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Presents a comment on the paper "Institutions as Production Systems," by Thomas J. Fararo and John Skvoretz that appear in the 1984 issue of the "Journal of Mathematical Sociology." Adoption of a formal representation of the rules, that govern institutionalized social action, as "production rules"; Assertion that the paper by Fararo and Skvoretz provides a clear and informative introduction to their approach and demonstrates the importance of their general line of inquiry for sociology; Views on the three aspects of their work: the proposed formalism, the more substantive view or interpretation they suggest of the subject matter and the question of empirical testing.

This paper proposes a class of Markov models of social mobility with duration memory. Several new duration memory structures as well as existing models, such as the Cornell model, are shown to be special cases of the general model. The model is also extended to heterogeneous populations thereby permitting age specific variants. Alternative axioms to cumulative inertia are included, pointing to new possibilities for duration specific modeling such as futuristic "memory" for currently planned programs. Given that duration effects are widespread and quite varied, the general model provides multiple possibilities for theoretically structuring these processes. [ABSTRACT FROM AUTHOR]

Mutually beneficial cooperation is a common part of economic systems as firms in partial cooperation with others can often make a higher sustainable profit. Though cooperative games were popular in 1950s, recent interest in noncooperative games is prevalent despite the fact that cooperative bargaining seems to be more useful in economic and political applications. In this paper we assume that the strategy space and time are inseparable with respect to a contract. Furthermore, it is assumed that each firm's strategy polygon is a geodesic polygon which changes its shape every point of time with the stubbornness strategy surface of firm's executive board follow a Gaussian free field. This gives us more flexibility to deal with generalized geodesic cooperative games which is the main contribution of this paper. Under this environment we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry fails to give a proper feedback Nash equilibrium. Cooperation occurs when two firms' strategies fall into each other's influence curvature in this strategy spacetime. Small firms in an economy dominated by large firms are subject to the influence of large firms. We determine an optimal feedback semicooperation of the small firm in this case using a Liouville-Feynman path integral method. [ABSTRACT FROM AUTHOR]

The Inequality Process (IP) has been tested and confirmed against data on incomes that are approximately gamma distributed. The IP's gamma pdf (probability density function) model expresses statistics of IP particle wealth algebraically in terms of IP parameters for the subset of IP parameters that generate approximately gamma distributions of particle wealth, a serious limitation, one leaving statistics of the many empirical distributions of income and wealth with heavier-than-gamma distribution right tails beyond algebraic expression in terms of IP particle parameters. This paper shows that an IP variance-gamma (VG) pdf model can do for the entire interval on which IP particle parameters are defined, (0,1), what the IP's gamma pdf model does for only a subset. This paper thus generalizes the IP's gamma pdf model, and it does so with no loss of parsimony since the IP's VG pdf model is, like the IP's gamma pdf model, expressed in terms of IP particle parameters. [ABSTRACT FROM AUTHOR]

Concept class analysis (CoCA) is a method for recovering cultural schemas in texts using a combination of word embedding and community detection models. Like survey-based forms of schematic class analysis (SCA), however, interpreting results can be difficult. Some of these interpretive difficulties are applicable across types of SCA, while others are unique to CoCA. In this paper, we propose a complete workflow for interpreting and analyzing CoCA output. We use the case of social identity schemas in a collection of over 13,000 U.S. political blog posts to outline a number of interpretive and analytical strategies and a robustness check to make sense of the cultural schemas recovered from texts. [ABSTRACT FROM AUTHOR]

Motivated by debates about California's net migration loss, we employ valued exponential-family random graph models to analyze the inter-county migration flow network in the United States. We introduce a protocol that visualizes the complex effects of potential underlying mechanisms and perform in silico knockout experiments to quantify their contribution to the California Exodus. We find that racial dynamics contribute to the California Exodus, urbanization ameliorates it, and political climate and housing costs have little impact. Moreover, the severity of the California Exodus depends on how one measures it, and California is not the state with the most substantial population loss. This paper demonstrates how generative statistical models can provide mechanistic insights beyond simple hypothesis-testing. [ABSTRACT FROM AUTHOR]

The article presents an introduction to the paper "Ethnic Preferences, Social Distance Dynamics, and Residential Segregation: Theoretical Explanations Using Simulation Analysis," by Mark Fossett and the commentaries following it.

In this paper, by defining two types of signed detour distances and corresponding detour distance matrices, we introduce the notion of detour distance compatibility for signed graphs and later applying these concepts, we give yet another characterization of balance in signed graphs. Further, we discuss signed detour spectra of certain classes of unbalanced signed graphs. [ABSTRACT FROM AUTHOR]

This paper develops and illustrates a method for empirically designing an income tax system that people will regard as fair. The paper begins with the classical Principles of Tax Justice, viz., as pretax income increases, three quantities should also increase – posttax income, tax amount, and tax rate. GSOEP data on residents' pretax income and the posttax income they regard as fair are used to estimate a just linear income tax system. Analytic results include a signature standard form of the tax system showing the intertwined fates of poor and rich and the conditions which threaten fairness. Empirical results show that the estimated tax system lowers taxes for a majority of respondents, especially the relatively poorer, and substantially reduces inequality. [ABSTRACT FROM AUTHOR]

This paper studies structures for efficient and stable integration of multi-community networks where establishing bridges across communities incur additional link cost compared to those within communities. Building on the connections models with direct and indirect benefits, we show that the efficient structure for homogeneous cost and benefit parameters, and for communities of arbitrary size, always has a diameter no greater than 3. We further show that for non-trivial cases, integration always follows one of these three structures: single star, two hub-connected stars, and a new structure we introduce in this paper as parallel hyperstar, which is a special core/periphery structure with parallel bridges that connect the core nodes of different communities. Then we investigate stability conditions of these structures, using the standard pairwise stability, as well as post-transfer pairwise stability, a new stability notion we introduce in this paper, which allows for bilateral utility transfers. We show that while the parallel hyperstar structure can never be both efficient and pairwise stable, once post-transfer pairwise stability is used, efficiency guarantees stability. Furthermore, we show that all possible efficient structures can be simultaneously post-transfer pairwise stable. In the end, we provide some numerical results and discussion of empirical evidences. [ABSTRACT FROM AUTHOR]

This article is a tribute to Thomas J. Fararo, a pioneer in the field of mathematical sociology. Fararo believed that mathematical sociology should focus on the theoretical unification of different theories and frameworks. The article provides biographical details about Fararo's life and his contributions to the field. It also includes papers from three scholars who discuss Fararo's impact on sociological theory through mathematical modeling and the prospects for achieving his vision of unification. The article emphasizes the importance of communication and collaboration across research groups for successful theoretical integration. [Extracted from the article]

This paper applies information-theoretic measures to consider the systemic effects on individual incomes of complex patterns of social and economic discrimination by race, ethnicity, and gender in the U.S. It estimates non-parametric indices of joint, conditional or incremental, and mutual information between income, social identity, and observable economic characteristics obtained using large-scale cross-sectional data from that economy. The paper advances new conceptual and empirical approaches to the nature and measurement of economic discrimination and inequalities of opportunity, founded on the formal informativeness of measures of social identity on economic outcomes. Estimated values for indices of informational association also cast new light on the effects of the intersections of gender and race/ethnicity on income, perverse patterns in the effects of education across different groups, and a few notable dynamic changes in patterns of income distribution in that economy over the past 40 years. [ABSTRACT FROM AUTHOR]

Fragmentation, echo chambers, and their amelioration in social networks have been a growing concern in the academic and non-academic world. This paper shows how, under the assumption of homophily, echo chambers and fragmentation are system-immanent phenomena of highly flexible social networks, even under ideal conditions for heterogeneity. We achieve this by finding an analytical, network-based solution to the Schelling model and by proving that weak ties do not hinder the process. Furthermore, we derive that no level of positive algorithmic bias in the form of rewiring is capable of preventing fragmentation and its effect on reducing the fragmentation speed is negligible. [ABSTRACT FROM AUTHOR]

In recent months, the figure of Greta Thunberg and the theme of climate changings quickly became the focus of the debate. This has led to a polarization effect in opinion forming about the climate subject. Starting from the analysis of this phenomenon, we develop an opinion dynamics model in which several types of contrarian agents are considered. Each agent is supposed to have an opinion on several topics related to each other; thus, the opinions being formed on these topics are also mutually dependent. The aim of the paper is to investigate the indirect effects of contrarian agents on the collective opinion about these topics. Several numerical tests are presented in order to highlight the main features of the model. [ABSTRACT FROM AUTHOR]

In this paper, we present an empirical study of the opinion dynamics of a large-scale sample of online social network users. We estimate users' opinions as continuous scalars based on their subscriptions to information sources and analyze how friendship connections affect the dynamics of these estimations. Distinguishing between positive (toward friends' opinions) and negative (away from friends' opinions) opinion shifts, we find that the existence and magnitude of both types of shifts are positively related (largely through linear or inverted U-shaped form) to the distance in opinions between a user and their friends. The distance additionally moderates the balance between positive and negative movements: if the distance is within a certain moderate range, there is a relatively high chance of a positive shift. [ABSTRACT FROM AUTHOR]

Principal eigenvectors of adjacency matrices are often adopted as measures of centrality for a graph or digraph. However, previous principal-eigenvector-like measures for a digraph usually consider only the strongly connected component whose adjacency submatrix has the largest eigenvalue. In this paper, for each and every strongly connected component in a digraph, we add weights to diagonal elements of its member nodes in the adjacency matrix such that the modified matrix will have the new unique largest eigenvalue and corresponding principal eigenvectors. Consequently, we use the new principal eigenvectors of the modified matrices, based on different strongly connected components, not only to compose centrality measures but also to identify bowtie structures for a digraph. [ABSTRACT FROM AUTHOR]

This paper analyzes the dynamics of collective action through collective reputation, which indicates the extent to which groups succeed. Many previous works introduced psychological traits such as irrationality and a sense of fairness to explain the diffusion of collective action. However, this paper analyzes the relationship between cooperation and dynamic change in group size using game-theoretic models. The results show the sets of parameters in which positive feedback between cooperation and group size occurs. In these parameter sets, cooperation creates a good collective image (reputation) and encourages outsiders to join the group. In turn, the group expansion gives them incentives to cooperate. Additionally, when this positive feedback functions, punishment is found to be unnecessary for cooperation. [ABSTRACT FROM AUTHOR]

The purpose of this note is to consider the effect of perception noise when voters form public opinions. We provide a simple theoretical framework that will form the basis to investigate empirically the effect of news uncertainty on voters' attentiveness when forming public opinion, or nowcasts. An attentive voter will consistently update their information set. Therefore, if voters' nowcasts are consistent, any revision of the nowcasts must only reflect new information. We specifically consider how news uncertainty may affect voter attentiveness. The paper focuses on US presidential competence and popularity indices. We find that the nowcasts are consistent during periods of low news uncertainty but highly persistent when news uncertainty is high. [ABSTRACT FROM AUTHOR]

Latent class analysis (LCA) is a cross-sectional latent variable mixture modeling (LVMM) approach. Like all LVMM approaches, LCA aims to find heterogeneity within the population by identifying homogenous subgroups of individuals, with each subgroup (called latent class) possessing a unique set of characteristics that differentiate it from other subgroups. LCA can be carried out with categorical latent and indicator variables. But, LCA is unable to examine the association between respective items and the latent variable among categories of individuals. Multiple-group LCA, in particular, is a useful extension of LCA which enables the testing of homogeneity of the class patterns between groups of the individual through a series of constraints. In this paper, we have performed a multi-group latent class analysis for measuring self reported academic dishonesty among the students of University of Jammu. From the analysis, three general behaviors of academic cheaters are identified as rare, frequent, and instant cheaters. Further, from the multi-group LCA, it is envisaged that female students of University of Jammu are more instantaneous cheaters than male students. Students who are self-reported cheaters from sciences and humanities of the University of Jammu are persistent in cheating whereas from professional courses they are more occasional. [ABSTRACT FROM AUTHOR]

This paper intends to simulate a simple artificial society divided into two populations: criminal and non-criminal. The time evolution of the system is modeled using a set of differential equations, borrowing relevant features from the prey-predator, epidemic spread, and harvesting models. Each population can switch type upon interaction. The stability and equilibrium points of this system are examined, concluding that harvesting and interaction rates play an important role in the evolution of the system toward different stable equilibria between populations, which eventually coalesce into one. The results indicate that as long as the harvesting and conversion rates remain sufficiently small, the criminal population thrives. However, when either of the two crosses a certain value, the criminal population becomes extinct. [ABSTRACT FROM AUTHOR]

Mark Fossett's new research, published here in the Journal of Mathematical Sociology, is arguably the most important advance in studies of residential segregation in the past decade. While this study of the role of preferences in creating the patterns of residential separation does not answer all the questions about how preferences create separation in the residential mosaic, it provides a major extension of Schelling's seminal work of three decades ago. The paper shows clearly that preferences do matter and that the set of simulations leave little doubt that residential preferences and their underlying social dynamics have the capacity to generate high levels of ethnic segregation. The agent-based modeling technique, on which the results are based, is a major advance on previouswork using agent-based modeling and will set the standard for further studies of the underlying processes that create residential separation in U.S. cities. [ABSTRACT FROM AUTHOR]

In digraphs representing asymmetric relations, the measured scores of previous spectral rankings are usually dominated by nodes in the largest strongly connected component. In our previous work, we proposed hierarchical alpha centrality to give higher scores for more reachable nodes not in the largest strongly connected component. However, without careful consideration of damping parameters, the scores obtained by this method may be unbounded. In this paper, we normalize the adjacency matrix to be stochastic, subsequently damping the resulting Markov chain with a reciprocal perturbation at each and every non-zero transition, and propose a new hierarchical measure of centrality for asymmetric relations. The proposed measure simplifies damping and ensures that the measured scores are bounded. [ABSTRACT FROM AUTHOR]

"Contentious politics" has become the main label to define a wide range of previously separated fields of research encompassing topics such as collective action, radicalization, armed insurgencies, and terrorism. Over the past two decades, scholars have tried to bring these various strands together into a unified field of study. In so doing, they have developed a methodology to isolate and analyze the common social and cognitive mechanisms underlying several diverse historical phenomena such as "insurgencies," "revolutions," "radicalization," or "terrorism." A multidisciplinary approach was adopted open to contributions from diverse fields such as economics, sociology, and psychology. The aim of this paper is to add to the multidisciplinarity of the field of Contentious Politics (CP) and introduce the instruments of Agent-Based Modeling and network game-theory to the study of some fundamental mechanisms analyzed within this literature. In particular, the model presented in this paper describes the dynamics of one process, here defined as "the radicalization of politics," and its main underlying mechanisms. Their mechanics are analyzed in diverse social contexts differentiated by the values of four parameters: the extent of repression, inequality, social tolerance, and interconnectivity. The model can be used to explain the basic dynamics underlying different phenomena such as the development of radicalization, populism, and popular rebellions. In the final part, different societies characterized by diverse values of the aforementioned four parameters are tested through Python simulations, thereby offering an overview of the different outcomes that the mechanics of our model can shape according to the contexts in which they operate. [ABSTRACT FROM AUTHOR]

Temporal motivation theory (TMT) has been criticized for its static representation and neglect of the environment. In this paper, I develop goal sampling theory (GST) to appease these criticisms and extend our understanding of goal choices beyond momentary preferences and into dynamic updating and sampling behavior across time. GST draws from temporal motivational theory, sampling models of impression formation, and organizational theory on how the environment constrains behavior and situates aspects of each into a formal model of goal sampling. Doing so addresses the limitations of our prior thinking, introduces new concepts and predictions, and provides a mathematical framework that lends itself to computational modeling. [ABSTRACT FROM AUTHOR]

This paper presents a stochastic dynamic mathematical model, in which a Family Policy Index (XFPI) is included to measure and compare two different models of provision of resources to support families with children from 0 to 3 years old. The main variables in this model are the XFPI, fertility, mortality, emigration and immigration rates. This mathematical model was validated in two different countries, Spain and Norway, during the 2007–2015 period. A sensitivity analysis was applied to simulate the future trend (2016–2030), examining the influence of providing public pre-school services (0 to 3 years) on (XISF). The results obtained show that these services may indeed have an influence on fertility rates, as long as they are developed extensively. [ABSTRACT FROM AUTHOR]

This section introduces a series of research using computer simulation for sociological theory construction. The five papers in this issue cover a broad range of topics. Organizational ecology theory is the focus of the paper by Michael Hannan and James Ranger-Moore. Their simulation combines stochastic models that have been shown to represent ecological phenomena with other theoretically derived processes. Their empirical benchmarks are organizational population size distributions. These distributions are known at only a few points in time. The simulation model generates these size distributions to test hypotheses about organizational growth in an ecological system. The paper by William Feinberg is an example of using simulation for social policy analysis. The issue concerns the efficacy of an affirmative action policy for re-hiring reduction in force employees. The paper reaches the counter-intuitive result that there is little difference in outcomes between traditional seniority based re-hiring and affirmative action re-hiring procedures. The paper by Chanoch Jacobsen, Richard Bronson, and Daniel Vekstein uses the Systems Dynamics simulation methodology to evaluate a macro-social theory of normative regulation.

In this paper, we examined the effect of deliberative democracy on the polarization of opinion. Through three case analyses, we find that deliberative democracy has two major components – provision of information and group discussion. Polarization of opinion can be explained by several theories: social identity theory, social comparison, and confirmation bias. We constructed a deliberative democracy model that reflected these mechanisms of polarization. We found that deliberative democracy actually decreased polarization of opinion when group discussion was a strong factor. Our study provides guidelines for an institutional design incorporating deliberative democracy, with emphasis on the composition of unbiased group discussions. [ABSTRACT FROM AUTHOR]

In this paper, we analyze data on the opinion dynamics of 1,660,927 users of an online social network using formal models of opinion formation. We have observed that moderate users have a tendency to follow the average opinion of their online friends, which we interpret as a presence of bounded confidence. Further, we have discovered that the probability of moving toward the average opinion goes down if the difference between it and the user's opinion is too large. Another interesting feature uncovered is that if a user's opinion and the average opinion of their online friends are very similar, the influence also decreases. [ABSTRACT FROM AUTHOR]

When and for whom does it pay to make high-quality products? In this paper, I address this question through the lens of Harrison White's socioeconomic models of production. The socioeconomic models relate economist incentives of cost-efficiency to sociological insights into the construction of quality on markets. Differences in firm size and quality sustain distinct market niches whose appeal to producers vary. The ordering of niches by quality and associated implications for profitability establish the incentive structure of the market. As illustration, I trace the evolution of the Californian wine industry from its nadir under prohibition to today. The account motivates a productive reading of the socio-economic models that tempers their analytical focus and broadens their scope of application. [ABSTRACT FROM AUTHOR]

The article deals with the development of mathematical sociology in Japan and introduces the articles featured in the 1989 issue of the Journal of Mathematical Sociology. A burgeoning of interest in mathematical sociology may well be traced back even to prewar Japan. A study of the structure of Japanese families by Teizo Toda in 1937 is such an example. In that study, Toda showed by examining census data that the distribution of types of families was determined by the age of first marriage of those involved, although he did not use a model building method explicitly. However, it was not until the mid-1960's that mathematical sociology was pursued as such. Around 1970, the Tokyo University Press published a set of sociology textbooks of eighteen volumes including one volume titled Mathematical Sociology edited by Yasuda. This was the first book in Japan which had the title of mathematical sociology as such. In the 1970's, there emerged more than a few semi-formal societies scattered within the nation for the study of mathematical sociology, which were unified into a nationwide semi-formal society formed in 1980. A dozen of active core members and about two more dozens of scholars and students had regular meetings twice a year by coming together for a few nights. Mathematical sociology in Japan has plunged into a specialty stage in the sense that a formal society, the Japanese Association for Mathematical Sociology, was set up and an official journal was newly published.

This paper examines, both conceptually and mathematically, five attempts of mathematizing Blau's theory of differentiation in organizations, which seem to have suffered rather suspicion or neglect than serious attention from organizational researchers. Such attitudes toward the mathematization hitherto are not ungrounded. Meyer was unfortunately guided by his misconception of the role of deductive theories. Hummon failed to point out logical unsufficiency of luaus verbal inference. Lands model was too ambiguously constructed. Baseline models by Mayhew et al lacked a substantive study of organizational differentiation. The simultaneous differential equation model by Hummon et al was not particularly an organizational model. All but the last attempts involve even some important mathematical errors, which make their failures decisive. This paper, however, do not intend to show, by examining those attempts, that mathematical modeling should in general appear as unpromising, Appropriately constructed mathematical models are still believed to be helpful to the theoretical study of differentiation in organizations. [ABSTRACT FROM AUTHOR]

Many social and other networks exhibit stable size scaling relationships, such that features such as mean degree or reciprocation rates change slowly or are approximately constant as the number of vertices increases. Statistical network models built on top of simple Bernoulli baseline (or reference) measures often behave unrealistically in this respect, leading to the development of sparse reference models that preserve features such as mean degree scaling. In this paper, we generalize recent work on the micro-foundations of such reference models to the case of sparse directed graphs with non-vanishing reciprocity, providing a dynamic process interpretation of the emergence of stable macroscopic behavior. [ABSTRACT FROM AUTHOR]

The current study mathematically models key factors influencing Risk Perception (RP) that involves knowledge inferred from present situations and social learning, past information and priming effect. It is a generalized perception-based model and in the present paper, it is applied to Autism Spectrum Disorder (ASD). The computational model has been simulated for numerous rounds in two phases to find a quantitative value of the model factors. In the first phase, the model reflected dependency of RP upon recent past events and priming, while second phase revealed that social learning modulates RP, even in ASD. This further proves that peer-interaction plays a crucial role in building perception. Thus, our work provides a mathematical framework to evaluate perception objectively in any situation, such as risky/danger-situations. [ABSTRACT FROM AUTHOR]

This article presents a letter from the editor, which discusses this special issue of the “Journal of Mathematical Sociology. ” The journal discusses the third Joint American-Japanese Conferences on Mathematical Sociology at the Center for the Study of Cultural and Environmental Foundations of the Mind in Hokkaido University in Japan. The papers in the article present the utility of mathematical sociology concepts, ideas, techniques, perspectives, and approaches.

Pricing practices of firms are an important yet the least studied aspect of the price phenomenon in sociology. This paper answers the question: why do firms, even in the same market, tend to use different pricing practices – value-informed, competition-informed, or cost-informed pricing – to set prices? To that end, this study constructs a formal dynamic flocking model to investigate the inter-dynamics between market uncertainties and the viability of the three pricing practices. The model is a substantial revision and extension of Harrison White's static W(y) market model by reformulating the latter into a dynamic one and by explicitly incorporating different market uncertainties into the model as variables. The study shows that each kind of pricing practice is only viable under certain distributions of market uncertainties. The theory is then used to explain the distribution of pricing practices among firms in the Burgundy wine market. Theoretical and methodological innovations and the implications for firms and for sociological research on markets and uncertainties are also discussed. [ABSTRACT FROM AUTHOR]

Raub and Snijders (1997) show that, under the assumption of S-shaped utility, conditions for cooperation in social dilemmas are more restrictive if outcomes represent losses than if outcomes represent gains. They neglected two interesting issues in their paper: conditions for cooperation in social dilemmas with both losses and gains as outcomes, and the effect of probability weighing on these conditions. In this paper it is shown that, under assumptions of Prospect Theory, conditions for cooperation are best if dilemmas include both positive and negative outcomes, and that these conditions improve with increasing loss aversion. Furthermore, it is shown that probability weighing can effect conditions to cooperate as well. [ABSTRACT FROM AUTHOR]

The paper is concerned with a celebrated collection of love poems, the 14th century Italian poet Francis Petrarch's Canzoniere. A striking feature of these poems is the emotional ups and downs experienced by Petrarch and his platonic mistress Laura. Recently, attempts have been made to model these emotional swings by catastrophe theory or nonlinear differential equations. This paper takes a different approach. Starting with a pair of differential equations that model the dynamics of the emotions of the two individuals, we formulate an optimal control problem. A key hypothesis of this problem is that Petrarch was a rational addict of his desire for Laura. With specific functional forms and parameter values we identify a stable limit cycle that gives a representation of the oscillating emotions of Laura and Petrarch. [ABSTRACT FROM AUTHOR]

This paper is concerned with a piecewise-deterministic differential game model of political regime changes. We modify and study the model proposed by Boucekkine et al. in [7]. The original model does not allow all players to take full controls as the situation progresses. Hence, it does not lead to closed-loop strategies. We fix the problem by deriving and using a system of quasi-variational inequalities associated with the differential game, and proving a criterion for the regime change. As a result, we find Markovian strategies for all players. A numerical example for illustration of the method is given. Implications of the results to political changes in a society are discussed. Some results are extended to more general models that incorporate gradual and abrupt changes, as well as continuous and impulse controls. [ABSTRACT FROM AUTHOR]

In a recent paper, Petersen (1988) considered a continuous state space failure time process. The central result provided in that paper was that the destination-specific rate of transition of the process can be specified in two steps. First, one specifies the overall rate at which a change occurs. Then, one specifies the probability density function of the destination state, given that a transition occurred. This two-step property was used in deriving the likelihood of the data and was exploited for purposes of estimation. The overall rate of transition can be estimated from the data on durations between changes in the dependent variable. The density for the new value of the dependent variable, given a change, can be estimated from the data on the values of the dependent variable after the change. This paper extends these results in two ways. First, it is shown that one can derive the likelihood of the process directly from the destination-specific rate of transition, without going through its decomposition into the overall rate times the density of the destination state, given a transition. Once the likelihood is derived, estimation is comparatively straightforward. Second, it is shown how one can derive, at each point in time, a more standard regression function for the continuous dependent variable, where its value is expressed in terms of its conditional mean plus an error term. [ABSTRACT FROM AUTHOR]

The article focuses on ordered pairs of arcs and demiarcs. In a recent paper researchers F. Harary and R. Havelock set themselves the task of expressing the transfer of information in terms of the theory of digraphs supplemented inter alia with the notion of demiarcs. Researcher K.E. Rosengren presented and combined the two concepts of direction and initiative of an information flow. The main idea of this paper has been to apply the concept of ordered pairs not only to points but also to demiarcs and arcs. This idea seems to have certain advantages. It makes it possible to express neatly the two concepts of direction and initiative. It clarifies an ambiguous point in Harary's and Havelock's otherwise sterling exposition, the equalization of initiating demiarc with outgoing demiarc. It produces formal explications of certain aspects of communicative power and of the gatekeeper concept. The field that is defined by the interface of digraph theory and studies of communication is largely an untilled one.

The index "the proportion of a cohort that have become delinquent by a given age," here called the "prevalence of delinquency," is an important social indicator. In the present paper, we indicate methods by which this index can be estimated from data, and correct errors in previous sex- and racespecific prevalence estimates published by Monahan (1960) for the city of Philadelphia. The difference between the sexes and between the races shown by these corrected prevalence estimates are of sufficient magnitude to render suspect any comparisons of prevalences of delinquency among cohorts which do not take account of the sex and race compositions of the cohorts to be compared. [ABSTRACT FROM AUTHOR]

The article focuses on prediction logic and quasi-independence in empirical evaluation of formal theory. In the paper by researchers D.K. Hildebrand, J.D. Laing and H.L. Rosenthal, a paradigm for the statement and empirical evaluation of a class of propositions predicting specific relations between qualitative variables was proposed. The approach represents a substantial departure from traditional modes of analysis. Consequently, it is not surprising that one encounters resistance and misunderstanding in those who work in different traditions. The lengthy critique of the paper by researchers L.A. Goodman and W.H. Kruskal, henceforth G&K, illustrates the inappropriateness of evaluating the paradigm using traditional perspectives. G&K operate in two contexts: measures of association and multiplicative models for probabilities in cross-classifications. The primary objective in the paper discussed by G&K was to design a general model that provides a distinct and operationally interpretable measure of the prediction success attained in a population by any logically distinct proposition stated, a priori, in the prediction logic.

Presents an introduction to the July 1977 issue of the "Journal of Mathematical Sociology."

Presents information regarding various articles which appear in January 1973 issue of the periodical "Journal of Mathematical Sociology." Presentation of two models of coalition formation and payoff allocation by James D. Laing and Richard J. Morrison; Problems related to sociometric studies.

Recent work revives the classic idea that the sense of justice is the first line of defense against inequality and shows that the link depends, in part, on ideas of the just reward. This paper extends earlier work, making three new contributions: (1) it expands the just reward scenarios from the micro scenarios (which start with the individual's idea of the just reward) to six new macro scenarios (which start with the distribution of everyone's ideas of the just reward); (2) it expands the set of justice measures from three to four, including now the proportion underrewarded; and (3) it obtains results for all the new cases, identifying the conditions that lead to radically different connections between inequality and justice. [ABSTRACT FROM AUTHOR]

For measuring the centrality in a digraph, Bonacich and Lloyd summarized a vector, from the power series of an attenuated adjacency matrix, as the alpha centrality. However, scores of alpha centrality are usually dominated by nodes in the strongly connected component, which owns the largest eigenvalue of the adjacency matrix. In this paper, based on reachability between strongly connected components, we consider not only the largest eigenvalue but also the other smaller ones to attenuate the adjacency matrix hierarchically; and obtain a measure from the power series of the hierarchically attenuated adjacency matrix. Consequently, we propose the hierarchical alpha centrality, which can yield higher scores for nodes at higher hierarchies of reachability in a digraph. [ABSTRACT FROM AUTHOR]

The paper presents results derived from a series of simulations of signed networks (i.e., networks containing positive and negative links) subject to a balancing process. The dynamics are followed in a space defined by variations in the proportion of positive links introduced and the tolerance to imbalance. The authors claim to have discovered boundaries in the space separating it into three distinct regions. One region probably displays the characteristics of self-organized criticality, which may have implications for the theory of extreme events. [ABSTRACT FROM AUTHOR]

The diffusion of Internet-based Intangible Network Goods (IINGs) shows new characteristics completely different from that of traditional material products. This paper aims to establish new models to describe and predict IING's diffusion at the aggregate level. Firstly, we transform the key factors affecting IING's diffusion into driving forces, resistant forces, and variable forces. Secondly, we analyse the dynamic changes of these forces in different diffusion stages and obtain the acceleration model of IING's diffusion. Then, since acceleration is the second derivative of scale, we further establish the scale model of IING's diffusion. As the scale model can predict the number of IING's adopters at a particular time and the acceleration model can explain the dynamic changes of scale, we combine them as the acceleration-scale model to describe IING's diffusion. Finally, we make comparisons between the acceleration-scale model and the Bass model based on three cases. Different from the previous studies, we found that IING's diffusion rate is asymmetric. The diffusion rate of successful IING is right skewed while the diffusion rate of failed IING is left skewed. The results also shows that the acceleration-scale model has a better predictive performance than the Bass model, no matter the diffusion is successful or failed [ABSTRACT FROM AUTHOR]

In this paper, we extend the voter model (VM) and the threshold voter model (TVM) to include external influences modeled as a jump process. We study the newly-formulated models both analytically and computationally, employing diffusion approximations and mean field approximations. We derive results pertaining to the probability of reaching consensus on a particular opinion and also the expected consensus time. We find that although including an external influence leads to a faster consensus in general, this effect is more pronounced in the VM as compared to the TVM. Our findings suggest the potential importance of external influences in addition to local interactions. [ABSTRACT FROM AUTHOR]