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## 1. chinaXiv:202201.00057 [pdf]

Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory and exobiology. Most measures of these quantities, such as Shannon entropy and related complexity measures, are only defined for objects drawn from a statistical ensemble and cannot be computed for single objects. We attempt to fill this gap by introducing the notion of a ladderpath which describes how an object can be decomposed into an hierarchical structure using repetitive elements. From the ladderpath two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath theory can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and origins of life. The ladderpath theory provides a novel characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.

## 2. chinaXiv:202110.00056 [pdf]

Subjects: Mathematics >> Applied Mathematics
Subjects: Information Science and Systems Science >> Other Disciplines of Information Science and Systems Science

 The shortest path problem (SPP) is a classic problem and appears in a wide range of applications. Although a variety of algorithms already exist, new advances are still being made, mainly tuned for particular scenarios to have better performances. As a result, they become more and more technically complex and sophisticated. Here we developed a novel nature-inspired algorithm to compute all possible shortest paths between two nodes in a graph: Resonance Algorithm (RA), which is surprisingly simple and intuitive. Besides its simplicity, RA turns out to be much more time-efficient for large-scale graphs than the extended Dijkstra's algorithm (such that it gives all possible shortest paths). Moreover, RA can handle any undirected, directed, or mixed graphs, irrespective of loops, unweighted or positively-weighted edges, and can be implemented in a fully decentralized manner. These good properties ensure RA a wide range of applications.