Showing papers by "Santa Fe Institute published in 1995"

The evolution of emergent computation

Abstract: A simple evolutionary process can discover sophisticated methods for emergent information processing in decentralized spatially extended systems. The mechanisms underlying the resulting emergent computation are explicated by a technique for analyzing particle-based logic embedded in pattern-forming systems. Understanding how globally coordinated computation can emerge in evolution is relevant both for the scientific understanding of natural information processing and for engineering new forms of parallel computing systems.

Landscapes and Their Correlation Functions

Abstract: Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimization, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary," i.e., they are (up to an additive constant) eigenfunctions of a graph Laplacian. It is shown that elementary landscapes are characterized by their correlation functions. The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape. Two types of correlation functions are investigated here: the correlation of a time series sampled along a random walk on the landscape and the correlation function with respect to a partition of the set of all vertex pairs.

Estimating functions of probability distributions from a finite set of samples

Abstract: This paper addresses the problem of estimating a function of a probability distribution from a finite set of samples of that distribution. A Bayesian analysis of this problem is presented, the optimal properties of the Bayes estimators are discussed, and as an example of the formalism, closed form expressions for the Bayes estimators for the moments of the Shannon entropy function are derived. Then numerical results are presented that compare the Bayes estimator to the frequency-counts estimator for the Shannon entropy. We also present the closed form estimators, all derived elsewhere, for the mutual information, ${\mathrm{\ensuremath{\chi}}}^{2}$ covariance, and some other statistics. (c) 1995 The American Physical Society

Genetic algorithms: An overview

Abstract: Genetic algorithms (GAs) are computer programs that mimic the processes of biological evolution in order to solve problems and to model evolutionary systems. In this paper I describe the appeal of using ideas from evolution to solve computational problems, give the elements of simple GAs, survey some application areas of GAs, and give a detailed example of how a GA was used on one particularly interesting problem—automatically discovering good strategies for playing the Prisoner’s Dilemma. The paper concludes with a short introduction to the theory of GAs.

The Troubling Aspects of a Building Block Hypothesis for Genetic Programming

Abstract: In this paper we carefully formulate a Schema Theorem for Genetic Programming (GP) using a schema definition that accounts for the variable length and the non-homologous nature of GP's representation. In a manner similar to early GA research, we use interpretations of our GP Schema Theorem to obtain a GP Building Block definition and to state a “classical” Building Block Hypothesis (BBH): that GP searches by hierarchically combining building blocks. We report that this approach is not convincing for several reasons: it is difficult to find support for the promotion and combination of building blocks solely by rigourous interpretation of a GP Schema Theorem; even if there were such support for a BBH, it is empirically questionable whether building blocks always exist because partial solutions of consistently above average fitness and resilience to disruption are not assured; also, a BBH constitutes a narrow and imprecise account of GP search behavior.

Self-organization of markets: an example of a computational approach

Abstract: A model of decentralized trade is simulated with firms that produce a given commodity, and consumers who repeatedly wish to purchase one unit of that commodity. Consumers ‘shop around’, while firms may attract the attention of potential customers by sending information signals and offering good service. The main objective of this paper is to present an example of a computational approach to address the following question: How do self-organized markets emerge in the economy, and what are their characteristics?

Maximizing Predictability in the Stock and Bond Markets

Abstract: We construct portfolios of stocks and of bonds that are maximally predictable with respect to a set of ex ante observable economic variables, and show that these levels of predictability are statistically significant, even after controlling for data-snooping biases. We disaggregate the sources for predictability by using several asset groups, including industry-sorted portfolios, and find that the sources of maximal predictability shift considerably across asset classes and sectors as the return-horizon changes. Using three out-of-sample measures of predictability, we show that the predictability of the maximally predictable portfolio is genuine and economically significant.

How Swarms Build Cognitive Maps

Abstract: Swarms of social insects construct trails and networks of regular traffic via a process of pheromone laying and following. These patterns constitute what is known in brain science as a cognitive map. The main difference lies in the fact that the insects write their spatial memories in the environment, while the mammalian cognitive map lies inside the brain. This analogy can be more than a poetic image, and can be further justified by a direct comparison with the neural processes associated with the construction of cognitive maps in the hippocampus. We investigate via analysis and numerical simulation the formation of trails and networks in a collection of insect-like agents. The agents interact in simple ways which are determined by experiments with real ants

Generic excitable dynamics on a two-dimensional map

Abstract: This paper introduces a two-dimensional map exhibiting several generic properties reported in excitable systems. The elementary dynamic that is analogous to that of neural elements, is analyzed using phase plane methods. Bifurcations from nonautonomous to autonomous, and from periodic to chaotic solutions are studied in a small region of parameter space. The basic implementation of distributed excitable networks using coupled maps lattices is described in one- and two-dimensional media with nearest-neighbor coupling.

Elements of a Theory of Simulation

Abstract: Artificial Life and the more general area of Complex Systems does not have a unified theoretical framework although most theoretical work in these areas is based on simulation. This is primarily due to an insufficient representational power of the classical mathematical frameworks for the description of discrete dynamical systems of interacting objects with often complex internal states.

What makes an optimization problem hard

Abstract: We address the question: “Are some classes of combinatorial optimization problems intrinsically harder than others, without regard to the algorithm one uses, or can difficulty only be assessed relative to particular algorithms?” We provide a measure of the hardness of a particular optimization problem for a particular optimization algorithm and present two algorithm-independent quantities that use this measure to provide answers to our question. In the first of these we average hardness over all possible algorithms and show that according to this quantity, there are no distinctions between optimization problems. In this sense no problems are intrinsically harder than others. For the second quantity, rather than average over all algorithms, we consider the level of hardness of a problem (or class of problems) for the associated optimal algorithm. By this criteria there are classes of problems that are intrinsically harder than others.

Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices

Abstract: Implicit in the prices of traded financial assets are Arrow- Debreu state prices or, in the continuous-state case, the state-price density (SPD). We construct an estimator for the SPD implicit in option prices and derive an asymptotic sampling theory for this estimator to gauge its accuracy. The SPD estimator provides an arbitrage-free method of pricing new, more complex, or less liquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility 'smiles' for option prices. We perform Monte Carlo simulation experiments to show that the SPD estimator can be successfully extracted from option prices and we present an empirical application using S&P 500 index options.

Adaptive walks with noisy fitness measurements.

Abstract: Adaptive walks constitute an optimization technique for searching a space of possible solutions, for example, a space of different molecules. The goal is to find a point in space (a molecule) that is optimal or near-optimal in some property, generally referred to as the ‘fitness’, such as its ability to bind to a given receptor. Adaptive walking, an analog of natural selection, is a powerful technique for searching landscapes. However, errors in the measurements will cause errors in the adaptive walks. Mutant molecules of higher fitness may be ignored or mutants of lower fitness may be accepted. To examine the effect of measurement error on adaptive walks, we simulate single-agent hill-climbing walks on NK landscapes of varying ruggedness where Gaussian noise is added to the fitness values to model measurement error. We consider both constant measurement noise and noise whose variance decays exponentially with fitness. We show that fitness-independent noise can cause walks to ‘melt’ off the peaks in a landscape, wandering in larger regions as the noise increases. However, we also show that a small amount of noise actually helps the walk perform better than with no noise. For walks in which noise decreases exponentially with fitness, the most characteristic behavior is that the walk meanders throughout the landscape until it stumbles across a point of relatively high fitness, then it climbs the landscape towards the nearest peak. Finally, we characterize the balance between selection pressure and noise and show that there are several classes of walk dynamic behavior.

Let's call it plectics

Abstract: A decade ago, when the Santa Fe Institute was being organized, I coined a word for our principal area of research, a broad transdisciplinary subject covering aspects of simplicity and complexity as well as the properties of complex adaptive systems, including composite complex adaptive systems consisting of many adaptive agents. Unfortunately, I became discouraged about using the term after it met with a lukewarm response from a few of my colleagues. I comforted myself with the thought that perhaps a special name was unnecessary.

Mean Field Theory of the Edge of Chaos

Abstract: Is there an Edge of Chaos, and if so, can evolution take us to it? Many issues have to be settled before any definitive answer can be given. For quantitative work, we need a good measure of complexity. We suggest that convergence time is an appropriate and useful measure. In the case of cellular automata, one of the advantages of the convergence-time measure is that it can be analytically approximated using a generalized mean field theory.

Elements of a Theory of Simulation

Abstract: Artificial Life and the more general area of Complex Systems does not have a unified theoretical framework although most theoretical work in these areas is based on simulation. This primarily due to an insufficient representational power of the classical mathematical frameworks for the description of discrete dynamical systems of interacting objects with often complex internal states. Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However, simulation also qualifies as a separate species of system representation with its own motivations, characteristics, and implications. This work outlines how simulation can be rooted in mathematics and shows which properties some of the elements of such a mathematical framework has. The properties of simulation are described and analyzed in terms of properties of dynamical systems. It is shown how and why a simulation produces emergent behavior and why the analysis of the dynamics of the system being simulated always is an analysis of emergent phenomena. Indeed, the single fundamental class of properties of the natural world that simulation will open to new understanding, is that which occurs only in the dynamics produced by the interactions of the components of complex systems. Simulation offers a synthetic, formal framework for the experimental mathematics of representation and analysis of complex dynamical systems. A notion of a universal simulator and the definition of simulatability is proposed. This allows a description of conditions under which simulations can distribute update functions over system components, thereby determining simulatabilty. The connection between the notion of simulatabilty and the notion of computability is defined and the concepts are distinguished. The basis of practical detection methods for determining effectively non-simulatable systems in practice is presented. The conceptual framework is illustrated, computability, dynamics, emergence, system representation, universal simulator.

The Usefulness of Recombination

Abstract: In this paper, we examine the usefulness of recombination from two points of view First, the problem of crossover disruption is investigated This is done by comparing two Genetic Algorithms with different crossover operators (one-point and uniform) to each other on NK-landscapes with different values of K relative to N, and with different epistatic interactions (random and nearest neighbor) Second, the usefulness of recombination in relation to the location of local optima in the fitness landscape is investigated

General relation between variance-time curve and power spectral density for point processes exhibiting 1/fβ-fluctuations, with special reference to heart rate variability

Abstract: Counting statistics in the form of the variance-time curve provides an alternative to spectral analysis for point processes exhibiting 1/f β-fluctuations, such as the heart beat. However, this is true only for β<1. Here, the case of general β is considered. To that end, the mathematical relation between the variance-time curve and power spectral density in the presence of 1/f β-noise is worked out in detail. A modified version of the variance-time curve is presented, which allows us to deal also with the case β?1. Some applications to the analysis of heart rate variability are given.

Libraries of random-sequence polypeptides produced with high yield as carboxy-terminal fusions with ubiquitin.

Abstract: Libraries of random-sequence polypeptides have been shown to be valuable sources of novel molecules possessing a variety of useful biologic-like activities, some of which may hold promise as potential vaccines and therapeutics. Previous random peptide expression systems were limited to low levels of peptide production and often to short sequences. Here we describe a series of libraries designed for increased polypeptide length. Cloned as carboxy-terminal extensions of ubiquitin, the fusions were produced in E. coli at high levels, and were purified to homogeneity. The majority of the extension proteins examined could be cleaved from ubiquitin by treatment with a ubiquitin-fusion hydrolase. The libraries described here are appropriate sources of novel polypeptides with desired binding or catalytic function, as well as tools with which to examine inherent properties of proteins as a whole. Toward the latter goal, we have examined structural properties of random-sequence proteins purified from these libraries. Quite surprisingly, fluorescence emission spectra of intrinsic tryptophan residues in several purified fusion proteins, under native-like and denaturing conditions, often resemble those expected for folded and unfolded states, respectively. The results presented here detail an important expansion in the range of potential uses for random-sequence polypeptide libraries.

Anomalous convergence of Lyapunov exponent estimates

Abstract: Numerical experiments reveal that estimates of the Lyapunov exponent for the logistic map xt+1=f(xt)=4xt(1-xt) are anomalously precise: they are distributed with a standard deviation that scales as 1/N, where N is the length of the trajectory, not as 1/ √N , the scaling expected from an informal interpretation of the central limit theorem. We show that this anomalous convergence follows from the fact that the logistic map is conjugate to a constant-slope map. The Lyapunov estimator is just one example of a ‘‘chaotic walk’’; we show that whether or not a general chaotic walk exhibits anomalously small variance depends only on the autocorrelation of the chaotic process.

Process for the production of stochastically-generated transcription or translation products

Abstract: The present invention is directed to a process for the production of a peptide, polypeptide, or protein having a predetermined property. In accordance with one embodiment, the process begins by producing by way of synthetic polynucleotide coupling, stochastically generated polynucleotide sequences. A library of expression vectors containing such stochastically generated polynucleotide sequences is formed. Next, host cells containing the vectors are cultured so as to produce peptides, polypeptides, or proteins encoded by the stochastically generated polynucleotide sequences. Screening or selection is carried out on such host cells to identify a peptide, polypeptide, or protein produced by the host cells which has the predetermined property. The stochastically generated polynucleotide sequence which encodes the identified peptide, polypeptide, or protein is then isolated and used to produce the peptide, polypeptide, or protein having the predetermined property.

A Measure of Landscapes

Abstract: The structure of a fitness landscape is still an ill-defined concept. This paper introduces a statistical fitness landscape analysis, that can be used on a multitude of fitness landscapes. The result of this analysis is a statistical model that, together with some statistics denoting the explanatory and predictive value of this model, can serve as a measure for the structure of the landscape. The analysis is based on a statistical time series analysis known as the Box-Jenkins approach, that, among others, estimates the autocorrelations of a time series fitness values generated by a random walk on the landscape. From these estimates, a correlation of length for the landscape can be derived.