Introduction Chaotic systems are governed by deterministic dynamics, but exhibit sensitive dependence on initial conditions.The Lyapunov time horizon \( T_L \) is the inverse of the largest Lyapunov exponent \( \lambda_{\max} \), and has generally been regarded as the limit of deterministic predictability for free-running trajectories. Beyond this horizon, exponential error growth destroys pointwise forecast…
Quantization can mathematically be defined as a process of mapping a continuous set of values (X ⊆ R) to a discrete set (Q ⊂ R) with a finite number of values |Q|. It can be expressed as the following function: Q(x) = qi, for x ∈ Si ⊂ X, where each subset Si (called a…
Volatility in financial markets, major fluctuations in weather conditions, the outbreak of infectious diseases, the unpredictability of interactions among different animal species, and intermittent failures of power grids are phenomena from diverse fields but have two things in common. Firstly, they are manifestations of high-to-extreme uncertainty, and secondly, the environments in which they operate are…
Minimum Spanning Tree (MST) offers powerful applications in a wide range of domains, including circuit design, computer science, electrical grids, financial markets, and telecom networks. They are also indirectly leveraged (e.g., as algorithm subroutines) for solving other critical problems, such as the Traveling Salesman or Minimum Cut problems. Broadly speaking, MST aims to connect a set…