Top PDF Exploring some topologies of coupled chaotic networks

Exploring some topologies of coupled chaotic networks

Exploring some topologies of coupled chaotic networks

Those two maps have also been fully explored with the hope of generating pseudo-random numbers [6]. However the collapsing of iterates of dynamical systems or at least the existence of very short periodic orbits, their non constant invariant measure, and the easily recognized shape of the function in the phase space should lead to avoid the use of such one-dimensional map (logistic, baker, or tent, etc.) or two dimensional map (H´enon, standard or Belykh, etc.) as a pseudo-random number generator (see [7] for a sur- vey). However, the very simple implementation in computer program of chaotic dynamical systems led some authors to use it as a base of cryptosystem [8]. They are topologically conjugate, that means they have similar topological properties (distribution, chaoticity, etc.) however due to the structure of number in computer realization their numerical behaviour dif- fers drastically. Therefore the original idea here is to combine features of tent (T µ ) and logistic (L µ ) maps to achieve new
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Exploring the magnetic topologies of cool stars

Exploring the magnetic topologies of cool stars

Partly convective cool stars possess an internal structure similar to that of the Sun, i.e. an inner radiative zone and an outer convective envelope supposedly separated by a tachocline. Hence, it is generally assumed that their magnetic fields — as revealed by activity or direct measurements — are generated by a solar-like dynamo. However, some cool partly-convective stars strongly differ from the Sun, either in depth of their convective zone or rotation rate, and the impact of these differences on their dynamo is mostly unknown. On the other hand, main sequence stars less massive than ∼ 0 . 35 M ⊙
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Exploration of topologies of coupled nonlinear maps (Chaos theory)

Exploration of topologies of coupled nonlinear maps (Chaos theory)

Dynamical systems which present mixing behavior and that are highly sensitive to initial conditions are called chaotic. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems This effect popularly known as the as the butterfly effect, renders long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. Mastering the global properties of those dynamical systems is today a challenging issue we try to fix exploring several topologies of network of coupled maps.
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Coupled complex networks : structure, adaptation and processes

Coupled complex networks : structure, adaptation and processes

networks, and in particular, how efficient correlated structures are in spreading flows. We present a model of constrained epidemic spreading, aiming to capture the resource constraints existing in coupled networks where, unlike connected nodes in a single network, coupled nodes often share resources, like time, energy, and memory. Using an extensive computer simulation, we analyse the model dynamics on networks with various topologies, revealing a qualitatively different result than the one obtained in recent studies, thus questioning their robustness, while also providing a possible explanation for the random coupling found in biological networks, which according to previous studies was considered less spreading-efficient. We complete the chapter with a discussion, calling for more future work about this topic, and especially more theoretical results. To complement the theoretical work considered in the previous chapters, in chapter 6 we present a large-scale empirical study of interacting underground and street networks in the entire metropolitan areas of both London and New York. While intermodality was largely considered in the transportation science literature, most studies on the topic do not provide a topological analysis of the network’s graph, a fact that has yet to be addressed in the complex networks literature. We aim to fill this gap in the literature while exploring the utility of coupled complex networks modelling, as well as demonstrating that they can deal with the scale and empirical complexity of real-world network exemplars.
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Explosive Synchronization in Complex Dynamical Networks Coupled with Chaotic Systems

Explosive Synchronization in Complex Dynamical Networks Coupled with Chaotic Systems

DOI: 10.4236/wjm.2019.911016 246 World Journal of Mechanics scale-free network model whose degree distribution obeys a power-law distribu- tion [3], is proposed by Barabási and Albert in 1999. Since then, they make great progress of complex networks and become the theoretical basis of modern com- plex networks. Synchronization, as a collective dynamical behavior, is an impor- tant and interesting direction of complex networks. In the past two decades, synchronization of complex networks has extensively attracted increasing atten- tion and practical applications [4]-[10], such as parallel computing. However, all the reported cases examples are of continuous phase transitions.
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Dynamic topologies for sustainable and energy efficient traffic engineering in communication networks

Dynamic topologies for sustainable and energy efficient traffic engineering in communication networks

Energy use in the global ICT industry is the largest and most significant con- tributor to its carbon footprint, both within the information as well as the communication technology domains. In the ICT sector power is essential to enable both task operations and accomplishment [64]. Electricity is needed to run services, applications and equipment; and for related activities, such as manufacturing and distribution [65]. As presented in the European Com- mission in [66], the total electricity usage of the ICT sector in the European Union was estimated to be 119 TWh in 2005, which corresponds to 4.3% of overall electricity consumption, or 0.6% of total energy consumption. Also, for the U.S., it is estimated that ICT’s share of electricity consumption was approximately 8% in 2008 [67]. The amount of energy consumed by the ICT sector is also increasing rapidly. Bilal et al. [68], for example, have observed that the energy consumption estimates for IT infrastructure for the year 2011 are double than those of 2006 because of the increase in the traffic and subse- quent increase in the network hardware. The contributors to the ICT energy footprint is considerable. Plepys [69] has estimated that Internet equipment consumed approximately 8% of the total power in the United States in 2002 with the prediction to 50% growth within a decade. As predicted in [70], the energy consumption growth of telecom networks in the coming years is in- creasing.
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A new physiology image encryption algorithm based on two dimensional coupled chaotic Map

A new physiology image encryption algorithm based on two dimensional coupled chaotic Map

Key space is the total number of different keys that can be used in the encryption[14,15].There are six parameters in the improved chaotic equation,in theory,the key space of each parameter is 10 14 , due to the actual precision of computer, the key space of each parameter was 10 6 , so the key space of the two-dimensional coupled chaotic map is 1.0*10 36 .It has obvious superiority,and it is easier to implement the algorithm by using hardware. Simulation results show that , even under the condition of existing computer precision,the key space is large enough.And 10 35 =2 117 ,it means that, an attacker needs a 117-bit computer to decode the algorithm.
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Traveling Wave Solutions, Periodic and Chaotic Solutions of a PDE Approximation of Coupled Chua's Circuits.

Traveling Wave Solutions, Periodic and Chaotic Solutions of a PDE Approximation of Coupled Chua's Circuits.

The coupled system is an example of CNNs, as described by Chua in his book [7]. According to Chua, all the CNNs have much in common as each cell can be a model from a biological, neurological, chemical or electronic system. Compared to other systems, electrical circuit net- works are simpler to build, therefore, provide a practical, low cost method to simulate the other networks. We study traveling wave solutions to this CNN system since the existence of such solutions is one of the most prominent features of the network. We notice that our system is one of the simplest generalizations of FitzHugh-Nagumo equation, which is a second order bistable PDE coupled with linear first order ODE. The slow system we consider has two complex eigen- values while in FitzHugh-Nagumos system the one-dimensional slow system has only one real eigenvalue.
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Worst case dimensioning of wireless sensor networks under uncertain topologies

Worst case dimensioning of wireless sensor networks under uncertain topologies

However, it is necessary to assume, besides other factors, a specific network topology before network calculus can be applied. This might be difficult in many application scenarios as the exact routing topology often cannot even roughly be known beforehand. As a very obvious example imagine that the sensor nodes are dropped from a plane. Nevertheless, some parameters restricting the resulting topology might be known. The number of nodes in a sensor field or the maximum hop- distance in the field might be examples for such restricting fac- tors. In particular, such restrictions might be enforced by care- ful topology control of the sensor network, as for example in [5]. While our proposal does not depend on such restrictions it will be discussed how much a worst case dimensioning can benefit from such prerequisites.
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Reliability of communication networks with delay constraints: computational complexity and complete topologies

Reliability of communication networks with delay constraints: computational complexity and complete topologies

Let G = (V ,E) be a graph with a distinguished set of terminal vertices K ⊆ V. We define the K-diameter of G as the maximum distance between any pair of vertices of K. If the edges fail randomly and independently with known probabilities (vertices are always operational), the diameter-constrained K-terminal reliability of G, R K (G,D), is defined as the probability that surviving edges span a subgraph whose K-diameter does not exceed D. In general, the computational complexity of evaluating R K (G,D) is NP-hard, as this measure subsumes the classical K-terminal reliability R K (G), known to belong to this complexity class. In this note, we show that even though for two terminal vertices s and t and D = 2, R {s,t} (G,D) can be determined in polynomial time, the problem of calculating R {s,t} (G,D) for fixed values of D, D ≥ 3, is NP-hard. We also generalize this result for any fixed number of terminal vertices. Although it is very unlikely that general efficient algorithms exist, we present a recursive formulation for the calculation of R {s,t} (G,D) that yields a polynomial time evaluation algo- rithm in the case of complete topologies where the edge set can be partitioned into at most four equi-reliable classes.
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Blocking in wavelength routing networks, Part II: Mesh topologies

Blocking in wavelength routing networks, Part II: Mesh topologies

We have applied our iterative decomposition algorithm to a realistic example of a backbone network, namely, the NSFNET irregular topology shown in Figure 7. Since we will be using trac data reported in [5], following that study, we have also augmented the 14-node NSFNET topology by adding two ctitious nodes, nodes 1 and 16 in Figure 7, to capture the eect of NSFNET's connections to Canada's communication network, CA*net. The resulting topology consists of 16 nodes and a total of 240 source-destination pairs. As in the previous subsection, we have decided to present detailed results for the call blocking probabilities of only a small number of pairs, and to summarize the results for the whole network. Specically, we present detailed results for the blocking probabilities of calls involving nodes along the path (3,5,6,7,9,12,15,16). (We note, however, that the shortest path used by some of these calls is not a sub-path of (3,5,6,7,9,12,15,16); for instance, the shortest path for calls between nodes 3 and 15 is (3,5,11,15).) The 28 source-destination pairs in this path, along with the corresponding shortest path lengths and the labels used in Figures 8 through 11 are shown in Table 4.
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Throughput Analysis of Fading Sensor Networks with Regular and Random Topologies

Throughput Analysis of Fading Sensor Networks with Regular and Random Topologies

This paper addresses the throughput problem for large sensor networks with Rayleigh fading channels. To provide insight on the impact of the topology on the network per- formance, we compare networks with a random topology and three regular topologies. Placing nodes in regular lat- tices has an obvious advantage in terms of coverage [16], so we are not addressing coverage issues here. We define the (per-link) throughput as the expected number of successful packet transmissions of a given link per timeslot. The end-to- end throughput over a multihop connection, defined as the minimum of the throughput values of the links involved, is a performance measure of a route and the MAC scheme.
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Feature-rich networks: going beyond complex network topologies

Feature-rich networks: going beyond complex network topologies

Martin Atzmueller is Associate Professor at the Department of Cognitive Science and Artificial Intelligence at Tilburg University as well as Visiting Professor at the Université Sorbonne Paris Cité. He earned his habilitation (Dr. habil.) in 2013 at the University of Kassel, where he also was appointed as adjunct professor (Privatdozent). Further, he received his Ph.D. (Dr. rer. nat.) in Computer Science from the University of Würzburg in 2006. He studied Computer Science at the University of Texas at Austin (USA) and at the University of Würzburg where he completed his MSc in Computer Science. His research areas include data science, data mining network analysis, wearable sensors and big data. He has published more than 200 scientific articles in top venues, e.g., the International Joint Conference on Artificial Intelligence (IJCAI), the European Conference on Machine Learning and Principles and Practice on Knowledge Discovery in Databases (ECML PKDD), the IEEE Conference on Social Computing (SocialCom), the ACM/IEEE International Conference on Advances in Social Networks Analysis and Mining (ASONAM), the ACM International Conference on Information and Knowledge Management (CIKM) and the ACM Conference on Hypertext and Social Media (HT). He is the winner of several Best Paper and Innovation Awards. He regularly acts as PC member of several top-tier conferences and as co-organizer on a number of international workshops, conferences, and tutorials on the topics of data science and network science, in particular on community detection and mining attributed networks. He can be contacted at m.atzmuller@uvt.nl, and his web site is at https://martin.atzmueller.net. Contact info: Tilburg University, Department of Cognitive Science and Artificial Intelligence, Warandelaan 2, 5037 AB Tilburg, Netherlands, Tel: +31-(0)13 466 4736, m.atzmuller@uvt.nl
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Coupled Clustering Ensemble by Exploring Data Interdependence

Coupled Clustering Ensemble by Exploring Data Interdependence

Clustering ensembles combine multiple partitions of data into a single clustering solution. It is an effective technique for improving the quality of clustering results. Current clustering ensemble algorithms are usually built on the pairwise agree- ments between clusterings that focus on the similarity via consensus functions, between data objects that induce similarity measures from partitions and re-cluster objects, and between clusters that collapse groups of clusters into meta-clusters. In most of those models, there is a strong assumption on IIDness (i.e. independent and identical distribution), which states that base clusterings perform independently of one another and all objects are also independent. In the real-world, however, objects are generally likely related to each other through features that are either explicit or even implicit. There is also latent but definite relationship among intermediate base clusterings because they are derived from the same set of data. All these demand a further investigation of clustering ensembles that explores the interdependence characteristics of data. To solve this problem, a new coupled clustering ensemble (i.e. CCE) framework that works on the interdependence nature of objects and intermediate base clusterings is proposed in this paper. The main idea is to model the coupling relationship between objects by aggregating the similarity of base clusterings, and the interactive relationship among objects by addressing their neighbor- hood domains. Once these interdependence relationships are discovered, they will act as critical supplements to clustering ensembles. We verified our proposed framework by using three types of consensus function: clustering-based, object-based, and cluster-based. Substantial experiments on multiple synthetic and real-life benchmark data sets indicate that CCE can ef- fectively capture the implicit interdependence relationships among base clusterings and among objects with higher clustering accuracy, stability, and robustness compared to 14 state-of-the-art techniques, supported by statistical analysis. In addition, we show that the final clustering quality is dependent on the data characteristics (e.g. quality and consistency) of base clus- terings in terms of sensitivity analysis. Finally, the applications in document clustering, as well as on the data sets with much larger size and dimensionality, further demonstrate the effectiveness, efficiency, and scalability of our proposed models. CCS Concepts: rComputing methodologies → Ensemble methods; Learning latent representations; rInformation sys- tems → Clustering; rApplied computing → Document analysis;
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14. Iterative sequence of maps in a metric space with
some chaotic properties

14. Iterative sequence of maps in a metric space with some chaotic properties

A general discrete dynamical system is sometimes defined as a pair (X, f ) con- sisting of a set X together with a continuous map f from X into itself. The subject dynamical system has its roots in classical mechanics, where X is taken as the set of all possible states of a system and the transformation f is the time evolution map. Chaotic dynamical systems constitute a special class of dynamical systems. During the last four decades discrete dynamical systems, in particular chaotic dynamical systems, have been studied extensively. Although there is no universally accepted mathematical definition of chaos, it is generally believed that if for a system the dis- tance between two nearby points increases and the distance between two far away points decreases with time, the system is said to be chaotic. The first mathematical definition of chaos was given by Li and Yorke [8] in 1975. Robinson’s chaos [9] is another type of chaos. Later, Devaney [4] characterized chaos in a somewhat differ- ent way. Devaney’s definition of chaos is one of the most popular and most widely known definitions of chaos for the discrete dynamical systems. The three conditions of Devaney’s definition are i) topological transitivity, ii) denseness properties of the set of periodic points and iii) sensitive dependence on initial conditions. Later it was shown by Banks et al [1] that conditions i) and ii) together imply condition iii). Although chaotic behaviors of continuous maps in general metric spaces are difficult to study, some progress has been made in this direction during the last three decades. Most of these research papers are concerned with compact metric
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An Effective Routing Algorithm with Chaotic Neurodynamics for Optimizing Communication Networks

An Effective Routing Algorithm with Chaotic Neurodynamics for Optimizing Communication Networks

this information, the routing algorithm [1,30] shows high performance for the communication network. Thus, we expect that the performance of the chaotic routing algo- rithm [14-19] is also enhanced if the node obtains not only the shortest distance information but also the wait- ing-time information at adjacent nodes. Further, using memory information obtaining from the refractory effect of the chaotic neuron, the improved chaotic routing algo- rithm may show better performance than the Echenique routing algorithm [1,30] by introducing the waiting-time information at adjacent nodes. From the above view- points, we improved the previous chaotic routing algo- rithm [14-19] by introducing the shortest distance infor- mation and the waiting time information at adjacent nodes [20]. Then, we confirmed that the improved cha- otic routing algorithm has high performance in complex networks such as small-world networks [31] and scale- free networks [32]. However, in the previous works [14- 20], we evaluated the chaotic routing algorithm for ideal communication networks, wherein each node has equal transmission capability for routing the packets and equal buffer size for storing the packets. To check whether the chaotic routing algorithm is practically applicable, it is important to evaluate its performance under realistic conditions. In 2007, M. Hu et al. proposed a realistic communication network in which the largest storage ca- pacity and processing capability were introduced [5]. Newman et al. proposed scale-free networks with com- munity structures [33]; these networks effectively ex- tract communities in real complex networks using the shortest path betweenness. In addition, the scale-free networks [33] have a common structure in real complex networks such as collaboration networks or communica- tion networks. In this study, we evaluate the chaotic routing algorithm for communication networks [5,33] to which realistic conditions are introduced. We confirmed that the chaotic routing algorithm by effectively pre- venting the congestion of packets, exhibits better per- formance than the conventional routing algorithms. Further, results indicate that the improved chaotic rout- ing algorithm can be realized in low-cost communica- tion networks in contrast to other conventional routing algorithms.
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Impulsive synchronization of drive response chaotic delayed neural networks

Impulsive synchronization of drive response chaotic delayed neural networks

On the other hand, due to the transmission speed of signals or information between neurons is finite, neural networks with coupling delay should be considered. Motivated by the above discussions, in this paper, we investigate the impulsive synchronization of drive- response chaotic delayed neural networks. Firstly, we give some sufficient conditions for achieving synchronization, from which we can easily estimate the largest impulsive inter- vals for given neural networks and impulsive gains. Secondly, we adopt adaptive strategy to design adaptive impulsive controllers for relaxing the restrictions. Noticeably, the de- signed controllers are universal for different neural networks. Finally, we perform some numerical examples to verify the obtained results.
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Exploring chaotic time series and phase spaces:from dynamical systems to visual analytics

Exploring chaotic time series and phase spaces:from dynamical systems to visual analytics

Despite groups of points cannot be correlated to anchors in the LAMP scatterplot, it still valid to explain them in terms of variable ranges.. Adapted from Pagliosa and Telea ( 2019 ).[r]

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Dynamic Bandwidth-Efficient BCube Topologies for Virtualized Data Center Networks

Dynamic Bandwidth-Efficient BCube Topologies for Virtualized Data Center Networks

Topology mapping is a well-known action in operating virtual network that allows mapping an arbitrary virtual network topology on the fix topology of the physical layer. In a virtualization environment, topology mapping stands for expressing a requested VNet topology sent to the service providers in terms of specific layout patterns of the interconnections of network elements, such as links and nodes, along with a set of specific service-oriented constraints, such as CPU capacity and link bandwidth [ 23 ]. Various parameters are considered in designing a topology mapping algorithm. Despite the freedom that this approach provides, it could impose a considerable overhead in both mapping action itself and also in the operation of the network because of non-optimal solution obtained from a particular algorithm, especially when many VNets are mapped on the same physical layer. This disadvantage could be very significant in the case of big physical layer networks that are more popular in resource sharing approaches such as cloud computing. In the topology mapping, there is always a downward mapping between the virtual layer elements and the physical layer elements. This one-way approach would result in cases in which the mapped topology on the physical layer and the original requested topology have a significant topological distance despite having a negligible distance in terms of requested service-oriented constraints. This disparity, which is the result of unawareness of the VNet about the actual physical topology, could result in a premature default of the service because of component failures or DC traffic congestion.
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Efficient reengineering of meso-scale topologies for functional networks in biomedical applications

Efficient reengineering of meso-scale topologies for functional networks in biomedical applications

The established network reconstruction algorithms for reconstruction of signalling networks using phosphorylation data in response to external stimuli typically solve a combinatorial, mixed-integer optimization problem in order to minimize the error of a network-based signalling model with given experimental data. Nodes represent target proteins and edges (connections between nodes) represent the cascade direction of stimulated protein phosphorylation. However, if the number n of network nodes increases, then the number of potential networks to be analyzed will increase at least exponentially with n. Thus, any algorithm using an exhaustive search analyzing all possible networks with n nodes will become impractical even at modest n. Since most mechanisms which are relevant for applications involve multiple pathways and their crosstalk, there is a need for algorithms which avoid the pitfalls of detailed network reengineering in only one step.
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