LAND USE OPTIMIZATION USING SELF-ORGANIZING ALGORITHMS

ABSTRACT. In many spatial systems the interaction between various regions decreases dramatically with distance. This suggests that local trade-offs may be more important than global ones in land use planning and that a decentralized, parallel optimization of the individual regions may be an attractive supplement to more centralized optimization approaches. In this paper, we solve a forest planning problem using a series of decentralized approaches. The approaches can be characterized as self-organizing algorithms and are modeled in the framework of a cellular automaton. We compare our results with those obtained by more centralized approaches, viz. a large sample approach, simulated annealing, and a genetic algorithm. We find that the self-organizing algorithms generally converge much faster to solutions which are at least as good as those obtained by simulated annealing and the genetic algorithm.     

Schubert cycles, differential forms and D-modules on varieties of unseparated flags

Proper homogeneous G-spaces (where G is semisimple algebraic group) over positive characteristic fields k can be divided into two classes, the first one being the flag varieties G/P and the second one consisting of varieties of unseparated flags (proper homogeneous spaces not isomorphic to flag varieties as algebraic varieties). In this paper we compute the Chow ring of varieites of unseparated flags, show that the Hodge cohomology of usual flag varieties extends to the general setting of proper homogeneous spaces and give an example showing (by geometric means) that the D -affinity of Beilinson and Bernstein fails for varieties of unseparated flags.     

Displacement or Residual Test in the Application of Implicit Methods for Stiff Problems

The stopping criterion in the iterative solution of the non-linearequations that arise in connection with the use of implicitmethods for the solution of stiff systems of ordinary differentialequations is studied. The conclusion is that there must be aconsistent choice between the type of error estimator and thevector used for the test of convergence and stopping criterion.     

WILDLIFE RESERVES,POPULATIONS, AND HUNTING OUTCOME WITH SMART WILDLIFE

We consider a hunting area and a wildlife reserve and answer the question: How does clever migration decision affect the social optimal and the private optimal hunting levels and population stocks? We analyze this in a model allowing for two‐way migration between hunting and reserve areas, where the populations’ migration decisions depend on both hunting pressure and relative population densities. In the social optimum a pure stress effect on the behavior of smart wildlife exists. This implies that the population level in the wildlife reserve tends to increase and the population level in the hunting area and hunting levels tend to decrease. On the other hand, the effect on stock tends to reduce the population in the wildlife reserve and increase the population in the hunting area and thereby also increase hunting. In the case of the private optimum, open‐access is assumed and we find that the same qualitative results arise when comparing a situation with and without stress effects, but of course at a higher level of hunting. We also show that when net social benefits of hunting dominate the net social benefits of populations, wildlife reserves are optimally placed in areas of low carrying capacity and vice versa.     

Causal Data Interpolation in Hilbert Space

Consider a Hilbert space equipped with a ‘time-structure’,i.e. a resolution Eof the identity on defined on subsets ofsome linearly ordered set . In this paper, we consider the problemof interpolating vectors in exactly or approximately by meansof Hilbert-Schmidt operators C which are causal with respectto E. The deterministic cases Cxy and Cx_iy_i (1in) are dealtwith as well as the random case Cxy. In particular we examinethe set-up where x and y are the sample paths of stochasticprocesses (X_t) and (Y_t).     

A Twisted Sampling Theorem

A generalized sampling theorem is proved for a set of functionsf that are well behaved in the frequency domain. Specifically,let W be a positive bounded integrable function, let be a reconstructionfunction, and let A denote the operation of multiplication inthe frequency domain by a bounded function A(s). Then coefficientsh_n (–<n<) are determined to minimize the maximalL²-error in an approximation scheme for functions f ranging over the set is the Fourier of f. Formulae are given for the minimal obtainablemaximal error, and the optimal choice (choices) of h_n (–<n<)is characterized through its discrete Fourier transform .     

The Design of Structural Design Norms

Abstract

This paper deals with the analysis of prismatic and nonprismatic members with axial restraints, where their material is permitted to be stressed well beyond its elastic limit. This loading on the members causes the modulus of elasticity of the material to vary along their length. The mathematical formulation of this problem, as well as its analysis, is based on the method of equivalent systems that was developed by the first author. This method permits replacement of the original nonlinear member of variable stiffness E^xI^x, with one of uniform stiffness E¹I^l, that has the same length, boundary conditions, and elastic line as the original variable stiffness member. It is proven mathematically that this equivalency exists and that the solution of the equivalent system using linear analysis yields the same results as the solution of the original nonlinear variable stiffness member. Deflections and rotations may be easily obtained using equivalent systems, and the member can be analyzed in both elastic and inelastic ranges, all the way to failure, thus permitting observation of progressive deterioration of the ability of the member to resist load, stress, and de-formation. In this manner, practical critical limits regarding these modes of behavior can be established.     

AN INDICATOR FOR ECOSYSTEM EXTERNALITIES IN FISHING

Ecosystem externalities arise when one use of an ecosystem affects its other uses through the production functions of the ecosystem. We use simulations with a size‐spectrum ecosystem model to investigate the ecosystem externality created by fishing of multiple species. The model is based upon general ecological principles and is calibrated to the North Sea. Two fleets are considered: a “forage fish” fleet targeting species that mature at small sizes and a “large fish” fleet targeting large piscivorous species. Based on the marginal analysis of the present value of the rent, we develop a benefit indicator that explicitly divides the consequences of fishing into internal and external benefits. This analysis demonstrates that the forage fish fleet has a notable economic impact on the large fish fleet, but the reverse is not true. The impact can be either negative or positive, which entails that for optimal economic exploitation, the forage fishery has to be adjusted according to the large fish fishery. With the present large fish fishery in the North Sea, the two fisheries are well adjusted; however, the present combined exploitation level is too high to achieve optimal economic rents.     

OPTIMAL CONTROL OF MULTIPLE-USE PRODUCTS: THE CASE OF TIMBER,FORAGE AND WATER PRODUCTION

ABSTRACT. A thorough analysis of the optimal control of multiple-use forest management at the stand level reveals that the results of earlier studies, which seem to contradict each other, are in fact part of a common solution space. We provide an explanation for this result by showing that it is caused by the growth function and the interaction between the timber and forage production functions. We discuss the sensibility of the results using this new knowledge. Most optimal control models focusing on multiple-use forest management have applied production functions that are quadratic in the state variable. This makes explicit solutions easy because the first order derivative is linear. However, in reality, production is often better described by more complex nonlinear functions, but, unfortunately, such functions are difficult to handle in an optimal control framework. We illustrate how the convenience of the quadratic production function can be combined with better approximations to nonlinear production functions.