6294288
The Processes of Scientific Discovery: The Strategy of Experimentation
Abstract Hans Krebs' discovery, in 1932, of the urea cycle was a major event in biochemistry. This article describes a program, KEKADA, which models the heuristics Hans Krebs used in this discovery. KEKADA reacts to surprises, formulates explanations, and carries out experiments in the same manner as the evidence in the form of laboratory notebooks and interviews indicates Hans Krebs did. Furthermore, we answer a number of questions about the nature of the heuristics used by Krebs, in particular: How domain-specific are the heuristics? To what extent are they idiosyncratic to Krebs? To what extent do they represent general strategies of problem-solving search? The relative generality of KEKADA allows us to view the control structure of KEKADA and its domain-independent heuristics as a model of scientific experimentation that should apply over a broad domain.
37804897
Directions for Qualitative Reasoning
Sacks & Doyle provide an excellent overview of the fundamental limitations of the SPQR representations for reasoning about the qualitative properties of dynamic systems. We take this opportunity to outline some new directions for qualitative reasoning. In this paper, we provide a rigorous mathematical characterization for the term “qualitative property” in the context of static and dynamic systems. Based on these characterizations, we show that interval representations are well suited for reasoning about the qualitative properties of static systems such as qualitative comparative statics and qualitative stability. Moreover, we also show that symbolic computations help in the derivation of useful global properties of dynamic systems which can be used to guide numerical sampling of differential equations. The integration of symbolic and numeric methods provides a powerful approach for automating the qualitative analysis of differential equations.
5581562
Computer science as empirical inquiry: symbols and search
Computer science is the study of the phenomena surrounding computers. The founders of this society understood this very well when they called themselves the Association for Computing Machinery. The machine—not just the hardware, but the programmed, living machine—is the organism we study.
10043574
Scientific Model-Building as Search in Matrix Spaces
Many reported discovery systems build discrete models of hidden structure, properties, or processes in the diverse fields of biology, chemistry, and physics. We show that the search spaces underlying many well-known systems are remarkably similar when re-interpreted as search in matrix spaces. A small number of matrix types are used to represent the input data and output models. Most of the constraints can be represented as matrix constraints; most notably, conservation laws and their analogues can be represented as matrix equations. Typically, one or more matrix dimensions grow as these systems consider more complex models after simpler models fail, and we introduce a notation to express this. The novel framework of matrix-space search serves to unify previous systems and suggests how at least two of them can be integrated. Our analysis constitutes an advance toward a generalized account of model-building in science.
16243913
Experiments with a Heuristic Compiler
This report describes some experiments in constructing a compiler that makes use of heuristic problem~solving techniques such as those incorporated in the General Problem Solver (GPS) [1]. The experiments were aimed at the dual objectives of throwing light on some of the problems of constructing more powerful programming languages and compilers, and of testing whether the task of writing a computer program can be regarded as a "problem" in the sense in which that term is used in GPS. The present paper is concerned primarily with the second objective--with analyzing some of the problem-solving processes that are involved in writing computer programs. At the present stage of their development, no claims will be made for the heuristic programming procedures described here as practical approaches to the construction of compilers. Their interest lies in what they teach us about the nature of the programming task.
6846387
Causality and Model Abstraction
Abstract Much of science and engineering is concerned with characterizing processes by equations describing the relations that hold among parameters of objects and govern their behavior over time. In formal descriptions of processes in terms of parameters and equations, the notion of causality is rarely made explicit. Formal treatments of the foundations of sciences have avoided discussions of causation and spoken only of functional relations among variables. Nevertheless, the notion of causality plays an important role in our understanding of phenomena. Even when we describe the behavior of a system formally in terms of acausal, mathematical relations, we often give an informal, intuitive explanation of why the system behaves the way it does in terms of cause-effect relations. In this paper, we will present an operational definition of causal ordering. The definition allows us to extract causal dependency relations among variables implicit in a model of a system, when a model is represented as a set of acausal, mathematical relations. Our approach is based on the theory of causal ordering first presented by Simon [22]. The paper shows how to use the theory and its extension in reasoning about physical systems. Further, the paper studies the relation of the theory to the problems of model aggregation.
1182152
Stability of k -Means Clustering
We consider the stability of k-means clustering problems. Clustering stability is a common heuristics used to determine the number of clusters in a wide variety of clustering applications. We continue the theoretical analysis of clustering stability by establishing a complete characterization of clustering stability in terms of the number of optimal solutions to the clustering optimization problem. Our results complement earlier work of Ben-David, von Luxburg and Pal, by settling the main problem left open there. Our analysis shows that, for probability distributions with finite support, the stability of k-means clusterings depends solely on the number of optimal solutions to the underlying optimization problem for the data distribution. These results challenge the common belief and practice that view stability as an indicator of the validity, or meaningfulness, of the choice of a clustering algorithm and number of clusters.
145761361
CaMeRa: A computational model of multiple representations
This research aims to clarify, by constructing and testing a computer simulation, the use of multiple representations in problem solving, focusing on their role in visual reasoning. The model is motivated by extensive experimental evidence in the literature for the features it incorporates, but this article focuses on the system's structure. We illustrate the model's behavior by simulating the cognitive and perceptual processes of an economics expert as he teaches some well-learned economics principles while drawing a graph on a blackboard. Data in the experimental literature and concurrent verbal protocols were used to guide construction of a linked production system and parallel network, CaMeRa (Computation with Multiple Representations), that employs a “Mind's Eye” representation for pictorial information, consisting of a bitmap and associated node-link structures. Propositional list structures are used to represent verbal information and reasoning. Small individual pieces from the different representations are linked on a sequential and temporary basis to form a reasoning and inferencing chain, using visually encoded information recalled to the Mind's Eye from long-term memory and from cues recognized on an external display. CaMeRa, like the expert, uses the diagrammatic and verbal representations to complement one another, thus exploiting the unique advantages of each.
17561186
Situated Action: A Symbolic Interpretation
The congeries of theoretical views collectively referred to as “situated action” (SA) claim that humans and their interactions with the world cannot be understood using symbol-system models and methodology, but only by observing them within real-world contexts or building nonsymbolic models of them. SA claims also that rapid, real-time interaction with a dynamically changing environment is not amenable to symbolic interpretation of the sort espoused by the cognitive science of recent decades. Planning and representation, central to symbolic theories, are claimed to be irrelevant in everyday human activity. 
 
We will contest these claims, as well as their proponents' characterizations of the symbol-system viewpoint. We will show that a number of existing symbolic systems perform well in temporally demanding tasks embedded in complex environments, whereas the systems usually regarded as exemplifying SA are thoroughly symbolic (and representational), and, to the extent that they are limited in these respects, have doubtful prospects for extension to complex tasks. As our title suggests, we propose that the goals set forth by the proponents of SA can be attained only within the framework of symbolic systems. The main body of empirical evidence supporting our view resides in the numerous symbol systems constructed in the past 35 years that have successfully simulated broad areas of human cognition.
38908855
Large-Scale SVD and Subspace-Based Methods for Information Retrieval
A theoretical foundation for latent semantic indexing (LSI) is proposed by adapting a model first used in array signal processing to the context of information retrieval using the concept of subspaces. It is shown that this subspace-based model coupled with minimal description length (MDL) principle leads to a statistical test to determine the dimensions of the latent-concept subspaces in LSI. The effect of weighting on the choice of the optimal dimensions of latent-concept subspaces is illustrated. It is also shown that the model imposes a so-called low-rank-plus-shift structure that is approximately satisfied by the cross-product of the term-document matrices. This structure can be exploited to give a more accurate updating scheme for LSI and to correct some of the misconception about the achievable retrieval accuracy in LSI updating. Variants of Lanczos algorithms are illustrated with numerical test results on Cray T3E using document collections generated from World Wide Web.
6270234
Spectral Relaxation for K-means Clustering
The popular K-means clustering partitions a data set by minimizing a sum-of-squares cost function. A coordinate descend method is then used to find local minima. In this paper we show that the minimization can be reformulated as a trace maximization problem associated with the Gram matrix of the data vectors. Furthermore, we show that a relaxed version of the trace maximization problem possesses global optimal solutions which can be obtained by computing a partial eigendecomposition of the Gram matrix, and the cluster assignment for each data vectors can be found by computing a pivoted QR decomposition of the eigenvector matrix. As a by-product we also derive a lower bound for the minimum of the sum-of-squares cost function.