text:
Fujiko Fujio

Fujiko Fujio (藤子 不二雄) was a manga writing duo formed by Japanese manga artists Hiroshi Fujimoto (藤本 弘) and Motoo Abiko (安孫子 素雄). Professional debut in 1951 (under the authors' names "Abiko Motoo, Fujimoto Hiroshi"). Used the Fujiko Fujio name from 1953 until dissolution of the partnership in 1987, upon Fujimoto's illness. The pair was best known for their popular comedies, including Obake no Q-Tarō, Ninja Hattori-kun, Kaibutsu-kun, Perman, Kiteretsu Daihyakka, and Doraemon, which is officially recognized as a cultural icon of modern Japan. Some of their influences have included Osamu Tezuka as well as international cartoons and comic books.

Pen name
From their debut, they collaborated and wrote individually under one pen name. But after 1988 they published under separate names.

Fujiko Fujio
Used from July 1953 to around January 1988.

All works (collaboration, one person's work) published under one pen name "Fujiko Fujio".

Fujiko F. Fujio
Pen name used by Fujimoto since 1989.

The above is notation without symbols.

The official notation is Fujiko・F・Fujio (藤子・F・不二雄).

Fujiko Fujio A
Pen name used by Abiko since 1988.

The above is notation without symbols.

The official notation is Fujiko Fujio Ⓐ (藤子不二雄Ⓐ).

As a reminder, "Fujiko A. Fujio" is a non-existent name notation. If it exists, it is a misunderstanding or typo.

Biography
Hiroshi Fujimoto and Motoo Abiko were both from Toyama Prefecture. Fujimoto was born on December 1, 1933, and Abiko on March 10, 1934. Abiko transferred to Fujimoto's elementary school in Takaoka City and happened to see Fujimoto drawing in a notebook. The two became lifelong friends, and during the early years of their friendship kept their illustrations hidden from friends and classmates out of embarrassment.

In junior high school they were greatly influenced by Osamu Tezuka and his manga series Shin Takarajima. Fujimoto built a homemade episcope and together they wrote a piece for it called Tenküma, which was their first collaborative work. They started submitting work to periodicals such as Manga Shōnen and opened a joint savings account through Japan Post to which they both contributed funds and which they used to purchase art supplies. They divided all income and expenses equally between each other, a practice they continued throughout the life of their partnership.

In high school they made their publishing debut, Tenshi no Tama-chan being adopted for serialization by Mainichi Shogakusei Shimbun in 1951. That same year they paid a visit to Tezuka's residence in Takarazuka, Hyōgo and showed him illustrations for their work titled Ben Hur. Tezuka complimented the two, some years later commenting that he knew then they were going to be major figures in the manga industry. Abiko and Fujimoto treasured the meeting with the respected Tezuka, and kept the Ben Hur illustrations for their entire lives. It was at this time they decided to make their partnership permanent, initially adopting the name Tezuka Fujio out of respect, later changing this to Azhizuka Fujio when they perceived adoption of the Tezuka name as too close to that of their idol.

Because both Fujimoto and Abiko were eldest sons respectively, they decided to take company jobs after graduating from high school in 1952. Fujimoto found employment with a confectionery company, and Abiko began working for the Toyama Newspaper Company. However, Fujimoto quit within a matter of days. Fujimoto then dedicated his time to submitting work to periodicals, with Abiko assisting him on the weekends. Their first serial as Ashizuka Fujio was terminated in a few episodes, followed by success with the post-apocalyptic science fiction series Utopia: The Last World War (UTOPIA—最後の世界大戦).

They elected to move to Tokyo in 1954 as professional manga artists at Fujimoto's urging, Abiko only reluctantly as he had steady employment at the Toyama Newspaper Company. Their first place of residence was a two-tatami mat room at the second floor of a watch shop. They eventually moved to the Tokiwa-sō apartment complex when Tezuka offered them a room that he was moving out of. Together with Hiroo Terada and several other manga artists of the period, they formed a collaborative group called "New Manga Party" (新漫画党). At the apartment complex where the group was based, they enjoyed a period of productivity that had Fujimoto and Abiko carry up to six serials a month for publication. Additionally, Abiko contributed to Tezuka's works as an artist assistant, such as drawing a blizzard on the last page of Jungle Emperor.

The workload proved excessive, and in 1955 on return to Toyama for Japanese New Year the pair missed all the deadlines for their serials. The loss of credibility with publishers hurt Fujimoto and Abiko for a year. During the Tokiwa-sō era, they purchased a television set in Akihabara and made independent films with an 8mm camera. By 1959 they left Tokiwa-sō and moved to Kawasaki in Kanagawa Prefecture. In the 1960s Fujimoto and Abiko founded Fujiko Studio Co., Ltd., a joint manga production company. Fujimoto found time to get married in 1962, at the age of 28.

In 1963 Fujimoto and Abiko established Studio Zero with Shin'ichi Suzuki, Shotaro Ishimori, Jirō Tsunoda and Kiyoichi Tsunoda. Later Fujio Akatsuka joined, and at its peak the studio employed about 80 people. The studio produced several animated series and stood in for Mushi Production for an episode of Astro Boy. For Fujimoto and Abiko these were some of their most productive years, resulting in series such as Obake no Q-Tarō which eventually were made into anime series on television. Abiko got married in 1966 at the age of 32. Fujimoto concentrated on titles for children, with a particular interest in science fiction.

In 1968, Abiko started making manga for a more mature audience, with titles such as Kuroi Salesman. In the 1970s, Abiko focused on both adult and boys manga. The style was full of black humor.

In the 1970s, Fujimoto focused on both adult and childhood manga. His style was notable for its sense of wonder.

Doraemon was created in 1969. Since around 1974, its popularity has skyrocketed among Japanese children. CoroCoro Comic released its first issue in 1977 to showcase the works of Fujiko Fujio. With syndication of Doraemon on TV Asahi in 1979, a surge of popularity saw up to a dozen collaborative and solo works by Fujimoto and Abiko picked up for publication and syndication throughout the 1980s. Doraemon is the only work by the duo to ever get an official release in English-speaking countries, most notably the United States. However, English dubs of work such as Perman and Ninja Hattori-kun aired in Asia.

In 1987, citing creative differences, Fujimoto and Abiko ended their long partnership to concentrate on solo projects. From now on, Abiko would work at Fujiko Studio K.K. and Fujimoto in Fujiko F. Fujio Pro K.K.

Abiko adopted the pen name Fujiko Fujio A.

Fujimoto adopted the pen name Fujiko F. Fujio.

According to Abiko, the cause for the dissolution of the partnership was due to Fujimoto discovering he had stomach cancer in 1986 (Since it was not announced, neither Fujimoto nor Abiko knew the exact name of the disease), and both Fujimoto and Abiko had a desire to settle copyright and financial issues before the other died.

Fujimoto died of liver failure at a hospital in Shinjuku on September 23, 1996.

A documentary was aired on TV Asahi on February 19, 2006, chronicling the life and times of Fujiko F. Fujio.

A Fujiko F. Fujio museum opened in Kawasaki, Kanagawa on September 3, 2011, which features a reproduction of Fujio's studio and a display of their artwork.

Abiko died at his home in Kawasaki on April 6, 2022.

Awards

 * Fujiko Fujio
 * 1963 – Shogakukan Manga Award (Susume Roboket and Tebukuro Tecchan)
 * 1973 – Japan Cartoonists Association Award Excellence Award (Doraemon)
 * 1981 – Kawasaki City's Cultural Prize (川崎市文化賞) (Fujiko Fujio)
 * 1982 – Shogakukan Manga Award for children's manga (Doraemon)
 * 1984 – "Movie day" Special Achievement Medal (Fujiko Fujio)
 * 1984 – Golden Gloss Prize (ゴールデングロス賞) (Movie Doraemon)

 * Fujiko F. Fujio
 * 1989,1990,1991,1992,1993,1994,1996,1997,and more – Golden Gloss Prize (ゴールデングロス賞) (Movie Doraemon etc.)
 * 1989 – "Movie day" Certificate of appreciation (Fujiko F. Fujio)
 * 1994 – Japan Cartoonists Association Award Minister of Education Award (Doraemon)
 * 1995 – Fujimoto Award Encouragement Award (Fujiko F. Fujio (Movie Doraemon series production))
 * 1996 – "Movie day" Special Achievement Medal (Fujiko F. Fujio)
 * 1997 – The first Tezuka Osamu Cultural Prize Grand Prize (Doraemon)

 * Fujiko Fujio A
 * 1990 – Fujimoto Award Special prize (Fujiko Fujio A (Movie Shonen jidai producer))
 * 1990 – Yamaji Fumiko Cultural Foundation Special Award (Fujiko Fujio A (Shonen jidai producer))
 * 2005 – Japan Cartoonists Association Award Minister of Education, Culture, Sports, Science and Technology Award (All works)
 * 2008 – Order of the Rising Sun (Fujiko Fujio A)
 * 2014 – Tezuka Osamu Cultural Prize Special Award (Manga Michi and Ai... Shirisomeshi Koro ni...)

Works

 * All works (Japanese)
 * Fujiko Fujio's Serialization list
 * Fujiko Fujio's One-shot list

title: Fujiko Fujio


text:
Talk:Charter

Untitled
mediaevel is a valid spelling of medieval Steeev 21:16, 4 Dec 2003 (UTC)

Charter vs. Chartered
I was looking for a working definition of becoming chartered in a scientific field and could not find one. Is this something that could be written into this page? Examples: C.Phys. (Chartered Physicist, exclusive to the Institute of Physics), C.Eng. (Chartered Engineer, exclusive to the Engineering Council UK) or C.Sci. (Chartered Scientist, exclusive to the Science Council). Perhaps it could be added to the disambig, is this viable?

Letters patent
How is the relation homos (in English language) between the concept of a (royal) Charter and a (royal) Letters patent? As far as my eyes can se, there is no references between these two articles. /Tuomas 13:26, 11 Oct 2004 (UTC)

Merge with article on Royal Charter?
Would it be a good idea to merge this article with that on Royal Charter? --Johan Magnus 23:36, 10 Nov 2004 (UTC)

 * If you wanted to put sections on Royal Charters and Letters patent in this article, that'd probably be OK I think, but this article should remain where it is and not be a redirect to either. This article is woefully underdeveloped; however, although it is linked historically with Royal Charter, the concept of a "charter" has become applicable in a wide variety of situations that have no immediate connection to royalty. older ≠ wiser 02:04, Nov 11, 2004 (UTC)

 * The article has evolved considerable since this suggestion. -- 8^D BD2412gab 22:57, 2005 Apr 14 (UTC)

i got no idea what your talking about but i say yes!

Split into multiple articles accessible from a disambiguation page
I Agree with this suggestion. There are far too many more or less unrelated terms in this article. stufff 14:38, 21 September 2006 (UTC)

 * I agree as well.- Itsfullofstars 19:32, 16 January 2007 (UTC)
 * I agree: There are far too many things in this article; to make a disambig may create too many stubs; I still say o for it. YB3 (talk • contribs) 23:49, 25 February 2007 (UTC)
 * Me too. But who's going to do it??? --66.183.115.230 13:04, 17 May 2007 (UTC)
 * I don't understand what you guys want to do here. You say you want to split them, however, you don't want to make a bunch of small stubs. What other way around it is there? Eric Wester 21:32, 27 August 2007 (UTC)
 * Heck yeah. What does charter school have to do with charter bus? Luna —Preceding comment was added at 14:31, 21 February 2008 (UTC)

Article change
I'm hoping that this isn't a contentious change; the article doesn't seem to be too active, and hasn't evolved, though the comments on this talk page seems to agree that it needs to be changed. I think (perhaps) that this change will make it more useful as a reference from other articles, with a more international applicability; I'm certain that it can be much improved by better writers than myself. Giving it a "law connection" seems appropriate, but I doubt that it's high on anyone's list of things wanted. Regards, Notuncurious (talk) 21:19, 29 May 2008 (UTC)

US state charters
This is an obviously missing section. State charters are important in the US, as they are what largely regulate the banking industry, legal bar associations, medical licensure, etc., which are largely not national affairs (aside from compliance with particular federal regulations), nor municipal ones. Honestly, it's weird that I cannot find any meaningful redirect target for common terms like bank charter and chartered bank. — SMcCandlish ☏ ¢ 😼  21:29, 13 March 2021 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Charter


text:
Soused

Soused may refer to:
 * An informal term for being under the influence of alcohol intoxication
 * Soused (album), by Sunn O))) in collaboration with Scott Walker

title: Soused


text:
Social simulation

Social simulation is a research field that applies computational methods to study issues in the social sciences. The issues explored include problems in computational law, psychology, organizational behavior, sociology, political science, economics, anthropology, geography, engineering, archaeology and linguistics.

Social simulation aims to cross the gap between the descriptive approach used in the social sciences and the formal approach used in the natural sciences, by moving the focus on the processes/mechanisms/behaviors that build the social reality.

In social simulation, computers support human reasoning activities by executing these mechanisms. This field explores the simulation of societies as complex non-linear systems, which are difficult to study with classical mathematical equation-based models. Robert Axelrod regards social simulation as a third way of doing science, differing from both the deductive and inductive approach; generating data that can be analysed inductively, but coming from a rigorously specified set of rules rather than from direct measurement of the real world. Thus, simulating a phenomenon is akin to generating it—constructing artificial societies. These ambitious aims have encountered several criticisms.

The social simulation approach to the social sciences is promoted and coordinated by four regional associations, the European Social Simulation Association (ESSA) for Europe, the Asian Social Simulation Association (ASSA) for Asia, the Computational Social Science Society of the Americas (CSSS) in North America, and the Pan-Asian Association for Agent-based Approach in Social Systems Sciences (PAAA) in Pacific Asia.

History and development
The history of the agent-based model can be traced back to the Von Neumann machine, a theoretical machine capable of reproducing itself. The device von Neumann proposed would follow precisely detailed instructions to fashion a copy of itself. The concept was then improved by von Neumann's friend Stanislaw Ulam, also a mathematician; Ulam suggested that the machine be built on paper, as a collection of cells on a grid. The idea intrigued von Neumann, who drew it up—creating the first of devices later termed cellular automata.

Another improvement was brought by mathematician, John Conway. He constructed the well-known Game of Life. Unlike the von Neumann's machine, Conway's Game of Life operated by simple rules in a virtual world in the form of a 2-dimensional checkerboard.

The birth of the agent-based model as a model for social systems was primarily brought about by a computer scientist, Craig Reynolds. He tried to model the reality of lively biological agents, known as the artificial life, a term coined by Christopher Langton.

Joshua M. Epstein and Robert Axtell developed the first large scale agent model, the Sugarscape, to simulate and explore the role of social phenomena such as seasonal migrations, pollution, sexual reproduction, combat, transmission of disease, and even culture.

Kathleen M. Carley published "Computational Organizational Science and Organizational Engineering" defining the movement of simulation into organizations, established a journal for social simulation applied to organizations and complex socio-technical systems: Computational and Mathematical Organization Theory, and was the founding president of the North American Association of Computational Social and Organizational Systems that morphed into the current CSSSA.

Nigel Gilbert published with Klaus G. Troitzsch the first textbook on social simulation: "Simulation for the Social Scientist" (1999) and established its most relevant journal: the Journal of Artificial Societies and Social Simulation.

More recently, Ron Sun developed methods for basing agent-based simulation on models of human cognition, known as cognitive social simulation (see )

Topics
Here are some sample topics that have been explored with social simulation:

 * Social norms: Robert Axelrod has used simulations to investigate the foundation of morality; others have modeled the emergence of norms using memes, or how social norms and emotions can regulate each other.
 * Institutions: by investigating under what conditions agents manage to coordinate, or by modeling the works of Robert Putnam on civic traditions
 * Reputation, for example by making agents with a model of reputation from Pierre Bourdieu (image, social esteem, and prestige) and observing their behavior in a virtual marketplace.
 * Knowledge transmission and the social process of science: there is a special section on that topic in the Journal of Artificial Societies and Social Simulation
 * Elections: Kim (2011) has modeled a psychological model of judgement from previous research (notably featuring motivated reasoning), and compared the statistical regularities of the simulation with empirical observations of voter behavior; others have compared delegation methods.
 * Economics: see computational economics and agent-based computational economics.

Types of simulation and modeling
Social simulation can refer to a general class of strategies for understanding social dynamics using computers to simulate social systems. Social simulation allows for a more systematic way of viewing the possibilities of outcomes.

There are four major types of social simulation:
 * 1) System level simulation.
 * 2) System level modeling.
 * 3) Agent-based simulation.
 * 4) Agent-based modeling.

A social simulation may fall within the rubric of computational sociology which is a recently developed branch of sociology that uses computation to analyze social phenomena. The basic premise of computational sociology is to take advantage of computer simulations in the construction of social theories. It involves the understanding of social agents, the interaction among these agents, and the effect of these interactions on the social aggregate. Although the subject matter and methodologies in social science differ from those in natural science or computer science, several of the approaches used in contemporary social simulation originated from fields such as physics and artificial intelligence.

System level simulation
System Level Simulation (SLS) is the oldest level of social simulation. System level simulation looks at the situation as a whole. This theoretical outlook on social situations uses a wide range of information to determine what should happen to society and its members if certain variables are present. Therefore, with specific variables presented, society and its members should have a certain response to the new situation. Navigating through this theoretical simulation will allow researchers to develop educated ideas of what will happen under some specific variables.

For example, if NASA were to conduct a system level simulation it would benefit the organization by providing a cost-effective research method to navigate through the simulation. This allows the researcher to steer through the virtual possibilities of the given simulation and develop safety procedures, and to produce proven facts about how a certain situation will play out.

System level modeling
System level modeling (SLM) aims to specifically predict (unlike system level simulation's generalization in prediction) and convey any number of actions, behaviors, or other theoretical possibilities of nearly any person, object, construct et cetera within a system using a large set of mathematical equations and computer programming in the form of models.

A model is a representation of a specific thing ranging from objects and people to structures and products created through mathematical equations and are designed, using computers, in such a way that they are able to stand-in as the aforementioned things in a study. Models can be either simplistic or complex, depending on the need for either; however, models are intended to be simpler than what they are representing while remaining realistically similar in order to be used accurately. They are built using a collection of data that is translated into computing languages that allow them to represent the system in question. These models, much like simulations, are used to help us better understand specific roles and actions of different things so as to predict behavior and the like.

Agent-based simulation
Agent-based social simulation (ABSS) consists of modeling different societies after artificial agents, (varying on scale) and placing them in a computer simulated society to observe the behaviors of the agents. From this data it is possible to learn about the reactions of the artificial agents and translate them into the results of non-artificial agents and simulations. Three main fields in ABSS are agent-based computing, social science, and computer simulation.

Agent-based computing is the design of the model and agents, while the computer simulation is the part of the simulation of the agents in the model and the outcomes. The social science is a mixture of sciences and social part of the model. It is where the social phenomena is developed and theorized. The main purpose of ABSS is to provide models and tools for agent-based simulation of social phenomena. With ABSS we can explore different outcomes for phenomena where we might not be able to view the outcome in real life. It can provide us valuable information on society and the outcomes of social events or phenomena.

Agent-based modeling
Agent-based modeling (ABM) is a system in which a collection of agents independently interact on networks. Each individual agent is responsible for different behaviors that result in collective behaviors. These behaviors as a whole help to define the workings of the network. ABM focuses on human social interactions and how people work together and communicate with one another without having one, single "group mind". This essentially means that it tends to focus on the consequences of interactions between people (the agents) in a population. Researchers are better able to understand this type of modeling by modeling these dynamics on a smaller, more localized level. Essentially, ABM helps to better understand interactions between people (agents) who, in turn, influence one another (in response to these influences). Simple individual rules or actions can result in coherent group behavior. Changes in these individual acts can affect the collective group in any given population.

Agent-based modeling is an experimental tool for theoretical research. It enables one to deal with more complex individual behaviors, such as adaptation. Overall, through this type of modeling, the creator, or researcher, aims to model behavior of agents and the communication between them in order to better understand how these individual interactions impact an entire population. In essence, ABM is a way of modeling and understanding different global patterns.

Current research
There are several current research projects that relate directly to modeling and agent-based simulation the following are listed below with a brief overview.

 * "Generative e-Social Science for Socio-Spatial Simulation" or (GENESIS) is a research node of the UK National Centre for e-Social Science funded by the UK research council ESRC.
 * "National e-Infrastructure for Social Simulation" or (NeISS) is a UK-based project funded by JISC.
 * "Network Models Governance and R&D collaboration networks" or (N.E.M.O) is a research centre whose main focus is to identify ways to create and to assess desirable network structures for typical functions; (e.g. knowledge, creation, transfer, and distribution.) This research will ultimately aid policy-makers at all political levels in improving the effectiveness and efficiency of network-based policy instruments at promoting the knowledge economy in Europe.
 * "Agent-based Simulations of Market and Consumer Behavior" is another research group that is funded by the Unilever Corporate Research. The current research that is being conducted is investigating the usefulness of agent-based simulations for modeling consumer behavior and to show the potential value and insights it can add to long-established marketing methods.
 * "New and Emergent World Models Through Individual, Evolutionary and Social Learning" or (New Ties) is a three-year project that will ultimately create a virtual society developed by agent-based simulation. The project will develop a simulated society capable of exploring the environment and developing its own image of this environment and the society through interaction. The goal of the research project is for the simulated society to exhibit individual learning, evolutionary learning and social learning.
 * Bruch and Mare's project on neighborhood segregation: The purpose of the study is to figure out the reasoning for neighborhood segregation based on race, and to figure out the tipping point or when people become uncomfortable with the integration levels into their neighborhood, and decide to flee from the neighborhood. They set up a model using flash cards, and put the agent's house in the middle and put houses of different races surrounding the agent's house. They asked people how comfortable they would feel with different situations; if they were okay with one situation, they asked another until the neighborhood was fully integrated. Bruch and Mare's results showed that the tipping point was at 50%. When a neighborhood became 50% minority and 50% white, people of both races began to become uncomfortable and white flight began to rise. The use of agent-based modeling showed how useful it can be in the world of sociology, people did not have to answer why they would become uncomfortable, just which situation they were uncomfortable with.
 * The MAELIA Program (Multi-Agent Emergent Norms Assessment) is a project dealing with the relationships between the users and managers of a natural resource, in that case water, and the related norms and laws that are to be built within them (conventions) or are imposed to them by other actors (institutions). The purpose of the project is to build a generic multiscale platform which is planned to deal with water conflict-related issues.
 * The Mosi-Agil project is a four-year program funded by the Autonomous Region of Madrid through the program MOSI-AGIL-CM (grant S2013/ICE-3019, co-funded by EU Structural Funds FSE and FEDER). It aims at creating a body of knowledge and practical tools which are necessary to handle more effectively the behavior of occupants of large facilities. Therefore, the project studies the development of ambient intelligence and intelligent environments supported by the use of Agent-Based Social Simulation.

Agent-based modeling is most useful in providing a bridge between micro and macro levels, which is a large part of what sociology studies. Agent-based models are most appropriate for studying processes that lack central coordination, including the emergence of institutions that, once established, impose order from the top down. The models focus on how simple and predictable local interactions generate familiar but highly detailed global patterns, such as emergence of norms and participation of collective action. Michael W. Macy and Robert Willer researched a recent survey of applications and found that there were two main problems with agent-based modeling the self-organization of social structure and the emergence of social order. Below is a brief description of each problem Macy and Willer believe there to be;
 * 1) "Emergent structure. In these models, agents change location or behavior in response to social influences or selection pressures. Agents may start out undifferentiated and then change location or behavior so as to avoid becoming different or isolated (or in some cases, overcrowded). Rather than producing homogeneity, however, these conformist decisions aggregate to produce global patterns of cultural differentiation, stratification, and homophilic clustering in local networks. Other studies reverse the process, starting with a heterogeneous population and ending in convergence: the coordination, diffusion, and sudden collapse of norms, conventions, innovations, and technological standards."
 * 2) "Emergent social order. These studies show how egoistic adaptation can lead to successful collective action without either altruism or global (top down) imposition of control. A key finding across numerous studies is that the viability of trust, cooperation, and collective action depends decisively on the embeddedness of interaction."

These examples simply show the complexity of our environment and that agent-based models are designed to explore the minimal conditions, the simplest set of assumptions about human behavior, required for a given social phenomenon to emerge at a higher level of organization.

Criticisms
Since its creation, computerized social simulation has been the target of some criticism in regard to its practicality and accuracy. Social simulation's simplification of the complex to form models from which we can better understand the latter is sometimes seen as a draw back, as using fairly simple models to simulate real life with computers is not always the best way to predict behavior.

Most of the criticism seems to be aimed at agent-based models and simulation and how they work:

 * 1) Simulations, being man-made from mathematical interfaces, predict human behavior in a far too simple manner in regard to the complexities of humanity and our actions.
 * 2) Simulations cannot enlighten researchers as to how people interact or behave in ways not programmed into their models. For this reason, the scope of simulations are limited in that the researchers must already know what they are going to find (to a degree, for they cannot find anything they themselves did not place in the model) at least vaguely, possibly skewing the results.
 * 3) Due to the complexities of what is being measured, simulations must be analyzed in unbiased ways; however, with the model running on a pre-made set of instructions coded into it by a modeler, biases exist almost universally.
 * 4) It is highly difficult and often impractical to attempt to link the findings from the abstract world the simulation creates and our complex society and all of its variation.

Researchers working in social simulation might respond that the competing theories from the social sciences are far simpler than those achieved through simulation and therefore suffer the aforementioned drawbacks much more strongly. Theories in some social science tend to be linear models that are not dynamic, and are generally inferred from small laboratory experiments (laboratory tests are most common in psychology but rare in sociology, political science, economics and geography). The behavior of populations of agents under these models is rarely tested or verified against empirical observation.

title: Social simulation


text:
User:TittoAssini

= Collective Intelligence =
 * Social simulation
 * Collective intelligence
 * Social software
 * Network_effect
 * Collaborative software

Peer-to-Peer

 * http://p2psockets.jxta.org/servlets/ProjectHome
 * Peer-to-peer

Semantic Web Enabled P2P Applications

 * edutella
 * Conzilla

Wiki Technology

 * Wiki:WikiFarms
 * Wiki:WikiEngines
 * Wiki software
 * Wiki:EddiesWiki single exe - saves simple files.
 * Eclipse Wiki Plugin

= Wikipedia and other Dictionaries/Wikis =
 * Javapedia
 * The Free On-line Dictionary of Computing
 * PlanetMath
 * Philosophy Pages and Dictionary
 * Metamath

Wiki Useful Links

 * User:Angela/useful stuff

Ideas for Wikipedia

 * A Web annotation system could transform the whole Web into a Wiki by allowing unlimited editing of any web site.
 * Display Wikipedia's as a semantic network (as a graph).
 * Provide a way for users to type the links across Wikipedia entries (as kind-of,part-of,etc.). In time this would create a Wikipedia ontology similar to WordNet.
 * Add at the bottom of every page a link to search on Google for the article's name.
 * The Editor should be WYSIWYG and have a spelling checker.

= MDA =

= My Stuff =
 * User:TittoAssini/test
 * User:TittoAssini/servers
 * my home page.

= Enlightenment = Nisargadatta Maharaj

title: User:TittoAssini


text:
Separation of variables

In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.

Ordinary differential equations (ODE)
A differential equation for the unknown $$f(x)$$ will be separable if it can be written in the form

 * $$\frac{d}{dx} f(x) = g(x)h(f(x))$$

where $$g$$ and $$h$$ are given functions. This is perhaps more transparent when written using $$y = f(x)$$ as:

 * $$\frac{dy}{dx}=g(x)h(y).$$

So now as long as h(y) ≠ 0, we can rearrange terms to obtain:

 * $${dy \over h(y)} = g(x) \, dx,$$

where the two variables x and y have been separated. Note dx (and dy) can be viewed, at a simple level, as just a convenient notation, which provides a handy mnemonic aid for assisting with manipulations. A formal definition of dx as a differential (infinitesimal) is somewhat advanced.

Alternative notation
Those who dislike Leibniz's notation may prefer to write this as

 * $$\frac{1}{h(y)} \frac{dy}{dx} = g(x),$$

but that fails to make it quite as obvious why this is called "separation of variables". Integrating both sides of the equation with respect to $$x$$, we have

or equivalently,

 * $$\int \frac{1}{h(y)} \, dy = \int g(x) \, dx $$

because of the substitution rule for integrals.

If one can evaluate the two integrals, one can find a solution to the differential equation. Observe that this process effectively allows us to treat the derivative $$\frac{dy}{dx}$$ as a fraction which can be separated. This allows us to solve separable differential equations more conveniently, as demonstrated in the example below.

(Note that we do not need to use two constants of integration, in equation ($$) as in
 * $$\int \frac{1}{h(y)} \, dy + C_1 = \int g(x) \, dx + C_2,$$

because a single constant $$C = C_2 - C_1$$ is equivalent.)

Example
Population growth is often modeled by the "logistic" differential equation

 * $$\frac{dP}{dt}=kP\left(1-\frac{P}{K}\right)$$

where $$P$$ is the population with respect to time $$t$$, $$k$$ is the rate of growth, and $$K$$ is the carrying capacity of the environment. Separation of variables now leads to

\begin{align} & \int\frac{dP}{P\left(1-P/K \right)}=\int k\,dt \end{align} $$ which is readily integrated using partial fractions on the left side yielding

 * $$P(t)=\frac{K}{1+Ae^{-kt}}$$

where A is the constant of integration. We can find $$A$$ in terms of $$P\left(0\right)=P_0$$ at t=0. Noting $$e^0=1$$ we get

 * $$A=\frac{K-P_0}{P_0}.$$

Generalization of separable ODEs to the nth order
Much like one can speak of a separable first-order ODE, one can speak of a separable second-order, third-order or nth-order ODE. Consider the separable first-order ODE:
 * $$\frac{dy}{dx}=f(y)g(x)$$

The derivative can alternatively be written the following way to underscore that it is an operator working on the unknown function, y:
 * $$\frac{dy}{dx}=\frac{d}{dx}(y)$$

Thus, when one separates variables for first-order equations, one in fact moves the dx denominator of the operator to the side with the x variable, and the d(y) is left on the side with the y variable. The second-derivative operator, by analogy, breaks down as follows:
 * $$\frac{d^2y}{dx^2} = \frac{d}{dx}\left(\frac{dy}{dx}\right) = \frac{d}{dx}\left(\frac{d}{dx}(y)\right)$$

The third-, fourth- and nth-derivative operators break down in the same way. Thus, much like a first-order separable ODE is reducible to the form
 * $$\frac{dy}{dx}=f(y)g(x)$$

a separable second-order ODE is reducible to the form
 * $$\frac{d^2y}{dx^2}=f\left(y'\right)g(x)$$

and an nth-order separable ODE is reducible to
 * $$\frac{d^ny}{dx^n}=f\!\left(y^{(n-1)}\right)g(x)$$

Example
Consider the simple nonlinear second-order differential equation:$$y=(y')^2.$$This equation is an equation only of y   and y' , meaning it is reducible to the general form described above and is, therefore, separable. Since it is a second-order separable equation, collect all x variables on one side and all y'  variables on the other to get:$$\frac{d(y')}{(y')^2}=dx.$$Now, integrate the right side with respect to x and the left with respect to y':$$\int \frac{d(y')}{(y')^2}=\int dx.$$This gives$$-\frac{1}{y'}=x+C_1,$$which simplifies to:$$y'=-\frac{1}{x+C_1}~.$$This is now a simple integral problem that gives the final answer:$$y=C_2-\ln|x+C_1|.$$

Partial differential equations
The method of separation of variables is also used to solve a wide range of linear partial differential equations with boundary and initial conditions, such as the heat equation, wave equation, Laplace equation, Helmholtz equation and biharmonic equation.

The analytical method of separation of variables for solving partial differential equations has also been generalized into a computational method of decomposition in invariant structures that can be used to solve systems of partial differential equations.

Example: homogeneous case
Consider the one-dimensional heat equation. The equation is

The variable u denotes temperature. The boundary condition is homogeneous, that is

Let us attempt to find a solution which is not identically zero satisfying the boundary conditions but with the following property: u is a product in which the dependence of u on x, t is separated, that is:

Substituting u back into equation $$ and using the product rule,

Since the right hand side depends only on x and the left hand side only on t, both sides are equal to some constant value −λ. Thus:

and

−λ here is the eigenvalue for both differential operators, and T(t) and X(x) are corresponding eigenfunctions.

We will now show that solutions for X(x) for values of λ ≤ 0 cannot occur:

Suppose that λ < 0. Then there exist real numbers B, C such that

 * $$X(x) = B e^{\sqrt{-\lambda} \, x} + C e^{-\sqrt{-\lambda} \, x}.$$

From $$ we get

and therefore B = 0 = C which implies u is identically 0.

Suppose that λ = 0. Then there exist real numbers B, C such that

 * $$X(x) = Bx + C.$$

From $$ we conclude in the same manner as in 1 that u is identically 0.

Therefore, it must be the case that λ > 0. Then there exist real numbers A, B, C such that
 * $$T(t) = A e^{-\lambda \alpha t},$$

and
 * $$X(x) = B \sin(\sqrt{\lambda} \, x) + C \cos(\sqrt{\lambda} \, x).$$

From $$ we get C = 0 and that for some positive integer n,

 * $$\sqrt{\lambda} = n \frac{\pi}{L}.$$

This solves the heat equation in the special case that the dependence of u has the special form of $$.

In general, the sum of solutions to $$ which satisfy the boundary conditions $$ also satisfies $$ and $$. Hence a complete solution can be given as

 * $$u(x,t) = \sum_{n = 1}^{\infty} D_n \sin \frac{n\pi x}{L} \exp\left(-\frac{n^2 \pi^2 \alpha t}{L^2}\right),$$

where Dn are coefficients determined by initial condition.

Given the initial condition

 * $$u\big|_{t=0}=f(x),$$

we can get

 * $$f(x) = \sum_{n = 1}^{\infty} D_n \sin \frac{n\pi x}{L}.$$

This is the sine series expansion of f(x) which is amenable to Fourier analysis. Multiplying both sides with $\sin \frac{n\pi x}{L}$ and integrating over $$ results in

 * $$D_n = \frac{2}{L} \int_0^L f(x) \sin \frac{n\pi x}{L} \, dx.$$

This method requires that the eigenfunctions X, here $\left\{\sin \frac{n\pi x}{L}\right\}_{n=1}^{\infty}$, are orthogonal and complete. In general this is guaranteed by Sturm–Liouville theory.

Example: nonhomogeneous case
Suppose the equation is nonhomogeneous,

with the boundary condition the same as $[0, L]$.

Expand h(x,t), u(x,t) and f(x) into

where hn(t) and bn can be calculated by integration, while un(t) is to be determined.

Substitute $$ and $$ back to $$ and considering the orthogonality of sine functions we get

 * $$u'_{n}(t)+\alpha\frac{n^{2}\pi^{2}}{L^{2}}u_{n}(t)=h_{n}(t),$$

which are a sequence of linear differential equations that can be readily solved with, for instance, Laplace transform, or Integrating factor. Finally, we can get
 * $$u_{n}(t)=e^{-\alpha\frac{n^{2}\pi^{2}}{L^{2}} t} \left (b_{n}+\int_{0}^{t}h_{n}(s)e^{\alpha\frac{n^{2}\pi^{2}}{L^{2}} s} \, ds \right).$$

If the boundary condition is nonhomogeneous, then the expansion of $$ and $$ is no longer valid. One has to find a function v that satisfies the boundary condition only, and subtract it from u. The function u-v then satisfies homogeneous boundary condition, and can be solved with the above method.

Example: mixed derivatives
For some equations involving mixed derivatives, the equation does not separate as easily as the heat equation did in the first example above, but nonetheless separation of variables may still be applied. Consider the two-dimensional biharmonic equation

 * $$\frac{\partial^4 u}{\partial x^4} + 2\frac{\partial^4 u}{\partial x^2\partial y^2} + \frac{\partial^4 u}{\partial y^4} = 0.$$

Proceeding in the usual manner, we look for solutions of the form

 * $$u(x,y) = X(x)Y(y)$$

and we obtain the equation

 * $$\frac{X^{(4)}(x)}{X(x)} + 2\frac{X(x)}{X(x)}\frac{Y(y)}{Y(y)} + \frac{Y^{(4)}(y)}{Y(y)} = 0.$$

Writing this equation in the form

 * $$E(x) + F(x)G(y) + H(y) = 0,$$

Taking the derivative of this expression with respect to $$ x $$ gives $$ E'(x)+F'(x)G(y)=0 $$ which means $$ G(y)=const. $$ or $$ F'(x)=0 $$ and likewise, taking derivative with respect to $$ y $$ leads to $$ F(x)G'(y)+H'(y)=0 $$ and thus $$ F(x)=const. $$ or $$ G'(y)=0 $$, hence either F(x) or G(y) must be a constant, say −λ. This further implies that either $$-E(x)=F(x)G(y)+H(y)$$ or $$-H(y)=E(x)+F(x)G(y)$$ are constant. Returning to the equation for X and Y, we have two cases

 * $$\begin{align}

X''(x) &= -\lambda_1X(x) \\ X^{(4)}(x) &= \mu_1X(x) \\ Y^{(4)}(y) - 2\lambda_1Y''(y) &= -\mu_1Y(y) \end{align}$$

and

 * $$\begin{align}

Y''(y) &= -\lambda_2Y(y) \\ Y^{(4)}(y) &= \mu_2Y(y) \\ X^{(4)}(x) - 2\lambda_2X''(x) &= -\mu_2X(x) \end{align}$$

which can each be solved by considering the separate cases for $$\lambda_i<0, \lambda_i=0, \lambda_i>0$$ and noting that $$\mu_i=\lambda_i^2$$.

Curvilinear coordinates
In orthogonal curvilinear coordinates, separation of variables can still be used, but in some details different from that in Cartesian coordinates. For instance, regularity or periodic condition may determine the eigenvalues in place of boundary conditions. See spherical harmonics for example.

Partial differential equations
For many PDEs, such as the wave equation, Helmholtz equation and Schrödinger equation, the applicability of separation of variables is a result of the spectral theorem. In some cases, separation of variables may not be possible. Separation of variables may be possible in some coordinate systems but not others, and which coordinate systems allow for separation depends on the symmetry properties of the equation. Below is an outline of an argument demonstrating the applicability of the method to certain linear equations, although the precise method may differ in individual cases (for instance in the biharmonic equation above).

Consider an initial boundary value problem for a function $$ u(x,t) $$ on $$ D = \{(x,t): x \in [0,l], t \geq 0 \}$$ in two variables:

 * $$ (Tu)(x,t) = (Su)(x,t) $$

where $$T$$ is a differential operator with respect to $$x$$ and $$S$$ is a differential operator with respect to $$t$$ with boundary data:

 * $$(Tu)(0,t) = (Tu)(l,t) = 0$$ for $$ t \geq 0$$
 * $$(Su)(x,0)=h(x) $$ for $$ 0 \leq x \leq l$$

where $$h$$ is a known function.

We look for solutions of the form $$u(x,t) = f(x) g(t)$$. Dividing the PDE through by $$f(x)g(t)$$ gives

 * $$ \frac{Tf}{f} = \frac{Sg}{g} $$

The right hand side depends only on $$x$$ and the left hand side only on $$ t$$ so both must be equal to a constant $$ K $$, which gives two ordinary differential equations

 * $$Tf = Kf, Sg = Kg$$

which we can recognize as eigenvalue problems for the operators for $$T$$ and $$S$$. If $$T$$ is a compact, self-adjoint operator on the space $$L^2[0,l]$$ along with the relevant boundary conditions, then by the Spectral theorem there exists a basis for $$L^2[0,l]$$ consisting of eigenfunctions for $$T$$. Let the spectrum of $$T$$ be $$E$$ and let $$f_{\lambda}$$ be an eigenfunction with eigenvalue $$\lambda \in E$$. Then for any function which at each time $$t$$ is square-integrable with respect to $$x$$, we can write this function as a linear combination of the $$f_{\lambda}$$. In particular, we know the solution $$u$$ can be written as

 * $$u(x,t) = \sum_{\lambda \in E} c_{\lambda}(t)f_{\lambda}(x)$$

For some functions $$c_{\lambda}(t)$$. In the separation of variables, these functions are given by solutions to $$ Sg = Kg $$

Hence, the spectral theorem ensures that the separation of variables will (when it is possible) find all the solutions.

For many differential operators, such as $$\frac{d^2}{dx^2}$$, we can show that they are self-adjoint by integration by parts. While these operators may not be compact, their inverses (when they exist) may be, as in the case of the wave equation, and these inverses have the same eigenfunctions and eigenvalues as the original operator (with the possible exception of zero).

Matrices
The matrix form of the separation of variables is the Kronecker sum.

As an example we consider the 2D discrete Laplacian on a regular grid:

 * $$L = \mathbf{D_{xx}}\oplus\mathbf{D_{yy}}=\mathbf{D_{xx}}\otimes\mathbf{I}+\mathbf{I}\otimes\mathbf{D_{yy}}, \,$$

where $$\mathbf{D_{xx}} $$ and $$\mathbf{D_{yy}} $$ are 1D discrete Laplacians in the x- and y-directions, correspondingly, and $$\mathbf{I} $$ are the identities of appropriate sizes. See the main article Kronecker sum of discrete Laplacians for details.

Software
Some mathematical programs are able to do separation of variables: Xcas among others.

title: Separation of variables