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.
|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.|
|We present high-resolution observations of a quiescent solar prominence that consists of a vertical and a horizontal foot encircled by an overlying spine and has ubiquitous counter-streaming mass flows. While the horizontal foot and the spine were connected to the solar surface, the vertical foot was suspended above the solar surface and was supported by a semicircular bubble structure. The bubble first collapsed, then reformed at a similar height, and finally started to oscillate for a long time. We find that the collapse and oscillation of the bubble boundary were tightly associated with a flare-like feature located at the bottom of the bubble. Based on the observational results, we propose that the prominence should be composed of an overlying horizontal spine encircling a low-lying horizontal and vertical foot, in which the horizontal foot consists of shorter field lines running partially along the spine and has ends connected to the solar surface, while the vertical foot consists of piling-up dips due to the sagging of the spine fields and is supported by a bipolar magnetic system formed by parasitic polarities (i.e., the bubble). The upflows in the vertical foot were possibly caused by the magnetic reconnection at the separator between the bubble and the overlying dips, which intruded into the persistent downflow field and formed the picture of counter-streaming mass flows. In addition, the counter-streaming flows in the horizontal foot were possibly caused by the imbalanced pressure at the both ends.|