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Rewiring driven evolution of quenched frustrated signed network 淬火受挫签名网络的重布线驱动演化
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-01-16 DOI: 10.1088/2632-072x/ad1a1a
Sven Benjamin Kožić, Salvatore Marco Giampaolo, Vinko Zlatić
A framework for studying the behavior of a classically frustrated signed network in the process of random rewiring is developed. We describe jump probabilities for change in frustration and formulate a theoretical estimate in terms of the master equation. Stationary thermodynamic distribution and moments are derived from the master equation and compared to numerical simulations. Furthermore, an exact solution of the probability distribution is provided through suitable mapping of rewiring dynamic to birth and death processes with quadratic asymptotically symmetric transition rates.
我们建立了一个框架,用于研究随机重新布线过程中经典受挫签名网络的行为。我们描述了沮度变化的跳跃概率,并根据主方程提出了理论估计。根据主方程推导出静态热力学分布和矩,并与数值模拟进行比较。此外,通过将重新布线动态映射到具有二次渐近对称转换率的出生和死亡过程,提供了概率分布的精确解。
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引用次数: 0
Epidemic modelling requires knowledge of the social network 流行病建模需要社会网络知识
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-01-09 DOI: 10.1088/2632-072x/ad19e0
Samuel Johnson
‘Compartmental models’ of epidemics are widely used to forecast the effects of communicable diseases such as COVID-19 and to guide policy. Although it has long been known that such processes take place on social networks, the assumption of ‘random mixing’ is usually made, which ignores network structure. However, ‘super-spreading events’ have been found to be power-law distributed, suggesting that the underlying networks may be scale free or at least highly heterogeneous. The random-mixing assumption would then produce an overestimation of the herd-immunity threshold for given R0; and a (more significant) overestimation of R0 itself. These two errors compound each other, and can lead to forecasts greatly overestimating the number of infections. Moreover, if networks are heterogeneous and change in time, multiple waves of infection can occur, which are not predicted by random mixing. A simple SIR model simulated on both Erdős–Rényi and scale-free networks shows that details of the network structure can be more important than the intrinsic transmissibility of a disease. It is therefore crucial to incorporate network information into standard models of epidemics.
流行病的 "区隔模型 "被广泛用于预测 COVID-19 等传染病的影响和指导政策。尽管人们早已知道此类过程发生在社会网络中,但通常会假设 "随机混合",从而忽略了网络结构。然而,"超级传播事件 "被发现是幂律分布的,这表明底层网络可能是无尺度的,或者至少是高度异构的。因此,在给定 R0 的情况下,随机混杂假设会导致高估群体免疫阈值;同时也会导致(更显著的)高估 R0 本身。这两个误差相互叠加,会导致预测大大高估感染数量。此外,如果网络是异质的并随时间发生变化,则可能会出现多波感染,而随机混合则无法预测这种情况。在厄尔多斯-雷尼网络和无标度网络上模拟的简单 SIR 模型表明,网络结构的细节可能比疾病的内在传播性更重要。因此,将网络信息纳入流行病的标准模型至关重要。
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引用次数: 0
Inferring comparative advantage via entropy maximization 通过熵最大化推断比较优势
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-12-28 DOI: 10.1088/2632-072x/ad1411
Matteo Bruno, Dario Mazzilli, Aurelio Patelli, Tiziano Squartini, Fabio Saracco
We revise the procedure proposed by Balassa to infer comparative advantage, which is a standard tool in Economics to analyze specialization (of countries, regions, etc). Balassa’s approach compares a country’s export of a given product with what would be expected from a benchmark based on the total volumes of countries and product flows. Based on results in the literature, we show that implementing Balassa’s idea leads to conditions for estimating parameters conflicting with the information content of the model itself. Moreover, Balassa’s approach does not implement any statistical validation. Hence, we propose an alternative procedure to overcome such a limitation, based upon the framework of entropy maximization and implementing a proper test of hypothesis: the ‘key products’ of a country are, now, the ones whose production is significantly larger than expected, under a null-model constraining the same amount of information defining Balassa’s approach. What we found is that country diversification is always observed, regardless of the strictness of the validation procedure. Besides, the ranking of countries’ fitnesses is only partially affected by the details of the validation scheme employed for the analysis while large differences are found to affect the rankings of product complexities. The routine for implementing the entropy-based filtering procedures employed here is freely available through the official Python Package Index PyPI.
我们修改了巴拉萨提出的推断比较优势的程序,这是经济学分析(国家、地区等)专业化的标准工具。巴拉萨的方法是将一国特定产品的出口量与基于国家总量和产品流量的基准预期值进行比较。根据文献中的结果,我们发现,实施巴拉萨的想法会导致参数估计条件与模型本身的信息内容相冲突。此外,Balassa 的方法没有进行任何统计验证。因此,我们基于熵最大化的框架,提出了另一种克服这种局限性的方法,并实施了适当的假设检验:现在,一个国家的 "关键产品 "是指在与巴拉萨方法相同的信息量约束下的无效模型中,产量明显大于预期的产品。我们发现,无论验证程序多么严格,国家多样化始终存在。此外,国家适合度的排序只受到分析中采用的验证方案细节的部分影响,而巨大的差异则会影响产品复杂性的排序。本文采用的基于熵的过滤程序的实施例程可通过官方 Python 软件包索引 PyPI 免费获取。
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引用次数: 0
Computational phase transition signature in Gibbs sampling 吉布斯采样中的计算相变特征
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-12-27 DOI: 10.1088/2632-072x/ad1410
Hariphan Philathong, Vishwanathan Akshay, Igor Zacharov, Jacob Biamonte
Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors—be it quantum or stochastic annealing devices—which embed problem instances and evolve a physical system into a low-energy ensemble to recover a probability distribution. At a critical constraint to variable ratio, satisfiability (SAT) problem instances exhibit a SAT-UNSAT transition (frustrated to frustration free). Algorithms require increasing computational resources from this critical point. This is a so called, algorithmic or computational phase transition and has extensively been studied. In this paper we consider the complexity in sampling and recovering ground states from resultant distributions of a physics based processor. In particular, we first consider the ideal Gibbs distributions at some fixed inverse temperature and observe that the success probability in sampling and recovering ground states decrease for instances starting at the critical density. Furthermore, simulating the Gibbs distribution, we employ Ising spin dynamics, which play a crucial role in understanding of non-equilibrium statistical physics, to find their steady states of 2-SAT Hamiltonians. We observe that beyond the critical density, the probability of sampling ground states decreases. Our results apply to several contemporary devices and provide a means to experimentally probe a signature of the computational phase transition.
吉布斯采样是各种计算机算法的基础。这些算法将被基于物理的处理器所取代--无论是量子还是随机退火设备--它们嵌入问题实例,并将物理系统演化为低能集合,以恢复概率分布。在临界约束与变量比率下,可满足性(SAT)问题实例会出现 SAT-UNSAT 过渡(受挫到无挫折)。从这个临界点开始,算法所需的计算资源不断增加。这就是所谓的算法或计算相变,并已被广泛研究。在本文中,我们考虑了从基于物理的处理器的结果分布中采样和恢复基态的复杂性。特别是,我们首先考虑了在某个固定反演温度下的理想吉布斯分布,并观察到从临界密度开始的实例,采样和恢复基态的成功概率会降低。此外,在模拟吉布斯分布的过程中,我们采用了在理解非平衡统计物理方面起着关键作用的伊辛自旋动力学,以找到 2-SAT 哈密尔顿的稳定状态。我们观察到,超过临界密度后,采样基态的概率会降低。我们的结果适用于几种当代设备,并提供了一种通过实验探测计算相变特征的方法。
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引用次数: 0
From statistical physics to social sciences: the pitfalls of multi-disciplinarity 从统计物理学到社会科学:多学科性的陷阱
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-12-08 DOI: 10.1088/2632-072x/ad104a
Jean-Philippe Bouchaud
This is the English version of my inaugural lecture at Collège de France in 2021. I reflect on the difficulty of multi-disciplinary research, which often hinges on unexpected epistemological and methodological differences, for example about the scientific status of models. What is the purpose of a model? What are we ultimately trying to establish: rigorous theorems or ad-hoc calculation recipes; absolute truth, or heuristic representations of the world? I argue that the main contribution of statistical physics to social and economic sciences is to make us realise that unexpected behaviour can emerge at the aggregate level, that isolated individuals would never experience. Crises, panics, opinion reversals, the spread of rumours or beliefs, fashion effects and the zeitgeist, but also the existence of money, lasting institutions, social norms and stable societies, must be understood in terms of collective belief and/or trust, self-sustained by interactions, or on the contrary, the rapid collapse of this belief or trust. The appendix contains my opening remarks to the workshop ‘More is Different’, as a tribute to Phil Anderson.
这是我2021年在法兰西学院的就职演讲的英文版。我对多学科研究的困难进行了反思,这种困难往往取决于认识论和方法论上意想不到的分歧,例如关于模型科学地位的分歧。模型的目的是什么?我们最终要建立的是什么:严格的定理,还是临时的计算方法;是绝对真理,还是对世界的启发式表述?我认为,统计物理学对社会和经济科学的主要贡献在于,它让我们认识到,在总体层面上可能会出现意外的行为,而这些行为是孤立的个体永远不会经历的。无论是危机、恐慌、舆论逆转、谣言或信仰的传播、时尚效应和时代精神,还是货币的存在、持久的制度、社会规范和稳定的社会,都必须从集体信仰和/或信任的角度来理解,并通过互动来自我维持,或者相反,这种信仰或信任会迅速崩溃。附录中是我在 "更多就是不同 "研讨会上的开场白,以此向菲尔-安德森致敬。
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引用次数: 0
Energy landscapes of some matching-problem ensembles 一些匹配问题集合的能量景观
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-11-30 DOI: 10.1088/2632-072x/ad0d88
Till Kahlke, Alexander K Hartmann
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This method provides insight into the complexity of the energy landscape of different ensembles. Erdős–Rényi graphs and ring graphs with randomly added edges are considered, and two types of distributions for the random edge weights are used. Fast and scalable algorithms exist for maximum weight matching, allowing us to study large graphs with more than 105 nodes. Our results show that the structure of the energy landscape for standard ensembles of matching is simple, comparable to the energy landscape of a ferromagnet. Nonetheless, for some of the ensembles presented here, our results allow for the presence of complex energy landscapes in the spirit of a replica-symmetry breaking scenario.
我们对最大重量匹配问题及其能量景观的行为进行了数值研究。我们采用了自旋玻璃分析中改编的扰动方法。这种方法有助于深入了解不同集合的能量景观的复杂性。我们考虑了带有随机添加边缘的厄尔多斯-雷尼图和环图,并使用了两种随机边缘权重分布。最大权重匹配存在快速且可扩展的算法,使我们能够研究超过 105 个节点的大型图。我们的结果表明,标准匹配集合的能量景观结构很简单,与铁磁体的能量景观相当。然而,对于本文介绍的一些集合,我们的结果允许存在复杂的能量景观,这与复制对称破缺情景的精神不谋而合。
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引用次数: 0
Zoo guide to network embedding Zoo 网络嵌入指南
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-11-29 DOI: 10.1088/2632-072x/ad0e23
A Baptista, R J Sánchez-García, A Baudot, G Bianconi
Networks have provided extremely successful models of data and complex systems. Yet, as combinatorial objects, networks do not have in general intrinsic coordinates and do not typically lie in an ambient space. The process of assigning an embedding space to a network has attracted great interest in the past few decades, and has been efficiently applied to fundamental problems in network inference, such as link prediction, node classification, and community detection. In this review, we provide a user-friendly guide to the network embedding literature and current trends in this field which will allow the reader to navigate through the complex landscape of methods and approaches emerging from the vibrant research activity on these subjects.
网络为数据和复杂系统提供了极为成功的模型。然而,作为组合对象,网络一般没有内在坐标,通常也不位于环境空间中。在过去几十年里,为网络分配嵌入空间的过程引起了人们的极大兴趣,并被有效地应用于网络推断的基本问题,如链接预测、节点分类和群落检测。在这篇综述中,我们为网络嵌入文献和这一领域的当前趋势提供了一个用户友好指南,读者可以从中了解到在这些主题的活跃研究活动中出现的各种方法和途径的复杂情况。
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引用次数: 1
Quantifying the hierarchical adherence of modular documents 量化模块化文件的层级一致性
IF 2.7 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-11-23 DOI: 10.1088/2632-072x/ad0a9b
Alexandre Benatti, Ana C M Brito, Diego R Amancio, Luciano da F Costa
Several natural and artificial structures are characterized by an intrinsic hierarchical organization. The present work describes a methodology for quantifying the degree of adherence between a given hierarchical template and a respective modular document (e.g. books or homepages with content organized into modules) organized as a respective content network. The original document, which in the case of the present work concerns Wikipedia pages, is transformed into a respective content network by first dividing the document into parts or modules. Then, the contents (words) of each pair of modules are compared in terms of the coincidence similarity index, yielding a respective weight. The adherence between the hierarchical template and the content network can then be measured by considering the coincidence similarity between the respective adjacency matrices, leading to the respective hierarchical adherence index. In order to provide additional information about this adherence, four specific indices are also proposed, quantifying the number of links between non-adjacent levels, links between nodes in the same level, converging links between adjacent levels, and missing links. The potential of the approach is illustrated respectively to model-theoretical networks as well as to real-world data obtained from Wikipedia. In addition to confirming the effectiveness of the suggested concepts and methods, the results suggest that real-world documents do not tend to substantially adhere to respective hierarchical templates.
一些自然和人工结构都具有内在的分层组织特征。本作品描述了一种方法,用于量化给定分层模板与作为各自内容网络组织起来的各自模块文档(如内容组织成模块的书籍或主页)之间的一致性程度。原始文档(在本工作中涉及维基百科页面)被转化为相应的内容网络时,首先要将文档划分为若干部分或模块。然后,根据重合相似性指数对每对模块的内容(词)进行比较,得出各自的权重。然后,通过考虑各自邻接矩阵之间的重合相似度,得出各自的分层粘合指数,从而衡量分层模板与内容网络之间的粘合度。为了提供有关这种粘附性的更多信息,还提出了四个具体指数,分别量化非相邻层级之间的链接数、同一层级节点之间的链接数、相邻层级之间的趋同链接数和缺失链接数。在模型理论网络和从维基百科获得的真实世界数据中,分别说明了该方法的潜力。除了证实所建议的概念和方法的有效性之外,研究结果还表明,现实世界中的文档并不倾向于严格遵守各自的层次模板。
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引用次数: 0
Encapsulation Structure and Dynamics in Hypergraphs 超图中的封装结构和动力学
Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-11-09 DOI: 10.1088/2632-072x/ad0b39
Timothy LaRock, Renaud Lambiotte
Abstract Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world hypergraphs, focusing on the encapsulation of their hyperedges, which is the extent that smaller hyperedges are subsets of larger hyperedges. Building on the concept of line graphs, our measures quantify the relations existing between hyperedges of different sizes and, as a byproduct, the compatibility of the data with a simplicial complex representation -- whose encapsulation would be maximum. We then turn to the impact of the observed structural patterns on diffusive dynamics, focusing on a variant of threshold models, called encapsulation dynamics, and demonstrate that non-random patterns can accelerate the spreading in the system.
超图已经成为一种强大的建模框架,用于表示具有多路交互的系统,即交互可能涉及任意数量的代理的系统。在这里,我们将探讨真实世界超图的属性,重点关注其超边的封装,即较小的超边是较大超边的子集的程度。基于线形图的概念,我们的测量量化了不同大小的超边之间存在的关系,作为副产品,数据与简单复杂表示的兼容性——其封装将是最大的。然后,我们转向观察到的结构模式对扩散动力学的影响,重点关注阈值模型的一种变体,称为封装动力学,并证明非随机模式可以加速系统中的扩散。
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引用次数: 3
Impact of tropical teleconnections on the long-range predictability of the atmosphere at midlatitudes: A reduced-order multi-scale model perspective 热带遥相关对中纬度大气长期可预测性的影响:一个降阶多尺度模式视角
Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-19 DOI: 10.1088/2632-072x/ad04e8
Stephane VANNITSEM
Abstract Teleconnections between the tropical and the extratropical climates are often considered as a potential source of long-term predictability at seasonal to decadal time scales in the extratropics. This claim is taken up in the present work by investigating the predictability of a coupled ocean-atmosphere extratropical model under a one-way forcing generated by a tropical model. Both models display a chaotic dynamics, and the dominant variable of the extratropical model displays a high correlation with the tropical forcing in the reference simulation, inducing a low-frequency variability signal in the extratropics. &#xD;&#xD;Numerical experiments emulating the presence of initial condition errors in the tropical model are conducted to clarify their impact on the predictability in the extratropics. It is shown that: (i) The correlation skill of the dominant observable affected by the forcing is considerably degraded at interannual time scales due to the presence of initial condition errors in the tropics, considerably limiting the potential of teleconnections; (ii) averaging of an ensemble of forecasts -- with a small number of members -- may substantially improve the quality of the forecasts; and (iii) temporal averaging may also improve the quality of the forecasts (at the expense of being able to forecast extreme events), in particular when the forcing affects weakly the observable under interest.&#xD;
热带和温带气候之间的遥相关通常被认为是温带地区在季节到年代际时间尺度上长期可预测性的潜在来源。本工作通过研究热带模式产生的单向强迫下海洋-大气耦合的温带模式的可预测性,采纳了这一主张。两种模式均表现为混沌动力学,且在参考模拟中,温带模式的主导变量与热带强迫表现出高度相关,在温带地区诱发低频变率信号。通过模拟热带模式中初始条件误差存在的数值实验,阐明了初始条件误差对温带可预测性的影响。结果表明:(i)由于热带地区存在初始条件误差,受强迫影响的主要观测值的相关能力在年际时间尺度上大大降低,大大限制了遥相关的可能性;(ii)对一组预测进行平均处理(只有少数成员),可大大提高预测的质量;(iii)时间平均也可以提高预报的质量(以牺牲预测极端事件的能力为代价),特别是当强迫对感兴趣的可观测值影响较弱时。
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引用次数: 0
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Journal of Physics Complexity
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