Global map

A natural question to ask is whether, in going backwards in time, the set of predecessor states can themselves be obtained from (possibly some other) CA rule It is certainly not a-priori obvious that if the global map defined by a local process is invertible, its inverse must also be defined by a local process. In 1972, Richardson [rich72] was in fact able to show that the inverse of an invertible CA rule is itself a CA rule. His proof unfortunately did not provide a scheme by which the inverse map could actually be constructed. A trivial example of unequal inverses are the elementary shift-right and shift-left rules, R240 and R170, respectively. 

Technically, Moore proved that a CA is surjective if and only if the restriction of its global map to finite configurations is injective, where a finite configuration means that only finitely many sites of the lattice are non-quiescent. 

Fig. 10-6 Global map of major ocean currents. AND = ARC = Arctic convergence.

Hansen M, Potapov P, Moore R, Hancher M, Turubanova S, Tyukavina A, Thau D, et al. High-resolution global maps of 21 st-century forest cover change. Science, 2013. 342(6160) pp. 850-853. doi 10.1126/science.l244693... 

Global map of average mixed layer depths In (a) February and (b) August based on hydrographic data collected from 1941 through 2002. Source After de Boyer Montegut, C., ef al. (2004). Journal of Geophysical Research 109, Cl 2003. (See companion website for color version.)... 

The present-day deep-water concentration gradients of O2. phosphate, nitrate, and dissolved silicon are illustrated in Figure 10.3 as a global map at 4000 m and in Figure 10.4 as a longitudinal profile running down the middle of the Atlantic Ocean. 

A global map of quartz abundance is given in Figure 14.12. In this case, the contribution of quartz is presented as the contribution to the bulk sediment from which biogenic carbonate and silica have been removed. This map is very similar to the global distribution of dust presented in Figure 11.4, reflecting the importance of aeolian transport for this detrital silicate. 

Global mapping of FeO, Th, and Ti02 concentrations, especially, has allowed the abundance and distribution of different compositional regions of the lunar crust to be determined, and has provided new insights into heterogeneities in the mantle (Jolliff et al., 2000 Giguere et al., 2000). 

The formation of three-branch horseshoes in scattering systems can be modeled by a global mapping like (4.7) and (4.8) with the potential [10]... 

Figure 10 Global map of aerosol UV-flux attenuation factor rj= 1-F,er/Fd(air = l-exp -(k/b)AI, estimated from the aerosol index map. The conversion factor k/b= 0.25, was obtained from the clear sky radiative transfer calculations, assuming single layer (dust or smoke) between 2and 4 km and solar zenith angle 30°. The map shows that aersosol absorption can produce very large reduction in UV flux ( 50%) in certain parts of the world (from plate 2 of Krotkov et al. 1998).

In Part I of this book, I attempted to make some global maps of the paranormal, to sketch in the shape of the continents and mark the major cities. We need these kinds of maps... 

Figure 2.1. Diagram of factors controlling the main inputs and outputs of soil carbon, superimposed over a global map of soil organic carbon stocks. DOC, POC, and DIC stand for dissolved organic C, particulate organic C, and dissolved inorganic C, respectively. The background soil organic carbon (SOC) map (Miller Projection 1 100,000,000). See color insert. Reprinted from Davidson, E. A., and Janssens, I. A. (2006). Temperature sensitivity of soil carbon decomposition and feedbacks to climate change. Nature 440,165-173, with permission from Macmillan.

See color insert following page 140.) Global map of insolation in units of kWh/m2/d. (Source Earth Observatory, NASA.)... 

Paolini G, Shapland R, van Hoorn W, Mason J, Hopkins A (2006) Global mapping of pharmacological space. Nat Biotechnol 24 805-815... 

V. Global Mapping of Surface Hydration and Protein Fluctuations... 

V. GLOBAL MAPPING OF SURFACE HYDRATION AND PROTEIN FLUCTUATIONS... 

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