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An ecological flow network is a weighted directed graph in which nodes are species, edges are "who eats whom" relationships and weights are rates of energy or nutrients transfer between species. Allometric scaling is a ubiquitous feature…
Metabolic allometry, a common pattern in nature, is a close-to-3/4-power scaling law between metabolic rate and body mass in organisms, across and within species. An analogous relationship between metabolic rate and water volume in river…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
Metabolism of living organisms is a foundation of life. The metabolic rate (energy production per unit time) increases slower than organisms' mass. When this phenomenon is considered across different species, it is called interspecific…
An analogy between the fractal nature of networks of arteries and that of systems of rivers has been drawn in the previous works. However, the deep structure of the hierarchy of blood vessels has not yet been revealed. This paper is devoted…
We examine the scaling law $B \propto M^{\alpha}$ which connects organismal metabolic rate $B$ with organismal mass $M$, where $\alpha$ is commonly held to be 3/4. Since simple dimensional analysis suggests $\alpha=2/3$, we consider this to…
Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific…
In prokaryotic genomes the number of transcriptional regulators is known to quadratically scale with the total number of protein-coding genes. Toolbox model was recently proposed to explain this scaling for metabolic enzymes and their…
Food webs can be regarded as energy transporting networks in which the weight of each edge denotes the energy flux between two species. By investigating 21 empirical weighted food webs as energy flow networks, we found several ubiquitous…
The growth and scaling of organs is a fundamental aspect of animal development. However, how organs grow to the right size and shape required by physiological demands, remains largely unknown. Here, we provide a framework combining theory…
One of the major characteristics of living organisms is metabolic rate, which is the amount of energy produced per unit of time. When the mass of organisms increases, the metabolic rate also increases (usually as a power function of mass),…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
The law of allometric growth is one of basic rules for understanding urban evolution. The general form of this law is allometric scaling law. However, the deep meaning and underlying rationale of the scaling exponents remain to be brought…
We scrutinize the temporally-resolved speed of active cargo transport in living cells, and show intermittent bursting motions. These nonlinear fluctuations follow a scaling law over several decades of time and space, the statistical…
Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
Many complex systems obey allometric, or power, laws y=Yx^{a}. Here y is the measured value of some system attribute a, Y is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values…
At the basic geometric level, the distribution networks carrying vital materials in living organisms, and the units such as the nephrons and alveoli, form a scaling structure named here the site model. This unified view of the allometry of…