Search

Searching over a sorted list is a classical problem in computer science. Binary Search takes at most log 2 ⁡ n + 1 tries to find an item in a sorted list of size n. Interpolation Search achieves an average time complexity of O (log ⁡ log ⁡ n ) for uniformly distributed data. Hybrids of Binary Search and Interpolation Search are also available to handle data with unknown distributions. This paper analyzes the computation cost of these methods and shows that interpolation can significantly affect their performance—accordingly, a new method, Interpolation Once Binary Search (IOBS), is proposed. The experimental results show that IOBS outperforms the hybrids of Binary Search and Interpolation Search for nonuniformly distributed data. [ABSTRACT FROM AUTHOR]

The ordered weighted averaging (OWA) operator was proposed by Yager back in 1988 and constitutes a parameterized family of aggregation functions between the minimum and the maximum. The purpose of this paper is to perform a bibliometric review of this aggregation operator during the last 35 years through the Web of Science (WoS) Core Collection database and the Visualization of Similarities (VOS) viewer software. The results show that the OWA operator is an increasingly popular aggregation operator, especially in Computer Science. The results also allow the assertion that Yager, as expected, is still the most influential and productive author. Moreover, the study reveals that institutions from over 80 countries have contributed to OWA research, highlighting the high presence of Chinese universities and the emergence of Pakistani ones. Other interesting findings are presented to provide a comprehensive and up-to-date analysis of the OWA operator literature. [ABSTRACT FROM AUTHOR]

Starting from the contribution of such thinkers as the famous Giordano Bruno (1583) and the great mathematician and physicist Henri Poincaré (1889) and the surprising discovery of the meteorologist Edward Lorenz (1963), we consider the expansion of the mathematics of chaos in this article, paying attention to topology, qualitative geometry, and Catastrophe Theory, on the one hand, and addressing the possibilities derived from the new Computer Science as Quantum Algorithms and the advances in Artificial Intelligence, on the other. We especially highlight the section on computing chaos, which we consider to be new calculation and analysis instruments, such as machine learning and its algorithm called reservoir computing, through which we can know the dynamics of a chaotic system. With past data, with equations like Karamoto–Sivashinsky, one can improve predictions of the system eight times further ahead than in previous methods. Integrating the machine learning approach and traditional model-based prediction, one could obtain accurate predictions twelve Lyapunov times. As we know, in the framework of chaos theory, it is habitually accepted that the idea of long-term prediction seems impossible because we live under a veil of uncertainty. But with technological advances, the landscape begins to change, both in chaos theory and in its applications, especially in the field of economics, to which we devote particular attention, carrying out as an example the analysis of the evolution of the Madrid Stock Exchange in the 2006–2013 crisis. Above all this, a reflection of a general nature is necessary to enlighten us on the possibility of opening a new horizon. [ABSTRACT FROM AUTHOR]