Robustness and fragility in coupled oscillator networks under targeted attacks.

Robustness of multipartite networks in face of random node failure

Our daily lives rely on all kinds of complex networks. However, complex networks in reality often suffer from random failures and/or attacks that can cause failures to their nodes/edges. A network can totally lose its functionalities due to nodes/edges failures. It is, therefore, of great significance to assess the robustness of complex networks confronted with failures. The network robustness analysis is helpful for assuring the reliability of complex networks. In our previous work, we had experimentally investigated the robustness of a special type of networks called k-partite networks. Simulation results have discovered that k-partite networks are robust to random node failures. In this work, we aim to investigate the underlying mathematical principle for the robustness property of k-partite networks. To do so, we have developed the mathematical theory to calculate the robustness of k-partite networks to random node failures. The developed theory mathematically uncovers the continuous phase transition of the robustness of k-partite networks under random node failures. In order to check if the developed theory is correct, we experimentally test the robustness of computer generated k-partite networks. The experimental results and the one calculated using the proposed theory comply with each other, which proves that the proposed theory is correct.

In real complex systems, the overall function is maintained through the connections among nodes. Failures of some nodes will destroy the connectivity of the system and thus damage the function of the system. In some complex systems, some nodes can form ``interdependency groups" through hidden interdependencies, and the failure of one node will damage the rest of the nodes in the interdependency group. In this paper, we investigate the effects of the interdependency strength of the nodes, the size distribution and the size of the interdependency groups on the cascading dynamics and the robustness of complex networks. Through numerical simulation and theoretical analysis, it is found that the cascading failure of the networks can be divided into two processes at the scale level: ``intra-group cascading" and ``inter-group cascading". In the process of intra-group cascading, the failure of one node will cause damage to the failure of other nodes in the group through the dependence between nodes, thus inducing the failure of more nodes and resulting in greater destructive force. In the process of intra-group cascading, the failure of one node will cause damage to other nodes in the group through the interdependence between nodes, thus inducing the failure of more nodes and resulting in greater destructive power. In the process of inter-group cascading, the failed nodes will cause the fragmentation of the networks, which leads to some nodes outside the interdependency group isolate from the giant component and go to fail. Under the synergistic effects of these two processes, it is found that there are continuous and discontinuous phase transition phenomena in the cascade dynamics of the network. The occurrence of these two kinds of phase transition phenomena is related to the interdependency strength of nodes, the network degree distribution and the size distribution of the interdependence group. This means that by controlling the characteristics of interdependency groups, such as the interdependence strength of the nodes in the interdependency group or the size distribution of interdependency groups, sudden system collapse can be avoided and thus the robustness of the network can be improved.

Coupled oscillator networks occur in various domains such as biology, astrophysics and electronics. In this paper, we present a comprehensive procedure for rapid and accurate simulation of large coupled oscillator networks using widely accepted, fully-nonlinear perturbation projection vector (PPV) phase macromodels. We validate our method against full simulation of 20times20 coupled network of Brusselator biochemical oscillator and obtain computational speedups of 170x over full simulation. Furthermore, we apply the method to study self-organization phenomenon of Brusselator under asymmetric coupling and time period variations.

Electrically induced phase transitions are being investigated for applications in steep-slope transistors, neuromorphic computing, and coupled oscillator networks. Here, we present an avenue to integrate a layered 2D phase transition material 1T-TaS <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> with monolayer MoS <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> via direct synthesis. We experimentally demonstrate that the charge density wave (CDW) based phase transition is preserved when grown directly on MoS <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> , however a 42% reduction in the ON/OFF ratio compared to exfoliated devices is observed. First principles calculations of the 1T-TaS <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> /MoS <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> heterostructure reveal a 39% reduction in the bandgap of 1T-TaS <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> compared to the free-standing 1T-TaS <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> case.

Risk factors for nodal failure after radiochemotherapy and image guided brachytherapy in locally advanced cervical cancer: An EMBRACE analysis

Coupled oscillator networks (CONs) occur in various domains such as biology and electronics. The nonlinear phenomenon of “injection locking” leads to frequency synchronization among the oscillators in a CON. In this chapter, we first obtain simplified tools to analyze the phenomenon of injection locking and present the Generalized Adler’s equation. The Generalized Adler’s equation is applicable for analyzing the injection locking in any type of oscillator. We demonstrate the use of Generalized Adler’s equation for injection locking analysis on a ring oscillator and a Hodgkin-Huxley neuronal oscillator. Next, we describe efficient system-level simulation techniques (synchronized steady state and transient) for coupled oscillator networks using the Perturbation Projection Vector (PPV) phase macromodel of the oscillator. The coupled oscillator simulation techniques are generic in nature and can be applied for the simulation of any coupled oscillator network, like the ones found in biological or electronic systems. We apply our system-level techniques on a −G m LC (harmonic) and a Hodgkin-Huxley (non-harmonic) CON.

Robustness in response to unexpected events is always desirable for real-world networks. To improve the robustness of any networked system, it is important to analyze vulnerability to external perturbation such as random failures or adversarial attacks occurring to elements of the network. In this paper, we study an emerging problem in assessing the robustness of complex networks: the vulnerability of the clustering of the network to the failure of network elements. Specifically, we identify vertices whose failures will critically damage the network by degrading its clustering, evaluated through the average clustering coefficient. This problem is important because any significant change made to the clustering, resulting from element-wise failures, could degrade network performance such as the ability for information to propagate in a social network. We formulate this vulnerability analysis as an optimization problem, prove its NP-completeness and non-monotonicity, and offer two algorithms to identify the vertices most important to clustering. Finally, we conduct comprehensive experiments in synthesized social networks generated by various well-known models as well as traces of real social networks. The empirical results over other competitive strategies show the efficacy of our proposed algorithms.

A set of N identical oscillators (clocks) are connected to form a mutually synchronous network. General matrix expressions are derived for the phase error spectrum at each oscillator when the network operates in the linear regime. For certain topologies of practical interest the phase error variance and the correlation between the errors at different oscillators is computed and compared in their behavior for large N . The results presented assume no thermal noise and no delay between the oscillators. However, the theory can be easily extended to include these two effects.

In this chapter we describe phenomenon of ragged synchronizability. First we give a theoretical introduction about detecting of the complete synchronization in the network of coupled systems. As an example we choose a network of non-diagonally coupled forced van der Pol oscillators.We present construction of the single electrical van der Pol oscillator and array of such systems. We show numerical and experimental results of the existence of the complete synchronization in the array and we discuss it in the very detailed way. We also consider the synchronization in clusters, experimentally in the small array and numerically in the larger network. Our numerical simulations show good agreement with the experimental observations.

In many distributed computing systems that are prone to either induced or spontaneous node failures, the number of available computing resources is dynamically changing in a random fashion. A load-balancing (LB) policy for such systems should therefore be robust, in terms of workload re-allocation and effectiveness in task completion, with respect to the random absence and re-emergence of nodes as well as random delays in the transfer of workloads among nodes. In this paper two LB policies for such computing environments are presented: The first policy takes an initial LB action to preemptively counteract the consequences of random failure and recovery of nodes. The second policy compensates for the occurrence of node failure dynamically by transferring loads only at the actual failure instants. A probabilistic model, based on the concept of regenerative processes, is presented to assess the overall performance of the system under these policies. Optimal performance of both policies is evaluated using analytical, experimental and simulation-based results. The interplay between node-failure/recovery rates and the mean load-transfer delay are highlighted.

Modeling Patient-specific Risk Factors for Central Lung Tumor SBRT Planning

Cascading failures take place between networks after initial failures occur in interdependent networks. Most previous studies are limited to undirected networks, while many real-world networks are directed. For interdependent directed networks, earlier studies focused on random initial failures. How the interdependent directed networks respond to targeted attacks has not been addressed. In this work, we develop a general theoretical framework for analyzing the robustness in interdependent directed networks under targeted attack on nodes with high or low degrees (in-degrees or out-degrees). We find that for degree heterogeneous networks, targeted attacks perform more efficiently in breaking down the system than random failures, with the degree-based attacks being the most efficient way. Interestingly, we find that system robustness first increases then decreases as the degree heterogeneity increases, showing a peak, which helps understand system robustness and enables the better design of robust infrastructure systems.

This paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy. The coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties. The definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real. Considering that each genetic oscillator consists of a large number of biochemical molecules, we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization. Not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant. Theoretical analysis of multisynchronization is carried out by the control theory approach, and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established. At last, numerical simulations are exploited to demonstrate the effectiveness of our results.

In modern times, satellite-based global positioning and navigation systems, such as the GPS, include precise time-keeping devices, e.g. atomic clocks, which are crucial for navigation and for a wide range of economic and industrial applications. However, precise timing might not be available when the environment renders satellite equipment inoperable. In response to this critical need, we have been carrying out, over the past three years, theory and preliminary experiments [Buono et al., 2018a; Buono et al., 2018b; Palacios et al., 2020], towards developing a novel and inexpensive precision timing device that can function independently of GPS availability. The fundamental idea is to exploit collective behavior generated by networks of coupled nonlinear oscillators. Common sense may suggest that synchronized oscillations may lead to higher accuracy. Previous works show, however, that it is not synchronization but rather, traveling wave patterns, in which consecutive oscillators are out of phase by a constant amount, that can better reduce the negative effects of noise and material imperfections which cause phase drift. In this work we advance the state-of-art in the network-based concept by studying, mainly computationally, collective behavior in networks of Colpitts oscillators. These type of oscillators are chosen because they offer a wide range of advantages (such as the ability to tune up the oscillations over a broad frequency range). The results highlight the regions of parameter space, including coupling strength, where traveling wave patterns have the largest basins of attraction and the ability to reduce phase drift by a [Formula: see text] scaling law, where [Formula: see text] is the number of oscillators in the network. The results should also provide guidelines for follow-up design and fabrication tasks of a network-based technology for precision timing.