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A quantum version of the Monge--Kantorovich optimal transport problem is analyzed. The transport cost is minimized over the set of all bipartite coupling states $\rho^{AB}$, such that both of its reduced density matrices $\rho^A$ and $\rho^B$ of dimension $N$ are fixed. We show that, selecting the quantum cost matrix to be proportional to the projector on the antisymmetric subspace, the minimal transport cost leads to a semidistance between $\rho^A$ and $\rho^B$, which is bounded from below by the rescaled Bures distance and from above by the root infidelity. In the single qubit case we provide a semi-analytic expression for the optimal transport cost between any two states and prove that its square root satisfies the triangle inequality and yields an analogue of the Wasserstein distance of order two on the set of density matrices. We introduce an associated measure of proximity of quantum states, called SWAP-fidelity, and discuss its properties and applications in quantum machine learning., Comment: 15 pages including appendices, 4 figures. Version v2 includes a new quantity, SWAP-fidelity, and some applications

We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with k blocks of equal size. More precisely, we consider a random d-uniform hypergraph H with n vertices partitioned into k clusters of size s = n / k . Hyperedges e are added independently with probability p if e is contained within a single cluster and q otherwise, where 0 ≤ q p ≤ 1 . We present a spectral algorithm which recovers the clusters exactly with high probability, given mild conditions on n , k , p , q , and d. Our algorithm is based on the adjacency matrix of H, which is a symmetric n × n matrix whose ( u , v ) -th entry is the number of hyperedges containing both u and v. To the best of our knowledge, our algorithm is the first to guarantee exact recovery when the number of clusters k = Θ ( n ) .

In the planted partition problem, the $n$ vertices of a random graph are partitioned into $k$ "clusters," and edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively (where $0 \le q < p \le 1$). We give an efficient spectral algorithm that recovers the clusters with high probability, provided that the sizes of any two clusters are either very close or separated by $\geq \Omega(\sqrt n)$. We also discuss a generalization of planted partition in which the algorithm's input is not a random graph, but a random real symmetric matrix with independent above-diagonal entries. Our algorithm is an adaptation of a previous algorithm for the uniform case, i.e., when all clusters are size $n / k \geq \Omega(\sqrt n)$. The original algorithm recovers the clusters one by one via iterated projection: it constructs the orthogonal projection operator onto the dominant $k$-dimensional eigenspace of the random graph's adjacency matrix, uses it to recover one of the clusters, then deletes it and recurses on the remaining vertices. We show herein that a similar algorithm works in the nonuniform case., Comment: 22 pages, 4 figures

This chapter explains and estimates a model of accommodation clusters in tourist destinations. The model variables describe a destination’s intrinsic attraction, synergies between tourism activities, increasing congestion and capacity, and competition-driven technical changes. The model engages technology parameters at four physical scales, global markets for capital and visitors, regional destinations and innovations, destination-level clustering, and characteristic accommodation size. Parameters are estimated across 20 Caribbean destinations from 1986 to 1996. Combined with island-specific tourism policies, the model plausibly backcasts earlier tourism development for Aruba reproduces overshoot in accommodations in the late-1980s, and the following decade of disruptive fluctuations. Although the model over-estimates current hotel accommodation, the excess matches emergent uncontrolled growth of “alternative” accommodation, primarily condominiums, and vacation rentals. This case study illustrates how the cluster model’s components and parameters influence critical junctures in the growth trajectory of destinations.

The present study uses concurrent think-aloud verbal protocols alongside post-hoc interviews to explore how six teacher-raters determine a students' ability to explain academic concepts and argue for an academic stance supported by sources during a 25-minute group tertiary academic tutorial oral assessment. We explored how the raters arrived at decisions regarding the quality of students' academic stance and engagement in light of difficulties with rater attention in real-time, L2 language concerns, assessing engagement in a group oral setting, and the use of spoken citation to support speakers’ claims. Substantial differences in rater practice, beliefs and interpretation of assessment criteria were all found during the assessment of student performance, confirming a number of difficulties faced by raters assessing the academic ability of multiple participants over lengthy extended, interactional discourse. The findings shed real-time conceptions of (un)successful academic stance and engagement in group oral contexts, as well as confirm the usefulness of verbal protocols in revealing previously hidden complications for group oral assessments in an academic context, with accompanying suggestions for resolving such complications.

The spatio-temporal relationship between tourism product similarity and spatial proximity has not been adequately studied empirically because of data and methodological limitations. New forms of data available at high temporal frequencies and low levels of spatial aggregation, together with large commercial data and expanding computational ability allow a variety of theories, old and new to be explored and evaluated more meticulously and systemically than has been possible hitherto. This study uses spatial visualization and data harvesting to synthesize a variety of data for exploring the evolution of hotel clusters and co-location synergies in US cities. The findings question the reliability of the current data to be used for identifying and analyzing the formation of tourist destination clusters and their dynamics. We conclude that synthesizing social media and large commercial data can generate a more robust database for research on tourism development and planning and improving opportunities for the examining spatial patterns of tourism activities. We also devise a protocol to combine &lsquo, social media&rsquo, sources with big commercial sources for tourism development and planning, and eventually other sectors.

This chapter presents a method for modelling resilience in economic systems confronted by multiple irregular shocks. For this, investment portfolio theory is reformulated as a protected production function. This function determines the share of output that is dedicated to protection as economic agents attempt to maintain their preferred level of consumption and safety in the face of exogenous hazards. With this, resilience becomes the ability of production to withstand and recover from the repeated shocks. This mechanism is illustrated via model comprising aggregated domestic sector and a single export sector trading with a larger regional system. Solving the model, first as a comparative static system gives multiple stable and unstable equilibrium solutions for the level of economic activity. Equating these solutions gives the level of protection that offers greatest well-being. This production–protection relationship is then incorporated into a time-step simulation showing how the economy evolves in response to random shocks and concatenated disturbances, including irregular collapses beyond the desired resilience regime. Within this dynamic model, solutions to the static model appear as weak attractors. Thus, a further contribution of the paper is that it bridges between equilibrium and evolutionary economics, and comparable challenges in other disciplines. The method is advanced as a closure for a social accounting-event matrix based approach.

Purpose: To examine the impact of a nicotine replacement therapy (NRT) enhancement on quit outcomes. Design: Observational study using an intent to treat as treated analysis. Setting: Not available. Participants: A total of 4022 Idaho tobacco users aged ≥18 years who received services from the Idaho Tobacco Quitline or Idaho’s web-based program. Intervention: One-call phone or web-based participants were sent a single 4- or 8-week NRT shipment. Multiple-call participants were sent NRT in a single 4-week shipment or two 4-week shipments (second shipment sent only to those completing a second coaching call). Measures: North American Quitline Consortium recommended Minimal Data Set items collected at registration and follow-up. Thirty-day point prevalence quit rates were assessed at 7-month follow-up. Analysis: Multiple logistic regression models were used to examine the effects of program type and amount of NRT sent to participants while controlling for demographic and tobacco use characteristics. Results: Abstinence rates were significantly higher among 8-week versus 4-week NRT recipients (42.5% vs 33.3%). The effect was only significant between multiple-call program participants who received both 4-week NRT shipments versus only the first of 2 possible 4-week shipments (51.1% vs 31.1%). Costs per quit were lowest among web-based participants who received 4 weeks of NRT (US$183 per quit) and highest among multiple-call participants who received only 1 of 2 possible NRT shipments (US$557 per quit). Conclusion: To better balance cost with clinical effectiveness, funders of state-based tobacco cessation services may want to consider (1) allowing tobacco users to choose between phone- and web-based programs while (2) limiting longer NRT benefits only to multiple-call program participants.

Background The aim of this systematic review was to determine the effectiveness of Internet interventions in promoting smoking cessation among adult tobacco users relative to other forms of intervention recommended in treatment guidelines. Methods This review followed Cochrane Collaboration guidelines for systematic reviews. Combinations of "Internet," "web-based," and "smoking cessation intervention" and related keywords were used in both automated and manual searches. We included randomized trials published from January 1990 through to April 2015. A modified version of the Cochrane risk of bias assessment tool was used. We calculated risk ratios (RRs) for each study. Meta-analysis was conducted using random-effects method to pool RRs. Presentation of results follows the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines. Results Forty randomized trials involving 98,530 participants were included. Most trials had a low risk of bias in most domains. Pooled results comparing Internet interventions to assessment-only/waitlist control were significant (RR 1.60, 95% confidence interval [CI] 1.15-2.21, I (2)=51.7%; four studies). Pooled results of largely static Internet interventions compared to print materials were not significant (RR 0.83, 95% CI 0.63-1.10, I (2)=0%; two studies), whereas comparisons of interactive Internet interventions to print materials were significant (RR 2.10, 95% CI 1.25-3.52, I (2)=41.6%; two studies). No significant effects were observed in pooled results of Internet interventions compared to face-to-face counseling (RR 1.35, 95% CI 0.97-1.87, I (2)=0%; four studies) or to telephone counseling (RR 0.95, 95% CI 0.79-1.13, I (2)=0%; two studies). The majority of trials compared different Internet interventions; pooled results from 15 such trials (24 comparisons) found a significant effect in favor of experimental Internet interventions (RR 1.16, 95% CI 1.03-1.31, I (2)=76.7%). Conclusion Internet interventions are superior to other broad reach cessation interventions (ie, print materials), equivalent to other currently recommended treatment modes (telephone and in-person counseling), and they have an important role to play in the arsenal of tobacco-dependence treatments.

Purpose: To describe changes in health-related quality of life (HRQOL) related to variation in demographic characteristics, program goals, and program participation, among health coaching program participants. Design: A retrospective observational study of a health coaching program. Setting and Participants: A total of 2169 adults enrolled in an individually purchased or employer-sponsored health plan from a large health and well-being company, who participated in a health coaching program between January 2016 and April 2017. Intervention: The health coaching program used evidence-based behavior change strategies to encourage skill development, self-monitoring, and goal setting/achievement. Health coaching program modalities included online and telephonic coaching sessions. Measures: Demographic characteristics (gender, age, race, income), goal categories (weight management, fitness, nutrition, stress management, other), program modality (online, telephonic, both), engagement level (low, medium, high), and Healthy Days, a validated HRQOL measure developed by the Centers for Disease Control and Prevention. Analysis: t Tests, mixed analysis of variance (ANOVA). Results: There were significant ( P < .05) reductions in average total unhealthy days (UHDs) across all goal categories. Mixed ANOVAs identified a significant main effect for time, for all demographic characteristics ( P values < .05), and a significant effect for program modality ( P < .0001), time ( P < .0001), and interaction effects, between program modality and time, on average UHD ( P = .01). Conclusion: Our findings indicate significant reductions in UHD, following 6 months of health coaching, and support the use of HRQOL measures, which are known to be highly correlated with traditional measures of health, to evaluate health coaching programs.

This paper describes the goals and development of a rural tourism Studio for Masters-level students in the Southern Tier of Western New York over the last decade. The main goal of the Studios has been to explore how tourism may be used to promote general economic development in a relatively impoverished rural area and so help to improve living conditions, including housing. The studio experience is considered to be an important part of the preparation for a career in planning. Studios almost always enter into, and attempt to contribute to, an ongoing planning and development process and are undertaken with the cooperation of local communities and agencies. The paper describes the background of students, their disciplinary skills and work experience, ethnic, age and geographic mix, and general unfamiliarity with rural issues. Also described are the various constraints and compromises with respect to course requirements and schedules, location, local participation and engaging communities. The paper...

Transmission-line modelling (TLM) is a valuable technique for numerical simulation of electromagnetic fields. Recently, investigations have been successfully carried out into the use of the TLM approach on unstructured meshes However, as the local characteristics of mesh geometry will clearly make an impact upon the fidelity of simulations, it is necessary to examine suitable techniques for mesh optimisation. Three different methods have been investigated here to find optimal meshes for subsequent TLM simulations: the centroidal Voronoi Tessellation method, the optimal Delaunay triangulation method and a spring relaxation method. These different techniques are assessed in terms of maximum efficiency of the subsequent TLM simulations and the computational cost that is incurred to identify them. Several different canonical examples of mesh are considered to determine the generality of the conclusions drawn.

Discussion of agglomeration and clustering in the tourist area life cycle (TALC) literature has not led to a corresponding change of the principal equation used to formalize the model. This paper proposes a modification that accounts for the synergies between the accommodation, entertainment, and other components of a tourist destination. The modified model is contrasted with the original TALC and estimated for a cross-section of Caribbean and other island destinations. Estimations based on visitor expenditures and experts' evaluations of destination authenticity are compared. The results illustrate how parameters representing synergy and congestion vary across tourism styles and time. The implications for destination growth are illustrated by comparing the solution to the proposed model with the TALC. The model exposes a core dilemma that while destinations should realize positive synergies to achieve self-sustaining growth, with this threshold achieved, the resulting pace of investment may drive destinations to overshoot, and uneven growth.

The paper aims to offer a good guideline for anyone who intends to do a futures or a foresight exercise for rural communities. The case presented is the one of the future of rural communities in Romania. The article begins with a brief presentation of the prevailing rural situation in Romania followed by a dialogue regarding suggestions for the possible objectives of a foresight exercise and the methods used (e.g. visioning, alternative futures, scenarios).

At a round table discussion that took place in Bucharest during a mutual learning workshop, on 9th–11th of June 2010, around 15 futurists were asked to look at this picture of a little African girl. It appears on the cover of UNESCO's Education for All Global Monitoring Report 2010, which has the specific title: ‘Reaching the Marginalized’. The futurists were asked: how would you justify the work you do to the girl in the photograph. Here are some of the answers.

This commentary responds to some of the issues raised in Zia Sardar's paper “Welcome to Postnormal Times” noting and attempting to explain points of difference and similarity. From Sardar's invocation of the 3C's of complexity, chaos and contradiction emerges the idea that our postnormal times might be likened to the strange times following the Great Plague that gave rise to the Alliterative Revival. Speculating further, it is questioned whether, in such strange times, utopian futures studies substitute for prayer.

This paper explores suggestions in the literature that the tourism industry is “chaotic” by transforming a previously developed resort model into discrete logistic equation (DLE), a widely researched chaos model. Given parameters characteristic of the industry, the logistic tourism model (LTM) explains, for example, the hesitant take-off of tourism, the role of agglomeration during the rapid growth phase, and why even in maturity, with slower average growth, a resort maintains its high growth potential and propensity for chaos. These and other findings suggest that globalizing industries, such as tourism, may exhibit quite different dynamics from those captured by traditional growth models or localized supply-demand elasticity models.

Our paper outlines the preparation of a Framework for Sustainable Tourism on the Caribbean Island of Aruba from the standpoint of futurists involved in public policy. Despite remarkable success with tourism over nearly half-a century, Arubans have become periodically concerned about the long-run sustainability of their major industry, their culture, and their Island. The paper explains the historic industrial epochs that have led to the demographic layering and cultural division of labor, the development of tourism from its beginnings in the 1950s, and to present-day concerns about over-development and migration behind the setting up of a National Tourism Council (NTC) in 2001. The basic issues confronted by the NTC were set within the overarching question of “how far and how fast” tourism in Aruba could or should expand. Following on from three exploratory scenarios, the Framework prepared by the authors makes proposals for expansion of tourism in distinctive culture regions and corresponding tourism products over the next two generations of Arubans at a pace that matches emerging needs, but below the carrying capacity of the Island. The paper explains the historic context, pragmatic assumptions made, empirical evidence used, and connects the approach to other papers in this issue.

This paper seeks the Zeitgeist of Futures from 1968 to the present. The primary effort is to discern the topics addressed by Futures over the years, how these have changed, what methods, time horizons, and moods are expressed. One goal is to shed light on questions such as whether FUTURES, or “futures studies” in general, anticipates the future or simply adds commentary on the present. If the former, by how much: if the latter, is the commentary useful? Another goal, assuming the answer is positive is to assess whether articles in FUTURES provide a “data base” for scenario building, modeling, or Delphi? Although the starting point addressed in this article is to explore trends in the use of vocabulary, and its correlations with “real world events” the goal is to comprehend connections and associations as revealed in FUTURES articles, as a step toward paradigm recognition and Zeitgeist.

Most futures methodologies might be termed “heuristic”, that is a way to promote learning, discovery, and problem solving through trial and error. This paper describes one such approach, used primarily in teaching a Masters planning program class Global Issues and Futures in a class designed to raise awareness of a variety of global concerns. After explaining the underlying framework and concepts, and their foundation in previous futures studies, the core equations, data, and a classroom application are described. The method serves primarily to raise questions rather than answer them; to broaden the perspective that students will bring to their later careers. 1

This paper explains and implements a portfolio-based framework for analyzing the progression and consequences of disruptions to small-region economies. The first section discusses the underlying relationship between hazards, events, protection, disruptions, and disasters in regional economic systems. Such systems typically are adaptive in that they constantly adjust their levels and patterns of protection and compensation to changes in the frequency and magnitude of disruptions. The section explains how portfolio theory may be re-conceptualized to address policy choices related to the above issues. The second section explains conceptual issues in defining variables and specifying the production function balancing performance and protection. This function in turn defines the optimal expenditure for each actor against which their risk-tolerance is measured. Potential “tipping points” from singularly large or cascaded shocks, including disruptions from “lumpy” investment, suggest disaster-mitigating strategies that maximize societal utility or reduce tendencies to major disaster. In the third section, this theory is implemented empirically as a computer simulation model for a stylized open economy driven by tourism and oil refining. The simulations show how the potential for major disruptions varies with policy, increasing rapidly with the risk-propensity of policy makers. They also suggest how appropriate regional economic policy, notably rebalancing and export portfolio and rescheduling major investments, might reduce the likelihood of such events.

In this paper, we consider the planted partition model, in which $n = ks$ vertices of a random graph are partitioned into $k$ "clusters," each of size $s$. Edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively (where $0 \le q < p \le 1$). We give an efficient algorithm that, with high probability, recovers the clusters as long as the cluster sizes are are least $\Omega(\sqrt{n})$. Informally, our algorithm constructs the projection operator onto the dominant $k$-dimensional eigenspace of the graph's adjacency matrix and uses it to recover one cluster at a time. To our knowledge, our algorithm is the first purely spectral algorithm which runs in polynomial time and works even when $s = \Theta(\sqrt n)$, though there have been several non-spectral algorithms which accomplish this. Our algorithm is also among the simplest of these spectral algorithms, and its proof of correctness illustrates the usefulness of the Cauchy integral formula in this domain., Comment: 21 pages + title page

My paper describes a portfolio theoretic framework for exploring the causes and consequences of major disruptions on regions and communities. The approach can be related to theories of financial portfolio management, optimal insurance, moral hazard, and ambiguous uncertainty, and the empirical literature on sustainable livelihoods, robust engineering, and disaster management. The present paper explains how Markowitz (1959) portfolio management theory may be adapted to the situation of a small region facing periodic and irregular disruptions in local and export markets, and used to select a portfolio of disaster mitigating strategies that maximize societal utility. This theory is implemented empirically using a computer simulation model. Model simulations show how the potential for major disruptions varies with economic policy, increasing rapidly with the risk-propensity of policy-makers or policies that increase the likelihood of concatenated events. Moreover, strategies that reduce ambiguity or ...

In a recent paper in Futures, Chenoweth and Feitelson test of the validity of the projections of the Global 2000 Report to the President and The Resourceful Earth: A Response to Global 2000 . This commentary critiques their approach, focusing on their comparison of the two studies' Year 2000 projections, and the pitfalls for near-term tests of long-term projections. Empirically, their paper does little to resolve the neo-Malthusian and Cornucopian debate. Nonetheless, given the past history of this acrimonious debate, their conclusions may undermine current efforts to balance global economic, social, and environmental concerns.

My paper The delayed impacts of plant closures in a reformulated Leontief model showed that the time-varying impacts of changes to a regional economy could be approximated usefully by a simple elaboration of the Leontief inverse (Cole, 1988). I have applied the method in a variety of situations, typically to calculate the shifts in community income and its distribution following a major catastrophe. In all cases I use a single or multi-region social accounting matrix. Since Jackson et al (1997) have been unable to reproduce my results I shall begin with a step-by-step demonstration. Then I shall show that their failure lies in their treatment of the external (rest-of- world) sector. This appears to arise from their overly restrictive definition of input-output analysis in relation to other types of model, and their confusion as to the difference between simplification, approximation, and model validation.

In Closing the Case on Closure in Cole's Model Randall Jackson and Moss Madden critique my solution to the time-lagged regional input-output model. My rebuttal demonstrates that they: i) interpret my model incorrectly, ii) are inconsistent in their own specification, and iii) make inapplicable numerical comparisons between short- and long-term solutions. I show also iv) the correct solution to the totally closed model is neither trivial, nor singular, and v) this resolves the apparent paradox of infinite multipliers in a finite world. Moreover, vi) in my model, injecting exogenous demands equal to export earnings correctly reproduces the base output levels. The standard model does not meet this test.

The paper uses a reformulated input-output approach to calculate the medium-run regional economic impact of plant closures or similar changes taking nun account expenditure lags. The approach lends to a straightforward modification of the generalized Lecontief inverse method. An example is used show that the inclusion of expenditure lags m impact analysis ran he quite substantial and that the usual approach of partitioning the accounts into infinitely last and infinitely slow activities, and the Consequent assumption that equilibrium is reached, is an especially weak approximation. Revising the contribution of all activities to account for expenditure lags changes both short- and medium-term predictions by up to a factor of two. The approach has a variety of applications, but may be especially useful for calculating the distributed impact over time on household income, local taxes, employment, and other businesses.

Explores possibilities for simulating the effects of continuous disruptions to an economy using a multi‐sector social accounting model. The underlying thesis for the model is that disruptions (due to events ranging from potholes to earthquakes) are a constant and unavoidable aspect of development and that all institutions and production activities are structured and adapt over time so as to balance performance and protection. The first sections explain the role of input‐output tables, especially social accounts, as the basic framework for evaluating systemic vulnerability to disaster. The next sections explain the underlying behavioral components of the model: how the profile of protection versus disruption and costs of protection are determined, and how adaptation of the protection profile to changing events and societal discounting affects protection. In the final sections, these elements are integrated into a multi‐sector social accounting model of the Niagara Frontier region of New York State – affected by industrial decline and currency fluctuations is dependent on a major hydro‐electric power facility that is considered vulnerable to a variety of unscheduled events. Results focus on how disruptions and responses to them propagate over time and between actors.

Futures studies and planning follow parallel and sometimes overlapping paths. Both are idealistic activities seeking to make people's futures more secure and more fulfilling. Many futurists wish that their dreams could be implemented, and many planners dream that their work could be less shortsighted and parochial. If only to fulfill these needs, these groups should pay more attention to each other. In this article, I attempt to strengthen the bridge between futurists and planners. My observations come from the perspective of someone with a professional and pedagogical interest in both planning and futures studies. I illustrate past, current, and potential contributions of futures studies to planning as follows: (1) the beginnings of futures studies in science fiction films, journals, and international development; (2) the role of envisioning, polling, and forecasting methods; and (3) the challenges of linking futures studies methods to planning. I then argue for a diverse approach in terms of me...

I explain how object-oriented mapping may be carried out in spreadsheets, by use of simple user-created maps and macros. The method has uses for teaching, research, and policy. The advantage over current add-in mapping is that the macros can be written by users with basic spreadsheet skills, the procedures are relatively fast, new maps may be drawn or imported, and the macros can be adapted to a variety of applications such as real-time animation, or used in planning situations where ‘time is of the essence’. The paper raises a number of issues as to the inflexibility of some GIS modeling capabilities and spreadsheet mapping capability. The approach is illustrated for Quattro Pro for Windows and Excel with Visual Basic, with two classroom applications, and extensions to decision support, animation, and cellular modeling.

In this paper, a review of mechatronics is presented with emphasis on the desired qualities of university graduates as viewed by industry. A detailed description of a sequence of two new courses on automotive mechatronic systems and a specialized laboratory are discussed. The new coursework has been added to the curriculum towards the degree of systems engineer at Oakland University and will be first offered in Fall '97. The development of the courses and the laboratory has been supported by Ford Motor Company.

Geographers deal with global and local space and their interrelationships and thus bring new insights, perspectives, and methods to global questions. This is appealing to futurists since the principle of ‘think globally-act locally’ has been an inspiration for many years. In this paper I explore how old and new approaches in geography, as well as new information technologies such as the World Wide Web (WWW) and Geographic Information Systems (GIS), might contribute to global modeling. I briefly review also the history of global economy models to discover lessons for future attempts to construct global models, not least how prevailing paradigms and institutional expediency determine the intellectual effort, and its impact. I then describe some of the new directions being undertaken by global modelers, quantitative geographers and regional scientists in the 1990s, and the possibilities and challenges for the next few years, and their contribution to the knowledge building process and its context.