Beta rank function: A smooth double-Pareto-like distribution

Fontanelli, Oscar; Miramóntes, Pedro; Mansilla, Ricardo; Cocho, G.; Li, Wentian

doi:10.1080/03610926.2020.1800739

Cited by 6 publications

(4 citation statements)

References 52 publications

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“…Which goes in line with [85]; now, when we plug in the values from the simulation (N = 2.70546008 = max{ln(log 10 (p))}), we obtain,…”

Section: 2supporting

confidence: 69%

“…Where r is the rank value, N is the maximum value, C is a normalization constant and a, b ∈ R are two constants to be determined [160], furthermore, it has been observed that many types of data follow this distribution: ranks of articles and citations in journals, linguistic data, citation profile, English, and Spanish letter frequency distribution, and more; this distribution, depending on the value of the constants a, b, may give rise to other common probability distributions, that is, when a = b = 0, it yields a constant random variable, when a = 0, b = 1 we may obtain a uniform distribution, when b = 0 it becomes a Pareto distribution, when a = b it yields a Lavalette distribution [85]. Here we will determine the constants a, b for the equilibrium distributions of both the T-cell differentiation and the HIV infection processes, as well as the R 2 fitting values for said functions.…”

Section: 2mentioning

confidence: 99%

See 1 more Smart Citation

In silico model of infection of a CD4(+) T-cell by a human immunodeficiency type 1 virus, and a mini-review on its molecular pathophysiology

Vivanco-Lira¹,

José-Raúl²

2021

Preprint

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“…Which goes in line with [85]; now, when we plug in the values from the simulation (N = 2.70546008 = max{ln(log 10 (p))}), we obtain,…”

Section: 2supporting

confidence: 69%

Section: 2mentioning

confidence: 99%

In silico model of infection of a CD4(+) T-cell by a human immunodeficiency type 1 virus, and a mini-review on its molecular pathophysiology

Vivanco-Lira¹,

José-Raúl²

2021

Preprint

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show abstract

“…It is worth noticing that the histogram of node strength in log-scale is not symmetric around the peak; an example of this can be seen in Fig. 5 B. Consequently, we have applied the Beta Rank Function (BRF), which is a rank-size function, and a family of probability distributions that exhibits Paretian behavior in both tails, with different exponents 46 . BRF has the form of , where r is the rank of the observation of size X , and a , b are free parameters.…”

Section: Resultsmentioning

confidence: 99%

Intermunicipal travel networks of Mexico during the COVID-19 pandemic

Fontanelli

Guzmán²,

Viveros

et al. 2023

Sci Rep

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Human mobility networks are widely used for diverse studies in geography, sociology, and economics. In these networks, nodes usually represent places or regions and links refer to movement between them. They become essential when studying the spread of a virus, the planning of transit, or society’s local and global structures. Therefore, the construction and analysis of human mobility networks are crucial for a vast number of real-life applications. This work presents a collection of networks that describe the human travel patterns between municipalities in Mexico in the 2020–2021 period. Using anonymized mobile location data, we constructed directed, weighted networks representing the volume of travels between municipalities. We analysed changes in global, local, and mesoscale network features. We observe that changes in these features are associated with factors such as COVID-19 restrictions and population size. In general, the implementation of restrictions at the start of the COVID-19 pandemic in early 2020, induced more intense changes in network features than later events, which had a less notable impact in network features. These networks will result very useful for researchers and decision-makers in the areas of transportation, infrastructure planning, epidemic control and network science at large.

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“…In [59] we introduced the Beta Rank Function distribution (BRF), which is the probability distribution of a random variable whose rank-size function is the DGBD. This family of probability distributions can be defined through its quantile function x(u) = A(1−u) b /u a [60].…”

Section: Beta Rank Functionmentioning

confidence: 99%

Human mobility patterns in Mexico City and their links with socioeconomic variables during the COVID-19 pandemic

Fontanelli¹,

Valdivia²,

Romero³

et al. 2022

Preprint

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The availability of cellphone geolocation data provides a remarkable opportunity to study human mobility patterns and how these patterns are affected by the recent pandemic. Two simple centrality metrics allow us to measure two different aspects of mobility in origindestination networks constructed with this type of data: variety of places connected to a certain node (degree) and number of people that travel to or from a given node (strength). In this contribution, we present an analysis of node degree and strength in daily origindestination networks for Greater Mexico City during 2020. Unlike what is observed in many complex networks, these origin-destination networks are not scale free. Instead, there is a characteristic scale defined by the distribution peak; centrality distributions exhibit a skewed two-tail distribution with power law decay on each side of the peak. We found that high mobility areas tend to be closer to the city center, have higher population and better socioeconomic conditions. Areas with anomalous behavior are almost always on the periphery of the city, where we can also observe qualitative difference in mobility patterns between east and west. Finally, we study the effect of mobility restrictions due to the outbreak of the COVID-19 pandemics on these mobility patterns.

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Beta rank function: A smooth double-Pareto-like distribution

Cited by 6 publications

References 52 publications

In silico model of infection of a CD4(+) T-cell by a human immunodeficiency type 1 virus, and a mini-review on its molecular pathophysiology

In silico model of infection of a CD4(+) T-cell by a human immunodeficiency type 1 virus, and a mini-review on its molecular pathophysiology

Intermunicipal travel networks of Mexico during the COVID-19 pandemic

Human mobility patterns in Mexico City and their links with socioeconomic variables during the COVID-19 pandemic

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