Complex Theory Research Articles

ON TOPOLOGICAL COMPLEXITY OF GORENSTEIN SPACES

In this paper, using Sullivan's approach to rational homotopy theory of simply-connected finite type CW complexes, we endow the $\mathbb{Q}$-vector space $\mathcal{E}xt_{C^{\ast}(X;\mathbb{Q})}(\mathbb{Q}, C^{\ast}(X;\mathbb{Q}))$ with a graded commutative algebra structure. This leads us to introduce the $\mathcal{E}xt$-version of higher (resp. module, homology) topological complexity of $X_0$, the rationalization of $X$ (resp. of $X$ over $\mathbb{Q}$). We then compare these invariants and their respective ordinary ones for Gorenstein spaces.
 We also highlight, in this context, the benefit of Adams-Hilton models over a field of odd characteristics especially through two cases, the first one when the space is a $2$-cell CW-complex and the second one when it is a suspension.

Being My Neighbours’ Keeper: Interrogating the Management of the Terrorism–Migration Nexus in West Africa Sub-Region

Cooperation among neighbouring countries is critical for managing security threats like terrorism and migration. Despite their proximity, states often struggle to cooperate for various reasons, including a lack of solidarity, which can harm regional peace and stability. This study uses qualitative research to examine West African nations’ cooperation in combating Islamist terrorism and aiding affected individuals across borders. Applying regional security complex theory and transnationalism, we assess how terrorism-driven migration impacts regional security, peace and development, highlighting cooperation challenges. This study redefines ‘neighbour’ in international relations, emphasising proactive international solidarity and shared responsibility to address insecurity.

The theory of the regional security complex — Case study, the riparian states of the Black Sea

Known in Antiquity as the Pontus Euxinus, the Black Sea has been the bridge between European and Eastern civilizations since ancient times. Possessing a multi-varied mosaic of cultures, the Black Sea area has facilitated over the centuries, both the development of commercial and political relations and the maintenance and production of conflicts, being like the Sword of Damocles. Located at the intersection of three security zones (Euro-Atlantic, Russian, and Eastern), the Black Sea is currently a vulnerable space in terms of security. Heir to Byzantine culture, most of the riparian states have a complicated internal and external policy, being caught between the idealism of the Western world and the realism of the Eastern European space. At the same time, the revisionism of the Russian Federation and Turkey in terms of foreign policy will also mean a change in the dynamics of the relations between the states bordering the Black Sea, which could result either in its return to the status of a Russian lake or in a division of the spheres of influence between the Russian Federation and Turkey. In this sense, in order to analyze the future security dynamics of the riparian states, we used the theory of the regional security complex, which we consider very appropriate in our study of the Black Sea region.

Multimodal knowledge graph construction for risk identification in water diversion projects

The operation risks of water diversion projects involve numerous influencing factors, complex interrelationships, and heterogeneous data from multiple sources. This study presents a multimodal knowledge graph construction approach for water diversion projects, aiming to comprehend and identify the key risks associated with engineering operation and their propagation patterns. Utilizing term-masked pre-trained language models enhances comprehension of specialized terminology and identifies risk entities within the text. Employing high-order residual convolutional neural networks improves the processing capability for complex graph data, extracting risk information from images. Aggregating multimodal knowledge graphs based on the semantic relationships among entities and conditional probability to determine the coupled features of different risks. Employing complex network theory, analyze node degree and betweenness centrality to identify the diffusion effects and propagation levels of risks. The results indicate that the knowledge extraction accuracy of our method is high (with an average F1 score of 95.85%), enabling the qualitative analysis and quantitative calculation of operational risks in engineering. Relevant studies can effectively enhance the reliability of engineering safety management and reduce the impact of engineering risks on water supply security.

John Charlton Polkinghorne, 1930–2021

AbstractJohn Charlton Polkinghorne was very successful in two careers: as a theoretical physicist and as a theologian. As a physicist at Cambridge, he was one of the pioneers of applying complex variable theory to the study of properties of scattering amplitudes and contributed to the theory of strong (nuclear) interactions. In addition, he was a successful teacher, with many of his students gaining senior academic positions in universities. A postmaster's son from Weston‐super‐Mare, he married Ruth Martin, also a mathematics student at Cambridge. They had three children. John surprised many, apart from those who knew him closely, by resigning from his Chair at Cambridge to study for ordination in the Anglican Church. He became an influential theologian devoting much study to the interaction of science and religion. His position might be summed up in a phrase he was fond of, “God holds the Universe in being”, which was John's solution to what is called the fine‐tuning problem in physics: that the parameters of Nature turn out to be exquisitely adjusted to allow our universe to exist in its richness. John was a formidable administrator, became President of Queens' College, Cambridge, and chaired UK government committees on research ethics.

Unimodular Plebański gravity

We present new action principles for unimodular gravity, defined in the chiral Plebański formulation based on (complex) two-forms and a complex SO(3) connection. In these theories, just as in their analogues in the metric formulation, the cosmological constant does not take a prescribed value but is an integration constant whose value can differ between different (classical) solutions. We discuss some subtleties when identifying Lorentzian solutions in the generally complex theory, and show how these theories can be reduced to a ‘pure connection’ form similar to Krasnov’s pure connection formalism for general relativity.

Higher-Order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs. Codes and datasets are available at https://github.com/Yiminghh/HiGCN.

Thermal analysis of a perforated laminated plate with multiple random elliptical holes by specially formulated finite elements

The high-efficient and accurate analysis of anisotropic composite media weakened by a large amount of holes or cuts is still a great challenge in practical composite engineering. In this work, specially-proposed polygonal finite element enclosing an arbitrarily oriented elliptical hole in general anisotropic composite media is formulated for thermal analysis in the framework of hybrid finite element theory. Two independent temperature field approximations are defined for the present special element: Intra-element temperature field and element frame temperature field. The former defined inside the element is written in the form of truncated summation of the weighted special fundamental solutions, which are derived using the Stroh complex theory and conformal mapping whilst the latter is implemented by the conventional shape function interpolation. Then the hybrid variational functional is employed to combine them together to generate an element stiffness equation with respect to nodal temperature and an optional relationship between the interpolation coefficients. The element stiffness matrix is symmetric and involves element boundary integrals only. Compared to the traditional finite element, the distinctive element-boundary-integral and enclosed-elliptical-hole features make the present element significantly improve the meshing effort around an elliptical hole by reducing the number of elements and decreasing the meshing difficulty, and more importantly, effectively capture the critical variation of physical fields around the elliptical hole without locally-refined meshes. Moreover, the present special element can be incorporated directly into the conventional finite element system without any difficulty for extensive analysis. Finally, several typical examples are simulated by the present special elements to demonstrate their effectiveness.

A total rip-off—crack propagation in paper

The explanation of material properties starts at a young age identifying materials using words such as strong or brittle, but it is not until higher education that we teach how and why materials break along with what brittle really means. It is an important concept to understand, as a material that could be thought strong can be made to appear weak with the addition of a very small crack. As force is applied, these cracks, introduced through dents, scratches or even from the manufacturing process, can rapidly grow, leading to catastrophic failure. To help educators explain this concept in class without the need for specialised equipment or teaching complex theory, we present a set of accessible experiments on the fracture strength of paper strips. We show how the complexity of the experiment can be modified for various age groups, ranging from an engaging session for younger students pulling paper strips to a more involved extended practical using analytical solutions and fitting to determine the fracture strength of paper. These experiments have been delivered successfully to students of various ages and have led to stimulating discussions on the subject of materials science and engineering.

The Euler’s harmonic holomorphic regenerative universe

The Cartesian dualism is a precursor to Euler’s complex theory, that completes the Descartes-Leibnitz monadic conception using the natural quanta (non-splitting e, π) along with their topological torsion in the form of dual isomorphism. The complete Euler’s identity controls a bounded regenerative/ recurrent multiverse (a kind of multigraph) by two regenerative exponential functions, one quantic, e = exp (1) and another gravitational, g0 ≡ 10 = exp (1) with the fixed points, g0 = π2 and (g0g0) respectively. Physically, the fixed points give the well-defined the unit gravity (g0 m/s2) and light self-ignition velocity of a stable recurrent self-sustained process, provided the rate of mass production just equals the rate removal. This is the Euler’s fictitious regenerative universe - like our world, a quantum autocatalytic reaction system. The present paper describes such a system controlled by thermal gravitational waves, in the case the critical solar system.

Uncovering the endogenous features of potassium salts' global transfer: A complex network perspective.

Potassium is a decisive strategic resource to ensure food safety production and supply, which many nations define as a critical metal. Due to the unbalanced distribution of resources and production capacity and the separation of the primary potassium-consuming and supplying countries, international trade is the main supply channel for potassium-consuming countries to acquire enough resources. Understanding the characteristics of potassium trade networks and the evolution of trade patterns is essential for supply security. To explore this issue, this paper employs the complex network theory to quantitatively analyze the evolution characteristics of the global potassium trade network (PTN) from 2000 to 2021. The results show (1) Overall, the potassium trade shows a trend of gradual prosperity, efficiency, and concentration; (2) During the two decades, the main exporting countries of potassium remained stable, while imports changed significantly; (3) The evolution of the potassium trade community has characterized the fragmentation-regionalization-high concentration over time; (4) The trade flow of PTN is unbalanced, and few countries show outstanding capabilities but a single function. These findings would help trade policymakers manage the supply of strategic raw materials more effectively.

Don’t Call It a Failure: Systemic Risk Governance for Complex Financial Systems

The probability that an event will avalanche into an impairment of essential services constitutes a “systemic risk.” Owing to the inherent complexities of modern societies, the outbreak of a novel disease or the failure of a financial institution can rapidly escalate into an impact significantly larger than the initial event. Through the lens of complex system theory, this article draws a parallel between financial crises and disasters to contend that the regulatory framework for financial systemic risk is unequipped to address its fundamental dynamics. Epitomized by the market failure rationale, financial regulation is premised on a reductionist view that purports both systemic risk and law as external to the actions of market participants. Conversely, this article advances a twofold conceptual framework. First, it shows that systemic risk emerges from the same complex dynamics that generate the financial system. Second, it understands law as an agent of complexity, thus contributing to the emergence of finance and its inherent instability. Normatively, this conceptual framework reveals the limits of current regulatory approaches and constructs a holistic risk governance framework that is akin to the one adopted to govern disaster risks.

Kein Sündenfall der Frau, sondern ein Fanal der Erziehung zur Freiheit in der Urgeschichte der Bibel

Abstract Not a Fall of Woman, but a Fanal for Education for Freedom in the Bible’s Creation Story The article aims at a re-evaluation of the so-called Fall of Man narrative in Genesis 2:4–3:24, which since the early church interpretation has been linked to the loss of the image of God, which man had lost because he had partaken of the tree of knowledge in a forbidden way, whereby the woman is assigned a special guilt because she had seduced the man. This, however, was in no way the intention of the authors of this story in the 4th century BCE. Rather, the story is in dialogue with late-wisdom texts that, on the one hand, deny man the knowledge of good and evil, such as Qohelet and Job 28, or consider this knowledge to be a creative endowment of man, so Ben Sira. According to Gen 2–3, God has granted man the freedom of choice, which man can and does fail at, which is to be countered in the book of Deuteronomy by a complex theory of education.

PeerG: A P2P botnet detection method based on representation learning and graph contrastive learning

P2P botnets are distributed with complex topology and communication behavior, making them harder to detect and remove. Individuals or organizations can effectively detect P2P botnets by analyzing abnormal behaviors in network traffic. Existing works focus on extracting deterministic traffic interaction features, which are highly dependent on statistical features. Moreover, these methods are mainly aimed at generalized botnet detection and lack specificity for detecting P2P botnets. They ignore the topological information of P2P botnets, resulting in unsatisfactory detection accuracy. Among the few existing methods targeting P2P botnets, they consider the topological information but mainly rely on classical graph theory statistical features, such as degree, feature vector centrality, etc. This limits the generalization ability of the detection model. In this paper, we delve into the topological features of P2P botnets from the perspective of complex graph theory. We propose a P2P botnet detection method that combines representation learning and graph contrastive learning, dubbed PeerG. Specifically, we construct the communication graphs based on the flow interaction behavior between components of the P2P botnets. The Line algorithm is employed to embed the nodes of the communication graph into a low-dimensional representation vector space. Subsequently, the graph contrastive learning approach is utilized to optimize the feature extractor, enabling it to capture more representative node features. PeerG serves as a benchmark detection model for identifying P2P botnet nodes. Additionally, we devise two optimized contrastive detection strategies (PeerG-PreG and PeerG-PreF) based on graph-level and feature-level to boost the performance of PeerG. Extensive experiments demonstrate that PeerG brings significant improvements in detection accuracy over state-of-art detection methods. Furthermore, compared with PeerG, the detection strategies PeerG-PreG and PeerG-PreF have further improved detection performance, and achieve the best detection accuracy among multiple filtered P2P botnet types.

Interplay of network topologies in aviation delay propagation: A complex network and machine learning analysis

In this study, the fundamental characteristics of flight delay propagation and the key factors influencing such propagation are investigated. Three distinct types of networks were constructed: an aviation network, a traffic flow network, and a delay propagation network. Employing complex network theory, an analysis of the fundamental topological attributes of each network was conducted, exploring the interrelations among these attributes. Findings reveal a notable resemblance between the network topology attributes of the delay propagation network and the traffic flow network. The delay propagation network overall adheres to scale-free network attributes, with a few dominant major airports playing a pivotal role in the delay propagation process. Furthermore, it was uncovered that smaller airports are more susceptible to the influence of delay propagation than their larger counterparts. Delays, in a general sense, exhibit a pronounced tendency to aggregate and spread extensively within the realm of smaller airports. Regarding delay propagation, airport traffic emerges as the primary factor precipitating this phenomenon, with a feature importance score reaching 0.889. An escalation in airport traffic significantly amplifies the extent of delay propagation, yet concurrently, this escalation is not incessant but stabilizes beyond a certain threshold.

The effect of incentive policies on the diffusion of construction and demolition waste recycling: A government perspective.

Construction and demolition (C&D) waste recycling plays a significant role in waste reduction and carbon reduction, which is critical for sustainable development. However, due to various limitations such as financial problems, C&D waste recycling industry is not well developed in developing countries. To address this problem, this study combines complex network theory and evolutionary game theory to analyse the diffusion of C&D waste recycling behaviour among enterprises under governmental incentive policies within a complex network context. The results demonstrate that the size of the network has limited effects on behaviour diffusion in Watts-Strogatz small-world network. Additionally, the study highlights the clear impact of governmental incentive probability, initial rate and connection degree on the diffusion path. By quantitatively investigating the effects of incentive tools, this study contributes to the knowledge of C&D waste management and provides valuable implications for stakeholders seeking to promote the diffusion of C&D waste recycling.

Financial risk contagion based on dynamic multi-layer network between banks and firms

Banks and firms play pivotal roles within the financial system and serve as primary channels for systemic risk contagion. While progress has been made in understanding risk contagion within financial network systems, many studies tend to overlook the intricate interplay of multi-channel risk transmission and the dynamic evolution of network structures. Leveraging complex network theory, we have developed a dynamic multi-layer financial network risk transmission model that encompasses traditional bank–firm lending relationships and incorporates dynamic short-term loans. Through our analysis of various parameters such as loan recovery ratios, cross-shareholding ratios, network structures, short-term loan ratios, and attack strategies, we have made significant observations: In scenarios where both the interbank lending network and cross-shareholding network among firms exhibit random network structure, the financial network presents the highest level of risk. Excessive deviations in network average degrees, either too high or too low, can also heighten network vulnerability. An increase in the recovery ratio of interbank loans and the cross-shareholding ratio among firms corresponds to an escalation in systemic risk. Nodes with higher lending assets, more liquid assets, greater total assets, or higher out-degrees within the network become significant contributors to an elevated network bankruptcy rate when subjected to targeted attacks. Notably, the dynamic short-term loan network significantly amplifies systemic risks, with this amplification effect intensifying as the scale of short-term loans increases. From both macro and micro perspectives, our findings furnish regulatory authorities with novel analytical tools and insights to effectively mitigate and manage systemic risks in the financial sector.

Local, colocal, and antilocal properties of modules and complexes over commutative rings

This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocality is an alternative way in which global properties are locally controlled in a finite affine open covering. For example, injectivity of modules over non-Noetherian commutative rings is not preserved by localizations, while homotopy injectivity of complexes of modules is not preserved by localizations even for Noetherian rings. The latter also applies to the contraadjustedness and cotorsion properties. All the mentioned properties of modules or complexes over commutative rings are actually antilocal. They are also colocal, if one presumes contraadjustedness. Generally, if the left class in a (hereditary complete) cotorsion theory for modules or complexes of modules over commutative rings is local and preserved by direct images with respect to affine open immersions, then the right class is antilocal. If the right class in a cotorsion theory for contraadjusted modules or complexes of contraadjusted modules is colocal and preserved by such direct images, then the left class is antilocal. As further examples, the class of flat contraadjusted modules is antilocal, and so are the classes of acyclic, Becker-coacyclic, or Becker-contraacyclic complexes of contraadjusted modules. The same applies to the classes of homotopy flat complexes of flat contraadjusted modules and acyclic complexes of flat contraadjusted modules with flat modules of cocycles.

Disentangling the complexity of human–nature interactions

Abstract Human–nature interactions have been identified as an important leverage point for achieving sustainability. Processes to recognize, protect, improve and reimagine human–nature interactions will be central to shift the world to more sustainable and equitable pathways and futures. In the context of the interconnected and rapidly changing Anthropocene, work on human–nature interactions must move beyond dominant linear assumptions of a relatively simple and easily and predictably manipulated world to acknowledge and engage with the complex, dynamic, asymmetrical and unequal nature of the interactions connecting people and nature. Based on three key features highlighted by the study of complex social–ecological systems (SES)—that these systems are relational, open and dynamic—we propose three new directions for the study and management of human–nature interactions that can help to acknowledge and disentangle the globally intertwined and dynamic nature of these interactions. These features suggest new directions and foci for sustainability science: the inseparable and relational qualities of the interactions between people and nature; the cross‐scale nature of these relationships; and the continuously evolving and changing form of these relationships. To bridge the gap between the theory of complex, inseparable and unequal human–nature interactions and the reductionist tendencies in research and practice, SES research raises opportunities to connect local action and global learning; to mobilize and develop new cross‐scale and relational capacities to encourage synergies and avoid trade‐offs; and to explore, experiment and learn our way forward onto more sustainable and equitable pathways. Read the free Plain Language Summary for this article on the Journal blog.

An empirical assessment of whether urban green ecological networks have the capacity to store higher levels of carbon

Carbon–neutral growth is a crucial long-term climatic aim in the context of global warming. This paper introduces complex network theory and explores its potential application to achieve this goal. Specifically, we investigate the spatial and temporal distribution of nodes and sources in the ecological network, and examine whether a relationship exists between the topological index of network nodes and the landscape pattern index of ecological source areas. We also determine the contribution of nodes to the carbon stock of the entire network by exploring the correlation between the carbon stock of nodes and sources to develop an optimization strategy based on the synergistic effect of node-source carbon enhancement. Finally, we test the effect of network optimization through robustness. Our results show that: (1) The correlation topological feature index analysis reveals that the degree distribution of the node network's topological characteristics becomes dispersed and modular, exhibiting the characteristics of small-world networks according to a large clustering coefficient. The heterogeneity and extent of ecological source landscapes have increased by modularity index but remain distributed and locally fragmented; (2) According to correlation analysis, by enhancing the eccentricity of the node topology, the patch cohesion index (COHESION) of the ecological source site can maximize the contribution of the node to the enhancement of the carbon stock benefits of the source site; (3) According to the tests on the robustness of nodes and edges and the robustness of network links, network stability is improved and carbon sink capacity is enhanced. Simultaneously, the restoration and rejuvenation of ecological space through national ecological construction projects can effectively improve the carbon sink within the organized region, contributing to the carbon neutrality aim. This research gives scientific and quantifiable references for potential ecological construction projects for sustainable cities and the optimization of urban ecological space structure.