Ubiquity of Benford's law and emergence of the reciprocal distribution

Friar, J. L.; Goldman, T.; Pérez–Mercader, Juan

doi:10.1016/j.physleta.2016.03.045

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…It is possible that the decreasing relative cost of replication compared to total metabolism as cell size increases allows for this potential inefficiency ('potential' because we have not quantified the utility of the non-coding DNA). It has also been proposed that the underlying distribution leading to equation (4.8) is a Benford distribution, and that this gives genomes the following properties: (i) upon combination of genes the minimal error possible is made (maximum fidelity) and (ii) the information contained in the genes is transferred at the maximum possible rate (minimizing distortion) [100,102,103]. Thus far, in this paper we have analysed the thermodynamic efficiency of the computational processes; however, the above connection opens up important future efforts which should focus on the connection between the thermodynamic efficiency of both computation and communication within cells.…”

Section: (F) Thermodynamic Efficiency Of Gene Replicationmentioning

confidence: 99%

The thermodynamic efficiency of computations made in cells across the range of life

Kempes

Wolpert

Cohen

et al. 2017

Phil. Trans. R. Soc. A.

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Biological organisms must perform computation as they grow, reproduce, and evolve. Moreover, ever since Landauer's bound was proposed it has been known that all computation has some thermodynamic cost -and that the same computation can be achieved with greater or smaller thermodynamic cost depending on how it is implemented. Accordingly an important issue concerning the evolution of life is assessing the thermodynamic efficiency of the computations performed by organisms. This issue is interesting both from the perspective of how close life has come to maximally efficient computation (presumably under the pressure of natural selection), and from the practical perspective of what efficiencies we might hope that engineered biological computers might achieve, especially in comparison with current computational systems. Here we show that the computational efficiency of translation, defined as free energy expended per amino acid operation, outperforms the best supercomputers by several orders of magnitude, and is only about an order of magnitude worse than the Landauer bound. However this efficiency depends strongly on the size and architecture of the cell in question. In particular, we show that the useful efficiency of an amino acid operation, defined as the bulk energy per amino acid polymerization, decreases for increasing bacterial size and converges to the polymerization 1 arXiv:1706.05043v1 [q-bio.OT] 15 Jun 2017 cost of the ribosome. This cost of the largest bacteria does not change in cells as we progress through the major evolutionary shifts to both single and multicellular eukaryotes. However, the rates of total computation per unit mass are nonmonotonic in bacteria with increasing cell size, and also change across different biological architectures including the shift from unicellular to multicellular eukaryotes.

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Section: (F) Thermodynamic Efficiency Of Gene Replicationmentioning

confidence: 99%

The thermodynamic efficiency of computations made in cells across the range of life

Kempes

Wolpert

Cohen

et al. 2017

Phil. Trans. R. Soc. A.

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“…The Central Limit Theorem, which gives rise to normal and lognormal distributions, is one of the most powerful and useful concepts in probability theory [Pitman, 1999] (see Chapter 3). It has an obverse: random samples chosen from random probability distributions are collectively described by the reciprocal distribution [Friar et al, 2016, Hill, 1995, Berger and Hill, 2008, Hamming, 1970. In other words, if random samples are taken from random probability distributions (in such a way that the overall process is scale neutral), and the results combined, then the resulting combined samples converge to the reciprocal distribution.…”

Section: Discussionmentioning

confidence: 99%

“…In other words, if random samples are taken from random probability distributions (in such a way that the overall process is scale neutral), and the results combined, then the resulting combined samples converge to the reciprocal distribution. Thus as the normal distribution is a robust result of aggregating samples, the reciprocal distribution is the robust result of aggregating distributions -the reciprocal distribution is therefore sometimes termed "the distribution of distributions" [Friar et al, 2016]. (This phenomenon is best known for giving rise to the logarithmic distribution of first digits in many types of data, known as Benford's Law, but underlying this phenomenon is the reciprocal distribution.…”

Section: Discussionmentioning

confidence: 99%

Distributional models of ocean carbon export

Ma¹

2019

Woods Hole Open Access Server (WHOAS) at the MBLWHOI Library

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Each year, surface ocean ecosystems export sinking particles containing gigatons of carbon into the ocean's interior. This particle flux connects the entire ocean microbiome and constitutes a fundamental aspect of marine microbial ecology and biogeochemical cycles. Particle flux is also variable and intricately complex, impeding its mechanistic or quantitative description. In this thesis we pair compilations of available data with novel mathematical models to explore the relationships between particle flux and other key variables -temperature, net primary production, and depth. Particular use is made of (probability) distributional descriptions of quantities that are known to vary appreciably. First, using established thermodynamic dependencies for primary production and respiration, a simple mechanistic model is developed relating export efficiency (i.e. the fraction of primary production that is exported out of the surface ocean via particle flux) to temperature. The model accounts for the observed variability in export efficiency due to temperature without idealizing out the remaining variability that evinces particle flux's complexity. This model is then used to estimate the metabolically-driven change in average export efficiency over the era of long-term global sea surface temperature records, and it is shown that the underlying mechanism may help explain glacial-interglacial atmospheric carbon dioxide drawdown. The relationship between particle flux and net primary production is then explored. Given that these are inextricable but highly variable and measured on different effective scales, it is hypothesized that a quantitative relationship emerges between collections of the two measurements -i.e. that they can be related not measurement-by-measurement but rather via their probability distributions. It is shown that on large spatial or temporal scales both are consistent with lognormal distributions, as expected if each is considered as the collective result of many subprocesses. A relationship is then derived between the log-moments of their distributions and agreement is found between independent estimates of this relationship, suggesting that upper ocean particle flux is predictable from net primary production on large spatiotemporal scales. Finally, the attenuation of particle flux with depth is explored. It is shown that while several particle flux-versus-depth models capture observations equivalently, these carry very different implications mechanistically and for magnitudes of export out of the surface ocean. A model is then proposed for this relationship that accounts for measurements of both the flux profile and of the settling velocity distribution of particulate matter, and is thus more consistent with and constrained by empirical knowledge. Possible future applications of these models are discussed, as well as how they could be tested and/or constrained observationally.Despite the premise that a thesis represents individual effort, to get here has taken a large and diverse village, each member...

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On the Universal Quantitative Pattern of the Distribution of Initial Characters in General Dictionaries: The Exponential Distribution is Valid for Various Languages

Shulzinger

Bormashenko

2017

Journal of Quantitative Linguistics

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Ubiquity of Benford's law and emergence of the reciprocal distribution

Cited by 4 publications

References 16 publications

The thermodynamic efficiency of computations made in cells across the range of life

The thermodynamic efficiency of computations made in cells across the range of life

Distributional models of ocean carbon export

On the Universal Quantitative Pattern of the Distribution of Initial Characters in General Dictionaries: The Exponential Distribution is Valid for Various Languages

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