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About 10,000 papers for “node stability”
Vı́tor Araújo, Maria JosÉ Pacifico§ · Dynamical Systems · 2006
We study the dynamics of generic unfoldings of saddle-node circle local diffeomorphisms from the measure theoretical point of view, obtaining statistical and stochastic stability results for deterministic and random perturbations in this kind of one-parameter families.
Cited by 0
Fan Zhang, Qingyuan Linghu, Jiadong Xie et al. · 2023
Quantifying node importance on engagement dynamics is critical to support network stability. We can motivate or retain the users in a social platform according to their importance s.t. the network is more sustainable. Existing studies validate that the coreness of a node is the "best practice" on network topology to estimate the engagement of the node. In this paper, the importance of a node is the effect on the engagement of other nodes when its engagement is strengthened or weakened. Specifically, the importance of a node is quantified via two novel concepts: the anchor power to measure the engagement effect of node strengthening (i.e., the overall coreness gain) and the collapse power to measure the engagement effect of node weakening (i.e., the overall coreness loss). We find the computation of the two concepts can be naturally integrated into a shell component-based framework, and propose a unified static algorithm to compute both the anchored and collapsed followers. For evolving networks, efficient maintenance techniques are designed to update the follower sets of each node, which is faster than redoing the static algorithm by around 3 orders of magnitude. Extensive experiments on real-life data demonstrate the effectiveness of our model and the efficiency of our algorithms.
Cited by 9
Lone Aagesen · Molecular Phylogenetics and Evolution · 2005
Cited by 18
Clark Robinson · Transactions of the American Mathematical Society · 1978
recently proved the global structural stability of a one parameter unfolding of a saddle node when the nonwandering set is finite and transversality conditions are satisfied.(The diffeomorphism is Morse-Smale except for the saddle node.)Using their local unfolding of a saddle node and our method of compatible families of unstable disks (instead of the more restrictive method of compatible systems of unstable tubular families), we are able to extend one of their results to the case where the nonwandering set is infinite.We assume that a saddle node is introduced away from the rest of the nonwandering set, which is hyperbolic (Axiom A), and that a (strong) transversality condition is satisfied.
Cited by 0Open access
Clark Robinson · Transactions of the American Mathematical Society · 1978
S. Newhouse, J. Palis, and F. Takens have recently proved the global structural stability of a one parameter unfolding of a saddle node when the nonwandering set is finite and transversality conditions are satisfied. (The diffeomorphism is Morse-Smale except for the saddle node.) Using their local unfolding of a saddle node and our method of compatible families of unstable disks (instead of the more restrictive method of compatible systems of unstable tubular families), we are able to extend one of their results to the case where the nonwandering set is infinite. We assume that a saddle node is introduced away from the rest of the nonwandering set which is hyperbolic (Axiom A), and that a (strong) transversality condition is satisfied.
Cited by 6
Lucas Hedström (21688891), Antón Carcedo (21688894), Ludvig Lizana (2440240) · Figshare · 2025
at an effective community size of 0.88Mb across all chromosomes. The mean internal node strength is binned by the stability. We observe a nearly linear relationship between the two quantities, indicating that the internal strength within a community is a good predictor of community stability between bootstrapped samples.
Cited by 0Open access
Chiranjit Mitra, Anshul Choudhary, Sudeshna Sinha et al. · Physical review. E · 2017
Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world networked dynamical systems such as ecosystems, power grids, the human brain, etc. This necessitates the development of appropriate quantifiers of stability of multiple stable states of such systems. Motivated by the concept of basin stability (BS) [P. J. Menck et al., Nat. Phys. 9, 89 (2013)1745-247310.1038/nphys2516], we propose here the general framework of multiple-node basin stability for gauging the global stability and robustness of networked dynamical systems in response to nonlocal perturbations simultaneously affecting multiple nodes of a system. The framework of multiple-node BS provides an estimate of the critical number of nodes that, when simultaneously perturbed, significantly reduce the capacity of the system to return to the desired stable state. Further, this methodology can be applied to estimate the minimum number of nodes of the network to be controlled or safeguarded from external perturbations to ensure proper operation of the system. Multiple-node BS can also be utilized for probing the influence of spatially localized perturbations or targeted attacks to specific parts of a network. We demonstrate the potential of multiple-node BS in assessing the stability of the synchronized state in a deterministic scale-free network of Rössler oscillators and a conceptual model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics.
Cited by 95Open access
Lisa Shoaf, Mark A. Pitt · Perception & Psychophysics · 2002
Cited by 25Open access
Yi Tao · WSEAS TRANSACTIONS ON SYSTEMS · 2022
During the analysis of the power network, a node type conversion will occur under certain extreme conditions. This brings the problem of stability of the power system voltage. This article extracts the characteristic equation of the system voltage critical point by establishing a node voltage-branch current to the power network equation. Therefore, the corresponding solution equation group was in the conversion process of the PQ-PV node. Through this equation group, the difference in the difference between the voltage value of the node and the critical point voltage is formed to determine the system stability after the node type conversion is converted. In the process of calculating the voltage critical point, the improved Newton iteration method is used to avoid Jacques bizarre. This method allows calculations to smoothly reach a state of convergence. The simulation calculation shows that the method proposed in this article is correct and effective.
Cited by 0Open access
Christian Anderson · Data Archiving and Networked Services (DANS) · 2022
We invite you to browse the data here: https://oceanchaos.shinyapps.io/motif/ Protein-protein interaction networks (PPIs) are large and complex, yet self-organize to sustain all known life. To help understand the building blocks of these systems, we analyze small subgraphs (called "motifs" in this study) where all proteins can interact positively, negatively or not at all. There are 132 such 3-protein networks that are topologically unique (A->B->C is the same as B->C->A and C->B->A and B->A->C etc, so only such network is simulated), and 22,662 4-protein networks. Using the model d[A]/dt = (synthesis rate) - (degradation rate)*[A] + kBA*[B]*[A]^(Hill coefficient) + kCA*[C]*[A]^(Hill coefficient) + ..., we choose 1,000 biologically plausible values for the parameters, find all fixed points of the system, and determine the stability of those points. Previous research had suggested that a switch from a stable fixed-point equilibrium, to a limit cycle, to divergence to infinity was to be expected as the three possible behaviors. Instead, we determined that the behavior space of the typical motif included many different numbers of fixed points in complex combinations of stable and unstable (a median of 6 and 12 distinct fixed point combinations). We also discover that divergence to infinity is not at all uncommon at known biological values, despite such a result likely being fatal to the cell, suggesting a substantial degree of selection and regulation. The zip file includes: - Lists of which motifs are isomorphic to each other (3-motifs: isomorph_list.txt; 4-motifs: isomorph_list4.txt) - Julia code for generating our results for 3- and 4-motifs (farm3_log.jl and farm4_log.jl respectively). These were run on a supercomputer cluster for ~25k hours of CPU time to get 1,000 results for one member of each isomorph group. The results are stored in: - stab[n]_[motif id]_pars.txt files, storing the parameter values of all simulations for n-motifs - stab[n]_[motif id]_spec.txt files, which provide the spectral radius of the system's Jacobian at each fixed point. (-999 means no fixed points were found at the parameter values) - stab[n]_[motif id]_aux.txt files, in the format [time to solve the system] [n numbers representing log-protein concentrations at the first fixed point] [the second fixed point] ... Note that while these results are informed by biochemical networks, they are very general and would apply to any network.
Cited by 0Open access
Ranajoy Chatterjee, Mukti Routray · Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering · 2012
Cited by 1
Bartosz Brusilowicz, Janusz Szafran · 2014
Cited by 0
Srinka Basu, Ujjwal Maulik, Oishik Chatterjee · IEEE Transactions on Computational Social Systems · 2016
In complex network analysis, the problem of ranking individual nodes based on their importance has attracted increasing attention from the scientific community due to its vast application, such as identification of influential spreaders for viral marketing or epidemic control, bottlenecks for traffic congestion control, and so on. The growing literature proposes a number of measures to determine the rank order of the network entities where complete information about the nodes and their interaction is available. Degree centrality, PageRank, eigenvector centrality, closeness centrality are few such popular measures. In most real-life scenarios, however, the information about the underlying network is incomplete or affected due to noise. The few works that study the effects of incomplete information on the rank orders show the vulnerability of the rank orders in various topologies. In this paper, we investigate the effects of noise, both random and nonrandom, on the aggregated rank orders determined from the degree, PageRank, eigenvector centrality, and closeness centrality-based rankings. This paper reveals an important insight that even the simple Borda Count ranking has the potential to improve on the accuracy of rank orders in networks with uncertainty. This paper shows the existence of stable nodes in various networks and indicates that the design of the consensus approach based on the properties of the stable nodes can further improve the stability of the rank orders.
Cited by 14
Marc E. Levenston · Journal of Biomechanics · 1997
Cited by 8
Christian Anderson · Mendeley Data · 2022
We invite you to browse the data here: https://oceanchaos.shinyapps.io/motif/ Protein-protein interaction networks (PPIs) are large and complex, yet self-organize to sustain all known life. To help understand the building blocks of these systems, we analyze small subgraphs (called "motifs" in this study) where all proteins can interact positively, negatively or not at all. There are 132 such 3-protein networks that are topologically unique (A->B->C is the same as B->C->A and C->B->A and B->A->C etc, so only such network is simulated), and 22,662 4-protein networks. Using the model d[A]/dt = (synthesis rate) - (degradation rate)*[A] + kBA*[B]*[A]^(Hill coefficient) + kCA*[C]*[A]^(Hill coefficient) + ..., we choose 1,000 biologically plausible values for the parameters, find all fixed points of the system, and determine the stability of those points. Previous research had suggested that a switch from a stable fixed-point equilibrium, to a limit cycle, to divergence to infinity was to be expected as the three possible behaviors. Instead, we determined that the behavior space of the typical motif included many different numbers of fixed points in complex combinations of stable and unstable (a median of 6 and 12 distinct fixed point combinations). We also discover that divergence to infinity is not at all uncommon at known biological values, despite such a result likely being fatal to the cell, suggesting a substantial degree of selection and regulation. The zip file includes: - Lists of which motifs are isomorphic to each other (3-motifs: isomorph_list.txt; 4-motifs: isomorph_list4.txt) - Julia code for generating our results for 3- and 4-motifs (farm3_log.jl and farm4_log.jl respectively). These were run on a supercomputer cluster for ~25k hours of CPU time to get 1,000 results for one member of each isomorph group. The results are stored in: - stab[n]_[motif id]_pars.txt files, storing the parameter values of all simulations for n-motifs - stab[n]_[motif id]_spec.txt files, which provide the spectral radius of the system's Jacobian at each fixed point. (-999 means no fixed points were found at the parameter values) - stab[n]_[motif id]_aux.txt files, in the format [time to solve the system] [n numbers representing log-protein concentrations at the first fixed point] [the second fixed point] ... Note that while these results are informed by biochemical networks, they are very general and would apply to any network.
Cited by 0Open access
Hiratani, naoki, Mehta, Yash, Lillicrap, Timothy et al. · UCL Discovery (University College London) · 2023
To survive, animals must adapt synaptic weights based on external stimuli and \nrewards. And they must do so using local, biologically plausible, learning rules – a \nhighly nontrivial constraint. One possible approach is to perturb neural activity (or \nuse intrinsic, ongoing noise to perturb it), determine whether performance increases \nor decreases, and use that information to adjust the weights. This algorithm – known \nas node perturbation – has been shown to work on simple problems, but little is \nknown about either its stability or its scalability with respect to network size. We \ninvestigate these issues both analytically, in deep linear networks, and numerically, \nin deep nonlinear ones. We show analytically that in deep linear networks with \none hidden layer, both learning time and performance depend very weakly on \nhidden layer size. However, unlike stochastic gradient descent, when there is model \nmismatch between the student and teacher networks, node perturbation is always \nunstable. The instability is triggered by weight diffusion, which eventually leads to \nvery large weights. This instability can be suppressed by weight normalization, at \nthe cost of bias in the learning rule. We confirm numerically that a similar instability, \nand to a lesser extent scalability, exist in deep nonlinear networks trained on both \na motor control task and image classification tasks. Our study highlights the \nlimitations and potential of node perturbation as a biologically plausible learning \nrule in the brain.
Cited by 9Open access
A. Kazemi, Ali Mosallanejad · 2006
Oneofthemajorcauses ofvoltage instability is thereactive powerlimit ofthesystem. Improving the system's reactive powerhandling capacity viaFlexible AC transmission System(FACTS)devices isa remedyfor prevention ofvoltage instability andhencevoltage collapse. In thispaper,theeffects oftwoFACTS controllers, STATCOM andUPFC,onvoltage stability will bestudied. Continuation PowerFlow(CPF), withaccurate modelof thesecontrollers, isusedforthisstudy. Applying saddle nodebifurcation theorywiththeuseofPowerSystem Analysis Toolbox(PSAT), theoptimal location ofthese controllers isdetermined. Thestudy hasbeencarried outon the6-busandIEEE14-Bus TestSystems andresults are presented. Indexterms-FACTSdevices, Voltage Stability, Bifurcation Theorem'
Cited by 0
Ming‐Chia Li · Computers & Mathematics with Applications · 2005
Cited by 4
Philippe Van Bogaert · Ghent University Academic Bibliography (Ghent University) · 2007
Cited by 1
Álvarez Faura, M. del Carme, Blesa Aguilera, Maria Josep, Serna Iglesias, María José · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2007
In the area of communication systems, stability refers to the property of keeping the amount of traffic in the system always bounded over time. Different communication system models have been proposed in order to capture the unpredictable behavior of some users and applications. Among those proposed models the adversarial queueing theory (AQT) model turned out to be the most adequate to analyze an unpredictable network. Until now, most of the research done in this field did not consider the possibility of the adversary to produce failures on the network structure. The adversarial models proposed in this work are inspired by the AQT model, but incorporating the possibility of dealing with node and link failures provoked by the adversary. Such failures produce temporal disruptions of the connectivity of the system and increase the collisions of packets in the intermediate hosts of the network, and thus the average traffic load. Under such a scenario, the network is required to be equipped with some mechanism for dealing with those collisions. In addition to proposing adversarial models for faulty systems we study the relation between the robustness of the stability of the system and the management of the queues affected by the failures. When the adversary produces link or node failures the queues associated to the corresponding links can be affected in may different ways depending on whether they can receive or serve packets or they can not. We show that, in most of the cases, very simple network topologies and protocols, which were known to be universally stable, i.e. stable under any allowed configuration of the system, in the AQT model, turn out to be unstable when considering some of the newly proposed adversarial models. Thus showing that in general stability is not a robust property in the presence of failures.
Cited by 0Open access