Power laws, Pareto distributions and Zipf's law

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.Comment: 28 pages, 16 figures, minor corrections and additions in this versio

On Convergence and Threshold Properties of Discrete Lotka-Volterra Population Protocols

In this work we focus on a natural class of population protocols whose dynamics are modelled by the discrete version of Lotka-Volterra equations. In such protocols, when an agent $a$ of type (species) $i$ interacts with an agent $b$ of type (species) $j$ with $a$ as the initiator, then $b$'s type becomes $i$ with probability $P\_{ij}$. In such an interaction, we think of $a$ as the predator, $b$ as the prey, and the type of the prey is either converted to that of the predator or stays as is. Such protocols capture the dynamics of some opinion spreading models and generalize the well-known Rock-Paper-Scissors discrete dynamics. We consider the pairwise interactions among agents that are scheduled uniformly at random. We start by considering the convergence time and show that any Lotka-Volterra-type protocol on an $n$-agent population converges to some absorbing state in time polynomial in $n$, w.h.p., when any pair of agents is allowed to interact. By contrast, when the interaction graph is a star, even the Rock-Paper-Scissors protocol requires exponential time to converge. We then study threshold effects exhibited by Lotka-Volterra-type protocols with 3 and more species under interactions between any pair of agents. We start by presenting a simple 4-type protocol in which the probability difference of reaching the two possible absorbing states is strongly amplified by the ratio of the initial populations of the two other types, which are transient, but "control" convergence. We then prove that the Rock-Paper-Scissors protocol reaches each of its three possible absorbing states with almost equal probability, starting from any configuration satisfying some sub-linear lower bound on the initial size of each species. That is, Rock-Paper-Scissors is a realization of a "coin-flip consensus" in a distributed system. Some of our techniques may be of independent value

Nodal dynamics, not degree distributions, determine the structural controllability of complex networks

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set (PDS), is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.Comment: 1 Figures, 6 page

Fluctuation scaling in complex systems: Taylor's law and beyond

Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form "$fluctuations \approx const.\times average^\alpha$", where the exponent $\alpha$ is predominantly in the range $[1/2, 1]$. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names \emph{Taylor's law} or \emph{fluctuation scaling}. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling.Comment: 33 pages, 20 figures, 2 tables, submitted to Advances in Physic

Measuring and modelling the response of Klebsiella pneumoniae KPC prey to Bdellovibrio bacteriovorus predation, in human serum and defined buffer

In worldwide conditions of increasingly antibiotic-resistant hospital infections, it is important to research alternative therapies. Bdellovibrio bacteriovorus bacteria naturally prey on Gram-negative pathogens, including antibiotic-resistant strains and so B. bacteriovorus have been proposed as "living antibiotics" to combat antimicrobially-resistant pathogens. Predator-prey interactions are complex and can be altered by environmental components. To be effective B. bacteriovorus predation needs to work in human body fluids such as serum where predation dynamics may differ to that studied in laboratory media. Here we combine mathematical modelling and lab experimentation to investigate the predation of an important carbapenem-resistant human pathogen, Klebsiella pneumoniae, by B. bacteriovorus in human serum versus buffer. We show experimentally that B. bacteriovorus is able to reduce prey numbers in each environment, on different timescales. Our mathematical model captures the underlying dynamics of the experimentation, including an initial predation-delay at the predator-prey-serum interface. Our research shows differences between predation in buffer and serum and highlights both the potential and limitations of B. bacteriovorus acting therapeutically against K. pneumoniae in serum, informing future research into the medicinal behaviours and dosing of this living antibacterial

Equal fitness paradigm explained by a trade-off between generation time and energy production rate

Most plant, animal and microbial species of widely varying body size and lifestyle are nearly equally fit as evidenced by their coexistence and persistence through millions of years. All organisms compete for a limited supply of organic chemical energy, derived mostly from photosynthesis, to invest in the two components of fitness: survival and production. All organisms are mortal because molecular and cellular damage accumulates over the lifetime; life persists only because parents produce offspring. We call this the equal fitness paradigm. The equal fitness paradigm occurs because: (1) there is a trade-off between generation time and productive power, which have equal-but-opposite scalings with body size and temperature; smaller and warmer organisms have shorter lifespans but produce biomass at higher rates than larger and colder organisms; (2) the energy content of biomass is essentially constant, ~22.4 kJ g−1 dry body weight; and (3) the fraction of biomass production incorporated into surviving offspring is also roughly constant, ~10–50%. As organisms transmit approximately the same quantity of energy per gram to offspring in the next generation, no species has an inherent lasting advantage in the struggle for existence. The equal fitness paradigm emphasizes the central importance of energy, biological scaling relations and power–time trade-offs in life history, ecology and evolution

Environmental pleiotropy and demographic history direct adaptation under antibiotic selection

Evolutionary rescue following environmental change requires mutations permitting population growth in the new environment. If change is severe enough to prevent most of the population reproducing, rescue becomes reliant on mutations already present. If change is sustained, the fitness effects in both environments, and how they are associated-termed 'environmental pleiotropy'-may determine which alleles are ultimately favoured. A population's demographic history-its size over time-influences the variation present. Although demographic history is known to affect the probability of evolutionary rescue, how it interacts with environmental pleiotropy during severe and sustained environmental change remains unexplored. Here, we demonstrate how these factors interact during antibiotic resistance evolution, a key example of evolutionary rescue fuelled by pre-existing mutations with pleiotropic fitness effects. We combine published data with novel simulations to characterise environmental pleiotropy and its effects on resistance evolution under different demographic histories. Comparisons among resistance alleles typically revealed no correlation for fitness-i.e., neutral pleiotropy-above and below the sensitive strain's minimum inhibitory concentration. Resistance allele frequency following experimental evolution showed opposing correlations with their fitness effects in the presence and absence of antibiotic. Simulations demonstrated that effects of environmental pleiotropy on allele frequencies depended on demographic history. At the population level, the major influence of environmental pleiotropy was on mean fitness, rather than the probability of evolutionary rescue or diversity. Our work suggests that determining both environmental pleiotropy and demographic history is critical for predicting resistance evolution, and we discuss the practicalities of this during in vivo evolution

HIV Treatment as Prevention: Debate and Commentary-Will Early Infection Compromise Treatment-as-Prevention Strategies?

Universal HIV testing and immediate antiretroviral therapy for infected individuals has been proposed as a way of reducing the transmission of HIV and thereby bringing the HIV epidemic under control. It is unclear whether transmission during early HIV infection—before individuals are likely to have been diagnosed with HIV and started on antiretroviral therapy—will compromise the effectiveness of treatment as prevention. This article presents two opposing viewpoints by Powers, Miller, and Cohen, and Williams and Dye, followed by a commentary by Fraser

Academic careers in Computer Science: Continuance and transience of lifetime co-authorships

International audienceScholarly publications reify fruitful collaborations between co-authors. A branch of research in the Science Studies focuses on analyzing the co-authorship networks of established scientists. Such studies tell us about how their collaborations developed through their careers. This paper updates previous work by reporting a transversal and a longitudinal studies spanning the lifelong careers of a cohort of researchers from the DBLP bibliographic database. We mined 3,860 researchers' publication records to study the evolution patterns of their co-authorships. Two features of co-authors were considered: 1) their expertise, and 2) the history of their partnerships with the sampled researchers. Our findings reveal the ephemeral nature of most collaborations: 70% of the new co-authors were only one-shot partners since they did not appear to collaborate on any further publications. Overall, researchers consistently extended their co-authorships 1) by steadily enrolling beginning researchers (i.e., people who had never published before), and 2) by increasingly working with confirmed researchers with whom they already collaborated