Utility-service provision as an example of a complex system

Utility–service provision is a process in which products are transformed by appropriate devices into services satisfying human needs and wants. Utility products required for these transformations are usually delivered to households via separate infrastructures, i.e., real-world networks such as, e.g., electricity grids and water distribution systems. owever, provision of utility products in appropriate quantities does not itself guarantee hat the required services will be delivered because the needs satisfaction task requires not only utility products but also fully functional devices. Utility infrastructures form complex networks and have been analyzed as such using complex network theory. However, little research has been conducted to date on integration of utilities and associated services within one complex network. This paper attempts to fill this gap in knowledge by modelling utility–service provision within a household with a hypergraph in which products and services are represented with nodes whilst devices are hyperedges spanning between them. Since devices usually connect more than two nodes, a standard graph would not suffice to describe utility–service provision problem and therefore a hypergraph was chosen as a more appropriate representation of the system. This paper first aims to investigate the properties of hypergraphs, such as cardinality of nodes, betweenness, degree distribution, etc. Additionally, it shows how these properties can be used while solving and optimizing utility– service provision problem, i.e., constructing a so-called transformation graph. The transformation graph is a standard graph in which nodes represent the devices, storages for products, and services, while edges represent the product or service carriers. Construction of different transformation graphs to a defined utility– service provision problem is presented in the paper to show how the methodology is applied to generate possible solutions to provision of services to households under given local conditions, requirements and constraints

Maximizing Output and Recognizing Autocatalysis in Chemical Reaction Networks is NP-Complete

Background: A classical problem in metabolic design is to maximize the production of desired compound in a given chemical reaction network by appropriately directing the mass flow through the network. Computationally, this problem is addressed as a linear optimization problem over the "flux cone". The prior construction of the flux cone is computationally expensive and no polynomial-time algorithms are known. Results: Here we show that the output maximization problem in chemical reaction networks is NP-complete. This statement remains true even if all reactions are monomolecular or bimolecular and if only a single molecular species is used as influx. As a corollary we show, furthermore, that the detection of autocatalytic species, i.e., types that can only be produced from the influx material when they are present in the initial reaction mixture, is an NP-complete computational problem. Conclusions: Hardness results on combinatorial problems and optimization problems are important to guide the development of computational tools for the analysis of metabolic networks in particular and chemical reaction networks in general. Our results indicate that efficient heuristics and approximate algorithms need to be employed for the analysis of large chemical networks since even conceptually simple flow problems are provably intractable

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

A graph database for feature characterization of dislocation networks

Three-dimensional dislocation networks control the mechanical properties such as strain hardening of crystals. Due to the complexity of dislocation networks and their temporal evolution, analysis tools are needed that fully resolve the dynamic processes of the intrinsic dislocation graph structure. We propose the use of a graph database for the analysis of three-dimensional dislocation networks obtained from discrete dislocation dynamics simulations. This makes it possible to extract (sub-)graphs and their features with relative ease. That allows for a more holistic view of the evolution of dislocation networks and for the extraction of homogenized graph features to be incorporated into continuum formulation. As an illustration, we describe the static and dynamic analysis of spatio-temporal dislocation graphs as well as graph feature analysis

Graph Learning and Its Applications: A Holistic Survey

Graph learning is a prevalent domain that endeavors to learn the intricate relationships among nodes and the topological structure of graphs. These relationships endow graphs with uniqueness compared to conventional tabular data, as nodes rely on non-Euclidean space and encompass rich information to exploit. Over the years, graph learning has transcended from graph theory to graph data mining. With the advent of representation learning, it has attained remarkable performance in diverse scenarios, including text, image, chemistry, and biology. Owing to its extensive application prospects, graph learning attracts copious attention from the academic community. Despite numerous works proposed to tackle different problems in graph learning, there is a demand to survey previous valuable works. While some researchers have perceived this phenomenon and accomplished impressive surveys on graph learning, they failed to connect related objectives, methods, and applications in a more coherent way. As a result, they did not encompass current ample scenarios and challenging problems due to the rapid expansion of graph learning. Different from previous surveys on graph learning, we provide a holistic review that analyzes current works from the perspective of graph structure, and discusses the latest applications, trends, and challenges in graph learning. Specifically, we commence by proposing a taxonomy from the perspective of the composition of graph data and then summarize the methods employed in graph learning. We then provide a detailed elucidation of mainstream applications. Finally, based on the current trend of techniques, we propose future directions.Comment: 20 pages, 7 figures, 3 table