and PTG. Method A statistical model of PTG was tested in a sample of participants diagnosed with a variety of cancers (N=313). Results An initial principal components analysis of the measure used to assess rumination revealed three components: intrusive rumination, deliberate rumination of benefits, and life purpose rumination. SEM results indicated that the model fit the data well and that 30% of the variance in PTG was explained by the variables. Trauma severity was directly related to distress, but not to PTG. Deliberately ruminating on benefits and social support were directly related to PTG. Life purpose rumination and intrusive rumination were associated with distress. Conclusions The model showed that in addition to having unique correlating factors, distress was not related to PTG, thereby providing support for the notion that these are discrete constructs in the post-diagnosis experience. The statistical model provides support that post-diagnosis experience is simultaneously shaped by positive and negative life changes and that one or the other outcome may be prevalent or may occur concurrently. As such, an implication for practice is the need for supportive care that is holistic in nature.

An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

A stochastic model for natural feature representation

This paper presents a robust stochastic model for the incorporation of natural features within data fusion algorithms. The representation combines Isomap, a non-linear manifold learning algorithm, with Expectation Maximization, a statistical learning scheme. The representation is computed offline and results in a non-linear, non-Gaussian likelihood model relating visual observations such as color and texture to the underlying visual states. The likelihood model can be used online to instantiate likelihoods corresponding to observed visual features in real-time. The likelihoods are expressed as a Gaussian Mixture Model so as to permit convenient integration within existing nonlinear filtering algorithms. The resulting compactness of the representation is especially suitable to decentralized sensor networks. Real visual data consisting of natural imagery acquired from an Unmanned Aerial Vehicle is used to demonstrate the versatility of the feature representation.

Discovering characteristics of stochastic collections of process models

Process models in organizational collections are typically modeled by the same team and using the same conventions. As such, these models share many characteristic features like size range, type and frequency of errors. In most cases merely small samples of these collections are available due to e.g. the sensitive information they contain. Because of their sizes, these samples may not provide an accurate representation of the characteristics of the originating collection. This paper deals with the problem of constructing collections of process models, in the form of Petri nets, from small samples of a collection for accurate estimations of the characteristics of this collection. Given a small sample of process models drawn from a real-life collection, we mine a set of generation parameters that we use to generate arbitrary-large collections that feature the same characteristics of the original collection. In this way we can estimate the characteristics of the original collection on the generated collections.We extensively evaluate the quality of our technique on various sample datasets drawn from both research and industry.

Shrinking neighborhood evolution : a novel stochastic algorithm for numerical optimization

Focusing on the conditions that an optimization problem may comply with, the so-called convergence conditions have been proposed and sequentially a stochastic optimization algorithm named as DSZ algorithm is presented in order to deal with both unconstrained and constrained optimizations. The principle is discussed in the theoretical model of DSZ algorithm, from which we present the practical model of DSZ algorithm. Practical model efficiency is demonstrated by the comparison with the similar algorithms such as Enhanced simulated annealing (ESA), Monte Carlo simulated annealing (MCS), Sniffer Global Optimization (SGO), Directed Tabu Search (DTS), and Genetic Algorithm (GA), using a set of well-known unconstrained and constrained optimization test cases. Meanwhile, further attention goes to the strategies how to optimize the high-dimensional unconstrained problem using DSZ algorithm.

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Maximum-likelihood estimates of the parameters of stochastic differential equations are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed-form expression for the transitional probability density function of the process is not available. As a result, a large number of competing estimation procedures have been proposed. This article provides a critical evaluation of the various estimation techniques. Special attention is given to the ease of implementation and comparative performance of the procedures when estimating the parameters of the Cox–Ingersoll–Ross and Ornstein–Uhlenbeck equations respectively.