Statistical mechanics of attractor neural network models with synaptic depression
Synaptic depression is known to control gain for presynaptic inputs. Since cortical neurons receive thousands of presynaptic inputs, and their outputs are fed into thousands of other neurons, the synaptic depression should influence macroscopic properties of neural networks. We employ simple neural network models to explore the macroscopic effects of synaptic depression. Systems with the synaptic depression cannot be analyzed due to asymmetry of connections with the conventional equilibrium statistical-mechanical approach. Thus, we first propose a microscopic dynamical mean field theory. Next, we derive macroscopic steady state equations and discuss the stabilities of steady states for various types of neural network models.
Attractor dynamics in local neuronal networks
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.
A Hybrid Oscillatory Interference/Continuous Attractor Network Model of Grid Cell Firing
Bush, D.; Burgess, N.
2014-01-01
Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some aspects of the two mechanisms are complementary, suggesting that a combined model may best account fo...
Algorithms for Finding Small Attractors in Boolean Networks
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.
Si Wu
2016-02-01
Full Text Available Owing to its many computationally desirable properties, the model of continuous attractor neural networks (CANNs has been successfully applied to describe the encoding of simple continuous features in neural systems, such as orientation, moving direction, head direction, and spatial location of objects. Recent experimental and computational studies revealed that complex features of external inputs may also be encoded by low-dimensional CANNs embedded in the high-dimensional space of neural population activity. The new experimental data also confirmed the existence of the M-shaped correlation between neuronal responses, which is a correlation structure associated with the unique dynamics of CANNs. This body of evidence, which is reviewed in this report, suggests that CANNs may serve as a canonical model for neural information representation.
Pattern recognition using asymmetric attractor neural networks
Jin, Tao; Zhao, Hong
2005-12-01
The asymmetric attractor neural networks designed by the Monte Carlo- (MC-) adaptation rule are shown to be promising candidates for pattern recognition. In such a neural network with relatively low symmetry, when the members of a set of template patterns are stored as fixed-point attractors, their attraction basins are shown to be isolated islands embedded in a “chaotic sea.” The sizes of these islands can be controlled by a single parameter. We show that these properties can be used for effective pattern recognition and rejection. In our method, the pattern to be identified is attracted to a template pattern or a chaotic attractor. If the difference between the pattern to be identified and the template pattern is smaller than a predescribed threshold, the pattern is attracted to the template pattern automatically and thus is identified as belonging to this template pattern. Otherwise, it wanders in a chaotic attractor for ever and thus is rejected as an unknown pattern. The maximum sizes of these islands allowed by this kind of neural networks are determined by a modified MC-adaptation rule which are shown to be able to dramatically enlarge the sizes of the islands. We illustrate the use of our method for pattern recognition and rejection with an example of recognizing a set of Chinese characters.
Pattern recognition using asymmetric attractor neural networks
The asymmetric attractor neural networks designed by the Monte Carlo- (MC-) adaptation rule are shown to be promising candidates for pattern recognition. In such a neural network with relatively low symmetry, when the members of a set of template patterns are stored as fixed-point attractors, their attraction basins are shown to be isolated islands embedded in a ''chaotic sea.'' The sizes of these islands can be controlled by a single parameter. We show that these properties can be used for effective pattern recognition and rejection. In our method, the pattern to be identified is attracted to a template pattern or a chaotic attractor. If the difference between the pattern to be identified and the template pattern is smaller than a predescribed threshold, the pattern is attracted to the template pattern automatically and thus is identified as belonging to this template pattern. Otherwise, it wanders in a chaotic attractor for ever and thus is rejected as an unknown pattern. The maximum sizes of these islands allowed by this kind of neural networks are determined by a modified MC-adaptation rule which are shown to be able to dramatically enlarge the sizes of the islands. We illustrate the use of our method for pattern recognition and rejection with an example of recognizing a set of Chinese characters
Cortical attractor network dynamics with diluted connectivity.
Rolls, Edmund T; Webb, Tristan J
2012-01-24
The connectivity of the cerebral cortex is diluted, with the probability of excitatory connections between even nearby pyramidal cells rarely more than 0.1, and in the hippocampus 0.04. To investigate the extent to which this diluted connectivity affects the dynamics of attractor networks in the cerebral cortex, we simulated an integrate-and-fire attractor network taking decisions between competing inputs with diluted connectivity of 0.25 or 0.1, and with the same number of synaptic connections per neuron for the recurrent collateral synapses within an attractor population as for full connectivity. The results indicated that there was less spiking-related noise with the diluted connectivity in that the stability of the network when in the spontaneous state of firing increased, and the accuracy of the correct decisions increased. The decision times were a little slower with diluted than with complete connectivity. Given that the capacity of the network is set by the number of recurrent collateral synaptic connections per neuron, on which there is a biological limit, the findings indicate that the stability of cortical networks, and the accuracy of their correct decisions or memory recall operations, can be increased by utilizing diluted connectivity and correspondingly increasing the number of neurons in the network, with little impact on the speed of processing of the cortex. Thus diluted connectivity can decrease cortical spiking-related noise. In addition, we show that the Fano factor for the trial-to-trial variability of the neuronal firing decreases from the spontaneous firing state value when the attractor network makes a decision. This article is part of a Special Issue entitled "Neural Coding". PMID:21875702
Topological origin of global attractors in gene regulatory networks
Zhang, YunJun; Ouyang, Qi; Geng, Zhi
2015-02-01
Fixed-point attractors with global stability manifest themselves in a number of gene regulatory networks. This property indicates the stability of regulatory networks against small state perturbations and is closely related to other complex dynamics. In this paper, we aim to reveal the core modules in regulatory networks that determine their global attractors and the relationship between these core modules and other motifs. This work has been done via three steps. Firstly, inspired by the signal transmission in the regulation process, we extract the model of chain-like network from regulation networks. We propose a module of "ideal transmission chain (ITC)", which is proved sufficient and necessary (under certain condition) to form a global fixed-point in the context of chain-like network. Secondly, by examining two well-studied regulatory networks (i.e., the cell-cycle regulatory networks of Budding yeast and Fission yeast), we identify the ideal modules in true regulation networks and demonstrate that the modules have a superior contribution to network stability (quantified by the relative size of the biggest attraction basin). Thirdly, in these two regulation networks, we find that the double negative feedback loops, which are the key motifs of forming bistability in regulation, are connected to these core modules with high network stability. These results have shed new light on the connection between the topological feature and the dynamic property of regulatory networks.
Reconstruction of the El Nino attractor with neural networks
Based on a combined data set of sea surface temperature, zonal surface wind stress and upper ocean heat content the dynamics of the El Nino phenomenon is investigated. In a reduced phase space spanned by the first four EOFs two different stochastic models are estimated from the data. A nonlinear model represented by a simulated neural network is compared with a linear model obtained with the Principal Oscillation Pattern (POP) analysis. While the linear model is limited to damped oscillations onto a fix point attractor, the nonlinear model recovers a limit cycle attractor. This indicates that the real system is located above the bifurcation point in parameter space supporting self-sustained oscillations. The results are discussed with respect to consistency with current theory. (orig.)
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.
Spatial asymmetric retrieval states in binary attractor neural network
In this paper we show that during the retrieval process in a binary Hebb attractor neural network, spatial localized states can be observed when the connectivity of the network is distance-dependent and there is an asymmetry between the retrieval and the learning states
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…
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. PMID:27119986
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. PMID:21778527
Detecting a Singleton Attractor in a Boolean Network Utilizing SAT Algorithms
Tamura, Takeyuki; Akutsu, Tatsuya
The Boolean network (BN) is a mathematical model of genetic networks. It is known that detecting a singleton attractor, which is also called a fixed point, is NP-hard even for AND/OR BNs (i.e., BNs consisting of AND/OR nodes), where singleton attractors correspond to steady states. Though a naive algorithm can detect a singleton attractor for an AND/OR BN in O(n 2n) time, no O((2-ε)n) (ε > 0) time algorithm was known even for an AND/OR BN with non-restricted indegree, where n is the number of nodes in a BN. In this paper, we present an O(1.787n) time algorithm for detecting a singleton attractor of a given AND/OR BN, along with related results. We also show that detection of a singleton attractor in a BN with maximum indegree two is NP-hard and can be polynomially reduced to a satisfiability problem.
Boolean Factor Analysis by Attractor Neural Network
Frolov, A. A.; Húsek, Dušan; Muraviev, I. P.; Polyakov, P.Y.
2007-01-01
Roč. 18, č. 3 (2007), s. 698-707. ISSN 1045-9227 R&D Projects: GA AV ČR 1ET100300419; GA ČR GA201/05/0079 Institutional research plan: CEZ:AV0Z10300504 Keywords : recurrent neural network * Hopfield-like neural network * associative memory * unsupervised learning * neural network architecture * neural network application * statistics * Boolean factor analysis * dimensionality reduction * features clustering * concepts search * information retrieval Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.769, year: 2007
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.
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. PMID:26754972
Effect of synapse dilution on the memory retrieval in structured attractor neural networks
BRUNEL,N
1993-01-01
We investigate a simple model of structured attractor neural network (ANN). In this network a module codes for the category of the stored information, while another group of neurons codes for the remaining information. The probability distribution of stabilities of the patterns and the prototypes of the categories are calculated, for two different synaptic structures. The stability of the prototypes is shown to increase when the fraction of neurons coding for the category goes down. Then the ...
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. PMID:26997659
Navigating cancer network attractors for tumor-specific therapy
Creixell, Pau; Schoof, Erwin; Erler, Janine Terra;
2012-01-01
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.......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...
Neural attractor network for application in visual field data classification
The purpose was to introduce a novel method for computer-based classification of visual field data derived from perimetric examination, that may act as a ' counsellor', providing an independent 'second opinion' to the diagnosing physician. The classification system consists of a Hopfield-type neural attractor network that obtains its input data from perimetric examination results. An iterative relaxation process determines the states of the neurons dynamically. Therefore, even 'noisy' perimetric output, e.g., early stages of a disease, may eventually be classified correctly according to the predefined idealized visual field defect (scotoma) patterns, stored as attractors of the network, that are found with diseases of the eye, optic nerve and the central nervous system. Preliminary tests of the classification system on real visual field data derived from perimetric examinations have shown a classification success of over 80%. Some of the main advantages of the Hopfield-attractor-network-based approach over feed-forward type neural networks are: (1) network architecture is defined by the classification problem; (2) no training is required to determine the neural coupling strengths; (3) assignment of an auto-diagnosis confidence level is possible by means of an overlap parameter and the Hamming distance. In conclusion, the novel method for computer-based classification of visual field data, presented here, furnishes a valuable first overview and an independent 'second opinion' in judging perimetric examination results, pointing towards a final diagnosis by a physician. It should not be considered a substitute for the diagnosing physician. Thanks to the worldwide accessibility of the Internet, the classification system offers a promising perspective towards modern computer-assisted diagnosis in both medicine and tele-medicine, for example and in particular, with respect to non-ophthalmic clinics or in communities where perimetric expertise is not readily available
Neural attractor network for application in visual field data classification
Fink, Wolfgang
2004-07-01
The purpose was to introduce a novel method for computer-based classification of visual field data derived from perimetric examination, that may act as a ' counsellor', providing an independent 'second opinion' to the diagnosing physician. The classification system consists of a Hopfield-type neural attractor network that obtains its input data from perimetric examination results. An iterative relaxation process determines the states of the neurons dynamically. Therefore, even 'noisy' perimetric output, e.g., early stages of a disease, may eventually be classified correctly according to the predefined idealized visual field defect (scotoma) patterns, stored as attractors of the network, that are found with diseases of the eye, optic nerve and the central nervous system. Preliminary tests of the classification system on real visual field data derived from perimetric examinations have shown a classification success of over 80%. Some of the main advantages of the Hopfield-attractor-network-based approach over feed-forward type neural networks are: (1) network architecture is defined by the classification problem; (2) no training is required to determine the neural coupling strengths; (3) assignment of an auto-diagnosis confidence level is possible by means of an overlap parameter and the Hamming distance. In conclusion, the novel method for computer-based classification of visual field data, presented here, furnishes a valuable first overview and an independent 'second opinion' in judging perimetric examination results, pointing towards a final diagnosis by a physician. It should not be considered a substitute for the diagnosing physician. Thanks to the worldwide accessibility of the Internet, the classification system offers a promising perspective towards modern computer-assisted diagnosis in both medicine and tele-medicine, for example and in particular, with respect to non-ophthalmic clinics or in communities where perimetric expertise is not readily available.
Neural attractor network for application in visual field data classification
Fink, Wolfgang [Doheny Eye Institute, Keck School of Medicine at the University of Southern California, Los Angeles, CA 90033 (United States); California Institute of Technology, Pasadena, CA 91125 (United States)
2004-07-07
The purpose was to introduce a novel method for computer-based classification of visual field data derived from perimetric examination, that may act as a ' counsellor', providing an independent 'second opinion' to the diagnosing physician. The classification system consists of a Hopfield-type neural attractor network that obtains its input data from perimetric examination results. An iterative relaxation process determines the states of the neurons dynamically. Therefore, even 'noisy' perimetric output, e.g., early stages of a disease, may eventually be classified correctly according to the predefined idealized visual field defect (scotoma) patterns, stored as attractors of the network, that are found with diseases of the eye, optic nerve and the central nervous system. Preliminary tests of the classification system on real visual field data derived from perimetric examinations have shown a classification success of over 80%. Some of the main advantages of the Hopfield-attractor-network-based approach over feed-forward type neural networks are: (1) network architecture is defined by the classification problem; (2) no training is required to determine the neural coupling strengths; (3) assignment of an auto-diagnosis confidence level is possible by means of an overlap parameter and the Hamming distance. In conclusion, the novel method for computer-based classification of visual field data, presented here, furnishes a valuable first overview and an independent 'second opinion' in judging perimetric examination results, pointing towards a final diagnosis by a physician. It should not be considered a substitute for the diagnosing physician. Thanks to the worldwide accessibility of the Internet, the classification system offers a promising perspective towards modern computer-assisted diagnosis in both medicine and tele-medicine, for example and in particular, with respect to non-ophthalmic clinics or in communities where
Multitasking attractor networks with neuronal threshold noise.
Agliari, Elena; Barra, Adriano; Galluzzi, Andrea; Isopi, Marco
2014-01-01
We consider the multitasking associative network in the low-storage limit and we study its phase diagram with respect to the noise level T and the degree d of dilution in pattern entries. We find that the system is characterized by a rich variety of stable states, including pure states, parallel retrieval states, hierarchically organized states and symmetric mixtures (remarkably, both even and odd), whose complexity increases as the number of patterns P grows. The analysis is performed both analytically and numerically: Exploiting techniques based on partial differential equations, we are able to get the self-consistencies for the order parameters. Such self-consistency equations are then solved and the solutions are further checked through stability theory to catalog their organizations into the phase diagram, which is outlined at the end. This is a further step towards the understanding of spontaneous parallel processing in associative networks. PMID:24121044
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.
Hyperbolic Plykin attractor can exist in neuron models
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...
Robustness of unstable attractors in arbitrarily sized pulse-coupled networks with delay
We consider arbitrarily large networks of pulse-coupled oscillators with non-zero delay where the coupling is given by the Mirollo–Strogatz function. We prove that such systems have unstable attractors (saddle periodic orbits whose stable set has non-empty interior) in an open parameter region for three or more oscillators. The evolution operator of the system can be discontinuous and we propose an improved model with continuous evolution operator
Algorithms and Complexity Analyses for Control of Singleton Attractors in Boolean Networks
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.
A Model Combining Oscillations and Attractor Dynamics for Generation of Grid Cell Firing
Michael E Hasselmo; Brandon, Mark P.
2012-01-01
Different models have been able to account for different features of the data on grid cell firing properties, including the relationship of grid cells to cellular properties and network oscillations. This paper describes a model that combines elements of two major classes of models of grid cells: models using interference of oscillations and models using attractor dynamics. This model includes a population of units with oscillatory input representing input from the medial septum. These units ...
Coexisting chaotic attractors in a single neuron model with adapting feedback synapse
Li Chunguang [Institute of Electronic Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: cgli@uestc.edu.cn; Chen Guanrong [Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong (China)]. E-mail: gchen@ee.cityu.edu.hk
2005-03-01
In this paper, we consider the nonlinear dynamical behavior of a single neuron model with adapting feedback synapse, and show that chaotic behaviors exist in this model. In some parameter domain, we observe two coexisting chaotic attractors, switching from the coexisting chaotic attractors to a connected chaotic attractor, and then switching back to the two coexisting chaotic attractors. We confirm the chaoticity by simulations with phase plots, waveform plots, and power spectra.
Effect of synapse dilution on the memory retrieval in structured attractor neural networks
Brunel, N.
1993-08-01
We investigate a simple model of structured attractor neural network (ANN). In this network a module codes for the category of the stored information, while another group of neurons codes for the remaining information. The probability distribution of stabilities of the patterns and the prototypes of the categories are calculated, for two different synaptic structures. The stability of the prototypes is shown to increase when the fraction of neurons coding for the category goes down. Then the effect of synapse destruction on the retrieval is studied in two opposite situations : first analytically in sparsely connected networks, then numerically in completely connected ones. In both cases the behaviour of the structured network and that of the usual homogeneous networks are compared. When lesions increase, two transitions are shown to appear in the behaviour of the structured network when one of the patterns is presented to the network. After the first transition the network recognizes the category of the pattern but not the individual pattern. After the second transition the network recognizes nothing. These effects are similar to syndromes caused by lesions in the central visual system, namely prosopagnosia and agnosia. In both types of networks (structured or homogeneous) the stability of the prototype is greater than the stability of individual patterns, however the first transition, for completely connected networks, occurs only when the network is structured.
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.
Unstable periodic orbits and attractor of the barotropic ocean model
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.
Entropies from Markov Models as Complexity Measures of Embedded Attractors
Julián D. Arias-Londoño
2015-06-01
Full Text Available This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes.
Attractor and Boundedness of Switched Stochastic Cohen-Grossberg Neural Networks
Chuangxia Huang
2016-01-01
Full Text Available We address the problem of stochastic attractor and boundedness of a class of switched Cohen-Grossberg neural networks (CGNN with discrete and infinitely distributed delays. With the help of stochastic analysis technology, the Lyapunov-Krasovskii functional method, linear matrix inequalities technique (LMI, and the average dwell time approach (ADT, some novel sufficient conditions regarding the issues of mean-square uniformly ultimate boundedness, the existence of a stochastic attractor, and the mean-square exponential stability for the switched Cohen-Grossberg neural networks are established. Finally, illustrative examples and their simulations are provided to illustrate the effectiveness of the proposed results.
The asymptotic number of attractors in the random map model
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as its image. We derive here explicit formulae for the statistical distribution of the number of attractors in the system. As in related results, the number of operations involved by our formulae increases exponentially with n; therefore, they are not directly applicable to study the behaviour of systems where n is large. However, our formulae can be used to derive useful asymptotic expressions, as we show
Unraveling chaotic attractors by complex networks and measurements of stock market complexity
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
By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness, and global exponential stability of periodic solution for shunting inhibitory cellular neural networks with impulses, dxij/dt=-aijxij-ΣCkl(set-membershipsign)Nr(i,j)Cijklfij[xkl(t)]xij+Lij(t), t>0,t≠tk; Δxij(tk)=xij(tk+)-xij(tk-)=Ik[xij(tk)], k=1,2,... . Furthermore, the numerical simulation shows that our system can occur in many forms of complexities, including periodic oscillation and chaotic strange attractor. To the best of our knowledge, these results have been obtained for the first time. Some researchers have introduced impulses into their models, but analogous results have never been found.
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.
Lorenz-like attractors in a nonholonomic model of a rattleback
Gonchenko, A. S.; Gonchenko, S. V.
2015-09-01
We study chaotic dynamics in a nonholonomic model of a rattleback stone. We show that, for certain values of parameters that characterise geometrical and physical properties of the stone, a strange Lorenz-like attractor is observed in the model. We also study bifurcation scenarios for the appearance and break-down of this attractor.
Storage capacity of attractor neural networks with depressing synapses
We compute the capacity of a binary neural network with dynamic depressing synapses to store and retrieve an infinite number of patterns. We use a biologically motivated model of synaptic depression and a standard mean-field approach. We find that at T=0 the critical storage capacity decreases with the degree of the depression. We confirm the validity of our main mean-field results with numerical simulations
Paul Miller
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.
Explicit construction of chaotic attractors in Glass networks
Chaotic dynamics have been observed in example piecewise-affine models of gene regulatory networks. Here we show how the underlying Poincaré maps can be explicitly constructed. To do this, we proceed in two steps. First, we consider a limit case, where some parameters tend to ∞, and then consider the case with finite parameters as a perturbation of the previous one. We provide a detailed example of this construction, in 3-d, with several thresholds per variable. This construction is essentially a topological horseshoe map. We show that the limit situation is conjugate to the golden mean shift, and is thus chaotic. Then, we show that chaos is preserved for large parameters, relying on the structural stability of the return map in the limit case. We also describe a method to embed systems with several thresholds into binary systems, of higher dimensions. This shows that all results found for systems having several thresholds remain valid in the binary case.
Random Boolean Networks and Attractors of their Intersecting Circuits
Demongeot, Jacques; Elena, Adrien; Noual, Mathilde; Sené, Sylvain
2011-01-01
International audience The multi-scale strategy in studying biological regulatory networks analysis is based on two level of analysis. The first level is structural and consists in examining the architecture of the interaction graph underlying the network and the second level is functional and analyse the regulatory properties of the network. We apply this dual approach to the "immunetworks" involved in the control of the immune system. As a result, we show that the small number of attract...
Stochastic sensitivity analysis of the attractors for the randomly forced Ricker model with delay
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
Raza, Muhammad; Myrzakulov, Kairat; Momeni, Davood; Myrzakulov, Ratbay
2016-05-01
In this paper,we investigate the mathematical modeling for the cosmological attractors propagated in mimetic gravity upon which an interacting dark energy-dark matter is supposed to be existed. The average value of the interaction of these percentages, namely Γ i say, may be used to investigate generally the modeling of an attractor; the actual value could only be determined by data in any particular case. We have seen, for example, that it was led to investigate the subject of initially invariant submanifolds.
Monasson, R.; Rosay, S.
2014-03-01
The dynamics of a neural model for hippocampal place cells storing spatial maps is studied. In the absence of external input, depending on the number of cells and on the values of control parameters (number of environments stored, level of neural noise, average level of activity, connectivity of place cells), a "clump" of spatially localized activity can diffuse or remains pinned due to crosstalk between the environments. In the single-environment case, the macroscopic coefficient of diffusion of the clump and its effective mobility are calculated analytically from first principles and corroborated by numerical simulations. In the multienvironment case the heights and the widths of the pinning barriers are analytically characterized with the replica method; diffusion within one map is then in competition with transitions between different maps. Possible mechanisms enhancing mobility are proposed and tested.
Bistable Chimera Attractors on a Triangular Network of Oscillator Populations
Martens, Erik Andreas
2010-01-01
. This triangular network is the simplest discretization of a continuous ring of oscillators. Yet it displays an unexpectedly different behavior: in contrast to the lone stable chimera observed in continuous rings of oscillators, we find that this system exhibits two coexisting stable chimeras. Both...... chimeras are, as usual, born through a saddle-node bifurcation. As the coupling becomes increasingly local in nature they lose stability through a Hopf bifurcation, giving rise to breathing chimeras, which in turn get destroyed through a homoclinic bifurcation. Remarkably, one of the chimeras reemerges by...
Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators
We study the dynamics of the large N limit of the Kuramoto model of coupled phase oscillators, subject to white noise. We introduce the notion of shadow inertial manifold and we prove their existence for this model, supporting the fact that the long-term dynamics of this model is finite dimensional. Following this, we prove that the global attractor of this model takes one of two forms. When coupling strength is below a critical value, the global attractor is a single equilibrium point corresponding to an incoherent state. Otherwise, when coupling strength is beyond this critical value, the global attractor is a two-dimensional disc composed of radial trajectories connecting a saddle-point equilibrium (the incoherent state) to an invariant closed curve of locally stable equilibria (partially synchronized state). Our analysis hinges, on the one hand, upon sharp existence and uniqueness results and their consequence for the existence of a global attractor, and, on the other hand, on the study of the dynamics in the vicinity of the incoherent and coherent (or synchronized) equilibria. We prove in particular nonlinear stability of each synchronized equilibrium, and normal hyperbolicity of the set of such equilibria. We explore mathematically and numerically several properties of the global attractor, in particular we discuss the limit of this attractor as noise intensity decreases to zero
Chaotic inflation limits for non-minimal models with a Starobinsky attractor
We investigate inflationary attractor points by analysing 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 φ2n-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, contrary to the strong coupling Starobinsky attractor
Study of the attractor structure of an agent-based sociological model
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 Barabasi-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.
Study of the attractor structure of an agent-based sociological model
Timpanaro, Andre M; Prado, Carmen P C, E-mail: timpa@if.usp.br, E-mail: prado@if.usp.br [Instituto de Fisica da Universidade de Sao Paulo, Sao Paulo (Brazil)
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 Barabasi-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.
A model combining oscillations and attractor dynamics for generation of grid cell firing
Michael E Hasselmo
2012-05-01
Full Text Available Different models have been able to account for different features of the data on grid cell firing properties, including the relationship of grid cells to cellular properties and network oscillations. This paper describes a model that combines elements of two major classes of models of grid cells: models using interference of oscillations and models using attractor dynamics. This model includes a population of units with oscillatory input representing input from the medial septum. These units are termed heading angle cells because their connectivity depends upon heading angle in the environment as well as the spatial phase coded by the cell. These cells project to a population of grid cells. The sum of the heading angle input results in standing waves of circularly symmetric input to the grid cell population. Feedback from the grid cell population increases the activity of subsets of the heading angle cells, resulting in the network settling into activity patterns that resemble the patterns of firing fields in a population of grid cells. The properties of heading angle cells firing as conjunctive grid-by-head-direction cells can shift the grid cell firing according to movement velocity. The pattern of interaction of oscillations requires use of separate populations that fire on alternate cycles of the net theta rhythmic input to grid cells, similar to recent neurophysiological data on theta cycle skipping in medial entorhinal cortex.
How does noise affect the structure of a chaotic attractor: A recurrence network perspective
Jacob, Rinku; Misra, R; Ambika, G
2015-01-01
We undertake a preliminary numerical investigation to understand how the addition of white and colored noise to a time series affects the topology and structure of the underlying chaotic attractor. We use the methods and measures of recurrence networks generated from the time series for this analysis. We explicitly show that the addition of noise destroys the recurrence of trajectory points in the phase space. By using the results obtained from this analysis, we go on to analyse the light curves from a dominant black hole system and show that the recurrence network measures are effective in the analysis of real world data involving noise and are capable of identifying the nature of noise contamination in a time series.
A quantitative measure, mechanism and attractor for self-organization in networked complex systems
Georgiev, Georgi Yordanov
2012-01-01
Quantity of organization in complex networks here is measured as the inverse of the average sum of physical actions of all elements per unit motion multiplied by the Planck's constant. The meaning of quantity of organization is the inverse of the number of quanta of action per one unit motion of an element. This definition can be applied to the organization of any complex system. Systems self-organize to decrease the average action per element per unit motion. This lowest action state is the attractor for the continuous self-organization and evolution of a dynamical complex system. Constraints increase this average action and constraint minimization by the elements is a basic mechanism for action minimization. Increase of quantity of elements in a network, leads to faster constraint minimization through grouping, decrease of average action per element and motion and therefore accelerated rate of self-organization. Progressive development, as self-organization, is a process of minimization of action.
Jose eDavila-Velderrain
2015-04-01
Full Text Available 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.
Takashi Kanamaru
Full Text Available Corticopetal acetylcholine (ACh is released transiently from the nucleus basalis of Meynert (NBM into the cortical layers and is associated with top-down attention. Recent experimental data suggest that this release of ACh disinhibits layer 2/3 pyramidal neurons (PYRs via muscarinic presynaptic effects on inhibitory synapses. Together with other possible presynaptic cholinergic effects on excitatory synapses, this may result in dynamic and temporal modifications of synapses associated with top-down attention. However, the system-level consequences and cognitive relevance of such disinhibitions are poorly understood. Herein, we propose a theoretical possibility that such transient modifications of connectivity associated with ACh release, in addition to top-down glutamatergic input, may provide a neural mechanism for the temporal reactivation of attractors as neural correlates of memories. With baseline levels of ACh, the brain returns to quasi-attractor states, exhibiting transitive dynamics between several intrinsic internal states. This suggests that top-down attention may cause the attention-induced deformations between two types of attractor landscapes: the quasi-attractor landscape (Q-landscape, present under low-ACh, non-attentional conditions and the attractor landscape (A-landscape, present under high-ACh, top-down attentional conditions. We present a conceptual computational model based on experimental knowledge of the structure of PYRs and interneurons (INs in cortical layers 1 and 2/3 and discuss the possible physiological implications of our results.
Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys
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.
Colwell, Robert K; Gotelli, Nicholas J; Ashton, Louise A; Beck, Jan; Brehm, Gunnar; Fayle, Tom M; Fiedler, Konrad; Forister, Matthew L; Kessler, Michael; Kitching, Roger L; Klimes, Petr; Kluge, Jürgen; Longino, John T; Maunsell, Sarah C; McCain, Christy M; Moses, Jimmy; Noben, Sarah; Sam, Katerina; Sam, Legi; Shapiro, Arthur M; Wang, Xiangping; Novotny, Vojtech
2016-09-01
We introduce a novel framework for conceptualising, quantifying and unifying discordant patterns of species richness along geographical gradients. While not itself explicitly mechanistic, this approach offers a path towards understanding mechanisms. In this study, we focused on the diverse patterns of species richness on mountainsides. We conjectured that elevational range midpoints of species may be drawn towards a single midpoint attractor - a unimodal gradient of environmental favourability. The midpoint attractor interacts with geometric constraints imposed by sea level and the mountaintop to produce taxon-specific patterns of species richness. We developed a Bayesian simulation model to estimate the location and strength of the midpoint attractor from species occurrence data sampled along mountainsides. We also constructed midpoint predictor models to test whether environmental variables could directly account for the observed patterns of species range midpoints. We challenged these models with 16 elevational data sets, comprising 4500 species of insects, vertebrates and plants. The midpoint predictor models generally failed to predict the pattern of species midpoints. In contrast, the midpoint attractor model closely reproduced empirical spatial patterns of species richness and range midpoints. Gradients of environmental favourability, subject to geometric constraints, may parsimoniously account for elevational and other patterns of species richness. PMID:27358193
On coincidence problem and attractor solutions in ELKO dark energy model
Sadjadi, H Mohseni
2011-01-01
We study the critical points of a Universe dominated by ELKO spinor field dark energy and a barotropic matter in an almost general case. The coincidence problem and attractor solutions are discussed and it is shown the coincidence problem can not be alleviated in this model.
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...
Mulas, Marcello; Waniek, Nicolai; Conradt, Jörg
2016-01-01
After the discovery of grid cells, which are an essential component to understand how the mammalian brain encodes spatial information, three main classes of computational models were proposed in order to explain their working principles. Amongst them, the one based on continuous attractor networks (CAN), is promising in terms of biological plausibility and suitable for robotic applications. However, in its current formulation, it is unable to reproduce important electrophysiological findings and cannot be used to perform path integration for long periods of time. In fact, in absence of an appropriate resetting mechanism, the accumulation of errors over time due to the noise intrinsic in velocity estimation and neural computation prevents CAN models to reproduce stable spatial grid patterns. In this paper, we propose an extension of the CAN model using Hebbian plasticity to anchor grid cell activity to environmental landmarks. To validate our approach we used as input to the neural simulations both artificial data and real data recorded from a robotic setup. The additional neural mechanism can not only anchor grid patterns to external sensory cues but also recall grid patterns generated in previously explored environments. These results might be instrumental for next generation bio-inspired robotic navigation algorithms that take advantage of neural computation in order to cope with complex and dynamic environments. PMID:26924979
Vestibular and Attractor Network Basis of the Head Direction Cell Signal in Subcortical Circuits
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.
Noise in attractor networks in the brain produced by graded firing rate representations.
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.
A Mathematical Model of Chaotic Attractor in Tumor Growth and Decay
Ivancevic, Tijana T.; Bottema, Murk J.; Jain, Lakhmi C.
2008-01-01
We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance, as well as in temporal behavior. This is clearly a characteristic of dynamical systems sensitive to initial conditions. The new chaotic model of tumor growth and decay is biologically motivated. It has been developed as a live Mathematica demonstration, see...
On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0
We study the relations between the long-time dynamics of the Navier-Stokes-α model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes-α model converge to the trajectory attractor A0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor Aα of the Navier-Stokes-α model converges to the trajectory attractor A0 of the 3D Navier-Stokes system as α→0+. We also construct the minimal limit Amin(subset or equal A0) of the trajectory attractor Aα as α→0+ and prove that the set Amin is connected and strictly invariant. Bibliography: 35 titles.
Strange Attractors in the Vannimenus Model on an Arbitrary Order Cayley Tree
We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J1 and next-nearest-neighbour interactions J2 and J3 in the presence of an external magnetic field h. In this paper we study the phase diagram of the model using an iterative scheme for a renormalized effective nearest-neighbour coupling Kr and effective field per site Xr for spins on the rth level; it recovers, as particular cases, previous works by Vannimenus, Inawashiro et al, Mariz et al and Ganikhodjaev and Uguz. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of parameters.
Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics
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.
Dynamics of entanglement and 'attractor' states in the Tavis-Cummings model
Jarvis, C. E. A.; Rodrigues, D. A.; Györffy, B. L.; Spiller, T. P.; Short, A. J.; Annett, J. F.
2009-10-01
We study the time evolution of Nq two-level atoms (or qubits) interacting with a single mode of a quantized radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at {\\textstyle\\frac{t_{r}}{4}} , halfway between that start of the collapse and the first mini-revival peak, where tr is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an 'attractor state'. The set itself is termed the 'basin of attraction' and we concentrate on its features. Extending to more qubits, we find that attractors are a generic feature of the multiqubit Jaynes-Cummings model (JCM) and we therefore generalize the discovery by Gea-Banacloche for the one-qubit case. We give the 'basin of attraction' for Nq qubits and discuss the implications of the 'attractor' state in terms of the dynamics of Nq-body entanglement. We observe both the collapse and revival and the sudden birth/death of entanglement depending on the initial conditions.
Dynamics of Entanglement and `Attractor' states in The Tavis-Cummings Model
Jarvis, C E A; Györffy, B L; Spiller, T P; Short, A J; Annett, J F
2009-01-01
We study the time evolution of $N_q$ two-level atoms (or qubits) interacting with a single mode of the quantised radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at $\\sfrac{t_r}{4}$, halfway between that start of the collapse and the first mini revival peak, where $t_r$ is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an `attractor state'. The set itself is termed the basin of attraction and the features are at the center of our attention. Extending to more qubits, we find that attractors are a generic feature of the multi qubit Jaynes Cummings model (JCM) and we therefore generalise the discovery by Gea-Banacloche for the one qubit case. We give the `basin of attraction' for $N_q$ qubits and discuss the implications of the `attractor' state in terms of the dynamics of $N_q$-body entanglement. We observe both collapse a...
Dynamics of entanglement and 'attractor' states in the Tavis-Cummings model
We study the time evolution of Nq two-level atoms (or qubits) interacting with a single mode of a quantized radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at tr/4, halfway between that start of the collapse and the first mini-revival peak, where tr is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an 'attractor state'. The set itself is termed the 'basin of attraction' and we concentrate on its features. Extending to more qubits, we find that attractors are a generic feature of the multiqubit Jaynes-Cummings model (JCM) and we therefore generalize the discovery by Gea-Banacloche for the one-qubit case. We give the 'basin of attraction' for Nq qubits and discuss the implications of the 'attractor' state in terms of the dynamics of Nq-body entanglement. We observe both the collapse and revival and the sudden birth/death of entanglement depending on the initial conditions.
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
Bobrov, P.; Frolov, A.; Húsek, Dušan; Snášel, V.
Cham: Springer, 2014 - (Krömer, P.; Abraham, A.; Snášel, V.), s. 183-191. (Advances in Intelligent Systems and Computing. 303). ISBN 978-3-319-08155-7. ISSN 2194-5357. [IBICA 2014. International Conference on Innovations in Bio-Inspired Computing and Applications /5./. Ostrava (CZ), 23.06.2014-25.06.2014] Grant ostatní: GA MŠk(CZ) ED1.1.00/02.0070; GA MŠk(CZ) EE.2.3.20.0073 Institutional support: RVO:67985807 Keywords : brain computer interface * motor imagery * independent component analysis * attractor neural network with increasing activity Subject RIV: IN - Informatics, Computer Science
Wiegerinck, Wim; Schoenaker, Christiaan; Duane, Gregory
2016-04-01
Recently, methods for model fusion by dynamically combining model components in an interactive ensemble have been proposed. In these proposals, fusion parameters have to be learned from data. One can view these systems as parametrized dynamical systems. We address the question of learnability of dynamical systems with respect to both short term (vector field) and long term (attractor) behavior. In particular we are interested in learning in the imperfect model class setting, in which the ground truth has a higher complexity than the models, e.g. due to unresolved scales. We take a Bayesian point of view and we define a joint log-likelihood that consists of two terms, one is the vector field error and the other is the attractor error, for which we take the L1 distance between the stationary distributions of the model and the assumed ground truth. In the context of linear models (like so-called weighted supermodels), and assuming a Gaussian error model in the vector fields, vector field learning leads to a tractable Gaussian solution. This solution can then be used as a prior for the next step, Bayesian attractor learning, in which the attractor error is used as a log-likelihood term. Bayesian attractor learning is implemented by elliptical slice sampling, a sampling method for systems with a Gaussian prior and a non Gaussian likelihood. Simulations with a partially observed driven Lorenz 63 system illustrate the approach.
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. PMID:12675444
Trajectory attractors for the Sun–Liu model for nematic liquid crystals in 3D
In this paper we prove the existence of a trajectory attractor (in the sense of Chepyzhov and Vishik) for a nonlinear PDE system obtained from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier–Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered. (paper)
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.
Attractor comparisons based on density
Recognizing a chaotic attractor can be seen as a problem in pattern recognition. Some feature vector must be extracted from the attractor and used to compare to other attractors. The field of machine learning has many methods for extracting feature vectors, including clustering methods, decision trees, support vector machines, and many others. In this work, feature vectors are created by representing the attractor as a density in phase space and creating polynomials based on this density. Density is useful in itself because it is a one dimensional function of phase space position, but representing an attractor as a density is also a way to reduce the size of a large data set before analyzing it with graph theory methods, which can be computationally intensive. The density computation in this paper is also fast to execute. In this paper, as a demonstration of the usefulness of density, the density is used directly to construct phase space polynomials for comparing attractors. Comparisons between attractors could be useful for tracking changes in an experiment when the underlying equations are too complicated for vector field modeling
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.
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. PMID:24366137
Huang, Sui; Ernberg, Ingemar; Kauffman, Stuart
2009-01-01
Cell lineage commitment and differentiation are governed by a complex gene regulatory network. Disruption of these processes by inappropriate regulatory signals and by mutational rewiring of the network can lead to tumorigenesis. Cancer cells often exhibit immature or embryonic traits and dysregulated developmental genes can act as oncogenes. However, the prevailing paradigm of somatic evolution and multi-step tumorigenesis, while useful in many instances, offers no logically coherent reason ...
New BFA Method Based on Attractor Neural Network and Likelihood Maximization
Frolov, A. A.; Húsek, Dušan; Polyakov, P.Y.; Snášel, V.
2014-01-01
Roč. 132, 20 May (2014), s. 14-29. ISSN 0925-2312 Grant ostatní: GA MŠk(CZ) ED1.1.00/02.0070; GA MŠk(CZ) EE.2.3.20.0073 Institutional support: RVO:67985807 Keywords : recurrent neural network * associative memory * Hebbian learning rule * neural network application * data mining * statistics * Boolean factor analysis * information gain * dimension reduction * likelihood-maximization * bars problem Subject RIV: IN - Informatics, Computer Science Impact factor: 2.083, year: 2014
We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the near horizon background and the electric and magnetic charges and angular momentum carried by the black hole. If the entropy function has a unique extremum then this extremum must be independent of the asymptotic values of the moduli scalar fields and the solution exhibits attractor behaviour. If the entropy function has flat directions then the near horizon background is not uniquely determined by the extremization equations and could depend on the asymptotic data on the moduli fields, but the value of the entropy is still independent of this asymptotic data. We illustrate these results in the context of two derivative theories of gravity in several examples. These include Kerr black hole, Kerr-Newman black hole, black holes in Kaluza-Klein theory, and black holes in toroidally compactified heterotic string theory
On the Separability of Attractors in Grandmother Dynamic Systems with Structured Connectivity
Costa, L F
2007-01-01
The combination of complex networks and dynamic systems research is poised to yield some of the most interesting theoretic and applied scientific results along the forthcoming decades. The present work addresses a particularly important related aspect, namely the quantification of how well separated can the attractors be in dynamic systems underlined by four types of complex networks (Erd\\H{o}s-R\\'enyi, Barab\\'asi-Albert, Watts-Strogatz and as well as a geographic model). Attention is focused on grandmother dynamic systems, where each state variable (associated to each node) is used to represent a specific prototype pattern (attractor). By assuming that the attractors spread their influence among its neighboring nodes through a diffusive process, it is possible to overlook the specific details of specific dynamics and focus attention on the separability among such attractors. This property is defined in terms of two separation indices (one individual to each prototype and the other considering also the immedi...
Attractor Neural Network Combined with Likelihood Maximization Algorithm for Boolean Factor Analysis
Frolov, A.; Húsek, Dušan; Polyakov, P.Y.
Vol. 1. Berlin: Springer, 2012 - (Wang, J.; Yen, G.; Polycarpou, M.), s. 1-10. (Lecture Notes in Computer Science. 7367). ISBN 978-3-642-31345-5. ISSN 0302-9743. [ISNN 2012. International Symposium on Neural Networks /9./. Shenyang (CN), 11.07.2012-14.07.2012] R&D Projects: GA ČR GAP202/10/0262 Grant ostatní: GA MŠk(CZ) ED1.1.00/02.0070 Institutional research plan: CEZ:AV0Z10300504 Keywords : Associative Neural Network * Likelihood Maximization * Boolean Factor Analysis * Binary Matrix factorization * Noise XOR Mixing * Plato Problem * Information Gain * Bars problem * Data Mining * Dimension Reduction * Hebbian Learning * Anti-Hebbian Learning Subject RIV: IN - Informatics, Computer Science
Dark Energy from $\\alpha$-Attractors
Linder, Eric V
2015-01-01
A class of inflation theories called $\\alpha$-attractors has been investigated recently with interesting properties interpolating between quadratic potentials, the Starobinsky model, and an attractor limit. Here we examine their use for late time cosmic acceleration. We generalize the class and demonstrate how it can interpolate between thawing and freezing dark energy, and reduce the fine tuning of initial conditions, allowing $w\\approx-1$ for a prolonged period or as a de Sitter attractor.
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.
Modeling and controlling the two-phase dynamics of the p53 network: a Boolean network approach
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. (paper)
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.
Tetrapterous butterfly attractors in modified Lorenz systems
In this paper, the Lorenz-type tetrapterous butterfly attractors are firstly reported. With the introduction of multiple segment piecewise linear functions, these interesting and complex attractors are obtained from two different modified Lorenz models. This approach are verified in both simulations and experiments.
The Lorentz Attractor and Other Attractors in the Economic System of a Firm
A nonlinear model of the economic system of ''a firm'' is offered. It is shown that this model has several chaotic attractors, including the Lorentz attractor and a new attractor that, in our opinion, has not yet been described in the scientific literature. The chaotic nature of the attractors that were found was confirmed by computing the Lyapunov indicators. The functioning of our economic model is demonstrated with examples of firm behaviour that change the control parameters; these are well known in practice. In particular, it is shown that changes in the specific control parameters may change the system and avoid bankruptcy for the firm
A signature of attractor dynamics in the CA3 region of the hippocampus.
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
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.
Time Series Prediction Based on Chaotic Attractor
LIKe-Ping; CHENTian-Lun; GAOZi-You
2003-01-01
A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.
Recurrences of strange attractors
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.
This paper deals with attractors of generic dynamical systems. We introduce the notion of ε-invisible set, which is an open set of the phase space in which almost all orbits spend on average a fraction of time no greater than ε. For extraordinarily small values of ε (say, smaller than 2−100), these are large neighbourhoods of some parts of the attractors in the phase space which an observer virtually never sees when following a generic orbit. For any n ≥ 100, we construct a set Qn in the space of skew products over a solenoid with the fibre a circle having the following properties. Any map from Qn is a structurally stable diffeomorphism; the Lipschitz constants of the map and its inverse are no greater than L (where L is a universal constant that does not depend on n, say L n has a 2−n-invisible part of its attractor, whose size is comparable to that of the whole attractor. The set Qn is a ball of radius O(n−2) in the space of skew products with the C1 metric. It consists of structurally stable skew products. Small perturbations of these skew products in the space of all diffeomorphisms still have attractors with the same properties. Thus for all such perturbations, a sizable portion of the attractor is almost never visited by generic orbits and is practically never seen by the observer
Li, Qin; Wennborg, Anders; Aurell, Erik; Dekel, Erez; Zou, Jie-Zhi; Xu, Yuting; Huang, Sui; Ernberg, Ingemar
2016-03-01
The observed intercellular heterogeneity within a clonal cell population can be mapped as dynamical states clustered around an attractor point in gene expression space, owing to a balance between homeostatic forces and stochastic fluctuations. These dynamics have led to the cancer cell attractor conceptual model, with implications for both carcinogenesis and new therapeutic concepts. Immortalized and malignant EBV-carrying B-cell lines were used to explore this model and characterize the detailed structure of cell attractors. Any subpopulation selected from a population of cells repopulated the whole original basin of attraction within days to weeks. Cells at the basin edges were unstable and prone to apoptosis. Cells continuously changed states within their own attractor, thus driving the repopulation, as shown by fluorescent dye tracing. Perturbations of key regulatory genes induced a jump to a nearby attractor. Using the Fokker-Planck equation, this cell population behavior could be described as two virtual, opposing influences on the cells: one attracting toward the center and the other promoting diffusion in state space (noise). Transcriptome analysis suggests that these forces result from high-dimensional dynamics of the gene regulatory network. We propose that they can be generalized to all cancer cell populations and represent intrinsic behaviors of tumors, offering a previously unidentified characteristic for studying cancer. PMID:26929366
Collaborative networks: Reference modeling
L.M. Camarinha-Matos; H. Afsarmanesh
2008-01-01
Collaborative Networks: Reference Modeling works to establish a theoretical foundation for Collaborative Networks. Particular emphasis is put on modeling multiple facets of collaborative networks and establishing a comprehensive modeling framework that captures and structures diverse perspectives of
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
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.
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. PMID:23750942
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.
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...
Fermions, wigs, and attractors
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.
Single-field $\\alpha$-attractors
Linde, Andrei
2015-01-01
I describe a simple class of $\\alpha$-attractors, generalizing the single-field GL model of inflation in supergravity. The new class of models is defined for $0<\\alpha \\lesssim 1$, 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.
Frolov, A. A.; Húsek, Dušan; Muraviev, I. P.; Polyakov, P.Y.
2010-01-01
Roč. 73, č. 7-9 (2010), s. 1394-1404. ISSN 0925-2312 R&D Projects: GA ČR GA205/09/1079; GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10300504 Keywords : Boolean factor analysis * Hopfield neural Network * unsupervised learning * dimension reduction * data mining Subject RIV: IN - Informatics, Computer Science Impact factor: 1.429, year: 2010
Pugacheva, E
2015-01-01
In the offered review some key issues of social network analysis are discussed. This is a brief summary of social network characteristics, models of network formation, and the network perspective. The aim of this overview is to contribute to interdisciplinary dialogue among researchers in physics, mathematics, sociology, who share a common interest in understanding the network phenomena.
Strange attractor simulated on a quantum computer
Terraneo, M; Shepelyansky, D L
2003-01-01
Starting from the work of Lorenz, it has been realized that the dynamics of many various dissipative systems converges to so-called strange attractors. These objects are characterized by fractal dimensions and chaotic unstable dynamics of individual trajectories. They appear in nature in very different contexts, including applications to turbulence and weather forecast, molecular dynamics, chaotic chemical reactions, multimode solid state lasers and complex dynamics in ecological systems and physiology. The efficient numerical simulation of such dissipative systems can therefore lead to many important practical applications. Here we study a simple deterministic model where dynamics converges to a strange attractor, and show that it can be efficiently simulated on a quantum computer. Even if the dynamics on the attractor is unstable, dissipative and irreversible, a realistic quantum computer can simulate it in a reversible way, and, already with 70 qubits, will provide access to new informations unaccessible f...
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. PMID:26965665
Dimension of chaotic attractors
Farmer, J.D.; Ott, E.; Yorke, J.A.
1982-09-01
Dimension is perhaps the most basic property of an attractor. In this paper we discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors. The relevant definitions of dimension are of two general types, those that depend only on metric properties, and those that depend on probabilistic properties (that is, they depend on the frequency with which a typical trajectory visits different regions of the attractor). Both our example and the previous work that we review support the conclusion that all of the probabilistic dimensions take on the same value, which we call the dimension of the natural measure, and all of the metric dimensions take on a common value, which we call the fractal dimension. Furthermore, the dimension of the natural measure is typically equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers, and thus is usually far easier to calculate than any other definition. Because it is computable and more physically relevant, we feel that the dimension of the natural measure is more important than the fractal dimension.
Attractor merging crisis in chaotic business cycles
A numerical study is performed on a forced-oscillator model of nonlinear business cycles. An attractor merging crisis due to a global bifurcation is analyzed using the unstable periodic orbits and their associated stable and unstable manifolds. Characterization of crisis can improve our ability to forecast sudden major changes in economic systems
Attractors, Universality and Inflation
Downes, Sean; Sinha, Kuver
2012-01-01
Studies of the initial conditions for inflation have conflicting predictions from exponential suppression to inevitability. At the level of phase space, this conflict arises from the competing intuitions of CPT invariance and thermodynamics. After reviewing this conflict, we enlarge the ensemble beyond phase space to include scalar potential data. We show how this leads to an important contribution from inflection point inflation, enhancing the likelihood of inflation to an inverse cubic power law. In the process, we emphasize the attractor dynamics of the gravity-scalar system and the existence of universality classes from inflection point inflation. Finally, we comment on the predictivity of inflation in light of these results.
Trajectory attractors of equations of mathematical physics
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.
Chaotic attractors with separated scrolls
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.
Attractor Solutions in f(T) Cosmology
Jamil, Mubasher; Momeni, D.; Myrzakulov, Ratbay
2012-01-01
In this paper, we explore the cosmological implications of interacting dark energy model in a torsion based gravity namely $f(T)$. Assuming dark energy interacts with dark matter and radiation components, we examine the stability of this model by choosing different forms of interaction terms. We consider three different forms of dark energy: cosmological constant, quintessence and phantom energy. We then obtain several attractor solutions for each dark energy model interacting with other comp...
Optimal region of latching activity in an adaptive Potts model for networks of neurons
In statistical mechanics, the Potts model is a model for interacting spins with more than two discrete states. Neural networks which exhibit features of learning and associative memory can also be modeled by a system of Potts spins. A spontaneous behavior of hopping from one discrete attractor state to another (referred to as latching) has been proposed to be associated with higher cognitive functions. Here we propose a model in which both the stochastic dynamics of Potts models and an adaptive potential function are present. A latching dynamics is observed in a limited region of the noise(temperature)–adaptation parameter space. We hence suggest noise as a fundamental factor in such alternations alongside adaptation. From a dynamical systems point of view, the noise–adaptation alternations may be the underlying mechanism for multi-stability in attractor-based models. An optimality criterion for realistic models is finally inferred
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.
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...
Modeling Epidemic Network Failures
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. .
Inflationary Attractor from Tachyonic Matter
Guo, Z K; Cai, R G; Zhang, Y Z; Guo, Zong-Kuan; Piao, Yun-Song; Cai, Rong-Gen; Zhang, Yuan-Zhong
2003-01-01
We study the complete evolution of a flat and homogeneous universe dominated by tachyonic matter. We demonstrate the attractor behaviour of the tachyonic inflation using the Hamilton-Jacobi formalism. We else obtain analytical approximations to the trajectories of the tachyon field in different regions. The numerical calculation shows that an initial non-vanishing momentum does not prevent the onset of inflation. The slow-rolling solution is an attractor.
Inflationary attractor from tachyonic matter
Guo, Zong-Kuan; Piao, Yun-Song; Cai, Rong-Gen; Zhang, Yuan-Zhong
2003-08-01
We study the complete evolution of a flat and homogeneous universe dominated by tachyonic matter. We demonstrate the attractor behavior of tachyonic inflation using the Hamilton-Jacobi formalism. We also obtain analytical approximations for the trajectories of the tachyon field in different regions. The numerical calculation shows that an initial nonvanishing momentum does not prevent the onset of inflation. The slow-rolling solution is an attractor.
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...
Inflationary quasi-scale invariant attractors
Rinaldi, Massimiliano; Zerbini, Sergio; Venturi, Giovanni
2016-01-01
In a series of papers Kallosh, Linde, and collaborators have provided a unified description of single-field inflation with several types of potentials, ranging from power law to supergravity, in terms of just one parameter $\\alpha$. These so-called $\\alpha$-attractors predict a spectral index $n_{s}$ and a tensor-to-scalar ratio $r$, which are fully compatible with the latest Planck data. The only common feature of all $\\alpha$-attractors is the analyticity of the scalar potential in the non-canonical Einstein frame. In this paper we explore the case of non-analytic potentials and we find that they lead to a class of attractors characterized by quasi-scale invariance in the Jordan frame. In the canonical Einstein frame they all converge to a model with a linear potential and a universal relation between $r$ and $n_{s}$ that can fit the observational data. We show that the breaking of exact, classical, scale invariance in the Jordan frame can be attributed to one-loop corrections, in line with previous results...
Noise-induced attractor annihilation in the delayed feedback logistic map
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.
Noise-induced attractor annihilation in the delayed feedback logistic map
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.
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. E 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. PMID:22587158
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.
Chaos, turbulence and strange attractors
Using the turbulence example, the author recalls the two different conceptions of the nature of an erratic regime: the one in which a great number of elementary events are concerned (Landau) and the other one in which, on the contrary, a few number of elementary events are concerned (Ruelle and Takens). The last type of erratic comportment has a deterministic origin and is pointed by the adjective chaotic. Phase space for a dynamic system is presented and so the attractor nation. Chaos and notion of sensitiveness to initial conditions are defined. In scrutining the geometry of an attractor corresponding to a chaotic regime, the notion of strange attractor is shown. Some experiments results are given as illustration. Application field is recalled: for example, studies on hamiltonian chaos are made at DRFC (Department of research on controlled fusion at CEA) in relation with plasma instabilities
A Bio-Inspired QoS-Oriented Handover Model in Heterogeneous Wireless Networks
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.
Inflationary attractors and their measures
Several recent misconceptions about the measure problem in inflation and the nature of inflationary attractors are addressed. We clarify some issues regarding the Hamiltonian dynamics of a flat Friedmann–Lemaître–Robertson–Walker cosmology coupled to a massive scalar field. In particular we show that the focusing of the Liouville measure on attractor solutions is recovered by properly dealing with a gauge degree of freedom related to the rescaling of the spatial volume. Furthermore, we show how the Liouville measure formulated on a surface of constant Hubble rate, together with the assumption of constant a priory probability, induces a non-uniform probability distribution function on any other surfaces of other Hubble rates. The attractor behaviour is seen through the focusing of this function on a narrow range of physical observables. This qualitative behaviour is robust under change of potential and underlying measure. One can then conclude that standard techniques from Hamiltonian dynamics suffice to provide a satisfactory description of attractor solutions and the measure problem for inflationary dynamics. (fast track communications)
Intermittent control of coexisting attractors.
Liu, Yang; Wiercigroch, Marian; Ing, James; Pavlovskaia, Ekaterina
2013-06-28
This paper proposes a new control method applicable for a class of non-autonomous dynamical systems that naturally exhibit coexisting attractors. The central idea is based on knowledge of a system's basins of attraction, with control actions being applied intermittently in the time domain when the actual trajectory satisfies a proximity constraint with regards to the desired trajectory. This intermittent control uses an impulsive force to perturb one of the system attractors in order to switch the system response onto another attractor. This is carried out by bringing the perturbed state into the desired basin of attraction. The method has been applied to control both smooth and non-smooth systems, with the Duffing and impact oscillators used as examples. The strength of the intermittent control force is also considered, and a constrained intermittent control law is introduced to investigate the effect of limited control force on the efficiency of the controller. It is shown that increasing the duration of the control action and/or the number of control actuations allows one to successfully switch between the stable attractors using a lower control force. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method. PMID:23690639
A Network-of-Networks Model for Electrical Infrastructure Networks
Halappanavar, Mahantesh; Hogan, Emilie; Duncan, Daniel; Zhenyu,; Huang,; Hines, Paul D H
2015-01-01
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to solve these problems, but are subject to several limitations. One of the limitations is the ability to model a heterogeneous system in a consistent manner using the standard graph-theoretic formulation. In this paper, we propose a {\\em network-of-networks} approach for modeling power transmission networks in order to explicitly incorporate heterogeneity in the model. This model distinguishes between different components of the network that operate at different voltage ratings, and also captures the intra and inter-network connectivity patterns. By building the graph in this fashion we present a novel, and fundamentally different, perspective of power transmission networks. Consequently, this novel approach will have a significant impact on the graph-theoretic modeling of powe...
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.
Inverse fracture network modelling
The basic problem in analyzing flow and transport in fractured rock is that the flow may be largely governed by a poorly connected network of fractures. Flow in such a system cannot be modeled with traditional modelling techniques. Fracture network models also have a limitation, in that they are based on geological data on fracture geometry even though it is known that only a small portion of fractures observed is hydraulically active. This paper discusses a new technique developed for treating the problem as well as presents a modelling example carried out to apply it. The approach is developed in Lawrence Berkeley Laboratory and it treats the fracture zone as an 'equivalent discontinuum'. The discontinuous nature of the problem is represented through flow on a partially filled lattice. An equivalent discontinuum model is constructed by adding and removing conductive elements through a statistical inverse technique called 'simulated annealing'. The fracture network model is 'annealed' until the modified systems behaves like the observed. The further development of the approach continues at LBL and in a joint LBL/VTT collaboration project the possibilities to apply the technique in Finnish conditions are investigated
Cosmological attractors and initial conditions for inflation
Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei
2015-09-01
Inflationary α -attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincaré disk hyperbolic geometry. We refine these models by constructing Kähler potentials with built-in inflaton shift symmetry and by making a canonical choice of the Goldstino Kähler potential. The refined models are stable with respect to all scalar fields at all α ; no additional stabilization terms are required. The scalar potential V has a nearly Minkowski minimum at small values of the inflaton field φ and an infinitely long de Sitter (dS) valley of constant depth and width at large φ . Because of the infinite length of this shift-symmetric valley, the initial value of the inflaton field at the Planck density is expected to be extremely large. We show that the inflaton field φ does not change much until all fields lose their energy and fall to the bottom of the dS valley at large φ . This provides natural initial conditions for inflation driven by the inflaton field slowly rolling along the dS valley toward the minimum of the potential at small φ . A detailed description of this process is given for α -attractors in supergravity, but we believe that our general conclusions concerning naturalness of initial conditions for inflation are valid for a broad class of inflationary models with sufficiently flat potentials.
Statistical mechanical study of partial annealing of a neural network model
We study a neural network model in which both neurons and synaptic interactions evolve in time simultaneously. The time evolution of synaptic interactions is described by a Langevin equation including a Hebbian learning term with the learning coefficient ε, and a bias term which is the interaction of the Hopfield model. We assume that synaptic interactions change is much slower than neurons and we study the stationary states of synaptic interactions by the replica method. We draw phase diagrams taking into account the stability of solutions, and find that the temperature region in which the Hopfield attractor is stable increases as the learning coefficient increases. Theoretical results are confirmed by the direct numerical integration of the Langevin equation. Further, we study the characteristics of the resultant synaptic interactions by partial annealing in the parameter region where the Hopfield and the mixed states exist. We find two kinds of interactions, one of which has the Hopfield attractor and the other has the mixed state attractor. Each interaction is characterized mainly by the eigenvector belonging to the largest eigenvalue of the interaction as a matrix.
Generation and control of multi-scroll chaotic attractors in fractional order systems
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
Lattice Structures for Attractors I
Kalies, William D.; Mischaikow, Konstantin; Vandervorst, Robert C. A. M.
2013-01-01
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and noninvertible. We separate those properties which rely solely on algebraic structures from those that require some topological arguments, in order to lay a foundation for the development of algorithms to manipulate these structures computationally.
Attractors of equations of non-Newtonian fluid dynamics
This survey describes a version of the trajectory-attractor method, which is applied to study the limit asymptotic behaviour of solutions of equations of non-Newtonian fluid dynamics. The trajectory-attractor method emerged in papers of the Russian mathematicians Vishik and Chepyzhov and the American mathematician Sell under the condition that the corresponding trajectory spaces be invariant under the translation semigroup. The need for such an approach was caused by the fact that for many equations of mathematical physics for which the Cauchy initial-value problem has a global (weak) solution with respect to the time, the uniqueness of such a solution has either not been established or does not hold. In particular, this is the case for equations of fluid dynamics. At the same time, trajectory spaces invariant under the translation semigroup could not be constructed for many equations of non-Newtonian fluid dynamics. In this connection, a different approach to the construction of trajectory attractors for dissipative systems was proposed in papers of Zvyagin and Vorotnikov without using invariance of trajectory spaces under the translation semigroup and is based on the topological lemma of Shura-Bura. This paper presents examples of equations of non-Newtonian fluid dynamics (the Jeffreys system describing movement of the Earth's crust, the model of motion of weak aqueous solutions of polymers, a system with memory) for which the aforementioned construction is used to prove the existence of attractors in both the autonomous and the non-autonomous cases. At the beginning of the paper there is also a brief exposition of the results of Ladyzhenskaya on the existence of attractors of the two-dimensional Navier-Stokes system and the result of Vishik and Chepyzhov for the case of attractors of the three-dimensional Navier-Stokes system. Bibliography: 34 titles
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.
Attractors for Nonautonomous Parabolic Equations without Uniqueness
Nguyen Dinh Binh
2010-01-01
Full Text Available Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connectedness of the uniform global attractor.
Goldberg, S R; Evans, T S
2014-01-01
The distribution of the number of academic publications as a function of citation count for a given year is remarkably similar from year to year. We measure this similarity as a width of the distribution and find it to be approximately constant from year to year. We show that simple citation models fail to capture this behaviour. We then provide a simple three parameter citation network model using a mixture of local and global search processes which can reproduce the correct distribution over time. We use the citation network of papers from the hep-th section of arXiv to test our model. For this data, around 20% of citations use global information to reference recently published papers, while the remaining 80% are found using local searches. We note that this is consistent with other studies though our motivation is very different from previous work. Finally, we also find that the fluctuations in the size of an academic publication's bibliography is important for the model. This is not addressed in most mode...
A Network Synthesis Model for Generating Protein Interaction Network Families
Sayed Mohammad Ebrahim Sahraeian; Byung-Jun Yoon
2012-01-01
In this work, we introduce a novel network synthesis model that can generate families of evolutionarily related synthetic protein-protein interaction (PPI) networks. Given an ancestral network, the proposed model generates the network family according to a hypothetical phylogenetic tree, where the descendant networks are obtained through duplication and divergence of their ancestors, followed by network growth using network evolution models. We demonstrate that this network synthesis model ca...
Network model with structured nodes
Frisco, Pierluigi
2011-08-01
We present a network model in which words over a specific alphabet, called structures, are associated to each node and undirected edges are added depending on some distance measure between different structures. This model shifts the underlying principle of network generation from a purely mathematical one to an information-based one. It is shown how this model differs from the Barábasi-Albert and duplication models and how it can generate networks with topological features similar to biological networks: power law degree distribution, low average path length, clustering coefficient independent from the network size, etc. Two biological networks: S. cerevisiae gene network and E. coli protein-protein interaction network, are replicated using this model.
Noise Stabilized Random Attractor
Finn, J.M.; Tracy, E. R.; Cooke, W. E.; Richardson, A. S.
2005-01-01
A two dimensional flow model is introduced with deterministic behavior consisting of bursts which become successively larger, with longer interburst time intervals between them. The system is symmetric in one variable x and there are bursts on either side of x = 0, separated by the presence of an invariant manifold at x = 0. In the presence of arbitrarily small additive noise in the x direction, the successive bursts have bounded amplitudes and interburst intervals. This system with noise is ...
A neighbourhood evolving network model
Many social, technological, biological and economical systems are best described by evolved network models. In this short Letter, we propose and study a new evolving network model. The model is based on the new concept of neighbourhood connectivity, which exists in many physical complex networks. The statistical properties and dynamics of the proposed model is analytically studied and compared with those of Barabasi-Albert scale-free model. Numerical simulations indicate that this network model yields a transition between power-law and exponential scaling, while the Barabasi-Albert scale-free model is only one of its special (limiting) cases. Particularly, this model can be used to enhance the evolving mechanism of complex networks in the real world, such as some social networks development
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 ...
Emenheiser, Jeffrey; Chapman, Airlie; Pósfai, Márton; Crutchfield, James P.; Mesbahi, Mehran; D'Souza, Raissa M.
2016-09-01
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
Lifetime of chaotic attractors in a multidimensional laser system
We study the lifetimes of chaotic attractors at crises in a multidimensional laser system. This system describes the CO2 laser with modulated losses and is known as the four-level model. The critical exponents which are related to the lifetimes of the attractors are estimated in terms of the corresponding eigenvalues and the measured characteristic lifetime in the model. The critical exponents in this model and those of its center manifold version are in good agreement. We conjecture that generically in the four-level model the critical exponents are close to 1/2 at crises. In addition, we compare predictions of a simpler and popular model known as the two-level model with those of the above mentioned models. (author). 21 refs, 2 figs, 3 tabs
Dynamical modeling of the cholesterol regulatory pathway with Boolean networks
Corcos Laurent; Kervizic Gwenael
2008-01-01
Abstract Background Qualitative dynamics of small gene regulatory networks have been studied in quite some details both with synchronous and asynchronous analysis. However, both methods have their drawbacks: synchronous analysis leads to spurious attractors and asynchronous analysis lacks computational efficiency, which is a problem to simulate large networks. We addressed this question through the analysis of a major biosynthesis pathway. Indeed the cholesterol synthesis pathway plays a pivo...
Inflation as AN Attractor in Scalar Cosmology
Kim, Hyeong-Chan
2013-06-01
We study an inflation mechanism based on attractor properties in cosmological evolutions of a spatially flat Friedmann-Robertson-Walker spacetime based on the Einstein-scalar field theory. We find a new way to get the Hamilton-Jacobi equation solving the field equations. The equation relates a solution "generating function" with the scalar potential. We analyze its stability and find a later time attractor which describes a Universe approaching to an eternal-de Sitter inflation driven by the potential energy, V0>0. The attractor exists when the potential is regular and does not have a linear and quadratic terms of the field. When the potential has a mass term, the attractor exists if the scalar field is in a symmetric phase and is weakly coupled, λ<9V0/16. We also find that the attractor property is intact under small modifications of the potential. If the scalar field has a positive mass-squared or is strongly coupled, there exists a quasi-attractor. However, the quasi-attractor property disappears if the potential is modified. On the whole, the appearance of the eternal inflation is not rare in scalar cosmology in the presence of an attractor.
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
M. Terraneo; Georgeot, B.; D.L. Shepelyansky
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.
Modeling Dynamics of Information Networks
Rosvall, Martin; Sneppen, Kim
2003-01-01
We propose an information-based model for network dynamics in which imperfect information leads to networks where the different vertices have widely different number of edges to other vertices, and where the topology has hierarchical features. The possibility to observe scale free networks is linked to a minimally connected system where hubs remain dynamic.
Wild attractors and thermodynamic formalism
Bruin, Henk
2012-01-01
Fibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a one-parameter family $f_\\lambda$ of countably piecewise linear unimodal Fibonacci maps in order to study the thermodynamic formalism of dynamics where dissipativity of Lebesgue (and conformal) measure is responsible for phase transitions. We show that for the potential $\\phi_t = -t\\log|f'_\\lambda|$, there is a unique phase transition at some $t_1 \\le 1$, and the pressure $P(\\phi_t)$ is analytic (with unique equilibrium state) elsewhere. The pressure is majorised by a non-analytic $C^\\infty$ curve (with all derivatives equal to 0 at $t_1 < 1$) at the emergence of a wild attractor, whereas the phase transition at $t_1 = 1$ can be of any finite order for those $\\lambda$ for which $f_\\lambda$ is Lebesgue conservative. We also obtain results on the existence of conformal measures and equilibrium states, as well as the hyperbolic dimension and the dimension of th...
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.
Neural network mechanisms underlying stimulus driven variability reduction.
Deco, Gustavo; Hugues, Etienne
2012-01-01
It is well established that the variability of the neural activity across trials, as measured by the Fano factor, is elevated. This fact poses limits on information encoding by the neural activity. However, a series of recent neurophysiological experiments have changed this traditional view. Single cell recordings across a variety of species, brain areas, brain states and stimulus conditions demonstrate a remarkable reduction of the neural variability when an external stimulation is applied and when attention is allocated towards a stimulus within a neuron's receptive field, suggesting an enhancement of information encoding. Using an heterogeneously connected neural network model whose dynamics exhibits multiple attractors, we demonstrate here how this variability reduction can arise from a network effect. In the spontaneous state, we show that the high degree of neural variability is mainly due to fluctuation-driven excursions from attractor to attractor. This occurs when, in the parameter space, the network working point is around the bifurcation allowing multistable attractors. The application of an external excitatory drive by stimulation or attention stabilizes one specific attractor, eliminating in this way the transitions between the different attractors and resulting in a net decrease in neural variability over trials. Importantly, non-responsive neurons also exhibit a reduction of variability. Finally, this reduced variability is found to arise from an increased regularity of the neural spike trains. In conclusion, these results suggest that the variability reduction under stimulation and attention is a property of neural circuits. PMID:22479168
Neural network mechanisms underlying stimulus driven variability reduction.
Gustavo Deco
Full Text Available It is well established that the variability of the neural activity across trials, as measured by the Fano factor, is elevated. This fact poses limits on information encoding by the neural activity. However, a series of recent neurophysiological experiments have changed this traditional view. Single cell recordings across a variety of species, brain areas, brain states and stimulus conditions demonstrate a remarkable reduction of the neural variability when an external stimulation is applied and when attention is allocated towards a stimulus within a neuron's receptive field, suggesting an enhancement of information encoding. Using an heterogeneously connected neural network model whose dynamics exhibits multiple attractors, we demonstrate here how this variability reduction can arise from a network effect. In the spontaneous state, we show that the high degree of neural variability is mainly due to fluctuation-driven excursions from attractor to attractor. This occurs when, in the parameter space, the network working point is around the bifurcation allowing multistable attractors. The application of an external excitatory drive by stimulation or attention stabilizes one specific attractor, eliminating in this way the transitions between the different attractors and resulting in a net decrease in neural variability over trials. Importantly, non-responsive neurons also exhibit a reduction of variability. Finally, this reduced variability is found to arise from an increased regularity of the neural spike trains. In conclusion, these results suggest that the variability reduction under stimulation and attention is a property of neural circuits.
Developing Personal Network Business Models
Saugstrup, Dan; Henten, Anders
2006-01-01
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 on...
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.
Internet Network Resource Information Model
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.
Strange attractors in rattleback dynamics
Borisov, Aleksei V; Mamaev, Ivan S [Institute of Computer Science, Izhevsk (Russian Federation)
2003-04-30
This review is dedicated to the dynamics of the rattleback, a phenomenon with curious physical properties that is studied in nonholonomic mechanics. All known analytical results are collected here, and some results of our numerical simulation are presented. In particular, three-dimensional Poincare maps associated with dynamical systems are systematically investigated for the first time. It is shown that the loss of stability of periodic and quasiperiodic solutions, which gives rise to strange attractors, is typical of the three-dimensional maps related to rattleback dynamics. This explains some newly discovered properties of the rattleback related to the transition from regular to chaotic solutions at certain values of the physical parameters. (methodological notes)
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
Different routes to chaos via strange nonchaotic attractor in a quasiperiodically forced system
Venkatesan, A.; Lakshmanan, M
1998-01-01
This paper focusses attention on the strange nonchaotic attractors (SNA) of a quasiperiodically forced dynamical system. Several routes, including the standard ones by which the appearance of strange nonchaotic attractors takes place, are shown to be realizable in the same model over a two parameters ($f-\\epsilon$) domain of the system. In particular, the transition through torus doubling to chaos via SNA, torus breaking to chaos via SNA and period doubling bifurcations of fractal torus are d...
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.
General relativity as an attractor for scalar-torsion cosmology
Järv, Laur; Toporensky, Alexey
2016-01-01
We study flat Friedmann-Lemaître-Robertson-Walker cosmological models for a scalar field coupled nonminimally to teleparallel gravity with generic coupling and potential functions. The goal in this paper is to determine the conditions under which cosmological evolution tends to the limit where the variation of the gravitational "constant" ceases and the system evolves close to general relativity (GR). These conditions can be read off from the approximate analytical solutions describing the process in matter and potential domination eras. Only those models where the GR limit exists and is an attractor can be considered viable. We expect the results to hold in the original "pure tetrad" formulation as well as in the recently suggested covariant formulation of the teleparallel theory. In the former case the GR attractor simultaneously provides a mechanism for how cosmological evolution suppresses the problematic degrees of freedom stemming from the lack of local Lorentz invariance.
Global Attractors for a Nonclassical Diffusion Equation
Chun You SUN; Su Yun WANG; Cheng Kui ZHONG
2007-01-01
We prove the existence of global attractors in H10 (Ω) for a nonclassical diffusion equation.Two types of nonlinearity f are considered: one is the critical exponent, and the other is the polynomial growth of arbitrary order.
Singular-hyperbolic attractors are chaotic
Araujo, Vitor; Pacifico, Maria Jose; Pujals, Enrique; Viana, Marcelo
2005-01-01
We prove that a singular-hyperbolic attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their orbits coincide. Secondly, there exists a physical (or Sinai-Ruelle-Bowen) measure supported on the attractor whose ergodic basin covers a full Lebesgue (volume) measure subset of the topological basin of attraction. Moreover this measure has absolutely contin...
A plethora of strange nonchaotic attractors
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.
Effective field theory of non-attractor inflation
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.
Modeling of fluctuating reaction networks
Full Text:Various dynamical systems are organized as reaction networks, where the population size of one component affects the populations of all its neighbors. Such networks can be found in interstellar surface chemistry, cell biology, thin film growth and other systems. I cases where the populations of reactive species are large, the network can be modeled by rate equations which provide all reaction rates within mean field approximation. However, in small systems that are partitioned into sub-micron size, these populations strongly fluctuate. Under these conditions rate equations fail and the master equation is needed for modeling these reactions. However, the number of equations in the master equation grows exponentially with the number of reactive species, severely limiting its feasibility for complex networks. Here we present a method which dramatically reduces the number of equations, thus enabling the incorporation of the master equation in complex reaction networks. The method is examplified in the context of reaction network on dust grains. Its applicability for genetic networks will be discussed. 1. Efficient simulations of gas-grain chemistry in interstellar clouds. Azi Lipshtat and Ofer Biham, Phys. Rev. Lett. 93 (2004), 170601. 2. Modeling of negative autoregulated genetic networks in single cells. Azi Lipshtat, Hagai B. Perets, Nathalie Q. Balaban and Ofer Biham, Gene: evolutionary genomics (2004), In press
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.
Čech cohomology of attractors of discrete dynamical systems
Ruiz del Portal, Francisco R.; Sánchez-Gabites, J. J.
2014-10-01
Let f:Rn→Rn be a homeomorphism and K an asymptotically stable attractor for f. The aim of this paper is to study when the inclusion of K in its basin of attraction A(K) induces isomorphisms in Čech cohomology. We show that (i) this is true if coefficients are taken in Q or Zp (p prime) and (ii) it is true for integral cohomology if and only if the Čech cohomology of K or A(K) is finitely generated. We compute the Čech cohomology of periodic point free attractors of volume-contracting R3-homeomorphisms and present applications to quite general models in population dynamics.
Supersymmetry, attractors and cosmic censorship
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.
Supersymmetry, attractors and cosmic censorship
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
Drossel, Barbara
2007-01-01
This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and problems to solve, the basic concepts are introduced and important results concerning phase diagrams, numbers of relevant nodes and attractor properties are derived.
Cosmological Attractors and Initial Conditions for Inflation
Carrasco, John Joseph M; Linde, Andrei
2015-01-01
Inflationary $\\alpha$-attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincare disk hyperbolic geometry. We refine these models by constructing Kahler potentials with built-in inflaton shift symmetry and by making a canonical choice of the goldstino Kahler potential. The refined models are stable with respect to all scalar fields at all $\\alpha$, no additional stabilization terms are required. The scalar potential V has a nearly Minkowski minimum at small values of the inflaton field $\\varphi$, and an infinitely long dS valley of constant depth and width at large $\\varphi$. Because of the infinite length of this shift-symmetric valley, the initial value of the inflaton field at the Planck density is expected to be extremely large. We show that the inflaton field $\\varphi$ does not change much until all fields lose their energy and fall to the bottom of the dS valley at large $\\varphi$. This provides natural initial conditions for inflation driv...
Simplified models of biological networks.
Sneppen, Kim; Krishna, Sandeep; Semsey, Szabolcs
2010-01-01
The function of living cells is controlled by complex regulatory networks that are built of a wide diversity of interacting molecular components. The sheer size and intricacy of molecular networks of even the simplest organisms are obstacles toward understanding network functionality. This review discusses the achievements and promise of a bottom-up approach that uses well-characterized subnetworks as model systems for understanding larger networks. It highlights the interplay between the structure, logic, and function of various types of small regulatory circuits. The bottom-up approach advocates understanding regulatory networks as a collection of entangled motifs. We therefore emphasize the potential of negative and positive feedback, as well as their combinations, to generate robust homeostasis, epigenetics, and oscillations. PMID:20192769
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...
Advances in theoretical models of network science
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.
Security models for heterogeneous networking.
Mapp, Glenford E.; Aiash, Mahdi; Lasebae, Aboubaker; Phan, Raphael
2010-01-01
Security for Next Generation Networks (NGNs) is an attractive topic for many research groups. The Y-Comm security group believes that a new security approach is needed to address the security challenges in 4G networks. This paper sheds light on our approach of providing security for the Y-Comm architecture as an example of 4G communication frameworks. Our approach proposes a four-layer security integrated module to protect data and three targeted security models to protect different network e...
A Multilayer Model of Computer Networks
Shchurov, Andrey A.
2015-01-01
The fundamental concept of applying the system methodology to network analysis declares that network architecture should take into account services and applications which this network provides and supports. This work introduces a formal model of computer networks on the basis of the hierarchical multilayer networks. In turn, individual layers are represented as multiplex networks. The concept of layered networks provides conditions of top-down consistency of the model. Next, we determined the...
Target-Centric Network Modeling
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...... reporting formats, along with a tested process that facilitates the production of a wide range of analytical products for civilian, military, and hybrid intelligence environments. Readers will learn how to perform the specific actions of problem definition modeling, target network modeling, 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...
Asymmetric and symmetric chaotic attractors produced by the simplest jerk equivariant system are topologically characterized. In the case of this system with an inversion symmetry, it is shown that symmetric attractors bounded by genus-one tori are conveniently analyzed using a two-components Poincaré section. Resulting from a merging attractor crisis, these attractors can be easily described as being made of two folding mechanisms (here described as mixers), one for each of the two attractors co-existing before the crisis: symmetric attractors are thus described by a template made of two mixers. We thus developed a procedure for concatenating two mixers (here associated with unimodal maps) into a single one, allowing the description of a reduced template, that is, a template simplified under an isotopy. The so-obtained reduced template is associated with a description of symmetric attractors based on one-component Poincaré section as suggested by the corresponding genus-one bounding torus. It is shown that several reduced templates can be obtained depending on the choice of the retained one-component Poincaré section. (paper)
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
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.
Chaotic attractors of two-dimensional invertible maps
Andrey S. Kopeikin
1997-01-01
Full Text Available In this paper, we investigate the characteristics of quasihyperbolic attractors and quasiattractors in Invertible dissipative maps of the plane. The criteria which allow one to diagnose the indicated types of attractors in numerical experiments are formulated.
Hydraulic Modeling: Pipe Network Analysis
Datwyler, Trevor T.
2012-01-01
Water modeling is becoming an increasingly important part of hydraulic engineering. One application of hydraulic modeling is pipe network analysis. Using programmed algorithms to repeatedly solve continuity and energy equations, computer software can greatly reduce the amount of time required to analyze a closed conduit system. Such hydraulic models can become a valuable tool for cities to maintain their water systems and plan for future growth. The Utah Division of Drinking Water regulations...
Random attractors for asymptotically upper semicompact multivalue random semiflows
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.
Non-Supersymmetric Attractors in String Theory and Gauged Supergravity
In this article we briefly review the attractor mechanism in the context of N=2 supergravity theories arising from the compactification of type-IIA string theory on a Calabi-Yau manifold. We find non-supersymmetric attractors and discuss their stability. We further discuss the generalization of the attractor mechanism to N=2 gauged supergravity and explicitly construct configurations corresponding to Bianchi attractors
Spatial Models for Virtual Networks
Janssen, Jeannette
This paper discusses the use of spatial graph models for the analysis of networks that do not have a direct spatial reality, such as web graphs, on-line social networks, or citation graphs. In a spatial graph model, nodes are embedded in a metric space, and link formation depends on the relative position of nodes in the space. It is argued that spatial models form a good basis for link mining: assuming a spatial model, the link information can be used to infer the spatial position of the nodes, and this information can then be used for clustering and recognition of node similarity. This paper gives a survey of spatial graph models, and discusses their suitability for link mining.
Noise-enhanced reconstruction of attractors
Castro, R G
1997-01-01
In principle, the state space of a chaotic attractor can be partially or wholly reconstructed from interspike intervals recorded from experiment. Under certain conditions, the quality of a partial reconstruction, as measured by the spike train prediction error, can be increased by adding noise to the spike creation process. This phenomenon for chaotic systems is an analogue of stochastic resonance.
Recurrence quantification analysis in Liu's attractor
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
Metanetworks of artificially evolved regulatory networks
Danacı, Burçin
2014-01-01
We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which gets mutated in the course of evolution, while its phenotype is its set of dynamical attractors. Metanetworks in the genotype and phenotype spaces are formed, respectively, by genetic proximity and by phenotypic similarity, the latter weighted by the sizes of the basins of attraction of the shared attractors. We find that populations of evolved networks form giant clusters in genotype space, have Poissonian degree distributions but exhibit hierarchically organized $k$-core decompositions, while random populations of Boolean graphs are typically so far removed from each other genetically that they cannot form a metanetwork. In phenotype space, the metanetworks of evolved populations are super robust both under the elimination of weak connections and random removal of nodes. ...
Dynamical modeling of the cholesterol regulatory pathway with Boolean networks
Corcos Laurent
2008-11-01
Full Text Available Abstract Background Qualitative dynamics of small gene regulatory networks have been studied in quite some details both with synchronous and asynchronous analysis. However, both methods have their drawbacks: synchronous analysis leads to spurious attractors and asynchronous analysis lacks computational efficiency, which is a problem to simulate large networks. We addressed this question through the analysis of a major biosynthesis pathway. Indeed the cholesterol synthesis pathway plays a pivotal role in dislypidemia and, ultimately, in cancer through intermediates such as mevalonate, farnesyl pyrophosphate and geranyl geranyl pyrophosphate, but no dynamic model of this pathway has been proposed until now. Results We set up a computational framework to dynamically analyze large biological networks. This framework associates a classical and computationally efficient synchronous Boolean analysis with a newly introduced method based on Markov chains, which identifies spurious cycles among the results of the synchronous simulation. Based on this method, we present here the results of the analysis of the cholesterol biosynthesis pathway and its physiological regulation by the Sterol Response Element Binding Proteins (SREBPs, as well as the modeling of the action of statins, inhibitor drugs, on this pathway. The in silico experiments show the blockade of the cholesterol endogenous synthesis by statins and its regulation by SREPBs, in full agreement with the known biochemical features of the pathway. Conclusion We believe that the method described here to identify spurious cycles opens new routes to compute large and biologically relevant models, thanks to the computational efficiency of synchronous simulation. Furthermore, to the best of our knowledge, we present here the first dynamic systems biology model of the human cholesterol pathway and several of its key regulatory control elements, hoping it would provide a good basis to perform in silico
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
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....
Research on the model of home networking
Yun, Xiang; Feng, Xiancheng
2007-11-01
It is the research hotspot of current broadband network to combine voice service, data service and broadband audio-video service by IP protocol to transport various real time and mutual services to terminal users (home). Home Networking is a new kind of network and application technology which can provide various services. Home networking is called as Digital Home Network. It means that PC, home entertainment equipment, home appliances, Home wirings, security, illumination system were communicated with each other by some composing network technology, constitute a networking internal home, and connect with WAN by home gateway. It is a new network technology and application technology, and can provide many kinds of services inside home or between homes. Currently, home networking can be divided into three kinds: Information equipment, Home appliances, Communication equipment. Equipment inside home networking can exchange information with outer networking by home gateway, this information communication is bidirectional, user can get information and service which provided by public networking by using home networking internal equipment through home gateway connecting public network, meantime, also can get information and resource to control the internal equipment which provided by home networking internal equipment. Based on the general network model of home networking, there are four functional entities inside home networking: HA, HB, HC, and HD. (1) HA (Home Access) - home networking connects function entity; (2) HB (Home Bridge) Home networking bridge connects function entity; (3) HC (Home Client) - Home networking client function entity; (4) HD (Home Device) - decoder function entity. There are many physical ways to implement four function entities. Based on theses four functional entities, there are reference model of physical layer, reference model of link layer, reference model of IP layer and application reference model of high layer. In the future home network
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.
Probabilistic logic modeling of network reliability for hybrid network architectures
Wyss, G.D.; Schriner, H.K.; Gaylor, T.R.
1996-10-01
Sandia National Laboratories has found that the reliability and failure modes of current-generation network technologies can be effectively modeled using fault tree-based probabilistic logic modeling (PLM) techniques. We have developed fault tree models that include various hierarchical networking technologies and classes of components interconnected in a wide variety of typical and atypical configurations. In this paper we discuss the types of results that can be obtained from PLMs and why these results are of great practical value to network designers and analysts. After providing some mathematical background, we describe the `plug-and-play` fault tree analysis methodology that we have developed for modeling connectivity and the provision of network services in several current- generation network architectures. Finally, we demonstrate the flexibility of the method by modeling the reliability of a hybrid example network that contains several interconnected ethernet, FDDI, and token ring segments. 11 refs., 3 figs., 1 tab.
Energy modelling in sensor networks
D. Schmidt
2007-06-01
Full Text Available Wireless sensor networks are one of the key enabling technologies for the vision of ambient intelligence. Energy resources for sensor nodes are very scarce. A key challenge is the design of energy efficient communication protocols. Models of the energy consumption are needed to accurately simulate the efficiency of a protocol or application design, and can also be used for automatic energy optimizations in a model driven design process. We propose a novel methodology to create models for sensor nodes based on few simple measurements. In a case study the methodology was used to create models for MICAz nodes. The models were integrated in a simulation environment as well as in a SDL runtime framework of a model driven design process. Measurements on a test application that was created automatically from an SDL specification showed an 80% reduction in energy consumption compared to an implementation without power saving strategies.
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.
Free association transitions in models of cortical latching dynamics
Potts networks, in certain conditions, hop spontaneously from one discrete attractor state to another, a process we have called latching dynamics. When continuing indefinitely, latching can serve as a model of infinite recursion, which is nontrivial if the matrix of transition probabilities presents a structure, i.e. a rudimentary grammar. We show here, with computer simulations, that latching transitions cluster in a number of distinct classes: effectively random transitions between weakly correlated attractors; structured, history-dependent transitions between attractors with intermediate correlations; and oscillations between pairs of closely overlapping attractors. Each type can be described by a reduced set of equations of motion, which, once numerically integrated, matches simulations results. We propose that the analysis of such equations may offer clues on how to embed meaningful grammatical structures into more realistic models of specific recursive processes
Modelling of biochemical reaction networks
Gloppen Jørgensen, Arne Gunnar
2011-01-01
This report investigates signalling in reaction kinetic networks. The main topic is signalling between a substance being controlled by another substance and how this can be related to control theory. Different types of so-called natural controllers are compared and certain properties are investigated. Natural controllers are models on how a catalyst enzyme controls, for example the concentration, of a substance. There are sixteen different combinations of signalling between these substanc...
Hierarchical Models for Independence Structures of Networks
Sadeghi, Kayvan; Rinaldo, Alessandro
2016-01-01
We introduce a new family of network models, called hierarchical network models, that allow to represent in an explicit manner the stochastic dependence among the edges. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the edges of the network, called the dependency graph. Every network model of dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, w...
An evolving network model with community structure
Many social and biological networks consist of communities-groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting community structures in real-world complex networks. In this paper, we propose an evolving network model which exhibits community structure. The network model is based on the inner-community preferential attachment and inter-community preferential attachment mechanisms. The degree distributions of this network model are analysed based on a mean-field method. Theoretical results and numerical simulations indicate that this network model has community structure and scale-free properties
Brand Marketing Model on Social Networks
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.
Modeling the Dynamics of Compromised Networks
Soper, B; Merl, D M
2011-09-12
Accurate predictive models of compromised networks would contribute greatly to improving the effectiveness and efficiency of the detection and control of network attacks. Compartmental epidemiological models have been applied to modeling attack vectors such as viruses and worms. We extend the application of these models to capture a wider class of dynamics applicable to cyber security. By making basic assumptions regarding network topology we use multi-group epidemiological models and reaction rate kinetics to model the stochastic evolution of a compromised network. The Gillespie Algorithm is used to run simulations under a worst case scenario in which the intruder follows the basic connection rates of network traffic as a method of obfuscation.
Existence of the solutions and the attractors for the large-scale atmospheric equations
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.
RMBNToolbox: random models for biochemical networks
Niemi Jari
2007-05-01
Full Text Available Abstract Background There is an increasing interest to model biochemical and cell biological networks, as well as to the computational analysis of these models. The development of analysis methodologies and related software is rapid in the field. However, the number of available models is still relatively small and the model sizes remain limited. The lack of kinetic information is usually the limiting factor for the construction of detailed simulation models. Results We present a computational toolbox for generating random biochemical network models which mimic real biochemical networks. The toolbox is called Random Models for Biochemical Networks. The toolbox works in the Matlab environment, and it makes it possible to generate various network structures, stoichiometries, kinetic laws for reactions, and parameters therein. The generation can be based on statistical rules and distributions, and more detailed information of real biochemical networks can be used in situations where it is known. The toolbox can be easily extended. The resulting network models can be exported in the format of Systems Biology Markup Language. Conclusion While more information is accumulating on biochemical networks, random networks can be used as an intermediate step towards their better understanding. Random networks make it possible to study the effects of various network characteristics to the overall behavior of the network. Moreover, the construction of artificial network models provides the ground truth data needed in the validation of various computational methods in the fields of parameter estimation and data analysis.
Information Network Model Query Processing
Song, Xiaopu
Information Networking Model (INM) [31] is a novel database model for real world objects and relationships management. It naturally and directly supports various kinds of static and dynamic relationships between objects. In INM, objects are networked through various natural and complex relationships. INM Query Language (INM-QL) [30] is designed to explore such information network, retrieve information about schema, instance, their attributes, relationships, and context-dependent information, and process query results in the user specified form. INM database management system has been implemented using Berkeley DB, and it supports INM-QL. This thesis is mainly focused on the implementation of the subsystem that is able to effectively and efficiently process INM-QL. The subsystem provides a lexical and syntactical analyzer of INM-QL, and it is able to choose appropriate evaluation strategies and index mechanism to process queries in INM-QL without the user's intervention. It also uses intermediate result structure to hold intermediate query result and other helping structures to reduce complexity of query processing.
Multilayer weighted social network model
Murase, Yohsuke; Török, János; Jo, Hang-Hyun; Kaski, Kimmo; Kertész, János
2014-11-01
Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out to be overlapping. This implies that the society has a multilayered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of interlayer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multilayer WSN model, where the indirect interlayer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved.
Brand Marketing Model on Social Networks
Jolita Jezukevičiūtė; Vida Davidavičienė
2014-01-01
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 exploratoryanalys...
Tiling Spaces, Codimension One Attractors and Shape
Clark, Alex
2011-01-01
We show that any codimension one hyperbolic attractor of a di?eomorphism of a (d+1)-dimensional closed manifold is shape equivalent to a (d+1)-dimensional torus with a ?nite number of points removed, or, in the non-orientable case, to a space with a 2 to 1 covering by such a torus-less-points. Furthermore, we show that each orientable attractor is homeomorphic to a tiling space associated to an aperiodic tiling of Rd, but that the converse is generally not true. This work allows the de?nition of a new invariant for aperiodic tilings, in many cases ?ner than the cohomological or K-theoretic invariants studied to date.
Evidence for attractors in English intonation.
Braun, Bettina; Kochanski, Greg; Grabe, Esther; Rosner, Burton S
2006-06-01
Although the pitch of the human voice is continuously variable, some linguists contend that intonation in speech is restricted to a small, limited set of patterns. This claim is tested by asking subjects to mimic a block of 100 randomly generated intonation contours and then to imitate themselves in several successive sessions. The produced f0 contours gradually converge towards a limited set of distinct, previously recognized basic English intonation patterns. These patterns are "attractors" in the space of possible intonation English contours. The convergence does not occur immediately. Seven of the ten participants show continued convergence toward their attractors after the first iteration. Subjects retain and use information beyond phonological contrasts, suggesting that intonational phonology is not a complete description of their mental representation of intonation. PMID:16838543
Network Bandwidth Utilization Forecast Model on High Bandwidth Network
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.
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.
Contractive function systems, their attractors and metrization
Banakh, T.; Kubiś, Wieslaw; Novosad, N.; Nowak, M.; Strobin, F.
2015-01-01
Roč. 46, č. 2 (2015), s. 1029-1066. ISSN 1230-3429 R&D Projects: GA ČR(CZ) GA14-07880S Institutional support: RVO:67985840 Keywords : fractal * attractor * iterated function system * contracting function system Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2014 http://www.apcz.pl/czasopisma/index.php/TMNA/article/view/TMNA.2015.076
Holonomy Attractor Connecting Spaces of Different Curvature Responsible for ``Anomalies''
Binder, Bernd
2009-03-01
SO(3). MAP can be extended to a neural network, where the synaptic connection of the holonomy attractor is just the mathematical condition adjusting and bridging spaces with positive (spherical) and negative (hyperbolic) curvature allowing for lossless/supra spin currents. Another strategy is to look for existing spin/precession anomalies and corresponding nonlinear holonomy conditions at the most fundamental level from the quark level to the cosmic scale. In these sceneries the geodesic attractor could control holonomy and curvature near the fixed points. It was proposed in 2002 that this should happen with electrons in atomic orbits showing a Berry phase part of the Rydberg or Sommerfeld fine structure constant and in 2003 that this effect could be responsible for (in)stabilities in the nuclear range and in superconductors. In 2008 it was shown that the attractor is part of the chaotic mechanical dynamics successfully at work in the Gyro-twister fitness device, and in 2007-2009 that there could be some deep relevance to "anomalies" in many scenarios even on the cosmic scales. Thus, we will point to and discuss some possible future applications that could be utilized for metric engineering: generating artificial holonomy and curvature (DC effect) for propulsion, or forcing holonomy waves (AC effect) in hyperbolic space-time, which are just gravitational waves interesting for communication.
Lipschitz deviation and embeddings of global attractors
Hunt and Kaloshin (1999 Nonlinearity 12 1263–75) proved that it is possible to embed a compact subset X of a Hilbert space with upper box-counting dimension d N for any N > 2k + 1, using a linear map L whose inverse is Hölder continuous with exponent α N, dH(L(X)) ≥ min(N, dH(X)/(1 + τ(X)/2)). They also conjectured that 'many of the attractors associated with the evolution equations of mathematical physics have thickness exponent zero'. In this paper we introduce a variant of the thickness exponent, the Lipschitz deviation dev(X): we show that in both of the above results this can be used in place of the thickness exponent, and—appealing to results from the theory of approximate inertial manifolds—we prove that dev(X) = 0 for the attractors of a wide class of semilinear parabolic equations, thus providing a partial answer to the conjecture of Ott, Hunt and Kaloshin. In particular, dev(X) = 0 for the attractor of the 2D Navier–Stokes equations with forcing f in L2, while current results only guarantee that τ(X) = 0, when f in C∞
Multistability in Large Scale Models of Brain Activity.
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.
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
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
Analysis by fracture network modelling
This report describes the Fracture Network Modelling and Performance Assessment Support performed by Golder Associates Inc. during the Heisei-11 (1999-2000) fiscal year. The primary objective of the Golder Associates work scope during HY-11 was to provide theoretical and review support to the JNC HY-12 Performance assessment effort. In addition, Golder Associates provided technical support to JNC for the Aespoe Project. Major efforts for performance assessment support included analysis of PAWorks pathways and software documentation, verification, and performance assessment visualization. Support for the Aespoe project including 'Task 4' predictive modelling of sorbing tracer transport in TRUE-1 rock block, and integrated hydrogeological and geochemical modelling of Aespoe island for 'Task 5'. Technical information about Golder Associates HY-11 support to JNC is provided in the appendices to this report. (author)
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.
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...
Split attractor flow in N=2 minimally coupled supergravity
Ferrara, Sergio, E-mail: sergio.ferrara@cern.c [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547 (United States); Marrani, Alessio, E-mail: marrani@lnf.infn.i [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305-4060 (United States); Orazi, Emanuele, E-mail: emanuele.orazi@polito.i [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland)
2011-05-21
We classify the stability region, marginal stability walls (MS) and split attractor flows for two-center extremal black holes in four-dimensional N=2 supergravity minimally coupled to n vector multiplets. It is found that two-center (continuous) charge orbits, classified by four duality invariants, either support a stability region ending on an MS wall or on an anti-marginal stability (AMS) wall, but not both. Therefore, the scalar manifold never contains both walls. Moreover, the BPS mass of the black hole composite (in its stability region) never vanishes in the scalar manifold. For these reasons, the 'bound state transformation walls' phenomenon does not necessarily occur in these theories. The entropy of the flow trees also satisfies an inequality which forbids 'entropy enigma' decays in these models. Finally, the non-BPS case, due to the existence of a 'fake' superpotential satisfying a triangle inequality, can be treated as well, and it can be shown to exhibit a split attractor flow dynamics which, at least in the n=1 case, is analogous to the BPS one.
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. PMID:24580281
Introducing Synchronisation in Deterministic Network Models
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...... to the suggestion of suitable network models. An existing model for flow control is presented and an inherent weakness is revealed and remedied. Examples are given and numerically analysed through deterministic network modelling. Results are presented to highlight the properties of the suggested models...
Graph Annotations in Modeling Complex Network Topologies
Dimitropoulos, Xenofontas; Vahdat, Amin; Riley, George
2007-01-01
The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some non-trivial internal structure that varies across and differentiates among distinct types of links or nodes. In this work, we abstract such additional information as network annotations. We introduce a network topology modeling framework that treats annotations as an extended correlation profile of a network. Assuming we have this profile measured for a given network, we present an algorithm to rescale it in order to construct networks of varying size that still reproduce the original measured annotation profile. Using this methodology, we accurately capture the network properties essential for realistic simulations of network applications and protocols, or any other simulations involving complex network topologies, including modeling and simulation ...
Hybrid modeling of communication networks using Modelica
Färnqvist, Daniel; Strandemar, Katrin; Johansson, Karl Henrik; Hespanha, João Pedro
2002-01-01
Modeling and simulation of communication networks using the modeling language Modelica are discussed. Congestion control in packet-switched networks, such as the Internet, is today mainly analyzed through time-consuming simulations of individual packets. We show, by developing a model library based on a recent hybrid systems model, that Modelica provides an efficient platform for the analysis of communication networks. As an example, a comparison between the two congestion control protocols i...
Hierarchical relational models for document networks
Chang, Jonathan; Blei, David M.
2009-01-01
We develop the relational topic model (RTM), a hierarchical model of both network structure and node attributes. We focus on document networks, where the attributes of each document are its words, that is, discrete observations taken from a fixed vocabulary. For each pair of documents, the RTM models their link as a binary random variable that is conditioned on their contents. The model can be used to summarize a network of documents, predict links between them, and predi...
Attractors for the penalized Navier-Stokes equations
Consideration is given to the penalized form of the Navier-Stokes equations for a viscous incompressible fluid where the pressure and the incompressibility equations are suppressed and replaced by a penalty term in the momentum conservation equation. Here, the existence of an attractor for the penalized Navier-Stokes equation is studied, this attractor describing the long-time behavior of the solutions. Then the penalty parameter is allowed to tend to zero, and it is shown how the attractors of the penalized equations approximate the attractor of the exact equations. 19 references
Multiscaling in the YX model of networks
Holme, Petter; Minnhagen, Petter
2009-01-01
We investigate a Hamiltonian model of networks. The model is a mirror formulation of the XY model (hence the name) -- instead letting the XY spins vary, keeping the coupling topology static, we keep the spins conserved and sample different underlying networks. Our numerical simulations show complex scaling behaviors, but no finite-temperature critical behavior. The ground state and low-order excitations for sparse, finite graphs is a fragmented set of isolated network clusters. Configurations of higher energy are typically more connected. The connected networks of lowest energy are stretched out giving the network large average distances. For the finite sizes we investigate there are three regions -- a low-energy regime of fragmented networks, and intermediate regime of stretched-out networks, and a high-energy regime of compact, disordered topologies. Scaling up the system size, the borders between these regimes approach zero temperature algebraically, but different network structural quantities approach the...
Network model of bilateral power markets based on complex networks
Wu, Yang; Liu, Junyong; Li, Furong; Yan, Zhanxin; Zhang, Li
2014-06-01
The bilateral power transaction (BPT) mode becomes a typical market organization with the restructuring of electric power industry, the proper model which could capture its characteristics is in urgent need. However, the model is lacking because of this market organization's complexity. As a promising approach to modeling complex systems, complex networks could provide a sound theoretical framework for developing proper simulation model. In this paper, a complex network model of the BPT market is proposed. In this model, price advantage mechanism is a precondition. Unlike other general commodity transactions, both of the financial layer and the physical layer are considered in the model. Through simulation analysis, the feasibility and validity of the model are verified. At same time, some typical statistical features of BPT network are identified. Namely, the degree distribution follows the power law, the clustering coefficient is low and the average path length is a bit long. Moreover, the topological stability of the BPT network is tested. The results show that the network displays a topological robustness to random market member's failures while it is fragile against deliberate attacks, and the network could resist cascading failure to some extent. These features are helpful for making decisions and risk management in BPT markets.
Free energy, value, and attractors.
Ping Ao; Karl Friston
2012-01-01
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 be...
How to model wireless mesh networks topology
The specification of network connectivity model or topology is the beginning of design and analysis in Computer Network researches. Wireless Mesh Networks is an autonomic network that is dynamically self-organised, self-configured while the mesh nodes establish automatic connectivity with the adjacent nodes in the relay network of wireless backbone routers. Researches in Wireless Mesh Networks range from node deployment to internetworking issues with sensor, Internet and cellular networks. These researches require modelling of relationships and interactions among nodes including technical characteristics of the links while satisfying the architectural requirements of the physical network. However, the existing topology generators model geographic topologies which constitute different architectures, thus may not be suitable in Wireless Mesh Networks scenarios. The existing methods of topology generation are explored, analysed and parameters for their characterisation are identified. Furthermore, an algorithm for the design of Wireless Mesh Networks topology based on square grid model is proposed in this paper. The performance of the topology generated is also evaluated. This research is particularly important in the generation of a close-to-real topology for ensuring relevance of design to the intended network and validity of results obtained in Wireless Mesh Networks researches
Model Of Neural Network With Creative Dynamics
Zak, Michail; Barhen, Jacob
1993-01-01
Paper presents analysis of mathematical model of one-neuron/one-synapse neural network featuring coupled activation and learning dynamics and parametrical periodic excitation. Demonstrates self-programming, partly random behavior of suitable designed neural network; believed to be related to spontaneity and creativity of biological neural networks.
Magneto-electric network models in electromagnetism
Demenko, A.; Sykulski, J. K.
2006-01-01
Purpose – The aim of this paper is to develop network models of an electromagnetic field containing both eddy and displacement currents. The proposed network models provide good physical insight, help understanding of complicated electromagnetic phenomena and aid explanation of methods of analysis of electromagnetic systems. Design/methodology/approach – The models consist of magnetic and electric networks coupled via sources. The analogy between the finite element method and the loop and nod...
CIMS Network Protocol and Its Net Models
罗军舟; 顾冠群
1997-01-01
Computer communication network architectures for cims are based on the OSI Reference Model.In this paper,CIMS network protocol model is set up on the basis of the corresqonding service model.Then the authors present a formal specification of transport protocols by using an extended Predicate/Transition net system that is briefly introduced in the third part.Finally,the general methods for the Petri nets based formal specification of CIMS network protocols are outlined.
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...