网络绕道维持复杂性 网络绕道维持复杂性
Ernesto Estrada1, Jesús Gómez-Gardeñes2,3, Lucas Lacasa1
1Institute for Cross-Disciplinary Physics and Complex Systems, Consejo Superior de Investigaciones Científicas-Universitat de les Illes Balears, Palma de Mallorca 07122, Spain.
概括
复杂的网络开发"绕道",提供比最短的路径更容易的导航. 这些绕道有助于像人类大脑这样的系统保持复杂性和弹性.
科学领域:
- 网络科学 网络科学
- 复杂系统理论 复杂系统理论
- 数学建模的数学建模
背景情况:
- 现实世界的网络表现出复杂的拓结构,偏离正规或随机结构.
- 像瓦茨-斯特罗格茨和巴拉巴西-阿尔伯特这样的模型产生了枢纽和快捷方式,改善了连接性,但导致了导航效率低下和脆弱性.
- 复杂网络的无处不在表明了平衡连接性与航行性的潜在机制.
研究的目的:
- 在复杂的网络模型中研究网络绕道的生成.
- 开发一个数学理论来解释这些绕道的出现和巩固.
- 量化绕道所带来的航行效益,并评估它们在现实世界网络中的普及程度.
主要方法:
- 网络绕道的数学框架的理论开发.
- 分析网络拓和导航特性.
- 在各种现实世界网络数据集中应用和验证理论.
主要成果:
- 复杂的网络模型以热方式产生绕道,在拓上较长,但比最短的路径更容易航行.
- 一个数学理论成功阐明了这些绕道的形成和稳定.
- 量化了航行能力的增长,揭示了不同现实世界的网络中不同数量的绕道.
结论:
- 网络绕道是维持复杂性和增强现实世界系统中的可航行性的关键机制.
- 人类大脑表现出高度的复杂性,得到大量网络绕道的支持.
- 了解网络绕道对于理解复杂系统的可塑性和弹性至关重要.
相关概念视频
Network Function of a Circuit
324
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
324
Norton Equivalent Circuits
420
Norton's theorem is a fundamental concept in the field of electrical engineering that allows for the simplification of complex AC circuits. The theorem states that any two-terminal linear network can be replaced with an equivalent circuit that consists of an impedance, which is parallel with a constant current source. Figure 1 shows the AC circuit portioned into two parts: Circuit A and Circuit B, while Figure 2 depicts the circuit obtained by replacing Circuit A by its Norton equivalent...
420
Underflow Gates
79
Underflow gates are vital for controlling water flow in irrigation canals. The three main types of underflow gates — vertical, radial, and drum gates — serve different purposes while ensuring effective flow management. Vertical gates move up and down, generating a free-flowing water jet; radial gates pivot to regulate the flow; and drum gates rotate for precise adjustments. The flow through these gates is influenced by downstream conditions, resulting in free or drowned outflow.Free and...
79
Thevinin's Theorem
596
Thévenin's theorem plays a pivotal role in electrical circuit analysis, offering a solution to the challenges posed by variable loads within a circuit. In practical applications, it is common to encounter circuits where certain elements remain fixed while others fluctuate, often referred to as the "load." A typical household electrical outlet serves as a prime example of a variable load, as it can be connected to a variety of appliances, each with its own unique electrical...
596
Second-Order Circuits
1.4K
Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
1.4K
Fast Decoupled and DC Powerflow
234
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
234


