topological network
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A sound ecological security network (ESN) promotes the interconnection of ecological sources, improves the pattern of ecological security, and alleviates the degradation of an ecosystem. Rapid urbanization and land use changes may lead to serious fragmentation and islanding of landscape patches and further to deep disturbance of regional ESNs. However, most studies in the recent years focused on the methodological development of ESN identification, reconstruction, and optimization, but lacked the systematic assessment of the network after its construction. The purpose of this study is to use complex network analysis to systematically assess the constructed ESN for the urban agglomeration around Hangzhou (UAHB), a rapid urbanization region in China. By integrating landscape ecology theory, graph theory, and complex network analysis, we abstracted the ESN into a topological network and developed an index system to assess the abstracted network, which was based on the structural elements of the topological network (nodes, edges, and the overall network). Our results show that the connectivity and stability of the UAHB’s ESN have been improved in the last 20 years, although isolated nodes are still existing in the ESN. Our study also shows that the network’s robustness under human disturbance has been affected more than that under non-human disturbance. Finally, we proposed five optimization strategies from the perspective of topological structure and ecological function to maintain a sustainable and well-protected ecological system.

An algebraic interpretation of multilayer networks is introduced in relation to conscious experience, brain and body. The discussion is based on a network model for undirected multigraphs with coloured edges whose elements are time-evolving multilayers, representing complex experiential brain-body networks. These layers have the ability to merge by an associative binary operator, accounting for biological composition. As an extension, they can rotate in a formal analogy to how the activity inside layers would dynamically evolve. Under consciousness interpretation, we also studied a mathematical formulation of splitting layers, resulting in a formal analysis for the transition from conscious to non-conscious activity. From this construction, we recover core structures for conscious experience, dynamical content and causal efficacy of conscious interactions, predicting topological network changes after conscious layer interactions. Our approach provides a mathematical account of coupling and splitting layers co-arising with more complex experiences. These concrete results may inspire the use of formal studies of conscious experience not only to describe it, but also to obtain new predictions and future applications of formal mathematical tools.

The significant scientific work on the development of bio-active compound databases, computational technologies, and the integration of Information Technology with Biotechnology has brought a revolution in the domain of drug discovery. These tools facilitate the medicinal plant-based in silico drug discovery, which has become the frontier of pharmacological science. In this review article, we elucidate the methodology of in silico drug discovery for the medicinal plants and present an outlook on recent tools and technologies. Further, we explore the multi-component, multi-target, and multi-pathway mechanism of the bio-active compounds with the help of Network Pharmacology, which enables us to create a topological network between drug, target, gene, pathway, and disease.

A growing area of mathematics topological data analysis (TDA) uses fundamental concepts of topology to analyze complex, high-dimensional data. A topological network represents the data, and the TDA uses the network to analyze the shape of the data and identify features in the network that correspond to patterns in the data. These patterns extract knowledge from the data. TDA provides a framework to advance machine learning’s ability to understand and analyze large, complex data. This paper provides background information about TDA, TDA applications for large data sets, and details related to the investigation and implementation of existing tools and environments.

The complex network contains non-deterministic topological spaces under an invariance structural approach to create failures on a continual link during communication. The non-lineardynamic topological structure leads to problematic threading links on network nodes due to a non-identical path to route the data. To resolve this problem, we propose atri-logical algebraic mathematical construction model called homotopy based tri-topological network spa- ce using connected component graph $(T^3-C^2G)$ under network nonlinear structure,The Algebraic Invariance Linear Queuing Theory (HA/I/LQT) is used to resolve the link failure route propagation to make improved communication performance. This homotopy reduction to reduce the complex nature to make continual link based on Quillen topological structure space under the covariance tri-topological structure. Further, this makes tri-logical structure resembles the sequence of triangle structured route space to make the nearest point of node adjustment from the nearest path. This balances the M/M/G-$T^3$-Max queuing theory on triangular weightage in routing schemes to specify the dynamic homotopy topological structure to make continuous routing links to reduce the complex nature of network routing.

In this article, we propose a new method to perform topological network sampling. Topological network sampling is a process for extracting a subset of nodes and edges from a network, such that analyses on the sample provide results and conclusions comparable to the ones they would return if run on whole structure. We need network sampling because the largest online network datasets are accessed through low-throughput application programming interface (API) systems, rendering the collection of the whole network infeasible. Our method is inspired by the literature on network backboning, specifically the noise-corrected backbone. We select the next node to explore by following the edge we identify as the one providing the largest information gain, given the topology of the sample explored so far. We evaluate our method against the most commonly used sampling methods. We do so in a realistic framework, considering a wide array of network topologies, network analysis, and features of API systems. There is no method that can provide the best sample in all possible scenarios, thus in our results section, we show the cases in which our method performs best and the cases in which it performs worst. Overall, the noise-corrected network sampling performs well: it has the best rank average among the tested methods across a wide range of applications.

AbstractThe search for new materials requires effective methods for scanning the space of atomic configurations, in which the number is infinite. Here we present an extensive application of a topological network model of solid-state transformations, which enables one to reduce this infinite number to a countable number of the regions corresponding to topologically different crystalline phases. We have used this model to successfully generate carbon allotropes starting from a very restricted set of initial structures; the generation procedure has required only three steps to scan the configuration space around the parents. As a result, we have obtained all known carbon structures within the specified set of restrictions and discovered 224 allotropes with lattice energy ranging in 0.16–1.76 eV atom−1 above diamond including a phase, which is denser and probably harder than diamond. We have shown that this phase has a quite different topological structure compared to the hard allotropes from the diamond polytypic series. We have applied the tiling approach to explore the topology of the generated phases in more detail and found that many phases possessing high hardness are built from the tiles confined by six-membered rings. We have computed the mechanical properties for the generated allotropes and found simple dependences between their density, bulk, and shear moduli.