This document discusses the application of S-shaped curves, also known as logistic curves or S-curves, to model the evolution of systems over time. It provides background on the origin and development of S-curves as models of growth. S-curves have been widely used across many domains to describe trends like population growth, market penetration of new technologies, and diffusion of innovations. The document reviews several examples of S-curve applications and discusses their use in areas like technological forecasting and TRIZ problem solving. It argues that S-curves provide forecasting power because growth is ultimately limited by scarce resources based on mathematical concepts like Verhulst's logistic growth equation.
This document presents research analyzing net migration between Portuguese regions from 1996-2002 at the NUTS II level and 1991 and 2001 at the NUTS III level. Theoretical models of migration determinants are discussed, and empirical analysis is conducted using statistical data from the Portuguese National Institute of Statistics. Regression analysis finds that at the NUTS II level, real output growth positively impacts migration while unemployment and agricultural employment negatively impact it. At the NUTS III level, amenities like housing availability are also important determinants of migration.
This study explores a potential reposition of the triple helix model of university-industry-government relations in terms of micro-level analysis. In this direction, we evaluate the development of helix theory over time, by reviewing the relevant literature divided into three successive phases: the phase of theoretical foundation, the phase of conceptual expansion, and the phase of recent developments and systematic attempts of implementation. In this conceptual study, we estimate that a refocused triple helix model in terms of local development, by placing at the center of analysis the “living organization’s” dynamics in Stra.Tech.Man terms (synthesis of Strategy-Technology-Management), can be a possible direction of analytical enrichment.
The document provides documentation and a tutorial for implementing an S-curve motion profile in a MyoStat Motion Control system. An S-curve allows for smooth acceleration and deceleration during motion to prevent damage. The K69 parameter controls the S-curve function, with higher values creating a more pronounced curve. The tutorial instructs the user to set parameters, collect speed data, and graph results at different K69 values to observe the S-curve motion profile.
This document describes proposed changes to improve a model for estimating project S-curves based on project attributes and conditions. The key changes are:
1. Changing the model outputs from the polynomial function's parameters (a, b) to the inflection point position (p) and slope (s), which better indicate schedule performance.
2. Adding two new input factors - project difficulty and participant competence - to capture schedule influences beyond basic attributes like cost and duration.
3. Using fuzzy inference systems instead of neural networks to build transparent input-output relationships from historical project data, applying fuzzy clustering and hybrid training.
The goal is to develop a model that more accurately predicts project progress curves by incorporating schedule performance indicators
1) The document discusses the application of S-shaped logistic growth curves to model and forecast technological trends over time.
2) It specifically fits a logistic curve to data on annual TRIZ publications from 1996-2006 to illustrate the three parameters (κ, α, β) of the simple logistic model.
3) The ceiling parameter κ represents the expected maximum number of future publications, the growth period parameters α and β specify the linear-like growth phase, and tm indicates the midpoint time of the symmetric S-curve.
This document presents research analyzing net migration between Portuguese regions from 1996-2002 at the NUTS II level and 1991 and 2001 at the NUTS III level. Theoretical models of migration determinants are discussed, and empirical analysis is conducted using statistical data from the Portuguese National Institute of Statistics. Regression analysis finds that at the NUTS II level, real output growth positively impacts migration while unemployment and agricultural employment negatively impact it. At the NUTS III level, amenities like housing availability are also important determinants of migration.
This study explores a potential reposition of the triple helix model of university-industry-government relations in terms of micro-level analysis. In this direction, we evaluate the development of helix theory over time, by reviewing the relevant literature divided into three successive phases: the phase of theoretical foundation, the phase of conceptual expansion, and the phase of recent developments and systematic attempts of implementation. In this conceptual study, we estimate that a refocused triple helix model in terms of local development, by placing at the center of analysis the “living organization’s” dynamics in Stra.Tech.Man terms (synthesis of Strategy-Technology-Management), can be a possible direction of analytical enrichment.
The document provides documentation and a tutorial for implementing an S-curve motion profile in a MyoStat Motion Control system. An S-curve allows for smooth acceleration and deceleration during motion to prevent damage. The K69 parameter controls the S-curve function, with higher values creating a more pronounced curve. The tutorial instructs the user to set parameters, collect speed data, and graph results at different K69 values to observe the S-curve motion profile.
This document describes proposed changes to improve a model for estimating project S-curves based on project attributes and conditions. The key changes are:
1. Changing the model outputs from the polynomial function's parameters (a, b) to the inflection point position (p) and slope (s), which better indicate schedule performance.
2. Adding two new input factors - project difficulty and participant competence - to capture schedule influences beyond basic attributes like cost and duration.
3. Using fuzzy inference systems instead of neural networks to build transparent input-output relationships from historical project data, applying fuzzy clustering and hybrid training.
The goal is to develop a model that more accurately predicts project progress curves by incorporating schedule performance indicators
1) The document discusses the application of S-shaped logistic growth curves to model and forecast technological trends over time.
2) It specifically fits a logistic curve to data on annual TRIZ publications from 1996-2006 to illustrate the three parameters (κ, α, β) of the simple logistic model.
3) The ceiling parameter κ represents the expected maximum number of future publications, the growth period parameters α and β specify the linear-like growth phase, and tm indicates the midpoint time of the symmetric S-curve.
This document discusses three frameworks used by Gartner Group to analyze information systems research: the technology maturity curve, adoption curve, and identification of strategic technologies. The maturity curve tracks how a technology matures over time through various stages from embryonic to obsolescence. The adoption curve shows how technologies are adopted cumulatively by organizations over time. Considering where technologies fall on these curves can provide insights into appropriate research questions and methodologies. Identifying strategic technologies may help determine promising areas for new research.
This document describes proposed changes to improve a model for estimating project S-curves based on project attributes and conditions. The key changes are:
1. Changing the model outputs from the polynomial function's parameters (a, b) to the inflection point position (p) and slope (s), which better indicate schedule performance.
2. Adding two new input factors - project difficulty and participant competence - to capture schedule influences beyond basic attributes like cost and duration.
3. Using fuzzy inference systems instead of neural networks to build transparent input-output relationships from historical project data, applying fuzzy clustering and hybrid training.
The goal is to develop a model that more accurately predicts project progress curves by incorporating schedule performance indicators
This document discusses technology S-curves and their implications for renewable energy alternatives. It finds that both wind and geothermal energy are poised to become more economical than fossil fuels relatively soon based on historical data. Government R&D funding has been lower for wind and geothermal compared to solar, and funding for fossil fuels may be excessive given their diminishing performance. Analyzing renewable technologies through an S-curve lens provides insights not found using other approaches and has implications for future government and industry investment decisions.
The document discusses an S-curve model that relates per-capita income to insurance penetration. It finds:
1) Estimating life and non-life insurance penetration globally yields an S-curve, where income elasticity starts and ends at 1 but exceeds 1 at intermediate income levels.
2) For life insurance, the income at maximum elasticity is $15,000, while for non-life it is $10,000.
3) Using purchasing power parities rather than market exchange rates increases estimated penetration levels and elasticities for developing countries.
Tinjauan pustaka membahas konsep-konsep dasar listrik seperti arus listrik, tegangan, hambatan, hukum Ohm, dan pengukuran parameter listrik menggunakan alat pengukur seperti voltmeter dan amperemeter. Dibahas pula jenis-jenis resistor dan susunan resistor dalam rangkaian listrik.
The document provides documentation and a tutorial for implementing an S-curve motion profile in a MyoStat Motion Control system. An S-curve allows for smooth acceleration and deceleration during motion to prevent damage. The K69 parameter controls the S-curve function, with higher values creating a more pronounced curve. The tutorial instructs the user to set parameters, collect speed data, and graph results at different K69 values to observe the S-curve motion profile.
Ringkasan dokumen tersebut adalah:
1) Dokumen tersebut membahas tentang konsep dan teori kemiskinan menurut pandangan Islam dan model-model kemiskinan.
2) Pendidikan dianggap sebagai kebutuhan dasar manusia menurut model kebutuhan Galtung.
3) Terdapat berbagai faktor yang dapat menyebabkan terperangkapnya seseorang dalam kemiskinan seperti rendahnya pendidikan dan kesehatan.
The document discusses S curves, which are graphs of cumulative quantities like man-hours or costs plotted against time. It describes different types of S curves including baseline, target, and actual S curves. Baseline S curves show planned progress, target S curves show expected progress if tasks are completed as scheduled, and actual S curves show progress to date based on percentage completion. The document also discusses how to interpret and generate different types of S curves to analyze project schedule performance, progress, slippage, and other metrics.
It is a recent development in the field of Computer science, used to encode information within an abstract picture.Even though it provides same level of security as the bar codes, it ensures encoding of more amount of data as compared to the traditional ways of encoding.
Briefly respond to all the following questions. Make sure to explaVannaSchrader3
Briefly respond to all the following questions. Make sure to explain and backup your responses with facts and examples. This assignment should be in APA format and have to include at least two references.
Faced with the need to deliver risk ratings for your organization, you will have to substitute the organization’s risk preferences for your own. For, indeed, it is the organization’s risk tolerance that the assessment is trying to achieve, not each assessor’s personal risk preferences.
1. 1. What is the risk posture for each particular system as it contributes to the overall risk posture of the organization?
2. 2. How does each attack surface – its protections if any, in the presence (or absence) of active threat agents and their capabilities, methods, and goals through each situation—add up to a system’s particular risk posture?
3. 3. In addition, how do all the systems’ risks sum up to an organization’s computer security risk posture?
Complexity, Governance & Networks (2014) 71–78 71
DOI: 10.7564/14-CGN9
Complexity Theory and Its Evolution in Public
Administration and Policy Studies
L. Douglas Kiel
University of Texas at Dallas, School of Economic, Political and Policy Sciences
800 W. Campbell Road, Richardson, TX 75080 USA, 972-883-2019
E-mail: [email protected]
This paper traces the evolution of the application of the complexity sciences in the literature
of public administration and public policy. A four stage evolutionary model is used to track the
development of this literature. The evolution of the literature has now reached a third evolution-
ary stage. This third stage is a proliferant stage in the development of the literature in which
applications and knowledge production has increased dramatically.
Keywords: Complexity sciences, evolution, emergence, convergence, proliference, divergence,
public administration and policy studies.
1. Introduction
We are fortunate to live in a historical period of both rapid and substantial change.
This is a period in which human knowledge accumulates at rates that exacerbate efforts
to accommodate and store this knowledge. Keeping up with the accumulated knowledge
requires a singular focus that is rare in a world of continuous partial attention. The accel-
eration of knowledge as a global resource is also reflected in the acceleration of knowledge
regarding complexity studies in public administration and public policy. The period of
early research in this area has evolved, over the last quarter century, into a period of pro-
liferation in which scholars have applied an increasing array of methods to examine the
behaviors of complex governance, administrative, and policy systems.
In this paper I strive to explore the evolution of complexity studies in public admin-
istration and public policy. In particular, I view the knowledge accumulation in this area as
an evolutionary process. Tracing the evolution of what and how we know does not reduce
the uncertaint ...
The document discusses the application of S-shaped logistic growth curves for technological forecasting. It provides definitions for key terms related to logistic growth curves, including parameters like the asymptotic limit (κ), growth rate (α), and midpoint time (β). An example is given fitting an S-curve to past data on TRIZ publications to estimate parameters and potentially extrapolate future trends. The document advocates that S-curves can provide accurate forecasts if fitted quantitatively to sufficient past data rather than drawn arbitrarily. It also discusses using knowledge of limiting resources and causal factors when data is limited.
This document introduces the MISC (Mapping Innovations on the Sustainability Curve) methodology, which aims to accelerate the transition to sustainability. It does this through a participatory process using systems mapping based on insights from systems theory and process ecology. The maps reflect the sustainability curve, which shows that systems are most sustainable when they balance efficiency and resilience through appropriate diversity and interconnectivity. The MISC process involves stakeholders mapping their system and innovations to leverage transition points. It has been tested positively in several contexts as a way to facilitate cooperation across sectors in discussing sustainability transitions.
An Empirical And Theoretical Literature Review On Endogenous Growth In Latin ...Wendy Hager
This document provides a literature review on endogenous growth in Latin American economies. It summarizes three major theories of economic growth:
1) Neoclassical growth theory from the 1950s-1970s which viewed capital accumulation and technology as the main drivers of growth. This theory faced criticisms for treating factors like savings as exogenous.
2) Endogenous growth theory from the 1980s onward which endogenized technology and viewed factors like human capital and spillover effects from innovation as generating long-term growth.
3) The evolution of growth theory and its application to understanding economic growth in Latin American countries in recent decades, with a focus on factors like financial development, structural reforms, and institutions.
A triple helix system for knowledge based regional developmentIvan Kuznetsov
This document proposes introducing the concept of "Triple Helix Spaces" to describe the interaction between university, industry, and government spheres over time in knowledge-based regional development. It identifies three spaces: the Knowledge Space, Innovation Space, and Consensus Space. The Knowledge Space refers to the concentration of academic resources in a region. The Innovation Space describes how venture capital can intensify commercializing new technologies from universities. And the Consensus Space represents collaboration between regional leadership in academia, industry, and government to develop strategic plans. These spaces provide a framework for analyzing how regions transition from one Triple Helix configuration to another during economic renewal processes.
This document discusses theoretical ecology, which uses theoretical methods such as mathematical models, computational simulations, and data analysis to study ecological systems. It provides examples of different types of mathematical models used to model population dynamics and species interactions, including exponential growth models, logistic growth models, structured population models using matrices, predator-prey models, host-pathogen models, and competition/mutualism models. It also discusses how theoretical ecology aims to explain a variety of ecological phenomena and how computational modeling has benefited from increased computing power.
REGIONS and THIRD PLACES - Valuing and Evaluating Creativity for Sustainable ...Christiaan Weiler
In this presentation I will try to put culture and creativity in a specific context, including theoretical references, but concentrating on a practical approach. With outcomes of an action-research project three connected hypothesis are proposed. To complement the otherwise rather limited quantitative data for this relatively new subject, a collaborative methodology is proposed, that will help contextualize the work and directly engage stakeholders in the process.
To stay close to the title of the conference, I will focus on the elements concerning culture and creativity. Giving a purpose to culture and creativity can allow us to concentrate on what it does rather than what it is. The presented research project (still in search of funding...) positions culture in a strategic role for collaborative processes, and proposes the creative stance, as an alternative to the critical stance, for innovative governance and planning development.
The document discusses patterns of technological substitution that challenge the traditional S-curve model. It presents several historical examples that demonstrate more complex substitution patterns than the smooth S-curve, including: concatenated generations in steelmaking technologies; overlapping generations in IBM mainframe computers; and a case of long-term feedback reversing the substitution of DDT as an insecticide due to environmental concerns. The author argues that accounting for these complex real-world patterns requires broadening the theoretical framework for understanding technological substitutions.
Entropy law and the impossibility of perpetual economic growthKalasekar M
This document discusses the thermodynamic and ecological limitations of perpetual economic growth. It argues that while previous economic models have considered resource depletion and pollution, they fail to fully account for the entropy law and ecosystem services. The production and recycling process inevitably increases entropy and depletes finite ecosystem services. Depletion of critical ecosystem services can cause nonlinear environmental changes that disrupt the ability of markets to adapt. Given uncertainties around environmental thresholds, indefinite material economic growth carries an unacceptable risk of catastrophic impacts. The document concludes that responsible economic policy must avoid enforcing growth that exceeds sustainable levels.
The Schumacher Institute submitted a response to the Labour Party's consultation on developing an industrial strategy. Some key points made in the submission include:
- An industrial strategy should be based on principles of being challenge-led, mission-oriented, and values-driven, with a priority on sustainability.
- Fundamental ecosystem and social challenges like resource depletion, climate change, and inequality must inform the strategy.
- Concepts like the green economy, circular economy, and ideas around a "safe and just operating space" could help address these challenges through economic transformation.
- The strategy and policies should support mission-led businesses, corporate governance reform, localisation, and socio-technical innovation to enable the
Economic Growth Models and the Role of Physical ResourcesBenjamin Warr
Conventional economic theory assumes that technological progress is exogenous and that resource consumption is a consequence, not a cause, of growth. The reality is more complex. In effect energy consumption is just as much a driver or economic growth as it is a consequence.
Robert Merton adopted the Biblical parable, "the rich get richer and the poor get poorer," (Matthew, 13:12) in explaining the disproportionate credit given to eminent scientists relative to similar contributions from unknown scientists. In doing so, he established a basic sociological effect spanning, "...in varying degrees every social institution..." This pdf traces a brief history of scientific citations, establishes its relationship to models of relative proportionate growth and extends it to nonscalable randomness and/or extreme value theory. Along the way, "hot hands" in streaks of success are also considered.
A Matter Of Opinion How Ecological And Neoclassical Environmental Economists...Rick Vogel
This document discusses a survey of economic sustainability researchers from Germany on their views related to sustainability and economics. The survey aimed to understand how researchers from different schools of thought view these issues and how they group themselves. Key results include:
- Two primary clusters were identified, one largely representing the ecological economics school of thought and the other capturing the neoclassical view.
- However, both clusters shared a conceptual definition of sustainability that considers ecological, social and economic dimensions, and aims to preserve society's development potentials.
- Both clusters also agreed on critiquing "pure economic growth" strategies and identified many overlapping future research topics.
- Main divides were on how to achieve sustainability, including suitable policy measures.
This document discusses three frameworks used by Gartner Group to analyze information systems research: the technology maturity curve, adoption curve, and identification of strategic technologies. The maturity curve tracks how a technology matures over time through various stages from embryonic to obsolescence. The adoption curve shows how technologies are adopted cumulatively by organizations over time. Considering where technologies fall on these curves can provide insights into appropriate research questions and methodologies. Identifying strategic technologies may help determine promising areas for new research.
This document describes proposed changes to improve a model for estimating project S-curves based on project attributes and conditions. The key changes are:
1. Changing the model outputs from the polynomial function's parameters (a, b) to the inflection point position (p) and slope (s), which better indicate schedule performance.
2. Adding two new input factors - project difficulty and participant competence - to capture schedule influences beyond basic attributes like cost and duration.
3. Using fuzzy inference systems instead of neural networks to build transparent input-output relationships from historical project data, applying fuzzy clustering and hybrid training.
The goal is to develop a model that more accurately predicts project progress curves by incorporating schedule performance indicators
This document discusses technology S-curves and their implications for renewable energy alternatives. It finds that both wind and geothermal energy are poised to become more economical than fossil fuels relatively soon based on historical data. Government R&D funding has been lower for wind and geothermal compared to solar, and funding for fossil fuels may be excessive given their diminishing performance. Analyzing renewable technologies through an S-curve lens provides insights not found using other approaches and has implications for future government and industry investment decisions.
The document discusses an S-curve model that relates per-capita income to insurance penetration. It finds:
1) Estimating life and non-life insurance penetration globally yields an S-curve, where income elasticity starts and ends at 1 but exceeds 1 at intermediate income levels.
2) For life insurance, the income at maximum elasticity is $15,000, while for non-life it is $10,000.
3) Using purchasing power parities rather than market exchange rates increases estimated penetration levels and elasticities for developing countries.
Tinjauan pustaka membahas konsep-konsep dasar listrik seperti arus listrik, tegangan, hambatan, hukum Ohm, dan pengukuran parameter listrik menggunakan alat pengukur seperti voltmeter dan amperemeter. Dibahas pula jenis-jenis resistor dan susunan resistor dalam rangkaian listrik.
The document provides documentation and a tutorial for implementing an S-curve motion profile in a MyoStat Motion Control system. An S-curve allows for smooth acceleration and deceleration during motion to prevent damage. The K69 parameter controls the S-curve function, with higher values creating a more pronounced curve. The tutorial instructs the user to set parameters, collect speed data, and graph results at different K69 values to observe the S-curve motion profile.
Ringkasan dokumen tersebut adalah:
1) Dokumen tersebut membahas tentang konsep dan teori kemiskinan menurut pandangan Islam dan model-model kemiskinan.
2) Pendidikan dianggap sebagai kebutuhan dasar manusia menurut model kebutuhan Galtung.
3) Terdapat berbagai faktor yang dapat menyebabkan terperangkapnya seseorang dalam kemiskinan seperti rendahnya pendidikan dan kesehatan.
The document discusses S curves, which are graphs of cumulative quantities like man-hours or costs plotted against time. It describes different types of S curves including baseline, target, and actual S curves. Baseline S curves show planned progress, target S curves show expected progress if tasks are completed as scheduled, and actual S curves show progress to date based on percentage completion. The document also discusses how to interpret and generate different types of S curves to analyze project schedule performance, progress, slippage, and other metrics.
It is a recent development in the field of Computer science, used to encode information within an abstract picture.Even though it provides same level of security as the bar codes, it ensures encoding of more amount of data as compared to the traditional ways of encoding.
Briefly respond to all the following questions. Make sure to explaVannaSchrader3
Briefly respond to all the following questions. Make sure to explain and backup your responses with facts and examples. This assignment should be in APA format and have to include at least two references.
Faced with the need to deliver risk ratings for your organization, you will have to substitute the organization’s risk preferences for your own. For, indeed, it is the organization’s risk tolerance that the assessment is trying to achieve, not each assessor’s personal risk preferences.
1. 1. What is the risk posture for each particular system as it contributes to the overall risk posture of the organization?
2. 2. How does each attack surface – its protections if any, in the presence (or absence) of active threat agents and their capabilities, methods, and goals through each situation—add up to a system’s particular risk posture?
3. 3. In addition, how do all the systems’ risks sum up to an organization’s computer security risk posture?
Complexity, Governance & Networks (2014) 71–78 71
DOI: 10.7564/14-CGN9
Complexity Theory and Its Evolution in Public
Administration and Policy Studies
L. Douglas Kiel
University of Texas at Dallas, School of Economic, Political and Policy Sciences
800 W. Campbell Road, Richardson, TX 75080 USA, 972-883-2019
E-mail: [email protected]
This paper traces the evolution of the application of the complexity sciences in the literature
of public administration and public policy. A four stage evolutionary model is used to track the
development of this literature. The evolution of the literature has now reached a third evolution-
ary stage. This third stage is a proliferant stage in the development of the literature in which
applications and knowledge production has increased dramatically.
Keywords: Complexity sciences, evolution, emergence, convergence, proliference, divergence,
public administration and policy studies.
1. Introduction
We are fortunate to live in a historical period of both rapid and substantial change.
This is a period in which human knowledge accumulates at rates that exacerbate efforts
to accommodate and store this knowledge. Keeping up with the accumulated knowledge
requires a singular focus that is rare in a world of continuous partial attention. The accel-
eration of knowledge as a global resource is also reflected in the acceleration of knowledge
regarding complexity studies in public administration and public policy. The period of
early research in this area has evolved, over the last quarter century, into a period of pro-
liferation in which scholars have applied an increasing array of methods to examine the
behaviors of complex governance, administrative, and policy systems.
In this paper I strive to explore the evolution of complexity studies in public admin-
istration and public policy. In particular, I view the knowledge accumulation in this area as
an evolutionary process. Tracing the evolution of what and how we know does not reduce
the uncertaint ...
The document discusses the application of S-shaped logistic growth curves for technological forecasting. It provides definitions for key terms related to logistic growth curves, including parameters like the asymptotic limit (κ), growth rate (α), and midpoint time (β). An example is given fitting an S-curve to past data on TRIZ publications to estimate parameters and potentially extrapolate future trends. The document advocates that S-curves can provide accurate forecasts if fitted quantitatively to sufficient past data rather than drawn arbitrarily. It also discusses using knowledge of limiting resources and causal factors when data is limited.
This document introduces the MISC (Mapping Innovations on the Sustainability Curve) methodology, which aims to accelerate the transition to sustainability. It does this through a participatory process using systems mapping based on insights from systems theory and process ecology. The maps reflect the sustainability curve, which shows that systems are most sustainable when they balance efficiency and resilience through appropriate diversity and interconnectivity. The MISC process involves stakeholders mapping their system and innovations to leverage transition points. It has been tested positively in several contexts as a way to facilitate cooperation across sectors in discussing sustainability transitions.
An Empirical And Theoretical Literature Review On Endogenous Growth In Latin ...Wendy Hager
This document provides a literature review on endogenous growth in Latin American economies. It summarizes three major theories of economic growth:
1) Neoclassical growth theory from the 1950s-1970s which viewed capital accumulation and technology as the main drivers of growth. This theory faced criticisms for treating factors like savings as exogenous.
2) Endogenous growth theory from the 1980s onward which endogenized technology and viewed factors like human capital and spillover effects from innovation as generating long-term growth.
3) The evolution of growth theory and its application to understanding economic growth in Latin American countries in recent decades, with a focus on factors like financial development, structural reforms, and institutions.
A triple helix system for knowledge based regional developmentIvan Kuznetsov
This document proposes introducing the concept of "Triple Helix Spaces" to describe the interaction between university, industry, and government spheres over time in knowledge-based regional development. It identifies three spaces: the Knowledge Space, Innovation Space, and Consensus Space. The Knowledge Space refers to the concentration of academic resources in a region. The Innovation Space describes how venture capital can intensify commercializing new technologies from universities. And the Consensus Space represents collaboration between regional leadership in academia, industry, and government to develop strategic plans. These spaces provide a framework for analyzing how regions transition from one Triple Helix configuration to another during economic renewal processes.
This document discusses theoretical ecology, which uses theoretical methods such as mathematical models, computational simulations, and data analysis to study ecological systems. It provides examples of different types of mathematical models used to model population dynamics and species interactions, including exponential growth models, logistic growth models, structured population models using matrices, predator-prey models, host-pathogen models, and competition/mutualism models. It also discusses how theoretical ecology aims to explain a variety of ecological phenomena and how computational modeling has benefited from increased computing power.
REGIONS and THIRD PLACES - Valuing and Evaluating Creativity for Sustainable ...Christiaan Weiler
In this presentation I will try to put culture and creativity in a specific context, including theoretical references, but concentrating on a practical approach. With outcomes of an action-research project three connected hypothesis are proposed. To complement the otherwise rather limited quantitative data for this relatively new subject, a collaborative methodology is proposed, that will help contextualize the work and directly engage stakeholders in the process.
To stay close to the title of the conference, I will focus on the elements concerning culture and creativity. Giving a purpose to culture and creativity can allow us to concentrate on what it does rather than what it is. The presented research project (still in search of funding...) positions culture in a strategic role for collaborative processes, and proposes the creative stance, as an alternative to the critical stance, for innovative governance and planning development.
The document discusses patterns of technological substitution that challenge the traditional S-curve model. It presents several historical examples that demonstrate more complex substitution patterns than the smooth S-curve, including: concatenated generations in steelmaking technologies; overlapping generations in IBM mainframe computers; and a case of long-term feedback reversing the substitution of DDT as an insecticide due to environmental concerns. The author argues that accounting for these complex real-world patterns requires broadening the theoretical framework for understanding technological substitutions.
Entropy law and the impossibility of perpetual economic growthKalasekar M
This document discusses the thermodynamic and ecological limitations of perpetual economic growth. It argues that while previous economic models have considered resource depletion and pollution, they fail to fully account for the entropy law and ecosystem services. The production and recycling process inevitably increases entropy and depletes finite ecosystem services. Depletion of critical ecosystem services can cause nonlinear environmental changes that disrupt the ability of markets to adapt. Given uncertainties around environmental thresholds, indefinite material economic growth carries an unacceptable risk of catastrophic impacts. The document concludes that responsible economic policy must avoid enforcing growth that exceeds sustainable levels.
The Schumacher Institute submitted a response to the Labour Party's consultation on developing an industrial strategy. Some key points made in the submission include:
- An industrial strategy should be based on principles of being challenge-led, mission-oriented, and values-driven, with a priority on sustainability.
- Fundamental ecosystem and social challenges like resource depletion, climate change, and inequality must inform the strategy.
- Concepts like the green economy, circular economy, and ideas around a "safe and just operating space" could help address these challenges through economic transformation.
- The strategy and policies should support mission-led businesses, corporate governance reform, localisation, and socio-technical innovation to enable the
Economic Growth Models and the Role of Physical ResourcesBenjamin Warr
Conventional economic theory assumes that technological progress is exogenous and that resource consumption is a consequence, not a cause, of growth. The reality is more complex. In effect energy consumption is just as much a driver or economic growth as it is a consequence.
Robert Merton adopted the Biblical parable, "the rich get richer and the poor get poorer," (Matthew, 13:12) in explaining the disproportionate credit given to eminent scientists relative to similar contributions from unknown scientists. In doing so, he established a basic sociological effect spanning, "...in varying degrees every social institution..." This pdf traces a brief history of scientific citations, establishes its relationship to models of relative proportionate growth and extends it to nonscalable randomness and/or extreme value theory. Along the way, "hot hands" in streaks of success are also considered.
A Matter Of Opinion How Ecological And Neoclassical Environmental Economists...Rick Vogel
This document discusses a survey of economic sustainability researchers from Germany on their views related to sustainability and economics. The survey aimed to understand how researchers from different schools of thought view these issues and how they group themselves. Key results include:
- Two primary clusters were identified, one largely representing the ecological economics school of thought and the other capturing the neoclassical view.
- However, both clusters shared a conceptual definition of sustainability that considers ecological, social and economic dimensions, and aims to preserve society's development potentials.
- Both clusters also agreed on critiquing "pure economic growth" strategies and identified many overlapping future research topics.
- Main divides were on how to achieve sustainability, including suitable policy measures.
Application of probability in daily life and in civil engineeringEngr Habib ur Rehman
The document provides a history of the development of probability theory. It discusses how probability was first applied to games of chance but developed into a rigorous mathematical field over centuries. Early contributors included Cardano, Fermat, Pascal, Huygens, Bernoulli, and de Moivre. Key concepts like mathematical probability, errors, normal distribution, and Markov chains continued developing through the 18th-19th centuries. Modern probability theory is based on measure theory and used widely today in areas like statistics, science, engineering, and artificial intelligence. The document also gives examples of probability applications in everyday life like risk assessment, reliability analysis, and natural language processing.
This document provides an overview of the key concepts in sustainability assessment as presented in an introductory module developed by Prof. A. Lapkin of the University of Cambridge. It discusses definitions of sustainability from the 18th century focusing on sustainable forestry and traces the evolution of thinking on sustainability through the industrial revolution and enlightenment period. Key milestones discussed include the 1987 Brundtland Commission report which operationalized sustainable development around meeting needs, investing, technology, and institutions. The document also introduces stakeholders in sustainability assessment.
This document provides an overview of sustainability and sustainable development concepts from their origins in the 18th century through modern definitions and frameworks. It discusses early mentions of sustainability in relation to forestry management. Key periods and thinkers discussed include the Enlightenment, Marx, and the emergence of ideas around a global knowledge sphere. The Brundtland Commission report in 1987 is highlighted for providing an influential operational definition linking development, environment and equality. The document outlines stakeholder groups and goals of sustainability assessment, emphasizing a life cycle approach. Key concepts like footprint, costs, and useful function are also introduced.
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1. Application of S-Shaped Curves
Dmitry Kucharavy, Roland De Guio
To cite this version:
Dmitry Kucharavy, Roland De Guio. Application of S-Shaped Curves. TRIZ-Future Confer-
ence 2007: Current Scientific and Industrial Reality, Nov 2007, Frankfurt, Germany. pp.81-88.
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2. APPLICATION OF S-SHAPED CURVES
Dmitry Kucharavy, Roland De Guio
LGECO - Design Engineering Laboratory,
INSA Strasbourg - Graduate School of Science and Technology, France
Abstract
This paper deals with the application of S-shaped curves in the contexts of inventive problem solving,
innovation and technology forecasts. After explaining the origin of the logistic S-curve its application, as
seen in publications from different domains, is reviewed. Despite much criticism and the failure to apply the
logistic function for long-term forecasting, it continues to be a popular model for describing the evolution of
systems (technological, economical, social and others) over time. This paper can help researchers and
practitioners to understand the scope of application of S-shaped patterns, their limitations, and peculiarities.
Keywords
Laws of Technical systems evolution, Resource limitations, Technology Future Analysis, S-shaped curve,
S-curve.
1 INTRODUCTION
The regularity of systems' evolution as an initial slow
change, followed by a rapid change and then ending in a
slow change again are observed since statistical
observation was established in the mid 18th
century.
Various scientists and researchers discovered,
reinvented, and adapted the curves of nonlinear growth
many times for different domains of knowledge.
Therefore, S-shaped curves possess a lot of different
names: Logistic curve, Verhulst-Pearl equation, Pearl
curve, Richard's curve (Generalized Logistic), Growth
curve, Gompertz curve, S-curve, S-shaped pattern,
Saturation curve, Sigmoid(al) curve, Foster’s curve, Bass
model, and many others. Researches all around the world
apply S-shaped curves for projecting the performance of
technologies, to foresee population changes, for market
penetration analyses, for micro- and macro-economic
studies, for diffusion mechanisms of technological and
social inventions, for ecological modelling, and for many
other purposes.
What explains such a generic and universal application of
logistic S-curves?
2 HISTORY OF THE S-SHAPED CURVE
2.1 Origin of the logistic curve and its basic concept
The logistic function as a model of population growth was
first introduced by Belgian mathematician Pierre-Francois
Verhulst (1804-1849) in 1838 [3]. Verhulst derived his
logistic equation after he had read 'An essay on the
Principle of Population' of English demographer and
political economist Thomas Malthus (1766-1834). The
logistic equation was introduced to describe the self-
limiting growth of a population. This equation sometimes
called the Verhulst-Pearl equation according to its
rediscovery in 1920 by American zoologist and one of the
founders of biometry Raymond Pearl (1879-1940).
Early in the 20th century, Alfred James Lotka from John
Hopkins University, US and Vito Volterra from the
University of Rome, Italy working independently but in
parallel, generalized Verhulst’s growth equation to model
competition among different species. The Volterra-Lotka
model, also known as the predator-prey equations, has
opened the way to effectively managing competition in
biology, ecology and technology domains. Today this
model is frequently employed to describe the dynamics of
systems [4].
Different types of competition can be distinguished [4, 5]:
• competition of one species for resources;
• two competitors: pure competition (loss-loss),
predator-prey (win-loss), symbiosis (win-win),
parasitic (win-impervious), symbiotic (loss-indifferent),
and no competition;
• many competitors at the same time.
For example, a population of bacteria grows in a closed
bowl of broth. The rate of chemicals in the broth to
bacteria transformation is proportional to the number of
bacteria present and the concentration of transformable
chemicals. Thus, Verhulst’s equation for this particular
case can be written as:
M
NM
aN
dt
dN )( −
= (1)
Where, N(t) – number of bacteria at time t; M – amount of
transformable chemicals at t=0 (before growth starts); a -
parameter that represents the interaction between the
competitors.
Solution of equation (1) as a logistic function:
)(
1
)( bat
e
M
tN +−
+
= (2)
Where, b – is a constant, locating the process in time [5].
The law of natural growth over a period of time can be
described through periods of birth, growth, maturity,
decline and death for any system. This set of periods is
often called the life cycle of system.
A bell-shaped curve is usually applied as a template to
represent the rate of growth within a time span (see
Figure 1). Whereas cumulative growth (cumulative
number of "units" until any given points in time) follows an
S-curve. Thus the S-curve became a visual symbol of
cumulative growth. The simplest mathematical function
that produces an S-curve is called a logistic.
The essential meaning of this function is 'the rate of
growth is proportional to both the amount of growth
already accomplished and the amount of growth
remaining to be accomplished.' Understanding of that
concept helps to catch part of the answer to the question:
"Why does the S-curve approach possess forecasting
powers?"
3. We believe the forecasting power of the S-curve is due to
the basic concept of limiting resources that lies at the
basis of any growth process. In diverse areas, limiting
resources are named in different ways: scarcest
resources (geochemistry), restricted resources
(economy), limitation of resources (TRIZ
1
), resource
constraint (theory of constraints) etc.
Rateofgrowth
1980 2000 20402020
Cumulativegrowth
20101990 2030
birth
growth
maturity
decline
death
Figure 1. Life cycle bell-shaped curve and S-curve of
cumulative growth.
In most cases, applying an S-curve for forecasting
induces the correct measurement of the growth process
that in turn can be applied to identify the law of natural
growth quantitatively and to reveal the value of the ceiling
(upper limits of growth) and steepness of the growth
(slope of curve).
Obviously, the more precise the data and the bigger the
section of the S-curve they cover leads to a lower level of
uncertainties [6]. In other words, one can identify a more
accurate ceiling and steepness with a larger data set. This
effect causes some difficulties in applying an S-curve
forecast for emerging technologies, which have not yet
passed the "infant mortality" threshold (when the ratio of
new to old technology has not reached 0.1).
2.2 Application of S-shaped curves
The law of natural growth was derived from research in
Economics. The Malthusian growth model is the ancestor
of the logistic function of Pierre Verhulst. Benjamin
Gompertz in 1825 published work developing the
Malthusian growth model further for demographic study
(law of mortality). Since those times, S-shaped curves
have been applied for studies in population dynamics and
economic analyses.
In the early 1960s, S-shaped curves and envelop curves
were regularly employed for technological forecasting [7].
The application of the logistic curve in combination with
envelop curves for forecasting by extrapolation of trends
issued many fascinating results for lightning systems,
1
Theory of inventive problem solving
particle accelerators, aircrafts, microelectronics,
transportation systems, energy conversion technologies.
For instance, the diffusion of innovation theory, formalized
by Everett M. Rodgers [8] in 1962 postulated that
innovations would spread in society in an S-curve.
The law of natural growth seems as simple as it is
fundamental. Biologists have applied it to describe the
growth of a species under competition. It has been used
in medicine to describe the diffusion of epidemic diseases.
Market studies of new products, usually based on the law
of natural growth in a specific niche, use an S-curve
analysis.
Fisher J.C. and Pry R.H. in 1971 [9] have shown that data
describing the substitution of a new product or process for
an old one can be fitted extremely well by a simple
mathematical logistic function that produces an S-curve.
There are plenty examples of applying S-curves for
studying the future of complex systems. It is simply not
within the scope of this paper to count even the major
ones.
For instance, at the International Institute for Applied
Systems Analysis (IIASA
2
, Laxenburg, Austria) logistic S-
curves have been applied during the last 35 years for
studies about
• the future of primary energy sources and vectors,
• the evolution of agricultural technologies,
• the substitution of transportation systems,
• the development of discoveries,
• the elaboration of inventions and the diffusion of
innovation,
• the transformation of the aircraft industry,
• macro- and micro- economic trends,
• the growth of crime and terrorism,
• environmental changes and problems,
• the evolution of telecommunication systems,
• and for many others.
The International Journal of Technological Forecasting
and Social Change3
published more than 320 articles
from May 2002 to May 2007. About 14 articles considered
in particular the application of the logistic S-curve of
natural growth for forecasting purposes. More than 170
articles within this period mentioned S-curves on their
pages.
In usual forecasting and strategic planning practice S-
shaped curves enter as modular components in many
methods and techniques. Table 1 summarizes the
observed application of S-curves as a part of various
forecasting methods.
A study of the application of S-curves, summarized in
Table 1, shows that they are most often applied for
analysing past data in order to disclose new trends and
for proving known ones.
From a practical viewpoint, according to the results of
various research, the processes of diffusion of novelties,
substitution of systems, and competitive growth obey the
same law of natural growth. Thanks to its fractal aspects
2
IIASA is a nongovernmental, multidisciplinary,
international research institution; it was founded in
October 1972 by academies of science of 12 nations from
East and West. The institute now has 18 National full
Member Organizations [http://www.iiasa.ac.at/].
3
ISSN: 0040-1625 "A major forum for those wishing to
deal directly with the methodology and practice of
technological forecasting and future studies as planning
tools as they interrelate social, environmental and
technological factors."
4. [10] the law of natural growth can be applied for almost
any scale and complexity of systems from elementary
particles up to the evolution of stars and knowledge
acquisition.
Method name: Nature & Application:
Trend Impact
Analysis [16]
Quantitative. For extrapolation of
previously collected data
Curve fitting
technique [16]
Qualitative and quantitative. For
forecasting the critical variables
within the State of the Future
Index (SOFI) method
Decision Modelling
based on Fisher and
Pry model (1971)
Quantitative. For examining
market, technological, social
substitution dynamics
Statistical Modelling.
Time-series analysis
as a part of curve
fitting [15, pp.577-
595]
Qualitative and quantitative.
For trend extrapolation.
Text Mining for
Technology Forecast
[17, pp.194-197]
Quantitative.
For analysis of annual
publications, to prove informative
trends.
Life Cycle Analysis
in the framework of
strategic analysis
Qualitative.
To identify the stage of a system's
evolution.
Theory of Innovation
Diffusion [8]
Qualitative and quantitative.
For studying the technology
adaptation dynamic.
Emerging issues
analysis [18]
Quantitative.
For identifying the issues before
they reach the trend of problem
phase for engineering and non-
engineering fields.
Table 1. Applications of S-shaped curves in the
framework of other methods
3 S-CURVE IN THE FRAMEWORK OF TRIZ
In the scope of TRIZ research, in the mid 1970s it was
proposed to employ the S-curve model for the qualitative
study of technical systems evolution [1, 2]. In order to
facilitate the positioning of the analysed system onto a
logistic curve G.Altshuller proposed the application of
three supplementary statistical curves: changes of
number of inventions, changes of level of inventions, and
changes of profitability during time. It was proposed also
to apply a concept of three levels of resource limitations
during the life cycle of technical systems (Figure 2):
• first level – limitation of working principle (limits of
system's resources),
• second level – limitation of economic rationality (limits
of available resources from the environment), and
• third level – physical limits of resources in super-
system (e.g. limitations of fossil resources, limitations
of available space, limitations of renewable resources
– clean water).
In the scope of research into technological forecasting, we
are looking for a method for the application of the concept
of assessing multi-level resource limitations in order to
improve the reliability of the forecast for emerging
technologies that do not have enough history of their
evolution (lack of data and knowledge).
It is necessary to notice that a similar concept of scarce
resources was described as a Law of the Minimum by
German geochemist Justus von Liebig (1803-1873) in
1840. The Law of the Minimum states 'that growth is
controlled not by the total resources available, but by the
scarcest resource'.
For chemistry, such a concept is known as the rate
determining step, in management techniques as the
critical path. Derivatives from the law of the minimum can
be found in many areas of knowledge from economics,
environmental, social and technological sciences.
A
α
β
γ
3. Physical
limits of
resources in
super-
system
Time
Mainindicesofthesystem
1. Limits of
system’s
resources
B
2. Limits of
available
resources
I
phase
II
phase
III phase
Figure 2. Styled S-curve of technical systems evolution
and limits of resources
The law of natural growth and the S-curve play a key role
in the set of height laws of technical systems evolution,
postulated in TRIZ. The law of increasing Ideality of
technical systems is in fact the derivation of the enveloped
curve of successive substitutions of technical systems
(see Figure 3).
Mainindicesofthesystem
Time
21
3
4
5
Figure 3. Successive substitutions of new systems for old
ones following the law of Ideality growth.
Why does system 3 conquer system 2? In competition if
system 3 shows a better ratio of Performance to Expense
it has more chances to survive. Expense is our limiting
resource. And this is exactly the meaning of the law of
increasing Ideality: 'during their evolution the technical
systems tend to improve the ratio between system
performance and the expense required for this
performance.'
The trickiest question is how to calculate Ideality in
practice for particular systems [11]. After analysis of the
available sources of knowledge, we did not find any
5. feasible ideas and procedures for computing Ideality
(often called the 'Main index of the system'). It is not
surprising that the founder of TRIZ first proposed to apply
an S-curve analysis for qualitative analysis. Therefore,
vertical scales in most TRIZ publications are purely
qualitative or apply some arbitrary units.
Before presenting some data about TRIZ publications, it is
necessary to clarify the different viewpoints on what is a
'forecast'.
If someone tells us, "it will rain". Will it be a forecast, a
prediction or just a vision of the future? Usually we are
interested to know when and where "it will rain." It is
important to know how intensive it will be and how the
temperature will change afterwards.
Frequently observed TRIZ-forecasts resemble "it will rain."
For instance, the following assertion: motor vessels will be
substituted by water-jet vessels. Yes, they will! However,
it is interesting to know when?, were? and for which
application?
In order to avoid misunderstandings, we would like to
present our working definition of the term 'forecast'. We
define a technology forecast in the framework of our
research as "an explicit description of emergence,
performance, features, and impacts of a technology in a
particular place at a particular point of time in the future
for a definite application." If some of the components of
the above definition are omitted, such a description should
be considered as a vision of the future rather than as a
forecast. Visions of the future merit consideration and
study, however, they have another area of application and
should not be confused with forecasts.
In order to summarise the application of S-curves in the
TRIZ community we made an express survey of
publications at conferences within the time span 1999-
2006 (ETRIA
4
TFC 2001-2006, and TRIZCON
5
) and
publications on the website triz-journal.com 1997-2006
6
.
The same articles from different sources where taken into
account just once. Unfortunately, we had no opportunity
to consider publications from MATRIZ conferences and
many other publications in Russian, German, French,
Spanish, Japanese, Korean, Chinese, Polish, Czech and
others languages.
Excerpts from the results of our survey are presented in
Tables 2 and 3.
In total, 137 papers mention S-curve applicability over the
reviewed period. Most of them consider pure qualitative
analysis of arbitrary parameters. Some of them do not
consider any parameters on the vertical scale at all. The
authors of only 14 papers during nine years tried to
combine qualitative analysis with a quantitative one. Eight
papers out of 14 are case studies, concerned with
identifying a phase stage of the analysed system or
evolutionary trends for a particular technology. The
remaining five papers discuss the applicability of S-curve
analysis using arbitrary units with some ideas about
measurable parameters.
Different applications of the S-curve concept in TRIZ
publications are presented below (Table 3, Figure 4).
Dozens of various applications are grouped into five
groups.
4
Annual TRIZ Future Conference of European TRIZ
Association, Europe [http://www.etria.net ].
5
Annual Altshuller Institute for TRIZ Studies International
Conference, USA [ http://www.aitriz.org ].
6
The TRIZ Journal Article Archive [ http://www.triz-
journal.com ].
Year Source S-curve is mentioned
1997 triz-journal 13%
1998 triz-journal 3%
TRIZCON 15%
triz-journal 13%
1999 14%
TRIZCON 16%
triz-journal 11%
2000 12%
TRIZCON 19%
ETRIA TFC 13%
triz-journal 5%
2001 11%
TRIZCON 15%
ETRIA TFC 12%
triz-journal 12%
2002 12%
TRIZCON 27%
ETRIA TFC 6%
triz-journal 7%
2003 10%
TRIZCON 11%
ETRIA TFC 14%
triz-journal 8%
2004 10%
TRIZCON 8%
ETRIA TFC 16%
triz-journal 7%
2005 10%
TRIZCON 12%
ETRIA TFC 7%
triz-journal 8%
2006 8%
Table 2. Ratio of papers mentioning an S-curve in total
publications.
#
Application of
S-curve
11/1996
12/1999
01/2000
12/2002
01/2003
12/2006
1 Just mentioned 11 29 43
2
Case studies
using S-curve
3 3 5
3
Maturity of
technology
assessment in
context of
problem
solving
3 6 8
4
Analysis of
systems
evolution in
context of
forecasting
4 8 8
5
Non-grouped
hypothesis
0 3 3
Table 3. Number of papers in TRIZ publications grouped
according to application of S-curve concept.
6. In papers from the first group authors just refer to an S-
curve and apply common knowledge (mostly taken from
[1]) in order to illustrate proposed findings, speculations
and particularities. The S-curve concept is applied mainly
for educational purposes, in order to illustrate the stages
of system evolution, for the illustration of laws of technical
systems evolution, to provide information about natural
growth. In other words, in order to master the future of
technical and non-engineering (business, educational,
environmental) systems.
The second group of papers include publications
dedicated to the analysis of particular system evolution
using an S-curve. They describe the practical experiment
of employing quantitative data analysis in order to identify
the evolutionary stage of certain technologies.
Unfortunately, such papers are not so numerous even if
they attract the attention of many readers. The level of
"quantitativeness" in papers varies from data analysis
using fitting techniques to quasi-quantitative studies.
Papers from the third group discuss how to define the
direction of problem solving activities using an S-curve
and systematic technology assessment. Some papers
from this group present proposals about the integration of
S-curve analysis in several toolboxes for designing new
products.
Papers from the fourth group are focused on the
forecasting and strategic planning contexts. They propose
some rules and recommendations about analysis of
systems evolution, history of the system and trend studies
using S-curve analysis. The papers discuss the
application of the S-curve for engineering and non-
technical systems as well as short-term and long-term
perspectives with cascading S-curves. Several papers
from this group propose some recommendations for
effective evaluation of patents.
0% 20% 40% 60% 80% 100%
1996-1999
2000-2002
2003-2006
Just mentioned
Case studies using S-curve
In context of problem solving
In context of forecasting
Non-grouped hypothesis
Figure 4. Application of S-curve in TRIZ publications
(based on data from Table 3).
In the fifth group, several papers that do not fit any group
are collected. They represent some authors’ speculations,
early-ripe hypotheses, and ideas about combining the S-
curve concept with other theories and approaches for
uncommon needs.
4 ENVELOPE CURVE EXTRAPOLATION
There is an easy concept behind extrapolation
techniques: let past experience be a guide for future
expectations. One can distinguish several ways to apply
the envelope curve extrapolation in combination with the
logistic S-curve of natural growth.
One of the better known methods can be named "shift to
the super-systems". The main idea is to plot several
growth curves for alternative technologies using the same
key parameter and to fit the envelop curve for the
constructed curves (e.g. see Figure 4.2).
The application of envelope curves for long-term
technological forecasting started to be popular at the end
of the 1950s. This technique is still in use to develop long-
term visions. However, today for strategic planning it is
more important to foresee technology substitution time
and conditions. That is why envelop curve technique
results can be found in books, but not in articles and
conference papers.
There are many pitfalls and particularities of the process
for designing the envelop curve extrapolation of this first
type. It is commonplace to discuss whether the trend will
not continue as before or if it will continue. In fact, this
question can be dealt with by means of system dynamic
[19].
In order to emphasise another pitfall and repeat once
again the importance of careful selection the parameters
for the vertical scale, Figures 4.1 and 4.2 present two
diagrams. These two graphs are taken from the book [7]
to which G.Altshuller referred [2] when discussing the
applicability of S-curve analysis for inventive problem
solving and qualitative technology forecasting.
The same parameter was plotted in both graphs. The one
in Fig 4.1 is misleading. because an inappropriate scale
is used. Speed of matter, according to the laws of physics
cannot exceed 299 792 458 metres per second.
The analysis of such examples leads to multiple
questions. For instance, how can we be sure about the
appropriateness of the chosen scale beforehand? What is
a relevant parameter to elaborate an enveloped S-curve
for long-term forecasting? For example, should it be the
speed of the transportation system or should it be a time
to move the load or person from one location to another
one? It should be noted, today in Europe high speed
trains rise in popularity, because they connect city-centres
and the final trip takes less time.
Another way to apply the enveloped curve extrapolation
can be named "shift to the sub-systems." Several
interesting illustrations were presented in paper [10] of
T.Modis in 1994. By applying qualitative and quantitative
analyses of the computer market the author put forward a
fractal aspect of natural growth depicted by an S-curve.
One of the conclusions that were proved later suggests
that "any growth process can be analysed in terms of
natural growth sub-processes."
It is noticeable how one picture can replace a lot of text
explanations. For instance, the link between the slope of
the envelop curve and the rhythm of technology
substitutions (depicted by sub-S-curves) can be learned
from Figure 5 distinctly. Another interesting derivative
result from Figure 5 is the hint about shortening life-cycles
of technologies (sub-S-curves) when the envelop curve
flattens (in the beginning and at the end of natural
growth).
Due to the limitations of a conference paper, it is
impossible to present here all the richness of the
application of envelop curves. Here only two of many
ways are presented.
7. Figure 4.1. Speed trend curve plotted in 1961. Source [7]. Figure 4.2. Speed trend. Source [7].
Figure 5. Styled Envelop curve. An envelop logistic
pattern is decomposed into constituent logistics. The
horizontal axis represents time (Source [10]).
5 SOME FEEDBACK FROM PRACTICE
The target of our research is to improve the process of
forecasting for emerging technologies and the quality of
the forecasts produced. We next apply the following basic
assumptions:
• limitations of resources drive evolution of any
technology;
• thus, the technology’s future can be mapped using
knowledge about scarce resources;
• application of the law of natural growth with a logistic
S-curve, performed in a computable way, can
contribute essentially to the accuracy of the long-term
forecast.
In order to check the above assumptions and hypotheses
about reliable forecasting using OTSM-TRIZ7
knowledge
7
At the end of the 1970s the founder of TRIZ G.Altshuller
anticipated the further evolution of TRIZ towards a
General Theory of Powerful Thinking, which will be useful
two forecasting projects were performed during
September 2003 – December 2006 in collaboration with
the European Institute for Energy Research (EIFER),
Karlsruhe, Germany. Some theoretical and practical
results of these projects are described in reports and
conference papers [21, 22, 23].
In the framework of this paper, we would like only to
emphasise the question of measurable parameters for the
vertical scale of the S-curve of system evolution. This
question is a corner stone of the application of logistic S-
curves for medium- and long-term forecasts as we
perceive from theoretical and practical studies.
According to the law of Ideality increase [1], Ideality is
defined as a ratio between the system Performances and
the Expenses required for these performances.
∑
∑=
E
P
I (3)
Where, P – is system performance including all positive
results within the life-cycle of the system; E – is the
needed expenses of resources including all harmful and
undesirable effects within the life-cycle of the system.
The practical application of the Ideality concept [12]
shows us the necessity of taking into account not only the
technical aspects of Ideality (Pt, Et) for analysed systems
(see Equation 3), but also Economic, Social and
for dealing with non-engineering problems and complex
cross disciplinary problems as well. At the beginning of
the 1980s G.Altshuller initiated research to develop this
theory. OTSM is the Russian acronym usually applied to
indicate the General Theory of Powerful Thinking. For
details see paper of N.Khomenko et al. [20].
8. Environmental factors. Hence, in order to calculate
Ideality in practice it is necessary to measure somehow
Economic performance and expenses (Pe, Ee), Social
performance and expenses (Ps, Es), and Environmental
parameters (Pen, Een). Therefore, an instant Ideality can
be described as:
),,,( IenIsIeItfI = (4)
Where, It (technical Ideality) equals the ratio of ΣPt/ΣEt; Ie
– is economic Ideality (ΣPe/ΣEe); Is – is social Ideality
(ΣPs/ΣEs); Ien – is environmental Ideality (ΣPen/ΣEen).
For the purpose of system evolution forecasting it is
necessary to consider changes of Ideality over time
(within the forecasted timeframe at least). Consequently,
changes of Ideality over a time can be described as:
),,,(
dt
dIen
dt
dIs
dt
dIe
dt
dIt
f
dt
dI
= (5)
Currently, we are working on a practical way to solve this
equation or bypass it.
There are some practical approaches for measuring the
instant technological Ideality. However, it is an open
question: "How to quantify Idealities from other contexts
using compatible units?"
Analysis of technology forecasting practice gives the
evidence that it is only the technological context which is
not sufficient for reliable forecasting of system evolution.
The future state of certain technologies depends on the
nearest super-systems (contexts) transformations and
intrinsic interactions between super-systems, systems and
sub-systems. This processes demands more knowledge
which we can get from data about the technical feasibility
of emerging technologies and from known technology
barriers.
In order to handle situations with economic, social and
environmental issues a 'proverbial wisdom' is to perform a
series of interviews with experts (e.g. kind of Delphi
surveys). As we can sum up after the literature reviews,
such practice produces qualitative results with many
hidden biases [13, 14, 15].
* * *
In the practice of forecasting emerging technologies, there
is an inevitable question to be answered: How to forecast
the future of emerging technologies using an S-curve and
the law of natural growth before systems pass the 'infant
mortality' threshold (Figure 2, α point)?
The working hypothesis we are testing actually proposes
to measure the process of natural growth of knowledge to
predict the future of emerging technologies.
Before overcoming the 'infant mortality' threshold and
arriving at the exploitation phase of the life-cycle, a new
technology passes through exploration and
experimentation stages. Each phase has its learning
curve of knowledge growth (see Figure 6). Learning
curves represent knowledge acquisition in a percentage of
solved problems. Problems can be mapped [22] for
emerging technologies using techniques and methods
from OTSM-TRIZ [20].
There are still several questions to be answered and
tested through the practice of forecasting. An important
one, among others, is How to measure knowledge,
obtained within exploration and experimentation phases?
How can one calculate the time necessary for decisions
about the transition to the next phase (e.g.
experimentation)?
6 SUMMARY
The application of the law of natural growth has
imperishable value for the understanding of the
transformations of complex systems. Evolution of any kind
of system can be represented as successive S-curves of
technologies.
Knowledge acquisition,
in percente of readiness to
transit to the next phase100
0
50
25
75
Time
Exploration
(invention)
Experimentation
(Field test)
Exploitation
(innovation)
Figure 6. Knowledge acquisition for emerging technology.
One can find logistic curves inside S-curves due to the
fact that the logistic curves represent fractal aspects. One
can also find chaos by getting the logistic equation
discrete, especially within technology substitution phases.
The logistic S-curve of natural growth is a basic model of
the Volterra-Lotka equations, which are reliable for
describing and forecasting different forms of competition
and technology substitutions. Applied in a discrete form
with careful definition of competing 'species', logistic
equations would give a picture, where growth in
competition, self-organization, complex adaptive
behaviour, interactions in fractals can be shown.
One of the strongest points of S-curve application is that it
is based on nature. It represents a natural law of growth
by using simple logistic equations. Thus, quantitative
analysis of system transformation contributes essentially
to the reliability of forecasting.
The weak point of S-curve application is linked to the
necessity of applying data about the past of system
transformations in order to fill the logistic equation with
meaning. The results of studies [5] showed that "the more
precise the data and the bigger the section of the S-curve
they cover, the more accurately the parameters can be
recovered." In other words, when a system is closer to the
end of its evolution, it lessens the level of uncertainties
and increases the accuracy of the forecast with the S-
curve.
There is a question: 'When can we use an S-curve?' In
other words, 'When should we address cumulative
growth?' S-curves and logistic equations depict natural
growth in competition. When the analysed process can
not be measured as growth (or decline) in competition a
simple qualitative application of an S-curve usually
produces some misleading results and conclusions.
According to our experience and as reported in the results
of various literature, it is not trivial to identify appropriate
measurement parameters for the vertical scale of the S-
curve for medium- and long-term forecasting.
Nevertheless, it is unavoidable for getting a forecast, and
not only a vague moot vision. The obtained forecast can
be dramatically different, depending on the selected
parameter for measuring the evolution of the system.
"The ultimate test of the forecaster is an accurate
and reliable forecast not the elegant or easily
applied method."
9. ACKNOWLEDGMENTS
We wish to acknowledge the European Institute for
Energy Research (EIFER), Karlsruhe for support of the
research on Technology forecasting. We also would like
to thank our colleagues from the LICIA team of LGECO,
INSA Strasbourg for constructive discussions that helped
to clarify many points presented in this paper.
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Contact
Dmitry KUCHARAVY
LICIA / LGECO, INSA Strasbourg
24, Bd de la Victoire, 67084 Strasbourg, France
tel: +33 (0)3 88 14 47 10; fax: +33 (0)3 88 14 47 99
E-mail: dmitry.kucharavy@insa-strasbourg.fr