#342 Self-organization in entangled materials
Authors: Levente Varga, Áron Kapusi and Ferenc Járai-Szabó
Entangled materials are abundant and of very different usage. They can be found in living cells (cytoskeletal polymers), composite fiber reinforced polymers, non-woven textile fabrics and papers, glass wools, etc. However, little is known about the origin of the macroscopic collective properties of tangles. On one hand, mechanical properties have been studied experimentally by constant strain rate compressions, shearing tests, and electrical conductivity measurements. The experiments show a percolation transition both in rigidity and conductivity, followed by non-linear behaviors. These phenomena have been treated theoretically, as well, by means of different computational models. On the other hand, the rupture process of fibrous materials represents another topic of interest, which has been studied intensively by experiments and theoretical models. In this context, it is interesting to study a simpler situation when only one fiber is pulled out from the tangle. We have realized the experiment by using hemp tow as entangled material. The tangle has been placed in a paper-box, which has a small hole at the top. The whole system has been placed on a high precision digital scale. One fiber has been threaded through the hole and a stepper motor pulled it out with a very slow, constant velocity. By this setup we can measure the total force acting on the pulled fiber. It was observed that this force exhibit jumps of different sizes. The jump size distribution shows a power-law trend of exponent -2. This is a clear sign that a self-organization phenomenon is taking place in the system. This finding may be understood if we suppose that stick-slip avalanches appear in the system during the fiber pull out process. We study by a simple spring-block stick-slip model this avalanche-effect and its impact on the macroscopic properties of the entangled materials.
#343 Genetic-like algorithm applied on citation networks for evaluating scientific publications
Authors: Dávid Deritei, Levente Varga, István Papp, Ferenc Járai-Szabó, Zsolt I. Lázár, Răzvan V. Florian and Mária Ercsey-Ravasz
Citation networks of scientific publications track the evolution of human scientific knowledge in our modern age. Grasping the role of a publication in this complex system is a challenge for scientometry. We consider a biological analogy between the citation network and the evolutionary reproduction network. Taking a scientific publication as a biological organism, by this analogy, we define the cited papers as the “parents” and the publications citing the given work as the “offspring” or descendants. This way the fitness of a paper becomes exactly the number of its received citations, which is already the most common way of evaluation in scientometrics. We know, however, that the most basic units of evolution are not species or individuals, but genes, which survive and propagate through living organisms. In this case, let us consider these “memes” by Richard Dawkins as ideas or pieces of scientific knowledge. Assuming that every new work published introduces some new idea (e.g. mutation/variation in biology), this knowledge propagates down on the tree of descendants in a similar manner to genes. The content of the paper represents the "genome" of a node and it is composed of the own newly introduced memes (knowledge) and the weighted content of the papers cited. The more papers a given publication cites the more ideas it synthesizes, meaning that the weight of each of idea decreases in the new publication with the shared parenthood. In our study, we analyze this simple algorithm on different citation networks and show how the fitness defined for new ideas could be a better scientometric indicator than the simple citation number of papers. This model could also provide a framework of tracking individual ideas and innovations within the abundance of intertwined citations, giving additional insight from historical, sociological and economic perspectives.
#348 Variational Approaches to Self-Organization
Authors: Georgi Georgiev, Atanu Chatterjee, Thanh Vu and Germano Iannachione
We propose a variational approach to describe the evolution of complex systems from first principles as increased efficiency of physical action, which most simply is the product of the energy and time necessary for unit motion of their constituent elements. Modeled as flow networks, this efficiency is defined as decrease of action for one element to cross between two nodes. Expanded for complex systems, the principle of least action is, that systems tend to a state with zero variation of the average action for one element and one edge crossing, or this is a principle of Minimum Unit Action. We find a connection with another principle that of Maximum Total Action, or a tendency to increase total action of the system, to a state with zero variation of the sum of actions for all elements and their motions. We apply a positive feedback model based on a system of differential equations between the organization, the total amount of action in the system and other parameters such as the Free Energy Rate Density, the number of elements, the total flow of events and others. This results in exponential growth of those characteristics, and power law relations between them. We use a simple system, which is the Core Processing Unit (CPU) of computers, to compare to our model and find a good agreement. This confirms the size-complexity rule and leads to the conclusion that the decrease of unit action based on the Principle of Least Action, is connected to increase of the value of the other characteristics. Each cannot continue its change, without a change in the other. We propose size-density and complexity-density rules in addition to the established size-complexity one and a term “Devology” for studies of universal development and evolution of complex systems of physical, chemical, biological and socio-technical nature.
#351 A Grid based model for generating scale-free networks
Authors: Manjish Pal and Amit Kumar Verma
It has been observed that evolution of social networks is not a random process but there exists some key features which are responsible for their evolution. Formation of communities and hubs in social networks confirms this theory. Also degree distribution of these networks follows the power law i.e. $p(k) \propto k^{-\gamma}$ where $\gamma$ is usually 2 or 3. In this work we have proposed a model for generating scale-free networks. For this purpose we have modeled the network as undirected graph where nodes represent network members and edges represent connection among them. We create a grid of size $nxn$ on which we place the nodes with some probability such that the amount of nodes increases as we move away from the center. We move from the center of the grid in spiral order with at each time step adding a new node and connecting it to $m$ previously present nodes. Node which is closer to the center is more likely to get chosen for the connection. In our model we ensure that the probability that node $i$ will get selected at time $t$ for connection is $\frac{\frac{1}{r_i}}{\sum_{j=1}^{t-1}\frac{1}{r_j}}$. We first experimentally observe that the degree distribution of networks generated by our model is linear in log scale. We then provide a proof of correctness of the fact that the degree distribution indeed follows the power law.
#355 Gibbs-like Entropy Characteristics of an Agent based Opinion Dynamics Model with Stubborn Agents
Authors: Husin Alatas, Salamet Nurhimawan, Fikri Asmat and Choirul Aziz
We discuss a model of opinion dynamics using agent based model that take into account stubborn agents. The model is based on assumption that each agent has a level of opinion and level of connectivity which describes its relation with surrounding agents. We assume that the corresponding level of opinion of each agent as well as the level of connectivity parameter are changing by the following rule: (i) all opinions (connectivities) of the other agents are averaged with respect to the level of connectivity; (ii) subtracting the average value with the level of opinion of the associated agent and multiply the resulted value with a weight parameter called opinion (connectivity) perception index which describes the intrinsic characteristics of the corresponding agent; (iii) result from step (ii) is then summed with the associated agent level of opinion (connectivity) yielding updated level of opinion (connectivity). We introduce the existence of stubborn agents with zero opinion (connectivity) perception indices. We characterize the dynamical characteristics of the model by using the concept of Gibbs-like entropy. We found that the model shows a remarkable feature of transition due to the existence of stubborn agents. It is shown that the related level of opinion and its entropy can suddenly change rapidly to other level of opinion while leaving the level of connectivity relatively unchanged. The effects of opinion/connectivity variations to the dynamical characteristics of the model are also discussed.
Authors: Levente Varga, Áron Kapusi and Ferenc Járai-Szabó
Entangled materials are abundant and of very different usage. They can be found in living cells (cytoskeletal polymers), composite fiber reinforced polymers, non-woven textile fabrics and papers, glass wools, etc. However, little is known about the origin of the macroscopic collective properties of tangles. On one hand, mechanical properties have been studied experimentally by constant strain rate compressions, shearing tests, and electrical conductivity measurements. The experiments show a percolation transition both in rigidity and conductivity, followed by non-linear behaviors. These phenomena have been treated theoretically, as well, by means of different computational models. On the other hand, the rupture process of fibrous materials represents another topic of interest, which has been studied intensively by experiments and theoretical models. In this context, it is interesting to study a simpler situation when only one fiber is pulled out from the tangle. We have realized the experiment by using hemp tow as entangled material. The tangle has been placed in a paper-box, which has a small hole at the top. The whole system has been placed on a high precision digital scale. One fiber has been threaded through the hole and a stepper motor pulled it out with a very slow, constant velocity. By this setup we can measure the total force acting on the pulled fiber. It was observed that this force exhibit jumps of different sizes. The jump size distribution shows a power-law trend of exponent -2. This is a clear sign that a self-organization phenomenon is taking place in the system. This finding may be understood if we suppose that stick-slip avalanches appear in the system during the fiber pull out process. We study by a simple spring-block stick-slip model this avalanche-effect and its impact on the macroscopic properties of the entangled materials.
#343 Genetic-like algorithm applied on citation networks for evaluating scientific publications
Authors: Dávid Deritei, Levente Varga, István Papp, Ferenc Járai-Szabó, Zsolt I. Lázár, Răzvan V. Florian and Mária Ercsey-Ravasz
Citation networks of scientific publications track the evolution of human scientific knowledge in our modern age. Grasping the role of a publication in this complex system is a challenge for scientometry. We consider a biological analogy between the citation network and the evolutionary reproduction network. Taking a scientific publication as a biological organism, by this analogy, we define the cited papers as the “parents” and the publications citing the given work as the “offspring” or descendants. This way the fitness of a paper becomes exactly the number of its received citations, which is already the most common way of evaluation in scientometrics. We know, however, that the most basic units of evolution are not species or individuals, but genes, which survive and propagate through living organisms. In this case, let us consider these “memes” by Richard Dawkins as ideas or pieces of scientific knowledge. Assuming that every new work published introduces some new idea (e.g. mutation/variation in biology), this knowledge propagates down on the tree of descendants in a similar manner to genes. The content of the paper represents the "genome" of a node and it is composed of the own newly introduced memes (knowledge) and the weighted content of the papers cited. The more papers a given publication cites the more ideas it synthesizes, meaning that the weight of each of idea decreases in the new publication with the shared parenthood. In our study, we analyze this simple algorithm on different citation networks and show how the fitness defined for new ideas could be a better scientometric indicator than the simple citation number of papers. This model could also provide a framework of tracking individual ideas and innovations within the abundance of intertwined citations, giving additional insight from historical, sociological and economic perspectives.
#348 Variational Approaches to Self-Organization
Authors: Georgi Georgiev, Atanu Chatterjee, Thanh Vu and Germano Iannachione
We propose a variational approach to describe the evolution of complex systems from first principles as increased efficiency of physical action, which most simply is the product of the energy and time necessary for unit motion of their constituent elements. Modeled as flow networks, this efficiency is defined as decrease of action for one element to cross between two nodes. Expanded for complex systems, the principle of least action is, that systems tend to a state with zero variation of the average action for one element and one edge crossing, or this is a principle of Minimum Unit Action. We find a connection with another principle that of Maximum Total Action, or a tendency to increase total action of the system, to a state with zero variation of the sum of actions for all elements and their motions. We apply a positive feedback model based on a system of differential equations between the organization, the total amount of action in the system and other parameters such as the Free Energy Rate Density, the number of elements, the total flow of events and others. This results in exponential growth of those characteristics, and power law relations between them. We use a simple system, which is the Core Processing Unit (CPU) of computers, to compare to our model and find a good agreement. This confirms the size-complexity rule and leads to the conclusion that the decrease of unit action based on the Principle of Least Action, is connected to increase of the value of the other characteristics. Each cannot continue its change, without a change in the other. We propose size-density and complexity-density rules in addition to the established size-complexity one and a term “Devology” for studies of universal development and evolution of complex systems of physical, chemical, biological and socio-technical nature.
#351 A Grid based model for generating scale-free networks
Authors: Manjish Pal and Amit Kumar Verma
It has been observed that evolution of social networks is not a random process but there exists some key features which are responsible for their evolution. Formation of communities and hubs in social networks confirms this theory. Also degree distribution of these networks follows the power law i.e. $p(k) \propto k^{-\gamma}$ where $\gamma$ is usually 2 or 3. In this work we have proposed a model for generating scale-free networks. For this purpose we have modeled the network as undirected graph where nodes represent network members and edges represent connection among them. We create a grid of size $nxn$ on which we place the nodes with some probability such that the amount of nodes increases as we move away from the center. We move from the center of the grid in spiral order with at each time step adding a new node and connecting it to $m$ previously present nodes. Node which is closer to the center is more likely to get chosen for the connection. In our model we ensure that the probability that node $i$ will get selected at time $t$ for connection is $\frac{\frac{1}{r_i}}{\sum_{j=1}^{t-1}\frac{1}{r_j}}$. We first experimentally observe that the degree distribution of networks generated by our model is linear in log scale. We then provide a proof of correctness of the fact that the degree distribution indeed follows the power law.
#355 Gibbs-like Entropy Characteristics of an Agent based Opinion Dynamics Model with Stubborn Agents
Authors: Husin Alatas, Salamet Nurhimawan, Fikri Asmat and Choirul Aziz
We discuss a model of opinion dynamics using agent based model that take into account stubborn agents. The model is based on assumption that each agent has a level of opinion and level of connectivity which describes its relation with surrounding agents. We assume that the corresponding level of opinion of each agent as well as the level of connectivity parameter are changing by the following rule: (i) all opinions (connectivities) of the other agents are averaged with respect to the level of connectivity; (ii) subtracting the average value with the level of opinion of the associated agent and multiply the resulted value with a weight parameter called opinion (connectivity) perception index which describes the intrinsic characteristics of the corresponding agent; (iii) result from step (ii) is then summed with the associated agent level of opinion (connectivity) yielding updated level of opinion (connectivity). We introduce the existence of stubborn agents with zero opinion (connectivity) perception indices. We characterize the dynamical characteristics of the model by using the concept of Gibbs-like entropy. We found that the model shows a remarkable feature of transition due to the existence of stubborn agents. It is shown that the related level of opinion and its entropy can suddenly change rapidly to other level of opinion while leaving the level of connectivity relatively unchanged. The effects of opinion/connectivity variations to the dynamical characteristics of the model are also discussed.
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