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The cultural, economic, and nutritional importance of rice led many countries to investigate how domestic rice production can meet current and future demands. In rice production, the role of social capital and personal networks of producers compared to biophysical and economic assets, are less well understood even though case study analyses routinely indicate that they play an important role in production efficiency and sustainability. Using data from rice farmers in the Philippines, we sought to understand the role of social capital on farm productivity, technical efficiency, and the adoption of sustainable practices. Through social network analysis and structural equation modeling, we show the accumulation of social capital resources exhibits a positive impact on farm technical efficiency and the adoption of technology for water conservation. The results offer a different frame of reference for policymakers developing new approaches for sustainable rice production in terms of how dynamics between farmers may ultimately attain national and global sustainability goals.

The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and static output feedback is applied. The first step is to reconsider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback Hopf algebra used to describe dynamic output feedback, and the Hopf algebra of the shuffle group. These two combinatorial structures are combined to compute what will be called the Wiener-Fliess feedback product. It will be shown that this product has a natural interpretation as a transformation group acting on the plant and preserves the relative degree of the plant.

The concept of relative degree plays an important role in nonlinear control theory. It provides, for example, a necessary and sufficient condition for the existence of a feedback linearizing control law for a single-input, single-output (SISO) input-affine nonlinear state space system. It also gives a sufficient condition under which a left inverse exists. In applications it is common for systems to be composed of smaller interconnected subsystems. It is known that various feedback structures preserve relative degree, but it is largely unknown how to compute the relative degree of interconnected systems using only their properties. So the goal of this paper is to determine the relative degree of two nonlinear control systems interconnected in a variety of different ways. A collection of illustrative examples is given.

In this study, we examine the nature of scientific discourse among participants enrolled in two citizen science projects as they engage in collaborative modeling and problem solving. Specifically, we explore the nature of their conversation as they use, the Mental Modeler, an online collaborative modeling tool to facilitate science engagement, systems-thinking and reasoning. This paper applies an analytical approach that uses visual representations and the discourse around building these representations to understand the shifts in scientific discourse and interpret complex interaction patterns between participants and facilitators in the computer-based learning environment. Findings suggest that the Mental Modeler serves as a boundary object that empowers participants and facilitators to collaboratively engage with scientific topics and practices through the development of scientific discourse and deeper learning in problem solving contexts. Findings shows patterns for group modeling in terms of shifting from bottom-up level to top-down level of discussions. In addition, the results show greater group collaboration and interaction when participants engage in the discussion by using the Mental Modeler to plan and model the citizen science projects.

Acute socio-environmental crises often expose systemic problems that are linked by failures in management, environmental, or social systems. If recovery efforts are to address these systemic problems, these issues and the concerns of those impacted by the crisis need to be clearly articulated, rationally represented, and communicated to those responsible for the recovery. Although participatory approaches to crisis recovery often use environmental modeling, explicit ways in which stakeholders’ narratives and experiences can be translated into computer-based models for scenario analysis are not readily available to modelers or decision-makers. We present an approach to translating community narratives about crisis events using a free Fuzzy Cognitive Mapping software called Mental Modeler ( www.mentalmodeler.org ). We applied this process to the recent water crisis in Flint, Michigan, and demonstrate how participatory modeling can give communities a way to structure their thoughts, develop recovery actions, and communicate with those in charge of crisis recovery efforts.

Reducing uncertain outcomes of fishery management actions requires an understanding of how fishers will be affected by policy actions. This requires integrating the local expertise of commercial fishers and seafood processors into management planning to predict how regulatory changes could impact social-ecological systems. Participatory modeling between managers, scientists, and industry can be useful in integrating different perspectives and gaining a more comprehensive understanding of how different scenarios can cause direct and indirect impacts throughout fishery systems. We used group Fuzzy Cognitive Mapping exercises to describe the structure and dynamics of two economically important commercial fishery systems in Alaska, USA: the Bering Sea Pollock Catcher/Processor and Amendment 80 Groundfish fishery. Several components were identified by the fleets that had a relatively high number of links to other components in each system, including chum salmon catch for the pollock fleet and the deck sorting of halibut for the groundfish fleet. After identifying other critical relationships between regulatory, environmental, and operational changes, we developed a survey technique and regression analytical approach to define the shape of these relationships. Our results show both linear and non-linear relationships between bycatch regulations and fishing operations; thus, providing evidence counter to the traditional assumption that the relationships between policy and fishing operations are always linear and constant across variable levels of change. Our novel approach permits for more specific explorations of curvilinear patterns, social tipping points, and asymptotic limits to change, thereby allowing for improved assessments of the effects of regulatory and environmental change on fishing communities.

In environmental participatory modeling (PM), both computer and non-computer-based modeling techniques are used to aid participatory problem description, solution, and decision-making actions in environmental contexts. Although many PM case studies have been published, few efforts have sought to systematically describe and understand dominant PM processes or establish best practices for PM. As a first step, we have reviewed a random sample of environmental PM case study articles (n = 60) using a novel PM process evaluation instrument. We found that significant work likely remains for PM to fully support participatory and integrated planning processes. While PM reports systematically address knowledge integration and learning, they often neglect the facilitation of a multi-value perspective within a democratic process, and the integration across organizations within a governance system. If not reported, we suspect these aspects are also neglected in practice. We conclude with key research and practice issues for improving PM as an approach for real-world participatory planning and governance.

CONTEXT:\ud Conservation Agriculture (CA) usage, particularly in Southern Africa, has remained low with lower yield, higher weed pressure and lower soil quality cited as reasons for ‘disadoption’.\ud \ud OBJECTIVE:\ud Using a detailed case study of 50 farmers in two villages in Cabo Delgado (Northern Mozambique), this study seeks to test the hypothesis that farmers’ perceptions of CA are associated with distinctly different ‘mental models’ and if these “ways of thinking” overlap with farmers’ identified/self-identified groupings (e.g. CA users, ‘disadopters’ and conventional tillage users). Secondly, we examine whether these different mental models (perceptions) are associated with actual differences in on-farm measurements. Finally, we explore the hypothesis that ‘systems thinking’ (i.e., understanding nonlinear causal relationships and internal feedback loops that drive a complex system) and CA usage are positively associated.\ud \ud METHODS:\ud Fuzzy Cognitive Mapping (FCM) was used to elicit representations of farmers’ mental models. To explore the association between farmers’ mental models of CA/conventional practices and on-farm measurements we evaluated cowpea aboveground biomass, yield, weed cover, and soil quality parameters from the farmer’s main plot. We drew on network analysis to measure structural metrics of cognitive maps that provide important information about a person’s mental model (perceptions) of causal interdependencies of farming dynamics.\ud \ud RESULTS AND CONCLUSIONS:\ud We find evidence of two data-driven distinct clusters of farmers’ mental models that are in relative alignment with farmers’ identified/self-identified groupings. Cluster 1 mainly consists of conventional users and cluster 2 mainly consists of CA users/disadopters. While no significant differences in socio-demographic variables were observed, clusters of mental models were associated with key differences in on-farm measurements. Importantly, cluster 1, who tended to be conventional users, had lower yields, lower soil cover, significantly lower carbon stock and higher weed coverage than cluster 2. Soil quality indicators were higher in cluster 2 as were farmers’ overall revenue per hectare. Moreover, cluster 2 had significantly higher degrees of ‘systems thinking’ (measured through complex network analysis of graphical mental models) than cluster 1 which had higher forms of linear thinking. We argue that higher forms of experiential learning and practice of CA relate to higher degrees of systems thinking and stronger positive perceptions of CA, even among the CA ‘disadopters’.\ud \ud SIGNIFICANCE:\ud Our findings highlight the importance of systems thinking abilities and the need to consider detailed biophysical, socio-economic and mental modelling variables rather than simple binary measurements which may have led to erroneous conclusions on CA and thus has implications for how CA is understood and promoted in future.

Agent-based modeling (ABM) is an established technique to capture human-environment interactions in socio-ecological systems. As a micro-model, it explicitly represents each agent, such that heterogeneous decision-making processes (e.g. based on the beliefs and experiences of stakeholders) can anticipate the socio-environmental consequences of aggregated individual behaviors. In contrast to ABM, Fuzzy Cognitive Mapping takes a macro-level view of the world that represents causal connections between concepts rather than individual entities. Researchers have expressed interest in reconciling the two, i.e. taking a hybrid approach and drawing of the strengths of each to more accurately model socio-ecological interactions. The intuition is to take FCMs, which can be quickly developed using participatory modeling tools and use them to create a virtual population of agents with sophisticated decision-making processes. In this paper, we detail two ways in which this combination can be done, and highlight the key questions that modelers need to be mindful of.

The popularity of both citizen science and participatory modelling has given way to a growing number of case studies that all outline the benefits of more inclusive forms of conservation planning. Citizen science offers volunteers the opportunity to engage in environmental research while participatory modelling engages individuals in community-level environmental decision-making. Although both of these public-science collaborations are often said to lead to improved environmental decision-making, evidence for these outcomes in the peer reviewed literature remains sparse. We suggest that combining these fields has promise for developing community-supported research leading to conservation action. To demonstrate this approach, we present the infrastructure and use of a participatory modelling software called Mental Modeler ( http://www.mentalmodeler.org /), used with a citizen science web portal ( www.citsci.org ) that allows citizen scientists, scientists, and managers to: (1) collaboratively define local conservation issues of shared concern; (2) model and represent assumptions, evidence, and existing information about these issues; (3) run scenarios to discuss potential research or management options; and ultimately (4) co-develop citizen scientific research and conservation plans. Using case study data from two community groups working on locally-defined issues related to land management practices in the US, we demonstrate how coordinated learning through modelling practices can lead to the development of self-organized and co-created conservation action. We conclude that the development of online modelling tools holds strong promise for the fields of both citizen science and conservation biology.

Understanding abrupt change in social-ecological systems (SES), such as following major disasters, is key for restoration, adaptation, and sustainability. We describe an approach and case study using fuzzy cognitive mapping (FCM) and mental models to collectively represent local perceptions of Hurricane Irma in Key West, Florida. Using in-person FCM interviews, we sought to answer three overarching questions: 1) how did residents perceive SES relationships post-disaster, 2) how did these perceptions vary across three stakeholder groups consisting of those working in ocean recreation, resorts and inns, and non-tourism sectors, and 3) how did the aggregation of diverse opinions and perceptions affect the understanding of SES trade-offs regarding the coastal region’s resilience? Across all respondents, housing was the most commonly mentioned concept occurring in 39% of all models. Coral reefs were included in 71% of ocean recreation models, whereas tourism was included in 50% of resorts and inns models. While mangroves, seawalls, and beaches were rarely to never mentioned until prompted by the interviewer, scenario analyses revealed that shorelines play an important role in residents’ perceptions of how Hurricane Irma collectively impacted people and the environment. Sensitivity analyses revealed that the community, composed of a diverse representation of stakeholders, viewed core SES components similarly and trade-offs were acknowledged. Yet, different stakeholder groups perceived the SES in which they live in different ways, with each group perceiving greater damage to specific system components based on direct experience and knowledge. Our study demonstrates an approach for representing the collective perceptions of communities in post-disaster research, rebuilding, and restoration efforts.

Climate change is expected to have significant impacts on native, threatened and endangered wildlife. Understanding and modeling these impacts useful for wildlife managers, however, remain difficult due to complex climate change, and costly and high data requirements. Consequently, we proposed an easily-interpretable and data-efficient decision support approach to understand climate change impacts on the abundance of three endangered wetland birds (Hawaiian Stilt, Hawaiian Coot and Hawaiian Moorhen). We coupled a watershed model, AnnAGNPS, and ecological models using fuzzy-cognitive mapping software, Mental Modeler, in Hanalei watershed, Kauaźi. Results suggested that increased precipitation would increase Stilt abundance, but decrease Coot and Moorhen abundance. Decreasing precipitation might have negative effects for all three species. Moreover, decision-makers should pay equal attention to controlling components (water depth, food availability and disease) with system-wide influence. Finally, besides being adaptable to similar environmental contexts, our approach captured both direct and indirect climate change impacts through ecological connectivity. Proposed modeling framework is a potential decision-support tool for understanding local-scale climate change impacts.IPCC AR4 based climate change scenarios drove empirical watershed model, AnnAGNPS, simulations.Watershed dynamics functioned as scenarios for knowledge-driven ecological models of three wetland birds in Mental Modeler.Water depth, food availability and disease with system-wide influence would have profound impacts on bird abundance.Wildlife managers can use the tool in similar ecological contexts with even poor data, and easily interpret the results.

In this work a combinatorial description is provided of a Faa di Bruno type Hopf algebra which naturally appears in the context of Fliess operators in nonlinear feedback control theory. It is a connected graded commutative and non-cocommutative Hopf algebra defined on rooted circle trees. A cancellation free forest formula for its antipode is given., Comment: revised and updated

As devotion to a recreational activity increases with specialization, recreationists' ecological understanding (i.e., mental models) of the resource system is also expected to change. To test this hypothesis, we collected cognitive maps of northern pike (Esox lucius) ecology from anglers (N=235) and assessed their relation to anglers' level of specialization and preferred target species. We also compared angler cognitive maps with cognitive maps collected from fisheries scientists (N=17) to examine if increased specialization among anglers led to similar ecological understanding of formally-trained fishery professionals. Our results indicate that, regardless of target species, as anglers become more specialized they tend to refine their structural understanding of pike ecology by simplifying relations among the ecological factors that affect pike populations. Further, although the refined ecological understanding of more specialized anglers' was found to be structurally dissimilar to experts, the mental models of pike ecology of more specialized anglers, particularly those with experience of the target species pike, were found to be functionally similar to how trained fisheries biologists viewed pike ecology. Our results suggest that more specialized anglers develop simple heuristics to deal with complex ecological issues, which may in turn affect the uptake of information and the acceptability of management actions designed by agencies and managers. Management implications We present a quantitative method for measuring how anglers perceive the ecology of an exploited species (northern pike, E. lucius) using a combination of semi-quantitative fuzzy cognitive mapping and network metrics. The key finding is that as angler specialization increases, the knowledge of ecological dynamics is refined leading to mental models that are structurally different from academically trained fisheries biologists, but that behave functionally similar to experts. • Similar perceived functionality of key management interventions suggest limited conflict potential among pike managers and more specialized anglers with regards to acceptance of management policies. • Specialized anglers can be expected to perceive ecological dynamics similarly to academically trained fisheries scientists and thus may be allies in support of common management tools. • The simplification of mental models in highly specialized anglers suggest variation in how different anglers learn and uptake new ecological knowledge, which has implications for the design of outreach strategies.

The nonlinear system identification problem is solved for a multivariable nonlinear input–output system that can be represented in terms of a Chen–Fliess functional expansion. The problem is formulated in terms of a regression which is linear in the parameters and has a nonlinear regressor. An inductive implementation of the nonlinear regressor is developed using the underlying noncommutative algebraic and combinatorial structures. The method is demonstrated in an adaptive control application involving a two-input, two-output Lotka–Volterra dynamical system.

Coastal island communities face significant risks associated with increased natural hazards and other impacts associated with climate change. Further, deeply rooted social issues, lack of awareness or information, and inadequate infrastructure and planning may exacerbate risks to island socio-ecological systems. Understanding these relationships is often difficult, given the lack of methods available for communities to explicitly explore anticipated risks and potential adaptation strategies, in relation to the characteristics of their community socio-ecological system. Social learning has also been shown to foster adaptation to environmental changes, build social trust and empower diverse stakeholders, by offering opportunities for groups of individuals to challenge, negotiate and propose new norms, policies or programs. We present a three-phase social learning framework to facilitate stakeholder-driven scenario-based modeling, in order to inform community disaster planning in relation to the potential impacts of a tsunami. The participatory research was conducted in conjunction with a community disaster committee, representing the communities of the North Shore of O‘ahu, Hawai‘i. Through a series of iterative participatory modeling workshops using fuzzy-logic cognitive mapping, the community committee represented, explored and actively questioned their beliefs about the natural hazards that their community faces. Further, the modeling process allowed the committee to represent the communities’ dynamic nature, run tsunami hazard scenarios to quantify potential direct and indirect effects, and explicitly compare trade-offs of competing adaptation strategies. Changes in the committee's model representations that took place over time demonstrate a progression through single-, double- and triple-loop learning, indicating that social learning occurred across individual to institutional levels, and over short- to long-term time scales.

Given two nonlinear input-output systems written in terms of Chen-Fliess functional expansions, it is known that the feedback interconnected system is always well defined and in the same class. An explicit formula for the generating series of a single-input, single-output closed-loop system was provided by the first two authors in earlier work via Hopf algebra methods. This paper is a sequel. It has four main innovations. First, the full multivariable extension of the theory is presented. Next, a major simplification of the basic set up is introduced using a new type of grading that has recently appeared in the literature. This grading also facilitates a fully recursive algorithm to compute the antipode of the Hopf algebra of the output feedback group, and thus, the corresponding feedback product can be computed much more efficiently. The final innovation is an improved convergence analysis of the antipode operation, namely, the radius of convergence of the antipode is computed., Comment: background material expanded and reorganized, a few typos fixed

Departing from the traditional agricultural model of input-heavy, intensive agriculture via the use of agrochemicals and irrigated water, many international development projects have started to promote conservation agriculture in developing countries. However, relying solely on technical expertise, largely generated outside the rural communities in which they are applied, often does not consider whether local ecological and culturally influenced beliefs are consistent with the technologies being promoted for adoption. We suggest these disconnects can be linked to differing ‘mental models’ of scientific experts and rural agricultural communities regarding the nature of farming dynamics and predicted impacts of introduced farming practices. Using an agricultural development project in Nepal as a case study, this research seeks to understand the relationship between trends in expert and rural farmer reasoning and predictions regarding the outcomes associated with development technology based on these beliefs. Further, we seek to compare these mental model-based differences with local environmental conditions (using soil measurements) and agricultural outcomes in terms of farm production (i.e. yield). While researchers’ mental models predicted that minimum tillage would improve yield, mental models from two of the three villages predicted that yield would decrease. Local soil and yield measurements support the farmers’ mental model predictions. Our results indicated that conservation agriculture techniques should not be applied universally, development practitioners should engage in a two-way learning with local communities to benefit from locally situated knowledge.

Over the course of a school year, a high school biology class and a local watershed partnership worked together to design a study to determine the willingness to pay for ecosystem service restoration in a local degraded watershed. With research control given to the teacher and her classroom as part of their in-class honors biology curriculum, the result was a student designed/written, and professionally structured, research manuscript. The aim of this collaboration was to: (1) integrate quantitative social science into the K–12 science curriculum to foster learning about the nature of social science investigation in a real world context; (2) create a community-based science partnership; and (3) generate social science data useful for decision-making that could withstand scientific peer review. In this commentary, we present the written product of the classrooms' work to illustrate the type of information that can be generated by a participatory science education program, along with a reflection from the students and project researchers about opportunities and barriers to conducting authentic social science research in K–12 classrooms.

Cultural ecosystem services (CES) substantially contribute to human wellbeing as the nonmaterial benefits of ecosystems. However, they remain poorly understood due to their often nonmarket and intangible nature. We analyzed management characteristics of coastal and watershed – based CES in contrast to provisioning and regulatory services from surveys of environmental managers in Hawaii. CES were the most frequently managed type of ecosystem service, a top management priority among local-scale decision-makers and nongovernmental organizations, and managed for security. However, only 10% of managers could articulate specific policies they used to manage CES. Follow-up interviews with a subset of managers further revealed that half of all CES managed were considered to benefit people beyond the spatial scale in which management decisions were made. Identifying management characteristics of CES will inform the development of indicators to monitor changes in CES, and develop policies that maintain the relationship between ecosystem function, CES and human wellbeing.

Critical barriers to adaptation to climate change include the timely detection and agreed definition of problems requiring adaptive action. In the context of local scale coastal management in north-western Europe, challenges to problem detection and identification are exacerbated by the diffuse nature of administrative, sectoral, and legal rights and other professional governance obligations. Yet, if adaptation is to progress in a manner that is both locally legitimate and in accord with national policies, climate signals must be detected and climate impact problems framed in similar ways by two key groups; local scale ‘bottom-up’ experts and decision makers, and national scale ‘top–down’ scientists and policy makers. With reference to case study sites in Ireland and Scotland, we employ participatory modelling with coastal stakeholders using Fuzzy Cognitive Mapping (FCM) to trial its potential in measuring and assessing stakeholder perceptions of climate vulnerability both individually and collectively. We found that FCM not only offers insight into the existing detection and framing of climate signals in coastal decision making but also provides a structured communication platform from which climate problems might be coherently integrated into future coastal management deliberations as the adaptation process matures.

A new type of Chen-Fliess series is first introduced which depends on the input and delayed versions of the input. It is then shown how a class of analytic differential delay systems with a single delay and constant initial conditions has input-output maps representable in terms of this new functional series. As in the classical case, the coefficients can be computed by iterated Lie derivatives, but here the method is applied to an infinite dimensional embedding of the original state space system. Finally, the more technical issue of series convergence is addressed. Sufficient conditions are produced to guarantee convergence in both a local and global sense.

The authors regret that “rheumatoid arthritis; cancer; or diabetes” were listed as examples of components in the “Tissue injury or pathology” category instead of the “Comorbidities” category in Table 2 on page 1035 of our article. Additionally, the last sentence in the “Outcomes” category was removed. The corrected Table 2 is shown below. The authors would like to apologize for any inconvenience this may have caused.

Integrating stakeholder knowledge into natural resource governance is considered to add flexibility to social–ecological systems (SES) because knowledge diversity reduces rigidity, represents multiple perspectives, and promotes adaptability in decision-making. Characterizing the differences between knowledge systems, however, is not easily accomplished. There are few metrics readily available to compare one knowledge system to another. This paper characterizes knowledge about a model SES, the summer flounder fishery in the mid-Atlantic, to evaluate differences and similarities in the structural and functional characteristics of stakeholder mental models. To measure these differences, we collected Fuzzy-Logic Cognitive Maps (FCM) from several stakeholder groups (managers, scientists, harvesters, pre and post harvest sectors, and environmental NGOs) which comprise social agents within the SES. We then compared stakeholder groups’ maps using graph theory indices to characterize the structure and function of the model system. We then combined stakeholder FCM to generate a community map which represents a theoretical model of the combination of stakeholder knowledge. Our study indicates that while there may be benefits to integrating knowledge in resource decision-making, it also has costs associated with it. Although integrating knowledge may increase structural knowledge, it may also decrease precision in understanding of how a system functions and be overly focused on driving components which would reduce the ability of decision-makers to predict system reaction to a decision or policy plan.

BACKGROUND CONTEXT Low back pain (LBP) is a bio-psycho-social condition and LBP patients are treated by various health professionals with different training and presumed beliefs. Considering that theoretical foundations and emphases vary among health disciplines, it is possible that these professionals (eg, researchers and clinicians from different disciplines) possess different “mental models” of what and how various factors relate to LBP. A novel way to investigate individual thinking about particular processes is through the development and analysis of fuzzy-logic cognitive maps (FCM). FCMs are particularly useful for modeling interactions between variables in complex systems, such as LBP. This study aimed to use this approach to describe similarities and differences by which different health professionals think about LBP. METHODS Participants from different disciplines (n=28), who have contributed significantly to the understanding of LBP (eg, publications, contributions to societies, etc.), were selectively recruited for this study and represented the following disciplines: (1) basic science (n=6), (2) chiropractic (n=4), (3) spine surgery (n=2), (4) physical medicine & rehabilitation (n=2), (5) physical or exercise therapy (n=12), and (6) psychology (n=2). Each participant underwent a structured one-on-one interview to construct an FCM that represented the individual's understanding (mental model) of how factors related to LBP using Mental Modeler software ( www.mentalmodeler.org ). This process involved nomination of factors contributing to patients’ outcomes (ie, pain, disability, and quality of life) and the weighting of the connections (strength of the effect) between these factors. Factors from each model were tabulated and categorized into eight domains: (1) nociceptive detection and processing, (2) behavioral or lifestyle (3) tissue injury or pathology, (4) contextual, (5) psychological(6) social or work, (7) biomechanical, and (8) individual factors. To determine the importance of each factor expressed in the FCM, centrality was computed as: Centrality = |a|*(# of connections in)+|b|*(# of connections out), where a and b are the weighting or strength of the connections. Based on this definition, centrality of a factor increases by the number of connections to and from the specific factor in the FCM, as well as by the weighting of these connections. Centrality of each domain (sum of centrality for each factor within the designated domain) was expressed as a percentage of the eight domains and grouped by discipline. RESULTS A total of 263 factors were generated from the 28 FCM. Psychological factors was the most prominent domain accounting for 33% of the centrality across all six participant groups, and was the most “central” domain for four groups (chiropractic, physical medicine and rehabilitation, physical or exercise therapy, and psychology). Tissue injury or pathology accounted for 14.7% of the centrality across all groups and was the most “central” for the remaining two groups (basic science and spinal surgery). CONCLUSIONS Psychological factors were considered to be the most central or important to understanding LBP across disciplines, yet many of these professions do not specialize in the psychology of LBP. Although the selection of individuals and the relatively small sample size representing each discipline may bias the results, such findings support the notion that multidisciplinary interventions (which includes consideration of psychological factors) to treating patients with LBP is sensible.

BACKGROUND CONTEXT Low back pain (LBP) is a very complex problem with numerous bio-psycho-social factors interacting to impact pain, disability, and quality of life. To understand the dynamics of such a complex problem, it needs to be studied in its entirety (systems approach). Although this concept is accepted by the scientific and clinical communities, much research to date is conducted by specialized teams focusing on isolated factors related to LBP. Such a reductionist approach may be useful in some circumstances, but it also creates barriers for integrating knowledge between disciplines and ultimately precludes the understanding of the dynamics of the entire LBP problem. To leverage the knowledge shared among various stakeholders, an innovative process called collaborative modeling was developed within the field of systems science specifically for enhancing the understanding of complex, multifactorial systems dynamics. This study assessed the feasibility of using this approach for integrating multidisciplinary knowledge of LBP. METHODS Participants (n=29), who have contributed significant knowledge to the area of LBP (eg publications, contributions to societies, etc.), were selectively recruited for this study and represented diverse disciplines: Basic Science (n=7), Chiropractic (n=4), Spine Surgery (n=2), Physical Medicine & Rehabilitation (n=2), Physical or Exercise Therapy (n=12), and Psychology (n=2). Each participant underwent a structured one-on-one interview to construct a fuzzy-logic cognitive map (FCM) (Mental Modeler software, www.mentalmodeler.org ) representing his or her understanding of how factors related to LBP interact and affect patient outcomes (pain, disability and quality of life). All individual FCMs were then converted to adjacency matrices and integrated into one meta-model (Gephi software, www.gephi.org ). To demonstrate the integrated meta-model's potential, various intervention strategies listed in all FCMs were simulated and their relative effects on pain, disability, and quality of life were investigated. RESULTS The meta-model, that integrated the understanding of LBP of all participants, consisted of 272 factors and 1,429 connections representing interactions among these factors. Simulations of individual treatment interventions predicted that combined aerobic exercise, counseling, and education are likely to be the most effective intervention to reduce pain. Meditation, followed by cognitive behavioral therapy, had the greatest impact on reducing disability and improving quality of life. CONCLUSIONS The integration of 29 FCMs, representing diverse participants’ views of LBP dynamics, resulted in a model that was extremely complex, but still feasible to produce meaningful interpretations. The simulations provided outcomes that broadly agreed with data in the literature, which suggests that aerobic exercise, counseling, education, meditation, and cognitive behavioral therapy are effective LBP interventions. Although the selection of participants and the relatively small sample size may influence the results, the findings suggest that it is possible to integrate multidisciplinary knowledge of LBP into one meta-model. This approach could provide the framework for a larger, community-wide platform for further development and refinement of this meta-model. Such a meta-model could then be used to simulate other “what if” scenarios, to identify gaps in knowledge, and to inform new essential research directions to ultimately improve patient care and outcomes for LBP.

This paper has three objectives. The first objective is to provide a simpler proof concerning a sufficient condition due to Ferfera under which bilinearity is preserved for cascade interconnections. The next objective is to provide a specific counterexample to show that this condition does not apply to the feedback connection. The final objective is to show that the well-known correspondence between rational series and formal power series recognized by weighted finite-state automata can be generalized to produce a correspondence between the generating series of cascaded and feedback connected bilinear systems and a class of weighted Petri nets.

This study directly measured the load acting on the abutment of the osseointegrated implant system of transfemoral amputees during level walking, and studied the variability of the load within and among amputees. Twelve active transfemoral amputees (age: 54 +/- 12 years, mass: 84.3 +/- 16.3 kg, height: 17.8 +/- 0.10 m) fitted with an osseointegrated implant for over 1 year participated in the study. The load applied on the abutment was measured during unimpeded, level walking in a straight line using a commercial six-channel transducer mounted between the abutment and the prosthetic knee. The pattern and the magnitude of the three-dimensional forces and moments were revealed. Results showed a low step-to-step variability of each subject, but a high subject-to-subject variability in local extrema of body-weight normalized forces and moments and impulse data. The high subject-to-subject variability suggests that the mechanical design of the implant system should be customized for each individual, or that a fit-all design should take into consideration the highest values of load within a broad range of amputees. It also suggests specific loading regime in rehabilitation training are necessary for a given subject. Thus the loading magnitude and variability demonstrated should be useful in designing an osseointegrated implant system better able to resist mechanical failure and in refining the rehabilitation protocol.

It is shown that the notion of balancing a state space realization about a stable, isolated equilibrium point can be generalized to systems possessing stable invariant regular submanifolds of arbitrary dimension, for example, a stable limit cycle. ycle.

Fliess operators as input–output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory. In the classical analysis of these operators, certain growth conditions on the coe3cients in their series representations insure uniform and absolute convergence, provided every input is uniformly bounded by some 4xed upperbound. In some emerging applications, however, it is more natural to consider other classes of inputs. In this paper, Lp function spaces are considered. In particular, it is shown that the classic growth conditions also provide su3cient conditions for convergence and continuity when the admissible inputs are from a ball in Lp[t0 ;t 0 + T ], where T is bounded and p ? 1. In addition, stronger global growth conditions are given that apply even for the case where T is unbounded. When the coe3cients of a Fliess operator have a state space representation, it is shown that the state space model will always locally realize the correspondinginput–output map on Lp[t0 ;t 0 + T ] for su3ciently small T? 0. If certain well-posedness conditions are satis4ed then the state space model will globally realized the input–output mapping for unbounded T when the coe3cients satisfy the global growth condition. c � 2002 Elsevier Science B.V. All rights reserved.

This paper extends earlier work on balanced realizations for smooth nonlinear systems to the discrete time setting. The main idea behind the global balanced structure, if it exists, is that the linearized system along a nominal solution is balanced in the usual linear time-varying sense. Hence the global nonlinear balanced system is defined as the one that closes the commutative diagram between linearization and balancing.

The physico-chemical properties of two anti-asthmatic drugs, salmeterol xinafoate and fluticasone propionate, have been studied in both aqueous and non-aqueous solvent environments. Ultraviolet-visible (UV-Vis) spectroscopy, fluorescence spectroscopy and electrospray ionisation mass spectrometry (ESI-MS) have been used to characterise the interaction of the drugs in 70:30 (v/v) methanol/water solutions. First derivative UV-Vis spectra measurements indicate that an interaction takes place between the two drugs in a binary solvent system. Fluorescence studies indicate that an increase in the concentration of fluticasone propionate results in a decrease in the fluorescence signal of the salmeterol for mixed solutions of the drugs. Analysis of a mixture of the two drug solutions using mass spectrometry also shows evidence of salmeterol-fluticasone propionate interaction and dimer formation with respect to both the salmeterol and the fluticasone propionate. Model metered dose inhalers (MDI) of both individual samples and mixtures of the drugs were formulated as suspensions in solvent CFC-113. The extent of deposition onto different inhaler components, such as the aluminium alloy canister, Teflon coated canister and the metering valve was evaluated by high-performance liquid chromatography (HPLC) of the methanol/water washings of the deposited drug(s). Changing the nature of the surface properties of the container resulted in a significant difference in the extent of deposition. The deposition of the individual drugs was found to increase as the dispersion concentration of the drug increases. However, the formulation based on a combination of the two drugs was found to show different deposition behaviour compared to the individual drug formulations. The deposition of the drugs, onto the aluminium alloy canister and the metering valve, decreases as the combined dispersion concentration of the two drug increases.

This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel operators, and controllability and observability functions will be derived based on it. Furthermore a duality between the controllability and observability functions will be proven. The statespace realizations ofsuch operators provide new insights to nonlinear control systems theory.

A generalization of the zero-state observability function is considered for nonlinear systems. The linear time-invariant case is considered as an application in model reduction problems.

In linear system theory, Gramian matrices help quantify the input-tostate and state-to-output interactions in a state space model. In this paper two different existing generalizations of this idea are examined for the case of a stable bilinear system. One method is based on using the L 2 norm to measure signal sizes and leads to the notion of the controllability and observability functions, which are referred to collectively as energy functions. The other method is motivated by introducing algebraic generalizations of the linear system Lyapunov equations, the solutions of which are called the algebraic Gramians. While these generalizations are distinct, in this paper some new relationships between the two approaches are presented.