Including Preference and Social Distance Dynamics in Multi-Factor Theories of Segregation

All agree that many factors contribute to ethnic segregation, but controversy continues regarding the relevance of particular factors. In my paper I acknowledge the importance of discrimination, but I direct attention to the role of ethnic preferences and social distance dynamics. I do so because many dismiss the relevance of these factors for contemporary segregation without engaging formal theories and analytic models which suggest that dynamics associated with in-group attraction and out-group avoidance may take on increasing importance as past forms of discrimination slowly fade. Agent-based modeling shows promise for exploring the issue of whether prejudice against out-groups and affinity toward in-groups can build and sustain segregation in the absence of discrimination. Research drawing on this approach is at an early stage of development but is significant for highlighting two things. One is that the implications of preferences for segregation are strongly conditioned by the ethnic demography of the city. Another, closely tied to the first, is that different views about the implications of preferences for segregation often hinge on inconsistencies in how notions of integration and segregation are applied in discussions of individual location choices, the ethnic mix of single neighborhoods, and the ethnic distributions for all neighborhoods in a city. Critiques of agent-based models of Schelling-style preference effects will carry more force when they outline models indicating how location decisions guided by preferences documented in surveys can produce or sustain integration.     

Ethnic Preferences and Residential Segregation: A Commentary on Outcomes from Agent-Based Modeling

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.     

Ethnic Preferences,Social Distance Dynamics,and Residential Segregation: Theoretical Explorations Using Simulation Analysis∗

In this paper I consider theories of residential segregation that emphasize social distance and ethnic preference dynamics. I argue that these theories are more compelling than many critics have supposed, and I conclude that they deserve to be considered more carefully. I then use simulation methodology to assess the potential impact of social distance and ethnic preference dynamics on ethnic segregation under certain theoretically interesting conditions. Based on the results from the simulation analyses, I offer three conclusions: (1) status preferences and status dynamics have the capacity to produce high levels of status segregation but do not produce high levels of ethnic segregation under the specified simulation conditions; (2) ethnic preferences can, under certain theoretically interesting conditions specified in these simulations, produce high levels of ethnic segregation in the absence of housing discrimination; and (3) ethnic preferences and social distance dynamics can, when combined with status preferences, status dynamics, and demographic and urban-structural settings common in American cities, produce highly stable patterns of multi-group segregation and hyper-segregation (i.e., high levels of ethnic segregation on multiple dimensions) of minority populations. Based on these model-based theoretical explorations I speculate that the persistence of segregation in recent decades may have been overdetermined, that is, it may have been sustained by multiple sufficient causes including not only discrimination, but also social distance and preference dynamics. This raises the possibility that reductions in housing discrimination may not necessarily lead to large declines in ethnic segregation in the short run because social distance and preference dynamics may be able to sustain ethnic segregation at surprisingly high levels in the absence of housing discrimination.     

A generalization of chordal graphs

In a 3-connected planar triangulation, every circuit of length ≥ 4 divides the rest of the edges into two nontrivial parts (inside and outside) which are “separated” by the circuit. Neil Robertson asked to what extent triangulations are characterized by this property, and conjectured an answer. In this paper we prove his conjecture, that if G is simple and 3-connected and every circuit of length ≥ 4 has at least two “bridges,” then G may be built up by “clique-sums” starting from complete graphs and planar triangulations. This is a generalization of Dirac's theorem about chordal graphs.     

Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small,nonvanishing ripples

We study traveling waves in mass and spring dimer Fermi–Pasta–Ulam–Tsingou (FPUT) lattices in the long wave limit. Such lattices are known to possess nanopteron traveling waves in relative displacement coordinates. These nanopteron profiles consist of the superposition of an exponentially localized “core,” which is close to a Korteweg–de Vries solitary wave, and a periodic “ripple,” whose amplitude is small beyond all algebraic orders of the long wave parameter, although a zero amplitude is not precluded. Here we deploy techniques of spatial dynamics, inspired by results of Iooss and Kirchgässner, Iooss and James, and Venney and Zimmer, to construct mass and spring dimer nanopterons whose ripples are both exponentially small and also nonvanishing. We first obtain “growing front” traveling waves in the original position coordinates and then pass to relative displacement. To study position, we recast its traveling wave problem as a first-order equation on an infinite-dimensional Banach space; then we develop hypotheses that, when met, allow us to reduce such a first-order problem to one solved by Lombardi. A key part of our analysis is then the passage back from the reduced problem to the original one. Our hypotheses free us from working strictly with lattices but are easily checked for FPUT mass and spring dimers. We also give a detailed exposition and reinterpretation of Lombardi's methods, to illustrate how our hypotheses work in concert with his techniques, and we provide a dialog with prior methods of constructing FPUT nanopterons, to expose similarities and differences with the present approach.     

HOW RAPID SHOULD EMISSION REDUCTION BE? A GAME‐THEORETIC APPROACH

Abstract In this paper, we search for multistage realization of international environmental agreements. To analyze countries' incentives and the results of their interactions, we mathematically represent players' strategic preferences and apply a game‐theoretic approach to make predictions about their outcomes. The initial decision on emissions reduction is determined by the Stackelberg equilibrium concept. We generalize Barrett's static “emission” model to a dynamic framework and answer the question “how rapid should the emission reduction be?” It appears that sharper abatement is desirable in the early term, which is similar to the conclusion of the Stern review. Numerical example demonstrates that abatement dynamics of the coalition and the free‐rider differ when discounting of the future payoffs increases. We show that without incentives from external organizations or governments, such pollution reduction path can actually lead to a decline in the agreement's membership size.     

Computation Models for Parameterized Complexity

A parameterized computational problem is a set of pairs (x, k), where k is a distinguished item called “parameter”. FPT is the class of fixed-parameter tractable problems: for any fixed value of k, they are solvable in time bounded by a polynomial of degree α, where α is a constant not dependent on the parameter. In order to deal with parameterized intractability, Downey and Fellows have introduced a hierarchy of classes W[l] ? W[2] ? ? containing likely intractable parameterized problems, and they have shown that such classes have many natural, complete languages. In this paper we analyze several variations of the halting problem for nondeterministic Turing machines with parameterized time, and we show that its parameterized complexity strongly depends on some resources like the number of tapes, head and internal states, and on the size of the alphabet. Notice that classical polynomial-time complexity fails in distinguishing such features. As byproducts, we show that parameterized complexity is a useful tool for the study of the intrinsic power of some computational models, and we underline the different “computational powers” of some levels of the parameterized hierarchy.     

The impact of finite precision arithmetic and sensitivity on the numerical solution of partial differential equations

In this paper, we address some fundamental issues concerning “time marching” numerical schemes for computing steady state solutions of boundary value problems for nonlinear partial differential equations. Simple examples are used to illustrate that even theoretically convergent schemes can produce numerical steady state solutions that do not correspond to steady state solutions of the boundary value problem. This phenomenon must be considered in any computational study of nonunique solutions to partial differential equations that govern physical systems such as fluid flows. In particular, numerical calculations have been used to “suggest” that certain Euler equations do not have a unique solution. For Burgers' equation on a finite spatial interval with Neumann boundary conditions the only steady state solutions are constant (in space) functions. Moreover, according to recent theoretical results, for any initial condition the corresponding solution to Burgers' equation must converge to a constant as t → ∞. However, we present a convergent finite difference scheme that produces false nonconstant numerical steady state “solutions.” These erroneous solutions arise out of the necessary finite floating point arithmetic inherent in every digital computer. We suggest the resulting numerical steady state solution may be viewed as a solution to a “nearby” boundary value problem with high sensitivity to changes in the boundary conditions. Finally, we close with some comments on the relevance of this paper to some recent “numerical based proofs” of the existence of nonunique solutions to Euler equations and to aerodynamic design.     

Quadrature for meshless Nitsche's method

In this article, we study effect of numerical integration on Galerkin meshless method (GMM), applied to approximate solutions of elliptic partial differential equations with essential boundary conditions (EBC). It is well‐known that it is difficult to impose the EBC on the standard approximation space used in GMM. We have used the Nitsche's approach, which was introduced in context of finite element method, to impose the EBC. We refer to this approach as the meshless Nitsche's method (MNM). We require that the numerical integration rule satisfies (a) a “discrete Green's identity” on polynomial spaces, and (b) a “conforming condition” involving the additional integration terms introduced by the Nitsche's approach. Based on such numerical integration rules, we have obtained a convergence result for MNM with numerical integration, where the shape functions reproduce polynomials of degree k ≥ 1. Though we have presented the analysis for the nonsymmetric MNM, the analysis could be extended to the symmetric MNM similarly. Numerical results have been presented to illuminate the theoretical results and to demonstrate the efficiency of the algorithms.Copyright © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 265–288, 2014     

Li–Yorke chaos in higher dimensions: a review

Li and Yorke not only introduced the term “chaos” along with a mathematically rigorous definition of what they meant by it, but also gave a condition for chaos in scalar difference equations, their equally famous “period three implies chaos” result. Generalizations of the Li and Yorke definition of chaos to difference equations in ? ⁿ are reviewed here as well as higher dimensional conditions ensuring its existence, specifically the “snap-back repeller” condition of Marotto and its counterpart for saddle points. In addition, further generalizations to mappings in Banach spaces and complete metric spaces are considered. These will be illustrated with various simple examples including an application to chaotic dynamics on the metric space (?  ⁿ , D) of fuzzy sets on the base space ? ⁿ .     

Rigid Embeddings of Sasakian Hyperquadrics in $$\mathbb {C}^{n+1}$$

We give a classification of Sasakian manifolds that are CR-equivalent to hyperquadrics by describing their exact parameter space. For “ half” of the parameter space, we find an explicit representation by defining equations. This problem is related to the problem of finding pseudo-Kähler potentials with prescribed Ricci curvature.     

Wearing the Letter Jacket: Legitimate Participation in a Collaborative Science,Mathematics, Engineering,and Technology Education Reform Project

This study examines one NSF‐funded Collaborative for Excellence in Teacher Preparation and describes the complexities of such a science education reform effort. A theoretical model based in community, culture, and identity is used to address key questions: How did institutional ideologies, structures, policies, and practices influence the Collaborative's success? What unique problems were associated with the university and school partnership? How did K‐12 teachers' participation affect their development and the success of the Collaborative? Findings indicate that though K‐12 participants were deemed as “pedagogy experts” and shared the inquiry‐based culture espoused in the Collaborative, they felt both as project insiders and outsiders. This was due to issues of status between university faculty and K‐12 teachers; teachers' less‐than‐active role in the Collaborative; and the constraints and narrow focus that resulted from long‐established institutional, social, and political structures and that marginalized, delegitimized, excluded, and proved unattractive to teachers.     

ON THE VITALI-HAHN-SAKS-NIKODYM THEOREM

Abstract

The classical Vitali-Hahn-Saks-Nikodym Theorem [5, Thm. I.4.8] gives a limit criterion for when a sequence of strongly additive vector measures on a σ-field of sets having their range in a Banach space can be expected to be uniformly strongly additive. In [16, Cor. 8], Saeki proved that the limit condition on the sequence of vector measures could be substantially weakened as long as the Banach space in play is “good enough”. Saeki's result was based upon his work on a class of set functions too large to have Rosenthal's Lemma at his disposal. In Section 2, we prove Saeki's result with Rosenthal's Lemma at the basis of our work and then augment our characterization of Banach spaces enjoying Saeki's result in [1] with another natural equivalent condition. In Section 3 we extend Saeki's result to Boolean algebras having the Subsequential Interpolation property.     

Science Attitudes of Selected Middle School Students in China: A Preliminary Investigation of Similarities and Differences as a Function of Gender

Evaluating the attitudes of science students is important for teachers, curriculum developers, and those working with preservice teachers. Although in the United States a great deal of attitudinal research has been conducted with regard to science education, in the People's Republic of China very little work concerning science attitudes has been completed. This study will report on an evaluation of Chinese boys' and girls' attitudes toward selected science topics. Students attended a middle school in the city of Shanghai. Analysis indicated that when the male and female Chinese students differ in their response patterns, females select more intense responses (“strongly agree” as opposed to “agree,”“strongly disagree” as opposed to “disagree”). Furthermore, the surveyed females often selected responses suggesting that they were more interested in the science topics and issues presented in the survey.     

On superperfect noncomparability graphs

The class of superperfect graphs, which was previously studied by A. J. Hoffman, E. L. Johnson, and M. C. Golumbic, is a proper subclass of the class of perfect graphs; further, it properly contains the class of comparability graphs. In his book, Golumbic proves that, for split graphs, G is a comparability graph if and only if G is superperfect. Moreover, the fact that split graphs are exactly those graphs which are both triangulated and cotriangulated motivated Golumbic to ask if it is true or false that, for triangulated (or cotriangulated) graphs, G is a comparability graph if and only if G is superperfect. In the present paper, we determine those members of Gallai's list of minimal noncomparability graphs which are superperfect and, as a consequence, we find that the answer to the above question is “false” for triangulated and “true” for cotriangulated graphs.     

NOAH'S NONCONCAVITY: ON THE EXISTENCE OF NONTRIVIAL INTERIOR SOLUTIONS TO THE PROBLEM OF COST‐EFFECTIVE CONSERVATION PLANNING

Abstract The idea that species loss diminishes future information flows is a cornerstone of arguments for conservation planning. In his seminal work entitled The Noah's Ark Problem, Weitzman [1998] examines the problem of cost‐effective conservation planning from a theoretical perspective accounting for the affect planning has on the expected size of the biosphere's informative potential. This paper extends Weitzman's analysis by examining how his conclusions are altered by the introduction of a conservation authority that considers the value of information contained in the biosphere. Introducing nonquasiconcave preferences for the information contained in each species substantially modifies the characterization of a cost‐effective conservation plan. In particular, I find that a cost‐effective plan generally includes partial funding for many species and funds no species completely. This investigation is motivated by theoretical contributions to the information economics literature, a la Radner and Stiglitz [1984] , showing that the value function for information tends to exhibit increasing returns.     

Identification for Linear Stochastic Systems Driven by Fractional Brownian Motion

Abstract

We apply Grenander's method of sieves to the problem of identification or estimation of the “drift” function for linear stochastic systems driven by a fractional Brownian motion (fBm). We use an increasing sequence of finite dimensional subspaces of the parameter space as the natural sieves on which we maximise the likelihood function.     

Teachers' Understandings of Realistic Contexts to Capitalize on Students' Prior Knowledge

The theory of realistic mathematics education establishes that framing mathematics problems in realistic contexts can provide opportunities for guided reinvention. Using data from a study group, I examine geometry teachers' perspectives regarding realistic contexts during a lesson study cycle. I ask the following. (a) What are the participants' perspectives regarding realistic contexts that elicit students' prior knowledge? (b) How are the participants' perspectives of realistic contexts related to teachers' instructional obligations? (c) How do the participants draw upon these perspectives when designing a lesson? The participants identified five characteristics that are needed for realistic contexts: providing entry points to mathematics, using “catchy” and “youthful” contexts, selecting personal contexts for the students, using contexts that are not “too fake” or “forced,” and connecting to the lesson's mathematical content. These characteristics largely relate to the institutional, interpersonal, and individual obligations with some connections with the disciplinary obligation. The participants considered these characteristics when identifying a realistic context for a problem‐based lesson. The context promoted mathematical connections. In addition, the teachers varied the context to increase the relevance for their students. The study has implications for supporting teachers' implementation of problem‐based instruction by attending to teachers' perspectives regarding the obligations shaping their work.     

Light monotone Dialectica methods for proof mining

In view of an enhancement of our implementation on the computer, we explore the possibility of an algorithmic optimization of the various proof‐theoretic techniques employed by Kohlenbach for the synthesis of new (and better) effective uniform bounds out of established qualitative proofs in Numerical Functional Analysis. Concretely, we prove that the method (developed by the author in his thesis, as an adaptation to Dialectica interpretations of Berger's original technique for modified realizability and A‐translation) of “colouring” some of the quantifiers as “non‐computational” extends well to ε‐arithmetization, elimination‐of‐extensionality and model‐interpretation (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)