Prolegomenon to the relation between social theory and method*

Building on the work of Noam Chomsky (1963), this paper presents a hierarchy of grammars and associated computational automata in order to inform social theory construction and method. A detailed exposition of linguistic forms within the grammar hierarchy reveals clear analogues with common social scientific paradigms. Two of these paradigms (which are termed structural and process approaches) are already being widely exploited by formal methodological techniques. A third paradigm, which is rooted in a tradition of interpretive sociology, has been more resistant to formalization. Using arguments from theoretical computer science, the paper suggests that existing quantitative methodologies can be extended to accommodate qualitative arguments which subsume empirical domains as diverse as natural language and structurational phenomena.     

Can tools help unify organization theory? Perspectives on the state of computational modeling

Scholars engaged in the study of work group and organizational behavior are increasingly calling for the use of integrated methods in conducting research, including the wider adoption of computational models for generating and testing new theory. Our review of the state of modern computational modeling incorporating social structures reveals steady increases in the incorporation of dynamic, adaptive, and realistic behaviors of agents in network settings, yet exposes gaps that must be addressed in the next generation of organizational simulation systems. We compare 28 models according to more than two hundred evaluation criteria, ranging from simple representations of agent demographic and performance characteristics, to more richly defined instantiations of behavioral attributes, interaction with non-agent entities, model flexibility, communication channels, simulation types, knowledge, transactive memory, task complexity, and resource networks. Our survey assesses trends across the wide set of criteria, discusses practical applications, and proposes an agenda for future research and development. Michael J. Ashworth is a doctoral candidate in computational organization science at Carnegie Mellon University, where he conducts research on social, knowledge, and transactive memory networks along with their effects on group and organizational learning and performance. Practical outcomes of his work include improved understanding of the impact of technology, offshoring, and turnover on organizational performance. Mr. Ashworth has won several prestigious grants from the Sloan Foundation and the National Science Foundation to pursue his research on transactive memory networks. Journals in which his research has appeared include Journal of Mathematical Sociology, International Journal of Human Resource Management, and Proceedings of the International Conference on Information Systems. His recent work on managing human resource challenges in the electric power industry has been featured in the Wall Street Journal and on National Public Radio's ``Morning Edition.' Mr. Ashworth received his undergraduate degree in systems engineering from the Georgia Institute of Technology. Kathleen M. Carley is a professor at the Institute for Software Research International in the School of Computer Science at Carnegie Mellon University. She is the director of the center for Computational Analysis of Social and Organizational Systems (CASOS), a university-wide interdisciplinary center that brings together network analysis, computer science and organization science (www.casos.ece.cmu.edu). Prof. Carley carries out research that combines cognitive science, dynamic social networks, text processing, organizations, social and computer science in a variety of theoretical and applied venues. Her specific research areas are computational social and organization theory; dynamic social networks; multi-agent network models; group, organizational, and social adaptation, and evolution; statistical models for dynamic network analysis and evolution, computational text analysis, and the impact of telecommunication technologies on communication and information diffusion within and among groups. Prof. Carley has undergraduate degrees in economics and political science from MIT and a doctorate in sociology from Harvard University.     

Joint Reliability Function of Coherent Systems with Shared Heterogeneous Components

In this paper, we consider two coherent systems having shared components. We assume that in the two systems there are three different types of components; components of type one that just belong to the first system, components of type two that lie only in the second system and components of type three that are shared by the two systems. We use the concept of joint survival signature to assess the joint reliability function of the two systems. Using this concept, some representations for the joint reliability function of the system lifetimes are obtained under two different scenarios of component failures. In the first scenario, we assume that the components of the systems fail according to different counting processes such as non-homogeneous Poisson processes. In the second scenario, it is assumed that the component lifetimes of each type are exchangeable while the three types of component lifetimes can be independent or dependent. To illustrate the theoretical results, two systems with shared components are studied numerically and graphically.

     

Moduli for pairs of elliptic curves¶with isomorphic N-torsion

We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a “determinant” map from this moduli surface to (Z/N Z)^*; its fibers are the components of the surface. We define spaces of modular forms on these components and Hecke correspondences between them, and study how those spaces of modular forms behave as modules for the Hecke algebra. We discover that the component with determinant −1 is somehow the “dominant” one; we characterize the difference between its spaces of modular forms and the spaces of modular forms on the other components using forms with complex multiplication. In addition, we prove Atkin–Lehner-style results about these spaces of modular forms. Finally, we show some simplifications that arise when N is prime, including a complete determination of such CM-forms, and give numerical examples. Received: 20 September 2000 / Revised version: 7 February 2001     

Transition Probability of Brownian Motion in the Octant and its Application to Default Modelling

ABSTRACT

We derive a semi-analytical formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main theoretical result is a solution to the original problem expressed as an expansion into special functions and an eigenvalue which has to be chosen to allow a matching of the boundary condition. We discuss and test several computational methods to solve a finite-dimensional approximation to this nonlinear eigenvalue problem. Finally, we apply our results to the computation of default probabilities and credit valuation adjustments in a structural credit model with mutual liabilities.     

Self-regulation through social institutions: A framework for the design of open agent-based electronic marketplaces

In this paper, we argue that allowing self-interested agents to activate social institutions during runtime can improve the robustness (i.e., stability, reliability, or scalability) of open multiagent systems (MAS). Referring to sociological theory, we consider institutions to be rules that need to be activated and adopted by the agent population during runtime and propose a framework for self-regulation of MAS for the domain of electronic marketplaces. The framework consists of three different institutional types that are defined by the mechanisms and instances that generate, change or safeguard them. We suggest that allowing autonomous agents both the reasoning about their compliance with a rule and the selection of an adequate institutional types helps to balance the trade-off between the autonomy of self-interested agents and the maintenance of social order (cf. Castelfranchi, 2000) in MAS, and to ensure almost the same qualities as in closed environments. A preliminary report of the evaluation of the prototype by empirical simulations is given. Christian S. Hahn studied computer science and economics at Saarland University and received his diploma in 2004. Currently, he works in a project of the priority program ‘Socionics’ funded by the German Research Foundation at the German Research Center for Artificial Intelligence (DFKI). Bettina Fley studied sociology, economics, law, and social and economic history at the University of Hamburg and received her diploma in 2002. She currently works in a project in the priority program ‘Socionics’, which is funded by the German Research Foundation (DFG), at the Department of Technology Assessment at the Hamburg University of Technology. Michael Florian, received his master in sociology at the University of Münster, where he also finished his doctoral degree in 1993. Since 1995, he holds a position as a senior researcher (‘Oberingenieur’) at the Department of Technology Assessment at the Hamburg University of Technology and heads the sociological part of a project in the priority program ‘Socionics’ funded by the German Research Foundation (DFG).     

Agent‐based computational models and generative social science

This article argues that the agent‐based computational model permits a distinctive approach to social science for which the term “generative” is suitable. In defending this terminology, features distinguishing the approach from both “inductive” and “deductive” science are given. Then, the following specific contributions to social science are discussed: The agent‐based computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agent‐based modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agent‐based (“bottom up”) models. The agent‐based approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agent‐based modeling offers powerful new forms of hybrid theoretical‐computational work; these are particularly relevant to the study of non‐equilibrium systems. The agent‐based approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agent‐based modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. © 1999 John Wiley & Sons, Inc.     

On the Orderings and Groupings of Conditional Maximizations within ECM-Type Algorithms

Abstract

The ECM and ECME algorithms are generalizations of the EM algorithm in which the maximization (M) step is replaced by several conditional maximization (CM) steps. The order that the CM-steps are performed is trivial to change and generally affects how fast the algorithm converges. Moreover, the same order of CM-steps need not be used at each iteration and in some applications it is feasible to group two or more CM-steps into one larger CM-step. These issues also arise when implementing the Gibbs sampler, and in this article we study them in the context of fitting log-linear and random-effects models with ECM-type algorithms. We find that some standard theoretical measures of the rate of convergence can be of little use in comparing the computational time required, and that common strategies such as using a random ordering may not provide the desired effects. We also develop two algorithms for fitting random-effects models to illustrate that with careful selection of CM-steps, ECM-type algorithms can be substantially faster than the standard EM algorithm.     

Simplicity and reality in computational modeling of politics

Modeling a polity based on viable scientific concepts and theoretical understanding has been a challenge in computational social science and social simulation in general and political science in particular. This paper presents a computational model of a polity (political system) in progressive versions from simple to more realistic. The model, called SimPol to highlight the fundamental structures and processes of politics in a generic society, is developed using the combined methodologies of object-based modeling (OOM), the Unified Modeling Language (UML), and the methodology of Lakatos’ research programs. SimPol demonstrates that computational models of entire political systems are methodologically feasible and scientifically viable; they can also build on and progress beyond previous theory and research to advance our understanding of how polities operate across a variety of domains (simple vs. complex) and levels of analysis (local, national, international). Both simple and realistic models are necessary, for theoretical and empirical purposes, respectively.

Exact Tests for Interaction in Several 2 × 2 Tables

Abstract

The investigation of interaction in a series of 2 × 2 tables is warranted in a variety of research endeavors. Though many large-sample approaches for such investigations are available, the exact analysis of the problem has been formulated for the probability statistic only. We present several alternative statistics applicable in this context. We also give an efficient polynomial multiplication algorithm to compute exact distributions and tail areas for the family of stratum-additive statistics. Besides the probability statistic, these include the score, likelihood ratio, and other statistics. In addition to comparing, in empirical terms, the diverse computational strategies for exact interaction analysis, we also explore the theoretical linkages between them. Data from published papers are used for illustration.     

A Computationally Efficient Oracle Estimator for Additive Nonparametric Regression with Bootstrap Confidence Intervals

Abstract

This article makes three contributions. First, we introduce a computationally efficient estimator for the component functions in additive nonparametric regression exploiting a different motivation from the marginal integration estimator of Linton and Nielsen. Our method provides a reduction in computation of order n which is highly significant in practice. Second, we define an efficient estimator of the additive components, by inserting the preliminary estimator into a backfitting˙ algorithm but taking one step only, and establish that it is equivalent, in various senses, to the oracle estimator based on knowing the other components. Our two-step estimator is minimax superior to that considered in Opsomer and Ruppert, due to its better bias. Third, we define a bootstrap algorithm for computing pointwise confidence intervals and show that it achieves the correct coverage.     

Probabilistic Modelling of Monitoring and Maintenance of Multistate Monotone Systems with Dependent Components

In Gåsemyr and Natvig (2001) partial monitoring of components with applications to preventive system maintenance was considered for a binary monotone system of binary components. The purpose of the present paper is to extend this to a multistate monotone system of multistate components, where the states more realistically represent successive levels of performance ranging from the perfect functioning level down to the complete failure level. We start out close to the spirit of Arjas (1989) by using a marked point process with complete monitoring of all components, and hence of the system, as the basic reference framework. We then consider a marked point process linked to partial monitoring of some components, for instance in certain time intervals. Incorporation of information from the observed system history process is then treated. Mainly, we assume that the inspection strategy is determined by the observed component history process only, with a possible exception of a full or partial autopsy after an observed change of state of , the system. Furthermore, we consider how to arrive at the posterior distribution for the relevant parameter vector by a standard simulation procedure, the data augmentation method. The idea is to extend the observed data to the complete component history process. The theory is applied to an electrical power generation system for two nearby oilrigs with some standby components, as considered in Natvig et al. (1986).AMS 2000 Subject Classification: Primary 96B25; Secondary, 62N05, 60K10     

Computing the conditioning of the components of a linear least‐squares solution

In this paper, we address the accuracy of the results for the overdetermined full rank linear least‐squares problem. We recall theoretical results obtained in (SIAM J. Matrix Anal. Appl. 2007; 29 (2):413–433) on conditioning of the least‐squares solution and the components of the solution when the matrix perturbations are measured in Frobenius or spectral norms. Then we define computable estimates for these condition numbers and we interpret them in terms of statistical quantities when the regression matrix and the right‐hand side are perturbed. In particular, we show that in the classical linear statistical model, the ratio of the variance of one component of the solution by the variance of the right‐hand side is exactly the condition number of this solution component when only perturbations on the right‐hand side are considered. We explain how to compute the variance–covariance matrix and the least‐squares conditioning using the libraries LAPACK (LAPACK Users' Guide (3rd edn). SIAM: Philadelphia, 1999) and ScaLAPACK (ScaLAPACK Users' Guide. SIAM: Philadelphia, 1997) and we give the corresponding computational cost. Finally we present a small historical numerical example that was used by Laplace (Théorie Analytique des Probabilités. Mme Ve Courcier, 1820; 497–530) for computing the mass of Jupiter and a physical application if the area of space geodesy. Copyright © 2008 John Wiley & Sons, Ltd.     

Materials by design and the exciting role of quantum computation/simulation

It is now well-recognized that we are witnessing a golden age of innovation with novel materials, with discoveries important for both basic science and device applications—some of which will be treated at this Workshop. In this talk, we discuss the role of computation and simulation in the dramatic advances of the past and those we are witnessing today. We will also describe the growing acceptance and impact of computational materials science as a major component of materials research and its import for the future. In the process, we will demonstrate how the well-recognized goal driving computational physics/computational materials science—simulations of ever-increasing complexity on more and more realistic models—has been brought into greater focus with the introduction of greater computing power that is readily available to run sophisticated and powerful software codes like our highly precise full-potential linearized augmented plane wave (FLAPW) method, now also running on massively parallel computer platforms.We will then describe some specific advances we are witnessing today, and computation and simulation as a major component of quantum materials design and its import for the future, with the goal—to synthesize materials with desired properties in a controlled way via materials engineering on the atomic scale. The theory continues to develop along with computing power. With the universality and applicability of these methods to essentially all materials and properties, these simulations are starting to fill the increasingly urgent demands of material scientists and engineers.     

Almost arcwise connected continua without dense arc components

A continuum M is almost arcwise connected if each pair of nonempty open subsets of M can be joined by an arc in M. An almost arcwise connected plane continuum without a dense arc component can be defined by identifying pairs of endpoints of three copies of the Knaster indecomposable continuum that has two endpoints. In [7] K.R. Kellum gave this example and asked if every almost arcwise connected continuum without a dense arc component has uncountably many arc components. We answer Kellum's question by defining an almost arcwise connected plane continuum with only three arc components none of which are dense. A continuum M is almost Peano if for each finite collection $\text{C}$ of nonempty open subsets of M there is a Peano continuum in M that intersects each element of $\text{C}$. We define a hereditarily unicoherent almost Peano plane continuum that does not have a dense arc component. We prove that every almost arcwise connected planar λ-dendroid has exactly one dense arc component. It follows that every hereditarily unicoherent almost arcwise connected plane continuum without a dense arc component has uncountably many arc components. Using an example of J. Krasinkiewicz and P Minc [8], we define an almost Peano λ-dendroid that do not have a dense arc component. Using a theorem of J.B. Fugate and L. Mohler [3], we prove that every almost arcwise connected λ-dendroid without a dense arc component has uncountably many arc components. In Euclidean 3-space we define an almost Peano continuum with only countably many arc components no one of which is dense. It is not known if the plane contains a continuum with these properties.     

Communication Networks from the Enron Email Corpus “It's Always About the People. Enron is no Different”

The Enron email corpus is appealing to researchers because it represents a rich temporal record of internal communication within a large, real-world organization facing a severe and survival-threatening crisis. We describe how we enhanced the original corpus database and present findings from our investigation undertaken with a social network analytic perspective. We explore the dynamics of the structure and properties of the organizational communication network, as well as the characteristics and patterns of communicative behavior of the employees from different organizational levels. We found that during the crisis period, communication among employees became more diverse with respect to established contacts and formal roles. Also during the crisis period, previously disconnected employees began to engage in mutual communication, so that interpersonal communication was intensified and spread through the network, bypassing formal chains of communication. The findings of this study provide valuable insight into a real-world organizational crisis, which may be further used for validating or developing theories and dynamic models of organizational crises; thereby leading to a better understanding of the underlying causes of, and response to, organization failure. Jana Diesner is a Research Associate and Linguistic Programmer at the Center for Computational Analysis of Social and Organizational Systems at the School of Computer Science (CASOS), Carnegie Mellon University (CMU). She received her Masters in Communications from Dresden University of Technology in 2003. She had been a research scholar at the Institute for Complex Engineered System at CMU in 2001 and 2002. Her research combines computational linguistics, social network analysis and computational organization theory. Terrill L. Frantz is a post-doc researcher at the Center for Computational Analysis of Social and Organizational Systems (CASOS) in the School of Computer Science at Carnegie Mellon University. His research involves studying the dynamics of organization social-networks and behavior via computer modeling and simulation. He is developing an expertise in workforce integration strategy and policy evaluation during organization mergers. He earned his doctorate (Ed.D. in Organization Change) from Pepperdine University, a MBA from New York University and a BS in Business Administration (Computer Systems Management) from Drexel University. Prior to entering academic research, for nearly 20 years he was a software applications development manager in the global financial services and industrial chemicals industries; most recently as a Vice President in Information Technology at Morgan Stanley in Hong Kong, New York and London. Kathleen M. Carley is a professor at the Institute for Software Research International in the School of Computer Science at Carnegie Mellon University. She is the director of the center for Computational Analysis of Social and Organizational Systems (CASOS) <http://www.casos.cs.cmu.edu/>, a university wide interdisciplinary center that brings together network analysis, computer science and organization science (www.casos.ece.cmu.edu) and has an associated NSF funded training program for Ph.D. students. She carries out research that combines cognitive science, social networks and computer science to address complex social and organizational problems. Her specific research areas are computational social and organization theory, group, organizational and social adaptation and evolution, social and dynamic network analysis, computational text analysis, and the impact of telecommunication technologies and policy on communication, information diffusion, disease contagion and response within and among groups particularly in disaster or crisis situations.     

Diagnostics and rubrics for assessing learning across the computational science curriculum

We describe our experiences with learning assessment in a new computational science program. We report on the development and pilot testing of assessment tools in both core and cognate courses. Specifically, we detail a diagnostic assessment that predicted success in our introductory computational science course with reasonable reliability; we give an account of our use of an existing assessment tool to investigate how introducing computational thinking in a cognate course influences learning of the traditional course material; and we discuss rubric development for project evaluation.     

Multi-state Systems with Graduate Failure and Equal Transition Intensities

We consider unrecoverable homogeneous multi-state systems with graduate failures, where each component can work at M + 1 linearly ordered levels of performance. The underlying process of failure for each component is a homogeneous Markov process such that the level of performance of one component can change only for one level lower than the observed one, and the failures are independent for different components. We derive the probability distribution of the random vector X, representing the state of the system at the moment of failure and use it for testing the hypothesis of equal transition intensities. Under the assumption that these intensities are equal, we derive the method of moments estimators for probabilities of failure in a given state vector and the intensity of failure. At the end we calculate the reliability function for such systems. Received: May 18, 2007., Revised: July 8, 2008., Accepted: September 29, 2008.