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COVID-19: The unreasonable effectiveness of simple models COVID-19:简单模型的不合理有效性
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100034
Timoteo Carletti , Duccio Fanelli , Francesco Piazza

When the novel coronavirus disease SARS-CoV2 (COVID-19) was officially declared a pandemic by the WHO in March 2020, the scientific community had already braced up in the effort of making sense of the fast-growing wealth of data gathered by national authorities all over the world. However, despite the diversity of novel theoretical approaches and the comprehensiveness of many widely established models, the official figures that recount the course of the outbreak still sketch a largely elusive and intimidating picture. Here we show unambiguously that the dynamics of the COVID-19 outbreak belongs to the simple universality class of the SIR model and extensions thereof. Our analysis naturally leads us to establish that there exists a fundamental limitation to any theoretical approach, namely the unpredictable non-stationarity of the testing frames behind the reported figures. However, we show how such bias can be quantified self-consistently and employed to mine useful and accurate information from the data. In particular, we describe how the time evolution of the reporting rates controls the occurrence of the apparent epidemic peak, which typically follows the true one in countries that were not vigorous enough in their testing at the onset of the outbreak. The importance of testing early and resolutely appears as a natural corollary of our analysis, as countries that tested massively at the start clearly had their true peak earlier and less deaths overall.

当世界卫生组织于2020年3月正式宣布新型冠状病毒疾病SARS-CoV2 (COVID-19)为大流行时,科学界已经做好了准备,努力理解世界各国当局收集的快速增长的数据财富。然而,尽管有各种各样的新理论方法和许多广泛建立的模型的全面性,描述疫情过程的官方数据在很大程度上仍然描绘出一幅难以捉摸和令人生畏的画面。在这里,我们明确地表明,新冠肺炎疫情的动态属于SIR模型及其扩展的简单普适性类。我们的分析自然地使我们确定,任何理论方法都存在一个基本的限制,即在报告数据背后的测试框架的不可预测的非平稳性。然而,我们展示了这种偏差是如何自我一致地量化的,并用于从数据中挖掘有用和准确的信息。特别是,我们描述了报告率的时间演变如何控制表观流行高峰的发生,在爆发开始时检测力度不够的国家,表观流行高峰通常是在真实高峰之后出现的。早期和坚决检测的重要性似乎是我们分析的自然推论,因为在开始时进行大规模检测的国家显然更早出现了真正的高峰,总体上死亡人数更少。
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引用次数: 48
Energy transfer and thermodynamics of quantum gravity computation 量子引力计算的能量传递和热力学
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100050
Laszlo Gyongyosi

In a quantum gravity environment, the processes and events are causally non-separable because the term of time and the time-steps have no interpretable meaning in a non-fixed causality structure. Here, we study the energy transfer and thermodynamics of quantum gravity computations. We show that a non-fixed causality stimulates entropy transfer between the quantum gravity environment and the independent local systems of the quantum gravity space. We prove that the entropy transfer reduces the entropies of the contributing local systems and increases the entropy of the quantum gravity environment. We reveal on a smooth Cauchy slice that the space-time geometry of the quantum gravity environment dynamically adapts to the vanishing causality. We define the corresponding Hamiltonians and the causal development of the quantum gravity environment.

在量子引力环境中,过程和事件是因果不可分的,因为时间项和时间步长在非固定的因果结构中没有可解释的意义。在这里,我们研究了量子引力计算的能量传递和热力学。我们证明了一个非固定的因果关系刺激了量子引力环境和量子引力空间的独立局部系统之间的熵转移。我们证明了熵传递降低了贡献系统的熵,增加了量子引力环境的熵。我们在光滑柯西切片上揭示了量子引力环境的时空几何动态地适应于消失的因果关系。我们定义了相应的哈密顿量和量子引力环境的因果发展。
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引用次数: 1
The scaling of physics-informed machine learning with data and dimensions 基于物理的机器学习的数据和维度缩放
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100046
Scott T. Miller , John F. Lindner , Anshul Choudhary , Sudeshna Sinha , William L. Ditto

We quantify how incorporating physics into neural network design can significantly improve the learning and forecasting of dynamical systems, even nonlinear systems of many dimensions. We train conventional and Hamiltonian neural networks on increasingly difficult dynamical systems and compute their forecasting errors as the number of training data and number of system dimensions vary. A map-building perspective elucidates the superiority of Hamiltonian neural networks. The results clarify the critical relation among data, dimension, and neural network learning performance.

我们量化了将物理学纳入神经网络设计如何显著改善动态系统的学习和预测,甚至是多维非线性系统。我们在难度越来越大的动态系统上训练常规神经网络和哈密顿神经网络,并随着训练数据的数量和系统维数的变化计算其预测误差。地图构建的观点阐明了哈密顿神经网络的优越性。结果阐明了数据、维度和神经网络学习性能之间的关键关系。
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引用次数: 11
Generalized trapezoidal ogive curves for fatality rate modeling 用于死亡率建模的广义梯形ogive曲线
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100043
Johan René van Dorp , Ekundayo Shittu , Thomas A. Mazzuchi

The construction of a continuous family of distributions on a compact set is demonstrated by concatenating, in a continuous manner, three probability density functions with bounded support using a modified mixture technique. The construction technique is similar to that of generalized trapezoidal (GT) distributions, but contrary to GT distributions, the resulting density function is smooth within its bounded domain. The construction of Generalized Trapezoidal Ogive (GTO) distributions was motivated by the COVID-19 epidemic, where smoothness of an infection rate curve may be a desirable property combined with the ability to separately model three stages and their durations as the epidemic progresses, being: (1) an increasing infection rate stage, (2) an infection rate stage of some stability and (3) a decreasing infection rate stage. The resulting model allows for asymmetry of the infection rate curve opposite to, for example, the Gaussian Error Infection (GEI) rate curve utilized early on for COVID-19 epidemic projections by the Institute for Health Metrics and Evaluation (IHME). While other asymmetric distributions too allow for the modeling of asymmetry, the ability to separately model the above three stages of an epidemic’s progression is a distinct feature of the model proposed. The latter avoids unrealistic projections of an epidemic’s right-tail in the absence of right tail data, which is an artifact of any fatality rate model where a left-tail fit determines its right-tail behavior.

利用改进的混合技术,通过连续连接三个有界支持的概率密度函数,证明了紧集上连续分布族的构造。构造技术类似于广义梯形分布,但与广义梯形分布相反,得到的密度函数在其有界区域内是光滑的。构建广义梯形Ogive (GTO)分布的动机是受COVID-19流行的启发,其中感染率曲线的平滑性可能是理想的特性,并且能够根据流行病的进展分别对三个阶段及其持续时间进行建模,即:(1)感染率上升阶段,(2)感染率有一定稳定性的阶段和(3)感染率下降阶段。由此产生的模型允许感染率曲线的不对称性,例如,与卫生计量与评估研究所(IHME)早期用于COVID-19流行病预测的高斯误差感染(GEI)率曲线相反。虽然其他不对称分布也允许对不对称进行建模,但能够分别对流行病发展的上述三个阶段进行建模是所提出模型的一个显著特征。后者避免了在没有右尾数据的情况下对流行病右尾的不切实际的预测,右尾数据是任何死亡率模型的伪产物,其中左尾拟合决定了其右尾行为。
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引用次数: 0
Exact propagating wave solutions in reaction cross-diffusion system 反应交叉扩散系统的精确传播波解
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100049
Abdullah Aldurayhim , Vadim N. Biktashev

Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy reaction-cross-diffusion model with exact solutions in the form of propagating fronts. We propose a minimal model of this kind which involves two species linked by cross-diffusion, one of which governed by a linear equation and the other having a polynomial kinetic term. We classify the resulting exact propagating front solutions. Some of them have some features of the Fisher-KPP fronts and some features of the ZFK-Nagumo fronts.

除通常的自扩散项外,或代替自扩散项的反应扩散系统显示出有趣的特征,这些特征激发了它们的进一步研究。目前的工作旨在设计一个玩具反应-交叉扩散模型,其精确解以传播前沿的形式出现。我们提出了这类最小模型,它涉及两个由交叉扩散连接的物种,其中一个由线性方程控制,另一个具有多项式动力学项。我们对得到的精确传播前解进行分类。其中一些具有Fisher-KPP锋面的特征和zfk -南云锋面的特征。
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引用次数: 0
Topic reading dynamics of the Chinese Sina-Microblog 中文新浪微博的话题阅读动态
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100031
Fulian Yin , Jiale Wu , Xueying Shao , Jianhong Wu

A topic in the Sina-Microblog consists of multiple Weibos sharing a specific set of key words. Therefore, a reader of a Weibo may be susceptible to other Weibos of the same topic, and hence may undergo multiple transitions between the susceptible and the exposed states before eventually becoming infectious. This complicates the reading dynamics that traditional epidemic susceptible-exposed-infectious compartmental models cannot capture, and requires a different setting than a single Weibo forwarding dynamics model. Here we formulate a topic reading dynamics model; introduce some summative indices characterizing the reading “outbreak” potential; derive analytic formulae to calculate these indices; and examine the sensitivity of these indices and the ability of prediction on model parameters and on sampling frequencies. We conduct some numerical experiments based on historical data of popular reading topics in the Chinese Sina-Microblog. In our experiments, different sampling frequencies (4 h, 8 h or 12 h) nearcasting the turning points are feasible, in particular, a good nearcasting prediction for the accumulated R-users are 72 h with the sampling frequencies of every 4 h and every 12 h and 78 h with the sampling frequency of every 8 h.

新浪微博中的一个话题由多个微博组成,这些微博共享一组特定的关键词。因此,一个微博的读者可能会受到同一话题的其他微博的影响,因此可能会在易感状态和暴露状态之间经历多次转变,最终感染。这使得传统的流行病易感-暴露-感染区隔模型无法捕捉的阅读动态变得复杂,并且需要与单一微博转发动态模型不同的设置。在此,我们建立了一个话题阅读动态模型;介绍了表征读数“爆发”潜力的一些总结性指标;推导出计算这些指标的解析公式;并检验了这些指标对模型参数和采样频率的敏感性和预测能力。我们基于中文新浪微博热门阅读话题的历史数据进行了一些数值实验。在我们的实验中,不同的采样频率(4 h、8 h或12 h)都可以接近转折点,特别是对累积r -用户的较好的接近预测是72 h,每4 h采样一次,每12 h采样一次,每8 h采样一次。
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引用次数: 3
The interplay between physical activity and aging in locomotor fractal behavior 运动分形行为中体力活动与衰老的相互作用
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100045
Scott W. Ducharme , Richard E.A. van Emmerik

The complex organization of gait variability, or fractal dynamics, theoretically represents the adaptive capacity of the locomotor system. Prior studies suggest that fractal dynamics are sensitive to various individual constraints (e.g., age, neurological disease) and task constraints (e.g., walking speed or novel gait tasks). The purpose of this study was to determine if physical activity levels represent an additional individual constraint during walking. Fifteen young and 15 older adults walked on a treadmill at their preferred walking speed and at half of their preferred speed. Detrended fluctuation analysis was used to estimate the statistical persistence of stride time variability. Volume of physical activity was determined using a wearable monitor for 3-7 days. Habitual physical activity levels did not appear to have an effect on the fractal nature of stride-to-stride fluctuations in young adults. However, the least active older adults displayed higher scaling exponents compared to the more active older adults during slow walking. That is, less active older adults responded to the slow walking task by increasing fractal scaling, suggesting this task is more challenging and complex. These findings suggest that lower levels of habitual physical activity may represent an additional individual constraint in older but not young adults. When age and physical activity constraints are combined with a challenging slow walking task, the locomotor system of older adults may be more highly taxed, ultimately manifesting as stronger statistical persistence.

步态变异性的复杂组织,或分形动力学,理论上代表了运动系统的适应能力。先前的研究表明,分形动力学对各种个体约束(如年龄、神经疾病)和任务约束(如步行速度或新步态任务)都很敏感。本研究的目的是确定身体活动水平是否代表行走过程中额外的个体约束。15名年轻人和15名老年人以他们喜欢的速度和他们喜欢的速度的一半在跑步机上行走。采用无趋势波动分析估计步幅时间变异的统计持久性。使用可穿戴式监测仪测定3-7天的体力活动量。在年轻人中,习惯性的体育活动水平似乎对跨步波动的分形性质没有影响。然而,在慢走时,活动量最小的老年人比活动量较大的老年人表现出更高的缩放指数。也就是说,活动较少的老年人对慢走任务的反应是增加分形尺度,这表明这项任务更具挑战性和复杂性。这些发现表明,较低水平的习惯性体育活动可能是老年人而不是年轻人的额外个体限制。当年龄和体力活动限制与具有挑战性的缓慢行走任务相结合时,老年人的运动系统可能会受到更高的负担,最终表现出更强的统计持久性。
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引用次数: 1
Distinguished correlation properties of Chebyshev dynamical systems and their generalisations 切比雪夫动力系统的显著相关性质及其推广
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100035
Jin Yan, Christian Beck

We show that, among all smooth one-dimensional maps conjugated to an N-ary shift (a Bernoulli shift of N symbols), Chebyshev maps are distinguished in the sense that they have least higher-order correlations. We generalise our consideration and study a family of shifted Chebyshev maps, presenting analytic results for two-point and higher-order correlation functions. We also review results for the eigenvalues and eigenfunctions of the Perron-Frobenius operator of Nth order Chebyshev maps and their shifted generalisations. The spectrum is degenerate for odd N. Finally, we consider coupled map lattices (CMLs) of shifted Chebyshev maps and numerically investigate zeros of the temporal and spatial nearest-neighbour correlations, which are of interest in chaotically quantized field theories.

我们证明,在所有共轭到N元位移(N个符号的伯努利位移)的光滑一维映射中,切比雪夫映射的区别在于它们具有最少的高阶相关性。我们推广了我们的考虑并研究了一组移位的切比雪夫映射,给出了两点和高阶相关函数的解析结果。我们还回顾了n阶Chebyshev映射的Perron-Frobenius算子的特征值和特征函数及其移位推广的结果。最后,我们考虑了移位切比雪夫映射的耦合映射格(cml),并数值研究了混沌量子化场论中感兴趣的时空近邻相关的零点。
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引用次数: 4
Comment on “Estimation of COVID-19 dynamics “on a back-of-envelope”: Does the simplest SIR model provide quantitative parameters and predictions?” 评论“最简单的SIR模型能提供定量参数和预测吗?”
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100047
S. Rojas

This comment shows that data regarding cumulative confirmed cases from the coronavirus COVID-19 disease outbreak, in the period December 31, 2019–June 29, 2020 of some countries reported by the European Centre for Disease Prevention and Control, can be adjusted by the exact solution of the Kermack – McKendrick approximation of the SIR epidemiological model.

这一评论表明,欧洲疾病预防控制中心报告的一些国家2019年12月31日至2020年6月29日期间2019冠状病毒病COVID-19暴发的累积确诊病例数据可以通过SIR流行病学模型的Kermack - McKendrick近似的精确解进行调整。
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引用次数: 2
Hyers-Ulam stability and existence of solutions for weighted Caputo-Fabrizio fractional differential equations 加权Caputo-Fabrizio分数阶微分方程的Hyers-Ulam稳定性和解的存在性
Q1 Mathematics Pub Date : 2020-03-01 DOI: 10.1016/j.csfx.2020.100040
Xia Wu, Fulai Chen, Sufang Deng

In this paper, we study Hyers-Ulam stability and generalized Hyers-Ulam stability of linear equations with weighted Caputo-Fabrizio fractional derivative. We establish existence and uniqueness of solutions for nonlinear equations using Schaefer’s fixed point theorem. In addition, we present a generalized Hyers-Ulam stability result via the Gronwall inequality. Finally, two examples are given to illustrate our main results.

本文研究了具有加权Caputo-Fabrizio分数阶导数的线性方程的Hyers-Ulam稳定性和广义Hyers-Ulam稳定性。利用Schaefer不动点定理,建立了非线性方程解的存在唯一性。此外,我们还利用Gronwall不等式给出了一个广义的Hyers-Ulam稳定性结果。最后,给出了两个例子来说明我们的主要结果。
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引用次数: 3
期刊
Chaos, Solitons and Fractals: X
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