Lithologic Control on the Scaling Properties of the First-Order Streams of Drainage Networks: A Monofractal Analysis

The movement of water through the landscape can be investigated at different scales. This study dealt with the interrelation between bedrock lithology and the geometry of the overlying drainage systems. Parameters of fractal analysis, such as fractal dimension and lacunarity, were used to measure and quantify this relationship. The interrelation between bedrock lithology and the geometry of the drainage systems has been widely studied in the last decades. The quantification of this linkage has not yet been clearly established. Several studies have selected river basins or regularly shaped areas as study units, assuming them to be lithologically homogeneous. This study considered irregular distributions of rock types, establishing areas of the soil map (1:25,000) with the same lithologic information as study units. The tectonic stability and the low climatic variability of the study region allowed effective investigation of the lithologic controls on the drainage networks developed on the plutonic rocks, the metamorphic rocks, and the sedimentary materials existing in the study area. To exclude the effect of multiple in- and outflows in the lithologically homogeneous units, we focused this study on the first-order streams of the drainage networks. The geometry of the hydrologic features was quantified through traditional metrics of fluvial geomorphology and scaling parameters of fractal analysis, such as the fractal dimension, the reference density, and the lacunarity. The results demonstrate the scale invariance of both the drainage networks and the set of first-order streams at the study scale and a relationship between scaling in the lithology and the drainage network.

Scaling in Soil and Other Complex Porous Media

Scaling is becoming an increasingly important topic in the earth and environmental sciences as researchers attempt to understand complex natural systems through the lens of an ever-increasing set of methods and scales. The guest editors introduce the papers in this issue’s special section and present an overview of some of the work being done. Scaling remains one of the most challenging topics in earth and environmental sciences, forming a basis for our understanding of process development across the multiple scales that make up the subsurface environment. Tremendous progress has been made in discovery, explanation, and applications of scaling. And yet much more needs to be done and is being done as part of the modern quest to quantify, analyze, and manage the complexity of natural systems. Understanding and succinct representation of scaling properties can unveil underlying relationships between system structure and response functions, improve parameterization of natural variability and heterogeneity, and help us address societal needs by effectively merging knowledge acquired at different scales.

Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties

A novel class of graphs, here named quasiperiodic, are const ructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Far ey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy

UAS See-and-Avoid Strategy using a Fuzzy Logic Controller Optimized by Cross-Entropy in Scaling Factors and Membership Functions

This work aims to develop a novel Cross-Entropy (CE) optimization-based fuzzy controller for Unmanned Aerial Monocular Vision-IMU System (UAMVIS) to solve the seeand- avoid problem using its accurate autonomous localization information. The function of this fuzzy controller is regulating the heading of this system to avoid the obstacle, e.g. wall. In the Matlab Simulink-based training stages, the Scaling Factor (SF) is adjusted according to the specified task firstly, and then the Membership Function (MF) is tuned based on the optimized Scaling Factor to further improve the collison avoidance performance. After obtained the optimal SF and MF, 64% of rules has been reduced (from 125 rules to 45 rules), and a large number of real flight tests with a quadcopter have been done. The experimental results show that this approach precisely navigates the system to avoid the obstacle. To our best knowledge, this is the first work to present the optimized fuzzy controller for UAMVIS using Cross-Entropy method in Scaling Factors and Membership Functions optimization.

UAS See-and-Avoid Strategy using a Fuzzy Logic Controller Optimized by Cross-Entropy in Scaling Factors and Membership Functions.

This work aims to develop a novel Cross-Entropy (CE) optimization-based fuzzy controller for Unmanned Aerial Monocular Vision-IMU System (UAMVIS) to solve the seeand-avoid problem using its accurate autonomous localization information. The function of this fuzzy controller is regulating the heading of this system to avoid the obstacle, e.g. wall. In the Matlab Simulink-based training stages, the Scaling Factor (SF) is adjusted according to the specified task firstly, and then the Membership Function (MF) is tuned based on the optimized Scaling Factor to further improve the collison avoidance performance. After obtained the optimal SF and MF, 64% of rules has been reduced (from 125 rules to 45 rules), and a large number of real flight tests with a quadcopter have been done. The experimental results show that this approach precisely navigates the system to avoid the obstacle. To our best knowledge, this is the first work to present the optimized fuzzy controller for UAMVIS using Cross-Entropy method in Scaling Factors and Membership Functions optimization.

Estimate of the total volume of Svalbard glaciers, and their potential contribution to sea-level rise, using new regionally based scaling relationships

We present a set of new volume scaling relationships specific to Svalbard glaciers, derived from a sample of 60 volume–area pairs. Glacier volumes are computed from ground-penetrating radar (GPR)-retrieved ice thickness measurements, which have been compiled from different sources for this study. The most precise scaling models, in terms of lowest cross-validation errors, are obtained using a multivariate approach where, in addition to glacier area, glacier length and elevation range are also used as predictors. Using this multivariate scaling approach, together with the Randolph Glacier Inventory V3.2 for Svalbard and Jan Mayen, we obtain a regional volume estimate of 6700 ± 835 km3, or 17 ± 2 mm of sea-level equivalent (SLE). This result lies in the mid- to low range of recently published estimates, which show values as varied as 13 and 24 mm SLE. We assess the sensitivity of the scaling exponents to glacier characteristics such as size, aspect ratio and average slope, and find that the volume of steep-slope and cirque-type glaciers is not very sensitive to changes in glacier area.

Empirical laws of survival and evolution: Their universality and implications

Presented analysis of human and fly life tables proves that with the specified accuracy their entire survival and mortality curves are uniquely determined by a single point (e.g., by the birth mortality q0), according to the law, which is universal for species as remote as humans and flies. Mortality at any age decreases with the birth mortality q0. According to life tables, in the narrow vicinity of a certain q0 value (which is the same for all animals of a given species, independent of their living conditions), the curves change very rapidly and nearly simultaneously for an entire population of different ages. The change is the largest in old age. Because probability to survive to the mean reproductive age quantifies biological fitness and evolution, its universal rapid change with q0 (which changes with living conditions) manifests a new kind of an evolutionary spurt of an entire population. Agreement between theoretical and life table data is explicitly seen in the figures. Analysis of the data on basic metabolism reduces it to the maximal mean lifespan (for animals from invertebrates to mammals), or to the maximal mean fission time (for bacteria), and universally scales them with the total number of body atoms only. Phenomenological origin of this unification and universality of metabolism, survival, and evolution is suggested. Their implications and challenges are discussed.

A universal scaling law between gray matter and white matter of cerebral cortex

Neocortex, a new and rapidly evolving brain structure in mammals, has a similar layered architecture in species over a wide range of brain sizes. Larger brains require longer fibers to communicate between distant cortical areas; the volume of the white matter that contains long axons increases disproportionally faster than the volume of the gray matter that contains cell bodies, dendrites, and axons for local information processing, according to a power law. The theoretical analysis presented here shows how this remarkable anatomical regularity might arise naturally as a consequence of the local uniformity of the cortex and the requirement for compact arrangement of long axonal fibers. The predicted power law with an exponent of 4/3 minus a small correction for the thickness of the cortex accurately accounts for empirical data spanning several orders of magnitude in brain sizes for various mammalian species, including human and nonhuman primates.

Invariant scaling relationships for interspecific plant biomass production rates and body size

The allometric relationships for plant annualized biomass production (“growth”) rates, different measures of body size (dry weight and length), and photosynthetic biomass (or pigment concentration) per plant (or cell) are reported for multicellular and unicellular plants representing three algal phyla; aquatic ferns; aquatic and terrestrial herbaceous dicots; and arborescent monocots, dicots, and conifers. Annualized rates of growth G scale as the 3/4-power of body mass M over 20 orders of magnitude of M (i.e., G ∝ M3/4); plant body length L (i.e., cell length or plant height) scales, on average, as the 1/4-power of M over 22 orders of magnitude of M (i.e., L ∝ M1/4); and photosynthetic biomass Mp scales as the 3/4-power of nonphotosynthetic biomass Mn (i.e., Mp ∝ Mn3/4). Because these scaling relationships are indifferent to phylogenetic affiliation and habitat, they have far-reaching ecological and evolutionary implications (e.g., net primary productivity is predicted to be largely insensitive to community species composition or geological age).

Scaling the universe: Gravitational lenses and the Hubble constant

Gravitational lenses, besides being interesting in their own right, have been demonstrated to be suitable as “gravitational standard rulers” for the measurement of the rate of expansion of the Universe (Ho), as well as to constrain the values of the cosmological parameters such as Ωo and Λo that control the evolution of the volume of the Universe with cosmic time.

A joint hazard and time scaling model to compare survival curves.

To provide a more general method for comparing survival experience, we propose a model that independently scales both hazard and time dimensions. To test the curve shape similarity of two time-dependent hazards, h1(t) and h2(t), we apply the proposed hazard relationship, h12(tKt)/ h1(t) = Kh, to h1. This relationship doubly scales h1 by the constant hazard and time scale factors, Kh and Kt, producing a transformed hazard, h12, with the same underlying curve shape as h1. We optimize the match of h12 to h2 by adjusting Kh and Kt. The corresponding survival relationship S12(tKt) = [S1(t)]KtKh transforms S1 into a new curve S12 of the same underlying shape that can be matched to the original S2. We apply this model to the curves for regional and local breast cancer contained in the National Cancer Institute's End Results Registry (1950-1973). Scaling the original regional curves, h1 and S1 with Kt = 1.769 and Kh = 0.263 produces transformed curves h12 and S12 that display congruence with the respective local curves, h2 and S2. This similarity of curve shapes suggests the application of the more complete curve shapes for regional disease as templates to predict the long-term survival pattern for local disease. By extension, this similarity raises the possibility of scaling early data for clinical trial curves according to templates of registry or previous trial curves, projecting long-term outcomes and reducing costs. The proposed model includes as special cases the widely used proportional hazards (Kt = 1) and accelerated life (KtKh = 1) models.

Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulent shear flow.

The small viscosity asymptotics of the inertial range of local structure and of the wall region in wallbounded turbulent shear flow are compared. The comparison leads to a sharpening of the dichotomy between Reynolds number dependent scaling (power-type) laws and the universal Reynolds number independent logarithmic law in wall turbulence. It further leads to a quantitative prediction of an essential difference between them, which is confirmed by the results of a recent experimental investigation. These results lend support to recent work on the zero viscosity limit of the inertial range in turbulence.

Bioenergetic scaling: metabolic design and body-size constraints in mammals.

The cytosolic phosphorylation ratio ([ATP]/[ADP][P(i)]) in the mammalian heart was found to be inversely related to body mass with an exponent of -0.30 (r = 0.999). This exponent is similar to -0.25 calculated for the mass-specific O2 consumption. The inverse of cytosolic free [ADP], the Gibbs energy of ATP hydrolysis (delta G'ATP), and the efficiency of ATP production (energy captured in forming 3 mol of ATP per cycle along the mitochondrial respiratory chain from NADH to 1/2 O2) were all found to scale with body mass with a negative exponent. On the basis of scaling of the phosphorylation ratio and free cytosolic [ADP], we propose that the myocardium and other tissues of small mammals represent a metabolic system with a higher driving potential (a higher delta G'ATP from the higher [ATP]/[ADP][P(i)]) and a higher kinetic gain [(delta V/Vmax)/delta [ADP]] where small changes in free [ADP] produce large changes in steady-state rates of O2 consumption. From the inverse relationship between mitochondrial efficiency and body size we calculate that tissues of small mammals are more efficient than those of large mammals in converting energy from the oxidation of foodstuffs to the bond energy of ATP. A higher efficiency also indicates that mitochondrial electron transport is not the major site for higher heat production in small mammals. We further propose that the lower limit of about 2 g for adult endotherm body size (bumblebee-bat, Estrucan shrew, and hummingbird) may be set by the thermodynamics of the electron transport chain. The upper limit for body size (100,000-kg adult blue whale) may relate to a minimum delta G'ATP of approximately 55 kJ/mol for a cytoplasmic phosphorylation ratio of 12,000 M-1.