Water and the National Welfare—Programs in Search of a Policy

It is no secret to residents of the western states that water is a matter of primary public concern. Land and water policies are deeply imbedded in the region, and the imprint of federal water projects on the economic geography of the West is plain to see. It is increasingly clear, however, that no coherent national policy, past or present, has emerged from the massive federal effort in the field. There is no lack of interest, planning, and expenditure on the supply and quality of water, and much progress has been made in definition and measurement of the factors that determine an efficient water system. But sound principles are still honored as much in the breach as in the observance, and we still speak with a thousand voices on any water problem of real magnitude. The time is at hand when the plethora of overlapping and frequently quarrelsome federal agencies concerned with the development and allocation of water supplies and the protection of water quality must be subjected to the test of clearly formulated national objectives and of conceptually sound and consistent means of achieving them

Management of the North Pacific Fisheries: Economic Objectives and Issues

In this paper, we attempt to narrow the areas of conflict by specifying more precisely the objectives of fishery utilization (and, inferentially, of fisheries management) in the North Pacific, and by analysis of the extent to which the optimal combination of regulatory measures in a theoretical framework must be modified to accommodate the technological, administrative, and political complexities that beset an international fishery. The basic bioeconomic theory of an ocean fishery is modified to show its application to a typical case involving interdependent exploited species and international differences in market prices of both inputs and end products. The analysis is then cast in terms of the specific situation in the North Pacific. Alternative concepts of international regulation are examined from the standpoint of their economic repercussions, and recommendations are formulated for a longrun management program designed to yield continuing economic benefits as well as physical protection of the resources. Attention is centered on the Northeast Pacific, where the four major fishing powers are all actively engaged and in direct competition. The emphasis throughout is on what should be attempted rather than on what can be accomplished under present institutional and legal arrangements

Management of the North Pacific Fisheries: Economic Objectives and Issues

In this paper, we attempt to narrow the areas of conflict by specifying more precisely the objectives of fishery utilization (and, inferentially, of fisheries management) in the North Pacific, and by analysis of the extent to which the optimal combination of regulatory measures in a theoretical framework must be modified to accommodate the technological, administrative, and political complexities that beset an international fishery. The basic bioeconomic theory of an ocean fishery is modified to show its application to a typical case involving interdependent exploited species and international differences in market prices of both inputs and end products. The analysis is then cast in terms of the specific situation in the North Pacific. Alternative concepts of international regulation are examined from the standpoint of their economic repercussions, and recommendations are formulated for a longrun management program designed to yield continuing economic benefits as well as physical protection of the resources. Attention is centered on the Northeast Pacific, where the four major fishing powers are all actively engaged and in direct competition. The emphasis throughout is on what should be attempted rather than on what can be accomplished under present institutional and legal arrangements

Exact Synchronization for Finite-State Sources

We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult case of strictly asymptotic synchronization is treated in a sequel. In both cases, we find that an observer, on average, will synchronize to the source state exponentially fast and that, as a result, the average accuracy in an observer's predictions of the source output approaches its optimal level exponentially fast as well. Additionally, we show here how to analytically calculate the synchronization rate for exact epsilon-machines and provide an efficient polynomial-time algorithm to test epsilon-machines for exactness.Comment: 9 pages, 6 figures; now includes analytical calculation of the synchronization rate; updates and corrections adde

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 epsilon-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 sigma-algebra and the second (internal-state reduction) removes sigma-algebra components that are redundant for optimal prediction. For several classes of stochastic dynamical systems these reductions produce representations that are equivalent to epsilon-machines.Comment: 12 pages, 4 figures; 30 citations; Updates at http://www.santafe.edu/~cm

Spectral Simplicity of Apparent Complexity, Part II: Exact Complexities and Complexity Spectra

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainty, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. An appendix presents spectral decomposition calculations for one example in full detail.Comment: 27 pages, 12 figures, 2 tables; most recent version at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt2.ht

Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy-convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.Comment: 11 pages, 5 figures, http://www.santafe.edu/projects/CompMech/papers/2dnnn.htm