Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. The equations from which models of complex systems are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of natural systems that are considered fundamentally complex.
At USC Dornsife, we see snow differently. Discover how we view the complex and beautiful snowflake from every angle through the lenses of psychology, chemistry, poetry, physics, international relations — and more.
Many high-profile societal problems involve an individual or group repeatedly attacking another - from child-parent disputes, sexual violence against women, civil unrest, violent conflicts and acts of terror, to current cyber-attacks on national infrastructure and ultrafast cyber-trades attacking stockholders. There is an urgent need to quantify the likely severity and timing of such future acts, shed light on likely perpetrators, and identify intervention strategies. Here we present a combined analysis of multiple datasets across all these domains which account for >100,000 events, and show that a simple mathematical law can benchmark them all. We derive this benchmark and interpret it, using a minimal mechanistic model grounded by state-of-the-art fieldwork. Our findings provide quantitative predictions concerning future attacks; a tool to help detect common perpetrators and abnormal behaviors; insight into the trajectory of a 'lone wolf'; identification of a critical threshold for spreading a message or idea among perpetrators; an intervention strategy to erode the most lethal clusters; and more broadly, a quantitative starting point for cross-disciplinary theorizing about human aggression at the individual and group level, in both real and online worlds.
Scale-free networks have small characteristic path lengths, high clustering, and feature a power law in their degree distribution. They can be obtained by the well-known preferential attachment. However, this mechanism is non-local, in the sense that it requires knowledge of the entire graph in order for the graph to be updated. This strongly suggests that in both physical and practical realizations this mechanism is likely to be the epiphenomenon of some spatially local rule. Here, we present a completely local model that features preferential attachment as an emergent property of self-organized dynamics with memory. This model employs a mechanism similar to that used by ants to search for the optimal path as a consequence of the graph bearing more memory wherever more ants have walked. Such a model can also be realized in solid-state circuits, using non-linear passive elements with memory such as memristors, and thus can be tested experimentally. Since memory is a common trait of physical systems, we expect this mechanism to be a typical feature in the formation of real-world networks.
There are 4 datasets in this collection. Each is available as a .tar.gz file containing either .json or .csv files. When the JSON format is used, each .json file contains a single JSON object. The format of that object is dependent on the dataset. See below for details. The datasets have been prepared by Dimitar Nikolov.
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties appear to universally emerge. We propose that an important class of complex systems can be modelled as a construction of potentially infinitely many levels of organization all following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance in the pyramid of production entities of the movie industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering or modularity, their hierarchy, their fractality and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of the hierarchical nature of our world.
Complexity develops via the incorporation of innovative properties. Chess is one of the most complex strategy games, where expert contenders exercise decision making by imitating old games or introducing innovations. In this work, we study innovation in chess by analyzing how different move sequences are played at the population level. It is found that the probability of exploring a new or innovative move decreases as a power law with the frequency of the preceding move sequence. Chess players also exploit already known move sequences according to their frequencies, following a preferential growth mechanism. Furthermore, innovation in chess exhibits Heaps' law suggesting similarities with the process of vocabulary growth. We propose a robust generative mechanism based on nested Yule-Simon preferential growth processes that reproduces the empirical observations. These results, supporting the self-similar nature of innovations in chess are important in the context of decision making in a competitive scenario, and extend the scope of relevant findings recently discovered regarding the emergence of Zipf's law in chess.
A force that intricately links the rotation of the Earth with the direction of weather patterns in the atmosphere has been shown to play a crucial role in the creation of the hypnotic patterns created by the skirts of the Whirling Dervishes.
We study a simple voter model with two competing parties. In particular, we represent the case of political elections, where people can choose to support one of the two competitors or to remain neutral. People interact in a social network and their opinion depends on those of their neighbors. Therefore, people may change opinion over time, i.e., they can support one competitor or none. The two competitors try to gain the people's consensus by interacting with their neighbors and also with other people. In particular, competitors define temporal connections, following a strategy, to interact with people they do not know, i.e., with all the people that are not their neighbors. We analyze the proposed model to investigate which network strategies are more advantageous, for the competitors, in order to gain the popular consensus. As result, we found that the best network strategy depends on the topology of the social network. Finally, we investigate how the charisma of competitors affects the outcomes of the proposed model.
This is from 2004 but still work reading, as it is well in advance of what most people today are still saying about learning. But it is relevant to the theories of learning networks and connectivism. Among other things, it discusses:
network health - "For a system to be healthy, it must co-evolve with its environment: it changes in response to changes in its environment, and its environment changes in response to its changes"learning theories - "Co-evolution is fostered by disequilibrium and positive feedback" (ie., Boltzmann mechanisms and back propagation)openness - "open systems maintain a state of non-equilibrium… They participate in an open exchange with their world"content - "Transformation is strongly influenced by 'strange attractors'... In educational systems, they can be considered 'core ideas' and values or beliefs"self-organization - "require two major characteristics: openness and self-reference [and] Because it partners with its environment, the system develops increasing autonomy from the environment [and] the more freedom in self-organization, the more order"from Stephen Downes blog
The Center for Complex Networks and Systems Research (CNetS) is part of the Pervasive Technology Institute of Indiana University and the School of Informatics and Computing. The center was established in 2009 to consolidate and enhance the research efforts of the complex systems group, which has been active within the School since 2004. CNetS is meant to foster interdisciplinary research in all areas related to complex systems.
The types of problems that we work on include mining usage and traffic patterns in technological networks such as the Web and the Internet; studying the interaction between social dynamics and online behaviors; modeling the evolution of complex social and technological networks; developing adaptive, distributed, collaborative, agent-based applications for Web search and recommendation; understanding complex biological networks and complex reaction in biochemistry; developing models for the spread of diseases; understanding how coordinated behavior arises from the dynamical interaction of nervous system, body, and environment; studying social human behavior; exploring reasons underlying species diversity; studying the interplay between self-organization and natural selection; understanding how information arises and is used in biological systems; and so on. All these examples are characterized by complex nonlinear feedback mechanisms and it is now being increasingly recognized that the outcome of such interactions can only be understood through mathematical and computational models.
There is common ground in analysing financial systems and ecosystems, especially in the need to identify conditions that dispose a system to be knocked from seeming stability into another, less happy state.
We investigate the failure mechanisms of load sharing complex systems. The system is composed of multiple nodes or components whose failures are determined based on the interaction of their respective strengths and loads (or capacity and demand respectively) as well as the ability of a component to share its load with its neighbors when needed. We focus on two distinct mechanisms to model the interaction between components' strengths and loads. The failure mechanisms of these two models demonstrate temporal scaling phenomena, phase transitions and multiple distinct failure modes excited by extremal dynamics. For critical ranges of parameters the models demonstrate power law and exponential failure patterns. We identify the similarities and differences between the two mechanisms and the implications of our results to the failure mechanisms of complex systems in the real world.
This algorithm is a member of the ant colony algorithms family, in swarm intelligence methods, and it constitutes some metaheuristic optimizations. Initially proposed by Marco Dorigo in 1992 in his PhD thesis, the first algorithm was aiming to search for an optimal path in a graph, based on the behavior of ants seeking a path between their colony and a source of food.
Understanding demographic and migrational patterns constitutes a great challenge. Millions of individual decisions, motivated by economic, political, demographic, rational and/or emotional reasons underlie the high complexity of demographic dynamics. Significant advances in quantitatively understanding such complexity have been registered in recent years, as those involving the growth of cities but many fundamental issues still defy comprehension. We present here compelling empirical evidence of a high level of regularity regarding time and spatial correlations in urban sprawl, unravelling patterns about the inertia in the growth of cities and their interaction with each other. By using one of the world's most exhaustive extant demographic data basis—that of the Spanish Government's Institute INE, with records covering 111 years and (in 2011) 45 million people, distributed among more than 8000 population nuclei—we show that the inertia of city growth has a characteristic time of 15 years, and its interaction with the growth of other cities has a characteristic distance of 80 km. Distance is shown to be the main factor that entangles two cities (60% of total correlations). The power of our current social theories is thereby enhanced.
The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through each agent's `proper time' measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated power-law behavior and average exponents near -3/2. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bi-modal character, which is empirically borne out by our new years-long data on email. These novel perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, emergency handling.