Paul Cull

Oregon State University, Corvallis, Oregon, United States

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Publications (58)31.38 Total impact

  • Paul Cull
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    ABSTRACT: At first glance, Biology and Computer Science are diametrically opposed sciences. Biology deals with carbon based life forms shaped by evolution and natural selection. Computer Science deals with electronic machines designed by engineers and guided by mathematical algorithms. In this brief paper, we review biologically inspired computing. We discuss several models of computation which have arisen from various biological studies We show what these have in common, and conjecture how biology can still suggest answers and models for the next generation of computing problems. We discuss computation and argue that these biologically inspired models do not extend the theoretical limits on computation. We suggest that, in practice, biological models may give more succinct representations of various problems, and we mention a few cases in which biological models have proved useful. We also discuss the reciprocal impact of computer science on biology and cite a few significant contributions to biological science.
    No preview · Article · Jan 2013 · Bio Systems
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    Kang Wang · Xingcheng Liu · Paul Cull
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    ABSTRACT: Purpose – The purpose of this paper is to propose a novel decoding algorithm, to decrease the complexity in decoding conventional block turbo codes. Design/methodology/approach – In this algorithm, the signal-to-noise ratio (SNR) values of channels are adaptively estimated. After analyzing the relationship between the statistics of the received vectors R and the channel SNR, an adaptive method of tuning the decoding complexity is presented. Findings – Simulation results show that the proposed algorithm has greatly decreased the decoding complexity and sped up the decoding process while achieving better bit error rate performance. Originality/value – Simulation experiments described in this paper show that the proposed algorithm can decrease the decoding complexity, shorten the decoding time and achieve good decoding performance.
    Preview · Article · Aug 2010 · Kybernetes
  • Javad Azimi · Paul Cull · Xiaoli Fern
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    ABSTRACT: Cluster ensembles combine different clustering outputs to obtain a better partition of the data. There are two distinct steps in cluster ensembles, generating a set of initial partitions that are different from one another, and combining the partitions via a consensus functions to generate the final partition. Most of the previous consensus functions require the number of clusters to be specified a priori to obtain a good final partition. In this paper we introduce a new consensus function based on the Ant Colony Algorithms, which can automatically determine the number of clusters and produce highly competitive final clusters. In addition, the proposed method provides a natural way to determine outlier and marginal examples in the data. Experimental results on both synthetic and real-world benchmark data sets are presented to demonstrate the effectiveness of the proposed method in predicting the number of clusters and generating the final partition as well as detecting outlier and marginal examples from data.
    No preview · Conference Paper · Jun 2009
  • PAUL CULL · WILLIAM FRANK
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    ABSTRACT: G. Spencer Brown's book Laws of Form has been enjoying a vogue among social and biological scientists. Proponents claim that the book introduces a new logic ideally suited to their fields of study, and that the new logic solves the problems of self-reference. These claims are false. We show that Brown's system is Boolean algebra in an obscure notation, and that his “solutions” to the problems of self-reference are based on a misunderstanding of Russell's paradox.
    No preview · Article · Apr 2008 · International Journal of General Systems
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    Paul Cull
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    ABSTRACT: N. Rashevsky (1899-1972) was one of the pioneers in the application of mathematics to biology. With the slogan: mathematical biophysics : biology :: mathematical physics ; physics, he proposed the creation of a quantitative theoretical biology. Here, we will give a brief biography, and consider Rashevsky's contributions to mathematical biology including neural nets and relational biology. We conclude that Rashevsky was an important figure in the introduction of quantitative models and methods into biology.
    Preview · Article · May 2007 · Biosystems
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    Paul Cull
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    ABSTRACT: Some of the simplest models of population growth are one dimensional nonlinear difference equations. While such models can display wild behavior including chaos, the standard biological models have the interesting property that they display global stability if they display local stability. Various researchers have sought a simple explanation for this agreement of local and global stability. Here, we show that enveloping by a linear fractional function is sufficient for global stability. We also show that for seven standard biological models local stability implies enveloping and hence global stability. We derive two methods to demonstrate enveloping and show that these methods can easily be applied to the seven example models. Although enveloping by a linear fractional is a sufficient for global stability, we show by example that such enveloping is not necessary. We extend our results by showing that enveloping implies global stability even when f(x) is a discontinuous multi-function which might be a more reasonable description of real bilogical data. We show that our techniques can be applied to situations which are not population models. Finally, we give examples of population models which have local stability but not global stability.
    Preview · Article · May 2007 · Bulletin of Mathematical Biology
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    ABSTRACT: A novel adaptive threshold-decoding algorithm for block turbo codes (BTCs) was proposed. Simulations for a few combinations of BCH codes were carried out with the proposed algorithm and Chase algorithm for the purpose of comparison. The error correction performance with the suggested algorithm was negligibly degraded comparing with that using the Chase algorithm while it gained 1 dB at BER=10<sup>-4</sup> against Fragiacomo et al.'s results. Furthermore, the suggested algorithm reduced the number of codewords to be searched and speeded up the decoding process
    Preview · Conference Paper · Oct 2006
  • Paul Cull
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    ABSTRACT: We are gathered here today to celebrate the life and scientific career of Prof. Eduardo Caianiello. It is my task to present and as-sess one small area of his work-neural nets. I first met Prof. Caianiello many years ago when he visited the University of Chicago. After writing my thesis on neural nets, I subsequently worked with Prof. Ca-ianiello on various occasions at the Labora-torio di Cibernetica and at the University of Salerno. Hence my discussion will be biased by personal recollections and hence should count more as scientific heritage rather than as strict history.
    No preview · Chapter · Jul 2006
  • Paul Cull
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    ABSTRACT: Difference equations have been used in population biology from Fibonacci to May and Yorke and to the present day. They have also been used in other biological fields. Here, we describe a number of fairly well know examples. We give techniques and results about the analysis of linear and nonlinear difference equations. We also show that there are practical and theoretical limitations on the analysis of nonlinear models. 1 Introduction For almost 1000 years from Fibonacci's rabbits of 1200 to the present day, difference equations have been used as biological models. Here we will give a brief run through some of the rudiments of difference equations and describe some simple models used in biology. To keep the paper short, we will only discuss some models from population biology. We start with the story of Fibonacci's rabbits, where we find and solve a simple difference equation. We then generalize to kth order linear difference equations and outline the theory of these equations. We give stronger results about estimating and computing the solutions to nonnegative difference equations including those with inputs. We return to Fibonacci's model and show how it can be generalized to Leslie's matrix model. After a brief discussion of Leslie's model, we describe the generalization of these results contained in the Perron- Frobenius theorem. We then turn to a consideration of nonlinear models. We show that a number of these models can be analyzed quite easily, but that chaos and particularly sensitive dependence on initial conditions may make even simple appearing nonlinear models difficult to use in practice. We briefly show that enveloping can be used for many common population models. Finally, we consider universality and undecidability and argue that a complete theory of nonlinear difference equations is impossible. 1.1 Notation There are a few items of notation in this paper which may not be familiar. When we are talking about sequences, we often use the notation xn to mean the nth element of the sequence. But we also, ambiguously, use xn to mean the entire sequence. When we want to be careful, we use the notationxnto mean a whole sequence. There are two notions of bounding with special notation. (16) We say that
    No preview · Article · Jan 2006
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    MARGARET A. SANDERS · Paul Cull
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    ABSTRACT: Fibonacci numbers and difference equations show up in many counting prob- lems. Zeckendorf showed how to represent natural numbers in "binary" Fibonacci bases. Capocelli counted the number of 0 bits and 1 bits in such representation. Here we use the theory of difference equations to try to provide proofs for Capocelli's claims. We also inves- tigate generalization of the Fibonacci difference equation which may show behavior similar to that observed by Capocelli. In particular, we conjecture that "doubly non-negative" difference equations will have solutions whose ratios monotonically approach a limit.
    Preview · Article · Jan 2006
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    Paul Cull
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    ABSTRACT: Some of the simplest models of population growth are one-dimensional nonlinear difference equations. While such models can display wild behavior including chaos, the standard biological models have the interesting property that they display global stability if they display local stability. Various researchers have sought a simple explanation for this agreement of local and global stability. Here, we show that enveloping by a linear fractional function is sufficient for global stability. We also show that for seven standard biological models local stability implies enveloping and hence global stability. We derive two methods to demonstrate enveloping and show that these methods can easily be applied to the seven example models.
    Preview · Article · Oct 2005

  • No preview · Article · Jan 2005
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    P. Cull · M. Flahive · R. Robson

    Preview · Article · Jan 2005
  • Paul Cull
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    ABSTRACT: Convergence is a central problem in both computer science and in population biology. Will a program terminate? Will a population go to an equilibrium? In general these questions are quite difficult - even unsolvable. In this paper we will concentrate on very simple iterations of the form x(t+1) = f (x(t)) where each x(t) is simply a real number and f (x) is a reasonable real function with a single fixed point. For such a system, we say that an iteration is "globally stable" if it approaches the fixed point for all starting points. We will show that there is a simple method which assures global stability. Our method uses bounding of f (x) by a self-inverse function. We call this bounding "enveloping" and we show that enveloping implies global stability. For a number of standard population models, we show that local stability implies enveloping by a self-inverse linear fractional function and hence global stability. We close with some remarks on extensions and limitations of our method.
    No preview · Conference Paper · Jan 2005
  • Tai Hsu · Paul Cull

    No preview · Conference Paper · Jan 2005
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    ABSTRACT: Genomic sequence data is available for an ever-increasing number of organisms, but the full meaning of this data remains an enigma. String alignment is one approach for deciphering the information contained in genetic strings. Sequences which are conserved across species will help identify genes and other important structures. Similarity between species can be scored by measuring how well their sequences align. The walking tree method is an approximate string alignment method that can handle insertions, deletions, substitutions, translocations, and more than one level of inversion. We will describe this method and recent improvements which allow fast alignment of megabase strings. We will show examples in which the method located or discovered genes. We show how the method can be used to construct phylogenetic trees. We also show that the method can be used to identify essential regions for protein function.
    Preview · Article · Mar 2004 · Mathematical Biosciences
  • Tai Hsu · Paul Cull

    No preview · Conference Paper · Jan 2004
  • Paul Cull · Tai Hsu
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    ABSTRACT: The meaning of biological sequences is a central problem of modern biology. Although string matching is well-understood in the edit-distance model, biological strings with transpositions and inversions violate this model’s assumptions. To align biologically reasonable strings, we proposed the Walking Tree Method [4,5,6,7,8]; an approximate string alignment method that can handle insertion, deletions, substitutions, translocations, and more than one level of inversions. Our earlier versions were able to align whole bacterial genomes (1 Mbps) and discover and verify genes. As extremely long sequences can now be deciphered rapidly and accurately without amplification [2,3,15], speeding up the method becomes necessary. Via a technique that we call recurrence reduction in which some computations can be looked up rather than recomputed, we are able to significantly improve the performance, e.g. 400% for a 1-million base pair alignment. In theory, our method can align a length |P| string with a length |T| string in time |P||T|/(nlog |P|) using n processors in parallel. In practice, we can align 10 Mbps strings within a week using 30 processors.
    No preview · Conference Paper · Feb 2003
  • P. Cull
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    ABSTRACT: Since the seminal papers of Li and Yorke [5] and May [6] [7] the importance of chaos in science has been clear. But, the impressive theorems leading to an understanding of chaos have been largely proved for one-dimensional continuous maps and only conjectured to hold for more complicated systems. In this paper, we want to consider a simple but discontinuous family of maps, and ask how closely these maps, the linear fractionals, come to being chaotic. Our basic answers are that linear fractionals are easy to understand; that they do not show fully chaotic behavior in the technical sense; and that they do show behavior that would intuitively be considered chaotic. In particular, we show that many linear fractionals exhibit global asymptotic stability and do not show chaos; that rational coe cient linear fractionals may be periodic, but the the periods are restricted to be 1, 2, 3, 4, or 6; that more general periodicity is possible with irrational coe cients; that some linear fractionals are aperiodic but have chaotic-like orbits; that these aperiodic maps have invariant distributions, but such distributions are not attractive. We also show, following Cull and Cha ee [2], that linear fractionals may be used to show global stability of other nonlinear maps. In summary, linear fractionals are easy-to-understand nonlinear maps that have a variety of appli-cations, and these maps can display complex chaotic-like behavior.
    No preview · Article · Jan 2002
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    ABSTRACT: Tree patterns are natural candidates for representing rules and hypotheses in many tasks such as information extraction and symbolic mathematics. A tree pattern is a tree with labeled nodes where some of the leaves may be labeled with variables, whereas a tree instance has no variables. A tree pattern matches an instance if there is a consistent substitution for the variables that allows a mapping of subtrees to matching subtrees of the instance. A finite union of tree patterns is called a forest. In this paper, we study the learnability of tree patterns from queries when the subtrees are unordered. The learnability is determined by the semantics of matching as defined by the types of mappings from the pattern subtrees to the instance subtrees. We first show that unordered tree patterns and forests are not exactly learnable from equivalence and subset queries when the mapping between subtrees is one-to-one onto, regardless of the computational power of the learner. Tree and forest patterns are learnable from equivalence and membership queries for the one-to-one into mapping. Finally, we connect the problem of learning tree patterns to inductive logic programming by describing a class of tree patterns called Clausal trees that includes non-recursive single-predicate Horn clauses and show that this class is learnable from equivalence and membership queries.
    Full-text · Article · Aug 2001 · Machine Learning

Publication Stats

784 Citations
31.38 Total Impact Points

Institutions

  • 1974-2013
    • Oregon State University
      • • School of Electrical Engineering and Computer Science
      • • Department of Mathematics
      Corvallis, Oregon, United States
  • 1971
    • University of Chicago
      Chicago, Illinois, United States