As phylogenetic networks grow increasingly complicated, systematic methods for simplifying them to reveal properties will become more useful. This paper considers how to modify acyclic phylogenetic networks into other acyclic networks by... more
As phylogenetic networks grow increasingly complicated, systematic methods for simplifying them to reveal properties will become more useful. This paper considers how to modify acyclic phylogenetic networks into other acyclic networks by contracting specific arcs that include a set D . The networks need not be binary, so vertices in the networks may have more than two parents and/or more than two children. In general, in order to make the resulting network acyclic, additional arcs not in D must also be contracted. This paper shows how to choose D so that the resulting acyclic network is “pre-normal”. As a result, removal of all redundant arcs yields a normal network. The set D can be selected based only on the geometry of the network, giving a well-defined normal phylogenetic network depending only on the given network. There are CSD maps relating most of the networks. The resulting network can be visualized as a “wired lift” in the original network, which appears as the original ne...
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ABSTRACT Coevolution is the process of mutual adaptation of two populations. When a difficult optimization is performed with evolutionary computation, a population of adaptive test cases can strongly affect the progress of evolution. This... more
ABSTRACT Coevolution is the process of mutual adaptation of two populations. When a difficult optimization is performed with evolutionary computation, a population of adaptive test cases can strongly affect the progress of evolution. This study applies coevolution to the Tartarus task, a grid robot test problem. If the coevolving test cases are viewed as a form of parasite, then the question of virulence becomes an important feature of the algorithm. This study compares different types of parasites for the Tartarus problem. The impact of coevolution in this study is at odds with intuition and statistically significant. Analysis of the different types of coevolution suggests that disruptive crossover has a key effect. In the presence of disruptive crossover, coevolution may need to be modified to be effective. Examples of these modifications are presented. The key method of dealing with disruptive crossover is tracking the age of the Tartarus agents. The age of an agent is defined to be the number of selection steps the agent has survived. Using only older agents to drive coevolution of test cases substantially enhances the performance of one of the two type of coevolution studied.
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This paper proposes a revised Theory of Moves (TOM) to analyze matrix games between two players when payoffs are given as ordinals. The games are analyzed when a given player i must make the first move, when there is a finite limit n on... more
This paper proposes a revised Theory of Moves (TOM) to analyze matrix games between two players when payoffs are given as ordinals. The games are analyzed when a given player i must make the first move, when there is a finite limit n on the total number of moves, and when the game starts at a given initial state S.
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As phylogenetic networks become more widely studied and the networks grow larger, it may be useful to “simplify” such networks into especially tractable networks. Recent results have found methods to simplify networks into normal... more
As phylogenetic networks become more widely studied and the networks grow larger, it may be useful to “simplify” such networks into especially tractable networks. Recent results have found methods to simplify networks into normal networks. By definition, normal networks contain no redundant arcs. Nevertheless, there may be redundant arcs in networks where speciation events involving allopolyploidy occur. It is therefore desirable to find a different tractable class of networks that may contain redundant arcs. This paper proposes distinct-cluster tree-child networks as such a class, here abbreviated as DCTC networks. They are shown to have a number of useful properties, such as quadratic growth of the number of vertices with the number of leaves. A DCTC network is shown to be essentially a normal network to which some redundant arcs may have been added without losing the tree-child property. Every phylogenetic network can be simplified into a DCTC network depending only on the struct...
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Suppose N is a network---i.e., an acyclic directed graph with labelled leaves. By identifying a particular parent for each hybrid vertex, various trees can be displayed by N. Let Tr(N) denote the set of trees displayed by N. In general... more
Suppose N is a network---i.e., an acyclic directed graph with labelled leaves. By identifying a particular parent for each hybrid vertex, various trees can be displayed by N. Let Tr(N) denote the set of trees displayed by N. In general there can be many networks M such that Tr(N) = Tr(M). Suppose that the collection Tr(N) is given but N is not known. We study how to reconstruct N from Tr(N) in the case where N is regular, showing that such a regular network is uniquely determined. For certain smaller collections of trees displayed by a regular network N we give a more complicated method to reconstruct N. Simpler reconstruction procedures are given if N is normal.
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Let X X be a finite CW {\text {CW}} complex with the Z p r {Z_{{p^r}}} homology of an n n -sphere. Suppose Z p s {Z_{{p^s}}} acts cellularly on X X . The homology of the orbit space X / Z p s X/{Z_{{p^s}}} with coefficients Z p r... more
Let X X be a finite CW {\text {CW}} complex with the Z p r {Z_{{p^r}}} homology of an n n -sphere. Suppose Z p s {Z_{{p^s}}} acts cellularly on X X . The homology of the orbit space X / Z p s X/{Z_{{p^s}}} with coefficients Z p r {Z_{{p^r}}} is computed.
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This paper is intended to be a simple exposition of how to use cellular automata to generate a family of related fractals. We shall discuss the nature of cellular automata and show how they may be used to obtain interesting limit sets. In... more
This paper is intended to be a simple exposition of how to use cellular automata to generate a family of related fractals. We shall discuss the nature of cellular automata and show how they may be used to obtain interesting limit sets. In the process we shall find some numbers in various ways, and then we shall try to relate the different numbers so obtained. Proofs will only be suggested, and the reader will be referred elsewhere for details. In this paper the emphasis will be on clarifying the general line of the argument.
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Page 1. On the Ergodie Theory of Cellular Automata by STEPHEN J. WILLSON Iowa State University Ames, Iowa 50010 ABSTRACT When properly viewed, the transition rule of a cellular automaton becomes a map F from a set ~ to itself. ...
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A Semigroup on the Space of Compact Convex Bodies. [SIAM Journal on Mathematical Analysis 11, 448 (1980)]. Stephen J. Willson. Abstract. Let $C_0$ denote the space of all compact convex subsets of $R^n$ with nonempty interior. Give $C_0$... more
A Semigroup on the Space of Compact Convex Bodies. [SIAM Journal on Mathematical Analysis 11, 448 (1980)]. Stephen J. Willson. Abstract. Let $C_0$ denote the space of all compact convex subsets of $R^n$ with nonempty interior. Give $C_0$ its natural topology. ...
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On Coherent Growth of Configurations. [SIAM Journal on Mathematical Analysis 16, 316 (1985)]. Stephen J. Willson. Abstract. A configuration $X$ is an $m$-tuple of subsets of Euclidean $n$-space. A transition rule $F$ assigns to any $X$ a... more
On Coherent Growth of Configurations. [SIAM Journal on Mathematical Analysis 16, 316 (1985)]. Stephen J. Willson. Abstract. A configuration $X$ is an $m$-tuple of subsets of Euclidean $n$-space. A transition rule $F$ assigns to any $X$ a new configuration $FX$. ...
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Suppose that we seek a tree T giving the phylogenetic relationships among the species in a set S. A common method selects for such a tree a maximum parsimony tree using the genome of the species in S. Suppose that K is a proper subset of... more
Suppose that we seek a tree T giving the phylogenetic relationships among the species in a set S. A common method selects for such a tree a maximum parsimony tree using the genome of the species in S. Suppose that K is a proper subset of S. Then T induces a tree U which gives the same relationships among the species in K but omits the species of S which are not in K. Unfortunately, when T is a maximum parsimony tree for the species in S, then U need not be a maximum parsimony tree for the species in K. This phenomenon exhibits an inconsistency in the criterion of maximum parsimony-maximum parsimony trees for different groups of species may be "inconsistent". It implies that the addition of a new species scan change relationships already "established" for prior species if the trees are obtained by the criterion of maximum parsimony. The phenomenon occurs both in artificial examples and with real data. An alternative method for generating phylogenetic trees seeks to minimize such inconsistencies. For each group J consisting of four of the species, we find a tree T(J) describing the relationship only among the four species in J, for example by the use of maximum parsimony on those four species alone. In favorable cases one may combine all the trees T(J) into a single tree T that is consistent with all the trees T(J). If such a tree T exists, then it is unique, and there is a computationally efficient algorithm for finding the tree T. In unfavorable bases such a tree T does not exist, but there may still be a tree containing only "mild" inconsistencies with the trees T(J). A numerical measure is given for the inconsistency I(T) of a tree T in terms of the treelengths of the various trees with set J of leaves in comparison with the tree T. We may then seek a "minimally inconsistent tree T" that minimizes the inconsistency I(T). We describe procedures which find a tree T with low inconsistency I(T). Examples are provided using both artificial strings and data from the complete mitochondrial DNA sequences for 16 species. In particular, minimally inconsistent trees are identified for the 16 species. The definition permits a proof that the trees are in fact minimally inconsistent. The criterion can be applied in both a relative and an absolute sense.
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Page 1. Vol. 43, No. 1 DUKE MATHEMATICAL JOURNAL(C) Ma.rch 1976 HOMOLOGICAL DIMENSIONSOF THE ISOTROPY RING STEPHEN J. WILLSON 1. Introduction. In Willson [7] a ring called the isotropy ring was introducedto ...
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Computer vision-based techniques were developed and evaluated for classifying different shapes of germplasms (ear of corn). An algorithm was developed to discriminate round-shaped germplasms based on two features, i.e. circularity and... more
Computer vision-based techniques were developed and evaluated for classifying different shapes of germplasms (ear of corn). An algorithm was developed to discriminate round-shaped germplasms based on two features, i.e. circularity and dimensional ratio. Two different approaches based on fractal geometry and higher order invariant moments were used for classification of non-round shaped germplasms. In the fractal-based approach, two additional fractal
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EJ421908 - Teaching about Fractals.