ORGANIC PHOSPHORUS COMPOUNDS 70 PREPARATION AND PROPERTIES OF NEW PHOSPHORUS CONTAINING CHELATING AGENTS FOR CALCIUM AND MAGNESIUM IONS

Abstract

Dedicated to Professor Martin Schmeisser on the occasion of his 65th birthday.

Several phosphonic acids of the type H₂O₃PCH₂OCHRCO₂H, R = H, CH₃, CO₂H; [H₂O₃P(CH₂)_x]₂ Y, x = 1, 2; Y = O, S; and [o-H₂O₃P(CH₂)]₂C₆H₄ have been synthesized and their capacity to chelate with calcium has been determined.     

A new cadmium reduction device for the microplate determination of nitrate in water, soil, plant tissue, and physiological fluids

A reusable catalytic reductor consisting of 96 copperized-cadmium pins attached to a microplate lid was developed to simultaneously reduce nitrate (NO3-) to nitrite (NO2-) in all wells of a standard microplate. The resulting NO2- is analyzed colorimetrically by the Griess reaction using a microplate reader. Nitrate data from groundwater samples analyzed using the new device correlated well with data obtained by ion chromatography (r2 = 0.9959). Soil and plant tissue samples previously analyzed for NO3- in an interlaboratory validation study sponsored by the Soil Science Society of America were also analyzed using the new technique. For the soil sample set, the data are shown to correlate well with the other methods used (r2 = 0.9976). Plant data correlated less well, especially for samples containing low concentrations of NO3-. Reasons for these discrepancies are discussed, and new techniques to increase the accuracy of the analysis are explored. In addition, a method is presented for analyzing NO3- in physiological fluids (blood serum and urine) after matrix modification with Somogyi's reagent. A protocol for statistical validation of data when analyzing samples with complex matrixes is also established. The simplicity, adaptability, and low cost of the device indicate its potential for widespread application.     

The attractor—basin portrait of a cellular automaton

Local space-time structures, such as domains and the intervening dislocations, dominate a wide class of cellular automaton (CA) behavior. For such spatially-extended dynamics regular domains, vicinities, and attractors are introduced as organizing principles to identify the discretized analogs of attractors, basins, and separatrices: structures used in classifying dissipative continuous-state dynamical systems. We describe the attractor-basin portrait of nonlinear elementary CA rule 18, whose global dynamics is largely determined by a single regular attracting domain. The latter's basin is analyzed in terms of subbasin and portal structures associated with particle annihilation. The conclusion is that the computational complexity of such CA is more apparent than real. Transducer machines are constructed that automatically identify domain and dislocation structures in space-time, count the number of dislocations in a spatial pattern, and implement an isomorphism between rule 18 and rule 90. We use a transducer to trace dislocation trajectories, and confirm that in rule 18, isolated dislocation trajectories, as well as a dislocation gas, agree extremely well with the classical model of annihilating diffusive particles. The CA efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space-time.     

Symbolic dynamics of one-dimensional maps: Entropies,finite precision,and noise

In the study of nonlinear physical systems, one encounters apparently random or chaotic behavior, although the systems may be completely deterministic. Applying techniques from symbolic dynamics to maps of the interval, we compute two measures of chaotic behavior commonly employed in dynamical systems theory: the topological and metric entropies. For the quadratic logistic equation, we find that the metric entropy converges very slowly in comparison to maps which are strictly hyperbolic. The effects of finite precision arithmetric and external noise on chaotic behavior are characterized with the symbolic dynamics entropies. Finally, we discuss the relationship of these measures of chaos to algorithmic complexity, and use algorithmic information theory as a framework to discuss the construction of models for chaotic dynamics.     

How hidden are hidden processes? A primer on crypticity and entropy convergence

We investigate a stationary process's crypticity--a measure of the difference between its hidden state information and its observed information--using the causal states of computational mechanics. Here, we motivate crypticity and cryptic order as physically meaningful quantities that monitor how hidden a hidden process is. This is done by recasting previous results on the convergence of block entropy and block-state entropy in a geometric setting, one that is more intuitive and that leads to a number of new results. For example, we connect crypticity to how an observer synchronizes to a process. We show that the block-causal-state entropy is a convex function of block length. We give a complete analysis of spin chains. We present a classification scheme that surveys stationary processes in terms of their possible cryptic and Markov orders. We illustrate related entropy convergence behaviors using a new form of foliated information diagram. Finally, along the way, we provide a variety of interpretations of crypticity and cryptic order to establish their naturalness and pervasiveness. This is also a first step in developing applications in spatially extended and network dynamical systems.     

Reductions of Hidden Information Sources

In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the internal states and mechanisms. Unfortunately, there are often many possible models that are observationally equivalent. Here we show that the situation is not as arbitrary as one would think. We show that generators of hidden stochastic processes can be reduced to a minimal form and compare this reduced representation to that provided by computational mechanics – the ε-machine. On the way to developing deeper, measure-theoretic foundations for the latter, we introduce a new two-step reduction process. The first step (internal-event reduction) produces the smallest observationally equivalent σ-algebra and the second (internal-state reduction) removes σ-algebra components that are redundant for optimal prediction. For several classes of stochastic dynamical systems these reductions produce representations that are equivalent to ε-machines.     

Fluctuations and the onset of chaos

We consider the role of fluctuations on the onset and characteristics of chaotic behavior associated with period doubling subharmonic bifurcations. By studying the problem of forced dissipative motion of an anharmonic oscillator we show that the effect of noise is to produce a bifurcation gap in the set of available states. We discuss the possible experimental observation of this gap in many systems which display turbulent behavior.     

Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes

Journal of Statistical Physics - Among the predictive hidden Markov models that describe a given stochastic process, the $$\epsilon \text{-machine }$$ is strongly minimal in that it minimizes every...