STATISTICAL PROPERTIES OF MATHEMATICAL PROGRAMMING MODELS OF STOCHASTIC NETWORK EQUILIBRIUM*

ABSTRACT. Boyce et al. (1981, 1983) have proposed and implementd the use of observed entropy levels to estimate the travel-cost coefficient in mathematical programming models of network equilibrium which involve logit route-choice probabilities. This so-called “dispersion-constrained” model is shown to give severely biased and statistically inefficient underestimates. A natural counterpart, the entropy-maximizing model, is proposed here and overestimates the travel-cost coefficient with much lower bias and much higher statistical efficiency. Even though the two models are mathematically homeomorphic in some respects, they have vastly different statistical properties. It follows that the use of observed entropy levels is undesirable and should be avoided, since maximizing entropy provides an unambiguously superior alternative.     

An Equivalence Theorem to Integrate Entropy-Maximizing Submodels within Overall Mathematical-Programming Frameworks

This paper presents a lemma and a theorem which demonstrate equivalent ways of formulating certain mathematical-programming problems. The first shows, in general terms, how constraints can be “absorbed” into the objective function and vice versa. The second shows how such ideas can be applied to spatial analysis problems involving the minimization of development costs subject to interactions being determined by (suboptimal) entropy-maximizing models. This provides both a new perspective on the relationship between programming and entropy models, and formulations that are computationally convenient.     

Markovian Models of Movement Within Urban Spatial Structures

Much work has assumed that movement within urban spatial structures is an “adaptive” process. Nonetheless, mathematical models have not yet been specified and tested which formulate both how different individuals “adapt” over time in destination or route selection, and how predictions about aggregate movement can be derived from postulates about different persons. Two adaptive first-order Markov models for heterogeneous individuals are suggested by the literature. When formulated and tested, however, these models are inadequate to describe travel within urban spatial structures. This implies that the use of Markovian processes to model movement may be overrated. More confidence may be placed in other formulations such as linear learning models of route and destination choice.     

Conversion by the Numbers: Benefits and Pitfalls of Quantitative Modelling in the Study of Early Christian Growth

Proponents and critics of numerically modelling early Christian growth have missed many complexities of this approach. This study re‐examines quantitative modelling by conducting “thought experiments,” built from initial assumptions to population projections. First, an “apostolic mission” model assumes that Christianity grew via persuasive leaders; it projects a cubic growth curve. Second, a “values reproduction” model ties higher reproduction and conversion to certain Christian values; it projects an exponential curve. Next, a “social reaction” model links growth to interconfessional interactions; it projects a logistic curve. Such formal models reveal numerical parameters of conversion and the impact of various assumptions. Together, they illustrate the variability of early Christian population projections. They also showcase limitations of traditional quantitative modelling, which tends to oversimplify social conditions, to mischaracterise ancient religion, and to inspire teleological reasoning. Newer “network” models can overcome only some of these limitations. Used carefully, however, quantitative methods supplement familiar socio‐cultural approaches.     

Size and location of lightning-induced ionisation enhancements from measurement of VLF phase and amplitude perturbations on multiple antennas

A 600-km array of five Trimpi receivers (“elements”) has been set up in New Zealand broadside to the VLF (22.3 kHz) transmitter, NWC, some 6000 km west, with element separations varying from 8 km to 550 km. Although such a five-element array is inadequate for imaging of lightning-induced ionisation enhancements (LIEs) by VLF holography, or inverse scattering, estimates of LIE size and location can be made if the shape and form of the LIE can be guessed or assumed, with even fewer elements. With five elements, tests of the assumed model can be made as well.Owing to its transform properties, the simplest model to use for scattering inversion is the Gaussian LIE distribution. For this model, and for single mode propagation, an inversion process is derived here for the full range of LIE and path dimensions, ranging from those for which the receiver is in the diffraction far field to those in which “geometric optics” dominate. This inversion process has some validity for small LIEs of other shapes of simple form. For more extreme models, the dominance of geometry or diffraction can usually be established in individual cases which then allows simple scaling procedures to be used in scattering inversion.Some 70 Trimpi events were observed on all five elements during a single night in July. 1991 (late winter). These were used to determine LIE location and size, and to test the applicability of various LIE models. It was found that most LIEs that night occurred over the Tasman Sea near the great circle from the VLF transmitter, NWC, to Wellington, generally some 500 to 2000 km from Wellington, and with north-south dimensions of 100–250 km. Much longer east-west dimensions (oriented towards NWC) are suggested to account for the very strong Trimpis observed. While about half of these LIEs that night could have had a smooth lateral spread (e.g., Gaussian), the remainder required varying degrees of fine structure, from “flat” or Butterworth LIEs to multiple LIEs as might be expected from multiduct whistlers, to explain the observed diffraction pattern exhibiting maxima and minima as well as the wide angular range over which simultaneous Trimpis were observed.     

Tecolote,Guatemala: Archaeological Evidence for a Fortified Late Classic Maya Political Border

Abstract

Settlement pattern data in the lower Salt River valley of central Arizona, near Phoenix, have led to different models of Hohokam political community organization during the early Classic period (ca. A.D. 1150–1300). The “focal village” model posits political communities centered on a single large village with monumental architecture surrounded by smaller settlements. The “linear community” model envisions an elongated arrangement integrating populations distributed along the routes of irrigation canals. Each model has implications for the nature of cooperation within and between settlement clusters and the degree to which large-scale irrigation management influenced the development of Hohokam community organization. In this analysis, ceramic sourcing studies are used to outline networks of interaction to examine the different models. Our results provide some evidence for a crosscutting patchwork of geographically dispersed social groups which fits most comfortably within the linear community model.     

WHAT IS A SCHOLARLY PERSONA? TEN THESES ON VIRTUES,SKILLS, AND DESIRES

What is the problem that “epistemic virtues” seek to solve? This article argues that virtues, epistemic and otherwise, are the key characteristics of “scholarly personae,” that is, of ideal‐typical models of what it takes to be a scholar. Different scholarly personae are characterized by different constellations of virtues and skills or, more precisely, by different constellations of commitments to goods (epistemic, moral, political, and so forth), the pursuit of which requires the exercise of certain virtues and skills. Expanding Hayden White's notion of “historiographical styles” so as to encompass not only historians' writings, but also their nontextual “doings,” the article argues that different styles of “being a historian”—a meticulous archival researcher, an inspired feminist scholar, or an outstanding undergraduate teacher—can be analyzed productively in terms of virtues and skills. Finally, the article claims that virtues and skills, in turn, are rooted in desires, which are shaped by the examples of others as well as by promises of reward. This makes the scholarly persona not merely a useful concept for distinguishing among different types of historians, but also a critical tool for analyzing why certain models of “being a historian” gain in popularity, whereas others become “old‐fashioned.”     

The Optimal Nodal Location of Public Facilities With Price-Sensitive Demand

The purpose of this paper is to present some models for the location of public facilities in nodal networks that explicitly maximize social welfare by accounting for price-elastic demand functions. The models presented here are general; yet they are mathematically equivalent to the plant location problem and are therefore amenable to solution procedures developed for the plant location problem. The models presented here distinguish between two institutional environments that reflect the degree of power of the consumer to choose which facility to patronize. If consumers can be assigned arbitrarily to facilities and can be denied service, then the environment is one of public fiat. If consumers must be served at the facility of their choice, then a “serve-allcomers” environment exists. Separate models for each environment are specified, and the relationship between optimal assignments and pricing policies is developed.     

Estimation of OSL trap parameters by optical “cleaning” — a critical study

The so-called thermal “cleaning” applied in thermoluminescence analysis allows distinguishing TL signal originating from different traps of comparable thermal depths. Here, the detailed study on the suitability of a similar approach — which can be called optical “cleaning” — for the analysis of OSL process has been carried out by means of computer modelling. The optical “cleaning” is realized by short optical stimulation applied directly after irradiation. It turns out that this approach does not help to separate signals related to various traps having similar optical cross-section (OCS) values. For some sets of trap parameters, sufficiently good reconstruction of the trap optical cross-sections can be achieved by the analysis of the conventional OSL curve obtained directly after sample irradiation, while the OSL curve analysis after “cleaning” does not provide any additional data. For other cases the analysis of both curves with and without “cleaning” leads to optical cross-section values different from those assumed in the model, but just in such situations the optical “cleaning” can be helpful. The differences between the OSL components of the conventional curve and the one obtained after “cleaning” can be used as indicators of an incompatibility of the trap parameters obtained from the OSL analysis with their actual values.     

Preface

The current interest in Kant in the North American debate on criminal punishment arise from a deceptive hope: Kant seems as a sort of “antidote” useful to mitigate the results of correctional and merely intimidatory practice. Both the two current interpretations of his philosophy, for their typical post-modern statement, are yet improper and unproductive. Both Kant as a pioneer of so-called “limiting retributivism” and Kant theorist of “pure retributivism”, “purged” of the extreme application of the logic of jus talionis, do offer us an “antidote” that is ineffective against the justified malaise which is rampant amongst the ranks of utilitarians on the other side of the Atlantic. Rather than a genuine medicine, it seems to be a sweetener, designed perhaps to make the unconscionable logic of power more acceptable, but certainly not to limit it.     

Aggregation Decomposition and Aggregation Guidelines for a Class of Minimax and Covering Location Models

Facility location problems often involve movement between facilities to be located and customers/demand points, with distances between the two being important. For problems with many customers, demand point aggregation may be needed to obtain a computationally tractable model. Aggregation causes error, which should be kept small. We consider a class of minimax location models for which the aggregation may be viewed as a second‐order location problem, and use error bounds as aggregation error measures. We provide easily computed approximate “square root” formulas to assist in the aggregation process. The formulas establish that the law of diminishing returns applies when doing aggregation. Our approach can also facilitate aggregation decomposition for location problems involving multiple “separate” communities.     

The analysis of innovation processes

Methods are described for modelling both the speeds and the driving forces of innovation processes, namely Critical Path Schedules and Cash Flow Curves respectively. The differences between innovations in modern industrial conditions and simpler societies are discussed, and the models applied to early innovations, but the data are too fragmentary to make quantitative models, although they can be used qualitatively to show general trends. In early societies the speeds were very slow but benefit/cost ratios very high, whereas the reverse tends to be true on average for modern innovations. Long delay times are often found in early innovation processes and these are determined by a wide variety of cultural factors. Seldom has the progress of the technology itself been on the “Critical Path” of innovation processes. The “Critical Path” and “Cash Flow” methods can also be used to study other, non-innovative, complex processes.     

Importing Concepts from Biology into Political Science: The Case of Punctuated Equilibrium

From the 1950s to the 1990s, the “incrementalist” model dominated theories of policymaking. Since Baumgartner and Jones's Agendas and Instability in American Politics was published in 1993, however, the “punctuated equilibrium” model, borrowed from evolutionary biology, has supplanted the incrementalist model. But what do such alien models do to the discipline of political science, and what does the discipline do to the models, when they are thus imported? In this article, I first discuss the functions of concepts in political science, then discuss and analyze the creation and meaning of the concept of punctuated equilibrium in biology, then trace its transformation as it was initially adopted by political scientists, then analyze the manner in which its meaning developed and altered as it grew in popularity within the discipline, and finally assess its value to political science now. I will conclude with some general observations about the process of importing concepts from outside the discipline.     

Information Entropy of Non‐Probabilistic Processes

We derive an expression for the entropy of non‐probabilistic distributions encountered in spatial and mathematical mappings. The entropy of non‐probabilistic distributions can be formulated using probabilistic notions of the hypothetical random redistribution of finite information. We show that the discrete approximation to the information content of spatial maps can be based on the discrete hypergeometric distribution. The resultant “associative” entropy is distinct from the Shannon entropy for probability distributions and addresses several shortcomings of the current entropy paradigm as applied to spatial analysis. The associative entropy statistic is distributed approximately as a chi‐squared random variable under limitations of variation. We formulate a univariate logical equivalent of the associative entropy statistic, freeing the paradigm from the degrees of freedom constraint to which it has been traditionally shackled. This entropy has application in spatial analysis and fuzzy set theory. The associative entropy is based on the concept of proportional information and is related to the Getis G‐statistics of spatial association and the Chi‐squared statistics of sample means. We explore the utility of the theory when applied to spatial distribution of vegetation in New Brunswick, Canada. The limitations and implications of the entropy expression are discussed and suggestions are made for future applications of the theory. This work is part of the development of an information theory framework for the analysis of landscape patterns of animal habitat.     

Studying Rules Changes in the U.S. House: Evidence from an Alternative Empirical Model

Binder (1996) and Schickler (2000) define the current debate as to why the U.S. House has changed its standing rules regarding the majority rule and the minority rights. I revisit their empirical models—binary logit and ordered logit—and theoretically and statistically test the appropriateness of these models. I find that both of them are actually choosing inappropriate models. Their theoretical claims cannot be properly examined by utilizing their choices of models. In addition, the data do not satisfy the “parallel regression” assumption but do satisfy the “independence of irrelevant alternatives” assumption, which supports using an alternative multinomial logit model. I further extend the model, and find the dynamic nature of rules changes in the U.S. House. It appears there is no symmetry between the rules changes that promote the majority rule and the rules changes that enhance the minority rights.     

DAVID AS A BIBLICAL ‘GOOD-FELLA’ AND ‘THE GODFATHER’

Abstract

Scholars search for analogies with which to better understand biblical texts. David has been compared to the “outlaw”, “refugee”, “vassal”, “renegade”, “guerrilla”, “bandit chief”, “fugitive” and “fugitive hero”. This article suggest that there are better cultural-social analogies, i.e., David as a “goodfellan”while in exile from Saul and in the land of the Philistines, and upon accession to the throne, “The Godfather”.

This article also has, as a part of its purpose, the intent to unmask some of the behavior of David and of monarchy for what they are: essentially organized crime maintained in large part by the use of indiscriminate violence-supported by nonsensical myths and obvious hypocrisy.

Cross-cultural comparisons are made throughout between the David stories, gangster movies and systems of monarchy—especially the ad hoc feudal type. Historical questions aside: The David stories can be “cross-culturally” compared with gangster films as “art”.     

THE PRICE OF METAPHOR

In his critical response to our skeptical inquiry, “Does Culture Evolve?” (History and Theory, Theme Issue 38 [December 1999], 52–78), W. G. Runciman affirms that “Culture Does Evolve.” However, we find nothing in his essay that convinces us to alter our initial position. And we must confess that in composing an answer to Runciman, our first temptation was simply to urge those interested to read our original article–both as a basis for evaluating Runciman's attempted refutation of it and as a framework for reading this essay, which addresses in greater detail issues we have already raised. Runciman views the “selectionist paradigm” as a “scientific”“puzzle‐solving device” now validated by an “expanding literature” that has successfully modeled social and cultural change as “evolutionary.” All paradigms, however, including scientific ones, give rise to self‐validating “normal science.” The real issue, accordingly, is not whether explanations can be successfully manufactured on the basis of paradigmatic assumptions, but whether the paradigmatic assumptions are appropriate to the object of analysis. The selectionist paradigm requires the reduction of society and culture to inheritance systems that consist of randomly varying, individual units, some of which are selected, and some not; and with society and culture thus reduced to inheritance systems, history can be reduced to “evolution.” But these reductions, which are required by the selectionist paradigm, exclude much that is essential to a satisfactory historical explanation–particularly the systemic properties of society and culture and the combination of systemic logic and contingency. Now as before, therefore, we conclude that while historical phenomena can always be modeled selectionistically, selectionist explanations do no work, nor do they contribute anything new except a misleading vocabulary that anesthetizes history.     

WHO BENEFITS FROM KNOWLEDGE ABOUT THE HEALTH OF UNDOCUMENTED MEXICANS?

This article discusses the legal context in which health research of undocumented Mexicans takes place. Two lines of inquiry are brought together: the national debate on undocumented immigration and the maturing research on the health of Mexican Americans. Because of the politicized nature of immigration status, “immigration” is ignored as an explanatory variable. Several potential outcomes are examined, such as “ghost” programming and increased public health risks.     

Planning Culture—A Concept to Explain the Evolution of Planning Policies and Processes in Europe?

Abstract

This article examines the complex relations between spatial planning and its cultural context (including the specific socio-economic patterns and related cultural norms, values, traditions and attitudes). To be able to analyze the extent to which spatial planning adapts to external pressures such as Europeanization, a “culturized planning model” with the three dimensions “planning artefacts”, “planning environment” and “societal environment” is used. It can be observed that the “harmonization” of spatial planning practices can result from external pressures such as EU regulations as well as (horizontal) collective learning processes. However, “harmonization” does not necessarily result in convergence. Adaptational pressures such as Europeanization often result in the customization of existing structures, frames and policies (“planning artefacts” and “planning environment”) but do not fundamentally change the underlying core cultural traits (“societal environment”). These cultural traits are quite resistant to change and help maintain a diversity of planning cultures and policies in Europe.