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Journal articleEvans TS, Calmon L, Vasiliauskaite V, et al., 2020,
Longest path in the price model
, Scientific Reports, Vol: 10, Pages: 1-9, ISSN: 2045-2322The Price model, the directed version of the Barab\'{a}si-Albert model,produces a growing directed acyclic graph. We look at variants of the model inwhich directed edges are added to the new vertex in one of two ways: usingcumulative advantage (preferential attachment) choosing vertices in proportionto their degree, or with random attachment in which vertices are chosenuniformly at random. In such networks, the longest path is well defined and insome cases is known to be a better approximation to geodesics than the shortestpath. We define a reverse greedy path and show both analytically andnumerically that this scales with the logarithm of the size of the network witha coefficient given by the number of edges added using random attachment. Thisis a lower bound on the length of the longest path to any given vertex and weshow numerically that the longest path also scales with the logarithm of thesize of the network but with a larger coefficient that has some weak dependenceon the parameters of the model.
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Journal articleFalkenberg M, Lee J-H, Amano S-I, et al., 2020,
Identifying time dependence in network growth
, Physical Review & Research International, Vol: 2, Pages: 023352 – 1-023352 – 17, ISSN: 2231-1815Identifying power-law scaling in real networks—indicative of preferential attachment—has proved controversial. Critics argue that measuring the temporal evolution of a network directly is better than measuring the degree distribution when looking for preferential attachment. However, many of the established methods do not account for any potential time dependence in the attachment kernels of growing networks, or methods assume that node degree is the key observable determining network evolution. In this paper, we argue that these assumptions may lead to misleading conclusions about the evolution of growing networks. We illustrate this by introducing a simple adaptation of the Barabási-Albert model, the “k2 model,” where new nodes attach to nodes in the existing network in proportion to the number of nodes one or two steps from the target node. The k2 model results in time dependent degree distributions and attachment kernels, despite initially appearing to grow as linear preferential attachment, and without the need to include explicit time dependence in key network parameters (such as the average out-degree). We show that similar effects are seen in several real world networks where constant network growth rules do not describe their evolution. This implies that measurements of specific degree distributions in real networks are likely to change over time.
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Journal articleCiacci A, Falkenberg M, Manani KA, et al., 2020,
Understanding the transition from paroxysmal to persistent atrial fibrillation
, Physical Review Research, Vol: 2, Pages: 1-23, ISSN: 2643-1564Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterisedby the chaotic motion of electrical wavefronts in the atria. In clinicalpractice, AF is classified under two primary categories: paroxysmal AF, shortintermittent episodes separated by periods of normal electrical activity, andpersistent AF, longer uninterrupted episodes of chaotic electrical activity.However, the precise reasons why AF in a given patient is paroxysmal orpersistent is poorly understood. Recently, we have introduced the percolationbased Christensen-Manani-Peters (CMP) model of AF which naturally exhibits bothparoxysmal and persistent AF, but precisely how these differences emerge in themodel is unclear. In this paper, we dissect the CMP model to identify the causeof these different AF classifications. Starting from a mean-field model wherewe describe AF as a simple birth-death process, we add layers of complexity tothe model and show that persistent AF arises from the formation of temporallystable structural re-entrant circuits that form from the interaction ofwavefront collisions during paroxysmal AF. These results are compatible withrecent findings suggesting that the formation of re-entrant drivers in fibroticborder zones perpetuates persistent AF.
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Journal articleJensen H, 2020,
Universality classes and information-theoretic measures of complexity via group entropies
, Scientific Reports, Vol: 10, Pages: 1-11, ISSN: 2045-2322We introduce a class of information measures based on group entropies, allowing us to describe the information-theoreticalproperties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a seriesof natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. Theinformation measures proposed are suitably defined for describing universality classes of complex systems, each characterizedby a specific state space growth rate function.
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Journal articlePalmieri L, Jensen HJ, 2020,
Investigating critical systems via the distribution of correlation lengths
, PHYSICAL REVIEW RESEARCH, Vol: 2- Author Web Link
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Journal articleVasiliauskaite V, Evans TS, 2020,
Making communities show respect for order
, Applied Network Science, Vol: 5, Pages: 1-24, ISSN: 2364-8228In this work we give a community detection algorithm in which the communities both respects the intrinsic order of a directed acyclic graph and also finds similar nodes. We take inspiration from classic similarity measures of bibliometrics, used to assess how similar two publications are, based on their relative citation patterns. We study the algorithm’s performance and antichain properties in artificial models and in real networks, such as citation graphs and food webs. We show how well this partitioning algorithm distinguishes and groups together nodes of the same origin (in a citation network, the origin is a topic or a research field). We make the comparison between our partitioning algorithm and standard hierarchical layering tools as well as community detection methods. We show that our algorithm produces different communities from standard layering algorithms.
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Journal articleViegas E, Goto H, Kobayashi Y, et al., 2020,
Allometric scaling of mutual information in complex networks: a conceptual framework and empirical approach
, Entropy: international and interdisciplinary journal of entropy and information studies, Vol: 22, Pages: 1-14, ISSN: 1099-4300Complexity and information theory are two very valuable but distinct fields of research, yet sharing the same roots. Here, we develop a complexity framework inspired by the allometric scaling laws of living biological systems in order to evaluate the structural features of networks. This is done by aligning the fundamental building blocks of information theory (entropy and mutual information) with the core concepts in network science such as the preferential attachment and degree correlations. In doing so, we are able to articulate the meaning and significance of mutual information as a comparative analysis tool for network activity. When adapting and applying the framework to the specific context of the business ecosystem of Japanese firms, we are able to highlight the key structural differences and efficiency levels of the economic activities within each prefecture in Japan. Moreover, we propose a method to quantify the distance of an economic system to its efficient free market configuration by distinguishing and quantifying two particular types of mutual information, total and structural.
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Journal articleGoto H, Viegas E, Takayasu H, et al., 2019,
Dynamics of essential interaction between firms on financial reports
, PLoS One, Vol: 14, Pages: 1-16, ISSN: 1932-6203Companies tend to publish financial reports in order to articulate strategies, disclose key performance measurements as well as summarise the complex relationships with external stakeholders as a result of their business activities. Therefore, any major changes to business models or key relationships will be naturally reflected within these documents, albeit in an unstructured manner. In this research, we automatically scan through a large and rich database, containing over 400,000 reports of companies in Japan, in order to generate structured sets of data that capture the essential features, interactions and resulting relationships among these firms. In doing so, we generate a citation type network where we empirically observe that node creation, annihilation and link rewiring to be the dominant processes driving its structure and formation. These processes prompt the network to rapidly evolve, with over a quarter of the interactions between firms being altered within every single calendar year. In order to confirm our empirical observations and to highlight and replicate the essential dynamics of each of the three processes separately, we borrow inspiration from ecosystems and evolutionary theory. Specifically, we construct a network evolutionary model where we adapt and incorporate the concept of fitness within our numerical analysis to be a proxy real measure of a company’s importance. By making use of parameters estimated from the real data, we find that our model reliably replicates degree distributions and motif formations of the citation network, and therefore reproducing both macro as well as micro, local level, structural features. This is done with the exception of the real frequency of bidirectional links, which are primarily formed as a result of an entirely separate and distinct process, namely the equity investments from one company into another.
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Journal articleRajpal H, Rosas De Andraca FE, Jensen HJ, 2019,
Tangled worldview model of opinion dynamics
, Frontiers in Physics, Vol: 7, ISSN: 2296-424XWe study the joint evolution of worldviews by proposing a model of opinion dynamics, which is inspired in notions fromevolutionary ecology. Agents update their opinion on a specific issue based on their propensity to change – asserted by thesocial neighbours – weighted by their mutual similarity on other issues. Agents are, therefore, more influenced by neighbourswith similar worldviews (set of opinions on various issues), resulting in a complex co-evolution of each opinion. Simulationsshow that the worldview evolution exhibits events of intermittent polarization when the social network is scale-free. This, in turn,triggers extreme crashes and surges in the popularity of various opinions. Using the proposed model, we highlight the role ofnetwork structure, bounded rationality of agents, and the role of key influential agents in causing polarization and intermittentreformation of worldviews on scale-free networks.
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Journal articleCofré R, Herzog R, Corcoran D, et al., 2019,
A comparison of the maximum entropy principle across biological spatial scales
, Entropy: international and interdisciplinary journal of entropy and information studies, Vol: 21, Pages: 1-20, ISSN: 1099-4300Despite their differences, biological systems at different spatial scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are often hard to grasp due to the highly specialized nature of modern science and the parcelled terminology employed by various scientific sub-disciplines. To explore these common organizational features, this paper provides a comparative study of diverse applications of the maximum entropy principle, which has found many uses at different biological spatial scales ranging from amino acids up to societies. By presenting these studies under a common approach and language, this paper aims to establish a unified view over these seemingly highly heterogeneous scenarios.
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