The accuracy of alternative stochastic models of participation in group discussion†

Four related models of participation in group discussion are presented and compared in the accuracy with which they predict proportional participation, mean run length, mean recurrence time and the variances of runs and recurrences. For some quantities, such as proportional participation and mean run length, the most restricted model does virtually as well as the least restricted model; for other quantities it does not. None of the models does a good job of predicting variances of runs or recurrences.     

Some exhaustible Poisson process models of divorce by marriage cohort†

A one‐parameter exhaustible Poisson process model is formulated to represent the cumulative divorce trajectory of marriage cohorts. On the basis of recently published data of nine‐year cumulative records of all one‐year United States marriage cohorts, 1949–1958, it is found that the one‐parameter model does not provide an empirically adequate representation of cohort divorce trajectories. Therefore, two modifications of the basic model are explored. First, it is assumed that the longer the couples remain married the smaller is the probability of their becoming divorced (a cumulative inertia modification). Second, it is assumed that the cohort can be divided into two groups one of which is subject to risk of divorce while the other is not (a mover‐stayer modification). It is concluded that the latter model provides a better approximation to the empirically observed divorce trajectories. Given availability of disaggregated observations of divorces for marriage cohorts, the model could be used as a mathematical language for the construction of a theory of divorce differentials and changes in the divorce condition over time.     

Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

Symmetric measures of segregation,segregation curves,and Blackwell’s criterion

This paper first proposes a new way to use segregation curves to examine whether one distribution of people across groups (e.g., occupations or neighborhoods) is more segregated than another. It then uses Blackwell’s criterion to extend the argument to more than two types of people. The basic idea is that by introducing additional assumptions about the nature of segregation, one obtains a more complete ranking of distributions. The paper demonstrates that the assumption of “symmetry in types”–an assumption that appears frequently in the literature on segregation measurement–has implications for both segregation curves and Blackwell’s criterion.     

Markov models of occupational mobility: Theoretical development and empirical support. Part 1: Careers†

This paper, consisting of two parts, presents an analysis of the current state of Markov model , building for intragenerational occupational mobility. Part One examines theories of careers and Part Two theories of continuously operative job systems. Stress is given to the empirical support of the models and to the cumulative development of theory. Among the paper's findings are that several models proposed to span both occupational and geographical mobility have used only migration data; that analytic development is more cumulative for career models; and that there exists a basic divergence of findings from tests of models of careers and continuously operative job systems. In Part One we focus on individual behavior or subaggregates (cohorts).     

The structure of irreducible matrices †

Let A be an irreducible matrix with index of imprimitivity h is shown that there exists a permutation matrix P such that PAP^t is in a superdiagonal block form with k nonzero blocks if and only if k divides h It is also shown that a matrix in a superdiagonal block form without zero rows or columns is irreducible if and only if the product of the superdiagonal nonzero blocks is irreducible.     

Subpermanents of doubly stochastic matrices †

It is shown that if all subpermaneats of order k of an n × n doubly stochastic matrix are equal for some k ≤ n ? 2, then all the entries of the matrix must be equal to 1/n.     

Several Jordan-algebraic aspects of optimization†

We describe some concepts from the theory of Euclidean Jordan algebras and their use in optimization theory. This includes: primal-dual algorithms, optimality conditions, convexity of spectral functions, proof of some inequalities and a Jordan-algebraic version of Horn–Schur theorem     

Extension of standard models of ZFC to models of Nelson’s nonstandard set theory IST

A characterization of the standard models of ZFC set theory that are embeddable as the class of standard sets in models of the internal set theory IST and some of its versions is proposed. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 202–210, August, 1999.     

On the connectivity of social networks†

In the context of analyzing social structures through the use of graph theory, some binary matrix operations for valued graphs are presented. These operations are demonstrated in the analysis of social network data presented by Kapferer. Further examples of where the procedures should prove useful are suggested.     

Two-stage local M-estimation of additive models

This paper studies local M-estimation of the nonparametric components of additive models.A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives.Under very mild conditions,the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known.The established asymptotic results also hold for two particular local M-estimations:the local least squares and least absolute deviation estimations.However,for general two-stage local M-estimation with continuous and nonlinear ψ-functions,its implementation is time-consuming.To reduce the computational burden,one-step approximations to the two-stage local M-estimators are developed.The one-step estimators are shown to achieve the same effciency as the fully iterative two-stage local M-estimators,which makes the two-stage local M-estimation more feasible in practice.The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers.In addition,the practical implementation of the proposed estimation is considered in details.Simulations demonstrate the merits of the two-stage local M-estimation,and a real example illustrates the performance of the methodology.     

On Fiber Coefficients of Fiber Cones †

Let (R,𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R, and K an ideal containing I. When depth G(I) ≥ d ? 1, depth F_K(I) ≥ d ? 2, and r(I|K) < ∞, we calculate the fiber coefficients f_i(I). Under the above assumptions on depth G(I) and r(I|K), we give an upper bound for f₁(I), and also provide a characterization, in terms of f₁(I), of the condition depth F_K(I) ≥ d ? 2.     

Dynamic model of methane–water diffusion

This paper presents a mathematical model to describe the time evolution of the diffusion process of methane exchange between liquid and gaseous phases. In order to reach the equilibrium, the distribution of gas in the liquid phase decreases to a constant value over time. Generalized model is analyzed under the assumption that both, reversible and irreversible form of absorption and desorption, occur at the same time. For the application in case of the real system of methane–water, model is developed under the assumption that the processes of absorption and desorption are irreversible. From the experimental data are determined the coefficients of model and their dependence on initial conditions, with constant end conditions. This paper tests the introduced theoretical model on the existing experimental data.     

optimal consump0tion of an investment †

We consider a continuous-time stochastic model for the consumption of an invested resource. The optimal consumption policy is derived. A system of prices which stimulate the optimal consumption is identified. The optimal policy and payoff are found explicitly in the case where the interest process has independent increments.     

More about empirical evaluation of formal theory†

The purpose of this discussion is to transform the implicit equilibrium assumption endemic to network analysis into an explicit instrument for such analysis. I propose a formal model that brings together Coleman's restriction of Walras’ general equilibrium model and recent developments in describing the “social topology” of a multiple network system of actors such that a class of relational equilibria is defined. The specific equilibrium expected in a system is a function of the previously existing stratification of actors in the system. Corresponding to multiple observed networks, the model generates multiple equilibrium networks. The structural analysis of the observed networks can therefore be repeated on the equilibrium networks so as to assess the extent to which the analysis would differ if the observed relations were actually in an equilibrium state. Numerical illustration is provided by an analysis of alternative relational equilibria in the system of elite experts in methodological and mathematical sociology as such a system existed in 1975.     

Spatial segregation limit of a non-autonomous competition–diffusion system

This paper is concerned with the spatial behavior of the non-autonomous competition–diffusion system arising in population ecology. The limiting profile of the system is given as the competition rate tends to infinity. Our result shows that two competing species spatially segregate as the competition rates become large. Moreover, for the case of the same non-autonomous terms, we obtain the uniform convergence result.