Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.
Klarner, Hannes; Siebert, Heike
2015-01-01
This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.
Kimoto, Tomoyuki; Uezu, Tatsuya; Okada, Masato
2008-12-01
We study a neural network model for the inferior temporal cortex, in terms of finite memory loading and sparse coding. We show that an uncorrelated Hopfield-type attractor and some correlated attractors have multiple stability, and examine the retrieval dynamics for these attractors when the initial state is set to a noise-degraded memory pattern. Then, we show that there is a critical initial overlap: that is, the system converges to the correlated attractor when the noise level is large, and otherwise to the Hopfield-type attractor. Furthermore, we study the time course of the correlation between the correlated attractors in the retrieval dynamics. On the basis of these theoretical results, we resolve the controversy regarding previous physiologic experimental findings regarding neuron properties in the inferior temporal cortex and propose a new experimental paradigm.
Li, X Y; Yang, G W; Zheng, D S; Guo, W S; Hung, W N N
2015-01-01
Genetic regulatory networks are the key to understanding biochemical systems. One condition of the genetic regulatory network under different living environments can be modeled as a synchronous Boolean network. The attractors of these Boolean networks will help biologists to identify determinant and stable factors. Existing methods identify attractors based on a random initial state or the entire state simultaneously. They cannot identify the fixed length attractors directly. The complexity of including time increases exponentially with respect to the attractor number and length of attractors. This study used the bounded model checking to quickly locate fixed length attractors. Based on the SAT solver, we propose a new algorithm for efficiently computing the fixed length attractors, which is more suitable for large Boolean networks and numerous attractors' networks. After comparison using the tool BooleNet, empirical experiments involving biochemical systems demonstrated the feasibility and efficiency of our approach.
Attractors: architects of network organization?
Mpitsos, G J
2000-05-01
An attractor is defined here informally as a state of activity toward which a system settles. The settling or relaxation process dissipates the effects produced by external perturbations. In neural systems the relaxation process occurs temporally in the responses of each neuron and spatially across the network such that the activity settles into a subset of the available connections. Within limits, the set of neurons toward which the coordinated neural firing settles can be different from one time to another, and a given set of neurons can generate different types of attractor activity, depending on how the input environment activates the network. Findings such as these indicate that though information resides in the details of neuroanatomic structure, the expression of this information is in the dynamics of attractors. As such, attractors are sources of information that can be used not only in adaptive behavior, but also to effect the neural architecture that generates the attractor. The discussion here focuses on the latter possibility. A conjecture is offered to show that the relaxation dynamic of an attractor may 'guide' activity-dependent learning processes in such a way that synaptic strengths, firing thresholds, the physical connections between neurons, and the size of the network are automatically set in an optimal, interrelated fashion. This inter-relatedness among network parameters would not be expected from more classical, 'switchboard' approaches to neural integration. The ideas are discussed within the context of 'pulse-propagated networks' or equivalently as 'spike-activated networks' in which the specific order in time intervals between action potentials carries important information for cooperative activity to emerge among neurons in a network. Though the proposed ideas are forward-looking, being based on preliminary work in biological and artificial networks, they are testable in biological neural networks reconstructed from identified neurons in
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Ildefonso M De la Fuente
Full Text Available BACKGROUND: The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity. METHODOLOGY/PRINCIPAL FINDINGS: In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network. CONCLUSIONS/SIGNIFICANCE: We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns
Attractor dynamics in local neuronal networks
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Jean-Philippe eThivierge
2014-03-01
Full Text Available Patterns of synaptic connectivity in various regions of the brain are characterized by the presence of synaptic motifs, defined as unidirectional and bidirectional synaptic contacts that follow a particular configuration and link together small groups of neurons. Recent computational work proposes that a relay network (two populations communicating via a third, relay population of neurons can generate precise patterns of neural synchronization. Here, we employ two distinct models of neuronal dynamics and show that simulated neural circuits designed in this way are caught in a global attractor of activity that prevents neurons from modulating their response on the basis of incoming stimuli. To circumvent the emergence of a fixed global attractor, we propose a mechanism of selective gain inhibition that promotes flexible responses to external stimuli. We suggest that local neuronal circuits may employ this mechanism to generate precise patterns of neural synchronization whose transient nature delimits the occurrence of a brief stimulus.
Algorithms for Finding Small Attractors in Boolean Networks
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Hayashida Morihiro
2007-01-01
Full Text Available A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.
Monasson, R.; Rosay, S.
2013-06-01
We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding one-dimensional (1D) or 2D spatial maps or environments. Different maps correspond to random allocations (permutations) of the place fields. Based on replica calculations we show that, below critical levels for the noise in the neural response and for the number of environments, the network activity is spatially localized in one environment. For high noise and loads the network activity extends over space, either uniformly or with spatial heterogeneities due to the crosstalk between the maps, and memory of environments is lost. Remarkably the spatially localized regime is very robust against the neural noise until it reaches its critical level. Numerical simulations are in excellent quantitative agreement with our theoretical predictions.
Google matrix, dynamical attractors, and Ulam networks
Shepelyansky, D. L.; Zhirov, O. V.
2010-03-01
We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite-size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model generates directed Ulam networks with approximate scale-free scaling and characteristics being in certain features similar to those of the world wide web with approximate scale-free degree distributions as well as two characteristics similar to the web: a power-law decay in PageRank that mirrors the decay of PageRank on the world wide web and a sensitivity to the value α in PageRank. The simple dynamical attractors play here the role of popular websites with a strong concentration of PageRank. A variation in the Google parameter α or other parameters of the dynamical map can drive the PageRank of the Google matrix to a delocalized phase with a strange attractor where the Google search becomes inefficient.
An efficient approach of attractor calculation for large-scale Boolean gene regulatory networks.
He, Qinbin; Xia, Zhile; Lin, Bin
2016-11-07
Boolean network models provide an efficient way for studying gene regulatory networks. The main dynamics of a Boolean network is determined by its attractors. Attractor calculation plays a key role for analyzing Boolean gene regulatory networks. An approach of attractor calculation was proposed in this study, which improved the predecessor-based approach. Furthermore, the proposed approach combined with the identification of constant nodes and simplified Boolean networks to accelerate attractor calculation. The proposed algorithm is effective to calculate all attractors for large-scale Boolean gene regulatory networks. If the average degree of the network is not too large, the algorithm can get all attractors of a Boolean network with dozens or even hundreds of nodes.
Continuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons.
Yu, Jiali; Yi, Zhang; Zhou, Jiliu
2010-10-01
Continuous attractors of Lotka-Volterra recurrent neural networks (LV RNNs) with infinite neurons are studied in this brief. A continuous attractor is a collection of connected equilibria, and it has been recognized as a suitable model for describing the encoding of continuous stimuli in neural networks. The existence of the continuous attractors depends on many factors such as the connectivity and the external inputs of the network. A continuous attractor can be stable or unstable. It is shown in this brief that a LV RNN can possess multiple continuous attractors if the synaptic connections and the external inputs are Gussian-like in shape. Moreover, both stable and unstable continuous attractors can coexist in a network. Explicit expressions of the continuous attractors are calculated. Simulations are employed to illustrate the theory.
Stabilization of perturbed Boolean network attractors through compensatory interactions
2014-01-01
Background Understanding and ameliorating the effects of network damage are of significant interest, due in part to the variety of applications in which network damage is relevant. For example, the effects of genetic mutations can cascade through within-cell signaling and regulatory networks and alter the behavior of cells, possibly leading to a wide variety of diseases. The typical approach to mitigating network perturbations is to consider the compensatory activation or deactivation of system components. Here, we propose a complementary approach wherein interactions are instead modified to alter key regulatory functions and prevent the network damage from triggering a deregulatory cascade. Results We implement this approach in a Boolean dynamic framework, which has been shown to effectively model the behavior of biological regulatory and signaling networks. We show that the method can stabilize any single state (e.g., fixed point attractors or time-averaged representations of multi-state attractors) to be an attractor of the repaired network. We show that the approach is minimalistic in that few modifications are required to provide stability to a chosen attractor and specific in that interventions do not have undesired effects on the attractor. We apply the approach to random Boolean networks, and further show that the method can in some cases successfully repair synchronous limit cycles. We also apply the methodology to case studies from drought-induced signaling in plants and T-LGL leukemia and find that it is successful in both stabilizing desired behavior and in eliminating undesired outcomes. Code is made freely available through the software package BooleanNet. Conclusions The methodology introduced in this report offers a complementary way to manipulating node expression levels. A comprehensive approach to evaluating network manipulation should take an "all of the above" perspective; we anticipate that theoretical studies of interaction modification
ILP/SMT-Based Method for Design of Boolean Networks Based on Singleton Attractors.
Kobayashi, Koichi; Hiraishi, Kunihiko
2014-01-01
Attractors in gene regulatory networks represent cell types or states of cells. In system biology and synthetic biology, it is important to generate gene regulatory networks with desired attractors. In this paper, we focus on a singleton attractor, which is also called a fixed point. Using a Boolean network (BN) model, we consider the problem of finding Boolean functions such that the system has desired singleton attractors and has no undesired singleton attractors. To solve this problem, we propose a matrix-based representation of BNs. Using this representation, the problem of finding Boolean functions can be rewritten as an Integer Linear Programming (ILP) problem and a Satisfiability Modulo Theories (SMT) problem. Furthermore, the effectiveness of the proposed method is shown by a numerical example on a WNT5A network, which is related to melanoma. The proposed method provides us a basic method for design of gene regulatory networks.
Adaptive synchronization of neural networks with different attractors
Institute of Scientific and Technical Information of China (English)
Zhang Huaguang; Guan Huanxin; Wang Zhanshan
2007-01-01
This paper aims to present an adaptive control scheme for the synchronization of two classes of uncertain neural networks with different attractors. A new sufficient condition for the global synchronization of two kinds of neural networks with different attractors is derived. The proposed control method is efficient and easy to be implemented. Numerical simulation is used to show the effectiveness of the obtained result.
Reactivation in working memory: an attractor network model of free recall.
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Anders Lansner
Full Text Available The dynamic nature of human working memory, the general-purpose system for processing continuous input, while keeping no longer externally available information active in the background, is well captured in immediate free recall of supraspan word-lists. Free recall tasks produce several benchmark memory phenomena, like the U-shaped serial position curve, reflecting enhanced memory for early and late list items. To account for empirical data, including primacy and recency as well as contiguity effects, we propose here a neurobiologically based neural network model that unifies short- and long-term forms of memory and challenges both the standard view of working memory as persistent activity and dual-store accounts of free recall. Rapidly expressed and volatile synaptic plasticity, modulated intrinsic excitability, and spike-frequency adaptation are suggested as key cellular mechanisms underlying working memory encoding, reactivation and recall. Recent findings on the synaptic and molecular mechanisms behind early LTP and on spiking activity during delayed-match-to-sample tasks support this view.
Strong Attractors in Stochastic Adaptive Networks: Emergence and Characterization
Santos, Augusto Almeida; Krishnan, Ramayya; Moura, José M F
2016-01-01
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical systems, on the edges of a graph, exhibits \\emph{good} convergence properties, in particular, we prove a strong-stability result: a subset of binary matrices or graphs -- characterized by certain compatibility properties -- is a global almost sure attractor of the family of stochastic dynamical systems. To illustrate finer properties of the corresponding strong attractor, we present some simulation results that capture, e.g., the conspicuous phenomenon of emergence and downfall of leaders in social networks.
Dynamics of neural networks with continuous attractors
Fung, C. C. Alan; Wong, K. Y. Michael; Wu, Si
2008-10-01
We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.
Cosmological Attractor Models and Higher Curvature Supergravity
Cecotti, Sergio
2014-01-01
We study cosmological $\\alpha$-attractors in superconformal/supergravity models, where $\\alpha$ is related to the geometry of the moduli space. For $\\alpha=1$ attractors \\cite{Kallosh:2013hoa} we present a generalization of the previously known manifestly superconformal higher curvature supergravity model \\cite{Cecotti:1987sa}. The relevant standard 2-derivative supergravity with a minimum of two chiral multiplets is shown to be dual to a 4-derivative higher curvature supergravity, where in general one of the chiral superfields is traded for a curvature superfield. There is a degenerate case when both matter superfields become non-dynamical and there is only a chiral curvature superfield, pure higher derivative supergravity. Generic $\\alpha$-models \\cite{Kallosh:2013yoa} interpolate between the attractor point at $\\alpha=0$ and generic chaotic inflation models at large $\\alpha$, in the limit when the inflaton moduli space becomes flat. They have higher derivative duals with the same number of matter fields as...
Poret, Arnaud; Boissel, Jean-Pierre
2014-12-01
Target identification aims at identifying biomolecules whose function should be therapeutically altered to cure the considered pathology. An algorithm for in silico target identification using Boolean network attractors is proposed. It assumes that attractors correspond to phenotypes produced by the modeled biological network. It identifies target combinations which allow disturbed networks to avoid attractors associated with pathological phenotypes. The algorithm is tested on a Boolean model of the mammalian cell cycle and its applications are illustrated on a Boolean model of Fanconi anemia. Results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice. Nevertheless, it is expected that the algorithm is of interest for target identification.
Tracking dynamics of two-dimensional continuous attractor neural networks
Fung, C. C. Alan; Wong, K. Y. Michael; Wu, Si
2009-12-01
We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.
Roach, James; Sander, Leonard; Zochowski, Michal
Auto-associative memory is the ability to retrieve a pattern from a small fraction of the pattern and is an important function of neural networks. Within this context, memories that are stored within the synaptic strengths of networks act as dynamical attractors for network firing patterns. In networks with many encoded memories, some attractors will be stronger than others. This presents the problem of how networks switch between attractors depending on the situation. We suggest that regulation of neuronal spike-frequency adaptation (SFA) provides a universal mechanism for network-wide attractor selectivity. Here we demonstrate in a Hopfield type attractor network that neurons minimal SFA will reliably activate in the pattern corresponding to a local attractor and that a moderate increase in SFA leads to the network to converge to the strongest attractor state. Furthermore, we show that on long time scales SFA allows for temporal sequences of activation to emerge. Finally, using a model of cholinergic modulation within the cortex we argue that dynamic regulation of attractor preference by SFA could be critical for the role of acetylcholine in attention or for arousal states in general. This work was supported by: NSF Graduate Research Fellowship Program under Grant No. DGE 1256260 (JPR), NSF CMMI 1029388 (MRZ) and NSF PoLS 1058034 (MRZ & LMS).
Competition between synaptic depression and facilitation in attractor neural networks.
Torres, J.J.; Cortes, J.M.; Marro, J.; Kappen, H.J.
2007-01-01
We study the effect of competition between short-term synaptic depression and facilitation on the dynamic properties of attractor neural networks, using Monte Carlo simulation and a mean-field analysis. Depending on the balance of depression, facilitation, and the underlying noise, the network displ
Lerner, Itamar; Bentin, Shlomo; Shriki, Oren
2012-01-01
Localist models of spreading activation (SA) and models assuming distributed representations offer very different takes on semantic priming, a widely investigated paradigm in word recognition and semantic memory research. In this study, we implemented SA in an attractor neural network model with distributed representations and created a unified…
Analytical estimates of efficiency of attractor neural networks with inborn connections
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Solovyeva Ksenia
2016-01-01
Full Text Available The analysis is restricted to the features of neural networks endowed to the latter by the inborn (not learned connections. We study attractor neural networks in which for almost all operation time the activity resides in close vicinity of a relatively small number of attractor states. The number of the latter, M, is proportional to the number of neurons in the neural network, N, while the total number of the states in it is 2N. The unified procedure of growth/fabrication of neural networks with sets of all attractor states with dimensionality d=0 and d=1, based on model molecular markers, is studied in detail. The specificity of the networks (d=0 or d=1 depends on topology (i.e., the set of distances between elements which can be provided to the set of molecular markers by their physical nature. The neural networks parameters estimates and trade-offs for them in attractor neural networks are calculated analytically. The proposed mechanisms reveal simple and efficient ways of implementation in artificial as well as in natural neural networks of multiplexity, i.e. of using activity of single neurons in representation of multiple values of the variables, which are operated by the neural systems. It is discussed how the neuronal multiplexity provides efficient and reliable ways of performing functional operations in the neural systems.
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Wensheng Guo
Full Text Available In biological systems, the dynamic analysis method has gained increasing attention in the past decade. The Boolean network is the most common model of a genetic regulatory network. The interactions of activation and inhibition in the genetic regulatory network are modeled as a set of functions of the Boolean network, while the state transitions in the Boolean network reflect the dynamic property of a genetic regulatory network. A difficult problem for state transition analysis is the finding of attractors. In this paper, we modeled the genetic regulatory network as a Boolean network and proposed a solving algorithm to tackle the attractor finding problem. In the proposed algorithm, we partitioned the Boolean network into several blocks consisting of the strongly connected components according to their gradients, and defined the connection between blocks as decision node. Based on the solutions calculated on the decision nodes and using a satisfiability solving algorithm, we identified the attractors in the state transition graph of each block. The proposed algorithm is benchmarked on a variety of genetic regulatory networks. Compared with existing algorithms, it achieved similar performance on small test cases, and outperformed it on larger and more complex ones, which happens to be the trend of the modern genetic regulatory network. Furthermore, while the existing satisfiability-based algorithms cannot be parallelized due to their inherent algorithm design, the proposed algorithm exhibits a good scalability on parallel computing architectures.
Guo, Wensheng; Yang, Guowu; Wu, Wei; He, Lei; Sun, Mingyu
2014-01-01
In biological systems, the dynamic analysis method has gained increasing attention in the past decade. The Boolean network is the most common model of a genetic regulatory network. The interactions of activation and inhibition in the genetic regulatory network are modeled as a set of functions of the Boolean network, while the state transitions in the Boolean network reflect the dynamic property of a genetic regulatory network. A difficult problem for state transition analysis is the finding of attractors. In this paper, we modeled the genetic regulatory network as a Boolean network and proposed a solving algorithm to tackle the attractor finding problem. In the proposed algorithm, we partitioned the Boolean network into several blocks consisting of the strongly connected components according to their gradients, and defined the connection between blocks as decision node. Based on the solutions calculated on the decision nodes and using a satisfiability solving algorithm, we identified the attractors in the state transition graph of each block. The proposed algorithm is benchmarked on a variety of genetic regulatory networks. Compared with existing algorithms, it achieved similar performance on small test cases, and outperformed it on larger and more complex ones, which happens to be the trend of the modern genetic regulatory network. Furthermore, while the existing satisfiability-based algorithms cannot be parallelized due to their inherent algorithm design, the proposed algorithm exhibits a good scalability on parallel computing architectures.
Pattern Selection in Network of Coupled Multi-Scroll Attractors.
Li, Fan; Ma, Jun
2016-01-01
Multi-scroll chaotic attractor makes the oscillator become more complex in dynamic behaviors. The collective behaviors of coupled oscillators with multi-scroll attractors are investigated in the regular network in two-dimensional array, which the local kinetics is described by an improved Chua circuit. A feasible scheme of negative feedback with diversity is imposed on the network to stabilize the spatial patterns. Firstly, the Chua circuit is improved by replacing the nonlinear term with Sine function to generate infinite aquariums so that multi-scroll chaotic attractors could be generated under appropriate parameters, which could be detected by calculating the Lyapunov exponent in the parameter region. Furthermore, negative feedback with different gains (D1, D2) is imposed on the local square center area A2 and outer area A1 of the network, it is found that spiral wave, target wave could be developed in the network under appropriate feedback gain with diversity and size of controlled area. Particularly, homogeneous state could be reached after synchronization by selecting appropriate feedback gain and controlled size in the network. Finally, the distribution for statistical factors of synchronization is calculated in the two-parameter space to understand the transition of pattern region. It is found that developed spiral waves, target waves often are associated with smaller factor of synchronization. These results show that emergence of sustained spiral wave and continuous target wave could be effective for further suppression of spatiotemporal chaos in network by generating stable pacemaker completely.
Pattern Selection in Network of Coupled Multi-Scroll Attractors.
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Fan Li
Full Text Available Multi-scroll chaotic attractor makes the oscillator become more complex in dynamic behaviors. The collective behaviors of coupled oscillators with multi-scroll attractors are investigated in the regular network in two-dimensional array, which the local kinetics is described by an improved Chua circuit. A feasible scheme of negative feedback with diversity is imposed on the network to stabilize the spatial patterns. Firstly, the Chua circuit is improved by replacing the nonlinear term with Sine function to generate infinite aquariums so that multi-scroll chaotic attractors could be generated under appropriate parameters, which could be detected by calculating the Lyapunov exponent in the parameter region. Furthermore, negative feedback with different gains (D1, D2 is imposed on the local square center area A2 and outer area A1 of the network, it is found that spiral wave, target wave could be developed in the network under appropriate feedback gain with diversity and size of controlled area. Particularly, homogeneous state could be reached after synchronization by selecting appropriate feedback gain and controlled size in the network. Finally, the distribution for statistical factors of synchronization is calculated in the two-parameter space to understand the transition of pattern region. It is found that developed spiral waves, target waves often are associated with smaller factor of synchronization. These results show that emergence of sustained spiral wave and continuous target wave could be effective for further suppression of spatiotemporal chaos in network by generating stable pacemaker completely.
Models of Innate Neural Attractors and Their Applications for Neural Information Processing.
Solovyeva, Ksenia P; Karandashev, Iakov M; Zhavoronkov, Alex; Dunin-Barkowski, Witali L
2015-01-01
In this work we reveal and explore a new class of attractor neural networks, based on inborn connections provided by model molecular markers, the molecular marker based attractor neural networks (MMBANN). Each set of markers has a metric, which is used to make connections between neurons containing the markers. We have explored conditions for the existence of attractor states, critical relations between their parameters and the spectrum of single neuron models, which can implement the MMBANN. Besides, we describe functional models (perceptron and SOM), which obtain significant advantages over the traditional implementation of these models, while using MMBANN. In particular, a perceptron, based on MMBANN, gets specificity gain in orders of error probabilities values, MMBANN SOM obtains real neurophysiological meaning, the number of possible grandma cells increases 1000-fold with MMBANN. MMBANN have sets of attractor states, which can serve as finite grids for representation of variables in computations. These grids may show dimensions of d = 0, 1, 2,…. We work with static and dynamic attractor neural networks of the dimensions d = 0 and 1. We also argue that the number of dimensions which can be represented by attractors of activities of neural networks with the number of elements N = 10(4) does not exceed 8.
MODELS OF INNATE NEURAL ATTRACTORS AND THEIR APPLICATIONS FOR NEURALINFORMATION PROCESSING
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Ksenia P. Solovyeva
2016-01-01
Full Text Available In this work we reveal and explore a new class of attractor neural networks, based on inborn connections provided by model molecular markers, the molecular marker based attractor neural networks (MMBANN. Each set of markers has a metric, which is used to make connections between neurons containing the markers. We have explored conditions for the existence of attractor states, critical relations between their parameters and the spectrum of single neuron models, which can implement the MMBANN. Besides, we describe functional models (perceptron and SOM, which obtain significant advantages over the traditional implementation of these models, while using MMBANN. In particular, a perceptron, based on MMBANN, gets specificity gain in orders of error probabilities values, MMBANN SOM obtains real neurophysiological meaning, the number of possible grandma cells increases 1000-fold with MMBANN. MMBANN have sets of attractor states, which can serve as finite grids for representation of variables in computations. These grids may show dimensions of d = 0, 1, 2, ... We work with static and dynamic attractor neural networks of the dimensions d = 0 and d = 1. We also argue that the number of dimensions which can be represented by attractors of activities of neural networks with the number of elements N=104 does not exceed 8.
A SAT-based algorithm for finding attractors in synchronous Boolean networks.
Dubrova, Elena; Teslenko, Maxim
2011-01-01
This paper addresses the problem of finding attractors in synchronous Boolean networks. The existing Boolean decision diagram-based algorithms have limited capacity due to the excessive memory requirements of decision diagrams. The simulation-based algorithms can be applied to larger networks, however, they are incomplete. We present an algorithm, which uses a SAT-based bounded model checking to find all attractors in a Boolean network. The efficiency of the presented algorithm is evaluated by analyzing seven networks models of real biological processes, as well as 150,000 randomly generated Boolean networks of sizes between 100 and 7,000. The results show that our approach has a potential to handle an order of magnitude larger models than currently possible.
From Cellular Attractor Selection to Adaptive Signal Control for Traffic Networks
Tian, Daxin; Zhou, Jianshan; Sheng, Zhengguo; Wang, Yunpeng; Ma, Jianming
2016-03-01
The management of varying traffic flows essentially depends on signal controls at intersections. However, design an optimal control that considers the dynamic nature of a traffic network and coordinates all intersections simultaneously in a centralized manner is computationally challenging. Inspired by the stable gene expressions of Escherichia coli in response to environmental changes, we explore the robustness and adaptability performance of signalized intersections by incorporating a biological mechanism in their control policies, specifically, the evolution of each intersection is induced by the dynamics governing an adaptive attractor selection in cells. We employ a mathematical model to capture such biological attractor selection and derive a generic, adaptive and distributed control algorithm which is capable of dynamically adapting signal operations for the entire dynamical traffic network. We show that the proposed scheme based on attractor selection can not only promote the balance of traffic loads on each link of the network but also allows the global network to accommodate dynamical traffic demands. Our work demonstrates the potential of bio-inspired intelligence emerging from cells and provides a deep understanding of adaptive attractor selection-based control formation that is useful to support the designs of adaptive optimization and control in other domains.
An attractor-based complexity measurement for Boolean recurrent neural networks.
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Jérémie Cabessa
Full Text Available We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of ω-automata, and then translating the most refined classification of ω-automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits.
An attractor-based complexity measurement for Boolean recurrent neural networks.
Cabessa, Jérémie; Villa, Alessandro E P
2014-01-01
We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of ω-automata, and then translating the most refined classification of ω-automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits.
Sensory feedback in a bump attractor model of path integration.
Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P
2016-04-01
Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.
Detecting small attractors of large Boolean networks by function-reduction-based strategy.
Zheng, Qiben; Shen, Liangzhong; Shang, Xuequn; Liu, Wenbin
2016-04-01
Boolean networks (BNs) are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behaviour of systems. A central aim of Boolean-network analysis is to find attractors that correspond to various cellular states, such as cell types or the stage of cell differentiation. This problem is NP-hard and various algorithms have been used to tackle it with considerable success. The idea is that a singleton attractor corresponds to n consistent subsequences in the truth table. To find these subsequences, the authors gradually reduce the entire truth table of Boolean functions by extending a partial gene activity profile (GAP). Not only does this process delete inconsistent subsequences in truth tables, it also directly determines values for some nodes not extended, which means it can abandon the partial GAPs that cannot lead to an attractor as early as possible. The results of simulation show that the proposed algorithm can detect small attractors with length p = 4 in BNs of up to 200 nodes with average indegree K = 2.
Navigating cancer network attractors for tumor-specific therapy
DEFF Research Database (Denmark)
Creixell, Pau; Schoof, Erwin; Erler, Janine Terra
2012-01-01
Cells employ highly dynamic signaling networks to drive biological decision processes. Perturbations to these signaling networks may attract cells to new malignant signaling and phenotypic states, termed cancer network attractors, that result in cancer development. As different cancer cells reach...... these malignant states by accumulating different molecular alterations, uncovering these mechanisms represents a grand challenge in cancer biology. Addressing this challenge will require new systems-based strategies that capture the intrinsic properties of cancer signaling networks and provide deeper...... understanding of the processes by which genetic lesions perturb these networks and lead to disease phenotypes. Network biology will help circumvent fundamental obstacles in cancer treatment, such as drug resistance and metastasis, empowering personalized and tumor-specific cancer therapies....
Learning chaotic attractors by neural networks
Bakker, R; Schouten, JC; Giles, CL; Takens, F; van den Bleek, CM
2000-01-01
An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured time series. During training, the algorithm learns to short-term predict the time series. At the same time a criterion, developed by Diks, van Zwet, Takens, and de Goede (1996) is monitored th
An efficient algorithm for computing attractors of synchronous and asynchronous Boolean networks.
Directory of Open Access Journals (Sweden)
Desheng Zheng
Full Text Available Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD, we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly [Formula: see text] faster in computing attractors for empirical experimental systems.The software package is available at https://sites.google.com/site/desheng619/download.
An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks
Zheng, Desheng; Yang, Guowu; Li, Xiaoyu; Wang, Zhicai; Liu, Feng; He, Lei
2013-01-01
Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly faster in computing attractors for empirical experimental systems. Availability The software package is available at https://sites.google.com/site/desheng619/download. PMID:23585840
Hyperbolic Plykin attractor can exist in neuron models
DEFF Research Database (Denmark)
Belykh, V.; Belykh, I.; Mosekilde, Erik
2005-01-01
Strange hyperbolic attractors are hard to find in real physical systems. This paper provides the first example of a realistic system, a canonical three-dimensional (3D) model of bursting neurons, that is likely to have a strange hyperbolic attractor. Using a geometrical approach to the study...... of the neuron model, we derive a flow-defined Poincare map giving ail accurate account of the system's dynamics. In a parameter region where the neuron system undergoes bifurcations causing transitions between tonic spiking and bursting, this two-dimensional map becomes a map of a disk with several periodic...... holes. A particular case is the map of a disk with three holes, matching the Plykin example of a planar hyperbolic attractor. The corresponding attractor of the 3D neuron model appears to be hyperbolic (this property is not verified in the present paper) and arises as a result of a two-loop (secondary...
CMB and reheating constraints to \\alpha-attractor inflationary models
Eshaghi, Mehdi; Riazi, Nematollah; Kiasatpour, Ahmad
2016-01-01
After Planck 2013, a broad class of inflationary models called \\alpha-attractors was developed which has universal observational predictions. For small values of the parameter \\alpha, the models have good consistency with the recent CMB data. In this work, we first calculate analytically (and verify numerically) the predictions of these models for spectral index, n_s and tensor-to-scalar ratio, r and then using BICEP2/Keck 2015 data we impose constraints on \\alpha-attractors. Then, we study the reheating in \\alpha-attractors. The reheating temperature, T_{re} and the number of e-folds during reheating, N_{re} are calculated as functions of n_s. Using these results, we determine the range of free parameter \\alpha for two clasees of \\alpha-attractors which satisfy the constraints of recent CMB data.
Characterization of chaotic attractors under noise: A recurrence network perspective
Jacob, Rinku; Harikrishnan, K. P.; Misra, R.; Ambika, G.
2016-12-01
We undertake a detailed numerical investigation to understand how the addition of white and colored noise to a chaotic time series changes the topology and the structure of the underlying attractor reconstructed from the time series. We use the methods and measures of recurrence plot and recurrence network generated from the time series for this analysis. We explicitly show that the addition of noise obscures the property of recurrence of trajectory points in the phase space which is the hallmark of every dynamical system. However, the structure of the attractor is found to be robust even upto high noise levels of 50%. An advantage of recurrence network measures over the conventional nonlinear measures is that they can be applied on short and non stationary time series data. By using the results obtained from the above analysis, we go on to analyse the light curves from a dominant black hole system and show that the recurrence network measures are capable of identifying the nature of noise contamination in a time series.
Kaneko, K
1998-01-01
Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase. Such dominance of fragile attractors is understood by robustness of global attraction in the phase space. Change of the attractor strength and basin volume against the parameter and size are studied. In the partially ordered phase, the dynamics is often described as Milnor attractor network, which leads to a new interpretation of chaotic itinerancy. Noise-induced selection of fragile attractors is found that has a sharp dependence on the noise amplitude. Relevance of the observed results to neural dynamics and cell differentiation is also discussed.
A cortical attractor network with Martinotti cells driven by facilitating synapses.
Directory of Open Access Journals (Sweden)
Pradeep Krishnamurthy
Full Text Available The population of pyramidal cells significantly outnumbers the inhibitory interneurons in the neocortex, while at the same time the diversity of interneuron types is much more pronounced. One acknowledged key role of inhibition is to control the rate and patterning of pyramidal cell firing via negative feedback, but most likely the diversity of inhibitory pathways is matched by a corresponding diversity of functional roles. An important distinguishing feature of cortical interneurons is the variability of the short-term plasticity properties of synapses received from pyramidal cells. The Martinotti cell type has recently come under scrutiny due to the distinctly facilitating nature of the synapses they receive from pyramidal cells. This distinguishes these neurons from basket cells and other inhibitory interneurons typically targeted by depressing synapses. A key aspect of the work reported here has been to pinpoint the role of this variability. We first set out to reproduce quantitatively based on in vitro data the di-synaptic inhibitory microcircuit connecting two pyramidal cells via one or a few Martinotti cells. In a second step, we embedded this microcircuit in a previously developed attractor memory network model of neocortical layers 2/3. This model network demonstrated that basket cells with their characteristic depressing synapses are the first to discharge when the network enters an attractor state and that Martinotti cells respond with a delay, thereby shifting the excitation-inhibition balance and acting to terminate the attractor state. A parameter sensitivity analysis suggested that Martinotti cells might, in fact, play a dominant role in setting the attractor dwell time and thus cortical speed of processing, with cellular adaptation and synaptic depression having a less prominent role than previously thought.
Algorithms and Complexity Analyses for Control of Singleton Attractors in Boolean Networks
Directory of Open Access Journals (Sweden)
Wai-Ki Ching
2008-09-01
Full Text Available A Boolean network (BN is a mathematical model of genetic networks. We propose several algorithms for control of singleton attractors in BN. We theoretically estimate the average-case time complexities of the proposed algorithms, and confirm them by computer experiments. The results suggest the importance of gene ordering. Especially, setting internal nodes ahead yields shorter computational time than setting external nodes ahead in various types of algorithms. We also present a heuristic algorithm which does not look for the optimal solution but for the solution whose computational time is shorter than that of the exact algorithms.
Attractor dynamics of network UP states in the neocortex
Cossart, Rosa; Aronov, Dmitriy; Yuste, Rafael
2003-05-01
The cerebral cortex receives input from lower brain regions, and its function is traditionally considered to be processing that input through successive stages to reach an appropriate output. However, the cortical circuit contains many interconnections, including those feeding back from higher centres, and is continuously active even in the absence of sensory inputs. Such spontaneous firing has a structure that reflects the coordinated activity of specific groups of neurons. Moreover, the membrane potential of cortical neurons fluctuates spontaneously between a resting (DOWN) and a depolarized (UP) state, which may also be coordinated. The elevated firing rate in the UP state follows sensory stimulation and provides a substrate for persistent activity, a network state that might mediate working memory. Using two-photon calcium imaging, we reconstructed the dynamics of spontaneous activity of up to 1,400 neurons in slices of mouse visual cortex. Here we report the occurrence of synchronized UP state transitions (`cortical flashes') that occur in spatially organized ensembles involving small numbers of neurons. Because of their stereotyped spatiotemporal dynamics, we conclude that network UP states are circuit attractors-emergent features of feedback neural networks that could implement memory states or solutions to computational problems.
Dynamical movement primitives: learning attractor models for motor behaviors.
Ijspeert, Auke Jan; Nakanishi, Jun; Hoffmann, Heiko; Pastor, Peter; Schaal, Stefan
2013-02-01
Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.
Random sampling versus exact enumeration of attractors in random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Berdahl, Andrew; Shreim, Amer; Sood, Vishal; Paczuski, Maya; Davidsen, Joern [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Alberta (Canada)], E-mail: aberdahl@phas.ucalgary.ca
2009-04-15
We clarify the effect different sampling methods and weighting schemes have on the statistics of attractors in ensembles of random Boolean networks (RBNs). We directly measure the cycle lengths of attractors and the sizes of basins of attraction in RBNs using exact enumeration of the state space. In general, the distribution of attractor lengths differs markedly from that obtained by randomly choosing an initial state and following the dynamics to reach an attractor. Our results indicate that the former distribution decays as a power law with exponent 1 for all connectivities K>1 in the infinite system size limit. In contrast, the latter distribution decays as a power law only for K=2. This is because the mean basin size grows linearly with the attractor cycle length for K>2, and is statistically independent of the cycle length for K=2. We also find that the histograms of basin sizes are strongly peaked at integer multiples of powers of two for K<3.
Persistent dynamic attractors in activity patterns of cultured neuronal networks
Wagenaar, Daniel A.; Nadasdy, Zoltan; Potter, Steve M.
2006-05-01
Three remarkable features of the nervous system—complex spatiotemporal patterns, oscillations, and persistent activity—are fundamental to such diverse functions as stereotypical motor behavior, working memory, and awareness. Here we report that cultured cortical networks spontaneously generate a hierarchical structure of periodic activity with a strongly stereotyped population-wide spatiotemporal structure demonstrating all three fundamental properties in a recurring pattern. During these “superbursts,” the firing sequence of the culture periodically converges to a dynamic attractor orbit. Precursors of oscillations and persistent activity have previously been reported as intrinsic properties of the neurons. However, complex spatiotemporal patterns that are coordinated in a large population of neurons and persist over several hours—and thus are capable of representing and preserving information—cannot be explained by known oscillatory properties of isolated neurons. Instead, the complexity of the observed spatiotemporal patterns implies large-scale self-organization of neurons interacting in a precise temporal order even in vitro, in cultures usually considered to have random connectivity.
A source-attractor approach to network detection of radiation sources
Energy Technology Data Exchange (ETDEWEB)
Wu, Qishi [University of Memphis; Barry, M. L.. [New Jersey Institute of Technology; Grieme, M. [New Jersey Institute of Technology; Sen, Satyabrata [ORNL; Rao, Nageswara S [ORNL; Brooks, Richard R [Clemson University
2016-01-01
Radiation source detection using a network of detectors is an active field of research for homeland security and defense applications. We propose Source-attractor Radiation Detection (SRD) method to aggregate measurements from a network of detectors for radiation source detection. SRD method models a potential radiation source as a magnet -like attractor that pulls in pre-computed virtual points from the detector locations. A detection decision is made if a sufficient level of attraction, quantified by the increase in the clustering of the shifted virtual points, is observed. Compared with traditional methods, SRD has the following advantages: i) it does not require an accurate estimate of the source location from limited and noise-corrupted sensor readings, unlike the localizationbased methods, and ii) its virtual point shifting and clustering calculation involve simple arithmetic operations based on the number of detectors, avoiding the high computational complexity of grid-based likelihood estimation methods. We evaluate its detection performance using canonical datasets from Domestic Nuclear Detection Office s (DNDO) Intelligence Radiation Sensors Systems (IRSS) tests. SRD achieves both lower false alarm rate and false negative rate compared to three existing algorithms for network source detection.
Unstable periodic orbits and attractor of the barotropic ocean model
Directory of Open Access Journals (Sweden)
E. Kazantsev
1998-01-01
Full Text Available A numerical method for detection of unstable periodic orbits on attractors of nonlinear models is proposed. The method requires similar techniques to data assimilation. This fact facilitates its implementation for geophysical models. This method was used to find numerically several low-period orbits for the barotropic ocean model in a square. Some numerical particularities of application of this method are discussed. Knowledge of periodic orbits of the model helps to explain some of these features like bimodality of probability density functions (PDF of principal parameters. These PDFs have been reconstructed as weighted averages of periodic orbits with weights proportional to the period of the orbit and inversely proportional to the sum of positive Lyapunov exponents. The fraction of time spent in the vicinity of each periodic orbit has been compared with its instability characteristics. The relationship between these values shows the 93% correlation. The attractor dimension of the model has also been approximated as a weighted average of local attractor dimensions in vicinities of periodic orbits.
Doria, Felipe; Erichsen, Rubem; González, Mario; Rodríguez, Francisco B.; Sánchez, Ángel; Dominguez, David
2016-09-01
The ability of a metric attractor neural networks (MANN) to learn structured patterns is analyzed. In particular we consider collections of fingerprints, which present some local features, rather than being modeled by random patterns. The network retrieval proved to be robust to varying the pattern activity, the threshold strategy, the topological arrangement of the connections, and for several types of noisy configuration. We found that the lower the fingerprint patterns activity is, the higher the load ratio and retrieval quality are. A simplified theoretical framework, for the unbiased case, is developed as a function of five parameters: the load ratio, the finiteness connectivity, the density degree of the network, randomness ratio, and the spatial pattern correlation. Linked to the latter appears a new neural dynamics variable: the spatial neural correlation. The theory agrees quite well with the experimental results.
Observational constraints on the generalized $\\alpha$ attractor model
Shahalam, M; Myrzakul, Shynaray; Wang, Anzhong
2016-01-01
We study the generalized $\\alpha$ attractor model in context of late time cosmic acceleration; the model interpolates between freezing and thawing dark energy models. In the slow roll regime, the originally potential is modified whereas the modification ceases in the asymptotic regime and the effective potential behaves as quadratic. In our setting, field rolls slowly around the present epoch and mimics dark matter in future. We put observational constraints on the model parameters for which we use an integrated data base (SN+Hubble+BAO+CMB) for carrying out the data analysis.
Energy Technology Data Exchange (ETDEWEB)
Berdahl, Andrew; Shreim, Amer; Sood, Vishal; Davidsen, Joern; Paczuski, Maya [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4 (Canada)], E-mail: aberdahl@phas.ucalgary.ca
2008-06-15
We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in random Boolean networks (RBNs) and in the Drosophila polarity network by exact enumeration. A transient time is the duration of the transient from a starting state to an attractor. An avalanche is a special transient which starts as a single Boolean element perturbation of an attractor state. Significant differences at short times between the avalanche and the transient times for RBNs with small connectivity K-compared to the number of elements N-indicate that attractors tend to cluster in configuration space. In addition, one bit flip has a non-negligible chance to put an attractor state directly onto another attractor. This clustering is also present in the segment polarity gene network of Drosophila melanogaster, suggesting that this may be a robust feature of biological regulatory networks. We also define and measure a branching ratio for the state space networks and find evidence for a new timescale that diverges roughly linearly with N for 2{<=}K<
Unraveling chaotic attractors by complex networks and measurements of stock market complexity
Cao, Hongduo; Li, Ying
2014-03-01
We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel-Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.
Unraveling chaotic attractors by complex networks and measurements of stock market complexity
Energy Technology Data Exchange (ETDEWEB)
Cao, Hongduo; Li, Ying, E-mail: mnsliy@mail.sysu.edu.cn [Business School, Sun Yat-Sen University, Guangzhou 510275 (China)
2014-03-15
We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel–Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.
Unraveling chaotic attractors by complex networks and measurements of stock market complexity.
Cao, Hongduo; Li, Ying
2014-03-01
We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel-Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.
Attractors and the attraction basins of discrete-time cellular neural networks
Institute of Scientific and Technical Information of China (English)
Ma Runnian; Xi Youmin
2005-01-01
The dynamic behavior of discrete-time cellular neural networks(DTCNN), which is strict with zero threshold value, is mainly studied in asynchronous mode and in synchronous mode. In general, a k-attractor of DTCNN is not a convergent point.But in this paper, it is proved that a k-attractor is a convergent point if the strict DTCNN satisfies some conditions. The attraction basin of the strict DTCNN is studied, one example is given to illustrate the previous conclusions to be wrong, and several results are presented. The obtained results on k-attractor and attraction basin not only correct the previous results, but also provide a theoretical foundation of performance analysis and new applications of the DTCNN.
Dempere-Marco, Laura; Melcher, David P; Deco, Gustavo
2012-01-01
The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1) the presence of a visually salient item reduces the number of items that can be held in working memory, and 2) visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items. Our model suggests that working memory capacity is determined by two fundamental processes: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC) in contrast to the maximal upper capacity limit only reached under ideal conditions.
Directory of Open Access Journals (Sweden)
Laura Dempere-Marco
Full Text Available The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1 the presence of a visually salient item reduces the number of items that can be held in working memory, and 2 visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items. Our model suggests that working memory capacity is determined by two fundamental processes: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC in contrast to the maximal upper capacity limit only reached under ideal conditions.
Directory of Open Access Journals (Sweden)
Paul eMiller
2013-05-01
Full Text Available Randomly connected recurrent networks of excitatory groups of neurons can possess a multitude of attractor states. When the internal excitatory synapses of these networks are depressing, the attractor states can be destabilized with increasing input. This leads to an itinerancy, where with either repeated transient stimuli, or increasing duration of a single stimulus, the network activity advances through sequences of attractor states. We find that the resulting network state, which persists beyond stimulus offset, can encode the number of stimuli presented via a distributed representation of neural activity with non-monotonic tuning curves for most neurons. Increased duration of a single stimulus is encoded via different distributed representations, so unlike an integrator, the network distinguishes separate successive presentations of a short stimulus from a single presentation of a longer stimulus with equal total duration. Moreover, different amplitudes of stimulus cause new, distinct activity patterns, such that changes in stimulus number, duration and amplitude can be distinguished from each other. These properties of the network depend on dynamic depressing synapses, as they disappear if synapses are static. Thus short-term synaptic depression allows a network to store separately the different dynamic properties of a spatially constant stimulus.
Comparison of Phase Synchronizability of Several Regular Networks for Non-Phase-Coherent Attractors
Institute of Scientific and Technical Information of China (English)
ZHAO Jun-Chan; LU Jun-An; DING Chun
2008-01-01
Though applying master stability function method to analyse network complete synchronization has been well studied in chaotic dynamical systems,it does not work well for phase synchronization.Moreover,it is difficult to identify phase synchronization with the angle of rotation for non-phase-coherent attractors.We employ the recurrences plot method to detect phase synchronization for several regular networks with non-phase-coherent attractors.It is found that the coupling strength μ is different for different coupled networks.The coupling strength μ is reduced as completed coupled network scale enlarges,the coupling strength μ of star coupled network is irrelevant to network scale,and these two regular networks are easier to achieve phase synchronization.However,for ring and chain coupled networks,the larger the phase synchronization couple strength μ is,the larger the network scale is,and it is more difficult to achieve phase synchronization.For same scale network,once ring coupled structure becomes a chain coupled structure,phase synchronization becomes much more difficuit.
Stochastic sensitivity analysis of the attractors for the randomly forced Ricker model with delay
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina; Ryashko, Lev
2014-11-14
Stochastically forced regular attractors (equilibria, cycles, closed invariant curves) of the discrete-time nonlinear systems are studied. For the analysis of noisy attractors, a unified approach based on the stochastic sensitivity function technique is suggested and discussed. Potentialities of the elaborated theory are demonstrated in the parametric analysis of the stochastic Ricker model with delay nearby Neimark–Sacker bifurcation. - Highlights: • Stochastically forced regular attractors of the discrete-time nonlinear systems are studied. • Unified approach based on the stochastic sensitivity function technique is suggested. • Potentialities of the elaborated theory are demonstrated. • Parametric analysis of the stochastic Ricker model with delay is given.
Cortez, Vasco; Medina, Pablo; Goles, Eric; Zarama, Roberto; Rica, Sergio
2015-01-01
Statistical properties, fluctuations and probabilistic arguments are shown to explain the robust dynamics of the Schelling's social segregation model. With the aid of probability density functions we characterize the attractors for multiple external parameters and conditions. We discuss the role of the initial states and we show that, indeed, the system evolves towards well defined attractors. Finally, we provide probabilistic arguments to explain quantitatively the observed behavior.
Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model
Ovsyannikov, I. I.; Turaev, D. V.
2017-01-01
We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attractor for an open set of parameter values of the Lorenz model in the form of Yudovich-Morioka-Shimizu. The proof is based on detection of a homoclinic butterfly with a zero saddle value and rigorous verification of one of the Shilnikov criteria for the birth of the Lorenz attractor; we also supply a proof for this criterion. The results are applied in order to give an analytic proof for the existence of a robust, pseudohyperbolic strange attractor (the so-called discrete Lorenz attractor) for an open set of parameter values in a 4-parameter family of 3D Henon-like diffeomorphisms.
Local community detection as pattern restoration by attractor dynamics of recurrent neural networks.
Okamoto, Hiroshi
2016-08-01
Densely connected parts in networks are referred to as "communities". Community structure is a hallmark of a variety of real-world networks. Individual communities in networks form functional modules of complex systems described by networks. Therefore, finding communities in networks is essential to approaching and understanding complex systems described by networks. In fact, network science has made a great deal of effort to develop effective and efficient methods for detecting communities in networks. Here we put forward a type of community detection, which has been little examined so far but will be practically useful. Suppose that we are given a set of source nodes that includes some (but not all) of "true" members of a particular community; suppose also that the set includes some nodes that are not the members of this community (i.e., "false" members of the community). We propose to detect the community from this "imperfect" and "inaccurate" set of source nodes using attractor dynamics of recurrent neural networks. Community detection by the proposed method can be viewed as restoration of the original pattern from a deteriorated pattern, which is analogous to cue-triggered recall of short-term memory in the brain. We demonstrate the effectiveness of the proposed method using synthetic networks and real social networks for which correct communities are known.
Study of the attractor structure of an agent-based sociological model
Timpanaro, André M.; Prado, Carmen P. C.
2011-03-01
The Sznajd model is a sociophysics model that is based in the Potts model, and used for describing opinion propagation in a society. It employs an agent-based approach and interaction rules favouring pairs of agreeing agents. It has been successfully employed in modeling some properties and scale features of both proportional and majority elections (see for instance the works of A. T. Bernardes and R. N. Costa Filho), but its stationary states are always consensus states. In order to explain more complicated behaviours, we have modified the bounded confidence idea (introduced before in other opinion models, like the Deffuant model), with the introduction of prejudices and biases (we called this modification confidence rules), and have adapted it to the discrete Sznajd model. This generalized Sznajd model is able to reproduce almost all of the previous versions of the Sznajd model, by using appropriate choices of parameters. We solved the attractor structure of the resulting model in a mean-field approach and made Monte Carlo simulations in a Barabási-Albert network. These simulations show great similarities with the mean-field, for the tested cases of 3 and 4 opinions. The dynamical systems approach that we devised allows for a deeper understanding of the potential of the Sznajd model as an opinion propagation model and can be easily extended to other models, like the voter model. Our modification of the bounded confidence rule can also be readily applied to other opinion propagation models.
Predicting pancreas cell fate decisions and reprogramming with a hierarchical multi-attractor model.
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Joseph Xu Zhou
Full Text Available Cell fate reprogramming, such as the generation of insulin-producing β cells from other pancreas cells, can be achieved by external modulation of key transcription factors. However, the known gene regulatory interactions that form a complex network with multiple feedback loops make it increasingly difficult to design the cell reprogramming scheme because the linear regulatory pathways as schemes of causal influences upon cell lineages are inadequate for predicting the effect of transcriptional perturbation. However, sufficient information on regulatory networks is usually not available for detailed formal models. Here we demonstrate that by using the qualitatively described regulatory interactions as the basis for a coarse-grained dynamical ODE (ordinary differential equation based model, it is possible to recapitulate the observed attractors of the exocrine and β, δ, α endocrine cells and to predict which gene perturbation can result in desired lineage reprogramming. Our model indicates that the constraints imposed by the incompletely elucidated regulatory network architecture suffice to build a predictive model for making informed decisions in choosing the set of transcription factors that need to be modulated for fate reprogramming.
Chaotic inflation limits for non-minimal models with a Starobinsky attractor
Mosk, Benjamin
2014-01-01
We investigate inflationary attractor points by analyzing non-minimally coupled single field inflation models in two opposite limits; the `flat' limit in which the first derivative of the conformal factor is small and the `steep' limit, in which the first derivative of the conformal factor is large. We consider a subset of models that yield Starobinsky inflation in the steep conformal factor, strong coupling, limit and demonstrate that they result in chaotic inflation in the opposite flat, weak coupling, limit. The suppression of higher order powers of the inflaton field in the potential is shown to be related to the flatness condition on the conformal factor. We stress that the chaotic attractor behaviour in the weak coupling limit is of a different, less universal, character than the Starobinsky attractor. Agreement with the COBE normalisation cannot be obtained in both attractor limits at the same time and in the chaotic attractor limit the scale of inflation depends on the details of the conformal factor,...
Davila-Velderrain, Jose; Martinez-Garcia, Juan C.; Alvarez-Buylla, Elena R.
2015-01-01
Robust temporal and spatial patterns of cell types emerge in the course of normal development in multicellular organisms. The onset of degenerative diseases may result from altered cell fate decisions that give rise to pathological phenotypes. Complex networks of genetic and non-genetic components underlie such normal and altered morphogenetic patterns. Here we focus on the networks of regulatory interactions involved in cell-fate decisions. Such networks modeled as dynamical non-linear systems attain particular stable configurations on gene activity that have been interpreted as cell-fate states. The network structure also restricts the most probable transition patterns among such states. The so-called Epigenetic Landscape (EL), originally proposed by C. H. Waddington, was an early attempt to conceptually explain the emergence of developmental choices as the result of intrinsic constraints (regulatory interactions) shaped during evolution. Thanks to the wealth of molecular genetic and genomic studies, we are now able to postulate gene regulatory networks (GRN) grounded on experimental data, and to derive EL models for specific cases. This, in turn, has motivated several mathematical and computational modeling approaches inspired by the EL concept, that may be useful tools to understand and predict cell-fate decisions and emerging patterns. In order to distinguish between the classical metaphorical EL proposal of Waddington, we refer to the Epigenetic Attractors Landscape (EAL), a proposal that is formally framed in the context of GRNs and dynamical systems theory. In this review we discuss recent EAL modeling strategies, their conceptual basis and their application in studying the emergence of both normal and pathological developmental processes. In addition, we discuss how model predictions can shed light into rational strategies for cell fate regulation, and we point to challenges ahead. PMID:25954305
Determining a singleton attractor of a boolean network with nested canalyzing functions.
Akutsu, Tatsuya; Melkman, Avraham A; Tamura, Takeyuki; Yamamoto, Masaki
2011-10-01
In this article, we study the problem of finding a singleton attractor for several biologically important subclasses of Boolean networks (BNs). The problem of finding a singleton attractor in a BN is known to be NP-hard in general. For BNs consisting of n nested canalyzing functions, we present an O(1.799(n)) time algorithm. The core part of this development is an O(min(2(k/2) · 2(m/2), 2(k)) · poly(k, m)) time algorithm for the satisfiability problem for m nested canalyzing functions over k variables. For BNs consisting of chain functions, a subclass of nested canalyzing functions, we present an O(1.619(n)) time algorithm and show that the problem remains NP-hard, even though the satisfiability problem for m chain functions over k variables is solvable in polynomial time. Finally, we present an o(2(n)) time algorithm for bounded degree BNs consisting of canalyzing functions.
Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys
Institute of Scientific and Technical Information of China (English)
Pierluigi COLLI; Michel FR(E)MOND; Elisabetta ROCCA; Ken SHIRAKAWA
2006-01-01
In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely,we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor.
Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls
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Ciprian G. Gal
2006-11-01
Full Text Available In a previous article [7], we proposed a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions were derived from a mass conservation law and variational methods. In the present paper, we study the problem further. Using a Faedo-Galerkin method, we obtain the existence and uniqueness of a global solution to our problem, under more general assumptions than those in [7]. We then study its asymptotic behavior and prove the existence of an exponential attractor (and thus of a global attractor with finite dimension.
Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing
Broer, HW; Vitolo, R; Simo, C; Dumortier, F; Broer, H; Mawhin, J; Vanderbauwhede, A; Lunel, SV
2005-01-01
A class of strange attractors is described, occurring in a low-dimensional model of general atmospheric circulation. The differential equations of the system are subject to periodic forcing, where the period is one year - as suggested by Lorenz in 1984. The dynamics of the system is described in ter
A Cayley Tree Immune Network Model with Antibody Dynamics
Anderson, R W; Perelson, A S; Anderson, Russell W.; Neumann, Avidan U.; Perelson, Alan S.
1993-01-01
Abstract: A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analyzed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters, percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percola...
2013-01-01
Background Boolean models are increasingly used to study biological signaling networks. In a Boolean network, nodes represent biological entities such as genes, proteins or protein complexes, and edges indicate activating or inhibiting influences of one node towards another. Depending on the input of activators or inhibitors, Boolean networks categorize nodes as either active or inactive. The formalism is appealing because for many biological relationships, we lack quantitative information about binding constants or kinetic parameters and can only rely on a qualitative description of the type “A activates (or inhibits) B”. A central aim of Boolean network analysis is the determination of attractors (steady states and/or cycles). This problem is known to be computationally complex, its most important parameter being the number of network nodes. Various algorithms tackle it with considerable success. In this paper we present an algorithm, which extends the size of analyzable networks thanks to simple and intuitive arguments. Results We present lnet, a software package which, in fully asynchronous updating mode and without any network reduction, detects the fixed states of Boolean networks with up to 150 nodes and a good part of any present cycles for networks with up to half the above number of nodes. The algorithm goes through a complete enumeration of the states of appropriately selected subspaces of the entire network state space. The size of these relevant subspaces is small compared to the full network state space, allowing the analysis of large networks. The subspaces scanned for the analyses of cycles are larger, reducing the size of accessible networks. Importantly, inherent in cycle detection is a classification scheme based on the number of non-frozen nodes of the cycle member states, with cycles characterized by fewer non-frozen nodes being easier to detect. It is further argued that these detectable cycles are also the biologically more important ones
Noise in attractor networks in the brain produced by graded firing rate representations.
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Tristan J Webb
Full Text Available Representations in the cortex are often distributed with graded firing rates in the neuronal populations. The firing rate probability distribution of each neuron to a set of stimuli is often exponential or gamma. In processes in the brain, such as decision-making, that are influenced by the noise produced by the close to random spike timings of each neuron for a given mean rate, the noise with this graded type of representation may be larger than with the binary firing rate distribution that is usually investigated. In integrate-and-fire simulations of an attractor decision-making network, we show that the noise is indeed greater for a given sparseness of the representation for graded, exponential, than for binary firing rate distributions. The greater noise was measured by faster escaping times from the spontaneous firing rate state when the decision cues are applied, and this corresponds to faster decision or reaction times. The greater noise was also evident as less stability of the spontaneous firing state before the decision cues are applied. The implication is that spiking-related noise will continue to be a factor that influences processes such as decision-making, signal detection, short-term memory, and memory recall even with the quite large networks found in the cerebral cortex. In these networks there are several thousand recurrent collateral synapses onto each neuron. The greater noise with graded firing rate distributions has the advantage that it can increase the speed of operation of cortical circuitry.
Vestibular and Attractor Network Basis of the Head Direction Cell Signal in Subcortical Circuits
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Benjamin J Clark
2012-03-01
Full Text Available Accurate navigation depends on a network of neural systems that encode the moment-to-moment changes in an animal’s directional orientation and location in space. Within this navigation system are head direction (HD cells, which fire persistently when an animal’s head is pointed in a particular direction (Sharp et al., 2001a; Taube, 2007. HD cells are widely thought to underlie an animal’s sense of spatial orientation, and research over the last 25+ years has revealed that this robust spatial signal is widely distributed across subcortical and cortical limbic areas. Much of this work has been directed at understanding the functional organization of the HD cell circuitry, and precisely how this signal is generated from sensory and motor systems. The purpose of the present review is to summarize some of the recent studies arguing that the HD cell circuit is largely processed in a hierarchical fashion, following a pathway involving the dorsal tegmental nuclei → lateral mammillary nuclei → anterior thalamus → parahippocampal and retrosplenial cortical regions. We also review recent work identifying bursting cellular activity in the HD cell circuit after lesions of the vestibular system, and relate these observations to the long held view that attractor network mechanisms underlie HD signal generation. Finally, we summarize the work to date suggesting that this network architecture may reside within the tegmento-mammillary circuit.
Compact attractors for time-periodic age-structured population models
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Pierre Magal
2001-10-01
Full Text Available In this paper we investigate the existence of compact attractors for time-periodic age-structured models. So doing we investigate the eventual compactness of a class of abstract non-autonomous semiflow (non necessarily periodic. We apply this result to non-autonomous age-structured models. In the time periodic case, we obtain the existence of a periodic family of compact subsets that is invariant by the semiflow, and attract the solutions of the system.
How active perception and attractor dynamics shape perceptual categorization: a computational model.
Catenacci Volpi, Nicola; Quinton, Jean Charles; Pezzulo, Giovanni
2014-12-01
We propose a computational model of perceptual categorization that fuses elements of grounded and sensorimotor theories of cognition with dynamic models of decision-making. We assume that category information consists in anticipated patterns of agent-environment interactions that can be elicited through overt or covert (simulated) eye movements, object manipulation, etc. This information is firstly encoded when category information is acquired, and then re-enacted during perceptual categorization. The perceptual categorization consists in a dynamic competition between attractors that encode the sensorimotor patterns typical of each category; action prediction success counts as "evidence" for a given category and contributes to falling into the corresponding attractor. The evidence accumulation process is guided by an active perception loop, and the active exploration of objects (e.g., visual exploration) aims at eliciting expected sensorimotor patterns that count as evidence for the object category. We present a computational model incorporating these elements and describing action prediction, active perception, and attractor dynamics as key elements of perceptual categorizations. We test the model in three simulated perceptual categorization tasks, and we discuss its relevance for grounded and sensorimotor theories of cognition.
Continuous or discrete attractors in neural circuits? A self-organized switch at maximal entropy
Bernacchia, Alberto
2007-01-01
A recent experiment suggests that neural circuits may alternatively implement continuous or discrete attractors, depending on the training set up. In recurrent neural network models, continuous and discrete attractors are separately modeled by distinct forms of synaptic prescriptions (learning rules). Here, we report a solvable network model, endowed with Hebbian synaptic plasticity, which is able to learn either discrete or continuous attractors, depending on the frequency of presentation of stimuli and on the structure of sensory coding. A continuous attractor is learned when experience matches sensory coding, i.e. when the distribution of experienced stimuli matches the distribution of preferred stimuli of neurons. In that case, there is no processing of sensory information and neural activity displays maximal entropy. If experience goes beyond sensory coding, processing is initiated and the continuous attractor is destabilized into a set of discrete attractors.
Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics
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Toichiro Asada
2011-01-01
Full Text Available Complex dynamical features are explored in a discrete interregional macrodynamic model proposed by Asada et al., using numerical methods. The model is five-dimensional with four parameters. The results demonstrate patterns of dynamical behaviour, such as bifurcation processes and coexistence of attractors, generated by high-dimensional discrete systems. In three cases of two-dimensional parameter subspaces the stability of equilibrium region is determined and its boundaries, the flip and Neimark-Hopf bifurcation curves, are identified by means of necessary coefficient criteria. In the first case closed invariant curves (CICs are found to occur through 5D-crater-type bifurcations, and for certain ranges of parameter values a stable equilibrium coexists with an unstable CIC associated with the subcritical bifurcation, as well as with an outer stable CIC. A remarkable feature of the second case is the coexistence of two attracting CICs outside the stability region. In both these cases the related hysteresis effects are illustrated by numerical simulations. In the third case a remarkable feature is the apparent unfolding of an attracting CIC before it evolves to a chaotic attractor. Examples of CICs and chaotic attractors are given in subspaces of phase space.
Huang, S.; Ingber, D. E.
2000-01-01
Development of characteristic tissue patterns requires that individual cells be switched locally between different phenotypes or "fates;" while one cell may proliferate, its neighbors may differentiate or die. Recent studies have revealed that local switching between these different gene programs is controlled through interplay between soluble growth factors, insoluble extracellular matrix molecules, and mechanical forces which produce cell shape distortion. Although the precise molecular basis remains unknown, shape-dependent control of cell growth and function appears to be mediated by tension-dependent changes in the actin cytoskeleton. However, the question remains: how can a generalized physical stimulus, such as cell distortion, activate the same set of genes and signaling proteins that are triggered by molecules which bind to specific cell surface receptors. In this article, we use computer simulations based on dynamic Boolean networks to show that the different cell fates that a particular cell can exhibit may represent a preprogrammed set of common end programs or "attractors" which self-organize within the cell's regulatory networks. In this type of dynamic network model of information processing, generalized stimuli (e.g., mechanical forces) and specific molecular cues elicit signals which follow different trajectories, but eventually converge onto one of a small set of common end programs (growth, quiescence, differentiation, apoptosis, etc.). In other words, if cells use this type of information processing system, then control of cell function would involve selection of preexisting (latent) behavioral modes of the cell, rather than instruction by specific binding molecules. Importantly, the results of the computer simulation closely mimic experimental data obtained with living endothelial cells. The major implication of this finding is that current methods used for analysis of cell function that rely on characterization of linear signaling pathways or
Attractor-based models for individual and groups’ forecasting
Astakhova, N. N.; Demidova, L. A.; Kuzovnikov, A. V.; Tishkin, R. V.
2017-02-01
In this paper the questions of the attractors’ application in case of the development of the forecasting models on the base of the strictly binary trees have been considered. Usually, these models use the short time series as the training data sequence. The application of the principles of the attractors’ forming on the base of the long time series will allow creating the training data sequence more reasonably. The offered approach to creation of the training data sequence for the forecasting models on the base of the strictly binary trees was applied for the individual and groups’ forecasting of time series. At the same time the problems of one-objective and multiobjective optimization on the base of the modified clonal selection algorithm have been considered. The reviewed examples confirm the efficiency of the attractors’ application in sense of minimization of the used quality indicators of the forecasting models, and also the forecasting errors on 1 – 5 steps forward. Besides, the minimization of time expenditures for the development of the forecasting models is provided.
Guastello, Stephen J; Nathan, Dominic E; Johnson, Michelle J
2009-01-01
The principles of attractors and Lyapunov exponents were used to develop a reaching-to-grasp model for use in a robotic therapy system for stroke patients. Previously known models for these movements, the fifth order minimum jerk and the seventh order polynomial, do not account for the change in grasp aperture of the hand. The Lyapunov model was tested with reaching-to-grasp movements performed by five neurologically intact subjects and produced an average R-square = .97 over 15 replications for 41 different task events, reflecting a notable advantage over the fifth order (average R-square = .58) and seventh order (average R-square = .67) models. A similar level of success was obtained for the Lyapunov model that was specific to grasp aperture. The results indicated that intentional movements can be accurately characterized as attractor trajectories, and as functions of position along two Cartesian coordinates rather than as functions of time. The Lyapunov exponent model requires fewer parameters and provides an efficient platform for real-time implementation.
Rolls, Edmund T
2017-02-08
The art of memory (ars memoriae) used since classical times includes using a well-known scene to associate each view or part of the scene with a different item in a speech. This memory technique is also known as the "method of loci." The new theory is proposed that this type of memory is implemented in the CA3 region of the hippocampus where there are spatial view cells in primates that allow a particular view to be associated with a particular object in an event or episodic memory. Given that the CA3 cells with their extensive recurrent collateral system connecting different CA3 cells, and associative synaptic modifiability, form an autoassociation or attractor network, the spatial view cells with their approximately Gaussian view fields become linked in a continuous attractor network. As the view space is traversed continuously (e.g., by self-motion or imagined self-motion across the scene), the views are therefore successively recalled in the correct order, with no view missing, and with low interference between the items to be recalled. Given that each spatial view has been associated with a different discrete item, the items are recalled in the correct order, with none missing. This is the first neuroscience theory of ars memoriae. The theory provides a foundation for understanding how a key feature of ars memoriae, the ability to use a spatial scene to encode a sequence of items to be remembered, is implemented. © 2017 Wiley Periodicals, Inc.
Unstable attractors induce perpetual synchronization and desynchronization.
Timme, Marc; Wolf, Fred; Geisel, Theo
2003-03-01
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.
Dynamical Stability and Attractor of the Variable Generalized Chaplygin Gas Model
Institute of Scientific and Technical Information of China (English)
FU Huan-Huan; WU Ya-Bo; CHENG Fang-Yuan
2009-01-01
For the variable generalized Chaplygin gas (VGCG) as a dynamical system,its stability is analyzed and the related dynamical attractors are investigated.By analysis it is shown that there are two critical points corresponding to the matter-dominated phase and the VGCG dark energy-dominated phase,respectively.Moreover,when the parameters n,α and γ take some fixed values,the phase with ωVGCG=-0.92 is a dynamical attractor and the equation of state of VGCG reaches it from either ωVGCG＞-1 or ωVGCG＜-1,independent of the initial values of the dynamical system.This shows a satisfactory cosmological model:the early matter-dominated era,followed by the dark energy-dominated era.Meanwhile,the evolutions of density parameters Ωγ and ΩVGCG are quite different from each other.For different initial values of x and y,Ωγ decreases and flVGCG increases as the time grows,they will eventually approach Ωγ= 0 and ΩVGCG = 1.Furthermore,since different values of n or α may lead to different equation-of-state parameters ωVGC,we also discuss the constraints on the parameters n and α by the observation data.
Rajpoot, Subhash
2016-01-01
Applying the anholonomic frame deformation method, we construct various classes of cosmological solutions for effective Einstein -- Yang-Mills -- Higgs, and two measure theories. The types of models considered are Freedman-Lema\\^{i}tre-Robertson-Walker, Bianchi, Kasner and models with attractor configurations. The various regimes pertaining to plateau--type inflation, quadratic inflation, Starobinsky type and Higgs type inflation are presented.
Unity of cosmological inflation attractors.
Galante, Mario; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-04-10
Recently, several broad classes of inflationary models have been discovered whose cosmological predictions, in excellent agreement with Planck, are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a nonminimal coupling to gravity. These models, which we call ξ attractors, describe universal cosmological attractors (including Higgs inflation) and induced inflation models. Another class describes conformal attractors (including Starobinsky inflation and T models) and their generalization to α attractors. The aim of this Letter is to elucidate the common denominator of these attractors: their robust predictions stem from a joint pole of order 2 in the kinetic term of the inflaton field in the Einstein frame formulation prior to switching to the canonical variables. Model-dependent differences only arise at subleading level in the kinetic term. As a final step towards the unification of the different attractors, we introduce a special class of ξ attractors which is fully equivalent to α attractors with the identification α=1+(1/6ξ). While r is generically predicted to be of the order 1/N^{2}, there is no theoretical lower bound on r in this class of models.
Davila-Velderrain, Jose; Juarez-Ramiro, Luis; Martinez-Garcia, Juan C.; Alvarez-Buylla, Elena R
2015-01-01
Gene regulatory network (GRN) modeling is a well-established theoretical framework for the study of cell-fate specification during developmental processes. Recently, dynamical models of GRNs have been taken as a basis for formalizing the metaphorical model of Waddington's epigenetic landscape, providing a natural extension for the general protocol of GRN modeling. In this contribution we present in a coherent framework a novel implementation of two previously proposed general frameworks for m...
Structure of Kaehler potential for D-term inflationary attractor models
Energy Technology Data Exchange (ETDEWEB)
Nakayama, Kazunori [Tokyo Univ. (Japan). Dept. of Physics; Tokyo Univ., Chiba (Japan). Kavli IPMU (WPI), UTIAS; Saikawa, Ken' ichi [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Tokyo Institute of Technology (Japan). Dept. of Physics; Terada, Takahiro [Tokyo Univ. (Japan). Dept. of Physics; Asia Pacific Center for Theoretical Physics (APCTP), Pohang (Korea, Republic of); Yamaguchi, Masahide [Tokyo Institute of Technology (Japan). Dept. of Physics
2016-05-15
Minimal chaotic models of D-term inflation predicts too large primordial tensor perturbations. Although it can be made consistent with observations utilizing higher order terms in the Kaehler potential, expansion is not controlled in the absence of symmetries. We comprehensively study the conditions of Kaehler potential for D-term plateau-type potentials and discuss its symmetry. They include the α-attractor model with a massive vector supermultiplet and its generalization leading to pole inflation of arbitrary order. We extend the models so that it can describe Coulomb phase, gauge anomaly is cancelled, and fields other than inflaton are stabilized during inflation. We also point out a generic issue for large-field D-term inflation that the masses of the non-inflaton fields tend to exceed the Planck scale.
On the uniqueness of supersymmetric attractors
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Taniya Mandal
2015-10-01
Full Text Available In this paper we discuss the uniqueness of supersymmetric attractors in four-dimensional N=2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free attractors are unique. We generalise the analysis to axionic attractors and state the conditions for uniqueness explicitly. We consider the example of a two-parameter model and find all solutions to the supersymmetric attractor equations and discuss their uniqueness.
Two Unipolar Terminal-Attractor-Based Associative Memories
Liu, Hua-Kuang; Wu, Chwan-Hwa
1995-01-01
Two unipolar mathematical models of electronic neural network functioning as terminal-attractor-based associative memory (TABAM) developed. Models comprise sets of equations describing interactions between time-varying inputs and outputs of neural-network memory, regarded as dynamical system. Simplifies design and operation of optoelectronic processor to implement TABAM performing associative recall of images. TABAM concept described in "Optoelectronic Terminal-Attractor-Based Associative Memory" (NPO-18790). Experimental optoelectronic apparatus that performed associative recall of binary images described in "Optoelectronic Inner-Product Neural Associative Memory" (NPO-18491).
Synthetic Modeling of Autonomous Learning with a Chaotic Neural Network
Funabashi, Masatoshi
We investigate the possible role of intermittent chaotic dynamics called chaotic itinerancy, in interaction with nonsupervised learnings that reinforce and weaken the neural connection depending on the dynamics itself. We first performed hierarchical stability analysis of the Chaotic Neural Network model (CNN) according to the structure of invariant subspaces. Irregular transition between two attractor ruins with positive maximum Lyapunov exponent was triggered by the blowout bifurcation of the attractor spaces, and was associated with riddled basins structure. We secondly modeled two autonomous learnings, Hebbian learning and spike-timing-dependent plasticity (STDP) rule, and simulated the effect on the chaotic itinerancy state of CNN. Hebbian learning increased the residence time on attractor ruins, and produced novel attractors in the minimum higher-dimensional subspace. It also augmented the neuronal synchrony and established the uniform modularity in chaotic itinerancy. STDP rule reduced the residence time on attractor ruins, and brought a wide range of periodicity in emerged attractors, possibly including strange attractors. Both learning rules selectively destroyed and preserved the specific invariant subspaces, depending on the neuron synchrony of the subspace where the orbits are situated. Computational rationale of the autonomous learning is discussed in connectionist perspective.
Park, Jeryang; Rao, P Suresh C
2014-11-15
We present here a conceptual model and analysis of complex systems using hypothetical cases of regime shifts resulting from temporal non-stationarity in attractor strengths, and then present selected published cases to illustrate such regime shifts in hydrologic systems (shallow aquatic ecosystems; water table shifts; soil salinization). Complex systems are dynamic and can exist in two or more stable states (or regimes). Temporal variations in state variables occur in response to fluctuations in external forcing, which are modulated by interactions among internal processes. Combined effects of external forcing and non-stationary strengths of alternative attractors can lead to shifts from original to alternate regimes. In systems with bi-stable states, when the strengths of two competing attractors are constant in time, or are non-stationary but change in a linear fashion, regime shifts are found to be temporally stationary and only controlled by the characteristics of the external forcing. However, when attractor strengths change in time non-linearly or vary stochastically, regime shifts in complex systems are characterized by non-stationary probability density functions (pdfs). We briefly discuss implications and challenges to prediction and management of hydrologic complex systems.
Park, Jeryang; Rao, P. Suresh C.
2014-11-01
We present here a conceptual model and analysis of complex systems using hypothetical cases of regime shifts resulting from temporal non-stationarity in attractor strengths, and then present selected published cases to illustrate such regime shifts in hydrologic systems (shallow aquatic ecosystems; water table shifts; soil salinization). Complex systems are dynamic and can exist in two or more stable states (or regimes). Temporal variations in state variables occur in response to fluctuations in external forcing, which are modulated by interactions among internal processes. Combined effects of external forcing and non-stationary strengths of alternative attractors can lead to shifts from original to alternate regimes. In systems with bi-stable states, when the strengths of two competing attractors are constant in time, or are non-stationary but change in a linear fashion, regime shifts are found to be temporally stationary and only controlled by the characteristics of the external forcing. However, when attractor strengths change in time non-linearly or vary stochastically, regime shifts in complex systems are characterized by non-stationary probability density functions (pdfs). We briefly discuss implications and challenges to prediction and management of hydrologic complex systems.
Inverse Symmetric Inflationary Attractors
Odintsov, S D
2016-01-01
We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreove...
Tang, Sanyi; Xiao, Yanni; Cheke, Robert A
2008-03-01
Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host's intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.
On the Role of Synaptic Depression in the Performance of Attractor Neural Networks
Torres, Joaquín J.; Pantic, Lovorka; Kappen, Hilbert J.
2003-04-01
Using a biologically motivated model of synaptic depression and within a mean-field approach, we examined the role of synaptic depression in the capacity of a binary neural network with N units to store and retrieve P patterns. In the limit of α ≡ P/N → 0, our results demonstrate the appearance of a novel phase characterized by quick transitions from one memory state to another. This phenomenon might reflect the flexibility of real neural systems to receive and respond to novel and changing external stimuli. In addition, we have computed the maximum storage capacity of such a network in the limit of α ≠ 0 and T = 0. Supported by mean-field results and Monte Carlo simulations, we concluded that the critical storage capacity for effective retrieval of stable memory patterns decreases with the degree of the depression. Nevertheless, the storage of memories as oscillatory states will require a different definition of storage capacity. How such a new storage capacity depends on the synaptic depression is still an open question.
Imura, Jun-ichi; Ueta, Tetsushi
2015-01-01
This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.
Topology and dynamics of attractor neural networks: The role of loopiness
Zhang, Pan; Chen, Yong
2008-07-01
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. A large loopiness coefficient means a high probability of finding loops in the networks. We develop recursive equations for the overlap parameters of neural networks in terms of their loopiness. It was found that a large loopiness increases the correlation among the network states at different times and eventually reduces the performance of neural networks. The theory is applied to several network topological structures, including fully-connected, densely-connected random, densely-connected regular and densely-connected small-world, where encouraging results are obtained.
Mitsui, Takahito; Aihara, Kazuyuki
2015-01-01
Glacial-interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is $\\sim $40 kyr before the so-called middle Pleistocene transition between $\\sim$1.2 and $\\sim$0.7 Myr ago, and it is $\\sim $100 kyr after the transition. In this paper, the dynamics of glacial-interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle-node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaoti...
Goldstein, Kevin; Nampuri, Suresh
2014-01-01
The product of the areas of the event horizon and the Cauchy horizon of a non-extremal black hole equals the square of the area of the horizon of the black hole obtained from taking the smooth extremal limit. We establish this result for a large class of black holes using the second order equations of motion, black hole thermodynamics, and the attractor mechanism for extremal black holes. This happens even though the area of each horizon generically depends on the moduli, which are asymptotic values of scalar fields. The conformal field theory dual to the BTZ black hole facilitates a microscopic interpretation of the result. In addition, we demonstrate that certain quantities which vanish in the extremal case are zero when integrated over the region between the two horizons. We corroborate these conclusions through an analysis of known solutions.
Azpeitia, Eugenio; Muñoz, Stalin; González-Tokman, Daniel; Martínez-Sánchez, Mariana Esther; Weinstein, Nathan; Naldi, Aurélien; Álvarez-Buylla, Elena R; Rosenblueth, David A; Mendoza, Luis
2017-02-10
Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures.
Modeling multi-agent self-organization through the lens of higher order attractor dynamics
DEFF Research Database (Denmark)
Butner, Jonathan E.; Wiltshire, Travis; Munion, A.K.
2017-01-01
's behavior. We present four examples that differ in the number of variables used to depict the attractor dynamics (1, 2, and 6) and range from simulated to non-simulated data sources. We demonstrate that this is a flexible method that advances scientific study of SCD in a variety of multi-agent systems....... of attractor dynamic patterns. The advantage of this approach is that we are able to quantify the self-organized dynamics that agents exhibit, link these dynamics back to activity from individual agents, and relate it to other variables central to understanding the coordinative functionality of a system...
Blair, Hugh T; Wu, Allan; Cong, Jason
2014-02-01
Theories of neural coding seek to explain how states of the world are mapped onto states of the brain. Here, we compare how an animal's location in space can be encoded by two different kinds of brain states: population vectors stored by patterns of neural firing rates, versus synchronization vectors stored by patterns of synchrony among neural oscillators. It has previously been shown that a population code stored by spatially tuned 'grid cells' can exhibit desirable properties such as high storage capacity and strong fault tolerance; here it is shown that similar properties are attainable with a synchronization code stored by rhythmically bursting 'theta cells' that lack spatial tuning. Simulations of a ring attractor network composed from theta cells suggest how a synchronization code might be implemented using fewer neurons and synapses than a population code with similar storage capacity. It is conjectured that reciprocal connections between grid and theta cells might control phase noise to correct two kinds of errors that can arise in the code: path integration and teleportation errors. Based upon these analyses, it is proposed that a primary function of spatially tuned neurons might be to couple the phases of neural oscillators in a manner that allows them to encode spatial locations as patterns of neural synchrony.
Attractor switching in neuron networks and Spatiotemporal filters for motion processing
Subramanian, Easwara Naga
2008-01-01
From a broader perspective, we address two important questions, viz., (a) what kind of mechanism would enable a neuronal network to switch between various tasks or stored patterns? (b) what are the properties of neurons that are used by the visual system in early motion detection? To address (a) we
Non-minimal coupling and inflationary attractors
Yi, Zhu
2016-01-01
We show explicitly how the T-model, E-model and Hilltop inflations are obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. We argue that $\\xi$ attractors can give any observables $n_s$ and $r$ by this method. The existence of attractors imposes a challenge to distinguish different models.
Piecewise affine models of chaotic attractors: The Rössler and Lorenz systems
Amaral, Gleison F. V.; Letellier, Christophe; Aguirre, Luis Antonio
2006-03-01
This paper proposes a procedure by which it is possible to synthesize Rössler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.
Modeling and controlling the two-phase dynamics of the p53 network: a Boolean network approach
Lin, Guo-Qiang; Ao, Bin; Chen, Jia-Wei; Wang, Wen-Xu; Di, Zeng-Ru
2014-12-01
Although much empirical evidence has demonstrated that p53 plays a key role in tumor suppression, the dynamics and function of the regulatory network centered on p53 have not yet been fully understood. Here, we develop a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage. In particular, we map the fates of cells into two types of Boolean attractors, and we find that the apoptosis attractor does not exist for minor DNA damage, reflecting that the cell is reparable. As the amount of DNA damage increases, the basin of the repair attractor shrinks, accompanied by the rising of the apoptosis attractor and the expansion of its basin, indicating that the cell becomes more irreparable with more DNA damage. For severe DNA damage, the repair attractor vanishes, and the apoptosis attractor dominates the state space, accounting for the exclusive fate of death. Based on the Boolean network model, we explore the significance of links, in terms of the sensitivity of the two-phase dynamics, to perturbing the weights of links and removing them. We find that the links are either critical or ordinary, rather than redundant. This implies that the p53 network is irreducible, but tolerant of small mutations at some ordinary links, and this can be interpreted with evolutionary theory. We further devised practical control schemes for steering the system into the apoptosis attractor in the presence of DNA damage by pinning the state of a single node or perturbing the weight of a single link. Our approach offers insights into understanding and controlling the p53 network, which is of paramount importance for medical treatment and genetic engineering.
Institute of Scientific and Technical Information of China (English)
应阳君; 黄祖洽
2001-01-01
Frequency catastrophe is found in a cell Ca2+ nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.
Robledo, Alberto
2012-11-01
We show that the full features of the dynamics towards the Feigenbaum attractor, present in all low-dimensional maps with a unimodal leading component, form a hierarchical construction with modular organization that leads to a clear-cut emergent property. This well-known nonlinear model system combines a simple and precise definition, an intricate nested hierarchical dynamical structure, and emergence of a power-law dynamical property absent in the exponential-law that governs the dynamics within the modules. This classic nonlinear system is put forward as a working example for complex collective behavior.
Cosmological attractors in massive gravity
Dubovsky, S; Tkachev, I I
2005-01-01
We study Lorentz-violating models of massive gravity which preserve rotations and are invariant under time-dependent shifts of the spatial coordinates. In the linear approximation the Newtonian potential in these models has an extra ``confining'' term proportional to the distance from the source. We argue that during cosmological expansion the Universe may be driven to an attractor point with larger symmetry which includes particular simultaneous dilatations of time and space coordinates. The confining term in the potential vanishes as one approaches the attractor. In the vicinity of the attractor the extra contribution is present in the Friedmann equation which, in a certain range of parameters, gives rise to the cosmic acceleration.
Chueshov, Igor
2010-01-01
We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and the classical (nonlinear) elastic plate equation for in-plane motions on a flexible flat part of the boundary. The main peculiarity of the model is the assumption that the transversal displacements of the plate are negligible relative to in-plane displacements. This kind of models arises in the study of blood flows in large arteries. Our main result states the existence of a compact global attractor of finite dimension. We also show that the corresponding linearized system generates exponentially stable $C_0$-semigroup. We do not assume any kind of mechanical damping in the plate component. Thus our results means that dissipation of the energy in the fluid due to viscosity is sufficient to stabilize the system.
On the Well Posedness and Refined Estimates for the Global Attractor of the TYC Model
Directory of Open Access Journals (Sweden)
Gutierrez JuanB
2010-01-01
Full Text Available Abstract The Trojan Y Chromosome strategy (TYC is a theoretical method for eradication of invasive species. It requires constant introduction of artificial individuals into a target population, causing a shift in the sex ratio that ultimately leads to local extinction. In this work we demonstrate the existence of a unique weak solution to the infinite dimensional TYC system. Furthermore, we obtain improved estimates on the upper bounds for the Hausdorff and fractal dimensions of the global attractor of the TYC system, via the use of weighted Sobolev spaces. These results confirm that the TYC eradication strategy is a sound theoretical method of eradication of invasive species in a spatial setting. It also provides a solid ground for experiments in silico and validates the use of the TYC strategy in vivo.
A signature of attractor dynamics in the CA3 region of the hippocampus.
Directory of Open Access Journals (Sweden)
César Rennó-Costa
2014-05-01
Full Text Available The notion of attractor networks is the leading hypothesis for how associative memories are stored and recalled. A defining anatomical feature of such networks is excitatory recurrent connections. These "attract" the firing pattern of the network to a stored pattern, even when the external input is incomplete (pattern completion. The CA3 region of the hippocampus has been postulated to be such an attractor network; however, the experimental evidence has been ambiguous, leading to the suggestion that CA3 is not an attractor network. In order to resolve this controversy and to better understand how CA3 functions, we simulated CA3 and its input structures. In our simulation, we could reproduce critical experimental results and establish the criteria for identifying attractor properties. Notably, under conditions in which there is continuous input, the output should be "attracted" to a stored pattern. However, contrary to previous expectations, as a pattern is gradually "morphed" from one stored pattern to another, a sharp transition between output patterns is not expected. The observed firing patterns of CA3 meet these criteria and can be quantitatively accounted for by our model. Notably, as morphing proceeds, the activity pattern in the dentate gyrus changes; in contrast, the activity pattern in the downstream CA3 network is attracted to a stored pattern and thus undergoes little change. We furthermore show that other aspects of the observed firing patterns can be explained by learning that occurs during behavioral testing. The CA3 thus displays both the learning and recall signatures of an attractor network. These observations, taken together with existing anatomical and behavioral evidence, make the strong case that CA3 constructs associative memories based on attractor dynamics.
The 3-Attractor Water Model: Monte-Carlo Simulations with a New, Effective 2-Body Potential (BMW
Directory of Open Access Journals (Sweden)
Francis Muguet
2003-02-01
Full Text Available According to the precepts of the 3-attractor (3-A water model, effective 2-body water potentials should feature as local minima the bifurcated and inverted water dimers in addition to the well-known linear water dimer global minimum. In order to test the 3-A model, a new pair wise effective intermolecular rigid water potential has been designed. The new potential is part of new class of potentials called BMW (Bushuev-Muguet-Water which is built by modifying existing empirical potentials. This version (BMW v. 0.1 has been designed by modifying the SPC/E empirical water potential. It is a preliminary version well suited for exploratory Monte-Carlo simulations. The shape of the potential energy surface (PES around each local minima has been approximated with the help of Gaussian functions. Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble for a very wide range of state parameters up to the supercritical water regime. Thermodynamic properties are reported. The radial distributions functions (RDFs have been computed and are compared with the RDFs obtained from Neutron Scattering experimental data. Our preliminary Monte-Carlo simulations show that the seemingly unconventional hypotheses of the 3-A model are most plausible. The simulation has also uncovered a totally new role for 2-fold H-bonds.
Recurrences of strange attractors
Indian Academy of Sciences (India)
E J Ngamga; A Nandi; R Ramaswamy; M C Romano; M Thiel; J Kurths
2008-06-01
The transitions from or to strange nonchaotic attractors are investigated by recurrence plot-based methods. The techniques used here take into account the recurrence times and the fact that trajectories on strange nonchaotic attractors (SNAs) synchronize. The performance of these techniques is shown for the Heagy-Hammel transition to SNAs and for the fractalization transition to SNAs for which other usual nonlinear analysis tools are not successful.
Yoshida, Risa; Kimoto, Tomoyuki; Uezu, Tatsuya
2017-03-01
We analyze the structure of attractors in the classical XY model with an associative-memory-type interaction by the statistical mechanical method. Previously, it was found that when patterns are uncorrelated, points on a path connecting two memory patterns in the space of the order parameters are solutions of the saddle point equations (SPEs) in the case that p is O(1) irrespective of N and N ≫ 1, where p and N are the numbers of patterns and spins, respectively. This state is called the continuous attractor (CA). In this paper, we clarify the conditions for the existence and stability of the CA with and without the correlation a (0 ≤ a 0, we numerically study the case that patterns are subject to external noise and find that pc increases as the noise amplitude increases.
Sourcing Dark Matter and Dark Energy from $\\alpha$-attractors
Mishra, Swagat S.; Sahni, Varun; Shtanov, Yuri(Department of Physics, Taras Shevchenko National University, Kiev, Ukraine)
2017-01-01
Recently, Kallosh and Linde have drawn attention to a new family of superconformal inflationary potentials, subsequently called $\\alpha$-attractors. The $\\alpha$-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the $\\alpha$-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with ...
Vries, de R.Y.; Briels, W.J.; Feil, D.; Velde, te G.; Baerends, E.J.
1996-01-01
1990 Sakata and Sato applied the maximum entropy method (MEM) to a set of structure factors measured earlier by Saka and Kato with the Pendellösung method. They found the presence of non-nuclear attractors, i.e., maxima in the density between two bonded atoms. We applied the MEM to a limited set of
ATTRACTORS OF NONAUTONOMOUS SCHRODINGER EQUATIONS
Institute of Scientific and Technical Information of China (English)
刘玉荣; 刘曾荣; 郑永爱
2001-01-01
The long-time behaviour of a two-dimensional nonautonomous nonlinear SchrOdinger equation is considered. The existence of uniform attractor is proved and the up per bound of the uniform attractor' s Hausdorff dimension is given.
Directory of Open Access Journals (Sweden)
Francis F. Muguet
2005-04-01
Full Text Available MC simulations of a set of zigzag ((9,0-(14,0 and armchair ((6,6-(10,10carbon nanotubes immersed in water have been carried out in an NpT-ensemble (512 watermolecules, p=1 bar, T=298 K. Intermolecular interactions were described by BMWpotential according to which, besides the well-known linear water dimer bifurcated andinverted water dimers are metastable. In all cases, it was found that there are large periodicfluctuations of water occupancy inside the nanotubes. Decrease in the size of the nanotubediameter leads to a significant destruction of the H-bond network, and to a bifucarted dimerpopulation increase. Inverted dimer concentration relationship with the nanotube diameter ismore complicated. Population maximum for inverted dimers occurs for diameters of 10-11 ÃƒÂ¥. Water features different intermolecular structures not only inside carbon nanotubesbut also in the outer first hydration shells. The amount of bifurcated and inverted dimers issignificantly more important in the first hydration shell than in bulk water.
Hidden attractors in dynamical systems
Dudkowski, Dawid; Jafari, Sajad; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Prasad, Awadhesh
2016-06-01
Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system is called multistability. The final state, i.e., the attractor on which the multistable system evolves strongly depends on the initial conditions. Additionally, such systems are very sensitive towards noise and system parameters so a sudden shift to a contrasting regime may occur. To understand the dynamics of these systems one has to identify all possible attractors and their basins of attraction. Recently, it has been shown that multistability is connected with the occurrence of unpredictable attractors which have been called hidden attractors. The basins of attraction of the hidden attractors do not touch unstable fixed points (if exists) and are located far away from such points. Numerical localization of the hidden attractors is not straightforward since there are no transient processes leading to them from the neighborhoods of unstable fixed points and one has to use the special analytical-numerical procedures. From the viewpoint of applications, the identification of hidden attractors is the major issue. The knowledge about the emergence and properties of hidden attractors can increase the likelihood that the system will remain on the most desirable attractor and reduce the risk of the sudden jump to undesired behavior. We review the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations. We also describe numerical methods which allow identification of the hidden attractors.
Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing
Broer, H; Simo, C; Vitolo, R
2002-01-01
A low-dimensional model of general circulation of the atmosphere is investigated. The differential equations are subject to periodic forcing, where the period is one year. A three-dimensional Poincare mapping P depends on three control parameters F, G, and epsilon, the latter being the relative ampl
An attractor for natural supersymmetry
Cohen, Timothy; Hook, Anson; Torroba, Gonzalo
2012-12-01
We propose an attractor mechanism which generates the more minimal supersymmetric standard model from a broad class of supersymmetry breaking boundary conditions. The hierarchies in the fermion masses and mixings are produced by the same dynamics and a natural weak scale results from gaugino mediation. These features arise from augmenting the standard model with a new SU(3) gauge group under which only the third generation quarks are charged. The theory flows to a strongly interacting fixed point which induces a negative anomalous dimension for the third generation quarks and a positive anomalous dimension for the Higgs. As a result, a split-family natural spectrum and the flavor hierarchies are dynamically generated.
Recurrent motifs as resonant attractor states in the narrative field: a testable model of archetype.
Goodwyn, Erik
2013-06-01
At the most basic level, archetypes represented Jung's attempt to explain the phenomenon of recurrent myths and folktale motifs (Jung 1956, 1959, para. 99). But the archetype remains controversial as an explanation of recurrent motifs, as the existence of recurrent motifs does not prove that archetypes exist. Thus, the challenge for contemporary archetype theory is not merely to demonstrate that recurrent motifs exist, since that is not disputed, but to demonstrate that archetypes exist and cause recurrent motifs. The present paper proposes a new model which is unlike others in that it postulates how the archetype creates resonant motifs. This model necessarily clarifies and adapts some of Jung's seminal ideas on archetype in order to provide a working framework grounded in contemporary practice and methodologies. For the first time, a model of archetype is proposed that can be validated on empirical, rather than theoretical grounds. This is achieved by linking the archetype to the hard data of recurrent motifs rather than academic trends in other fields.
Symmetron and de Sitter attractor in a teleparallel model of cosmology
Sadjadi, H Mohseni
2016-01-01
In the teleparallel framework of cosmology, a quintessence with non-minimal couplings to the scalar torsion and a boundary term is considered. A conformal coupling to matter density is also taken into account. It is shown that the model can describe onset of cosmic acceleration after an epoch of matter dominated era, where dark energy is negligible, via $Z_2$ symmetry breaking. While the conformal coupling holds the Universe in a vacuum with zero dark energy density in the early epoch, the non-minimal couplings lead the Universe to a stable state with de Sitter expansion at late time.
Symmetron and de Sitter attractor in a teleparallel model of cosmology
Mohseni Sadjadi, H.
2017-01-01
In the teleparallel framework of cosmology, a quintessence with non-minimal couplings to the scalar torsion and a boundary term is considered. A conformal coupling to matter density is also taken into account. It is shown that the model can describe onset of cosmic acceleration after an epoch of matter dominated era, where dark energy is negligible, via Z2 symmetry breaking. While the conformal coupling holds the Universe in a state with zero dark energy density in the early epoch, the non-minimal couplings lead the Universe to a stable state with de Sitter expansion at late time.
Fermions, wigs, and attractors
Energy Technology Data Exchange (ETDEWEB)
Gentile, L.G.C., E-mail: lgentile@pd.infn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria 15120 (Italy); Dipartimento di Fisica “Galileo Galilei”, Università di Padova, via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Grassi, P.A., E-mail: pgrassi@mfn.unipmn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria 15120 (Italy); INFN, Gruppo Collegato di Alessandria, Sezione di Torino (Italy); Marrani, A., E-mail: alessio.marrani@fys.kuleuven.be [ITF KU Leuven, Celestijnenlaan 200D, 3001 Leuven (Belgium); Mezzalira, A., E-mail: andrea.mezzalira@ulb.ac.be [Physique Théorique et Mathématique Université Libre de Bruxelles, C.P. 231, 1050 Bruxelles (Belgium)
2014-05-01
We compute the modifications to the attractor mechanism due to fermionic corrections. In N=2,D=4 supergravity, at the fourth order, we find terms giving rise to new contributions to the horizon values of the scalar fields of the vector multiplets.
Bellucci, S; Marrani, A
2008-01-01
We review recent results in the study of attractor horizon geometries (with non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number n_{V} of Abelian vector multiplets, outlining the fundamentals of the special Kaehler geometry of the vector multiplets' scalar manifold (of complex dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS (non-supersymmetric) ones with non-vanishing central charge. For symmetric special Kaehler geometries, we present the complete classification of the orbits in the symplectic representation of the classical U-duality group (spanned by the black hole charge configuration supporting the attractors), as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon). Finally, we report on an analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attrac...
Energy Technology Data Exchange (ETDEWEB)
Linde, Andrei [Department of Physics and SITP, Stanford University,Stanford, California 94305 (United States)
2015-05-05
I describe a simple class of α-attractors, generalizing the single-field GL model of inflation in supergravity. The new class of models is defined for 0<α≲1, providing a good match to the present cosmological data. I also present a generalized version of these models which can describe not only inflation but also dark energy and supersymmetry breaking.
An integrated network model of psychotic symptoms.
Looijestijn, Jasper; Blom, Jan Dirk; Aleman, André; Hoek, Hans W; Goekoop, Rutger
2015-12-01
The full body of research on the nature of psychosis and its determinants indicates that a considerable number of factors are relevant to the development of hallucinations, delusions, and other positive symptoms, ranging from neurodevelopmental parameters and altered connectivity of brain regions to impaired cognitive functioning and social factors. We aimed to integrate these factors in a single mathematical model based on network theory. At the microscopic level this model explains positive symptoms of psychosis in terms of experiential equivalents of robust, high-frequency attractor states of neural networks. At the mesoscopic level it explains them in relation to global brain states, and at the macroscopic level in relation to social-network structures and dynamics. Due to the scale-free nature of biological networks, all three levels are governed by the same general laws, thereby allowing for an integrated model of biological, psychological, and social phenomena involved in the mediation of positive symptoms of psychosis. This integrated network model of psychotic symptoms (INMOPS) is described together with various possibilities for application in clinical practice.
Renormalization Group independence of Cosmological Attractors
Fumagalli, Jacopo
2016-01-01
The large class of inflationary models known as $\\alpha$- and $\\xi$-attractors give identical predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.
Boolean genetic network model for the control of C. elegans early embryonic cell cycles
2013-01-01
Background In Caenorhabditis elegans early embryo, cell cycles only have two phases: DNA synthesis and mitosis, which are different from the typical 4-phase cell cycle. Modeling this cell-cycle process into network can fill up the gap in C. elegans cell-cycle study and provide a thorough understanding on the cell-cycle regulations and progressions at the network level. Methods In this paper, C. elegans early embryonic cell-cycle network has been constructed based on the knowledge of key regulators and their interactions from literature studies. A discrete dynamical Boolean model has been applied in computer simulations to study dynamical properties of this network. The cell-cycle network is compared with random networks and tested under several perturbations to analyze its robustness. To investigate whether our proposed network could explain biological experiment results, we have also compared the network simulation results with gene knock down experiment data. Results With the Boolean model, this study showed that the cell-cycle network was stable with a set of attractors (fixed points). A biological pathway was observed in the simulation, which corresponded to a whole cell-cycle progression. The C. elegans network was significantly robust when compared with random networks of the same size because there were less attractors and larger basins than random networks. Moreover, the network was also robust under perturbations with no significant change of the basin size. In addition, the smaller number of attractors and the shorter biological pathway from gene knock down network simulation interpreted the shorter cell-cycle lengths in mutant from the RNAi gene knock down experiment data. Hence, we demonstrated that the results in network simulation could be verified by the RNAi gene knock down experiment data. Conclusions A C. elegans early embryonic cell cycles network was constructed and its properties were analyzed and compared with those of random networks
Relative stability of network states in Boolean network models of gene regulation in development.
Zhou, Joseph Xu; Samal, Areejit; d'Hérouël, Aymeric Fouquier; Price, Nathan D; Huang, Sui
2016-01-01
Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.
Is attentional blink a byproduct of neocortical attractors?
Directory of Open Access Journals (Sweden)
David N Silverstein
2011-05-01
Full Text Available This study proposes a computational model for attentional blink or blink of the mind, a phenomenon where a human subject misses perception of a later expected visual pattern as two expected visual patterns are presented less than 500 ms apart. A neocortical patch modeled as an attractor network is stimulated with a sequence of 14 patterns 100 ms apart, two of which are expected targets. Patterns that become active attractors are considered recognized. A neocortical patch is represented as a square matrix of hypercolumns, each containing a set of minicolumns with synaptic connections within and across both minicolumns and hypercolumns. Each minicolumn consists of locally connected layer 2/3 pyramidal cells with interacting basket cells and layer 4 pyramidal cells for input stimulation. All neurons are implemented using the Hodgkin-Huxley multi-compartmental cell formalism and include calcium dynamics, and they interact via saturating and depressing AMPA / NMDA and GABAA synapses. Stored patterns are encoded with global connectivity of minicolumns across hypercolumns and active patterns compete as the result of lateral inhibition in the network. Stored patterns were stimulated over time intervals to create attractor interference measurable with synthetic spike traces. This setup corresponds with item presentations in human visual attentional blink studies. Stored target patterns were depolarized while distractor patterns where hyperpolarized to represent expectation of items in working memory. Additionally, studies on the inhibitory effect of benzodiazopines on attentional blink in human subjects were compared with neocortical simulations where the GABAA receptor conductance and decay time were increased. Simulations showed increases in the attentional blink duration, agreeing with observations in human studies.
ATTRACTORS FOR THE BRUSSELATOR IN RN
Institute of Scientific and Technical Information of China (English)
Han Yongqian; Guo Boling
2007-01-01
We consider the reaction-diffusion system, a model of a certain chemical morphogenetic process and named Brusselator. For the Cauchy problem of this system with nondecaying initial data, the existence and uniqueness of the global solution is established. Moreover, it is proved that this system possesses a global attractor A in the corresponding phase space.
Cosmological attractors from alpha-scale supergravity
Roest, Diederik; Scalisi, Marco
2015-01-01
The Planck value of the spectral index can be interpreted as n(s) = 1 - 2/N in terms of the number of e-foldings N. An appealing explanation for this phenomenological observation is provided by alpha-attractors: the inflationary predictions of these supergravity models are fully determined by the cu
Coexistence of exponentially many chaotic spin-glass attractors.
Peleg, Y; Zigzag, M; Kinzel, W; Kanter, I
2011-12-01
A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.
Trajectory attractors of equations of mathematical physics
Energy Technology Data Exchange (ETDEWEB)
Vishik, Marko I; Chepyzhov, Vladimir V [Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow (Russian Federation)
2011-08-31
In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.
Armbruster, Benjamin
2011-01-01
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which has relevance for connectivity and the spread of infections. Second, we analyze the effect of node turnover, when nodes enter and leave the network, which has relevance for network models incorporating births, deaths, aging, and other demographic factors.
Boolean Network Model for Cancer Pathways: Predicting Carcinogenesis and Targeted Therapy Outcomes
Fumiã, Herman F.; Martins, Marcelo L.
2013-01-01
A Boolean dynamical system integrating the main signaling pathways involved in cancer is constructed based on the currently known protein-protein interaction network. This system exhibits stationary protein activation patterns – attractors – dependent on the cell's microenvironment. These dynamical attractors were determined through simulations and their stabilities against mutations were tested. In a higher hierarchical level, it was possible to group the network attractors into distinct cell phenotypes and determine driver mutations that promote phenotypic transitions. We find that driver nodes are not necessarily central in the network topology, but at least they are direct regulators of central components towards which converge or through which crosstalk distinct cancer signaling pathways. The predicted drivers are in agreement with those pointed out by diverse census of cancer genes recently performed for several human cancers. Furthermore, our results demonstrate that cell phenotypes can evolve towards full malignancy through distinct sequences of accumulated mutations. In particular, the network model supports routes of carcinogenesis known for some tumor types. Finally, the Boolean network model is employed to evaluate the outcome of molecularly targeted cancer therapies. The major find is that monotherapies were additive in their effects and that the association of targeted drugs is necessary for cancer eradication. PMID:23922675
Reverse engineering cellular decisions for hybrid reconfigurable network modeling
Blair, Howard A.; Saranak, Jureepan; Foster, Kenneth W.
2011-06-01
Cells as microorganisms and within multicellular organisms make robust decisions. Knowing how these complex cells make decisions is essential to explain, predict or mimic their behavior. The discovery of multi-layer multiple feedback loops in the signaling pathways of these modular hybrid systems suggests their decision making is sophisticated. Hybrid systems coordinate and integrate signals of various kinds: discrete on/off signals, continuous sensory signals, and stochastic and continuous fluctuations to regulate chemical concentrations. Such signaling networks can form reconfigurable networks of attractors and repellors giving them an extra level of organization that has resilient decision making built in. Work on generic attractor and repellor networks and on the already identified feedback networks and dynamic reconfigurable regulatory topologies in biological cells suggests that biological systems probably exploit such dynamic capabilities. We present a simple behavior of the swimming unicellular alga Chlamydomonas that involves interdependent discrete and continuous signals in feedback loops. We show how to rigorously verify a hybrid dynamical model of a biological system with respect to a declarative description of a cell's behavior. The hybrid dynamical systems we use are based on a unification of discrete structures and continuous topologies developed in prior work on convergence spaces. They involve variables of discrete and continuous types, in the sense of type theory in mathematical logic. A unification such as afforded by convergence spaces is necessary if one wants to take account of the affect of the structural relationships within each type on the dynamics of the system.
Logical Modeling and Dynamical Analysis of Cellular Networks.
Abou-Jaoudé, Wassim; Traynard, Pauline; Monteiro, Pedro T; Saez-Rodriguez, Julio; Helikar, Tomáš; Thieffry, Denis; Chaouiya, Claudine
2016-01-01
The logical (or logic) formalism is increasingly used to model regulatory and signaling networks. Complementing these applications, several groups contributed various methods and tools to support the definition and analysis of logical models. After an introduction to the logical modeling framework and to several of its variants, we review here a number of recent methodological advances to ease the analysis of large and intricate networks. In particular, we survey approaches to determine model attractors and their reachability properties, to assess the dynamical impact of variations of external signals, and to consistently reduce large models. To illustrate these developments, we further consider several published logical models for two important biological processes, namely the differentiation of T helper cells and the control of mammalian cell cycle.
Chaotic attractors with separated scrolls
Energy Technology Data Exchange (ETDEWEB)
Bouallegue, Kais, E-mail: kais-bouallegue@yahoo.fr [Department of Electrical Engineering, Higher Institute of Applied Sciences and Technology of Sousse, Sousse (Tunisia)
2015-07-15
This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
Directory of Open Access Journals (Sweden)
Yasser Roudi
2007-09-01
Full Text Available A fundamental problem in neuroscience is understanding how working memory--the ability to store information at intermediate timescales, like tens of seconds--is implemented in realistic neuronal networks. The most likely candidate mechanism is the attractor network, and a great deal of effort has gone toward investigating it theoretically. Yet, despite almost a quarter century of intense work, attractor networks are not fully understood. In particular, there are still two unanswered questions. First, how is it that attractor networks exhibit irregular firing, as is observed experimentally during working memory tasks? And second, how many memories can be stored under biologically realistic conditions? Here we answer both questions by studying an attractor neural network in which inhibition and excitation balance each other. Using mean-field analysis, we derive a three-variable description of attractor networks. From this description it follows that irregular firing can exist only if the number of neurons involved in a memory is large. The same mean-field analysis also shows that the number of memories that can be stored in a network scales with the number of excitatory connections, a result that has been suggested for simple models but never shown for realistic ones. Both of these predictions are verified using simulations with large networks of spiking neurons.
STU attractors from vanishing concurrence
Lévay, Péter
2010-01-01
Concurrence is an entanglement measure characterizing the {\\it mixed} state bipartite correlations inside of a pure state of an $n$-qubit system. We show that after organizing the charges and the moduli in the STU model of $N=2$, $d=4$ supergravity to a three-qubit state, for static extremal spherically symmetric BPS black hole solutions the vanishing condition for all of the bipartite concurrences on the horizon is equivalent to the attractor equations. As a result of this the macroscopic black hole entropy given by the three-tangle can be reinterpreted as a linear entropy characterizing the {\\it pure} state entanglement for an arbitrary bipartite split. Both for the BPS and non-BPS cases explicit expressions for the concurrences are obtained, with their vanishing on the horizon is demonstrated.
Modeling worldwide highway networks
Villas Boas, Paulino R.; Rodrigues, Francisco A.; da F. Costa, Luciano
2009-12-01
This Letter addresses the problem of modeling the highway systems of different countries by using complex networks formalism. More specifically, we compare two traditional geographical models with a modified geometrical network model where paths, rather than edges, are incorporated at each step between the origin and the destination vertices. Optimal configurations of parameters are obtained for each model and used for the comparison. The highway networks of Australia, Brazil, India, and Romania are considered and shown to be properly modeled by the modified geographical model.
Gravitational waves in $\\alpha-$attractors
Kumar, K Sravan; Moniz, Paulo Vargas; Das, Suratna
2015-01-01
We study inflation in the $\\alpha-$attractor model under a non-slow-roll dynamics with an ansatz proposed by Gong \\& Sasaki \\cite{Gong:2015ypa} of assuming $N=N\\left(\\phi\\right)$. Under this approach, we construct a class of local shapes of inflaton potential that are different from the T-models. We find this type of inflationary scenario predicts an attractor at $n_{s}\\sim0.967$ and $r\\sim0.00055$. In our approach, the non-slow-roll inflaton dynamics are related to the $\\alpha-$parameter which is the curvature of K\\"ahler geometry in the SUGRA embedding of this model.
DEFF Research Database (Denmark)
Andersen, Kasper Winther
Three main topics are presented in this thesis. The first and largest topic concerns network modelling of functional Magnetic Resonance Imaging (fMRI) and Diffusion Weighted Imaging (DWI). In particular nonparametric Bayesian methods are used to model brain networks derived from resting state f...... for their ability to reproduce node clustering and predict unseen data. Comparing the models on whole brain networks, BCD and IRM showed better reproducibility and predictability than IDM, suggesting that resting state networks exhibit community structure. This also points to the importance of using models, which...... allow for complex interactions between all pairs of clusters. In addition, it is demonstrated how the IRM can be used for segmenting brain structures into functionally coherent clusters. A new nonparametric Bayesian network model is presented. The model builds upon the IRM and can be used to infer...
Sakata, Katsumi; Ohyanagi, Hajime; Sato, Shinji; Nobori, Hiroya; Hayashi, Akiko; Ishii, Hideshi; Daub, Carsten O.; Kawai, Jun; Suzuki, Harukazu; Saito, Toshiyuki
2015-02-01
We present a system-wide transcriptional network structure that controls cell types in the context of expression pattern transitions that correspond to cell type transitions. Co-expression based analyses uncovered a system-wide, ladder-like transcription factor cluster structure composed of nearly 1,600 transcription factors in a human transcriptional network. Computer simulations based on a transcriptional regulatory model deduced from the system-wide, ladder-like transcription factor cluster structure reproduced expression pattern transitions when human THP-1 myelomonocytic leukaemia cells cease proliferation and differentiate under phorbol myristate acetate stimulation. The behaviour of MYC, a reprogramming Yamanaka factor that was suggested to be essential for induced pluripotent stem cells during dedifferentiation, could be interpreted based on the transcriptional regulation predicted by the system-wide, ladder-like transcription factor cluster structure. This study introduces a novel system-wide structure to transcriptional networks that provides new insights into network topology.
Modeling Epidemic Network Failures
DEFF Research Database (Denmark)
Ruepp, Sarah Renée; Fagertun, Anna Manolova
2013-01-01
This paper presents the implementation of a failure propagation model for transport networks when multiple failures occur resulting in an epidemic. We model the Susceptible Infected Disabled (SID) epidemic model and validate it by comparing it to analytical solutions. Furthermore, we evaluate...... the SID model’s behavior and impact on the network performance, as well as the severity of the infection spreading. The simulations are carried out in OPNET Modeler. The model provides an important input to epidemic connection recovery mechanisms, and can due to its flexibility and versatility be used...... to evaluate multiple epidemic scenarios in various network types....
Sneutrino Inflation with $\\alpha$-attractors
Kallosh, Renata; Roest, Diederik; Wrase, Timm
2016-01-01
Sneutrino inflation employs the fermionic partners of the inflaton and stabilizer field as right-handed neutrinos to realize the seesaw mechanism for light neutrino masses. A crucial ingredient in existing constructions for sneutrino (multi-)natural inflation is an unbroken discrete shift symmetry. We demonstrate that a similar construction applies to $\\alpha$-attractor models. In this case the hyperbolic geometry protects the neutrino Yukawa couplings to the inflaton field, and the masses of leptons and Higgs fields, from blowing up when the inflaton is super-Planckian. We find that the predictions for $n_s$ and $r$ for $\\alpha$-attractor cosmological models, compatible with the current cosmological data, are preserved in the presence of the neutrino sector.
Artificial neural network modelling
Samarasinghe, Sandhya
2016-01-01
This book covers theoretical aspects as well as recent innovative applications of Artificial Neural networks (ANNs) in natural, environmental, biological, social, industrial and automated systems. It presents recent results of ANNs in modelling small, large and complex systems under three categories, namely, 1) Networks, Structure Optimisation, Robustness and Stochasticity 2) Advances in Modelling Biological and Environmental Systems and 3) Advances in Modelling Social and Economic Systems. The book aims at serving undergraduates, postgraduates and researchers in ANN computational modelling. .
Classification of attractors for systems of identical coupled Kuramoto oscillators
Energy Technology Data Exchange (ETDEWEB)
Engelbrecht, Jan R. [Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467 (United States); Mirollo, Renato [Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467 (United States)
2014-03-15
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For N≠3 oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Classification of attractors for systems of identical coupled Kuramoto oscillators.
Engelbrecht, Jan R; Mirollo, Renato
2014-03-01
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Some properties for the attractors
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
For the continuous flows defined on a topological space,we have discussed some properties for the invariant sets and their domains of influence.We have proved the following open problem posed by C.Conley:an attractor in a locally connected compact Hausdorff invariant set has finitely many components.In the meantime,two necessary and sufficient conditions for a set to be an attractor have been given.
Chaotic Simulated Annealing by A Neural Network Model with Transient Chaos
Chen, L; Chen, Luonan; Aihara, Kazuyuki
1997-01-01
We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks. Unlike conventional neural networks only with point attractors, the proposed neural network has richer and more flexible dynamics, so that it can be expected to have higher ability of searching for globally optimal or near-optimal solutions. A significant property of this model is that the chaotic neurodynamics is temporarily generated for searching and self-organizing, and eventually vanishes with autonomous decreasing of a bifurcation parameter corresponding to the "temperature" in usual annealing process. Therefore, the neural network gradually approaches, through the transient chaos, to dynamical structure similar to such conventional models as the Hopfield neural network which converges to a stable equilibrium point. Since the optimization process of the transiently chaoti...
Inflation, Universality and Attractors
Scalisi, Marco
2016-01-01
In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a novel field-range bound, which is two orders of magnitude stronger than the original one derived by Lyth. On the other hand, we discuss the embedding of inflation in supergravity and prove that non-trivial hyperbolic K\\"ahler geometries induce an attractor for the inflationary observables: the spectral tilt tends automatically to the center of the Planck dome whereas the amount of primordial gravitational waves is directly...
Subdiffusive dynamics of bump attractors: mechanisms and functional roles.
Qi, Yang; Breakspear, Michael; Gong, Pulin
2015-02-01
Bump attractors are localized activity patterns that can self-sustain after stimulus presentation, and they are regarded as the neural substrate for a host of perceptual and cognitive processes. One of the characteristic features of bump attractors is that they are neutrally stable, so that noisy inputs cause them to drift away from their initial locations, severely impairing the accuracy of bump location-dependent neural coding. Previous modeling studies of such noise-induced drifting activity of bump attractors have focused on normal diffusive dynamics, often with an assumption that noisy inputs are uncorrelated. Here we show that long-range temporal correlations and spatial correlations in neural inputs generated by multiple interacting bumps cause them to drift in an anomalous subdiffusive way. This mechanism for generating subdiffusive dynamics of bump attractors is further analyzed based on a generalized Langevin equation. We demonstrate that subdiffusive dynamics can significantly improve the coding accuracy of bump attractors, since the variance of the bump displacement increases sublinearly over time and is much smaller than that of normal diffusion. Furthermore, we reanalyze existing psychophysical data concerning the spread of recalled cue position in spatial working memory tasks and show that its variance increases sublinearly with time, consistent with subdiffusive dynamics of bump attractors. Based on the probability density function of bump position, we also show that the subdiffusive dynamics result in a long-tailed decay of firing rate, greatly extending the duration of persistent activity.
González-Olivares, Eduardo; González-Yañez, Betsabé; Mena-Lorca, Jaime; Flores, Jose D
2013-04-01
The main purpose of this work is to analyze a Gause type predator-prey model in which two ecological phenomena are considered: the Allee effect affecting the prey growth function and the formation of group defence by prey in order to avoid the predation. We prove the existence of a separatrix curves in the phase plane, determined by the stable manifold of the equilibrium point associated to the Allee effect, implying that the solutions are highly sensitive to the initial conditions. Trajectories starting at one side of this separatrix curve have the equilibrium point (0,0) as their ω-limit, while trajectories starting at the other side will approach to one of the following three attractors: a stable limit cycle, a stable coexistence point or the stable equilibrium point (K,0) in which the predators disappear and prey attains their carrying capacity. We obtain conditions on the parameter values for the existence of one or two positive hyperbolic equilibrium points and the existence of a limit cycle surrounding one of them. Both ecological processes under study, namely the nonmonotonic functional response and the Allee effect on prey, exert a strong influence on the system dynamics, resulting in multiple domains of attraction. Using Liapunov quantities we demonstrate the uniqueness of limit cycle, which constitutes one of the main differences with the model where the Allee effect is not considered. Computer simulations are also given in support of the conclusions.
Noise-induced attractor annihilation in the delayed feedback logistic map
Energy Technology Data Exchange (ETDEWEB)
Pisarchik, A.N., E-mail: apisarch@cio.mx [Centro de Investigaciones en Optica, Loma del Bosque 115, Leon, Guanajuato (Mexico); Centre for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid (Spain); Martínez-Zérega, B.E. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon 1144, Paseos de la Montaña, Lagos de Moreno, Jalisco 47460 (Mexico)
2013-12-06
We study dynamics of the bistable logistic map with delayed feedback, under the influence of white Gaussian noise and periodic modulation applied to the variable. This system may serve as a model to describe population dynamics under finite resources in noisy environment with seasonal fluctuations. While a very small amount of noise has no effect on the global structure of the coexisting attractors in phase space, an intermediate noise totally eliminates one of the attractors. Slow periodic modulation enhances the attractor annihilation.
Modeling Evolving Innovation Networks
Koenig, Michael D.; Battiston, Stefano; Schweitzer, Frank
2007-01-01
We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increase their knowledge...
Boolean network model predicts cell cycle sequence of fission yeast.
Directory of Open Access Journals (Sweden)
Maria I Davidich
Full Text Available A Boolean network model of the cell-cycle regulatory network of fission yeast (Schizosaccharomyces Pombe is constructed solely on the basis of the known biochemical interaction topology. Simulating the model in the computer faithfully reproduces the known activity sequence of regulatory proteins along the cell cycle of the living cell. Contrary to existing differential equation models, no parameters enter the model except the structure of the regulatory circuitry. The dynamical properties of the model indicate that the biological dynamical sequence is robustly implemented in the regulatory network, with the biological stationary state G1 corresponding to the dominant attractor in state space, and with the biological regulatory sequence being a strongly attractive trajectory. Comparing the fission yeast cell-cycle model to a similar model of the corresponding network in S. cerevisiae, a remarkable difference in circuitry, as well as dynamics is observed. While the latter operates in a strongly damped mode, driven by external excitation, the S. pombe network represents an auto-excited system with external damping.
A Bio-Inspired QoS-Oriented Handover Model in Heterogeneous Wireless Networks
Directory of Open Access Journals (Sweden)
Daxin Tian
2014-01-01
Full Text Available We propose a bio-inspired model for making handover decision in heterogeneous wireless networks. It is based on an extended attractor selection model, which is biologically inspired by the self-adaptability and robustness of cellular response to the changes in dynamic environments. The goal of the proposed model is to guarantee multiple terminals’ satisfaction by meeting the QoS requirements of those terminals’ applications, and this model also attempts to ensure the fairness of network resources allocation, in the meanwhile, to enable the QoS-oriented handover decision adaptive to dynamic wireless environments. Some numerical simulations are preformed to validate our proposed bio-inspired model in terms of adaptive attractor selection in different noisy environments. And the results of some other simulations prove that the proposed handover scheme can adapt terminals’ network selection to the varying wireless environment and benefits the QoS of multiple terminal applications simultaneously and automatically. Furthermore, the comparative analysis also shows that the bio-inspired model outperforms the utility function based handover decision scheme in terms of ensuring a better QoS satisfaction and a better fairness of network resources allocation in dynamic heterogeneous wireless networks.
Moduli backreaction on inflationary attractors
Roest, Diederik; Scalisi, Marco; Werkman, Pelle
2016-12-01
We investigate the interplay between moduli dynamics and inflation, focusing on the Kachru-Kallosh-Linde-Trivedi scenario and cosmological α -attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for α -attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The gravitino mass is independent from the inflationary scale with no fine-tuning of the parameters. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e -folds due to the interplay with moduli.
Moduli Backreaction on Inflationary Attractors
Roest, Diederik; Werkman, Pelle
2016-01-01
We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $\\alpha$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $\\alpha$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.
Hyperbolic geometry of cosmological attractors
Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-01-01
Cosmological alpha attractors give a natural explanation for the spectral index n(s) of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial ro
Models of educational institutions' networking
Shilova Olga Nikolaevna
2015-01-01
The importance of educational institutions' networking in modern sociocultural conditions and a definition of networking in education are presented in the article. The results of research levels, methods and models of educational institutions' networking are presented and substantially disclosed.
Attractors of multivalued semiflows generated by differential inclusions and their approximations
Directory of Open Access Journals (Sweden)
Alexei V. Kapustian
2000-01-01
Full Text Available We prove the existence of global compact attractors for differential inclusions and obtain some results concerning the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. Applications are given to a model of regional economic growth.
Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics
Energy Technology Data Exchange (ETDEWEB)
Kuznetsov, Sergei P [Saratov Branch, Kotel' nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov (Russian Federation)
2011-02-28
Research is reviewed on the identification and construction of physical systems with chaotic dynamics due to uniformly hyperbolic attractors (such as the Plykin attraction or the Smale-Williams solenoid). Basic concepts of the mathematics involved and approaches proposed in the literature for constructing systems with hyperbolic attractors are discussed. Topics covered include periodic pulse-driven models; dynamics models consisting of periodically repeated stages, each described by its own differential equations; the construction of systems of alternately excited coupled oscillators; the use of parametrically excited oscillations; and the introduction of delayed feedback. Some maps, differential equations, and simple mechanical and electronic systems exhibiting chaotic dynamics due to the presence of uniformly hyperbolic attractors are presented as examples. (reviews of topical problems)
Energy cascade in internal wave attractors
Brouzet, Christophe; Joubaud, Sylvain; Sibgatullin, Ilias; Dauxois, Thierry
2016-01-01
One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction.
Generation and control of multi-scroll chaotic attractors in fractional order systems
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. [Department of Electrical and Computer Engineering, University of Sharjah, P.O. Box 27272, Sharjah (United Arab Emirates)] e-mail: wajdi@sharjah.ac.ae
2005-08-01
The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations.
Ceresole, A; Gnecchi, A; Marrani, A
2009-01-01
We examine few simple extremal black hole configurations of N=8, d=4 supergravity. We first elucidate the relation between the BPS Reissner-Nordstrom black hole and the non-BPS Kaluza-Klein dyonic black hole. Their classical entropy, given by the Bekenstein-Hawking formula, can be reproduced via the attractor mechanism by suitable choices of symplectic frame. Then, we display the embedding of the axion-dilaton black hole into N=8 supergravity.
Required criteria for recognizing new types of chaos: Application to the ``cord'' attractor
Letellier, Christophe; Aguirre, Luis A.
2012-03-01
After suggesting criteria to recognize a new system and a new attractor—and to make a distinction between them—the paper details the topological analysis of the “cord” attractor. This attractor, which resembles a cord between two leaves, is produced by a three-dimensional system that is obtained after a modification of the Lorenz-84 model for the global atmospheric circulation [L. A. Aguirre and C. Letellier, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.83.066209 83, 066209 (2011)]. The nontrivial topology of the attractor is described in terms of a template that corresponds to a reverse horseshoe, that is, to a spiral Rössler attractor with negative and positive global π twists. Due to its particular structure and to the fact that such a system has two variables from which the dynamics is poorly observable, this attractor qualifies as a challenging benchmark in nonlinear dynamics.
Oscillatory Attractors: A New Cosmological Phase
Bains, Jasdeep S; Wilczek, Frank
2015-01-01
In expanding FRW spacetimes, it is usually the case that homogeneous scalar fields redshift and their amplitudes approach limiting values: Hubble friction usually ensures that the field relaxes to its minimum energy configuration, which is usually a static configuration. Here we discover a class of relativistic scalar field models in which the attractor behavior is the field oscillating indefinitely, with finite amplitude, in an expanding FRW spacetime, despite the presence of Hubble friction. This is an example of spontaneous breaking of time translation symmetry. We find that the effective equation of state of the field has average value $\\langle w\\rangle=-1$, implying that the field itself could drive an inflationary or dark energy dominated phase. This behavior is reminiscent of ghost condensate models, but in the new models, unlike in the ghost condensate models, the energy-momentum tensor is time dependent, so that these new models embody a more definitive breaking of time translation symmetry. We explo...
Coevolutionary modeling in network formation
Al-Shyoukh, Ibrahim
2014-12-03
Network coevolution, the process of network topology evolution in feedback with dynamical processes over the network nodes, is a common feature of many engineered and natural networks. In such settings, the change in network topology occurs at a comparable time scale to nodal dynamics. Coevolutionary modeling offers the possibility to better understand how and why network structures emerge. For example, social networks can exhibit a variety of structures, ranging from almost uniform to scale-free degree distributions. While current models of network formation can reproduce these structures, coevolutionary modeling can offer a better understanding of the underlying dynamics. This paper presents an overview of recent work on coevolutionary models of network formation, with an emphasis on the following three settings: (i) dynamic flow of benefits and costs, (ii) transient link establishment costs, and (iii) latent preferential attachment.
Generalized Attractor Points in Gauged Supergravity
Energy Technology Data Exchange (ETDEWEB)
Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC; Kallosh, Renata; /Stanford U., Phys. Dept.; Shmakova, Marina; /KIPAC, Menlo Park /SLAC /Stanford U., Phys. Dept.
2011-08-15
The attractor mechanism governs the near-horizon geometry of extremal black holes in ungauged 4D N=2 supergravity theories and in Calabi-Yau compactifications of string theory. In this paper, we study a natural generalization of this mechanism to solutions of arbitrary 4D N=2 gauged supergravities. We define generalized attractor points as solutions of an ansatz which reduces the Einstein, gauge field, and scalar equations of motion to algebraic equations. The simplest generalized attractor geometries are characterized by non-vanishing constant anholonomy coefficients in an orthonormal frame. Basic examples include Lifshitz and Schroedinger solutions, as well as AdS and dS vacua. There is a generalized attractor potential whose critical points are the attractor points, and its extremization explains the algebraic nature of the equations governing both supersymmetric and non-supersymmetric attractors.
Non-slow-roll dynamics in $\\alpha-$attractors
Kumar, K Sravan; Moniz, Paulo Vargas; Das, Suratna
2015-01-01
In this paper we consider the $\\alpha-$attractor model and study inflation under a generalization of slow-roll dynamics. We follow the recently proposed Gong \\& Sasaki approach \\cite{Gong:2015ypa} of assuming $N=N\\left(\\phi\\right)$. We relax the requirement of inflaton potential flatness and consider a sufficiently steep one to support 60-efoldings. We find that this type of inflationary scenario predicts an attractor at $n_{s}\\approx0.967$ and $r\\approx5.5\\times10^{-4}$ which are very close to the predictions of the first chaotic inflationary model in supergravity (Goncharov-Linde model) \\cite{Goncharov:1983mw}. We show that even with non-slow-roll dynamics, the $\\alpha-$attractor model is compatible with any value of $r<0.1$. In addition, we emphasize that in this particular inflationary scenario, the standard consistency relation $\\left(r\\simeq-8n_{t}\\right)$ is significantly violated and we find an attractor for tensor tilt at $n_{t}\\approx-0.034$ as $r\\rightarrow0$. Any prominent detection of the ...
Model Diagnostics for Bayesian Networks
Sinharay, Sandip
2006-01-01
Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…
Global attractors for damped abstract nonlinear hyperbolic systems
Pinter, Gabriella Agnes
1997-12-01
This dissertation is concerned with the long time dynamics of a class of damped abstract hyperbolic systems that arise in the study of certain smart material structures, namely elastomers. The term smart material refers to a material capable of both sensing and responding actively to outside excitation. These properties make smart materials a prime canditate for actuation and sensing in next generation control systems. However, modeling and numerically simulating their behavior poses several difficulties. In this work we consider a model for elastomers developed by H. T. Banks, N. J. Lybeck, B. C. Munoz, L. C. Yanyo, formulate this model as an abstract evolution system, and study the long time behavior of its solutions. We remark that the question of existence and uniqueness of solutions for this class of systems is a challenging problem and was only recently solved by H. T. Banks, D. S. Gilliam and V. I. Shubov. Concerning the long time dynamics of the problem, we first prove that the system generates a weak dynamical system, and possesses a weak global attractor. Our main result is the existence of a "strong" dynamical system which has a compact global attractor. With the help of a Lyapunov function we are able to characterize the structure of this attractor. We also give a theorem that guarantees the stability of the global attractor with respect to varying parameters in the system. Our last result concerns the uniform differentiability of the dynamical system.
A geometrical approach to control and controllability of nonlinear dynamical networks.
Wang, Le-Zhi; Su, Ri-Qi; Huang, Zi-Gang; Wang, Xiao; Wang, Wen-Xu; Grebogi, Celso; Lai, Ying-Cheng
2016-04-14
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.
State space parsimonious reconstruction of attractor produced by an electronic oscillator
Aguirre, Luis A.; Freitas, Ubiratan S.; Letellier, Christophe; Sceller, Lois Le; Maquet, Jean
2000-02-01
This work discusses the reconstruction, from a set of real data, of a chaotic attractor produced by a well-known electronic oscillator, Chua's circuit. The mathematical representation used is a nonlinear differential equation of the polynomial type. One of the contributions of the present study is that structure selection techniques have been applied to help determine the regressors in the model. Models of the chaotic attractor obtained with and without structure selection were compared. The main differences between structure-selected models and complete structure models are: i) the former are more parsimonious that the latter, ii) fixed-point symmetry is guaranteed for the former, iii) for structure-selected models a trivial fixed point is also guaranteed, and iv) the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models.
Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics
Energy Technology Data Exchange (ETDEWEB)
Metz, F L; Theumann, W K [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre (Brazil)], E-mail: fernando@itf.fys.kuleuven.be, E-mail: theumann@if.ufrgs.br
2009-09-25
The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction are studied in this work allowing for the presence of a self-interaction for each unit. Phase diagrams of stationary states are obtained exhibiting phases of retrieval, symmetric and period-two cyclic states as well as correlated and frozen-in states, in the absence of noise. The frozen-in states are destabilized by synaptic noise and well-separated regions of correlated and cyclic states are obtained. Excitatory or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic behaviour.
Mining and modeling character networks
Bonato, Anthony; Elenberg, Ethan R; Gleich, David F; Hou, Yangyang
2016-01-01
We investigate social networks of characters found in cultural works such as novels and films. These character networks exhibit many of the properties of complex networks such as skewed degree distribution and community structure, but may be of relatively small order with a high multiplicity of edges. Building on recent work of beveridge, we consider graph extraction, visualization, and network statistics for three novels: Twilight by Stephanie Meyer, Steven King's The Stand, and J.K. Rowling's Harry Potter and the Goblet of Fire. Coupling with 800 character networks from films found in the http://moviegalaxies.com/ database, we compare the data sets to simulations from various stochastic complex networks models including random graphs with given expected degrees (also known as the Chung-Lu model), the configuration model, and the preferential attachment model. Using machine learning techniques based on motif (or small subgraph) counts, we determine that the Chung-Lu model best fits character networks and we ...
Existence of the atmosphere attractor
Institute of Scientific and Technical Information of China (English)
李建平; 丑纪范
1997-01-01
The global asymptotic behavior of solutions for the equations of large-scale atmospheric motion with the non-stationary external forcing is studied in the infinite-dimensional Hilbert space. Based on the properties of operators of the equations, some energy inequalities and the uniqueness theorem of solutions are obtained. On the assumption that external forces are bounded, the exsitence of the global absorbing set and the atmosphere attractor is proved, and the characteristics of the decay of effect of initial field and the adjustment to the external forcing are revealed. The physical sense of the results is discussed and some ideas about climatic numerical forecast are elucidated.
Black Hole Attractors in Extended Supergravity
Ferrara, Sergio
2007-01-01
We review some aspects of the attractor mechanism for extremal black holes of (not necessarily supersymmetric) theories coupling Einstein gravity to scalars and Maxwell vector fields. Thence, we consider N=2 and N=8, d=4 supergravities, reporting some recent advances on the moduli spaces associated to BPS and non-BPS attractor solutions supported by charge orbits with non-compact stabilizers.
Strange attractor simulated on a quantum computer
2002-01-01
We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature.
Strange Attractor in Immunology of Tumor Growth
Voitikova, M
1997-01-01
The time delayed cytotoxic T-lymphocyte response on the tumor growth has been developed on the basis of discrete approximation (2-dimensional map). The growth kinetic has been described by logistic law with growth rate being the bifurcation parameter. Increase in the growth rate results in instability of the tumor state and causes period-doubling bifurcations in the immune+tumor system. For larger values of tumor growth rate a strange attractor has been observed. The model proposed is able to describe the metastable-state production when time series data of the immune state and the number of tumor cells are irregular and unpredictable. This metastatic disease may be caused not by exterior (medical) factors, but interior density dependent ones.
The past attractor in inhomogeneous cosmology
Uggla, C; Wainwright, J; Ellis, G F R; Uggla, Claes; Elst, Henk van; Wainwright, John; Ellis, George F R
2003-01-01
We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of Einstein's field equations with a perfect fluid matter source as an autonomous system of evolution equations and constraints. This framework incorporates spatially homogeneous dynamics in a natural way as a special case, thereby placing earlier work on spatially homogeneous cosmology in a broader context, and allows us to draw on experience gained in that field using dynamical systems methods. One of our goals is to provide a precise formulation of the approach to the spacelike initial singularity in cosmological models, described heuristically by Belinski\\v{\\i}, Khalatnikov and Lifshitz. Specifically, we construct an invariant set which we conjecture forms the local past attractor for the evolution equations. We anticipate that this new formulation will provide the basis for ...
Synthesis of n-scroll attractors using saturated functions from high-level simulation
Energy Technology Data Exchange (ETDEWEB)
Munoz-Pacheco, J-M; Tlelo-Cuautle, E [Department of Electronics, INAOE, Luis Enrique Erro No. 1, Tonantzintla, Puebla, 72840 (Mexico)], E-mail: mpacheco@inaoep.mx, E-mail: e.tlelo@ieee.org
2008-02-15
Modeling and simulation of a chaotic oscillator based on saturated nonlinear functions (SNLFs) are presented for the synthesis of n-scrolls attractors. First, the oscillator is simulated at the electronic system level by applying state variables and piecewise-linear approximation. Second, the dynamic ranges are scaled to control the breaking points and slopes within practical values. Additionally, the frequency scaling of n-scrolls attractors is performed. Finally, the SNLF is synthesized using operational amplifiers to generate 2, 3, 4, 5 and 6-scrolls attractors. Theoretical results are confirmed by SPICE simulations to show the usefulness of the proposed synthesis approach.
Synthesis of n-scroll attractors using saturated functions from high-level simulation
Muñoz-Pacheco, J.-M.; Tlelo-Cuautle, E.
2008-02-01
Modeling and simulation of a chaotic oscillator based on saturated nonlinear functions (SNLFs) are presented for the synthesis of n-scrolls attractors. First, the oscillator is simulated at the electronic system level by applying state variables and piecewise-linear approximation. Second, the dynamic ranges are scaled to control the breaking points and slopes within practical values. Additionally, the frequency scaling of n-scrolls attractors is performed. Finally, the SNLF is synthesized using operational amplifiers to generate 2, 3, 4, 5 and 6-scrolls attractors. Theoretical results are confirmed by SPICE simulations to show the usefulness of the proposed synthesis approach.
The Physics of Neural Networks
Gutfreund, Hanoch; Toulouse, Gerard
The following sections are included: * Introduction * Historical Perspective * Why Statistical Physics? * Purpose and Outline of the Paper * Basic Elements of Neural Network Models * The Biological Neuron * From the Biological to the Formal Neuron * The Formal Neuron * Network Architecture * Network Dynamics * Basic Functions of Neural Network Models * Associative Memory * Learning * Categorization * Generalization * Optimization * The Hopfield Model * Solution of the Model * The Merit of the Hopfield Model * Beyond the Standard Model * The Gardner Approach * A Microcanonical Formulation * The Case of Biased Patterns * A Canonical Formulation * Constraints on the Synaptic Weights * Learning with Errors * Learning with Noise * Hierarchically Correlated Data and Categorization * Hierarchical Data Structures * Storage of Hierarchical Data Structures * Categorization * Generalization * Learning a Classification Task * The Reference Perceptron Problem * The Contiguity Problem * Discussion - Issues of Relevance * The Notion of Attractors and Modes of Computation * The Nature of Attractors * Temporal versus Spatial Coding * Acknowledgements * References
Dynamical modeling and analysis of large cellular regulatory networks
Bérenguier, D.; Chaouiya, C.; Monteiro, P. T.; Naldi, A.; Remy, E.; Thieffry, D.; Tichit, L.
2013-06-01
The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.
Logical Attractors: a Boolean Approach to the Dynamics of Psychosis
Kupper, Z.; Hoffmann, H.
A Boolean modeling approach to attractors in the dynamics of psychosis is presented: Kinetic Logic, originating from R. Thomas, describes systems on an intermediate level between a purely verbal, qualitative description and a description using nonlinear differential equations. With this method we may model impact, feedback and temporal evolution, as well as analyze the resulting attractors. In our previous research the method has been applied to general and more specific questions in the dynamics of psychotic disorders. In this paper a model is introduced that describes different dynamical patterns of chronic psychosis in the context of vocational rehabilitation. It also shows to be useful in formulating and exploring possible treatment strategies. Finally, some of the limitations and benefits of Kinetic Logic as a modeling tool for psychology and psychiatry are discussed.
Internet Network Resource Information Model
Institute of Scientific and Technical Information of China (English)
陈传峰; 李增智; 唐亚哲; 刘康平
2002-01-01
The foundation of any network management systens is a database that con-tains information about the network resources relevant to the management tasks. A networkinformation model is an abstraction of network resources, including both managed resources andmanaging resources. In the SNMP-based management framework, management information isdefined almost exclusively from a "device" viewpoint, namely, managing a network is equiva-lent to managing a collection of individual nodes. Aiming at making use of recent advances indistributed computing and in object-oriented analysis and design, the Internet management ar-chitecture can also be based on the Open Distributed Processing Reference Model (RM-ODP).The purpose of this article is to provide an Internet Network Resource Information Model.First, a layered management information architecture will be discussed. Then the Internetnetwork resource information model is presented. The information model is specified usingObject-Z.
Complex Networks in Psychological Models
Wedemann, R. S.; Carvalho, L. S. A. V. D.; Donangelo, R.
We develop schematic, self-organizing, neural-network models to describe mechanisms associated with mental processes, by a neurocomputational substrate. These models are examples of real world complex networks with interesting general topological structures. Considering dopaminergic signal-to-noise neuronal modulation in the central nervous system, we propose neural network models to explain development of cortical map structure and dynamics of memory access, and unify different mental processes into a single neurocomputational substrate. Based on our neural network models, neurotic behavior may be understood as an associative memory process in the brain, and the linguistic, symbolic associative process involved in psychoanalytic working-through can be mapped onto a corresponding process of reconfiguration of the neural network. The models are illustrated through computer simulations, where we varied dopaminergic modulation and observed the self-organizing emergent patterns at the resulting semantic map, interpreting them as different manifestations of mental functioning, from psychotic through to normal and neurotic behavior, and creativity.
Attractor Control Using Machine Learning
Duriez, Thomas; Noack, Bernd R; Cordier, Laurent; Segond, Marc; Abel, Markus
2013-01-01
We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with finite number of actuators (multiple inputs) and sensors (multiple outputs). The control law maps outputs into inputs and is optimized with respect to a cost function, containing physics via the dynamical or statistical properties of the attractor to be controlled. Thus, we are capable of exploiting nonlinear mechanisms, e.g. chaos or frequency cross-talk, serving the control objective. This optimization is based on genetic programming, a branch of machine learning. This machine learning control is successfully applied to the stabilization of nonlinearly coupled oscillators and maximization of Lyapunov exponent of a forced Lorenz system. We foresee potential applications to most nonlinear multiple inputs/multiple outputs control problems, particulary in experiments.
Developing Personal Network Business Models
DEFF Research Database (Denmark)
Saugstrup, Dan; Henten, Anders
2006-01-01
on the 'state of the art' in the field of business modeling. Furthermore, the paper suggests three generic business models for PNs: a service oriented model, a self-organized model, and a combination model. Finally, examples of relevant services and applications in relation to three different cases......The aim of the paper is to examine the issue of business modeling in relation to personal networks, PNs. The paper builds on research performed on business models in the EU 1ST MAGNET1 project (My personal Adaptive Global NET). The paper presents the Personal Network concept and briefly reports...... are presented and analyzed in light of business modeling of PN....
2008-12-01
well, then a Euclidean distance would be appropriate. The quadratic assignment procedure ( QAP ) (Krackhardt, 1987) could be used to compare the...Networks. Journal of Applied Psychology, 71(1): 50-55. Krackhardt, D. (1987). QAP Partialling as a Test of Spuriousness. Social Networks, 9, 171-186
Decaying turbulence and developing chaotic attractors
Bershadskii, A
2016-01-01
Competition between two main attractors of the distributed chaos, one associated with translational symmetry (homogeneity) and another associated with rotational symmetry (isotropy), has been studied in freely decaying turbulence. It is shown that, unlike the case of statistically stationary homogeneous isotropic turbulence, the attractor associated with rotational symmetry (and controlled by Loitsyanskii integral) can dominate turbulent local dynamics in an intermediate stage of the decay, because the attractor associated with translational symmetry (and controlled by Birkhoff-Saffman integral) is still not developed enough. The DNS data have been used in order to support this conclusion.
Chaotic Attractor Crisis and Climate Sensitivity: a Transfer Operator Approach
Tantet, A.; Lucarini, V.; Lunkeit, F.; Dijkstra, H. A.
2015-12-01
The rough response to a smooth parameter change of some non-chaotic climate models, such as the warm to snowball-Earth transition in energy balance models due to the ice-albedo feedback, can be studied in the framework of bifurcation theory, in particular by analysing the Lyapunov spectrum of fixed points or periodic orbits. However, bifurcation theory is of little help to study the destruction of a chaotic attractor which can occur in high-dimensional General Circulation Models (GCM). Yet, one would expect critical slowing down to occur before the crisis, since, as the system becomes susceptible to the physical instability mechanism responsible for the crisis, it turns out to be less and less resilient to exogenous perturbations and to spontaneous fluctuations due to other types of instabilities on the attractor. The statistical physics framework, extended to nonequilibrium systems, is particularly well suited for the study of global properties of chaotic and stochastic systems. In particular, the semigroup of transfer operators governs the evolution of distributions in phase space and its spectrum characterises both the relaxation rate of distributions to a statistical steady-state and the stability of this steady-state to perturbations. If critical slowing down indeed occurs in the approach to an attractor crisis, the gap in the spectrum of the semigroup of transfer operators is expected to shrink. We show that the chaotic attractor crisis due to the ice-albedo feedback and resulting in a transition from a warm to a snowball-Earth in the Planet Simulator (PlaSim), a GCM of intermediate complexity, is associated with critical slowing down, as observed by the slower decay of correlations before the crisis (cf. left panel). In addition, we demonstrate that this critical slowing down can be traced back to the shrinkage of the gap between the leading eigenvalues of coarse-grained approximations of the transfer operators and that these eigenvalues capture the
Network models in anatomical systems.
Esteve-Altava, Borja; Marugán-Lobón, Jesús; Botella, Héctor; Rasskin-Gutman, Diego
2011-01-01
Network theory has been extensively used to model the underlying structure of biological processes. From genetics to ecology, network thinking is changing our understanding of complex systems, specifically how their internal structure determines their overall behavior. Concepts such as hubs, scale-free or small-world networks, common in the complexity literature, are now used more and more in sociology, neurosciences, as well as other anthropological fields. Even though the use of network models is nowadays so widely applied, few attempts have been carried out to enrich our understanding in the classical morphological sciences such as in comparative anatomy or physical anthropology. The purpose of this article is to introduce the usage of network tools in morphology; specifically by building anatomical networks, dealing with the most common analyses and problems, and interpreting their outcome.
Telecommunications network modelling, planning and design
Evans, Sharon
2003-01-01
Telecommunication Network Modelling, Planning and Design addresses sophisticated modelling techniques from the perspective of the communications industry and covers some of the major issues facing telecommunications network engineers and managers today. Topics covered include network planning for transmission systems, modelling of SDH transport network structures and telecommunications network design and performance modelling, as well as network costs and ROI modelling and QoS in 3G networks.
Chaotically spiking attractors in suspended mirror optical cavities
Marino, Francesco
2010-01-01
A high-finesse suspended mirror Fabry-Perot cavity is experimentally studied in a regime where radiation pressure and photothermal effect are both relevant. The competition between these phenomena, operating at different time scales, produces unobserved dynamical scenarios where an initial Hopf instability is followed by the birth of small-amplitude chaotic attractors which erratically but deterministically trigger optical spikes. The observed dynamical regimes are well reproduced by a detailed physical model of the system.
Campus network security model study
Zhang, Yong-ku; Song, Li-ren
2011-12-01
Campus network security is growing importance, Design a very effective defense hacker attacks, viruses, data theft, and internal defense system, is the focus of the study in this paper. This paper compared the firewall; IDS based on the integrated, then design of a campus network security model, and detail the specific implementation principle.
A plethora of strange nonchaotic attractors
Indian Academy of Sciences (India)
Surendra Singh Negi; Ramakrishna Ramaswamy
2001-01-01
We show that it is possible to devise a large class of skew-product dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is non-positive. Furthermore, we show that quasiperiodic forcing, which has been a hallmark of essentially all hitherto known examples of such dynamics is not necessary for the creation of SNAs.
How chaotic are strange nonchaotic attractors
Glendinning, Paul; Jaeger, Tobias; Keller, Gerhard
2006-01-01
We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general classes of quasiperiodically forced systems. Further, we include an elementary proof of a classic result by...
Maximal switchability of centralized networks
Vakulenko, Sergei; Morozov, Ivan; Radulescu, Ovidiu
2016-08-01
We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of N s weakly connected satellites, a property that we call n/N s -centrality. If the hub dynamics is slow, we obtain that the large time network dynamics is completely defined by the hub dynamics. Moreover, such networks are maximally flexible and switchable, in the sense that they can switch from a globally attractive rest state to any structurally stable dynamics when the response time of a special controller hub is changed. In particular, we show that a decrease of the controller hub response time can lead to a sharp variation in the network attractor structure: we can obtain a set of new local attractors, whose number can increase exponentially with N, the total number of nodes of the nework. These new attractors can be periodic or even chaotic. We provide an algorithm, which allows us to design networks with the desired switching properties, or to learn them from time series, by adjusting the interactions between hubs and satellites. Such switchable networks could be used as models for context dependent adaptation in functional genetics or as models for cognitive functions in neuroscience.
Effective field theory of non-attractor inflation
Energy Technology Data Exchange (ETDEWEB)
Akhshik, Mohammad [Department of Physics, Sharif University of Technology,Tehran (Iran, Islamic Republic of); School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P. O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Firouzjahi, Hassan [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P. O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Jazayeri, Sadra [Department of Physics, Sharif University of Technology,Tehran (Iran, Islamic Republic of)
2015-07-29
We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter η. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.
Neural network modeling of emotion
Levine, Daniel S.
2007-03-01
This article reviews the history and development of computational neural network modeling of cognitive and behavioral processes that involve emotion. The exposition starts with models of classical conditioning dating from the early 1970s. Then it proceeds toward models of interactions between emotion and attention. Then models of emotional influences on decision making are reviewed, including some speculative (not and not yet simulated) models of the evolution of decision rules. Through the late 1980s, the neural networks developed to model emotional processes were mainly embodiments of significant functional principles motivated by psychological data. In the last two decades, network models of these processes have become much more detailed in their incorporation of known physiological properties of specific brain regions, while preserving many of the psychological principles from the earlier models. Most network models of emotional processes so far have dealt with positive and negative emotion in general, rather than specific emotions such as fear, joy, sadness, and anger. But a later section of this article reviews a few models relevant to specific emotions: one family of models of auditory fear conditioning in rats, and one model of induced pleasure enhancing creativity in humans. Then models of emotional disorders are reviewed. The article concludes with philosophical statements about the essential contributions of emotion to intelligent behavior and the importance of quantitative theories and models to the interdisciplinary enterprise of understanding the interactions of emotion, cognition, and behavior.
Nonequilibrium model on Apollonian networks.
Lima, F W S; Moreira, André A; Araújo, Ascânio D
2012-11-01
We investigate the majority-vote model with two states (-1,+1) and a noise parameter q on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter q. Previous results on the Ising model in Apollonian networks have reported no presence of a phase transition. We also studied the effect of redirecting a fraction p of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio γ/ν, β/ν, and 1/ν for several values of rewiring probability p. The critical noise q{c} and U were also calculated. Therefore, the results presented here demonstrate that the majority-vote model belongs to a different universality class than equilibrium Ising model on Apollonian network.
Inflationary Attractors and Perturbation Spectra in Generally Coupled Gravity
Amendola, L; Occhionero, F; Amendola, Luca; Bellisai, Diego; Occhionero, Franco; Observatory, Rome Astronomical
1993-01-01
A generic outcome of theories with scalar-tensor coupling is the existence of inflationary attractors, either power-law or de Sitter. The fluctuations arising during this phase are Gaussian and their spectrum depends on the wavenumber $k$ according to the power-law $k^{1/(1-p)}$, where $p$ is the inflationary power-law exponent. We investigate to which extent these properties depend on the coupling function and on the potential. We find the class of models in which viable attractors exist. Within this class, we find that the cosmic expansion and the scaling of the fluctuation spectrum are independent of the coupling function. Further, the analytical solution of the Fokker-Planck equation shows that the deviations from Gaussianity are negligible.
A chaotic attractor in timing noise from the Vela pulsar?
Harding, Alice K.; Shinbrot, Troy; Cordes, James M.
1990-01-01
Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.
Algebraic Statistics for Network Models
2014-02-19
AFRL-OSR-VA-TR-2014-0070 (DARPA) Algebraic Statistics for Network Models SONJA PETROVIC PENNSYLVANIA STATE UNIVERSITY 02/19/2014 Final Report...DARPA GRAPHS Phase I Algebraic Statistics for Network Models FA9550-12-1-0392 Sonja Petrović petrovic@psu.edu1 Department of Statistics Pennsylvania...Department of Statistics, Heinz College , Machine Learning Department, Cylab Carnegie Mellon University 1. Abstract This project focused on the family of
Supersymmetry, attractors and cosmic censorship
Energy Technology Data Exchange (ETDEWEB)
Bellorin, Jorge [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: jorge.bellorin@uam.es; Meessen, Patrick [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: patrick.meessen@cern.ch; Ortin, Tomas [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: tomas.ortin@cern.ch
2007-01-29
We show that requiring unbroken supersymmetry everywhere in black-hole-type solutions of N=2, d=4 supergravity coupled to vector supermultiplets ensures in most cases absence of naked singularities. We formulate three specific conditions which we argue are equivalent to the requirement of global supersymmetry. These three conditions can be related to the absence of sources for NUT charge, angular momentum, scalar hair and negative energy, although the solutions can still have globally defined angular momentum and non-trivial scalar fields, as we show in an explicit example. Furthermore, only the solutions satisfying these requirements seem to have a microscopic interpretation in string theory since only they have supersymmetric sources. These conditions exclude, for instance, singular solutions such as the Kerr-Newman with M=|q|, which fails to be everywhere supersymmetric. We also present a re-derivation of several results concerning attractors in N=2, d=4 theories based on the explicit knowledge of the most general solutions in the timelike class.
Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks
Directory of Open Access Journals (Sweden)
Liang Jinghang
2012-08-01
network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. Conclusions Stochastic Boolean networks (SBNs are proposed as an efficient approach to modelling gene regulatory networks (GRNs. The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.
Advances in theoretical models of network science
Institute of Scientific and Technical Information of China (English)
FANG Jin-qing; BI Qiao; LI Yong
2007-01-01
In this review article, we will summarize the main advances in network science investigated by the CIAE Group of Complex Network in this field. Several theoretical models of network science were proposed and their topological and dynamical properties are reviewed and compared with the other models. Our models mainly include a harmonious unifying hybrid preferential model, a large unifying hybrid network model, a quantum interference network, a hexagonal nanowire network, and a small-world network with the same degree. The models above reveal some new phenomena and findings, which are useful for deeply understanding and investigating complex networks and their applications.
Strange Attractors Characterizing the Osmotic Instability
Tzenov, Stephan I
2014-01-01
In the present paper a simple dynamical model for computing the osmotically driven fluid flow in a variety of complex, non equilibrium situations is derived from first principles. Using the Oberbeck-Boussinesq approximation, the basic equations describing the process of forward osmosis have been obtained. It has been shown that these equations are very similar to the ones used to model the free Rayleigh-Benard convection. The difference is that while in the case of thermal convection the volume expansion is driven by the coefficient of thermal expansion, the key role for the osmotic instability is played by the coefficient of isothermal compressibility. In addition, it has been shown that the osmotic process represents a propagation of standing waves with time-dependent amplitudes and phase velocity, which equals the current velocity of the solvent passing through the semi-permeable membrane. The evolution of the amplitudes of the osmotic waves is exactly following the dynamics of a strange attractor of Loren...
Current approaches to gene regulatory network modelling
Directory of Open Access Journals (Sweden)
Brazma Alvis
2007-09-01
Full Text Available Abstract Many different approaches have been developed to model and simulate gene regulatory networks. We proposed the following categories for gene regulatory network models: network parts lists, network topology models, network control logic models, and dynamic models. Here we will describe some examples for each of these categories. We will study the topology of gene regulatory networks in yeast in more detail, comparing a direct network derived from transcription factor binding data and an indirect network derived from genome-wide expression data in mutants. Regarding the network dynamics we briefly describe discrete and continuous approaches to network modelling, then describe a hybrid model called Finite State Linear Model and demonstrate that some simple network dynamics can be simulated in this model.
Structure learning for Bayesian networks as models of biological networks.
Larjo, Antti; Shmulevich, Ilya; Lähdesmäki, Harri
2013-01-01
Bayesian networks are probabilistic graphical models suitable for modeling several kinds of biological systems. In many cases, the structure of a Bayesian network represents causal molecular mechanisms or statistical associations of the underlying system. Bayesian networks have been applied, for example, for inferring the structure of many biological networks from experimental data. We present some recent progress in learning the structure of static and dynamic Bayesian networks from data.
Network model of security system
Directory of Open Access Journals (Sweden)
Adamczyk Piotr
2016-01-01
Full Text Available The article presents the concept of building a network security model and its application in the process of risk analysis. It indicates the possibility of a new definition of the role of the network models in the safety analysis. Special attention was paid to the development of the use of an algorithm describing the process of identifying the assets, vulnerability and threats in a given context. The aim of the article is to present how this algorithm reduced the complexity of the problem by eliminating from the base model these components that have no links with others component and as a result and it was possible to build a real network model corresponding to reality.
A new transient network model for associative polymer networks
Wientjes, R.H.W.; Jongschaap, R.J.J.; Duits, M.H.G.; Mellema, J.
1999-01-01
A new model for the linear viscoelastic behavior of polymer networks is developed. In this model the polymer system is described as a network of spring segments connected via sticky points (as in the Lodge model). [Lodge, A. S., “A network theory of flow birefringence and stress in concentrated poly
Lateral thinking, from the Hopfield model to cortical dynamics.
Akrami, Athena; Russo, Eleonora; Treves, Alessandro
2012-01-24
Self-organizing attractor networks may comprise the building blocks for cortical dynamics, providing the basic operations of categorization, including analog-to-digital conversion, association and auto-association, which are then expressed as components of distinct cognitive functions depending on the contents of the neural codes in each region. To assess the viability of this scenario, we first review how a local cortical patch may be modeled as an attractor network, in which memory representations are not artificially stored as prescribed binary patterns of activity as in the Hopfield model, but self-organize as continuously graded patterns induced by afferent input. Recordings in macaques indicate that such cortical attractor networks may express retrieval dynamics over cognitively plausible rapid time scales, shorter than those dominated by neuronal fatigue. A cortical network encompassing many local attractor networks, and incorporating a realistic description of adaptation dynamics, may be captured by a Potts model. This network model has the capacity to engage long-range associations into sustained iterative attractor dynamics at a cortical scale, in what may be regarded as a mathematical model of spontaneous lateral thought. This article is part of a Special Issue entitled: Neural Coding.
Generalized Pole Inflation: Hilltop, Natural, and Chaotic Inflationary Attractors
Terada, Takahiro
2016-01-01
A new paradigm for inflationary model building appeared recently, in which inflationary observables are determined by the structure of a pole in the inflaton kinetic term rather than the shape of the inflaton potential. We comprehensively study this framework with an arbitrary order of the pole taking into account possible additional poles in the kinetic term or in the potential. Depending on the setup, the canonical potential becomes the form of hilltop or plateau models, variants of natural inflation, or monomial or polynomial chaotic inflation. We demonstrate attractor behavior of these models and compute corrections from the additional poles to the inflationary observables.
Black Hole Attractors and Pure Spinors
Energy Technology Data Exchange (ETDEWEB)
Hsu, Jonathan P.; Maloney, Alexander; Tomasiello, Alessandro
2006-02-21
We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to {Sigma}f{sub k} = Im(C{Phi}), where {Phi} is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, {Phi} = {Omega} and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.
GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
戴正德; 杜先云
2001-01-01
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.
Homogenization of attractors for a class of nonlinear parabolic equations
Institute of Scientific and Technical Information of China (English)
WANG Guo-lian; ZHANG Xing-you
2004-01-01
The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.
Random attractors for asymptotically upper semicompact multivalue random semiflows
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.
Embedding of global attractors and their dynamics
de Moura, Eleonora Pinto; Sánchez-Gabites, Jaime J
2010-01-01
Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then there is an ordinary differential equation in ${\\mathbb R}^{m+1}$, with $m >d$, that has unique solutions and reproduces the dynamics on $A$. Moreover, the dynamical system generated by this new ordinary differential equation has a global attractor $X$ arbitrarily close to $LA$, where $L$ is a homeomorphism from $A$ into ${\\mathbb R}^{m+1}$.
Erice Lectures on Black Holes and Attractors
Ferrara, Sergio; Marrani, A
2008-01-01
These lectures give an elementary introduction to the subject of four dimensional black holes (BHs) in supergravity and the Attractor Mechanism in the extremal case. Some thermodynamical properties are discussed and some relevant formulae for the critical points of the BH effective potential are given. The case of Maxwell-Einstein-axion-dilaton (super)gravity is discussed in detail. Analogies among BH entropy and multipartite entanglement of qubits in quantum information theory, as well moduli spaces of extremal BH attractors, are also discussed.
Ortiz-Gutiérrez, Elizabeth; García-Cruz, Karla; Azpeitia, Eugenio; Castillo, Aaron; Sánchez, María de la Paz; Álvarez-Buylla, Elena R.
2015-01-01
Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes. PMID:26340681
Target-Centric Network Modeling
DEFF Research Database (Denmark)
Mitchell, Dr. William L.; Clark, Dr. Robert M.
In Target-Centric Network Modeling: Case Studies in Analyzing Complex Intelligence Issues, authors Robert Clark and William Mitchell take an entirely new approach to teaching intelligence analysis. Unlike any other book on the market, it offers case study scenarios using actual intelligence repor....... Working through these cases, students will learn to manage and evaluate realistic intelligence accounts.......In Target-Centric Network Modeling: Case Studies in Analyzing Complex Intelligence Issues, authors Robert Clark and William Mitchell take an entirely new approach to teaching intelligence analysis. Unlike any other book on the market, it offers case study scenarios using actual intelligence......, and collaborative sharing in the process of creating a high-quality, actionable intelligence product. The case studies reflect the complexity of twenty-first century intelligence issues by dealing with multi-layered target networks that cut across political, economic, social, technological, and military issues...
Bubbling and riddling of higher-dimensional attractors
Energy Technology Data Exchange (ETDEWEB)
Kapitaniak, Tomasz; Maistrenko, Yuri; Grebogi, Celso
2003-07-01
We analyze the bifurcation in which one of the unstable periodic orbits embedded in a higher-dimensional chaotic attractor becomes unstable transversely to the attractor. The existence of such local transversal instability may cause the bubbling of the attractor in the invariant manifold or it may cause the riddling of the basin of attraction.
An extended gene protein/products boolean network model including post-transcriptional regulation
2014-01-01
Background Networks Biology allows the study of complex interactions between biological systems using formal, well structured, and computationally friendly models. Several different network models can be created, depending on the type of interactions that need to be investigated. Gene Regulatory Networks (GRN) are an effective model commonly used to study the complex regulatory mechanisms of a cell. Unfortunately, given their intrinsic complexity and non discrete nature, the computational study of realistic-sized complex GRNs requires some abstractions. Boolean Networks (BNs), for example, are a reliable model that can be used to represent networks where the possible state of a node is a boolean value (0 or 1). Despite this strong simplification, BNs have been used to study both structural and dynamic properties of real as well as randomly generated GRNs. Results In this paper we show how it is possible to include the post-transcriptional regulation mechanism (a key process mediated by small non-coding RNA molecules like the miRNAs) into the BN model of a GRN. The enhanced BN model is implemented in a software toolkit (EBNT) that allows to analyze boolean GRNs from both a structural and a dynamic point of view. The open-source toolkit is compatible with available visualization tools like Cytoscape and allows to run detailed analysis of the network topology as well as of its attractors, trajectories, and state-space. In the paper, a small GRN built around the mTOR gene is used to demonstrate the main capabilities of the toolkit. Conclusions The extended model proposed in this paper opens new opportunities in the study of gene regulation. Several of the successful researches done with the support of BN to understand high-level characteristics of regulatory networks, can now be improved to better understand the role of post-transcriptional regulation for example as a network-wide noise-reduction or stabilization mechanisms. PMID:25080304
CNEM: Cluster Based Network Evolution Model
Directory of Open Access Journals (Sweden)
Sarwat Nizamani
2015-01-01
Full Text Available This paper presents a network evolution model, which is based on the clustering approach. The proposed approach depicts the network evolution, which demonstrates the network formation from individual nodes to fully evolved network. An agglomerative hierarchical clustering method is applied for the evolution of network. In the paper, we present three case studies which show the evolution of the networks from the scratch. These case studies include: terrorist network of 9/11 incidents, terrorist network of WMD (Weapons Mass Destruction plot against France and a network of tweets discussing a topic. The network of 9/11 is also used for evaluation, using other social network analysis methods which show that the clusters created using the proposed model of network evolution are of good quality, thus the proposed method can be used by law enforcement agencies in order to further investigate the criminal networks
Attractor switching by neural control of chaotic neurodynamics.
Pasemann, F; Stollenwerk, N
1998-11-01
Chaotic attractors of discrete-time neural networks include infinitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback control. Here we explore the control of unstable periodic orbits in a chaotic neural network with only two neurons. Analytically, a local control algorithm is derived on the basis of least squares minimization of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementation, i.e. the same types of neurons are used for chaotic and controlling modules. The control signal is realized with one layer of neurons, allowing selective switching between different stabilized periodic orbits. For chaotic modules with noise, random switching between different periodic orbits is observed.
Biological transportation networks: Modeling and simulation
Albi, Giacomo
2015-09-15
We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and basic analytical features like the gradient flow structure of the fluid transportation network model and the impact of the model parameters on the geometry and topology of network formation are analyzed. We also present a numerical finite-element based discretization scheme and discuss sample cases of network formation simulations.
Attractor black holes and quantum distribution functions
Energy Technology Data Exchange (ETDEWEB)
Montanez, S. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Gomez, C. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Theory Group, Physics Department, CERN, 1211 Geneva 23 (Switzerland)
2007-05-15
Using the attractor mechanism and the wavefunction interpretation of the topological string partition function on a Calabi Yau threefold M we study the relation between the Bekenstein-Hawking-Wald entropy of BPS Calabi-Yau black holes and quantum distribution functions defined on H{sup 3}(M). We discuss the OSV conjecture in this context. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
The Hyperbolic Geometry of Cosmological Attractors
Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-01-01
Cosmological alpha-attractors give a natural explanation for the spectral index n_s of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future detection of gravity waves. Their embedding into
Large Global Coupled Maps with Multiple Attractors
Carusela, M F; Romanelli, L
1999-01-01
A system of N unidimensional global coupled maps (GCM), which support multiattractors is studied. We analize the phase diagram and some special features of the transitions (volume ratios and characteristic exponents), by controlling the number of elements of the initial partition that are in each basin of attraction. It was found important difference with widely known coupled systems with a single attractor.
Sneutrino Inflation with α-attractors
Energy Technology Data Exchange (ETDEWEB)
Kallosh, Renata; Linde, Andrei [Stanford Institute of Theoretical Physics and Department of Physics, Stanford University, Stanford, 94305 CA (United States); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Theoretical Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Wrase, Timm [Institute for Theoretical Physics, TU Wien, A-1040 Vienna (Austria)
2016-11-22
Sneutrino inflation employs the fermionic partners of the inflaton and stabilizer field as right-handed neutrinos to realize the seesaw mechanism for light neutrino masses. We show that one can improve the latest version of this scenario and its consistency with the Planck data by embedding it in the theory of cosmological α-attractors.
Semicontinuity of attractors for impulsive dynamical systems
Bonotto, E. M.; Bortolan, M. C.; Collegari, R.; Czaja, R.
2016-10-01
In this paper we introduce the concept of collective tube conditions which assures a suitable behaviour for a family of dynamical systems close to impulsive sets. Using the collective tube conditions, we develop the theory of upper and lower semicontinuity of global attractors for a family of impulsive dynamical systems.
Ising model for distribution networks
Hooyberghs, H; Giuraniuc, C; Van Schaeybroeck, B; Indekeu, J O
2012-01-01
An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of t...
Nonparametric Bayesian Modeling of Complex Networks
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Mørup, Morten
2013-01-01
Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...... for complex networks can be derived and point out relevant literature....
On the control of the chaotic attractors of the 2-d Navier-Stokes equations.
Smaoui, Nejib; Zribi, Mohamed
2017-03-01
The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.
Mathematical Modelling Plant Signalling Networks
Muraro, D.
2013-01-01
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.
Generalization performance of regularized neural network models
DEFF Research Database (Denmark)
Larsen, Jan; Hansen, Lars Kai
1994-01-01
Architecture optimization is a fundamental problem of neural network modeling. The optimal architecture is defined as the one which minimizes the generalization error. This paper addresses estimation of the generalization performance of regularized, complete neural network models. Regularization...
Plant Growth Models Using Artificial Neural Networks
Bubenheim, David
1997-01-01
In this paper, we descrive our motivation and approach to devloping models and the neural network architecture. Initial use of the artificial neural network for modeling the single plant process of transpiration is presented.
Random Boolean network models and the yeast transcriptional network
Kauffman, Stuart; Peterson, Carsten; Samuelsson, Björn; Troein, Carl
2003-12-01
The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean networks. We find that for ensembles of generated models, those with canalyzing Boolean rules are remarkably stable, whereas those with random Boolean rules are only marginally stable. Furthermore, substantial parts of the generated networks are frozen, in the sense that they reach the same state regardless of initial state. Thus, our ensemble approach suggests that the yeast network shows highly ordered dynamics.
Loonen, Anton J M; Ivanova, Svetlana A
2017-02-21
The non-reward attractor theory of depression describes this mood disorder as originating from a neuronal dysfunction that arises from increased vulnerability of a cortical network that detects failure to receive an expected reward. From an evolutionary standpoint, the concept that the cerebral cortex determines susceptibility to mood disorders is open to criticism. Instead, using the regulation of reward-seeking, and aversive events-avoiding behaviours of the earliest vertebrates as a start point, the authors have developed a theory of depression in which subcortical regulatory systems that involve the lateral and medial habenula, respectively, play a critical role in regulating these behaviours, and susceptibility to depressive symptoms. As these anatomical structures are well conserved through the evolution of early vertebrates to humans, the authors propose that this subcortical system remains operative. Integrating the evidence that supports the non-attractor theory of depression with this model of a subcortical regulation of behaviour, could offer fresh clues as to how psychological and biological factors interact to cause depression, as well as other mood and anxiety disorders.
Scalable Capacity Bounding Models for Wireless Networks
Du, Jinfeng; Medard, Muriel; Xiao, Ming; Skoglund, Mikael
2014-01-01
The framework of network equivalence theory developed by Koetter et al. introduces a notion of channel emulation to construct noiseless networks as upper (resp. lower) bounding models, which can be used to calculate the outer (resp. inner) bounds for the capacity region of the original noisy network. Based on the network equivalence framework, this paper presents scalable upper and lower bounding models for wireless networks with potentially many nodes. A channel decoupling method is proposed...
Foundations of implementing the competitive layer model by Lotka-Volterra recurrent neural networks.
Yi, Zhang
2010-03-01
The competitive layer model (CLM) can be described by an optimization problem. The problem can be further formulated by an energy function, called the CLM energy function, in the subspace of nonnegative orthant. The set of minimum points of the CLM energy function forms the set of solutions of the CLM problem. Solving the CLM problem means to find out such solutions. Recurrent neural networks (RNNs) can be used to implement the CLM to solve the CLM problem. The key point is to make the set of minimum points of the CLM energy function just correspond to the set of stable attractors of the recurrent neural networks. This paper proposes to use Lotka-Volterra RNNs (LV RNNs) to implement the CLM. The contribution of this paper is to establish foundations of implementing the CLM by LV RNNs. The contribution mainly contains three parts. The first part is on the CLM energy function. Necessary and sufficient conditions for minimum points of the CLM energy function are established by detailed study. The second part is on the convergence of the proposed model of the LV RNNs. It is proven that interesting trajectories are convergent. The third part is the most important. It proves that the set of stable attractors of the proposed LV RNN just equals the set of minimum points of the CLM energy function in the nonnegative orthant. Thus, the LV RNNs can be used to solve the problem of the CLM. It is believed that by establishing such basic rigorous theories, more and interesting applications of the CLM can be found.
Brand Marketing Model on Social Networks
Directory of Open Access Journals (Sweden)
Jolita Jezukevičiūtė
2014-04-01
Full Text Available The paper analyzes the brand and its marketing solutions onsocial networks. This analysis led to the creation of improvedbrand marketing model on social networks, which will contributeto the rapid and cheap organization brand recognition, increasecompetitive advantage and enhance consumer loyalty. Therefore,the brand and a variety of social networks are becoming a hotresearch area for brand marketing model on social networks.The world‘s most successful brand marketing models exploratoryanalysis of a single case study revealed a brand marketingsocial networking tools that affect consumers the most. Basedon information analysis and methodological studies, develop abrand marketing model on social networks.
Willie, Robert
2016-09-01
In this paper, we study a model system of equations of the time dependent Ginzburg-Landau equations of superconductivity in a Lorentz gauge, in scale of Hilbert spaces E^{α } with initial data in E^{β } satisfying 3α + β ≥ N/2, where N=2,3 is such that the spatial domain of the equations [InlineEquation not available: see fulltext.]. We show in the asymptotic dynamics of the equations, well-posedness of the dynamical system for a global exponential attractor {{U}}subset E^{α } compact in E^{β } if α >β , uniform differentiability of orbits on the attractor in E0\\cong L2, and the existence of an explicit finite bounding estimate on the fractal dimension of the attractor yielding that its Hausdorff dimension is as well finite. Uniform boundedness in (0,∞ )× Ω of solutions in E^{1/2}\\cong H1(Ω ) is in addition investigated.
Existence of the solutions and the attractors for the large-scale atmospheric equations
Institute of Scientific and Technical Information of China (English)
HUANG; Haiyang; GUO; Boling
2006-01-01
In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik's definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations.The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.
Non-BPS Attractors in 5d and 6d Extended Supergravity
Andrianopoli, L; Marrani, A; Trigiante, M
2008-01-01
We connect the attractor equations of a certain class of N=2, d=5 supergravities with their (1,0), d=6 counterparts, by relating the moduli space of non-BPS d=5 black hole/black string attractors to the moduli space of extremal dyonic black string d=6 non-BPS attractors. For d = 5 real special symmetric spaces and for N = 4,6,8 theories, we explicitly compute the flat directions of the black object potential corresponding to vanishing eigenvalues of its Hessian matrix. In the case N = 4, we study the relation to the (2,0), d=6 theory. We finally describe the embedding of the N=2, d=5 magic models in N=8, d=5 supergravity as well as the interconnection among the corresponding charge orbits.
Directory of Open Access Journals (Sweden)
Zhonglin Wang
2014-01-01
Full Text Available A permanent magnet synchronous motor (PMSM model with smooth air gap and an exogenous periodic input is introduced and analyzed in this paper. With a simple mathematical transformation, a new nonautonomous Lorenz-like system is derived from this PMSM model, and this new three-dimensional system can display the complicated dynamics such as the chaotic attractor and the multiperiodic orbits by adjusting the frequency and amplitude of the exogenous periodic inputs. Moreover, this new system shows a double-deck chaotic attractor that is completely different from the four-wing chaotic attractors on topological structures, although the phase portrait shapes of the new attractor and the four-wing chaotic attractors are similar. The exotic phenomenon has been well demonstrated and investigated by numerical simulations, bifurcation analysis, and electronic circuit implementation.
Energy landscapes of resting-state brain networks
Directory of Open Access Journals (Sweden)
Takamitsu eWatanabe
2014-02-01
Full Text Available During rest, the human brain performs essential functions such as memory maintenance, which are associated with resting-state brain networks (RSNs including the default-mode network (DMN and frontoparietal network (FPN. Previous studies based on spiking-neuron network models and their reduced models, as well as those based on imaging data, suggest that resting-state network activity can be captured as attractor dynamics, i.e., dynamics of the brain state toward an attractive state and transitions between different attractors. Here, we analyze the energy landscapes of the RSNs by applying the maximum entropy model, or equivalently the Ising spin model, to human RSN data. We use the previously estimated parameter values to define the energy landscape, and the disconnectivity graph method to estimate the number of local energy minima (equivalent to attractors in attractor dynamics, the basin size, and hierarchical relationships among the different local minima. In both of the DMN and FPN, low-energy local minima tended to have large basins. A majority of the network states belonged to a basin of one of a few local minima. Therefore, a small number of local minima constituted the backbone of each RSN. In the DMN, the energy landscape consisted of two groups of low-energy local minima that are separated by a relatively high energy barrier. Within each group, the activity patterns of the local minima were similar, and different minima were connected by relatively low energy barriers. In the FPN, all dominant energy were separated by relatively low energy barriers such that they formed a single coarse-grained global minimum. Our results indicate that multistable attractor dynamics may underlie the DMN, but not the FPN, and assist memory maintenance with different memory states.
Aspiras, Theus H.; Asari, Vijayan K.; Sakla, Wesam
2015-03-01
The human brain has the capability to process high quantities of data quickly for detection and recognition tasks. These tasks are made simpler by the understanding of data, which intentionally removes redundancies found in higher dimensional data and maps the data onto a lower dimensional space. The brain then encodes manifolds created in these spaces, which reveal a specific state of the system. We propose to use a recurrent neural network, the nonlinear line attractor (NLA) network, for the encoding of these manifolds as specific states, which will draw untrained data towards one of the specific states that the NLA network has encoded. We propose a Gaussian-weighted modular architecture for reducing the computational complexity of the conventional NLA network. The proposed architecture uses a neighborhood approach for establishing the interconnectivity of neurons to obtain the manifolds. The modified NLA network has been implemented and tested on the Electro-Optic Synthetic Vehicle Model Database created by the Air Force Research Laboratory (AFRL), which contains a vast array of high resolution imagery with several different lighting conditions and camera views. It is observed that the NLA network has the capability for representing high dimensional data for the recognition of the objects of interest through its new learning strategy. A nonlinear dimensionality reduction scheme based on singular value decomposition has found to be very effective in providing a low dimensional representation of the dataset. Application of the reduced dimensional space on the modified NLA algorithm would provide fast and more accurate recognition performance for real time applications.
Two-Layer Feedback Neural Networks with Associative Memories
Institute of Scientific and Technical Information of China (English)
WU Gui-Kun; ZHAO Hong
2008-01-01
We construct a two-layer feedback neural network by a Monte Carlo based algorithm to store memories as fixed-point attractors or as limit-cycle attractors. Special attention is focused on comparing the dynamics of the network with limit-cycle attractors and with fixed-point attractors. It is found that the former has better retrieval property than the latter. Particularly, spurious memories may be suppressed completely when the memories are stored as a long-limit cycle. Potential application of limit-cycle-attractor networks is discussed briefly.
Coherence resonance in bursting neural networks.
Kim, June Hoan; Lee, Ho Jun; Min, Cheol Hong; Lee, Kyoung J
2015-10-01
Synchronized neural bursts are one of the most noticeable dynamic features of neural networks, being essential for various phenomena in neuroscience, yet their complex dynamics are not well understood. With extrinsic electrical and optical manipulations on cultured neural networks, we demonstrate that the regularity (or randomness) of burst sequences is in many cases determined by a (few) low-dimensional attractor(s) working under strong neural noise. Moreover, there is an optimal level of noise strength at which the regularity of the interburst interval sequence becomes maximal-a phenomenon of coherence resonance. The experimental observations are successfully reproduced through computer simulations on a well-established neural network model, suggesting that the same phenomena may occur in many in vivo as well as in vitro neural networks.
Multistability in Large Scale Models of Brain Activity.
Directory of Open Access Journals (Sweden)
Mathieu Golos
2015-12-01
Full Text Available Noise driven exploration of a brain network's dynamic repertoire has been hypothesized to be causally involved in cognitive function, aging and neurodegeneration. The dynamic repertoire crucially depends on the network's capacity to store patterns, as well as their stability. Here we systematically explore the capacity of networks derived from human connectomes to store attractor states, as well as various network mechanisms to control the brain's dynamic repertoire. Using a deterministic graded response Hopfield model with connectome-based interactions, we reconstruct the system's attractor space through a uniform sampling of the initial conditions. Large fixed-point attractor sets are obtained in the low temperature condition, with a bigger number of attractors than ever reported so far. Different variants of the initial model, including (i a uniform activation threshold or (ii a global negative feedback, produce a similarly robust multistability in a limited parameter range. A numerical analysis of the distribution of the attractors identifies spatially-segregated components, with a centro-medial core and several well-delineated regional patches. Those different modes share similarity with the fMRI independent components observed in the "resting state" condition. We demonstrate non-stationary behavior in noise-driven generalizations of the models, with different meta-stable attractors visited along the same time course. Only the model with a global dynamic density control is found to display robust and long-lasting non-stationarity with no tendency toward either overactivity or extinction. The best fit with empirical signals is observed at the edge of multistability, a parameter region that also corresponds to the highest entropy of the attractors.
Dynamic synchronization and chaos in an associative neural network with multiple active memories.
Raffone, Antonino; van Leeuwen, Cees
2003-09-01
Associative memory dynamics in neural networks are generally based on attractors. Retrieval based on fixed-point attractors works if only one memory pattern is retrieved at the time, but cannot enable the simultaneous retrieval of more than one pattern. Stable phase-locking of periodic oscillations or limit cycle attractors leads to incorrect feature bindings if the simultaneously retrieved patterns share some of their features. We investigate retrieval dynamics of multiple active patterns in a network of chaotic model neurons. Several memory patterns are kept simultaneously active and separated from each other by a dynamic itinerant synchronization between neurons. Neurons representing shared features alternate their synchronization between patterns, thus multiplexing their binding relationships. Our model includes a mechanism for self-organized readout or decoding of memory pattern coherence in terms of short-term potentiation and short-term depression of synaptic weights.
Network Bandwidth Utilization Forecast Model on High Bandwidth Network
Energy Technology Data Exchange (ETDEWEB)
Yoo, Wucherl; Sim, Alex
2014-07-07
With the increasing number of geographically distributed scientific collaborations and the scale of the data size growth, it has become more challenging for users to achieve the best possible network performance on a shared network. We have developed a forecast model to predict expected bandwidth utilization for high-bandwidth wide area network. The forecast model can improve the efficiency of resource utilization and scheduling data movements on high-bandwidth network to accommodate ever increasing data volume for large-scale scientific data applications. Univariate model is developed with STL and ARIMA on SNMP path utilization data. Compared with traditional approach such as Box-Jenkins methodology, our forecast model reduces computation time by 83.2percent. It also shows resilience against abrupt network usage change. The accuracy of the forecast model is within the standard deviation of the monitored measurements.
Dimensions of attractors in pinched skew products
Gröger, M.; Jäger, T.
2011-01-01
We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findi...
Exponential Attractor for a Nonlinear Boussinesq Equation
Institute of Scientific and Technical Information of China (English)
Ahmed Y. Abdallah
2006-01-01
This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H20(0, 1) × L2(0, 1). The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H03(0, 1) × H10(0, 1).
Hypermoduli Stabilization, Flux Attractors, and Generating Functions
Larsen, Finn; Robbins, Daniel
2009-01-01
We study stabilization of hypermoduli with emphasis on the effects of generalized fluxes. We find a class of no-scale vacua described by ISD conditions even in the presence of geometric flux. The associated flux attractor equations can be integrated by a generating function with the property that the hypermoduli are determined by a simple extremization principle. We work out several orbifold examples where all vector moduli and many hypermoduli are stabilized, with VEVs given explicitly in terms of fluxes.
The Unity of Cosmological Attractors
Galante, Mario; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-01-01
Recently, several broad classes of inflationary models have been discovered whose cosmological predictions are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a non-minimal coupling to gravity. These models, which we will call $\\xi$-att
An acoustical model based monitoring network
Wessels, P.W.; Basten, T.G.H.; Eerden, F.J.M. van der
2010-01-01
In this paper the approach for an acoustical model based monitoring network is demonstrated. This network is capable of reconstructing a noise map, based on the combination of measured sound levels and an acoustic model of the area. By pre-calculating the sound attenuation within the network the noi
A system dynamics model for communications networks
Awcock, A. J.; King, T. E. G.
1985-09-01
An abstract model of a communications network in system dynamics terminology is developed as implementation of this model by a FORTRAN program package developed at RSRE is discussed. The result of this work is a high-level simulation package in which the performance of adaptive routing algorithms and other network controls may be assessed for a network of arbitrary topology.
Modelling delay propagation within an airport network
Pyrgiotis, N.; Malone, K.M.; Odoni, A.
2013-01-01
We describe an analytical queuing and network decomposition model developed to study the complex phenomenon of the propagation of delays within a large network of major airports. The Approximate Network Delays (AND) model computes the delays due to local congestion at individual airports and capture
Eight challenges for network epidemic models
Directory of Open Access Journals (Sweden)
Lorenzo Pellis
2015-03-01
Full Text Available Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to the inherent high-dimensionality of networks themselves, modelling transmission through networks is mathematically and computationally challenging. Even the simplest network epidemic models present unanswered questions. Attempts to improve the practical usefulness of network models by including realistic features of contact networks and of host–pathogen biology (e.g. waning immunity have made some progress, but robust analytical results remain scarce. A more general theory is needed to understand the impact of network structure on the dynamics and control of infection. Here we identify a set of challenges that provide scope for active research in the field of network epidemic models.
Dissipative relativistic standard map: Periodic attractors and basins of attraction
Energy Technology Data Exchange (ETDEWEB)
Lan, Boon Leong [Monash University, School of Engineering, Bandar Sunway, Selangor (Malaysia)], E-mail: lan.boon.leong@eng.monash.edu.my; Yapp, Clarence [Monash University, School of Engineering, Bandar Sunway, Selangor (Malaysia)
2008-09-15
The dissipative relativistic standard map, introduced by Ciubotariu et al. [Ciubotariu C, Badelita L, Stancu V. Chaos in dissipative relativistic standard maps. Chaos, Solitons and Fractals 2002;13:1253-67.], is further studied numerically for small damping in the resonant case. We find that the attractors are all periodic; their basins of attraction have fractal boundaries and are closely interwoven. The number of attractors increases with decreasing damping. For a very small damping, there are thousands of periodic attractors, comprising mostly of the lowest-period attractors of period one or two; the basin of attraction of these lowest-period attractors is significantly larger compared to the basins of the higher-period attractors.
Bottom-up model of self-organized criticality on networks.
Noël, Pierre-André; Brummitt, Charles D; D'Souza, Raissa M
2014-01-01
The Bak-Tang-Wiesenfeld (BTW) sandpile process is an archetypal, stylized model of complex systems with a critical point as an attractor of their dynamics. This phenomenon, called self-organized criticality, appears to occur ubiquitously in both nature and technology. Initially introduced on the two-dimensional lattice, the BTW process has been studied on network structures with great analytical successes in the estimation of macroscopic quantities, such as the exponents of asymptotically power-law distributions. In this article, we take a microscopic perspective and study the inner workings of the process through both numerical and rigorous analysis. Our simulations reveal fundamental flaws in the assumptions of past phenomenological models, the same models that allowed accurate macroscopic predictions; we mathematically justify why universality may explain these past successes. Next, starting from scratch, we obtain microscopic understanding that enables mechanistic models; such models can, for example, distinguish a cascade's area from its size. In the special case of a 3-regular network, we use self-consistency arguments to obtain a zero-parameter mechanistic (bottom-up) approximation that reproduces nontrivial correlations observed in simulations and that allows the study of the BTW process on networks in regimes otherwise prohibitively costly to investigate. We then generalize some of these results to configuration model networks and explain how one could continue the generalization. The numerous tools and methods presented herein are known to enable studying the effects of controlling the BTW process and other self-organizing systems. More broadly, our use of multitype branching processes to capture information bouncing back and forth in a network could inspire analogous models of systems in which consequences spread in a bidirectional fashion.
An evolutionary model of social networks
Ludwig, M.; Abell, P.
2007-07-01
Social networks in communities, markets, and societies self-organise through the interactions of many individuals. In this paper we use a well-known mechanism of social interactions — the balance of sentiment in triadic relations — to describe the development of social networks. Our model contrasts with many existing network models, in that people not only establish but also break up relations whilst the network evolves. The procedure generates several interesting network features such as a variety of degree distributions and degree correlations. The resulting network converges under certain conditions to a steady critical state where temporal disruptions in triangles follow a power-law distribution.
Modeling gene regulatory networks: A network simplification algorithm
Ferreira, Luiz Henrique O.; de Castro, Maria Clicia S.; da Silva, Fabricio A. B.
2016-12-01
Boolean networks have been used for some time to model Gene Regulatory Networks (GRNs), which describe cell functions. Those models can help biologists to make predictions, prognosis and even specialized treatment when some disturb on the GRN lead to a sick condition. However, the amount of information related to a GRN can be huge, making the task of inferring its boolean network representation quite a challenge. The method shown here takes into account information about the interactome to build a network, where each node represents a protein, and uses the entropy of each node as a key to reduce the size of the network, allowing the further inferring process to focus only on the main protein hubs, the ones with most potential to interfere in overall network behavior.
Unity of Cosmological Inflation Attractors
Galante, Mario; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-01-01
Recently, several broad classes of inflationary models have been discovered whose cosmological predictions, in excellent agreement with Planck, are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a nonminimal coupling to gravity. These
The model of social crypto-network
Directory of Open Access Journals (Sweden)
Марк Миколайович Орел
2015-06-01
Full Text Available The article presents the theoretical model of social network with the enhanced mechanism of privacy policy. It covers the problems arising in the process of implementing the mentioned type of network. There are presented the methods of solving problems arising in the process of building the social network with privacy policy. It was built a theoretical model of social networks with enhanced information protection methods based on information and communication blocks
Attractor scenarios and superluminal signals in k-essence cosmology
Kang, Jin U; Winitzki, Sergei
2007-01-01
Cosmological scenarios with k-essence are invoked in order to explain the observed late-time acceleration of the universe. These scenarios avoid the need for fine-tuned initial conditions (the "coincidence problem") because of the attractor-like dynamics of the k-essence field \\phi. It was recently shown that all k-essence scenarios with Lagrangians p=L(X)/\\phi^2, necessarily involve an epoch where perturbations of \\phi propagate faster than light (the "no-go theorem"). We carry out a comprehensive study of attractor-like cosmological solutions ("trackers") involving a k-essence scalar field \\phi and another matter component. The result of this study is a complete classification of k-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form p=K(\\phi)L(X) . Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous "no-go theorem" still holds for...
A systems biology approach to cancer: fractals, attractors, and nonlinear dynamics.
Dinicola, Simona; D'Anselmi, Fabrizio; Pasqualato, Alessia; Proietti, Sara; Lisi, Elisabetta; Cucina, Alessandra; Bizzarri, Mariano
2011-03-01
Cancer begins to be recognized as a highly complex disease, and advanced knowledge of the carcinogenic process claims to be acquired by means of supragenomic strategies. Experimental data evidence that tumor emerges from disruption of tissue architecture, and it is therefore consequential that the tissue level should be considered the proper level of observation for carcinogenic studies. This paradigm shift imposes to move from a reductionistic to a systems biology approach. Indeed, cell phenotypes are emergent modes arising through collective nonlinear interactions among different cellular and microenvironmental components, generally described by a phase space diagram, where stable states (attractors) are embedded into a landscape model. Within this framework cell states and cell transitions are generally conceived as mainly specified by the gene-regulatory network. However, the system's dynamics cannot be reduced to only the integrated functioning of the genome-proteome network, and the cell-stroma interacting system must be taken into consideration in order to give a more reliable picture. As cell form represents the spatial geometric configuration shaped by an integrated set of cellular and environmental cues participating in biological functions control, it is conceivable that fractal-shape parameters could be considered as "omics" descriptors of the cell-stroma system. Within this framework it seems that function follows form, and not the other way around.
ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS
Institute of Scientific and Technical Information of China (English)
Mu-rong Jiang; Bo-ling Guo
2001-01-01
In this paper, Ginzburg-Landau equation coupled with BBM equationwith periodic initial boundary value conditions are discreted by the finite difference method in spatial direction. Existence of the attractors for the spatially discreted Ginzburg-Landau-BBM equations is proved. For each mesh size, there exist attractors for the discretized system. Moreover, finite Hausdorff and fractal dimensions of the discrete attractors are obtained and the bounds are independent of the mesh sizes.
Modeling Diagnostic Assessments with Bayesian Networks
Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego
2007-01-01
This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…
A dynamic network model for interbank market
Xu, Tao; He, Jianmin; Li, Shouwei
2016-12-01
In this paper, a dynamic network model based on agent behavior is introduced to explain the formation mechanism of interbank market network. We investigate the impact of credit lending preference on interbank market network topology, the evolution of interbank market network and stability of interbank market. Experimental results demonstrate that interbank market network is a small-world network and cumulative degree follows the power-law distribution. We find that the interbank network structure keeps dynamic stability in the network evolution process. With the increase of bank credit lending preference, network clustering coefficient increases and average shortest path length decreases monotonously, which improves the stability of the network structure. External shocks are main threats for the interbank market and the reduction of bank external investment yield rate and deposits fluctuations contribute to improve the resilience of the banking system.
Invariability, orbits and fuzzy attractors
Perez-Gonzaga, S.; Lloret-Climent, M.; Nescolarde-Selva, J. A.
2016-01-01
In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality.
Bayesian estimation of the network autocorrelation model
Dittrich, D.; Leenders, R.T.A.J.; Mulder, J.
2017-01-01
The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of
Object Oriented Modeling Of Social Networks
Zeggelink, Evelien P.H.; Oosten, Reinier van; Stokman, Frans N.
1996-01-01
The aim of this paper is to explain principles of object oriented modeling in the scope of modeling dynamic social networks. As such, the approach of object oriented modeling is advocated within the field of organizational research that focuses on networks. We provide a brief introduction into the f
Agent-based modeling and network dynamics
Namatame, Akira
2016-01-01
The book integrates agent-based modeling and network science. It is divided into three parts, namely, foundations, primary dynamics on and of social networks, and applications. The book begins with the network origin of agent-based models, known as cellular automata, and introduce a number of classic models, such as Schelling’s segregation model and Axelrod’s spatial game. The essence of the foundation part is the network-based agent-based models in which agents follow network-based decision rules. Under the influence of the substantial progress in network science in late 1990s, these models have been extended from using lattices into using small-world networks, scale-free networks, etc. The book also shows that the modern network science mainly driven by game-theorists and sociophysicists has inspired agent-based social scientists to develop alternative formation algorithms, known as agent-based social networks. The book reviews a number of pioneering and representative models in this family. Upon the gi...
Woodward, Alexander; Froese, Tom; Ikegami, Takashi
2015-02-01
The state space of a conventional Hopfield network typically exhibits many different attractors of which only a small subset satisfies constraints between neurons in a globally optimal fashion. It has recently been demonstrated that combining Hebbian learning with occasional alterations of normal neural states avoids this problem by means of self-organized enlargement of the best basins of attraction. However, so far it is not clear to what extent this process of self-optimization is also operative in real brains. Here we demonstrate that it can be transferred to more biologically plausible neural networks by implementing a self-optimizing spiking neural network model. In addition, by using this spiking neural network to emulate a Hopfield network with Hebbian learning, we attempt to make a connection between rate-based and temporal coding based neural systems. Although further work is required to make this model more realistic, it already suggests that the efficacy of the self-optimizing process is independent from the simplifying assumptions of a conventional Hopfield network. We also discuss natural and cultural processes that could be responsible for occasional alteration of neural firing patterns in actual brains.
Edge exchangeable models for network data
Crane, Harry
2016-01-01
Exchangeable models for vertex labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distributions observed in many network datasets. Out of this mathematical impossibility emerges the question of how network data can be modeled in a way that reflects known empirical behaviors and respects basic statistical principles. We address this question by observing that edges, not vertices, act as the statistical units in most network datasets, making a theory of edge labeled networks more natural for most applications. Within this context we introduce the new invariance principle of {\\em edge exchangeability}, which unlike its vertex exchangeable counterpart can produce networks with sparse and/or power law structure. We characterize the class of all edge exchangeable network models and identify a particular two parameter family of models with suitable theoretical properties for statistical inference. We discuss issues of estimation from edge exchangeable models and compare our a...
Free Energy, Value, and Attractors
Directory of Open Access Journals (Sweden)
Karl Friston
2012-01-01
Full Text Available It has been suggested recently that action and perception can be understood as minimising the free energy of sensory samples. This ensures that agents sample the environment to maximise the evidence for their model of the world, such that exchanges with the environment are predictable and adaptive. However, the free energy account does not invoke reward or cost-functions from reinforcement-learning and optimal control theory. We therefore ask whether reward is necessary to explain adaptive behaviour. The free energy formulation uses ideas from statistical physics to explain action in terms of minimising sensory surprise. Conversely, reinforcement-learning has its roots in behaviourism and engineering and assumes that agents optimise a policy to maximise future reward. This paper tries to connect the two formulations and concludes that optimal policies correspond to empirical priors on the trajectories of hidden environmental states, which compel agents to seek out the (valuable states they expect to encounter.
Evolutionary Phylogenetic Networks: Models and Issues
Nakhleh, Luay
Phylogenetic networks are special graphs that generalize phylogenetic trees to allow for modeling of non-treelike evolutionary histories. The ability to sequence multiple genetic markers from a set of organisms and the conflicting evolutionary signals that these markers provide in many cases, have propelled research and interest in phylogenetic networks to the forefront in computational phylogenetics. Nonetheless, the term 'phylogenetic network' has been generically used to refer to a class of models whose core shared property is tree generalization. Several excellent surveys of the different flavors of phylogenetic networks and methods for their reconstruction have been written recently. However, unlike these surveys, this chapte focuses specifically on one type of phylogenetic networks, namely evolutionary phylogenetic networks, which explicitly model reticulate evolutionary events. Further, this chapter focuses less on surveying existing tools, and addresses in more detail issues that are central to the accurate reconstruction of phylogenetic networks.
Modeling Network Evolution Using Graph Motifs
Conway, Drew
2011-01-01
Network structures are extremely important to the study of political science. Much of the data in its subfields are naturally represented as networks. This includes trade, diplomatic and conflict relationships. The social structure of several organization is also of interest to many researchers, such as the affiliations of legislators or the relationships among terrorist. A key aspect of studying social networks is understanding the evolutionary dynamics and the mechanism by which these structures grow and change over time. While current methods are well suited to describe static features of networks, they are less capable of specifying models of change and simulating network evolution. In the following paper I present a new method for modeling network growth and evolution. This method relies on graph motifs to generate simulated network data with particular structural characteristic. This technique departs notably from current methods both in form and function. Rather than a closed-form model, or stochastic ...
A Farey tail for attractor black holes
de Boer, Jan; Cheng, Miranda C. N.; Dijkgraaf, Robbert; Manschot, Jan; Verlinde, Erik
2006-11-01
The microstates of 4d BPS black holes in IIA string theory compactified on a Calabi-Yau manifold are counted by a (generalized) elliptic genus of a (0,4) conformal field theory. By exploiting a spectral flow that relates states with different charges, and using the Rademacher formula, we find that the elliptic genus has an exact asymptotic expansion in terms of semi-classical saddle-points of the dual supergravity theory. This generalizes the known "Black Hole Farey Tail" of [1] to the case of attractor black holes.
A Farey Tail for Attractor Black Holes
De Boer, J; Dijkgraaf, R; Manschot, J; Verlinde, E; Boer, Jan de; Cheng, Miranda C.N.; Dijkgraaf, Robbert; Manschot, Jan; Verlinde, Erik
2006-01-01
The microstates of 4d BPS black holes in IIA string theory compactified on a Calabi-Yau manifold are counted by a (generalized) elliptic genus of a (0,4) conformal field theory. By exploiting a spectral flow that relates states with different charges, and using the Rademacher formula, we find that the elliptic genus has an exact asymptotic expansion in terms of semi-classical saddle-points of the dual supergravity theory. This generalizes the known "Black Hole Farey Tail" of [1] to the case of attractor black holes.
Attractor Explosions and Catalyzed Vacuum Decay
Energy Technology Data Exchange (ETDEWEB)
Green, Daniel; Silverstein, Eva; Starr, David
2006-05-05
We present a mechanism for catalyzed vacuum bubble production obtained by combining moduli stabilization with a generalized attractor phenomenon in which moduli are sourced by compact objects. This leads straightforwardly to a class of examples in which the Hawking decay process for black holes unveils a bubble of a different vacuum from the ambient one, generalizing the new endpoint for Hawking evaporation discovered recently by Horowitz. Catalyzed vacuum bubble production can occur for both charged and uncharged bodies, including Schwarzschild black holes for which massive particles produced in the Hawking process can trigger vacuum decay. We briefly discuss applications of this process to the population and stability of metastable vacua.
Dimensions of attractors in pinched skew products
Gröger, M
2011-01-01
We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.
3rd School on Attractor Mechanism
SAM 2007; The Attractor Mechanism: Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007
2010-01-01
This book is based upon lectures presented in June 2007 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara, M. Gunaydin, P. Levay, and T. Mohaupt. All lectures were given at a pedagogical, introductory level, which is reflected in the specific "flavor" of this volume. The book also benefits from extensive discussions about, and related reworking of, the various contributions. In addition, this volume contains contributions originating from short presentations of rece
Dimensions of Attractors in Pinched Skew Products
Gröger, M.; Jäger, T.
2013-05-01
We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.
Yang, Gang; Campbell, Colin; Albert, Réka
2016-12-01
Complex diseases can be modeled as damage to intracellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those corresponding to disease. Previous work designed compensatory interactions to stabilize an attractor of a Boolean network after single node damage. We generalize this method to a multinode damage scenario and to the simultaneous stabilization of multiple steady state attractors. We classify the emergent situations, with a special focus on combinatorial effects, and characterize each class through simulation. We explore how the structural and functional properties of the network affect its resilience and its possible repair scenarios. We demonstrate the method's applicability to two intracellular network models relevant to cancer. This work has implications in designing prevention strategies for complex disease.
Novel Principles and Methods for Computing with Attractors
Directory of Open Access Journals (Sweden)
Horia-Nicolai Teodorescu
2001-08-01
Full Text Available We briefly analyze several issues related to the "computing with attractors" domain. We present a point of view on the topic and several new concepts, methods, and techniques for computing with attractors. We discuss applications where this method may prove useful. We answer several questions related to the usefulness of this computing paradigm.
TRAJECTORY ATTRACTORS FOR NONCLASSICAL DIFFUSION EQUATIONS WITH FADING MEMORY
Institute of Scientific and Technical Information of China (English)
Yonghai WANG; Lingzhi WANG
2013-01-01
In this article,we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory.For this purpose,we will apply the method presented by Chepyzhov and Miranville [7,8],in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.
THE ATTRACTORS FOR LANDAU-LIFSHITZ-MAXWELL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Guo Boling; Su Fengqiu
2000-01-01
The existence of the attractors of the periodic initial value problem for the Landau-Lifshitz-Maxwell equations in one and two space dimensions is proved. We also get accurate estimates of the upper bounds of Hausdorff and fractal dimensions for the attractors by means of uniform a priori estimates for time and Lyapunov functional method.
Synchronization in Coupled Oscillators with Two Coexisting Attractors
Institute of Scientific and Technical Information of China (English)
ZHU Han-Han; YANG Jun-Zhong
2008-01-01
Dynamics in coupled Duffing oscillators with two coexisting symmetrical attractors is investigated. For a pair of Dutffng oscillators coupled linearly, the transition to the synchronization generally consists of two steps: Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.
Experimental confirmation of a new reversed butterfly-shaped attractor
Institute of Scientific and Technical Information of China (English)
Liu Ling; Su Yan-Chen; Liu Chong-Xin
2007-01-01
This paper reports a new reverse butterfly-shaped chaotic attractor and its experimental confirmation. Some basic dynamical properties, and chaotic behaviours of this new reverse butterfly attractor are studied. Simulation results support brief theoretical derivations. Furthermore, the system is experimentally confirmed by a simple electronic circuit.
Hidden attractor in the Rabinovich system, Chua circuits and PLL
Kuznetsov, N. V.; Leonov, G. A.; Mokaev, T. N.; Seledzhi, S. M.
2016-06-01
In this report the existence of hidden attractors in Rabinovich system, phase-locked loop and coupled Chua circuits is considered. It is shown that the existence of hidden attractors may complicate the analysis of the systems and significantly affect the synchronization.
Random graph models for dynamic networks
Zhang, Xiao; Newman, M E J
2016-01-01
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. In addition to computing equilibrium properties of these models, we demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data. This allows us, for instance, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate our methods with a selection of applications, both to computer-generated test networks and real-world examples.
Modelling the structure of complex networks
DEFF Research Database (Denmark)
Herlau, Tue
networks has been independently studied as mathematical objects in their own right. As such, there has been both an increased demand for statistical methods for complex networks as well as a quickly growing mathematical literature on the subject. In this dissertation we explore aspects of modelling complex....... The next chapters will treat some of the various symmetries, representer theorems and probabilistic structures often deployed in the modelling complex networks, the construction of sampling methods and various network models. The introductory chapters will serve to provide context for the included written...
Biodiversity: modelling angiosperms as networks.
Gottlieb, O R; Borin, M R
2000-11-01
In the neotropics, one of the last biological frontiers, the major ecological concern should not involve local strategies, but global effects often responsible for irreparable damage. For a holistic approach, angiosperms are ideal model systems dominating most land areas of the present world in an astonishing variety of form and function. Recognition of biogeographical patterns requires new methodologies and entails several questions, such as their nature, dynamics and mechanism. Demographical patterns of families, modelled via species dominance, reveal the existence of South American angiosperm networks converging at the central Brazilian plateau. Biodiversity of habitats, measured via taxonomic uniqueness, reveal higher creative power at this point of convergence than in more peripheral regions. Compositional affinities of habitats, measured via bioconnectivity, reveal the decisive role of ecotones in the exchange or redistribution of information, energy and organisms among the ecosystems. Forming dynamic boundaries, ecotones generate and relay evolutionary novelty, and integrate all neotropical ecosystems into a single vegetation net. Connectivity in such plant webs may depend on mycorrhizal links. If sufficiently general such means of metabolic transfer will require revision of the chemical composition of many plants.
Extremal Black Hole and Flux Vacua Attractors
Bellucci, S; Kallosh, R; Marrani, A
2007-01-01
These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axion-dilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the so-called ``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodge-decomposition techniques) is performed, respectively considering Type IIB compactified on $CY_{3}$ and its orientifolded version, associated with $\\frac{CY_{3}\\times T^{2}}{\\mathbb{Z}_{2}}$. Finally, recent...
Modeling of hysteresis in gene regulatory networks.
Hu, J; Qin, K R; Xiang, C; Lee, T H
2012-08-01
Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.
Nonconsensus opinion model on directed networks
Qu, B.; Li, Q.; Havlin, S.; Stanley, E.; Wang, H.
2014-01-01
Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are directed and are composed of both unidirectional and bidirectio
Radio channel modeling in body area networks
An, L.; Bentum, M.J.; Meijerink, A.; Scanlon, W.G.
2010-01-01
A body area network (BAN) is a network of bodyworn or implanted electronic devices, including wireless sensors which can monitor body parameters or to detect movements. One of the big challenges in BANs is the propagation channel modeling. Channel models can be used to understand wave propagation in
Radio channel modeling in body area networks
An, L.; Bentum, M.J.; Meijerink, A.; Scanlon, W.G.
2009-01-01
A body area network (BAN) is a network of bodyworn or implanted electronic devices, including wireless sensors which can monitor body parameters or to de- tect movements. One of the big challenges in BANs is the propagation channel modeling. Channel models can be used to understand wave propagation
Symmetric Encryption Model Based on Chaotic Attractors
Directory of Open Access Journals (Sweden)
Edilma Isabel Amaya Barrera
2016-10-01
Conclusions: the algorithm is presented as an alternative to traditional algorithms demonstrating greater efficiency in the management of computing resources and raises the groundwork for continuing their study on the interested academic community due to the variety of dynamical systems nonlinear.
Strange Attractors in Multipath propagation Detection and characterisation
Tannous, C; Angus, A G
2001-01-01
Multipath propagation of radio waves in indoor/outdoor environments shows a highly irregular behavior as a function of time. Typical modeling of this phenomenon assumes the received signal is a stochastic process composed of the superposition of various altered replicas of the transmitted one, their amplitudes and phases being drawn from specific probability densities. We set out to explore the hypothesis of the presence of deterministic chaos in signals propagating inside various buildings at the University of Calgary. The correlation dimension versus embedding dimension saturates to a value between 3 and 4 for various antenna polarizations. The full Liapunov spectrum calculated contains two positive exponents and yields through the Kaplan-Yorke conjecture the same dimension obtained from the correlation sum. The presence of strange attractors in multipath propagation hints to better ways to predict the behaviour of the signal and better methods to counter the effects of interference. The use of Neural Netwo...
Broken Scale Invariance, Alpha-Attractors and Vector Impurity
Akarsu, Ozgur; Kahya, Emre O; Ozdemir, Nese; Ozkan, Mehmet
2016-01-01
We show that if the {\\alpha}-attractor model is realized by the spontaneous breaking of the scale symmetry, then the stability and the dynamics of the vector field that gauges the scale symmetry severely constrains the {\\alpha}-parameter as 5/6 < {\\alpha} < 1, restricting the inflationary predictions in a very tiny region in the n_s vs r plane that are in great agreement with the latest Planck data. Although the different values of {\\alpha} do not make a tangible difference for n_s and r, they provide radically different scenarios for the post-inflationary dynamics which determines the standard BBN processes and the large scale isotropy of the universe.
Unified Hybrid Network Theoretical Model Trilogy
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The first of the unified hybrid network theoretical model trilogy (UHNTF) is the harmonious unification hybrid preferential model (HUHPM), seen in the inner loop of Fig. 1, the unified hybrid ratio is defined.
Kaura, P.; Misara, A.
2006-12-01
We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY_3(2,128) expressed as a degree-12 hypersurface in WCP^4[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the attractors could be connected to an elliptic curve fibered over C^8 which may also be "arithmetic" (in some cases, it is possible to interpret the extremization conditions as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that the attractors correspond to a version of A_1-singularity in the space Image(Z^6-->R^2/Z_2(embedded in R^3)) fibered over the complex structure moduli space. The potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP^5-->CP^{20}, fibered over the complex structure moduli space. We also discuss application of the equivalent Kallosh's attractor equations for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the atractor equations than the extremization of the black hole potential.
Network models in economics and finance
Pardalos, Panos; Rassias, Themistocles
2014-01-01
Using network models to investigate the interconnectivity in modern economic systems allows researchers to better understand and explain some economic phenomena. This volume presents contributions by known experts and active researchers in economic and financial network modeling. Readers are provided with an understanding of the latest advances in network analysis as applied to economics, finance, corporate governance, and investments. Moreover, recent advances in market network analysis that focus on influential techniques for market graph analysis are also examined. Young researchers will find this volume particularly useful in facilitating their introduction to this new and fascinating field. Professionals in economics, financial management, various technologies, and network analysis, will find the network models presented in this book beneficial in analyzing the interconnectivity in modern economic systems.
A Network Formation Model Based on Subgraphs
Chandrasekhar, Arun
2016-01-01
We develop a new class of random-graph models for the statistical estimation of network formation that allow for substantial correlation in links. Various subgraphs (e.g., links, triangles, cliques, stars) are generated and their union results in a network. We provide estimation techniques for recovering the rates at which the underlying subgraphs were formed. We illustrate the models via a series of applications including testing for incentives to form cross-caste relationships in rural India, testing to see whether network structure is used to enforce risk-sharing, testing as to whether networks change in response to a community's exposure to microcredit, and show that these models significantly outperform stochastic block models in matching observed network characteristics. We also establish asymptotic properties of the models and various estimators, which requires proving a new Central Limit Theorem for correlated random variables.
Strategic games on a hierarchical network model
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Among complex network models, the hierarchical network model is the one most close to such real networks as world trade web, metabolic network, WWW, actor network, and so on. It has not only the property of power-law degree distribution, but growth based on growth and preferential attachment, showing the scale-free degree distribution property. In this paper, we study the evolution of cooperation on a hierarchical network model, adopting the prisoner's dilemma (PD) game and snowdrift game (SG) as metaphors of the interplay between connected nodes. BA model provides a unifying framework for the emergence of cooperation. But interestingly, we found that on hierarchical model, there is no sign of cooperation for PD game, while the frequency of cooperation decreases as the common benefit decreases for SG. By comparing the scaling clustering coefficient properties of the hierarchical network model with that of BA model, we found that the former amplifies the effect of hubs. Considering different performances of PD game and SG on complex network, we also found that common benefit leads to cooperation in the evolution. Thus our study may shed light on the emergence of cooperation in both natural and social environments.
Gossip spread in social network Models
Johansson, Tobias
2017-04-01
Gossip almost inevitably arises in real social networks. In this article we investigate the relationship between the number of friends of a person and limits on how far gossip about that person can spread in the network. How far gossip travels in a network depends on two sets of factors: (a) factors determining gossip transmission from one person to the next and (b) factors determining network topology. For a simple model where gossip is spread among people who know the victim it is known that a standard scale-free network model produces a non-monotonic relationship between number of friends and expected relative spread of gossip, a pattern that is also observed in real networks (Lind et al., 2007). Here, we study gossip spread in two social network models (Toivonen et al., 2006; Vázquez, 2003) by exploring the parameter space of both models and fitting them to a real Facebook data set. Both models can produce the non-monotonic relationship of real networks more accurately than a standard scale-free model while also exhibiting more realistic variability in gossip spread. Of the two models, the one given in Vázquez (2003) best captures both the expected values and variability of gossip spread.
Towards reproducible descriptions of neuronal network models.
Directory of Open Access Journals (Sweden)
Eilen Nordlie
2009-08-01
Full Text Available Progress in science depends on the effective exchange of ideas among scientists. New ideas can be assessed and criticized in a meaningful manner only if they are formulated precisely. This applies to simulation studies as well as to experiments and theories. But after more than 50 years of neuronal network simulations, we still lack a clear and common understanding of the role of computational models in neuroscience as well as established practices for describing network models in publications. This hinders the critical evaluation of network models as well as their re-use. We analyze here 14 research papers proposing neuronal network models of different complexity and find widely varying approaches to model descriptions, with regard to both the means of description and the ordering and placement of material. We further observe great variation in the graphical representation of networks and the notation used in equations. Based on our observations, we propose a good model description practice, composed of guidelines for the organization of publications, a checklist for model descriptions, templates for tables presenting model structure, and guidelines for diagrams of networks. The main purpose of this good practice is to trigger a debate about the communication of neuronal network models in a manner comprehensible to humans, as opposed to machine-readable model description languages. We believe that the good model description practice proposed here, together with a number of other recent initiatives on data-, model-, and software-sharing, may lead to a deeper and more fruitful exchange of ideas among computational neuroscientists in years to come. We further hope that work on standardized ways of describing--and thinking about--complex neuronal networks will lead the scientific community to a clearer understanding of high-level concepts in network dynamics, and will thus lead to deeper insights into the function of the brain.
Pathway Analysis Based on Attractor and Cross Talk in Colon Cancer
2016-01-01
Colon cancer is the third and second most common cancer form in men and women worldwide. It is generally accepted that colon cancer mainly results from diet. The aim of this study was to identify core pathways which elucidated the molecular mechanisms in colon cancer. The microarray data of E-GEOD-44861 was downloaded from ArrayExpress database. All human pathways were obtained from Kyoto Encyclopedia of Genes and Genomes database. In total, 135 differential expressed genes (DEG) were identified using Linear Models for Microarray Data package. Differential pathways were identified with the method of attractor after overlapping with DEG. Pathway cross talk network (PCN) was constructed by combining protein-protein interactions and differential pathways. Cross talks of all pathways were obtained in PCN. There were 65 pathways with RankProd (RP) values 100. Five pathways were satisfied with P value 100, which were considered to be the most important pathways in colon cancer. In conclusion, the five pathways were identified in the center status of colon cancer, which may contribute to understanding the mechanism and development of colon cancer. PMID:27746583
Pathway Analysis Based on Attractor and Cross Talk in Colon Cancer
Directory of Open Access Journals (Sweden)
Yanxia Liu
2016-01-01
Full Text Available Colon cancer is the third and second most common cancer form in men and women worldwide. It is generally accepted that colon cancer mainly results from diet. The aim of this study was to identify core pathways which elucidated the molecular mechanisms in colon cancer. The microarray data of E-GEOD-44861 was downloaded from ArrayExpress database. All human pathways were obtained from Kyoto Encyclopedia of Genes and Genomes database. In total, 135 differential expressed genes (DEG were identified using Linear Models for Microarray Data package. Differential pathways were identified with the method of attractor after overlapping with DEG. Pathway cross talk network (PCN was constructed by combining protein-protein interactions and differential pathways. Cross talks of all pathways were obtained in PCN. There were 65 pathways with RankProd (RP values 100. Five pathways were satisfied with P value 100, which were considered to be the most important pathways in colon cancer. In conclusion, the five pathways were identified in the center status of colon cancer, which may contribute to understanding the mechanism and development of colon cancer.
Complex networks analysis in socioeconomic models
Varela, Luis M; Ausloos, Marcel; Carrete, Jesus
2014-01-01
This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary adds insights on the statistical mechanical approach, and on the most relevant computational aspects for the treatment of these systems. As the most frequently used model for interacting agent-based systems, a brief description of the statistical mechanics of the classical Ising model on regular lattices, together with recent extensions of the same model on small-world Watts-Strogatz and scale-free Albert-Barabasi complex networks is included. Other sections of the chapter are devoted to applications of complex networks to economics, finance, spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issues, including res...
Boolean networks with multiexpressions and parameters.
Zou, Yi Ming
2013-01-01
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean models, both synchronous and asynchronous, have been proposed in the literature. However, analytical study of these more general Boolean networks models is lagging. This paper aims to develop a concise theory for these different Boolean logic-based modeling methods. Boolean models for networks where each node can have more than two levels of expression and Boolean models with parameters are defined algebraically with examples provided. Certain classes of random asynchronous Boolean networks and deterministic moduli asynchronous Boolean networks are investigated in detail using the setting introduced in this paper. The derived theorems provide a clear picture for the attractor structures of these asynchronous Boolean networks.
Implementing network constraints in the EMPS model
Energy Technology Data Exchange (ETDEWEB)
Helseth, Arild; Warland, Geir; Mo, Birger; Fosso, Olav B.
2010-02-15
This report concerns the coupling of detailed market and network models for long-term hydro-thermal scheduling. Currently, the EPF model (Samlast) is the only tool available for this task for actors in the Nordic market. A new prototype for solving the coupled market and network problem has been developed. The prototype is based on the EMPS model (Samkjoeringsmodellen). Results from the market model are distributed to a detailed network model, where a DC load flow detects if there are overloads on monitored lines or intersections. In case of overloads, network constraints are generated and added to the market problem. Theoretical and implementation details for the new prototype are elaborated in this report. The performance of the prototype is tested against the EPF model on a 20-area Nordic dataset. (Author)
Survey of propagation Model in wireless Network
Directory of Open Access Journals (Sweden)
Hemant Kumar Sharma
2011-05-01
Full Text Available To implementation of mobile ad hoc network wave propagation models are necessary to determine propagation characteristic through a medium. Wireless mobile ad hoc networks are self creating and self organizing entity. Propagation study provides an estimation of signal characteristics. Accurate prediction of radio propagation behaviour for MANET is becoming a difficult task. This paper presents investigation of propagation model. Radio wave propagation mechanisms are absorption, reflection, refraction, diffraction and scattering. This paper discuss free space model, two rays model, and cost 231 hata and its variants and fading model, and summarized the advantages and disadvantages of these model. This study would be helpful in choosing the correct propagation model.
Boolean networks as modelling framework
Directory of Open Access Journals (Sweden)
Florian eGreil
2012-08-01
Full Text Available In a network, the components of a given system are represented as nodes, the interactions are abstracted as links between the nodes. Boolean networks refer to a class of dynamics on networks, in fact it is the simplest possible dynamics where each node has a value 0 or 1. This allows to investigate extensively the dynamics both analytically and by numerical experiments. The present article focuses on the theoretical concept of relevant components and the immediate application in plant biology, references for more in-depths treatment of the mathematical details are also given.
Modelling Microwave Devices Using Artificial Neural Networks
Directory of Open Access Journals (Sweden)
Andrius Katkevičius
2012-04-01
Full Text Available Artificial neural networks (ANN have recently gained attention as fast and flexible equipment for modelling and designing microwave devices. The paper reviews the opportunities to use them for undertaking the tasks on the analysis and synthesis. The article focuses on what tasks might be solved using neural networks, what challenges might rise when using artificial neural networks for carrying out tasks on microwave devices and discusses problem-solving techniques for microwave devices with intermittent characteristics.Article in Lithuanian
Modeling Evolution of Weighted Clique Networks
Institute of Scientific and Technical Information of China (English)
杨旭华; 蒋峰岭; 陈胜勇; 王万良
2011-01-01
We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique （maximal complete sub-graph） at. each time step. And the cliques in the network overlap with each other. The structural expansion of the weighted clique network is combined with the edges＇ weight and vertices＇ strengths dynamical evolution. The model is based on a weight-driven dynamics and a weights＇ enhancement mechanism combining with the network growth. We study the network properties, which include the distribution of vertices＇ strength and the distribution o~ edges＇ weight, and find that both the distributions follow the scale-free distribution. At the same time, we also find that the relationship between strength and degree of a vertex are linear correlation during the growth of the network. On the basis of mean-field theory, we study the weighted network model and prove that both vertices＇ strength and edges＇ weight of this model follow the scale-free distribution. And we exploit an algorithm to forecast the network dynamics, which can be used to reckon the distributions and the corresponding scaling exponents. Furthermore, we observe that mean-field based theoretic results are consistent with the statistical data of the model, which denotes the theoretical result in this paper is effective.
Modeling Evolution of Weighted Clique Networks
Yang, Xu-Hua; Jiang, Feng-Ling; Chen, Sheng-Yong; Wang, Wan-Liang
2011-11-01
We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique (maximal complete sub-graph) at each time step. And the cliques in the network overlap with each other. The structural expansion of the weighted clique network is combined with the edges' weight and vertices' strengths dynamical evolution. The model is based on a weight-driven dynamics and a weights' enhancement mechanism combining with the network growth. We study the network properties, which include the distribution of vertices' strength and the distribution of edges' weight, and find that both the distributions follow the scale-free distribution. At the same time, we also find that the relationship between strength and degree of a vertex are linear correlation during the growth of the network. On the basis of mean-field theory, we study the weighted network model and prove that both vertices' strength and edges' weight of this model follow the scale-free distribution. And we exploit an algorithm to forecast the network dynamics, which can be used to reckon the distributions and the corresponding scaling exponents. Furthermore, we observe that mean-field based theoretic results are consistent with the statistical data of the model, which denotes the theoretical result in this paper is effective.
Using cell fate attractors to uncover transcriptional regulation of HL60 neutrophil differentiation
Directory of Open Access Journals (Sweden)
Kauffman Stuart A
2009-02-01
Full Text Available Abstract Background The process of cellular differentiation is governed by complex dynamical biomolecular networks consisting of a multitude of genes and their products acting in concert to determine a particular cell fate. Thus, a systems level view is necessary for understanding how a cell coordinates this process and for developing effective therapeutic strategies to treat diseases, such as cancer, in which differentiation plays a significant role. Theoretical considerations and recent experimental evidence support the view that cell fates are high dimensional attractor states of the underlying molecular networks. The temporal behavior of the network states progressing toward different cell fate attractors has the potential to elucidate the underlying molecular mechanisms governing differentiation. Results Using the HL60 multipotent promyelocytic leukemia cell line, we performed experiments that ultimately led to two different cell fate attractors by two treatments of varying dosage and duration of the differentiation agent all-trans-retinoic acid (ATRA. The dosage and duration combinations of the two treatments were chosen by means of flow cytometric measurements of CD11b, a well-known early differentiation marker, such that they generated two intermediate populations that were poised at the apparently same stage of differentiation. However, the population of one treatment proceeded toward the terminally differentiated neutrophil attractor while that of the other treatment reverted back toward the undifferentiated promyelocytic attractor. We monitored the gene expression changes in the two populations after their respective treatments over a period of five days and identified a set of genes that diverged in their expression, a subset of which promotes neutrophil differentiation while the other represses cell cycle progression. By employing promoter based transcription factor binding site analysis, we found enrichment in the set of divergent
Introducing Synchronisation in Deterministic Network Models
DEFF Research Database (Denmark)
Schiøler, Henrik; Jessen, Jan Jakob; Nielsen, Jens Frederik D.;
2006-01-01
The paper addresses performance analysis for distributed real time systems through deterministic network modelling. Its main contribution is the introduction and analysis of models for synchronisation between tasks and/or network elements. Typical patterns of synchronisation are presented leading....... The suggested models are intended for incorporation into an existing analysis tool a.k.a. CyNC based on the MATLAB/SimuLink framework for graphical system analysis and design....
Neural network models of protein domain evolution
Sylvia Nagl
2000-01-01
Protein domains are complex adaptive systems, and here a novel procedure is presented that models the evolution of new functional sites within stable domain folds using neural networks. Neural networks, which were originally developed in cognitive science for the modeling of brain functions, can provide a fruitful methodology for the study of complex systems in general. Ethical implications of developing complex systems models of biomolecules are discussed, with particular reference to molecu...
Homophyly/Kinship Model: Naturally Evolving Networks
Li, Angsheng; Li, Jiankou; Pan, Yicheng; Yin, Xianchen; Yong, Xi
2015-10-01
It has been a challenge to understand the formation and roles of social groups or natural communities in the evolution of species, societies and real world networks. Here, we propose the hypothesis that homophyly/kinship is the intrinsic mechanism of natural communities, introduce the notion of the affinity exponent and propose the homophyly/kinship model of networks. We demonstrate that the networks of our model satisfy a number of topological, probabilistic and combinatorial properties and, in particular, that the robustness and stability of natural communities increase as the affinity exponent increases and that the reciprocity of the networks in our model decreases as the affinity exponent increases. We show that both homophyly/kinship and reciprocity are essential to the emergence of cooperation in evolutionary games and that the homophyly/kinship and reciprocity determined by the appropriate affinity exponent guarantee the emergence of cooperation in evolutionary games, verifying Darwin’s proposal that kinship and reciprocity are the means of individual fitness. We propose the new principle of structure entropy minimisation for detecting natural communities of networks and verify the functional module property and characteristic properties by a healthy tissue cell network, a citation network, some metabolic networks and a protein interaction network.
Modelling of virtual production networks
Directory of Open Access Journals (Sweden)
2011-03-01
Full Text Available Nowadays many companies, especially small and medium-sized enterprises (SMEs, specialize in a limited field of production. It requires forming virtual production networks of cooperating enterprises to manufacture better, faster and cheaper. Apart from that, some production orders cannot be realized, because there is not a company of sufficient production potential. In this case the virtual production networks of cooperating companies can realize these production orders. These networks have larger production capacity and many different resources. Therefore it can realize many more production orders together than each of them separately. Such organization allows for executing high quality product. The maintenance costs of production capacity and used resources are not so high. In this paper a methodology of rapid prototyping of virtual production networks is proposed. It allows to execute production orders on time considered existing logistic constraints.
Breeding novel solutions in the brain: a model of Darwinian neurodynamics.
Szilágyi, András; Zachar, István; Fedor, Anna; de Vladar, Harold P; Szathmáry, Eörs
2016-01-01
Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain - recurrent neural networks (acting as attractors), the action selection loop and implicit working memory - to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.
Characterization and Modeling of Network Traffic
DEFF Research Database (Denmark)
Shawky, Ahmed; Bergheim, Hans; Ragnarsson, Olafur
2011-01-01
This paper attempts to characterize and model backbone network traffic, using a small number of statistics. In order to reduce cost and processing power associated with traffic analysis. The parameters affecting the behaviour of network traffic are investigated and the choice is that inter......-arrival time, IP addresses, port numbers and transport protocol are the only necessary parameters to model network traffic behaviour. In order to recreate this behaviour, a complex model is needed which is able to recreate traffic behaviour based on a set of statistics calculated from the parameters values...
Simple model for river network evolution
Energy Technology Data Exchange (ETDEWEB)
Leheny, R.L. [The James Franck Institute and The Department of Physics, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637 (United States)
1995-11-01
We simulate the evolution of a drainage basin by erosion from precipitation and avalanching on hillslopes. The avalanches create a competition in growth between neighboring basins and play the central role in driving the evolution. The simulated landscapes form drainage systems that share many qualitative features with Glock`s model for natural network evolution and maintain statistical properties that characterize real river networks. We also present results from a second model with a modified, mass conserving avalanche scheme. Although the terrains from these two models are qualitatively dissimilar, their drainage networks share the same general evolution and statistical features.
Stochastic discrete model of karstic networks
Jaquet, O.; Siegel, P.; Klubertanz, G.; Benabderrhamane, H.
Karst aquifers are characterised by an extreme spatial heterogeneity that strongly influences their hydraulic behaviour and the transport of pollutants. These aquifers are particularly vulnerable to contamination because of their highly permeable networks of conduits. A stochastic model is proposed for the simulation of the geometry of karstic networks at a regional scale. The model integrates the relevant physical processes governing the formation of karstic networks. The discrete simulation of karstic networks is performed with a modified lattice-gas cellular automaton for a representative description of the karstic aquifer geometry. Consequently, more reliable modelling results can be obtained for the management and the protection of karst aquifers. The stochastic model was applied jointly with groundwater modelling techniques to a regional karst aquifer in France for the purpose of resolving surface pollution issues.
Queueing models for mobile ad hoc networks
Haan, de Roland
2009-01-01
This thesis presents models for the performance analysis of a recent communication paradigm: mobile ad hoc networking. The objective of mobile ad hoc networking is to provide wireless connectivity between stations in a highly dynamic environment. These dynamics are driven by the mobility of stations
Simple models of human brain functional networks.
Vértes, Petra E; Alexander-Bloch, Aaron F; Gogtay, Nitin; Giedd, Jay N; Rapoport, Judith L; Bullmore, Edward T
2012-04-10
Human brain functional networks are embedded in anatomical space and have topological properties--small-worldness, modularity, fat-tailed degree distributions--that are comparable to many other complex networks. Although a sophisticated set of measures is available to describe the topology of brain networks, the selection pressures that drive their formation remain largely unknown. Here we consider generative models for the probability of a functional connection (an edge) between two cortical regions (nodes) separated by some Euclidean distance in anatomical space. In particular, we propose a model in which the embedded topology of brain networks emerges from two competing factors: a distance penalty based on the cost of maintaining long-range connections; and a topological term that favors links between regions sharing similar input. We show that, together, these two biologically plausible factors are sufficient to capture an impressive range of topological properties of functional brain networks. Model parameters estimated in one set of functional MRI (fMRI) data on normal volunteers provided a good fit to networks estimated in a second independent sample of fMRI data. Furthermore, slightly detuned model parameters also generated a reasonable simulation of the abnormal properties of brain functional networks in people with schizophrenia. We therefore anticipate that many aspects of brain network organization, in health and disease, may be parsimoniously explained by an economical clustering rule for the probability of functional connectivity between different brain areas.
Modeling the hydrodynamics in tidal networks
Alebregtse, N.C.
2016-01-01
This thesis covers tidal propagation through networks of channels. Such networks are widespread and are often subject to discordant human and natural interests. First, the effect of a secondary channel on the tides in a main channel is explained with the use of an idealized model and the responsible
Network Design Models for Container Shipping
DEFF Research Database (Denmark)
Reinhardt, Line Blander; Kallehauge, Brian; Nielsen, Anders Nørrelund
This paper presents a study of the network design problem in container shipping. The paper combines the network design and fleet assignment problem into a mixed integer linear programming model minimizing the overall cost. The major contributions of this paper is that the time of a vessel route...
Cyber threat model for tactical radio networks
Kurdziel, Michael T.
2014-05-01
The shift to a full information-centric paradigm in the battlefield has allowed ConOps to be developed that are only possible using modern network communications systems. Securing these Tactical Networks without impacting their capabilities has been a challenge. Tactical networks with fixed infrastructure have similar vulnerabilities to their commercial counterparts (although they need to be secure against adversaries with greater capabilities, resources and motivation). However, networks with mobile infrastructure components and Mobile Ad hoc Networks (MANets) have additional unique vulnerabilities that must be considered. It is useful to examine Tactical Network based ConOps and use them to construct a threat model and baseline cyber security requirements for Tactical Networks with fixed infrastructure, mobile infrastructure and/or ad hoc modes of operation. This paper will present an introduction to threat model assessment. A definition and detailed discussion of a Tactical Network threat model is also presented. Finally, the model is used to derive baseline requirements that can be used to design or evaluate a cyber security solution that can be scaled and adapted to the needs of specific deployments.
Inflationary attractor in Gauss-Bonnet brane cosmology
Meng, X H; Meng, Xin-He; Wang, Peng
2003-01-01
The inflationary attractor properties of the canonical scalar field and Born-Infeld field are investigated in the Randall-Sundrum II scenario with a Gauss-Bonnet term in the bulk action. We find that the inflationary attractor property will always hold for canonical scalar fields for any allowed non-negative Gauss-Bonnet coupling. However, for Born-Infeld field, the Gauss-Bonnet coupling will be highly constrained for the inflationary attractor property to hold. We also briefly discuss the possibility of explaining the suppressed lower multiples and running scalar spectral index simultaneously in the scenario of Gauss-Bonnet brane inflation.
No fermionic wigs for BPS attractors in 5 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gentile, Lorenzo G.C., E-mail: lgentile@pd.infn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria I-15120 (Italy); Dipartimento di Fisica “Galileo Galilei”, Università di Padova, via Marzolo 8, I-35131 Padova (Italy); INFN, Sezione di Padova, via Marzolo 8, I-35131 Padova (Italy); Grassi, Pietro A., E-mail: pgrassi@mfn.unipmn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria I-15120 (Italy); INFN – Gruppo Collegato di Alessandria – Sezione di Torino (Italy); Marrani, Alessio, E-mail: alessio.marrani@fys.kuleuven.be [Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium); Mezzalira, Andrea, E-mail: andrea.mezzalira@ulb.ac.be [Physique Théorique et Mathématique, Université Libre de Bruxelles, C.P. 231, B-1050 Bruxelles (Belgium); Sabra, Wafic A., E-mail: ws00@aub.edu.lb [Centre for Advanced Mathematical Sciences and Physics Department, American University of Beirut (Lebanon)
2014-07-30
We analyze the fermionic wigging of 1/2-BPS (electric) extremal black hole attractors in N=2, D=5 ungauged Maxwell–Einstein supergravity theories, by exploiting anti-Killing spinors supersymmetry transformations. Regardless of the specific data of the real special geometry of the manifold defining the scalars of the vector multiplets, and differently from the D=4 case, we find that there are no corrections for the near-horizon attractor value of the scalar fields; an analogous result also holds for 1/2-BPS (magnetic) extremal black string. Thus, the attractor mechanism receives no fermionic corrections in D=5 (at least in the BPS sector)
Non-linear fate of internal wave attractors
Scolan, Hélène; Dauxois, Thierry
2013-01-01
We present a laboratory study on the instability of internal wave attractors in a trapezoidal fluid domain filled with uniformly stratified fluid. Energy is injected into the system via standing-wave-type motion of a vertical wall. Attractors are found to be destroyed by parametric subharmonic instability (PSI) via a triadic resonance which is shown to provide a very efficient energy pathway from long to short length scales. This study provides an explanation why attractors may be difficult or impossible to observe in natural systems subject to large amplitude forcing.
How chaotic are strange non-chaotic attractors?
Glendinning, Paul; Jäger, Tobias H.; Keller, Gerhard
2006-09-01
We show that the classic examples of quasiperiodically forced maps with strange non-chaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general classes of quasiperiodically forced systems. Further, we include an elementary proof of a classic result by Glasner and Weiss on sensitive dependence, and we clarify the structure of the attractor in an example with two-dimensional fibres also introduced by Grebogi et al.
Random Attractors of Stochastic Non-Newtonian Fluids
Institute of Scientific and Technical Information of China (English)
Chun-xiao GUO; Bo-ling GUO; Yong-qian HAN
2012-01-01
The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain.Firstly,we prove the existence of random attractors AH(ω) in H; Secondly,we prove the existence of random attractors Av(ω) in V.Then we verify regularity of the random attractors by showing that AH(ω) =Av(ω),which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.
IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
马军海; 任彪; 陈予恕
2004-01-01
Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.
A Model for Telestrok Network Evaluation
DEFF Research Database (Denmark)
Storm, Anna; Günzel, Franziska; Theiss, Stephan
2011-01-01
Different telestroke network concepts have been implemented worldwide to enable fast and efficient treatment of stroke patients in underserved rural areas. Networks could demonstrate the improvement in clinical outcome, but have so far excluded a cost-effectiveness analysis. With health economic...... was developed from the third-party payer perspective. In principle, it enables telestroke networks to conduct cost-effectiveness studies, because the majority of the required data can be extracted from health insurance companies’ databases and the telestroke network itself. The model presents a basis...
Model-based control of networked systems
Garcia, Eloy; Montestruque, Luis A
2014-01-01
This monograph introduces a class of networked control systems (NCS) called model-based networked control systems (MB-NCS) and presents various architectures and control strategies designed to improve the performance of NCS. The overall performance of NCS considers the appropriate use of network resources, particularly network bandwidth, in conjunction with the desired response of the system being controlled. The book begins with a detailed description of the basic MB-NCS architecture that provides stability conditions in terms of state feedback updates . It also covers typical problems in NCS such as network delays, network scheduling, and data quantization, as well as more general control problems such as output feedback control, nonlinear systems stabilization, and tracking control. Key features and topics include: Time-triggered and event-triggered feedback updates Stabilization of uncertain systems subject to time delays, quantization, and extended absence of feedback Optimal control analysis and ...
Modeling Network Traffic in Wavelet Domain
Directory of Open Access Journals (Sweden)
Sheng Ma
2004-12-01
Full Text Available This work discovers that although network traffic has the complicated short- and long-range temporal dependence, the corresponding wavelet coefficients are no longer long-range dependent. Therefore, a "short-range" dependent process can be used to model network traffic in the wavelet domain. Both independent and Markov models are investigated. Theoretical analysis shows that the independent wavelet model is sufficiently accurate in terms of the buffer overflow probability for Fractional Gaussian Noise traffic. Any model, which captures additional correlations in the wavelet domain, only improves the performance marginally. The independent wavelet model is then used as a unified approach to model network traffic including VBR MPEG video and Ethernet data. The computational complexity is O(N for developing such wavelet models and generating synthesized traffic of length N, which is among the lowest attained.
Graphical Model Theory for Wireless Sensor Networks
Energy Technology Data Exchange (ETDEWEB)
Davis, William B.
2002-12-08
Information processing in sensor networks, with many small processors, demands a theory of computation that allows the minimization of processing effort, and the distribution of this effort throughout the network. Graphical model theory provides a probabilistic theory of computation that explicitly addresses complexity and decentralization for optimizing network computation. The junction tree algorithm, for decentralized inference on graphical probability models, can be instantiated in a variety of applications useful for wireless sensor networks, including: sensor validation and fusion; data compression and channel coding; expert systems, with decentralized data structures, and efficient local queries; pattern classification, and machine learning. Graphical models for these applications are sketched, and a model of dynamic sensor validation and fusion is presented in more depth, to illustrate the junction tree algorithm.
Modeling trust context in networks
Adali, Sibel
2013-01-01
We make complex decisions every day, requiring trust in many different entities for different reasons. These decisions are not made by combining many isolated trust evaluations. Many interlocking factors play a role, each dynamically impacting the others.? In this brief, 'trust context' is defined as the system level description of how the trust evaluation process unfolds.Networks today are part of almost all human activity, supporting and shaping it. Applications increasingly incorporate new interdependencies and new trust contexts. Social networks connect people and organizations throughout
Network models of dissolution of porous media
Budek, Agnieszka
2012-01-01
We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant consumption. Moreover, the topology of the network is allowed to change dynamically during the simulation: as the diameters of the eroding pores become comparable with the interpore distances, the pores are joined together thus changing the interconnections within the network. With this model, we investigate different growth regimes in an evolving porous medium, identifying the mechanisms responsible for the emergence of specific patterns. We consider both the random and regular network and study the effect of the network geometry on the patterns. Finally, we consider practically important problem of finding an optimum flow rate that gives a maximum increase in permeability for a given amount of reactant.
Modelling subtle growth of linguistic networks
Kulig, Andrzej; Kwapien, Jaroslaw; Oswiecimka, Pawel
2014-01-01
We investigate properties of evolving linguistic networks defined by the word-adjacency relation. Such networks belong to the category of networks with accelerated growth but their shortest path length appears to reveal the network size dependence of different functional form than the ones known so far. We thus compare the networks created from literary texts with their artificial substitutes based on different variants of the Dorogovtsev-Mendes model and observe that none of them is able to properly simulate the novel asymptotics of the shortest path length. Then, we identify grammar induced local chain-like linear growth as a missing element in this model and extend it by incorporating such effects. It is in this way that a satisfactory agreement with the empirical result is obtained.
Kinetic attractor phase diagrams of active nematic suspensions: the dilute regime.
Forest, M Gregory; Wang, Qi; Zhou, Ruhai
2015-08-28
Large-scale simulations by the authors of the kinetic-hydrodynamic equations for active polar nematics revealed a variety of spatio-temporal attractors, including steady and unsteady, banded (1d) and cellular (2d) spatial patterns. These particle scale activation-induced attractors arise at dilute nanorod volume fractions where the passive equilibrium phase is isotropic, whereas all previous model simulations have focused on the semi-dilute, nematic equilibrium regime and mostly on low-moment orientation tensor and polarity vector models. Here we extend our previous results to complete attractor phase diagrams for active nematics, with and without an explicit polar potential, to map out novel spatial and dynamic transitions, and to identify some new attractors, over the parameter space of dilute nanorod volume fraction and nanorod activation strength. The particle-scale activation parameter corresponds experimentally to a tunable force dipole strength (so-called pushers with propulsion from the rod tail) generated by active rod macromolecules, e.g., catalysis with the solvent phase, ATP-induced propulsion, or light-activated propulsion. The simulations allow 2d spatial variations in all flow and orientational variables and full spherical orientational degrees of freedom; the attractors correspond to numerical integration of a coupled system of 125 nonlinear PDEs in 2d plus time. The phase diagrams with and without the polar interaction potential are remarkably similar, implying that polar interactions among the rodlike particles are not essential to long-range spatial and temporal correlations in flow, polarity, and nematic order. As a general rule, above a threshold, low volume fractions induce 1d banded patterns, whereas higher yet still dilute volume fractions yield 2d patterns. Again as a general rule, varying activation strength at fixed volume fraction induces novel dynamic transitions. First, stationary patterns saturate the instability of the isotropic
IP Network Management Model Based on NGOSS
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-yu; LI Hong-hui; LIU Feng
2004-01-01
This paper addresses a management model for IP network based on Next Generation Operation Support System (NGOSS). It makes the network management on the base of all the operation actions of ISP, It provides QoS to user service through the whole path by providing end-to-end Service Level Agreements (SLA) management through whole path. Based on web and coordination technology, this paper gives an implement architecture of this model.
Baird, Bill
1986-08-01
A neural network model describing pattern recognition in the rabbit olfactory bulb is analysed to explain the changes in neural activity observed experimentally during classical Pavlovian conditioning. EEG activity recorded from an 8×8 arry of 64 electrodes directly on the surface on the bulb shows distinct spatial patterns of oscillation that correspond to the animal's recognition of different conditioned odors and change with conditioning to new odors. The model may be considered a variant of Hopfield's model of continuous analog neural dynamics. Excitatory and inhibitory cell types in the bulb and the anatomical architecture of their connection requires a nonsymmetric coupling matrix. As the mean input level rises during each breath of the animal, the system bifurcates from homogenous equilibrium to a spatially patterned oscillation. The theory of multiple Hopf bifurcations is employed to find coupled equations for the amplitudes of these unstable oscillatory modes independent of frequency. This allows a view of stored periodic attractors as fixed points of a gradient vector field and thereby recovers the more familiar dynamical systems picture of associative memory.
Propagation of magnetic vortices using nanocontacts as tunable attractors
Manfrini, M.; Kim, Joo-Von; Petit-Watelot, S.; van Roy, W.; Lagae, L.; Chappert, C.; Devolder, T.
2014-02-01
Magnetic vortices in thin films are in-plane spiral spin configurations with a core in which the magnetization twists out of the film plane. Vortices result from the competition between atomic-scale exchange forces and long-range dipolar interactions. They are often the ground state of magnetic dots, and have applications in medicine, microwave generation and information storage. The compact nature of the vortex core, which is 10-20 nm wide, makes it a suitable probe of magnetism at the nanoscale. However, thus far the positioning of a vortex has been possible only in confined structures, which prevents its transport over large distances. Here we show that vortices can be propagated in an unconstrained system that comprises electrical nanocontacts (NCs). The NCs are used as tunable vortex attractors in a manner that resembles the propelling of space craft with gravitational slingshots. By passing current from the NCs to a ferromagnetic film, circulating magnetic fields are generated, which nucleate the vortex and create a potential well for it. The current becomes spin polarized in the film, and thereby drives the vortex into gyration through spin-transfer torques. The vortex can be guided from one NC to another by tuning attractive strengths of the NCs. We anticipate that NC networks may be used as multiterminal sources of vortices and spin waves (as well as heat, spin and charge flows) to sense the fundamental interactions between physical objects and fluxes of the next-generation spintronic devices.
Directory of Open Access Journals (Sweden)
András Szilágyi
2016-09-01
Full Text Available Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain – recurrent neural networks (acting as attractors, the action selection loop and implicit working memory – to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns with hereditary variation and novel variants appear due to (i noisy recall of patterns from the attractor networks, (ii noise during transmission of candidate solutions as messages between networks, and, (iii spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.
How Anatomy Shapes Dynamics: A Semi-Analytical Study of the Brain at Rest by a Simple Spin Model
Directory of Open Access Journals (Sweden)
Gustavo eDeco
2012-09-01
Full Text Available Resting state networks show a surprisingly coherent and robust spatiotemporal organization. Previous theoretical studies demonstrated that these patterns can be understood as emergent on the basis of the underlying neuroanatomical connectivity skeleton. Integrating the biologically realistic DTI/DSI based neuroanatomical connectivity into a brain model of Ising spin dynamics, we found the presence of latent ghost multi-stable attractors, which can be studied analytically. The multistable attractor landscape defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity. We demonstrate that the more entropy of attractors exists, the richer is the dynamical repertoire and consequently the brain network displays more capabilities of computation. We hypothesize therefore that human brain connectivity developed a scale free type of architecture in order to be able to store a large number of different and flexibly accessible brain functions
RANDOM ATTRACTORS FOR A STOCHASTIC HYDRODYNAMICAL EQUATION IN HEISENBERG PARAMAGNET
Institute of Scientific and Technical Information of China (English)
Guo Boling; Guo Chunxiao; Pu Xueke
2011-01-01
This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1.
The attractor of the stochastic generalized Ginzburg-Landau equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system.Then we prove the random system possesses a global random attractor in H01.
The attractor of the stochastic generalized Ginzburg-Landau equation
Institute of Scientific and Technical Information of China (English)
GUO BoLing; WANG GuoLian; Li DongLong
2008-01-01
The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in H01.
Features from the non-attractor beginning of inflation
Cai, Yi-Fu; Wang, Dong-Gang; Wang, Ziwei
2016-01-01
We study the effects of the non-attractor initial conditions for the canonical single-field inflation. The non-attractor stage can last only several $e$-folding numbers, and should be followed by hilltop inflation. This two-stage evolution leads to large scale suppression in the primordial power spectrum, which is favored by recent observations. Moreover we give a detailed calculation of primordial non-Guassianity due to the "from non-attractor to slow-roll" transition, and find step features in the local and equilateral shapes. We conclude that a plateau-like inflaton potential with an initial non-attractor phase yields interesting features in both power spectrum and bispectrum.
Attractors for stochastic strongly damped plate equations with additive noise
Directory of Open Access Journals (Sweden)
Wenjun Ma
2013-04-01
Full Text Available We study the asymptotic behavior of stochastic plate equations with homogeneous Neumann boundary conditions. We show the existence of an attractor for the random dynamical system associated with the equation.
Posterior Predictive Model Checking in Bayesian Networks
Crawford, Aaron
2014-01-01
This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…
Kitaev spin models from topological nanowire networks
Kells, G.; Lahtinen, V.; Vala, J.
2014-01-01
We show that networks of superconducting topological nanowires can realize the physics of exactly solvable Kitaev spin models on trivalent lattices. This connection arises from the low-energy theory of both systems being described by a tight-binding model of Majorana modes. In Kitaev spin models the
River Network Modeling Beyond Discharge at Gauges
David, C. H.; Famiglietti, J. S.; Salas, F. R.; Whiteaker, T. L.; Maidment, D. R.; Tolle, K.
2014-12-01
Over the past two decades, the estimation of water flow in river networks within hydro-meteorological models has mostly focused on simulations of natural processes and on their verification at available river gauges. Despite valuable existing skills in hydrologic modeling the accounting for anthropogenic actions in current models remains limited. The emerging availability of datasets containing measured dam outflows and reported irrigation withdrawals motivates their inclusion into simulations of flow in river networks. However, the development of advanced river network models accounting for such datasets of anthropogenic influences requires a detailed data model and a thorough handling of the various data types, sources and time scales. This contribution details the development of a consistent data model suitable for accounting some observations of anthropogenic modifications of the surface water cycle and presents the impact of such inclusion on simulations using the Routing Application for Parallel computatIon of Discharge (RAPID).
Constraints on \\alpha-attractor inflation and reheating
Ueno, Yoshiki
2016-01-01
We investigate a constraint on reheating followed by alpha-attractor-type inflation (the E-model and T-model) from an observation of the spectral index n_s. When the energy density of the universe is dominated by an energy component with the cosmic equation-of-state parameter w_{re} during reheating, its e-folding number N_{re} and the reheating temperature T_{re} are bounded depending on w_{re}. When the reheating epoch consists of two phases, where the energy density of the universe is dominated by uniform inflaton field oscillations in the first phase and by relativistic non-thermalised particles in the second phase, we find a constraint on the e-folding number of the first oscillation phase, N_{sc}, depending the parameters of the inflaton potential. For the simplest perturbative reheating scenario, we find the lower bound for a coupling constant of inflaton decay in the E-model and T-model depending on the model parameters. We also find a constraint on the $\\alpha$ parameter, \\alpha\\simgt 0.01, for the T...
A simple model for studying interacting networks
Liu, Wenjia; Jolad, Shivakumar; Schmittmann, Beate; Zia, R. K. P.
2011-03-01
Many specific physical networks (e.g., internet, power grid, interstates), have been characterized in considerable detail, but in isolation from each other. Yet, each of these networks supports the functions of the others, and so far, little is known about how their interactions affect their structure and functionality. To address this issue, we consider two coupled model networks. Each network is relatively simple, with a fixed set of nodes, but dynamically generated set of links which has a preferred degree, κ . In the stationary state, the degree distribution has exponential tails (far from κ), an attribute which we can explain. Next, we consider two such networks with different κ 's, reminiscent of two social groups, e.g., extroverts and introverts. Finally, we let these networks interact by establishing a controllable fraction of cross links. The resulting distribution of links, both within and across the two model networks, is investigated and discussed, along with some potential consequences for real networks. Supported in part by NSF-DMR-0705152 and 1005417.
Automated modelling of signal transduction networks
Directory of Open Access Journals (Sweden)
Aach John
2002-11-01
Full Text Available Abstract Background Intracellular signal transduction is achieved by networks of proteins and small molecules that transmit information from the cell surface to the nucleus, where they ultimately effect transcriptional changes. Understanding the mechanisms cells use to accomplish this important process requires a detailed molecular description of the networks involved. Results We have developed a computational approach for generating static models of signal transduction networks which utilizes protein-interaction maps generated from large-scale two-hybrid screens and expression profiles from DNA microarrays. Networks are determined entirely by integrating protein-protein interaction data with microarray expression data, without prior knowledge of any pathway intermediates. In effect, this is equivalent to extracting subnetworks of the protein interaction dataset whose members have the most correlated expression profiles. Conclusion We show that our technique accurately reconstructs MAP Kinase signaling networks in Saccharomyces cerevisiae. This approach should enhance our ability to model signaling networks and to discover new components of known networks. More generally, it provides a method for synthesizing molecular data, either individual transcript abundance measurements or pairwise protein interactions, into higher level structures, such as pathways and networks.
A survey of statistical network models
Goldenberg, Anna; Fienberg, Stephen E; Airoldi, Edoardo M
2009-01-01
Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry poin...
Quasi-attractor dynamics of lambda-phi^4-inflation
Kiselev, V V
2008-01-01
At high e-foldings of expansion, the inflation with the quartic potential exhibits the parametric attractor governed by the slowly running Hubble rate. This quasi-attractor simplifies the analysis of predictions for the inhomogeneity generated by the quantum fluctuations of inflaton. The quartic inflation is still marginally consistent with observations, if one suggests an extended version of tachyonic preheating stage with passing the region of negative potential, for instance.
Network Modeling and Simulation A Practical Perspective
Guizani, Mohsen; Khan, Bilal
2010-01-01
Network Modeling and Simulation is a practical guide to using modeling and simulation to solve real-life problems. The authors give a comprehensive exposition of the core concepts in modeling and simulation, and then systematically address the many practical considerations faced by developers in modeling complex large-scale systems. The authors provide examples from computer and telecommunication networks and use these to illustrate the process of mapping generic simulation concepts to domain-specific problems in different industries and disciplines. Key features: Provides the tools and strate
Performance modeling, stochastic networks, and statistical multiplexing
Mazumdar, Ravi R
2013-01-01
This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of introducing an appropriate mathematical framework for modeling and analysis as well as understanding the phenomenon of statistical multiplexing. The models, techniques, and results presented form the core of traffic engineering methods used to design, control and allocate resources in communication networks.The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the importan
Model Predictive Control of Sewer Networks
Pedersen, Einar B.; Herbertsson, Hannes R.; Niemann, Henrik; Poulsen, Niels K.; Falk, Anne K. V.
2017-01-01
The developments in solutions for management of urban drainage are of vital importance, as the amount of sewer water from urban areas continues to increase due to the increase of the world’s population and the change in the climate conditions. How a sewer network is structured, monitored and controlled have thus become essential factors for effcient performance of waste water treatment plants. This paper examines methods for simplified modelling and controlling a sewer network. A practical approach to the problem is used by analysing simplified design model, which is based on the Barcelona benchmark model. Due to the inherent constraints the applied approach is based on Model Predictive Control.
Passive control of chaotic system with multiple strange attractors
Institute of Scientific and Technical Information of China (English)
Song Yun-Zhong; Zhao Guang-Zhou; Qi Dong-Lian
2006-01-01
In this paper we present a new simple controller for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form.Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one,and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.
Characterization of Cocycle Attractors for Nonautonomous Reaction-Diffusion Equations
Cardoso, C. A.; Langa, J. A.; Obaya, R.
In this paper, we describe in detail the global and cocycle attractors related to nonautonomous scalar differential equations with diffusion. In particular, we investigate reaction-diffusion equations with almost-periodic coefficients. The associated semiflows are strongly monotone which allow us to give a full characterization of the cocycle attractor. We prove that, when the upper Lyapunov exponent associated to the linear part of the equations is positive, the flow is persistent in the positive cone, and we study the stability and the set of continuity points of the section of each minimal set in the global attractor for the skew product semiflow. We illustrate our result with some nontrivial examples showing the richness of the dynamics on this attractor, which in some situations shows internal chaotic dynamics in the Li-Yorke sense. We also include the sublinear and concave cases in order to go further in the characterization of the attractors, including, for instance, a nonautonomous version of the Chafee-Infante equation. In this last case we can show exponentially forward attraction to the cocycle (pullback) attractors in the positive cone of solutions.
Modeling acquaintance networks based on balance theory
Directory of Open Access Journals (Sweden)
Vukašinović Vida
2014-09-01
Full Text Available An acquaintance network is a social structure made up of a set of actors and the ties between them. These ties change dynamically as a consequence of incessant interactions between the actors. In this paper we introduce a social network model called the Interaction-Based (IB model that involves well-known sociological principles. The connections between the actors and the strength of the connections are influenced by the continuous positive and negative interactions between the actors and, vice versa, the future interactions are more likely to happen between the actors that are connected with stronger ties. The model is also inspired by the social behavior of animal species, particularly that of ants in their colony. A model evaluation showed that the IB model turned out to be sparse. The model has a small diameter and an average path length that grows in proportion to the logarithm of the number of vertices. The clustering coefficient is relatively high, and its value stabilizes in larger networks. The degree distributions are slightly right-skewed. In the mature phase of the IB model, i.e., when the number of edges does not change significantly, most of the network properties do not change significantly either. The IB model was found to be the best of all the compared models in simulating the e-mail URV (University Rovira i Virgili of Tarragona network because the properties of the IB model more closely matched those of the e-mail URV network than the other models
Network Modeling and Simulation (NEMSE)
2013-07-01
Emulator (CORE) modules, hardware components, wireless cards with links modifiable using Radio Frequency (RF) cabling and variable attenuators, and GNU ...universal Network Interface Card (NIC) cards - Cardbus, PCI, or miniPCI. o GNU radio : Free & open-source software development toolkit that provides...Layer Emulator (FPLE), GNU Radio , CORE & EMANE, Tech Warrior, CASCON (CAS Connectivity), and Rate Adaptive Video Coding (RAVC). Also described is the
Distributed Bayesian Networks for User Modeling
DEFF Research Database (Denmark)
Tedesco, Roberto; Dolog, Peter; Nejdl, Wolfgang
2006-01-01
by such adaptive applications are often partial fragments of an overall user model. The fragments have then to be collected and merged into a global user profile. In this paper we investigate and present algorithms able to cope with distributed, fragmented user models – based on Bayesian Networks – in the context...... of Web-based eLearning platforms. The scenario we are tackling assumes learners who use several systems over time, which are able to create partial Bayesian Networks for user models based on the local system context. In particular, we focus on how to merge these partial user models. Our merge mechanism...... efficiently combines distributed learner models without the need to exchange internal structure of local Bayesian networks, nor local evidence between the involved platforms....
Modeling Emergence in Neuroprotective Regulatory Networks
Energy Technology Data Exchange (ETDEWEB)
Sanfilippo, Antonio P.; Haack, Jereme N.; McDermott, Jason E.; Stevens, S.L.; Stenzel-Poore, Mary
2013-01-05
The use of predictive modeling in the analysis of gene expression data can greatly accelerate the pace of scientific discovery in biomedical research by enabling in silico experimentation to test disease triggers and potential drug therapies. Techniques that focus on modeling emergence, such as agent-based modeling and multi-agent simulations, are of particular interest as they support the discovery of pathways that may have never been observed in the past. Thus far, these techniques have been primarily applied at the multi-cellular level, or have focused on signaling and metabolic networks. We present an approach where emergence modeling is extended to regulatory networks and demonstrate its application to the discovery of neuroprotective pathways. An initial evaluation of the approach indicates that emergence modeling provides novel insights for the analysis of regulatory networks that can advance the discovery of acute treatments for stroke and other diseases.
Optimal transportation networks models and theory
Bernot, Marc; Morel, Jean-Michel
2009-01-01
The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.
Attractors of derivative complex Ginzburg-Landau equation in unbounded domains
Institute of Scientific and Technical Information of China (English)
GUO Boling; HAN Yongqian
2007-01-01
The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg- Landau (DCGL) equation in an unbounded domain ΩС R2 is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov's ε-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in R2 is detailed studied.
Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit
Energy Technology Data Exchange (ETDEWEB)
Kengne, J. [Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang (Cameroon); Njitacke Tabekoueng, Z.; Kamdoum Tamba, V.; Nguomkam Negou, A. [Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang (Cameroon); Department of Physics, Laboratory of Electronics and Signal Processing (LETS), Faculty of Science, University of Dschang, Dschang (Cameroon)
2015-10-15
In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pair of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.
Seven-disk manifold, α -attractors, and B modes
Ferrara, Sergio; Kallosh, Renata
2016-12-01
Cosmological α -attractor models in N =1 supergravity are based on the hyperbolic geometry of a Poincaré disk with the radius square R2=3 α . The predictions for the B modes, r ≈3 α 4/N2, depend on moduli space geometry and are robust for a rather general class of potentials. Here we notice that starting with M theory compactified on a 7-manifold with G2 holonomy, with a special choice of Betti numbers, one can obtain d =4 , N =1 supergravity with the rank 7 scalar coset [S/L (2 ) S O (2 ) ]7. In a model where these seven unit size Poincaré disks have identified moduli one finds that 3 α =7 . Assuming that the moduli space geometry of the phenomenological models is inherited from this version of M theory, one would predict r ≈10-2 for N =53 e -foldings. We also describe the related maximal supergravity and M/string theory models leading to preferred values 3 α =1 , 2, 3, 4, 5, 6, 7.
International migration network: topology and modeling.
Fagiolo, Giorgio; Mastrorillo, Marina
2013-07-01
This paper studies international migration from a complex-network perspective. We define the international migration network (IMN) as the weighted-directed graph where nodes are world countries and links account for the stock of migrants originated in a given country and living in another country at a given point in time. We characterize the binary and weighted architecture of the network and its evolution over time in the period 1960-2000. We find that the IMN is organized around a modular structure with a small-world binary pattern displaying disassortativity and high clustering, with power-law distributed weighted-network statistics. We also show that a parsimonious gravity model of migration can account for most of observed IMN topological structure. Overall, our results suggest that socioeconomic, geographical, and political factors are more important than local-network properties in shaping the structure of the IMN.
Enhanced Gravity Model of trade: reconciling macroeconomic and network models
Almog, Assaf; Garlaschelli, Diego
2015-01-01
The bilateral trade relations between world countries form a complex network, the International Trade Network (ITN), which is involved in an increasing number of worldwide economic processes, including globalization, integration, industrial production, and the propagation of shocks and instabilities. Characterizing the ITN via a simple yet accurate model is an open problem. The classical Gravity Model of trade successfully reproduces the volume of trade between two connected countries using known macroeconomic properties such as GDP and geographic distance. However, it generates a network with an unrealistically homogeneous topology, thus failing to reproduce the highly heterogeneous structure of the real ITN. On the other hand, network models successfully reproduce the complex topology of the ITN, but provide no information about trade volumes. Therefore macroeconomic and network models of trade suffer from complementary limitations but are still largely incompatible. Here, we make an important step forward ...
Preferential urn model and nongrowing complex networks.
Ohkubo, Jun; Yasuda, Muneki; Tanaka, Kazuyuki
2005-12-01
A preferential urn model, which is based on the concept "the rich get richer," is proposed. From a relationship between a nongrowing model for complex networks and the preferential urn model in regard to degree distributions, it is revealed that a fitness parameter in the nongrowing model is interpreted as an inverse local temperature in the preferential urn model. Furthermore, it is clarified that the preferential urn model with randomness generates a fat-tailed occupation distribution; the concept of the local temperature enables us to understand the fat-tailed occupation distribution intuitively. Since the preferential urn model is a simple stochastic model, it can be applied to research on not only the nongrowing complex networks, but also many other fields such as econophysics and social sciences.
Modeling, Optimization & Control of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat
2014-01-01
to check if the network is controllable. Afterward the pressure control problem in water supply systems is formulated as an optimal control problem. The goal is to minimize the power consumption in pumps and also to regulate the pressure drop at the end-users to a desired value. The formulated optimal...... in water network is pressure management. By reducing the pressure in the water network, the leakage can be reduced significantly. Also it reduces the amount of energy consumption in water networks. The primary purpose of this work is to develop control algorithms for pressure control in water supply...... systems. To have better understanding of water leakage, to control pressure and leakage effectively and for optimal design of water supply system, suitable modeling is an important prerequisite. Therefore a model with the main objective of pressure control and consequently leakage reduction is presented...
Grid architecture model of network centric warfare
Institute of Scientific and Technical Information of China (English)
Yan Tihua; Wang Baoshu
2006-01-01
NCW(network centric warfare) is an information warfare concentrating on network. A global network-centric warfare architecture with OGSA grid technology is put forward, which is a four levels system including the user level, the application level, the grid middleware layer and the resource level. In grid middleware layer, based on virtual hosting environment, a BEPL4WS grid service composition method is introduced. In addition, the NCW grid service model is built with the help of Eclipse-SDK-3.0.1 and Bpws4j.
A Network Model of Credit Risk Contagion
Directory of Open Access Journals (Sweden)
Ting-Qiang Chen
2012-01-01
Full Text Available A network model of credit risk contagion is presented, in which the effect of behaviors of credit risk holders and the financial market regulators and the network structure are considered. By introducing the stochastic dominance theory, we discussed, respectively, the effect mechanisms of the degree of individual relationship, individual attitude to credit risk contagion, the individual ability to resist credit risk contagion, the monitoring strength of the financial market regulators, and the network structure on credit risk contagion. Then some derived and proofed propositions were verified through numerical simulations.
Spatial Models and Networks of Living Systems
DEFF Research Database (Denmark)
Juul, Jeppe Søgaard
variables of the system. However, this approach disregards any spatial structure of the system, which may potentially change the behaviour drastically. An alternative approach is to construct a cellular automaton with nearest neighbour interactions, or even to model the system as a complex network....... Such systems are known to be stabilized by spatial structure. Finally, I analyse data from a large mobile phone network and show that people who are topologically close in the network have similar communication patterns. This main part of the thesis is based on six different articles, which I have co...
Stochastic modeling and analysis of telecoms networks
Decreusefond, Laurent
2012-01-01
This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an
Decomposed Implicit Models of Piecewise - Linear Networks
Directory of Open Access Journals (Sweden)
J. Brzobohaty
1992-05-01
Full Text Available The general matrix form of the implicit description of a piecewise-linear (PWL network and the symbolic block diagram of the corresponding circuit model are proposed. Their decomposed forms enable us to determine quite separately the existence of the individual breakpoints of the resultant PWL characteristic and their coordinates using independent network parameters. For the two-diode and three-diode cases all the attainable types of the PWL characteristic are introduced.
Implementation of a network model of hysteresis
Energy Technology Data Exchange (ETDEWEB)
Gruosso, G. [Dipartimento Elettronica e Informazione, Politecnico di Milano, P.za Leonardo da Vinci 32, I-20133 Milan (Italy); Repetto, M. [Dipartimento Ingegneria Elettrica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Turin (Italy)]. E-mail: maurizio.repetto@polito.it
2006-02-01
A network model of hysteresis based on elementary cells made up with piece-wise linear resistors and a linear capacitor has been presented in the literature and its theoretical properties have been investigated. This model allows to simulate hysteresis in a circuit solver without requiring any modification to its source code. Despite its appealing features, some cautions must be used for the treatment of the interface between the model and the rest of the circuit and for the handling of nonlinear resistors which can introduce some convergence problems in the network solution. These topics are investigated and some results on a simple test case are presented and discussed.
Modelling cooperative agents in infrastructure networks
Ligtvoet, A.; Chappin, E.J.L.; Stikkelman, R.M.
2010-01-01
This paper describes the translation of concepts of cooperation into an agent-based model of an industrial network. It first addresses the concept of cooperation and how this could be captured as heuristical rules within agents. Then it describes tests using these heuristics in an abstract model of
Evaluation of EOR Processes Using Network Models
DEFF Research Database (Denmark)
Larsen, Jens Kjell; Krogsbøll, Anette
1998-01-01
The report consists of the following parts: 1) Studies of wetting properties of model fluids and fluid mixtures aimed at an optimal selection of candidates for micromodel experiments. 2) Experimental studies of multiphase transport properties using physical models of porous networks (micromodels)...
Designing Network-based Business Model Ontology
DEFF Research Database (Denmark)
Hashemi Nekoo, Ali Reza; Ashourizadeh, Shayegheh; Zarei, Behrouz
2015-01-01
Survival on dynamic environment is not achieved without a map. Scanning and monitoring of the market show business models as a fruitful tool. But scholars believe that old-fashioned business models are dead; as they are not included the effect of internet and network in themselves. This paper...
Tkachova, P.; Krot, A.; Minervina, H.
It is well known that there is chaos in convective process in atmosphere and ocean. In particular,dynamic model of Lorenz [1] describes the Rayleigh-Benard convection phenomenon. Phase trajectories of Lorenz equation system are characterized by strange alternative properties: on the one hand, they diverge (because of positive Lyapunov exponents), on the second hand, they attract to the limited domain of phase space called an attractor [1]. The Lorenz attractor has specific geometrical structure and can be characterized by means of fractal dimension. In this connection the aim of this work is development of analysis of Lorenz attractor based on the proposed nonlinear decomposition into matrix series [2]. This analysis permits to estimate the values of characteristic parameters (including control one) of Lorenz attractors and predict their evolution in time. Using results of matrix decomposition [2], it is not difficult to see that the change of vector function (describing the Lorenz attractor) can be approximated by only linear and quadratic terms [3]. Because values of the first and second order derivatives can be calculated by means of numerical methods we can estimate the change of the vector function from computational experiment. In result, the values of parameters of the Lorenz's attractor can be estimated. This permits us to solve the identification task of the current dynamical state of a convective aerodynamic flows. Moreover, using the results of matrix decomposition we can estimate the minimal embedding dimension [4] for the Lorenz attractor based on experimental data. References: [1] P.Berge,Y.Pomeau and C.Vidal. L'ordre dans le chaos: Vers une approche deterministe de la turbulence. Hermann:Paris,1988. [2] A.M.Krot, "Matrix decompositions of vector functions and shift operators on the trajectories of a nonlinear dynamical system", Nonlinear Phenomena in Complex Systems,vol.4, N2, pp.106- 115, 2001. [3] A.M.Krot and P
Delay and Disruption Tolerant Networking MACHETE Model
Segui, John S.; Jennings, Esther H.; Gao, Jay L.
2011-01-01
To verify satisfaction of communication requirements imposed by unique missions, as early as 2000, the Communications Networking Group at the Jet Propulsion Laboratory (JPL) saw the need for an environment to support interplanetary communication protocol design, validation, and characterization. JPL's Multi-mission Advanced Communications Hybrid Environment for Test and Evaluation (MACHETE), described in Simulator of Space Communication Networks (NPO-41373) NASA Tech Briefs, Vol. 29, No. 8 (August 2005), p. 44, combines various commercial, non-commercial, and in-house custom tools for simulation and performance analysis of space networks. The MACHETE environment supports orbital analysis, link budget analysis, communications network simulations, and hardware-in-the-loop testing. As NASA is expanding its Space Communications and Navigation (SCaN) capabilities to support planned and future missions, building infrastructure to maintain services and developing enabling technologies, an important and broader role is seen for MACHETE in design-phase evaluation of future SCaN architectures. To support evaluation of the developing Delay Tolerant Networking (DTN) field and its applicability for space networks, JPL developed MACHETE models for DTN Bundle Protocol (BP) and Licklider/Long-haul Transmission Protocol (LTP). DTN is an Internet Research Task Force (IRTF) architecture providing communication in and/or through highly stressed networking environments such as space exploration and battlefield networks. Stressed networking environments include those with intermittent (predictable and unknown) connectivity, large and/or variable delays, and high bit error rates. To provide its services over existing domain specific protocols, the DTN protocols reside at the application layer of the TCP/IP stack, forming a store-and-forward overlay network. The key capabilities of the Bundle Protocol include custody-based reliability, the ability to cope with intermittent connectivity
Robust sequential working memory recall in heterogeneous cognitive networks
Rabinovich, Mikhail I.; Sokolov, Yury; Kozma, Robert
2014-01-01
Psychiatric disorders are often caused by partial heterogeneous disinhibition in cognitive networks, controlling sequential and spatial working memory (SWM). Such dynamic connectivity changes suggest that the normal relationship between the neuronal components within the network deteriorates. As a result, competitive network dynamics is qualitatively altered. This dynamics defines the robust recall of the sequential information from memory and, thus, the SWM capacity. To understand pathological and non-pathological bifurcations of the sequential memory dynamics, here we investigate the model of recurrent inhibitory-excitatory networks with heterogeneous inhibition. We consider the ensemble of units with all-to-all inhibitory connections, in which the connection strengths are monotonically distributed at some interval. Based on computer experiments and studying the Lyapunov exponents, we observed and analyzed the new phenomenon—clustered sequential dynamics. The results are interpreted in the context of the winnerless competition principle. Accordingly, clustered sequential dynamics is represented in the phase space of the model by two weakly interacting quasi-attractors. One of them is similar to the sequential heteroclinic chain—the regular image of SWM, while the other is a quasi-chaotic attractor. Coexistence of these quasi-attractors means that the recall of the normal information sequence is intermittently interrupted by episodes with chaotic dynamics. We indicate potential dynamic ways for augmenting damaged working memory and other cognitive functions. PMID:25452717
Research on Modeling of Genetic Networks Based on Information Measurement
Institute of Scientific and Technical Information of China (English)
ZHANG Guo-wei; SHAO Shi-huang; ZHANG Ying; LI Hai-ying
2006-01-01
As the basis of network of biology organism, the genetic network is concerned by many researchers.Current modeling methods to genetic network, especially the Boolean networks modeling method are analyzed. For modeling the genetic network, the information theory is proposed to mining the relations between elements in network. Through calculating the values of information entropy and mutual entropy in a case, the effectiveness of the method is verified.
Bayesian network modelling of upper gastrointestinal bleeding
Aisha, Nazziwa; Shohaimi, Shamarina; Adam, Mohd Bakri
2013-09-01
Bayesian networks are graphical probabilistic models that represent causal and other relationships between domain variables. In the context of medical decision making, these models have been explored to help in medical diagnosis and prognosis. In this paper, we discuss the Bayesian network formalism in building medical support systems and we learn a tree augmented naive Bayes Network (TAN) from gastrointestinal bleeding data. The accuracy of the TAN in classifying the source of gastrointestinal bleeding into upper or lower source is obtained. The TAN achieves a high classification accuracy of 86% and an area under curve of 92%. A sensitivity analysis of the model shows relatively high levels of entropy reduction for color of the stool, history of gastrointestinal bleeding, consistency and the ratio of blood urea nitrogen to creatinine. The TAN facilitates the identification of the source of GIB and requires further validation.
Modeling epidemics dynamics on heterogenous networks.
Ben-Zion, Yossi; Cohen, Yahel; Shnerb, Nadav M
2010-05-21
The dynamics of the SIS process on heterogenous networks, where different local communities are connected by airlines, is studied. We suggest a new modeling technique for travelers movement, in which the movement does not affect the demographic parameters characterizing the metapopulation. A solution to the deterministic reaction-diffusion equations that emerges from this model on a general network is presented. A typical example of a heterogenous network, the star structure, is studied in detail both analytically and using agent-based simulations. The interplay between demographic stochasticity, spatial heterogeneity and the infection dynamics is shown to produce some counterintuitive effects. In particular it was found that, while movement always increases the chance of an outbreak, it may decrease the steady-state fraction of sick individuals. The importance of the modeling technique in estimating the outcomes of a vaccination campaign is demonstrated.
The Kuramoto model in complex networks
Rodrigues, Francisco A; Ji, Peng; Kurths, Jürgen
2016-01-01
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in net...
Modelling Users` Trust in Online Social Networks
Directory of Open Access Journals (Sweden)
Iacob Cătoiu
2014-02-01
Full Text Available Previous studies (McKnight, Lankton and Tripp, 2011; Liao, Lui and Chen, 2011 have shown the crucial role of trust when choosing to disclose sensitive information online. This is the case of online social networks users, who must disclose a certain amount of personal data in order to gain access to these online services. Taking into account privacy calculus model and the risk/benefit ratio, we propose a model of users’ trust in online social networks with four variables. We have adapted metrics for the purpose of our study and we have assessed their reliability and validity. We use a Partial Least Squares (PLS based structural equation modelling analysis, which validated all our initial assumptions, indicating that our three predictors (privacy concerns, perceived benefits and perceived risks explain 48% of the variation of users’ trust in online social networks, the resulting variable of our study. We also discuss the implications and further research opportunities of our study.
Boolean Networks with Multi-Expressions and Parameters.
Zou, Yi Ming
2013-07-01
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean models, both synchronous and asynchronous, have been proposed in the literature. However, analytical study of these more general Boolean networks models is lagging. This paper aims to develop a concise theory for these different Boolean logic based modeling methods. Boolean models for networks where each node can have more than two levels of expression and Boolean models with parameters are defined algebraically with examples provided. Certain classes of random asynchronous Boolean networks and deterministic moduli asynchronous Boolean networks are investigated in detail using the setting introduced in this paper. The derived theorems provide a clear picture for the attractor structures of these asynchronous Boolean networks.
Features and heterogeneities in growing network models
Ferretti, Luca; Cortelezzi, Michele; Yang, Bin; Marmorini, Giacomo; Bianconi, Ginestra
2012-06-01
Many complex networks from the World Wide Web to biological networks grow taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document such as personal page, thematic website, news, blog, search engine, social network, etc., or the classification of a gene in a functional module. Moreover the feature of a node can be a continuous variable such as the position of a node in the embedding space. In order to account for these properties, in this paper we provide a generalization of growing network models with preferential attachment that includes the effect of heterogeneous features of the nodes. The main effect of heterogeneity is the emergence of an “effective fitness” for each class of nodes, determining the rate at which nodes acquire new links. The degree distribution exhibits a multiscaling behavior analogous to the the fitness model. This property is robust with respect to variations in the model, as long as links are assigned through effective preferential attachment. Beyond the degree distribution, in this paper we give a full characterization of the other relevant properties of the model. We evaluate the clustering coefficient and show that it disappears for large network size, a property shared with the Barabási-Albert model. Negative degree correlations are also present in this class of models, along with nontrivial mixing patterns among features. We therefore conclude that both small clustering coefficients and disassortative mixing are outcomes of the preferential attachment mechanism in general growing networks.
Deterministic Chaos Model for Self-Organized Adaptive Networks in Atmospheric Flows
Selvam, A M
2003-01-01
The complex spatiotemporal patterns of atmospheric flows resulting from the cooperative existence of fluctuations ranging in size from millimeters to thousands of kilometers are found to exhibit long-range spatial and temporal correlations manifested as the selfsimilar fractal geometry to the global cloud cover pattern and the inverse power law form for the atmospheric eddy energy spectrum. Such long-range spatial and temporal correlations are ubiquitous to extended natural dynamical systems and is a signature of the strange attractor design characterizing deterministic chaos or self-organized criticality. The unified network of global atmospheric circulations is analogous to the neural networks of the human brain.
Bifurcations and chaos control in discrete small-world networks
Institute of Scientific and Technical Information of China (English)
Li Ning; Sun Hai-Yi; Zhang Qing-Ling
2012-01-01
An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed.The control method is then applied to a discrete small-world network model.Qualitative analyses and simulations show that under a generic condition,the bifurcations and the chaos can be delayed or eliminated completely.In addition,the periodic orbits embedded in the chaotic attractor can be stabilized.
Network dynamics and systems biology
Norrell, Johannes A.
The physics of complex systems has grown considerably as a field in recent decades, largely due to improved computational technology and increased availability of systems level data. One area in which physics is of growing relevance is molecular biology. A new field, systems biology, investigates features of biological systems as a whole, a strategy of particular importance for understanding emergent properties that result from a complex network of interactions. Due to the complicated nature of the systems under study, the physics of complex systems has a significant role to play in elucidating the collective behavior. In this dissertation, we explore three problems in the physics of complex systems, motivated in part by systems biology. The first of these concerns the applicability of Boolean models as an approximation of continuous systems. Studies of gene regulatory networks have employed both continuous and Boolean models to analyze the system dynamics, and the two have been found produce similar results in the cases analyzed. We ask whether or not Boolean models can generically reproduce the qualitative attractor dynamics of networks of continuously valued elements. Using a combination of analytical techniques and numerical simulations, we find that continuous networks exhibit two effects---an asymmetry between on and off states, and a decaying memory of events in each element's inputs---that are absent from synchronously updated Boolean models. We show that in simple loops these effects produce exactly the attractors that one would predict with an analysis of the stability of Boolean attractors, but in slightly more complicated topologies, they can destabilize solutions that are stable in the Boolean approximation, and can stabilize new attractors. Second, we investigate ensembles of large, random networks. Of particular interest is the transition between ordered and disordered dynamics, which is well characterized in Boolean systems. Networks at the
String networks with junctions in competition models
Avelino, P P; Losano, L; Menezes, J; de Oliveira, B F
2016-01-01
In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high concentration of enemy species. We study the two- and three-dimensional evolution of such networks, both using stochastic network and mean field theory simulations. If the predation, reproduction and mobility probabilities do not vary in space and time, we find that the networks attain scaling regimes with a characteristic length roughly proportional to $t^{1/2}$, where $t$ is the physical time, thus showing that the presence of junctions, on its own, does not have a significant impact on their scaling properties.
String networks with junctions in competition models
Avelino, P. P.; Bazeia, D.; Losano, L.; Menezes, J.; de Oliveira, B. F.
2017-03-01
In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high concentration of enemy species. We study the two- and three-dimensional evolution of such networks, both using stochastic network and mean field theory simulations. If the predation, reproduction and mobility probabilities do not vary in space and time, we find that the networks attain scaling regimes with a characteristic length roughly proportional to t 1 / 2, where t is the physical time, thus showing that the presence of junctions, on its own, does not have a significant impact on their scaling properties.
Mobility Models for Next Generation Wireless Networks Ad Hoc, Vehicular and Mesh Networks
Santi, Paolo
2012-01-01
Mobility Models for Next Generation Wireless Networks: Ad Hoc, Vehicular and Mesh Networks provides the reader with an overview of mobility modelling, encompassing both theoretical and practical aspects related to the challenging mobility modelling task. It also: Provides up-to-date coverage of mobility models for next generation wireless networksOffers an in-depth discussion of the most representative mobility models for major next generation wireless network application scenarios, including WLAN/mesh networks, vehicular networks, wireless sensor networks, and
Green Network Planning Model for Optical Backbones
DEFF Research Database (Denmark)
Gutierrez Lopez, Jose Manuel; Riaz, M. Tahir; Jensen, Michael
2010-01-01
Communication networks are becoming more essential for our daily lives and critically important for industry and governments. The intense growth in the backbone traffic implies an increment of the power demands of the transmission systems. This power usage might have a significant negative effect...... on the environment in general. In network planning there are existing planning models focused on QoS provisioning, investment minimization or combinations of both and other parameters. But there is a lack of a model for designing green optical backbones. This paper presents novel ideas to be able to define...
Model Predictive Control of Sewer Networks
DEFF Research Database (Denmark)
Pedersen, Einar B.; Herbertsson, Hannes R.; Niemann, Henrik;
2016-01-01
The developments in solutions for management of urban drainage are of vital importance, as the amount of sewer water from urban areas continues to increase due to the increase of the world’s population and the change in the climate conditions. How a sewer network is structured, monitored...... and controlled have thus become essential factors for efficient performance of waste water treatment plants. This paper examines methods for simplified modelling and controlling a sewer network. A practical approach to the problem is used by analysing simplified design model, which is based on the Barcelona...
Intersecting Black Attractors in 8D N=1 Supergravity
Laamara, R Ahl; Hassani, F Z; Saidi, E H; Soumail, A A
2010-01-01
We study intersecting extremal black attractors in non chiral 8D N=1 supergravity with moduli space ((SO(2,N))/(SO(2)\\times SO(N)))\\times SO(1,1) and work out explicitly the attractor mechanism for various black p-brane configurations with the typical near horizon geometries AdS_{p+2} \\times S^{m} \\times T^{6-p-m}. We also give the classification of the solutions of the attractor equations in terms of the SO(N-k) subgroups of SO(2)\\times SO(N) symmetry of the moduli space as well as their interpretations in terms of both heterotic string on 2-torus and its type IIA dual. Other features such as non trivial SO(1,7) central charges Z_{{\\mu}_1...{\\mu}_{p}} in 8D N=1 supergravity and their connections to p-form gauge fields are also given. Key Words: 8D Supergravity, Superstring compactifications, Attractor Mechanism, Intersecting Attractors. PACS numbers: 04.70.-s, 11.25.-w, 04.65.+e, 04.70.-s, 04.50.+h, 04.70.Dy
Attractors and soak times in artisanal fi shing with traps
Directory of Open Access Journals (Sweden)
Evandro Figueiredo Sebastiani
2009-12-01
Full Text Available Traps are used by artisanal fishers as fishing gear in places where other fishing modalities are impeded or limited. The advantage of this type of fishing modality is the possibility of keeping fish alive and in the case of capturing species of low commercial value or size below the permitted minimum this fishing gear allows the release of such specimens back to nature, resulting in a sustainability aspect to the use of this fishing gear. This study aims to evaluate the effects of different attractors and times of submersion on the efficiency of the traps used. Sardines, shrimps and trash fish were employed as attractors. To evaluate the soak time, two periods were tested: 24 and 96 hours. The sardines, used as the attractor, resulted in a production of 1,296.4 ± 397.4g, significantly superior (p <0.05 to other attractors. In relation to the soak time, the period of 24 hours resulted in an average production of 1,719.2 ± 866.0g, significantly (p <0.05 superior to the period of 96 hours. The results led to the conclusion that to optimize this capture by fishing gear, sardines should be used as the attractor, together with a soak time of 24 hours.
Security Modeling on the Supply Chain Networks
Directory of Open Access Journals (Sweden)
Marn-Ling Shing
2007-10-01
Full Text Available In order to keep the price down, a purchaser sends out the request for quotation to a group of suppliers in a supply chain network. The purchaser will then choose a supplier with the best combination of price and quality. A potential supplier will try to collect the related information about other suppliers so he/she can offer the best bid to the purchaser. Therefore, confidentiality becomes an important consideration for the design of a supply chain network. Chen et al. have proposed the application of the Bell-LaPadula model in the design of a secured supply chain network. In the Bell-LaPadula model, a subject can be in one of different security clearances and an object can be in one of various security classifications. All the possible combinations of (Security Clearance, Classification pair in the Bell-LaPadula model can be thought as different states in the Markov Chain model. This paper extends the work done by Chen et al., provides more details on the Markov Chain model and illustrates how to use it to monitor the security state transition in the supply chain network.
An evolving model of online bipartite networks
Zhang, Chu-Xu; Zhang, Zi-Ke; Liu, Chuang
2013-12-01
Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models, resulting in either power-law or exponential degree distributions. However, many empirical results show that the user degree distribution actually follows a shifted power-law distribution, the so-called Mandelbrot’s law, which cannot be fully described by previous models. In this paper, we propose an evolving model, considering two different user behaviors: random and preferential attachment. Extensive empirical results on two real bipartite networks, Delicious and CiteULike, show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions. In addition, we introduce a structural parameter p, to demonstrate that the hybrid user behavior leads to the shifted power-law degree distribution, and the region of power-law tail will increase with the increment of p. The proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks.
Models and average properties of scale-free directed networks
Bernhardsson, Sebastian; Minnhagen, Petter
2006-08-01
We extend the merging model for undirected networks by Kim [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile merging, give rise to two distinct network types. We uncover that some nontrivial features of these two network types resemble two levels of a certain randomization/nonspecificity in the link reshuffling during network evolution. Furthermore, the same features show up, respectively, in metabolic networks and transcriptional networks. We introduce measures that single out the distinguishing features between the two prototype networks, as well as point out features that are beyond the prototypes.
Delivery Time Reliability Model of Logistics Network
Directory of Open Access Journals (Sweden)
Liusan Wu
2013-01-01
Full Text Available Natural disasters like earthquake and flood will surely destroy the existing traffic network, usually accompanied by delivery delay or even network collapse. A logistics-network-related delivery time reliability model defined by a shortest-time entropy is proposed as a means to estimate the actual delivery time reliability. The less the entropy is, the stronger the delivery time reliability remains, and vice versa. The shortest delivery time is computed separately based on two different assumptions. If a path is concerned without capacity restriction, the shortest delivery time is positively related to the length of the shortest path, and if a path is concerned with capacity restriction, a minimax programming model is built to figure up the shortest delivery time. Finally, an example is utilized to confirm the validity and practicality of the proposed approach.
An improved network model for railway traffic
Li, Keping; Ma, Xin; Shao, Fubo
In railway traffic, safety analysis is a key issue for controlling train operation. Here, the identification and order of key factors are very important. In this paper, a new network model is constructed for analyzing the railway safety, in which nodes are regarded as causation factors and links represent possible relationships among those factors. Our aim is to give all these nodes an importance order, and to find the in-depth relationship among these nodes including how failures spread among them. Based on the constructed network model, we propose a control method to ensure the safe state by setting each node a threshold. As the results, by protecting the Hub node of the constructed network, the spreading of railway accident can be controlled well. The efficiency of such a method is further tested with the help of numerical example.
Self-organized Collaboration Network Model Based on Module Emerging
Yang, Hongyong; Lu, Lan; Liu, Qiming
Recently, the studies of the complex network have gone deep into many scientific fields, such as computer science, physics, mathematics, sociology, etc. These researches enrich the realization for complex network, and increase understands for the new characteristic of complex network. Based on the evolvement characteristic of the author collaboration in the scientific thesis, a self-organized network model of the scientific cooperation network is presented by module emerging. By applying the theoretical analysis, it is shown that this network model is a scale-free network, and the strength degree distribution and the module degree distribution of the network nodes have the same power law. In order to make sure the validity of the theoretical analysis for the network model, we create the computer simulation and demonstration collaboration network. By analyzing the data of the network, the results of the demonstration network and the computer simulation are consistent with that of the theoretical analysis of the model.
Bayesian Network Based XP Process Modelling
Directory of Open Access Journals (Sweden)
Mohamed Abouelela
2010-07-01
Full Text Available A Bayesian Network based mathematical model has been used for modelling Extreme Programmingsoftware development process. The model is capable of predicting the expected finish time and theexpected defect rate for each XP release. Therefore, it can be used to determine the success/failure of anyXP Project. The model takes into account the effect of three XP practices, namely: Pair Programming,Test Driven Development and Onsite Customer practices. The model’s predictions were validated againsttwo case studies. Results show the precision of our model especially in predicting the project finish time.
Network Model Building (Process Mapping)
Blau, Gary; Yih, Yuehwern
2004-01-01
12 slides Provider Notes:See Project Planning Video (Windows Media) Posted at the bottom are Gary Blau's slides. Before watching, please note that "process mapping" and "modeling" are mentioned in the video and notes. Here they are meant to refer to the NSCORT "project plan"
Methodically Modeling the Tor Network
2012-08-01
iPlane [7] and CAIDA [3]. Third, determining a better client model would further increase confidence in experimental results. Producing a more robust...Bandwidth Speed Test. http://speedtest.net/. [3] CAIDA Data. http://www.caida.org/data. [4] DETER Testbed. http://www.isi.edu/deter. [5] Emulab
Keystone Business Models for Network Security Processors
Directory of Open Access Journals (Sweden)
Arthur Low
2013-07-01
Full Text Available Network security processors are critical components of high-performance systems built for cybersecurity. Development of a network security processor requires multi-domain experience in semiconductors and complex software security applications, and multiple iterations of both software and hardware implementations. Limited by the business models in use today, such an arduous task can be undertaken only by large incumbent companies and government organizations. Neither the “fabless semiconductor” models nor the silicon intellectual-property licensing (“IP-licensing” models allow small technology companies to successfully compete. This article describes an alternative approach that produces an ongoing stream of novel network security processors for niche markets through continuous innovation by both large and small companies. This approach, referred to here as the "business ecosystem model for network security processors", includes a flexible and reconfigurable technology platform, a “keystone” business model for the company that maintains the platform architecture, and an extended ecosystem of companies that both contribute and share in the value created by innovation. New opportunities for business model innovation by participating companies are made possible by the ecosystem model. This ecosystem model builds on: i the lessons learned from the experience of the first author as a senior integrated circuit architect for providers of public-key cryptography solutions and as the owner of a semiconductor startup, and ii the latest scholarly research on technology entrepreneurship, business models, platforms, and business ecosystems. This article will be of interest to all technology entrepreneurs, but it will be of particular interest to owners of small companies that provide security solutions and to specialized security professionals seeking to launch their own companies.
Dynamic Pathloss Model for Future Mobile Communication Networks
DEFF Research Database (Denmark)
Kumar, Ambuj; Mihovska, Albena Dimitrova; Prasad, Ramjee
2016-01-01
— Future mobile communication networks (MCNs) are expected to be more intelligent and proactive based on new capabilities that increase agility and performance. However, for any successful mobile network service, the dexterity in network deployment is a key factor. The efficiency of the network...... that incorporates the environmental dynamics factor in the propagation model for intelligent and proactively iterative networks...
Unified Model for Generation Complex Networks with Utility Preferential Attachment
Institute of Scientific and Technical Information of China (English)
WU Jian-Jun; GAO Zi-You; SUN Hui-Jun
2006-01-01
In this paper, based on the utility preferential attachment, we propose a new unified model to generate different network topologies such as scale-free, small-world and random networks. Moreover, a new network structure named super scale network is found, which has monopoly characteristic in our simulation experiments. Finally, the characteristics ofthis new network are given.
Modeling of Network Identification Capability.
1986-07-01
scalar moment is assumed to follow a Poisson distribution, as suggested by Lomnitz (1966). The A cumulative number of events occurring per year at or...Spectral Ratios from Point Sources in Plane-Layered Earth V Models," BSSA. 60, pp 1937-1987 Lomnitz . C. (1966). -Statistical Prediction of Earthquakes...Moment-Magritude Relations in Theory and Practice," J Geophy. Res., 89 (B7). pp. 6229-6235. Lomnitz , C. (1966), Statistical Prediction of Earthquakes
A Model of Mental State Transition Network
Xiang, Hua; Jiang, Peilin; Xiao, Shuang; Ren, Fuji; Kuroiwa, Shingo
Emotion is one of the most essential and basic attributes of human intelligence. Current AI (Artificial Intelligence) research is concentrating on physical components of emotion, rarely is it carried out from the view of psychology directly(1). Study on the model of artificial psychology is the first step in the development of human-computer interaction. As affective computing remains unpredictable, creating a reasonable mental model becomes the primary task for building a hybrid system. A pragmatic mental model is also the fundament of some key topics such as recognition and synthesis of emotions. In this paper a Mental State Transition Network Model(2) is proposed to detect human emotions. By a series of psychological experiments, we present a new way to predict coming human's emotions depending on the various current emotional states under various stimuli. Besides, people in different genders and characters are taken into consideration in our investigation. According to the psychological experiments data derived from 200 questionnaires, a Mental State Transition Network Model for describing the transitions in distribution among the emotions and relationships between internal mental situations and external are concluded. Further more the coefficients of the mental transition network model were achieved. Comparing seven relative evaluating experiments, an average precision rate of 0.843 is achieved using a set of samples for the proposed model.
The Kuramoto model in complex networks
Rodrigues, Francisco A.; Peron, Thomas K. DM.; Ji, Peng; Kurths, Jürgen
2016-01-01
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.
Psychometric Measurement Models and Artificial Neural Networks
Sese, Albert; Palmer, Alfonso L.; Montano, Juan J.
2004-01-01
The study of measurement models in psychometrics by means of dimensionality reduction techniques such as Principal Components Analysis (PCA) is a very common practice. In recent times, an upsurge of interest in the study of artificial neural networks apt to computing a principal component extraction has been observed. Despite this interest, the…
Modelling crime linkage with Bayesian networks
J. de Zoete; M. Sjerps; D. Lagnado; N. Fenton
2015-01-01
When two or more crimes show specific similarities, such as a very distinct modus operandi, the probability that they were committed by the same offender becomes of interest. This probability depends on the degree of similarity and distinctiveness. We show how Bayesian networks can be used to model
Structure of attractors for (a,b)-continued fraction transformations
Katok, Svetlana
2010-01-01
We study a two-parameter family of one-dimensional maps and related (a,b)-continued fractions suggested for consideration by Don Zagier. We prove that the associated natural extension maps have attractors with finite rectangular structure for the entire parameter set except for a Cantor-like set of one-dimensional Lebesgue zero measure that we completely describe. We show that the structure of these attractors can be "computed" from the data (a,b), and that for a dense open set of parameters the Reduction theory conjecture holds, i.e. every point is mapped to the attractor after finitely many iterations. We also show how this theory can be applied to the study of invariant measures and ergodic properties of the associated Gauss-like maps.
Strange attractors in weakly turbulent Couette-Taylor flow
Brandstater, A.; Swinney, Harry L.
1987-01-01
An experiment is conducted on the transition from quasi-periodic to weakly turbulent flow of a fluid contained between concentric cylinders with the inner cylinder rotating and the outer cylinder at rest. Power spectra, phase-space portraits, and circle maps obtained from velocity time-series data indicate that the nonperiodic behavior observed is deterministic, that is, it is described by strange attractors. Various problems that arise in computing the dimension of strange attractors constructed from experimental data are discussed and it is shown that these problems impose severe requirements on the quantity and accuracy of data necessary for determining dimensions greater than about 5. In the present experiment the attractor dimension increases from 2 at the onset of turbulence to about 4 at a Reynolds number 50-percent above the onset of turbulence.
Separation of attractors in 1-modulus quantum corrected special geometry
Bellucci, S; Marrani, A; Shcherbakov, A
2008-01-01
We study the solutions to the N=2, d=4 Attractor Equations in a dyonic, extremal, static, spherically symmetric and asymptotically flat black hole background, in the simplest case of perturbative quantum corrected cubic Special Kahler geometry consistent with continuous axion-shift symmetry, namely in the 1-modulus Special Kahler geometry described (in a suitable special symplectic coordinate) by the holomorphic Kahler gauge-invariant prepotential F=t^3+i*lambda, with lambda real. By performing computations in the ``magnetic'' charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing lambda). Namely, for a certain range of the quantum parameter lambda we find a ``splitting'' of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. This corresponds to the existence of ``area codes'' in the radial evolution of the scalar t, determined by the various disconnected regions of the moduli space, wh...
Hybrid simulation models of production networks
Kouikoglou, Vassilis S
2001-01-01
This book is concerned with a most important area of industrial production, that of analysis and optimization of production lines and networks using discrete-event models and simulation. The book introduces a novel approach that combines analytic models and discrete-event simulation. Unlike conventional piece-by-piece simulation, this method observes a reduced number of events between which the evolution of the system is tracked analytically. Using this hybrid approach, several models are developed for the analysis of production lines and networks. The hybrid approach combines speed and accuracy for exceptional analysis of most practical situations. A number of optimization problems, involving buffer design, workforce planning, and production control, are solved through the use of hybrid models.
Directory of Open Access Journals (Sweden)
Yin Li
2016-01-01
Full Text Available This paper investigates the existence of random attractor for stochastic Boussinesq equations driven by multiplicative white noises in both the velocity and temperature equations and estimates the Hausdorff dimension of the random attractor.
Global attractors of a degenerate parabolic equation and their error estimates
Institute of Scientific and Technical Information of China (English)
HU Xiaohong; ZHANG Xingyou
2004-01-01
The existences of the global attractor A? for a degenerate parabolic equation and of the homogenized attractorA0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between A? and A0 are given.
Upper Semicontinuity of Attractors for a Non-Newtonian Fluid under Small Random Perturbations
Directory of Open Access Journals (Sweden)
Jianxin Luo
2014-01-01
Full Text Available This paper investigates the limiting behavior of attractors for a two-dimensional incompressible non-Newtonian fluid under small random perturbations. Under certain conditions, the upper semicontinuity of the attractors for diminishing perturbations is shown.
Variety of strange pseudohyperbolic attractors in three-dimensional generalized Hénon maps
Gonchenko, A. S.; Gonchenko, S. V.
2016-12-01
In the present paper we focus on the problem of the existence of strange pseudohyperbolic attractors for three-dimensional diffeomorphisms. Such attractors are genuine strange attractors in that sense that each orbit in the attractor has positive maximal Lyapunov exponent and this property is robust, i.e., it holds for all close systems. We restrict attention to the study of pseudohyperbolic attractors that contain only one fixed point. Then we show that three-dimensional maps may have only 5 different types of such attractors, which we call the discrete Lorenz, figure-8, double-figure-8, super-figure-8, and super-Lorenz attractors. We find the first four types of attractors in three-dimensional generalized Hénon maps of form x ¯ = y, y ¯ = z, z ¯ = Bx + Az + Cy + g(y , z) , where A , B and C are parameters (B is the Jacobian) and g(0 , 0) =g‧(0 , 0) = 0.
Modeling Multistandard Wireless Networks in OPNET
DEFF Research Database (Denmark)
Zakrzewska, Anna; Berger, Michael Stübert; Ruepp, Sarah Renée
2011-01-01
Future wireless communication is emerging towards one heterogeneous platform. In this new environment wireless access will be provided by multiple radio technologies that are cooperating and complementing one another. The paper investigates the possibilities of developing such a multistandard sys...... system using OPNET Modeler. A network model consisting of LTE interworking with WLAN and WiMAX is considered from the radio resource management perspective. In particular, implementing a joint packet scheduler across multiple systems is discussed more in detail....
Investigating complex networks with inverse models
Wens, Vincent
2014-01-01
Recent advances in neuroscience have motivated the study of network organization in spatially distributed dynamical systems from indirect measurements. However, the associated connectivity estimation, when combined with inverse modeling, is strongly affected by spatial leakage. We formulate this problem in a general framework and develop a new approach to model spatial leakage and limit its effects. It is analytically compared to existing regression-based methods used in electrophysiology, which are shown to yield biased estimates of amplitude and phase couplings.
Model for the evolution of river networks
Energy Technology Data Exchange (ETDEWEB)
Leheny, R.L.; Nagel, S.R. (The James Franck Institute and the Department of Physics, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637 (United States))
1993-08-30
We have developed a model, which includes the effects of erosion both from precipitation and from avalanching of soil on steep slopes, to simulate the formation and evolution of river networks. The avalanches provide a mechanism for competition in growth between neighboring river basins. The changing morphology follows many of the characteristics of evolution set forth by Glock. We find that during evolution the model maintains the statistical characteristics measured in natural river systems.
Hopfield's Model of Patterns Recognition and Laws of Artistic Perception
Yevin, Igor; Koblyakov, Alexander
The model of patterns recognition or attractor network model of associative memory, offered by J.Hopfield 1982, is the most known model in theoretical neuroscience. This paper aims to show, that such well-known laws of art perception as the Wundt curve, perception of visual ambiguity in art, and also the model perception of musical tonalities are nothing else than special cases of the Hopfield’s model of patterns recognition.
Functional model of biological neural networks.
Lo, James Ting-Ho
2010-12-01
A functional model of biological neural networks, called temporal hierarchical probabilistic associative memory (THPAM), is proposed in this paper. THPAM comprises functional models of dendritic trees for encoding inputs to neurons, a first type of neuron for generating spike trains, a second type of neuron for generating graded signals to modulate neurons of the first type, supervised and unsupervised Hebbian learning mechanisms for easy learning and retrieving, an arrangement of dendritic trees for maximizing generalization, hardwiring for rotation-translation-scaling invariance, and feedback connections with different delay durations for neurons to make full use of present and past informations generated by neurons in the same and higher layers. These functional models and their processing operations have many functions of biological neural networks that have not been achieved by other models in the open literature and provide logically coherent answers to many long-standing neuroscientific questions. However, biological justifications of these functional models and their processing operations are required for THPAM to qualify as a macroscopic model (or low-order approximate) of biological neural networks.
Empirical generalization assessment of neural network models
DEFF Research Database (Denmark)
Larsen, Jan; Hansen, Lars Kai
1995-01-01
competing models. Since all models are trained on the same data, a key issue is to take this dependency into account. The optimal split of the data set of size N into a cross-validation set of size Nγ and a training set of size N(1-γ) is discussed. Asymptotically (large data sees), γopt→1......This paper addresses the assessment of generalization performance of neural network models by use of empirical techniques. We suggest to use the cross-validation scheme combined with a resampling technique to obtain an estimate of the generalization performance distribution of a specific model...
Distance distribution in configuration-model networks
Nitzan, Mor; Katzav, Eytan; Kühn, Reimer; Biham, Ofer
2016-06-01
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical simulations for networks with degenerate, binomial, and power-law degree distributions. The mean, mode, and variance of the distribution of shortest path lengths are also evaluated. These results provide expressions for central measures and dispersion measures of the distribution of shortest path lengths in terms of moments of the degree distribution, illuminating the connection between the two distributions.
Directory of Open Access Journals (Sweden)
Richard Eleftherios Boyatzis
2015-05-01
Full Text Available Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of a personal or shared vision: the positive emotional attractor (PEA and the negative emotional attractor (NEA. These two primary states are strange attractors, each characterized by three dimensions: (1 positive versus negative emotional arousal; (2 endocrine arousal of the parasympathetic nervous system versus sympathetic nervous system; and (3 neurological activation of the default mode network versus the task positive network. We argue that arousing the PEA is critical when creating or affirming a personal vision (i.e., sense of one’s purpose and ideal self. We begin our paper by reviewing the underpinnings of our PEA-NEA theory, briefly review each of the papers in this special issue, and conclude by discussing the practical implications of the theory.
Attractors and Dimensions for Discretizations of a NLS Equation with a Non-local Nonlinear Term
Institute of Scientific and Technical Information of China (English)
Shu Qing MA; Qian Shun CHANG
2002-01-01
In this paper we consider a semi-dicretized nonlinear Schrodinger (NLS) equation withlocal integral nonlinearity. It is proved that for each mesh size, there exist attractors for the discretizedsystem. The bounds for the Hausdorff and fractal dimensions of the discrete attractors are obtained,and the various bounds are independent of the mesh sizes. Furthermore, numerical experiments aregiven and many interesting phenomena are observed such as limit cycles, chaotic attractors and aso-called crisis of the chaotic attractors.
Compact Global Chaotic Attractors of Discrete Control Systems
Directory of Open Access Journals (Sweden)
Cheban David
2014-01-01
Full Text Available The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fv(n(xn, where v: Z+ → {1; 2; : : : ;m}. If m≥2 we give sufficient conditions (the family M := {f1; f2; : : : ; fm} of functions is contracting in the extended sense for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous dynamical systems (cocycles
Chaotic and hyperchaotic attractors of a complex nonlinear system
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Gamal M; Al-Kashif, M A; Farghaly, A A [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)
2008-02-08
In this paper, we introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.
Chaotic neural network applied to two-dimensional motion control.
Yoshida, Hiroyuki; Kurata, Shuhei; Li, Yongtao; Nara, Shigetoshi
2010-03-01
Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.
A improved Network Security Situation Awareness Model
Directory of Open Access Journals (Sweden)
Li Fangwei
2015-08-01
Full Text Available In order to reflect the situation of network security assessment performance fully and accurately, a new network security situation awareness model based on information fusion was proposed. Network security situation is the result of fusion three aspects evaluation. In terms of attack, to improve the accuracy of evaluation, a situation assessment method of DDoS attack based on the information of data packet was proposed. In terms of vulnerability, a improved Common Vulnerability Scoring System (CVSS was raised and maked the assessment more comprehensive. In terms of node weights, the method of calculating the combined weights and optimizing the result by Sequence Quadratic Program (SQP algorithm which reduced the uncertainty of fusion was raised. To verify the validity and necessity of the method, a testing platform was built and used to test through evaluating 2000 DAPRA data sets. Experiments show that the method can improve the accuracy of evaluation results.
A Networks Approach to Modeling Enzymatic Reactions.
Imhof, P
2016-01-01
Modeling enzymatic reactions is a demanding task due to the complexity of the system, the many degrees of freedom involved and the complex, chemical, and conformational transitions associated with the reaction. Consequently, enzymatic reactions are not determined by precisely one reaction pathway. Hence, it is beneficial to obtain a comprehensive picture of possible reaction paths and competing mechanisms. By combining individually generated intermediate states and chemical transition steps a network of such pathways can be constructed. Transition networks are a discretized representation of a potential energy landscape consisting of a multitude of reaction pathways connecting the end states of the reaction. The graph structure of the network allows an easy identification of the energetically most favorable pathways as well as a number of alternative routes.
Higher-dimensional models of networks
Spivak, David I
2009-01-01
Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations, especially those that include contexts of more than two entities. For these situations, one typically uses hypergraphs or simplicial complexes. In this paper, we provide a precise framework in which graphs, hypergraphs, simplicial complexes, and many other categories, all of which model higher graphs, can be studied side-by-side. We show how to transform a hypergraph into its nearest simplicial analogue, for example. Our framework includes many new categories as well, such as one that models broadcasting networks. We give several examples and applications of these ideas.
The noisy voter model on complex networks
Carro, Adrián; Miguel, Maxi San
2016-01-01
We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an uncorrelated network approximation, allowing to deal with the network structure as parametric heterogeneity. As an illustration, we study the noisy voter model, a modification of the original voter model including random changes of state. The proposed method is able to unfold the dependence of the model not only on the mean degree (the mean-field prediction) but also on more complex averages over the degree distribution. In particular, we find that the degree heterogeneity ---variance of the underlying degree distribution--- has a strong influence on the location of the critical point of a noise-induced, finite-size transition occurring in the model, on the local ordering of the system, and on the functional form of its temporal correlations. Finally, we show how this latter point opens the possibility of infe...
Threshold model of cascades in temporal networks
Karimi, Fariba
2012-01-01
Threshold models try to explain the consequences of social influence like the spread of fads and opinions. Along with models of epidemics, they constitute a major theoretical framework of social spreading processes. In threshold models on static networks, an individual changes her state if a certain fraction of her neighbors has done the same. When there are strong correlations in the temporal aspects of contact patterns, it is useful to represent the system as a temporal network. In such a system, not only contacts but also the time of the contacts are represented explicitly. There is a consensus that bursty temporal patterns slow down disease spreading. However, as we will see, this is not a universal truth for threshold models. In this work, we propose an extension of Watts' classic threshold model to temporal networks. We do this by assuming that an agent is influenced by contacts which lie a certain time into the past. I.e., the individuals are affected by contacts within a time window. In addition to th...
Institute of Scientific and Technical Information of China (English)
Zheng-de Dai
2002-01-01
In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is shown that the global attractor in E0 is actually equal to a global attractor in E1.
Entanglement effects in model polymer networks
Everaers, R.; Kremer, K.
The influence of topological constraints on the local dynamics in cross-linked polymer melts and their contribution to the elastic properties of rubber elastic systems are a long standing problem in statistical mechanics. Polymer networks with diamond lattice connectivity (Everaers and Kremer 1995, Everaers and Kremer 1996a) are idealized model systems which isolate the effect of topology conservation from other sources of quenched disorder. We study their behavior in molecular dynamics simulations under elongational strain. In our analysis we compare the measured, purely entropic shear moduli G to the predictions of statistical mechanical models of rubber elasticity, making extensive use of the microscopic structural and topological information available in computer simulations. We find (Everaers and Kremer 1995) that the classical models of rubber elasticity underestimate the true change in entropy in a deformed network significantly, because they neglect the tension along the contour of the strands which cannot relax due to entanglements (Everaers and Kremer (in preparation)). This contribution and the fluctuations in strained systems seem to be well described by the constrained mode model (Everaers 1998) which allows to treat the crossover from classical rubber elasticity to the tube model for polymer networks with increasing strand length within one transparant formalism. While this is important for the description of the effects we try to do a first quantitative step towards their explanation by topological considerations. We show (Everaers and Kremer 1996a) that for the comparatively short strand lengths of our diamond networks the topology contribution to the shear modulus is proportional to the density of entangled mesh pairs with non-zero Gauss linking number. Moreover, the prefactor can be estimated consistently within a rather simple model developed by Vologodskii et al. and by Graessley and Pearson, which is based on the definition of an entropic
Models and Algorithm for Stochastic Network Designs
Institute of Scientific and Technical Information of China (English)
Anthony Chen; Juyoung Kim; Seungjae Lee; Jaisung Choi
2009-01-01
The network design problem (NDP) is one of the most difficult and challenging problems in trans-portation. Traditional NDP models are often posed as a deterministic bilevel program assuming that all rele-vant inputs are known with certainty. This paper presents three stochastic models for designing transporta-tion networks with demand uncertainty. These three stochastic NDP models were formulated as the ex-pected value model, chance-constrained model, and dependent-chance model in a bilevel programming framework using different criteria to hedge against demand uncertainty. Solution procedures based on the traffic assignment algorithm, genetic algorithm, and Monte-Cado simulations were developed to solve these stochastic NDP models. The nonlinear and nonconvex nature of the bilevel program was handled by the genetic algorithm and traffic assignment algorithm, whereas the stochastic nature was addressed through simulations. Numerical experiments were conducted to evaluate the applicability of the stochastic NDP models and the solution procedure. Results from the three experiments show that the solution procedures are quite robust to different parameter settings.
Microbial growth modelling with artificial neural networks.
Jeyamkonda, S; Jaya, D S; Holle, R A
2001-03-20
There is a growing interest in modelling microbial growth as an alternative to time-consuming, traditional, microbiological enumeration techniques. Several statistical models have been reported to describe the growth of different microorganisms, but there are accuracy problems. An alternate technique 'artificial neural networks' (ANN) for modelling microbial growth is explained and evaluated. Published data were used to build separate general regression neural network (GRNN) structures for modelling growth of Aeromonas hydrophila, Shigella flexneri, and Brochothrix thermosphacta. Both GRNN and published statistical model predictions were compared against the experimental data using six statistical indices. For training data sets, the GRNN predictions were far superior than the statistical model predictions, whereas the GRNN predictions were similar or slightly worse than statistical model predictions for test data sets for all the three data sets. GRNN predictions can be considered good, considering its performance for unseen data. Graphical plots, mean relative percentage residual, mean absolute relative residual, and root mean squared residual were identified as suitable indices for comparing competing models. ANN can now become a vehicle whereby predictive microbiology can be applied in food product development and food safety risk assessment.
Modeling Dynamic Evolution of Online Friendship Network
Institute of Scientific and Technical Information of China (English)
吴联仁; 闫强
2012-01-01
In this paper,we study the dynamic evolution of friendship network in SNS (Social Networking Site).Our analysis suggests that an individual joining a community depends not only on the number of friends he or she has within the community,but also on the friendship network generated by those friends.In addition,we propose a model which is based on two processes:first,connecting nearest neighbors;second,strength driven attachment mechanism.The model reflects two facts:first,in the social network it is a universal phenomenon that two nodes are connected when they have at least one common neighbor;second,new nodes connect more likely to nodes which have larger weights and interactions,a phenomenon called strength driven attachment (also called weight driven attachment).From the simulation results,we find that degree distribution P(k),strength distribution P(s),and degree-strength correlation are all consistent with empirical data.
Features and heterogeneities in growing network models
Ferretti, Luca; Yang, Bin; Marmorini, Giacomo; Bianconi, Ginestra
2011-01-01
Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as personal page, thematic website, news, blog, search engine, social network, ect. or the classification of a gene in a functional module. Moreover the feature of a node can be a continuous variable such as the position of a node in the embedding space. In order to account for these properties, in this paper we provide a generalization of growing network models with preferential attachment that includes the effect of heterogeneous features of the nodes. The main effect of heterogeneity is the emergence of an "effective fitness" for each class of nodes, determining the rate at which nodes acquire new links. Beyond the degree distribution, in this paper we give a full characterization of the other relevant properties of the model. We evaluate the clustering coefficient and show ...
Network Strategies in the Voter Model
Javarone, Marco Alberto
2013-01-01
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 prop...
Performance modeling, loss networks, and statistical multiplexing
Mazumdar, Ravi
2009-01-01
This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of understanding the phenomenon of statistical multiplexing. The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the important ideas of Palm distributions associated with traffic models and their role in performance measures. Also presented are recent ideas of large buffer, and many sources asymptotics that play an important role in understanding statistical multiplexing. I
Artificial Neural Network Model for Predicting Compressive
Directory of Open Access Journals (Sweden)
Salim T. Yousif
2013-05-01
Full Text Available Compressive strength of concrete is a commonly used criterion in evaluating concrete. Although testing of the compressive strength of concrete specimens is done routinely, it is performed on the 28th day after concrete placement. Therefore, strength estimation of concrete at early time is highly desirable. This study presents the effort in applying neural network-based system identification techniques to predict the compressive strength of concrete based on concrete mix proportions, maximum aggregate size (MAS, and slump of fresh concrete. Back-propagation neural networks model is successively developed, trained, and tested using actual data sets of concrete mix proportions gathered from literature. The test of the model by un-used data within the range of input parameters shows that the maximum absolute error for model is about 20% and 88% of the output results has absolute errors less than 10%. The parametric study shows that water/cement ratio (w/c is the most significant factor affecting the output of the model. The results showed that neural networks has strong potential as a feasible tool for predicting compressive strength of concrete.
Influence of Deterministic Attachments for Large Unifying Hybrid Network Model
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Large unifying hybrid network model (LUHPM) introduced the deterministic mixing ratio fd on the basis of the harmonious unification hybrid preferential model, to describe the influence of deterministic attachment to the network topology characteristics,
New Federated Collaborative Networked Organization Model (FCNOM
Directory of Open Access Journals (Sweden)
Morcous M. Yassa
2012-01-01
Full Text Available Formation of Collaborative Networked Organization (CNO usually comes upon expected business opportunities and needs huge of negotiation during its lifecycle, especially to increase the Dynamic Virtual Organization (DVO configuration automation. Decision makers need more comprehensive information about CNO system to support their decisions. Unfortunately, there is no single formal modeling, tool, approach or any comprehensive methodology that covers all perspectives. In spite of there are some approaches to model CNO have been existed, these approaches model the CNO either with respect to the technology, or business without considering organizational behavior, federation modeling, and external environments. The aim of this paper is to propose an integrated framework that combines the existed modeling perspectives, as well as, proposes new ones. Also, it provides clear CNO boundaries. By using this approach the view of CNO environment becomes clear and unified. Also, it minimizes the negotiations within CNO components during its life cycle, supports DVO configuration automation, as well as, helps decision making for DVO, and achieves harmonization between CNO partners. The proposed FCNOM utilizes CommonKADS methodology organization model for describing CNO components. Insurance Collaborative Network has been used as an example to proof the proposed FCNOM model.
Systems biology of plant molecular networks: from networks to models
Valentim, F.L.
2015-01-01
Developmental processes are controlled by regulatory networks (GRNs), which are tightly coordinated networks of transcription factors (TFs) that activate and repress gene expression within a spatial and temporal context. In Arabidopsis thaliana, the key components and network structures of the GRNs
Attractor for a Viscous Coupled Camassa-Holm Equation
Directory of Open Access Journals (Sweden)
Tian Lixin
2010-01-01
Full Text Available The global existence of solution to a viscous coupled Camassa-Holm equation with the periodic boundary condition is investigated. We obtain the compact and bounded absorbing set and the existence of the global attractor for the viscous coupled Camassa-Holm equation in by uniform prior estimate.
On the Supersymmetry of Bianchi attractors in Gauged supergravity
Chakrabarty, Bidisha; Samanta, Rickmoy
2016-01-01
Bianchi attractors are near horizon geometries with homogeneous symmetries in the spatial directions. We construct supersymmetric Bianchi attractors in $\\mathcal{N}=2, d=4,5$ gauged supergravity coupled to vector and hypermultiplets. In $d=4$, in the Bianchi I class we construct an electric $1/4$ BPS $AdS_2\\times\\mathbb{R}^2$ geometry. In $d=5$ we consider gauged supergravity with a generic gauging of symmetries of the scalar manifold and the R symmetry. Analyzing the gaugino and hyperino conditions we show that when the fermionic shifts do not vanish there are no supersymmetric Bianchi attractors. When the central charge satisfies an extremization condition, some of the fermionic shifts vanish and supersymmetry requires that the symmetries of the scalar manifold be ungauged. This allows supersymmetric Bianchi attractors sourced by massless gauge fields and a cosmological constant. In the Bianchi I class we show that the anisotropic $AdS_3\\times\\mathbb{R}^2$ solution is $1/2$ BPS. We also construct a new clas...
Uniform perfectness of the attractor of bi-Lipschitz IFS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we prove that the attractor of C1, α bi-Lipschitz IFS in R is uniformly perfect if it is not a singleton. Then we construct an example to show that this does not hold for C1 bi-Lipschitz IFS in Rn.
Multistability and hidden attractors in a relay system with hysteresis
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Rubanov, Vasily G.
2015-01-01
For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the nei...
Attractor horizons in six-dimensional type IIB supergravity
Energy Technology Data Exchange (ETDEWEB)
Astefanesei, Dumitru, E-mail: dumitru.astefanesei@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Miskovic, Olivera, E-mail: olivera.miskovic@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Universidad Andres Bello, Departamento de Ciencias Fisicas, Republica 220, Santiago (Chile)
2012-08-14
We consider near horizon geometries of extremal black holes in six-dimensional type IIB supergravity. In particular, we use the entropy function formalism to compute the charges and thermodynamic entropy of these solutions. We also comment on the role of attractor mechanism in understanding the entropy of the Hopf T-dual solutions in type IIA supergravity.
Recurrence quantification analysis in Liu's attractor
Energy Technology Data Exchange (ETDEWEB)
Balibrea, Francisco [Universidad de Murcia, Departamento de Matematicas, Campus de Espinardo, 30100 Murcia (Spain)], E-mail: balibrea@um.es; Caballero, M. Victoria [Universidad de Murcia, Departamento de Metodos Cuantitativos para la Economia, Campus de Espinardo, 30100 Murcia (Spain)], E-mail: mvictori@um.es; Molera, Lourdes [Universidad de Murcia, Departamento de Metodos Cuantitativos para la Economia, Campus de Espinardo, 30100 Murcia (Spain)
2008-05-15
Recurrence Quantification Analysis is used to detect transitions chaos to periodical states or chaos to chaos in a new dynamical system proposed by Liu et al. This system contains a control parameter in the second equation and was originally introduced to investigate the forming mechanism of the compound structure of the chaotic attractor which exists when the control parameter is zero.
MAXIMUM-LIKELIHOOD-ESTIMATION OF THE ENTROPY OF AN ATTRACTOR
SCHOUTEN, JC; TAKENS, F; VANDENBLEEK, CM
1994-01-01
In this paper, a maximum-likelihood estimate of the (Kolmogorov) entropy of an attractor is proposed that can be obtained directly from a time series. Also, the relative standard deviation of the entropy estimate is derived; it is dependent on the entropy and on the number of samples used in the est
A non-reward attractor theory of depression.
Rolls, Edmund T
2016-09-01
A non-reward attractor theory of depression is proposed based on the operation of the lateral orbitofrontal cortex and supracallosal cingulate cortex. The orbitofrontal cortex contains error neurons that respond to non-reward for many seconds in an attractor state that maintains a memory of the non-reward. The human lateral orbitofrontal cortex is activated by non-reward during reward reversal, and by a signal to stop a response that is now incorrect. Damage to the human orbitofrontal cortex impairs reward reversal learning. Not receiving reward can produce depression. The theory proposed is that in depression, this lateral orbitofrontal cortex non-reward system is more easily triggered, and maintains its attractor-related firing for longer. This triggers negative cognitive states, which in turn have positive feedback top-down effects on the orbitofrontal cortex non-reward system. Treatments for depression, including ketamine, may act in part by quashing this attractor. The mania of bipolar disorder is hypothesized to be associated with oversensitivity and overactivity in the reciprocally related reward system in the medial orbitofrontal cortex and pregenual cingulate cortex.
Shadow Systems and Attractors in Reaction-Diffusion Equations,
1987-04-01
0 gives some information about the types of singular solutions that can occur at D1 = 0 . Ideally, one would then hope to obtain an attractor AD1,D...for D2 ) d°l and all D1 > 0. This 1’ 2 will involve a very difficult analysis of the existence and stability of large amplitude singular solutions near
Uniform attractors of non-autonomous dissipative semilinear wave equations
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The asymptotic long time behaviors of a certain type of non-autonomous dissipative semilinear wave equations are studied. The existence of uniform attractors is proved and their upper bounds for both Hausdorff and Fractal dimensions of uniform are given when the external force satisfies suitable conditions.
Attractors for stochastic lattice dynamical systems with a multiplicative noise
Institute of Scientific and Technical Information of China (English)
Tomás CARABALLO; Kening LU
2008-01-01
In this paper,we consider a stochastic lattice differential equation with diffusive nearest neighbor interaction,a dissipative nonlinear reaction term,and multiplicative white noise at each node.We prove the existence of a compact global random attractor which,pulled back,attracts tempered random bounded sets.
Network Data: Statistical Theory and New Models
2016-02-17
max scale): Number of graduating undergraduates funded by a DoD funded Center of Excellence grant for Education , Research and Engineering: The number...structured networks The major goals of this project are to develop and implement algorithms based on high dimensional statis- tics theory, especially...invariance to local deformation. These techniques have been adapted to modeling higher order visual areas such as area MT on two experimental datasets provided
Alexandrov, Natalia (Technical Monitor); Kuby, Michael; Tierney, Sean; Roberts, Tyler; Upchurch, Christopher
2005-01-01
This report reviews six classes of models that are used for studying transportation network topologies. The report is motivated by two main questions. First, what can the "new science" of complex networks (scale-free, small-world networks) contribute to our understanding of transport network structure, compared to more traditional methods? Second, how can geographic information systems (GIS) contribute to studying transport networks? The report defines terms that can be used to classify different kinds of models by their function, composition, mechanism, spatial and temporal dimensions, certainty, linearity, and resolution. Six broad classes of models for analyzing transport network topologies are then explored: GIS; static graph theory; complex networks; mathematical programming; simulation; and agent-based modeling. Each class of models is defined and classified according to the attributes introduced earlier. The paper identifies some typical types of research questions about network structure that have been addressed by each class of model in the literature.
Electronic circuits modeling using artificial neural networks
Directory of Open Access Journals (Sweden)
Andrejević Miona V.
2003-01-01
Full Text Available In this paper artificial neural networks (ANN are applied to modeling of electronic circuits. ANNs are used for application of the black-box modeling concept in the time domain. Modeling process is described, so the topology of the ANN, the testing signal used for excitation, together with the complexity of ANN are considered. The procedure is first exemplified in modeling of resistive circuits. MOS transistor, as a four-terminal device, is modeled. Then nonlinear negative resistive characteristic is modeled in order to be used as a piece-wise linear resistor in Chua's circuit. Examples of modeling nonlinear dynamic circuits are given encompassing a variety of modeling problems. A nonlinear circuit containing quartz oscillator is considered for modeling. Verification of the concept is performed by verifying the ability of the model to generalize i.e. to create acceptable responses to excitations not used during training. Implementation of these models within a behavioral simulator is exemplified. Every model is implemented in realistic surrounding in order to show its interaction, and of course, its usage and purpose.
Modeling social influence through network autocorrelation : constructing the weight matrix
Leenders, RTAJ
2002-01-01
Many physical and social phenomena are embedded within networks of interdependencies, the so-called 'context' of these phenomena. In network analysis, this type of process is typically modeled as a network autocorrelation model. Parameter estimates and inferences based on autocorrelation models, hin
A Universal Model of Commuting Networks
Lenormand, Maxime; Gargiulo, Floriana; Deffuant, Guillaume
2012-01-01
We test a recently proposed model of commuting networks on 80 case studies from different regions of the world (Europe and United-States) and with geographic units of different sizes (municipality, county, region). The model takes as input the number of commuters coming in and out of each geographic unit and generates the matrix of commuting flows betwen the geographic units. We show that the single parameter of the model, which rules the compromise between the influence of the distance and job opportunities, follows a universal law that depends only on the average surface of the geographic units. We verified that the law derived from a part of the case studies yields accurate results on other case studies. We also show that our model significantly outperforms the two other approaches proposing a universal commuting model (Balcan et al. (2009); Simini et al. (2012)), particularly when the geographic units are small (e.g. municipalities).
A network model for Ebola spreading.
Rizzo, Alessandro; Pedalino, Biagio; Porfiri, Maurizio
2016-04-01
The availability of accurate models for the spreading of infectious diseases has opened a new era in management and containment of epidemics. Models are extensively used to plan for and execute vaccination campaigns, to evaluate the risk of international spreadings and the feasibility of travel bans, and to inform prophylaxis campaigns. Even when no specific therapeutical protocol is available, as for the Ebola Virus Disease (EVD), models of epidemic spreading can provide useful insight to steer interventions in the field and to forecast the trend of the epidemic. Here, we propose a novel mathematical model to describe EVD spreading based on activity driven networks (ADNs). Our approach overcomes the simplifying assumption of homogeneous mixing, which is central to most of the mathematically tractable models of EVD spreading. In our ADN-based model, each individual is not bound to contact every other, and its network of contacts varies in time as a function of an activity potential. Our model contemplates the possibility of non-ideal and time-varying intervention policies, which are critical to accurately describe EVD spreading in afflicted countries. The model is calibrated from field data of the 2014 April-to-December spreading in Liberia. We use the model as a predictive tool, to emulate the dynamics of EVD in Liberia and offer a one-year projection, until December 2015. Our predictions agree with the current vision expressed by professionals in the field, who consider EVD in Liberia at its final stage. The model is also used to perform a what-if analysis to assess the efficacy of timely intervention policies. In particular, we show that an earlier application of the same intervention policy would have greatly reduced the number of EVD cases, the duration of the outbreak, and the infrastructures needed for the implementation of the intervention.