Computational Complexity

Complex systems (CS) involve many elements that interact at different scales in time and space. The challenges in modeling CS led to the development of novel computational tools with applications in a wide range of scientific areas. The computational problems posed by CS exhibit intrinsic difficulties that are a major concern in Computational Complexity Theory. This Special Issue (SI) focused on new theoretical and practical findings, and computational methods, applicable to difficult problems, whose solution demands extensive and powerful resources, approaching the limits of the available computer systems. It comprises 12 selected papers that are presented in the sequel in alphabetic order. In the paper “A Comparison of Classification Methods for Telediagnosis of Parkinson’s Disease”, Haydar Ozkan presents a novel telemedicine technology aimed to remotely detect Parkinson’s Disease by means of dysphonia features. Several feature transformation and machine-learning methods were implemented and tested [1]. The paper “A Complexity-Based Approach for the Detection of Weak Signals in Ocean Ambient Noise”, by Shashidhar Siddagangaiah, Yaan Li, Xijing Guo, Xiao Chen, Qunfei Zhang, Kunde Yang and Yixin Yang, proposes using dynamical and statistical complexity to detect the presence of weak ship noise embedded in ambient noise. They demonstrate that complexity performs better than the traditional spectrogram-based methods [2]. The paper “Empirical Laws and Foreseeing the Future of Technological Progress”, by António M. Lopes, J. A. Tenreiro Machado and Alexandra M. Galhano, revisits the Moore’s law (ML) as one of many empirical expressions that is used to characterize natural and artificial phenomena. The ML addresses technological progress and is expected to predict future trends. Data series of multiple sources, available for scientific and computational processing, can be described by means of mathematical expressions that, in some cases, follow simple expressions and empirical laws. However, the extrapolation toward the future is considered with skepticism by the scientific community, particularly in the case of phenomena involving complex behavior. The authors address these issues in the light of entropy and pseudo-state space. Their statistical and dynamical techniques lead to a more assertive perspective on the adoption of a given candidate law [3]. In “Entropy Complexity and Stability of a Nonlinear Dynamic Game Model with Two Delays”, Zhihui Han, Junhai Ma, Fengshan Si and Wenbo Ren propose a duopoly game model with double delays in hydropower market. They analyze the influence of time delay parameters on the system complexity [4]. In “Normalized Minimum Error Entropy Algorithm with Recursive Power Estimation”, Namyong Kim and Kihyeon Kwon present a normalized version of the minimum error entropy