Additive Dynamic Noise Research Articles

Performance and Robustness of Regional Image Segmentation Driven by Selected Evolutionary and Genetic Algorithms: Study on MR Articular Cartilage Images.

The analysis and segmentation of articular cartilage magnetic resonance (MR) images belongs to one of the most commonly routine tasks in diagnostics of the musculoskeletal system of the knee area. Conventional regional segmentation methods, which are based either on the histogram partitioning (e.g., Otsu method) or clustering methods (e.g., K-means), have been frequently used for the task of regional segmentation. Such methods are well known as fast and well working in the environment, where cartilage image features are reliably recognizable. The well-known fact is that the performance of these methods is prone to the image noise and artefacts. In this context, regional segmentation strategies, driven by either genetic algorithms or selected evolutionary computing strategies, have the potential to overcome these traditional methods such as Otsu thresholding or K-means in the context of their performance. These optimization strategies consecutively generate a pyramid of a possible set of histogram thresholds, of which the quality is evaluated by using the fitness function based on Kapur’s entropy maximization to find the most optimal combination of thresholds for articular cartilage segmentation. On the other hand, such optimization strategies are often computationally demanding, which is a limitation of using such methods for a stack of MR images. In this study, we publish a comprehensive analysis of the optimization methods based on fuzzy soft segmentation, driven by artificial bee colony (ABC), particle swarm optimization (PSO), Darwinian particle swarm optimization (DPSO), and a genetic algorithm for an optimal thresholding selection against the routine segmentations Otsu and K-means for analysis and the features extraction of articular cartilage from MR images. This study objectively analyzes the performance of the segmentation strategies upon variable noise with dynamic intensities to report a segmentation’s robustness in various image conditions for a various number of segmentation classes (4, 7, and 10), cartilage features (area, perimeter, and skeleton) extraction preciseness against the routine segmentation strategies, and lastly the computing time, which represents an important factor of segmentation performance. We use the same settings on individual optimization strategies: 100 iterations and 50 population. This study suggests that the combination of fuzzy thresholding with an ABC algorithm gives the best performance in the comparison with other methods as from the view of the segmentation influence of additive dynamic noise influence, also for cartilage features extraction. On the other hand, using genetic algorithms for cartilage segmentation in some cases does not give a good performance. In most cases, the analyzed optimization strategies significantly overcome the routine segmentation methods except for the computing time, which is normally lower for the routine algorithms. We also publish statistical tests of significance, showing differences in the performance of individual optimization strategies against Otsu and K-means method. Lastly, as a part of this study, we publish a software environment, integrating all the methods from this study.

Joint reconstruction and prediction\break of random dynamical systems under\break borrowing of strength.

We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo methods for the joint reconstruction and prediction of discrete time stochastic dynamical systems based on m-multiple time-series data, perturbed by additive dynamical noise. We introduce the Pairwise Dependent Geometric Stick-Breaking Reconstruction (PD-GSBR) model, which relies on the construction of an m-variate nonparametric prior over the space of densities supported over Rm. We are focusing on the case where at least one of the time-series has a sufficiently large sample size representation for an independent and accurate Geometric Stick-Breaking estimation, as defined in Merkatas et al. [Chaos 27, 063116 (2017)]. Our contention is that whenever the dynamical error processes perturbing the underlying dynamical systems share common characteristics, underrepresented data sets can benefit in terms of model estimation accuracy. The PD-GSBR estimation and prediction procedure is demonstrated specifically in the case of maps with polynomial nonlinearities of an arbitrary degree. Simulations based on synthetic time-series are presented.

On a topological closeness of perturbed Julia sets

In the present work we expand our previous work in [1] by introducing the Julia Deviation Distance and the Julia Deviation Plot in order to study the stability of the Julia sets of noise-perturbed Mandelbrot maps. We observe a power-law behaviour of the Julia Deviation Distance of the Julia sets of a family of additive dynamic noise Mandelbrot maps from the Julia set of the Mandelbrot map as a function of the noise level. Additionally, using the above tools, we support the invariance of the Julia set of a noise-perturbed Mandelbrot map under different noise realizations.

Noise-perturbed quaternionic Mandelbrot sets

Quaternionic Mandelbrot sets (abbreviated as M sets) have been a focus on the research in high-dimensional fractals. This paper explores the topological structure and the fission evolution of the quaternionic M sets under noise perturbations as well as the boundaries of their regions of stability. Our experimental results indicate that the additive dynamic noise displaces the M sets from the origin position, and the multiplicative dynamic noise shrinks the regions of stability of the M sets in a certain proportion. In addition, the influence of the output noise is mainly on the inner structure of the regions of stability. The presence of such noises leads to a decrease of the box dimension of the M sets except for the additive dynamic noise. It can be concluded that the earlier-mentioned noises have a great impact on the M sets.

ESTIMATING THE EMBEDDING DIMENSION AND DELAY TIME FROM CHAOTIC TIME SERIES WITH DYNAMIC NOISE

This paper considers the chaotic time series with additive dynamic noise. Defining the embedding dimension and delay time, we discuss their mathematical properties. A method of estimating the embedding dimension and delay time is proposed, and the consistency of the estimators is proved.

Effect of noise on the tuning properties of excitable systems

We analyze the effect of additive dynamical noise on simple phase-locking patterns in the Fitzhugh–Nagumo (FHN) two-dimensional system in the excitable regime. In the absence of noise, the response amplitude for this system displays a classical resonance as a function of driving frequency. This translates into V-shaped tuning curves, which represent the amplitude threshold for one firing per cycle as a function of forcing frequency. We show that noise opens up these tuning curves at mid-to-low frequencies. We explain this numerical result analytically using a heuristic form for the firing rate that incorporates the frequency dependence of the subthreshold voltage response. We also present stochastic phase-locking curves in the noise intensity-forcing period subspace of parameter space. The relevance of our findings for the tuning of electroreceptors of weakly electric fish and their encoding of amplitude modulations of high frequency carriers are briefly discussed. Our study shows that, in certain contexts, it is essential to take into account the frequency sensitivity of neural responses and their modification by sources of noise.

Simultaneous modeling of nonlinear deterministic and stochastic dynamics

We present a method which can simultaneously model the nonlinear deterministic and stochastic dynamics underlying an observed time series. It is formulated to treat Markov processes in continuous and discrete time. The procedure, which we call Sequin (Stochastic EQUation INference) is a generalization of that which we have developed previously for continuous time systems (Borland and Haken, 1992a,b; 1993a,b; Haken 1988). The theory behind the method as well as its numerical implementation is discussed. Simulations using Sequin to analyze finite-size time series stemming from nonlinear processes with additive and multiplicative dynamical noise in continuous time are shown. Furthermore, we show that Sequin can extract the underlying dynamics of discrete time noisy chaotic processes, such as the logistic map with additive dynamical noise. The success of the method in being able to characerize a system consisting partly of a deterministic chaotic element, and partly of a stochastic element indicates its possible application to many interesting real-world problems.