%A Richard F. Green %T Does Aggregation Prevent Competitive Exclusion? A Response to Atkinson and Shorrocks %R Report 85-1 %I University of Minnesota-Duluth %C Duluth, Minnesota %D June 1985 %X Atkinson and Shorrocks (J. Anim. Ecol. 50:461-471, 1981) have shown that competitors may coexist if they have aggregated distributions in discrete, ephemeral patches. It is shown that such coexistence will not occur if aggregation is due to eggs being laid in clusters, a mechanism of aggregation suggested by Atkinson and Shorrocks (Am. Nat. 124:336-351, 1984). %A P. C. Frombach %A K. Hutchence %A D. G. Vandenberghe %A J. H. Weston %A A. G. Law %T Predicting Masonry Block U-Values with a Microcomputer %R Report 85-2 %I University of Minnesota-Duluth %C Duluth, Minnesota %D June 1985 %X An integrated finite difference procedure to solve the heat transfer equations arising from the calculation of thermal resistance of hollow concrete masonry walls is described. This solution method has been implemented on microcomputers providing a CAD tool for designing masonry blocks of high thermal resistance. %A Ru-qian Lu %T Expert Union: United Service of Distributed Expert Systems %R Report 85-3 %I University of Minnesota-Duluth %C Duluth, Minnesota %D June 1985 %X A scheme for connecting expert systems in a network called an {\nit expert union} is described. Consultation scheduling algorithms used to select the appropriate expert(s) to solve problems are proposed, as are strategies for resolving contradictions. %A Max Benson %T On a Program Reliability Model Proposed by Lu %R Report 85-4 %I University of Minnesota-Duluth %C Duluth, Minnesota %D July 1985 %X A convergence question related to a program reliability model proposed by Lu is solved. According to this model, a positive number, called the reliability, is assigned to programs on the basis of the underlying program graph and the amount of testing that has been performed. It is shown that as more and more testing is performed, the reliability increases to one. %A James W. Rowell %T Inverse Closure and Spectral Collapse %R Report 85-5 %I University of Minnesota-Duluth %C Duluth, Minnesota %D September, 1985 %X Following recent work of B. Barnes, various conditions which guarantee inverse closure of a subalgebra of a Banach algebra are explored. Noting the connection between inverse closure and collapse of the spectral lattice, we then salvage the hull-boundary relations among lattices which remain when the given subalgebra is not necessarily inverse closed. %A James W. Rowell %T The Spectral Lattice for Seminormal Elements %R Report 85-6 %I University of Minnesota-Duluth %C Duluth, Minnesota %D 1985 %X Let A be a unital B*-algebra, and let T in A be hyponormal and semi-Fredholm. We show that there is an element Q = Q**2 = Q* in A with finite spectrum satisfying TQ = 0 = QT and T+Q in inv1(A), and use this result to analyze the spectral lattices for normal and seminormal elements of A. %A Linda Deneen %T Secret Encryption with Public Keys %R Report 85-7 %I University of Minnesota-Duluth %C Duluth, Minnesota %D October 1985 %X A description of some of the better known encryption systems is given. Emphasis is on a class of relatively new encryption systems known as public key encryption systems. The public key systems described are the Merkle-Hellman knapsack encryption system and the RSA encryption system. %A Richard F. Green %T An Impecunious Gambler in a Kind-Hearted Casino %R Report 86-1 %I University of Minnesota-Duluth %C Duluth, Minnesota %D January 1986 %X Let X be the largest amount that a gambler is ever ahead if he starts with $1 and wins or loses $1 each play until he goes broke. The distribution of X is found, and a generalized law of large numbers is proved. %A Mark A. Luker %T Author Language Manual, Version 1 %R Report 86-2 %I University of Minnesota-Duluth %C Duluth, Minnesota %D 1985 %X This manual is an overview of the Authoring Language AL. AL is a computer language for the IBM PC and XT personal computers which is designed to support the efficient development of computer assisted instructional materials. AL implements a variety of media including text display, keyboard response, graphics display, and an optional mouse or interactive videodisk. %A Mark A. Luker %T ADROIT PC/PILOT, PIL and TENCORE, A Critical Comparison of Four CAI Languages from the Vantage Point of Computer Science %R Report 86-3 %I University of Minnesota-Duluth %C Duluth, Minnesota %D January 1986 %X This paper presents a critical comparison of major approaches to the implementation of CAI courseware by examining four different CAI languages. This paper can serve as both a preliminary guide to language selection, and lead to a better understanding of the conflicting assumptions about CAI. %A Max Benson %A Kinley Larntz %A Michael Lavine %A Ronald Regal %T Convex Regions in Multiple Dimensions %R Report 86-4 %I University of Minnesota-Duluth %C Duluth, Minnesota %D May, 1986 %X Convex hulls and minimum covering ellipsoids are two methods for defining the region of space enclosed by given set of points. Algorithms to compute convex hulls and minimum covering ellipsoids were implemented. This paper describes some of the results of these investigations. %A Ronald R. Regal %T Applying Order Statistic Censored Normal Confidence Intervals to Time Censored Data %R Report 86-5 %I University of Minnesota-Duluth %C Duluth, Minnesota %D May, 1986 %X Monte Carlo methods are used in this paper to investigate the coverage probabilities of nominal 95% confidence intervals computed from samples of n = 4, 6, 8, and 10 normal random variables right censored by time limits such that a sample is censored with probability 0.05, 0.10, ..., 0.95. %A Ronald R. Regal %A Ernest B. Hook %T A Note on Standard Errors for Rates Derived From Two or More Incomplete Censuses %R Report 86-6 %I University of Minnesota-Duluth %C Duluth, Minnesota %D May, 1986 %X Capture-recapture methods have been used in many studies to estimate the rate of occurrence of a characteristic such as a birth defect in a population. This paper discusses the standard error of such an estimate. %A Ronald R. Regal %T Non-parametric Testing of a Nonstandard Two-Sample Problem %R Report 86-7 %I University of Minnesota-Duluth %C Duluth, Minnesota %D May, 1986 %X The two-sample problem is considered for a null hypothesis other than the standard H_0 : F = G. A stochastic process is described which can lead to several nonparametric tests of H_0 : G = 1- (1-F)^k. An analog of the Wilcoxon statistic is derived which can be extended to data with ties and some types of censoring. %A David Kingsley %T Exact Integer Multiplication Algorithms %R Report 86-8 %I University of Minnesota-Duluth %C Duluth, Minnesota %D May, 1986 %X This report describes the C language implementation of three well-known exact integer multiplication algorithms: the traditional algorithm, the divide-and-conquer algorithm, and the Schoenhage-Strassen algorithm. Comparative timings are given. %A Linda Deneen %A Gary Shute %T Polygonizations of Point Sets in the Plane %R Report 86-9 %I University of Minnesota-Duluth %C Duluth, Minnesota %D July, 1986 %X This paper examines the problem of finding the different ways that a set of $n$ points in the plane can be connected to form a simple polygon. Such a connection is called a polygonalization. Because the number arbitrary polygonizations can be exponential in $n$, attention is restricted to a special class of polygonizations, those that are nondegenerate and star-shaped. An algorithm and data structure for determining the nondegenerate star-shaped polygonalizations of a set of $n$ points in the plane is described. The running time of this algorithm is shown to be $O(n^5)$. %A Max Benson %T ENVIRONMENTS: An Algebraic Computing Technique %R Report 86-10 %I University of Minnesota-Duluth %C Duluth, Minnesota %D July, 1986 %X An environment is a representation of an algebraic structure within a program by a data structure and associated primitives. This paper describes a programming technique and its implementation in the C language based on environments. The programmer can encode algorithms in algebra by setting up the environment and then making high level calls on primitives for natural algebraic operations. An example of working program written using this technique is given which computes the Todd polynomials $T_n(y;c_1,\ldots,c_n)$. %A Richard F. Green %T The Use of Information by Risk-Sensitive Foragers %R Report 86-11 %I University of Minnesota-Duluth %C Duluth, Minnesota %D November, 1986 %X Caraco and Gillespie have recently presented a model illustrating risk-sensitive foraging behavior and determined the expected number of prey that would be caught using two different strategies. This paper uses the same model but considers a improved foraging strategy which takes account of a spider's success at a site. %A Max Benson %A Stephen S.-T. Yau %T Equivalences between Isolated Hypersurface Singularities %R Report 87-1 %I University of Minnesota-Duluth %C Duluth, Minnesota %D January, 1987 %X This paper gives a complete account of the relationship between six different types of holomorphic equivalences arising from complex function theory and singularity theory. Conditions for when these equivalences coincide are given and a number of examples are given. The final section describes the design of the software that has been used to compute many of the examples. %A Richard F. Green %T A Stochastic Model of Optimal Foraging: Systematic Search for Negative-Binomially Distributed Prey %R Report 87-2 %I University of Minnesota-Duluth %C Duluth, Minnesota %D February 1987 %X The optimal foraging strategy and the long-term average rate of finding prey that it achieves are found for an animal that searches systemically in a patchy environment in which the number of prey per patch has a negative binomial distribution. Several "candidate" strategies are illustrated and the rates of finding prey which they achieve are plotted against the rates that the strategies "try to achieve". %A Richard F. Green %T The Giving-Up-Time Rule as a Strategy for Animals Foraging Systematically in a Patchy Environment %R Report 87-3 %I University of Minnesota-Duluth %C Duluth, Minnesota %D March 1987 %X In this paper I give a method for finding the long-term average rate of finding prey achieved by a systematic forager using a giving- up-time rule to decide when to leave patches in which prey are distributed continuously and randomly. The method is illustrated in the case that patches are all of the same size and the number of prey per patch has a negative binomial distribution. The best giving-up-time and the rate that it achieves are found for particular cases, and the rate achieved for each is compared with the rates achieved by other strategies. %A Richard F. Green %T Optimal Foraging in Patches, Each of Which Contains the Same Number of Prey %R Report 87-4 %I University of Minnesota-Duluth %C Duluth, Minnesota %D April 1987 %X In this paper the optimal foraging strategy is found for an animal which searches for prey that are found in patches, each of which contains the same number of prey. It is assumed that: (1) patches are all of the same size and are superficially similar. (2) Prey are distributed at random within patches. (3) Search within each patch is systematic. This paper provides more mathematical details than are given in Green (1987b). The case in which search is random is also mentioned, as are cases in which the number of prey in each patch is either zero or some fixed value.