11
Nuevos métodos para laNuevos métodos para la
investigación de lainvestigación de la
comunicación social y loscomunicaci...
22
Objetivos de esta mañanaObjetivos de esta mañana
 Introducir los conceptos de laIntroducir los conceptos de la
teoría ...
33
Primeros ConceptosPrimeros Conceptos
DataesferaDataesfera
 lugar conceptual en el que todos los datoslugar conceptual ...
44
Teoría General de SistemasTeoría General de Sistemas
 Definición:Definición:
"... un sistema es una configuración de p...
55
Atributos de TGSAtributos de TGS
1. Compuesta de variables, i.e.,
elementos que pueden ser definidos o
descritos, por s...
66
Atributos de TSGAtributos de TSG
3. Un sistema tiene límites
 Conceptual
 jurídico: las empresas, la jurisdicción
 g...
77
Atributos de TSGAtributos de TSG
5. Un sistema aprende de los
cambios en sus variables o
ambiente
88
El Periódico como sistemaEl Periódico como sistema
Variable/agentsVariable/agents
Editorial
Publicidad
ProducciónCircul...
99
El Periódico como sistemaEl Periódico como sistema
Editorial
Publicidad
ProducciónCirculación
Administración
Variables ...
1010
““Environmental” ModelsEnvironmental” Models
Biosphere
Species
Sub-Species
Organism
Organs
Tissue
Cell
Chromosome
Gene
1111
El periódico como un sistemaEl periódico como un sistema--
ScalingScaling
Un sistema - y el análisis del sistema(s) -...
1212
Ejemplo de la herramienta deEjemplo de la herramienta de
modelado de simulación SimVenturemodelado de simulación SimV...
1313
Valor de los Sistemas de PensamientoValor de los Sistemas de Pensamiento
 Exige definir y enfocarse exactamente en
e...
1414
TGS como base para modelos deTGS como base para modelos de
simulación y análisis de la complejidadsimulación y anális...
1515
Resumen
 Datasphere oDatasphere o DataesferaDataesfera
 DatosDatos  AnálisisAnálisis  InformaciónInformación
 ...
1616
Herramientas para la ComplejidadHerramientas para la Complejidad
Complejidad y AplicadaComplejidad y Aplicada
 Compl...
1717
Herramientas para la ComplejidadHerramientas para la Complejidad
Complejidad y AplicadaComplejidad y Aplicada
 Fract...
1818
Transdiscipline Tools : SIGTransdiscipline Tools : SIG
 SIG:SIG: SSistemas deistemas de IInformaciónnformación
GGeog...
1919
Fractales y RedesFractales y Redes
2020
Análisis visual de la Complejidad y RedAnálisis visual de la Complejidad y Red
diagramasdiagramas
2121
Recursos en línea: Complejidad yRecursos en línea: Complejidad y
Análisis de Redes SocialesAnálisis de Redes Sociales...
2222
Red ejemplos gráficosRed ejemplos gráficos
2323
Social Network Analysis graphicsSocial Network Analysis graphics
2424
Herramientas para la Complejidad YHerramientas para la Complejidad Y
Complejidad AplicadaComplejidad Aplicada
 Compl...
2525
Análisis de la Leyes de PotenciaAnálisis de la Leyes de Potencia
 Leyes de Potencia: una relaciónLeyes de Potencia: ...
2626
Leyes de Potencia BiologíaLeyes de Potencia Biología
The “mouse-elephant” plot has the
exponent 7/6.
Source: http://w...
2727
Geography-Global Islands’ Area Power LawsGeography-Global Islands’ Area Power Laws
Source: Global Islands Power Laws....
2828
Contabilidad Forense - la Ley deContabilidad Forense - la Ley de
BenfordBenford
Source: http://paul.kedrosky.com/arch...
2929
Leyes de PotenciazonaLeyes de Potenciazona
urbanaurbana
3030
Leyes de Potenciazona urbanaLeyes de Potenciazona urbana
Source: 2007 Growth, innovation, scaling, and the pace of li...
3131
Inversa Ley de PotenciaInversa Ley de Potencia
20% de casos = 80% de total cuantidad
80% de total casos = 20%
3232
Lista de los periódicos del mundo en circulaciónLista de los periódicos del mundo en circulación
(000s)(000s)
ley de ...
3333
Clasificación jerárquica de la circulaciónClasificación jerárquica de la circulación
mundial de periódicosmundial de ...
3434
Clasificación jerárquica de la circulaciónClasificación jerárquica de la circulación
mundial de periódicosmundial de ...
3535
ResumenResumen
 Ver los fenómenos como sistemasVer los fenómenos como sistemas
 Utilice la teoría general de sistem...
3636
Gracias.
11
NuevosNuevos métodos paramétodos para lala
investigacióninvestigación de lade la
comunicacióncomunicación...
3737
IFIF time available….time available….
 Tom can introduce News MediaTom can introduce News Media
Genome ProjectGenome...
3838
““Environmental” ModelsEnvironmental” Models
Biosphere
Species
Sub-Species
Organism
Organs
Tissue
Cell
Chromosome
Gene
3939
Genes y cancerGenes y cancer
26 de julio de 2007, 9:33 PM CT
UM investigadores identificar los genes implicados en el...
4040
““Environmental” ModelsEnvironmental” Models
DATASPHEREBiosphere
Species
Sub-Species
Organism
Organs
Tissue
Cell
Chro...
4141
““Proyecto Genoma de MediosProyecto Genoma de Medios
Informativos”Informativos”
 Objectives:Objectives:
– Develop me...
4242
““Proyecto Genoma de MediosProyecto Genoma de Medios
Informativos”Informativos”
– ArticulateArticulate initialinitial...
4343
““Proyecto Genoma de MediosProyecto Genoma de Medios
Informativos”Informativos”
 Project processProject process
– Cr...
4444
Proyecto Genoma de MediosProyecto Genoma de Medios
InformativosInformativos
– Define/create databaseDefine/create dat...
4545
Clickstream Data Yields High-Resolution Maps ofClickstream Data Yields High-Resolution Maps of
ScienceScience
4646
Gracias.
11
NuevosNuevos métodos paramétodos para lala
investigacióninvestigación de lade la comunicacióncomunicación...
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Nuevos métodos para la investigación de la comunicación social y los medios de comunicación

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2do Congreso Investigadores Venezolanos de la Comunicación 1er Encuentro Latinoamericano Investigadores Transdisciplinarios de la Comunicación
Comunicación, ciudadanía y complejidad en clave latinoamericana

21 al 25 de abril de 2009
http://www.invecom.org/eventos/2009/index.php

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  • new methods for investigating social communications and media institutions
    nuevos métodos para la investigación de la comunicación social y los medios de comunicación
  • Objectives this morning
    Introduce concepts of General Systems Theory, Dynamic Systems, Complexity Theory and Applied Complexity
    Present examples of Applied Complexity.
    Emphasize the transdisciplinary nature (not inter-disciplinary) of Complexity
    Call for creation of “News Media Genome Project”
  • First Concepts
    Datasphere
    Conceptual place where all data exists in all formats
    Datasphere is accessible by all people to varying degree
    Data  Analysis  Information
    Information= “That which helps us make a decision”
    “Systems” and “sub-systems” in Datasphere function to process data, assist in analysis and generate Information
  • General Systems Theory
    Definition:“… system is a configuration of parts connected and joined together by a web of relationships”
    Analytic perspective and emphasis shifts from parts to the organization of and relationships between the parts (i.e.variables/agents/entities)
    Recognition that interactions are NOT static, but dynamic
    ================================================================================================================================
    GST focuses on the system's structure instead of on the system's function. It proposes that complex systems share some basic organizing principles irrespective of their purposes, and that these principles can be measured and modeled mathematically.
    Introduced by the Austrian biologist Ludwig von Bertalanffy (1901-72) and by the UK economist Kenneth Boulding (1910-93) around the year 1955.
    Source: http://en.wikipedia.org/wiki/Systems_theory
    “… system means a configuration of parts connected and joined together by a web of relationships”
    “…recognizing the interdependence between groups of individuals, structures and processes that enable an organization to function”
    “…The emphasis with systems theory shifts from parts to the organization of parts, recognizing interactions of the parts are not "static" and constant but "dynamic" processes.”
    Source: http://en.wikipedia.org/wiki/Systems_theory
    As a transdisciplinary, interdisciplinary and multiperspectival domain, the area brings together principles and concepts from ontology, philosophy of science, physics, computer science, biology, and engineering as well as geography, sociology, political science, psychotherapy (within family systems therapy) and economics among others. Systems theory thus serves as a bridge for interdisciplinary dialogue between autonomous areas of study as well as within the area of systems science itself.
    Source: http://www.survey-software-solutions.com/walonick/systems-theory.htm
    “A holist approach is to examine the system as a complete functioning unit. A reductionist approach looks downward and examines the subsystems within the system. The functionalist approach looks upward from the system to examine the role it plays in the larger system. All three approaches recognize the existence of subsystems operating within a larger system.”
    Source: http://www.geocities.com/seaskj/glossary.html#G
    Theory, created by von Bertalanffy, in which complex systems are viewed holistically, as amounting to more than the sum of the parts.*
    Source: http://www.opbf.org/open-plant-breeding/glossary/g
    There are many different kinds of system, such as solar systems, political systems, ecological systems (ecosystems), mechanical systems, legal systems, electrical systems, and so on.
    The concept of the pathosystem is based on the general systems theory.
    Systems theory is now divided into the general systems theory and complexity theory, which developed out of it. Systems theory is based on the concept of a pattern, and of systems levels, which are patterns of patterns.
  • Attributes of GST
    Composed of variables, i.e. elements that can be defined, or described, separately.
    Sub-variables. Tree-to-branch-to-leaf-to-cell
    There are relationships between variables
    Horizontal relationships
    Vertical (i.e. hierarchical) relationships
  • Attributes of GST
    A system has boundaries
    Conceptual
    Legal: corporate, jurisdiction
    Geographic
    Cultural
    A system has goals, self-defined or with a definition imposed by observer/researcher
    Make money
    Provide for group security, happiness, procreation
  • Attributes of GST
    A system learns from changes in its variables or environment
  • Newspaper as a system
    System has variables/agents/entities
    Editorial
    Office
    Advertising
    Circulation
    Production
  • Variables are related to other variables, and typically in a relationship that can be measured.
  • “Environmental” Models -- Datasphere
  • Newspaper as a system
    SCALEABILITY
    A system – and analysis of the system(s) – can be “scaled”
  • Screen shot of SIMVENTURE program
    Indicates that we can also use both QUALITATIVE AND QUANTITATIVE variables and measures. I.e. Qualitative = “Quality of Experience” and Quantitative=“Total Traffic”
    donde puede apreciarse que podemos utilizar tanto variables y medidas cualitativas como cuantitativas.
    Cualitativa: “Calidad de la experiencia”
    Cuantitativa: “Tráfico total”
  • Value of Systems Thinking
    Demands definition/focus on exactly what system are you talking about?
    Demands consideration of level of analysis, i.e. “zooming” levels of focus
    Demands definition of variables and then the relative importance of those variables
    Demands consideration of relationships between variables
  • GST as basis for simulation models & Complexity analysis
  • Summary
    Datasphere
    Data  Analysis  Information
    Systems
    Boundary
    Variables/agents/entities
    Relationships between variables
    System goals
    Feedback/”learning”
    Preparation for simulation modeling & Complexity Theory and Applied Complexity
  • Tools for Complexity y Applied Complexity
    Complexity – like fractals, statistics and SIG – is a “transdisciplinary” analytic method
    Fractal: A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.[2]
    A fractal often has the following features:[3]
    * It has a fine structure at arbitrarily small scales.
    * It is too irregular to be easily described in traditional Euclidean geometric language.
    * It is self-similar (at least approximately or stochastically).
    * It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).[4]
    * It has a simple and recursive definition.
    http://en.wikipedia.org/wiki/Fractal
    Social Network Analysis
    An example of a social network diagram. The node with the highest betweenness centrality is marked in yellow.
    Social network analysis (related to network theory) has emerged as a key technique in modern sociology. It has also gained a significant following in anthropology, biology, communication studies, economics, geography, information science, organizational studies, social psychology, and sociolinguistics as well as a popular topic of speculation and study.
    A social network is a social structure made of nodes (which are generally individuals or organizations) that are tied by one or more specific types of interdependency, such as values, visions, ideas, financial exchange, friendship, sexual relationships, kinship, dislike, conflict or trade.
    Social network analysis views social relationships in terms of nodes and ties. Nodes are the individual actors within the networks, and ties are the relationships between the actors. The resulting graph-based structures are often very complex. There can be many kinds of ties between the nodes. Research in a number of academic fields has shown that social networks operate on many levels, from families up to the level of nations, and play a critical role in determining the way problems are solved, organizations are run, and the degree to which individuals succeed in achieving their goals.
    http://en.wikipedia.org/wiki/Social_network_analysis
    Power Law(s)
    A power law is a special kind of mathematical relationship between two quantities. If one quantity is the frequency of an event, the relationship is a power-law distribution, and the frequencies decrease very slowly as the size of the event increases. For instance, an earthquake twice as large is four times as rare. If this pattern holds for earthquakes of all sizes, then the distribution is said to "scale". Power laws also describe other kinds of relationships, such as the metabolic rate of a species and its body mass (called Kleiber's law), and the size of a city and the number of patents it produces. What this relationship means is that there is no typical size in the conventional sense. Power laws are found throughout the natural and manmade worlds, and are an active area of scientific research.
    http://en.wikipedia.org/wiki/Power_law
    Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty. The basis for this "law" is that the values of real-world measurements are often distributed logarithmically, thus the logarithm of this set of measurements is generally distributed uniformly.
    This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). The result holds regardless of the base in which the numbers are expressed, although the exact proportions change.
    It is named after physicist Frank Benford, who stated it in 1938,[1] although it had been previously stated by Simon Newcomb in 1881.[2] Although many "proofs" of this law have been put forth (starting with Newcomb himself), none were mathematically rigorous[3] until Theodore P. Hill's in 1995.[4]
    http://en.wikipedia.org/wiki/Benford%27s_law
  • Tools for Complexity y Applied Complexity
    Fractals = A geometric figure that repeats itself under several levels of magnification, a shape that appears irregular at all scales of length, e.g. a fern
    =================================================================================
    Fractal: A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.[2]
    A fractal often has the following features:[3]
    * It has a fine structure at arbitrarily small scales.
    * It is too irregular to be easily described in traditional Euclidean geometric language.
    * It is self-similar (at least approximately or stochastically).
    * It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).[4]
    * It has a simple and recursive definition.
    http://en.wikipedia.org/wiki/Fractal
    A figura geométrica [http://en.wiktionary.org/wiki/geometric ] que se repite en virtud de varios niveles de aumento, una forma irregular [http://en.wiktionary.org/wiki/irregular ] que aparece en todas las escalas [http://en.wiktionary.org/wiki/scale ]de longitud [http://en.wiktionary.org/wiki/length ] por ejemplo, un helecho [http://en.wiktionary.org/wiki/fern]
    Social Network Analysis
    An example of a social network diagram. The node with the highest betweenness centrality is marked in yellow.
    Social network analysis (related to network theory) has emerged as a key technique in modern sociology. It has also gained a significant following in anthropology, biology, communication studies, economics, geography, information science, organizational studies, social psychology, and sociolinguistics as well as a popular topic of speculation and study.
    A social network is a social structure made of nodes (which are generally individuals or organizations) that are tied by one or more specific types of interdependency, such as values, visions, ideas, financial exchange, friendship, sexual relationships, kinship, dislike, conflict or trade.
    Social network analysis views social relationships in terms of nodes and ties. Nodes are the individual actors within the networks, and ties are the relationships between the actors. The resulting graph-based structures are often very complex. There can be many kinds of ties between the nodes. Research in a number of academic fields has shown that social networks operate on many levels, from families up to the level of nations, and play a critical role in determining the way problems are solved, organizations are run, and the degree to which individuals succeed in achieving their goals.
    http://en.wikipedia.org/wiki/Social_network_analysis
    Power Law(s)
    A power law is a special kind of mathematical relationship between two quantities. If one quantity is the frequency of an event, the relationship is a power-law distribution, and the frequencies decrease very slowly as the size of the event increases. For instance, an earthquake twice as large is four times as rare. If this pattern holds for earthquakes of all sizes, then the distribution is said to "scale". Power laws also describe other kinds of relationships, such as the metabolic rate of a species and its body mass (called Kleiber's law), and the size of a city and the number of patents it produces. What this relationship means is that there is no typical size in the conventional sense. Power laws are found throughout the natural and manmade worlds, and are an active area of scientific research.
    http://en.wikipedia.org/wiki/Power_law
    Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty. The basis for this "law" is that the values of real-world measurements are often distributed logarithmically, thus the logarithm of this set of measurements is generally distributed uniformly.
    This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). The result holds regardless of the base in which the numbers are expressed, although the exact proportions change.
    It is named after physicist Frank Benford, who stated it in 1938,[1] although it had been previously stated by Simon Newcomb in 1881.[2] Although many "proofs" of this law have been put forth (starting with Newcomb himself), none were mathematically rigorous[3] until Theodore P. Hill's in 1995.[4]
    http://en.wikipedia.org/wiki/Benford%27s_law
  • Transdiscipline Tools : SIG
    SIG: Sistemas de Información Geográfica
  • Fractals and Networks
    Source: http://universe-review.ca/R10-35-metabolic.htm
    Then in 1997, a couple of physicist and biologists successfully derive the 3/4 power-law using the concept of fractal. The theory considers the fact that the tissues of large organisms have a supply problem. That is what blood systems in animals and vascular plants are all about: transporting materials to and from tissues. Small organisms don't face the problem to the same extent. A very small organism has such a large surface area compared to its volume that it can get all the oxygen it needs through its body wall. Even if it is multicellular, none of its cells are very far from the outside body wall. But a large organism has a transport problem because most of its cells are far away from the supplies they need. Insects literally pipe air into their tissues in a branching network of tubes called tracheae. Mammals have richly branched air tubes, but they are confined to special organs, the lungs. Fish do a similar thing with gills. Trees use their richly dividing branches to supply their leaves with water and pump sugars back from the leaves to the trunk. The 3/4-power law is derived in part from the assumption that mammalian distribution networks are "fractal like" (Figure 03) and in part from the conjecture that natural selection has tended to maximize metabolic capacity "by maintaining networks that occupy a fixed percentage (6 - 7%) of the volume of the body".
  • Visual analysis of Complexity
    Network diagrams
    Just as we have learned to “read” a scatter or regression plot – look to the slope; look for outliers -- so too will be come to learn how to read visualizations of complex systems
  • Complexity and Social Networks Blog of the Institute for Quantitative Social Science and the Program on Networked Governance, Harvard University Welcome! The objective of this blog is to offer a forum for the discussion of the intertwined subjects of network analysis and complex systems theory. http://www.iq.harvard.edu/blog/netgov
    ==========================================================================================
    What is Social Network Analysis?
    Social network analysis is based on an assumption of the importance of relationships among interacting units. The social network perspective encompasses theories, models, and applications that are expressed in terms of relational concepts or processes. Along with growing interest and increased use of network analysis has come a consensus about the central principles underlying the network perspective. In addition to the use of relational concepts, we note the following as being important:
    * Actors and their actions are viewed as interdependent rather than independent, autonomous units
    * Relational ties (linkages) between actors are channels for transfer or "flow" of resources (either material or nonmaterial)
    * Network models focusing on individuals view the network structural environment as providing opportunities for or constraints on individual action
    * Network models conceptualize structure (social, economic, political, and so forth) as lasting patterns of relations among actors
    The unit of analysis in network analysis is not the individual, but an entity consisting of a collection of individuals and the linkages among them. Network methods focus on dyads (two actors and their ties), triads (three actors and their ties), or larger systems (subgroups of individuals, or entire networks.
    Source: Wasserman, S. and K. Faust, 1994, Social Network Analysis. Cambridge: Cambridge University Press.
  • Network graphic examples
    Source:
    Power Laws, Scale-Free Networks and Genome Biology (Molecular Biology Intelligence Unit) (Hardcover)
    by Eugene V. Koonin (Editor), Yuri I. Wolf (Editor), Georgy P. Karev (Editor)
    Source: http://www.amazon.com/Scale-Free-Networks-Biology-Molecular-Intelligence/dp/0387258833#reader
  • AGNA stands for Applied Graph & Network Analysis.
    Agna is a platform-independent application designed for social network analysis, sociometry and sequential analysis. This software can help you if you study communication relations in groups, kinship relations or the structure of animal behavior - to mention just a few realms where it can be used.
    WHAT IS NETWORK ANALYSIS
    Network analysis (or social network analysis) is a set of mathematical methods used in social psychology, sociology, ethology, and anthropology.
    This methodology assumes that the way the members of a group can communicate to each other affect some important properties of that group (such as performance, leadership, work satisfaction etc.)
    A network models generally a communication group. It consists of a number of nodes (each node corresponding to a member of the group) and a number of edges (each one being associated to a communication connection between two actors).
    Network data is stored in the adjacency matrix (or the sociomatrix). Commonly, the [i,j] element of the adjacency matrix refers to the communication behavior of actor ‘i’ to actor ‘j’.
    http://www.geocities.com/imbenta/agna/big_splash_1.gif
  • Tools for Complexity y Applied Complexity
    Complexity – like fractals, statistics and SIG – is a “transdisciplinary” analytic method
    Network analysis (Social Network Analysis)
    Power laws
    Geography
    Biology
    Forensic accounting (Benford’s Law)
    Urbanization
    ========================================================================================
    Power Law(s)
    A power law is a special kind of mathematical relationship between two quantities. If one quantity is the frequency of an event, the relationship is a power-law distribution, and the frequencies decrease very slowly as the size of the event increases. For instance, an earthquake twice as large is four times as rare. If this pattern holds for earthquakes of all sizes, then the distribution is said to "scale". Power laws also describe other kinds of relationships, such as the metabolic rate of a species and its body mass (called Kleiber's law), and the size of a city and the number of patents it produces. What this relationship means is that there is no typical size in the conventional sense. Power laws are found throughout the natural and manmade worlds, and are an active area of scientific research.
    http://en.wikipedia.org/wiki/Power_law
    Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty. The basis for this "law" is that the values of real-world measurements are often distributed logarithmically, thus the logarithm of this set of measurements is generally distributed uniformly.
    This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). The result holds regardless of the base in which the numbers are expressed, although the exact proportions change.
    It is named after physicist Frank Benford, who stated it in 1938,[1] although it had been previously stated by Simon Newcomb in 1881.[2] Although many "proofs" of this law have been put forth (starting with Newcomb himself), none were mathematically rigorous[3] until Theodore P. Hill's in 1995.[4]
    http://en.wikipedia.org/wiki/Benford%27s_law
  • Power Law Analysis
    Power law: a mathematical relationship between aspects of one type – size of stones in a pile of rocks – or two quantities. If one quantity is the frequency of an event, the relationship is a power-law distribution, and the frequencies decrease very slowly as the size of the event increases.
    Other kinds of relationships
    metabolic rate of a species and its body mass (called Kleiber's law)
    Size of a city and the number of patents it produces.
    ===============================================================================
    Power Laws
    the metabolic rate R for all organisms follows exactly the 3/4 power-law of the body mass, i.e., R M3/4. This is known as the Kleiber's Law. It holds good from the smallest bacterium to the largest animal (see Figure 01). The relation remains valid even down to the individual components of a single cell such as the mitochondrion, and the respiratory complexes (a subunit of the mitochondrion) as shown in Figure 02. It works for plants as well, though with a different ratio. This is one of the few all-encompassing principles in biology. But the law's universality is baffling: Why should so many species, with their variety of body plans, follow the same rules?
    Technical definition
    A power law is any polynomial relationship that exhibits the property of scale invariance. The most common power laws relate two variables and have the form
    f(x) = ax^k\! +o(x^k),
    where a and k are constants, and o(xk) is an asymptotically small function of x. Here, k is typically called the scaling exponent, where the word "scaling" denotes the fact that a power-law function satisfies f(c x) \propto f(x) where c is a constant. Thus, a rescaling of the function's argument changes the constant of proportionality but preserves the shape of the function itself. This point becomes clearer if we take the logarithm of both sides:
    \log\left(f(x)\right) = k \log x + \log a.
    Notice that this expression has the form of a linear relationship with slope k. Rescaling the argument produces a linear shift of the function up or down but leaves both the basic form and the slope k unchanged.
  • Source: http://www.bionik.tu-berlin.de/institut/xtutor1.htm
  • Source: Personal communication. Jose Luis HernandezDirector - ITHavana Medical Group cacerjlh@infomed.sld.cu  
  • Forensic Accounting – Benford’s Law
    Could you have applied Benford's Law to the distribution of most significant digit in the monthly series of Madoff returns, spotted something awry, and turned him in, without knowing anything about "split strike conversion" strategies?
    Source: http://paul.kedrosky.com/archives/2008/12/19/bernie_vs_benfo.html
    The upshot is that Bernie's performance numbers tracked Benford's surprisingly closely. In other words, a straightforward numerical analysis of his performance numbers – without recourse to knowledge about "split strike conversion" option strategies – would not necessarily have shown up the (alleged) fraud here. Matter of fact, had you done this sort of quantitative analysis as an SEC employee, your tendency might have been to be somewhat skeptical about claims of fraud.
    Now, this isn't meant to absolve Madoff. While he has been convicted of nothing, the allegations seem well substantiated, and he has apparently said some awfully incriminating things. Nevertheless, it is interesting to see that any fraud here was sufficiently sophisticated such that the proffered performance numbers were credible from a distributional point of view.
    Taking it one step further, it almost certainly means Madoff's numbers would have been generated algorithmically. He didn't pluck them from air at the end of each month. That is, I think, interesting in that it shows that this (alleged) con was at least somewhat more sophisticated than some of the noisier critics out there have been saying.
  • Urban area Power Laws
  • Urban area Power Laws
    Source: http://intersci.ss.uci.edu/wiki/index.php/Image:PaceOfLife.jpg and
  • A power law is a special kind of mathematical relationship between two quantities. If one quantity is the frequency of an event, the relationship is a power-law distribution, and the frequencies decrease very slowly as the size of the event increases. For instance, an earthquake twice as large is four times as rare. If this pattern holds for earthquakes of all sizes, then the distribution is said to "scale". Power laws also describe other kinds of relationships, such as the metabolic rate of a species and its body mass (called Kleiber's law), and the size of a city and the number of patents it produces. What this relationship means is that there is no typical size in the conventional sense. Power laws are found throughout the natural and manmade worlds, and are an active study of scientific research.
    Source: http://commons.wikimedia.org/wiki/File:Long_tail.svg
    Picture by Hay Kranen
  • Summary
    See phenomena as systems
    Use General Systems Theory to think about the phenomena
    Define the relationships between variables and how to measure those relationships
    Apply quantitative and qualitative methods to understand any phenomena
    Seek out colleagues in other disciplines with other methodologies. Try their methods.
  • “Environmental” Models
    Biosphere and scaling
    The condition of the cell, the chromosome, the gene can tell us important things about the condition of the organism AND, increasingly,
    Can tell us what can be expected in the future about the organism.
  • Genes and implications for cancer
    U-M researchers identify gene involved in breast cancer
    Scientists at the University of Michigan Comprehensive Cancer Center have identified a gene associated with the development of an aggressive form of breast cancer.
    The scientists observed that the gene, FOXP3, suppresses tumor growth. FOXP3 is located on the X chromosome, which means a single mutation can effectively silence the gene. This is unusual, as only one other gene associated with cancer has been found on the X chromosome.
    When one copy of the FOXP3 gene is silenced, the scientists found in studying mice, 90 percent of the mice spontaneously developed malignant tumors. The scientists also looked at FOXP3 in human breast tissue cells, comparing malignant and non-malignant cells. FOXP3 was found to be either deleted or mutated in a substantial portion of the cancer sample: about 80 percent of the cancer tissues studied did not express the gene at all.
    In addition, the scientists found FOXP3 to be a repressor of HER-2, a protein that typically marks a more aggressive form of breast cancer. The scientists believe FOXP3 suppresses the HER-2 gene. HER-2 can be activated by a number of different factors, but the scientists observed that when FOXP3 is normal, it keeps HER-2 levels low; when FOXP3 is missing or mutated, HER-2 levels are likely to rise.........
  • “Environmental” Models -- Datasphere
  • “Proyecto Genoma de Medios Informativos”
    Objectives:
    Develop methods to “map the genome” of media institutions
    Develop methods to conduct an autopsy of media institutions that have recently died
    Do this by looking at disciplines and methods from other disciplines
  • “Proyecto Genoma de Medios Informativos”
    Articulate initial mission statement
    Identify tools to conduct “condition of the institution” analysis (autopsy?) of existing media
    Create int’l database of media organization variables
    Create platform for collaboration on analysis
    Share knowledge of analytic tools from multiple disciplines
    Share evolution of methods and findings
  • Project process
    Create Web 2.0 website with …
    Methods for creating “standards” for metadata and data quality
    Web site objectives
    Data source sites
    Analytic tool sites
    Project management sub-sets and collaboration tools
  • Define/create database
    Metadata
    Who can submit/verify/edit data
    Evaluation methods of data quality
  • Source: Published online 9 March 2009 | Nature | doi:10.1038/458135a
    Box: Usage mapped
    From the article: web usage data outline map of knowledge
    Original article: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0004803#pone-0004803-g005
    http://0-www.nature.com.opac.sfsu.edu/news/2009/090309/full/458135a/box/1.html
    Online of images:
    http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0004803&imageURI=info:doi/10.1371/journal.pone.0004803.t006
  • Nuevos métodos para la investigación de la comunicación social y los medios de comunicación

    1. 1. 11 Nuevos métodos para laNuevos métodos para la investigación de lainvestigación de la comunicación social y loscomunicación social y los medios de comunicaciónmedios de comunicación Prof. Tom JohnsonProf. Tom Johnson Instituto de Periodismo AnalíticoInstituto de Periodismo Analítico Santa Fe, Nuevo Mexico USASanta Fe, Nuevo Mexico USA t o m @ j t j o h n s o n . c o mt o m @ j t j o h n s o n . c o m Prof. Pedro SotolongoProf. Pedro Sotolongo Presidente Fundador de la Cátedra“Presidente Fundador de la Cátedra“ de Complejidad” de La Habanade Complejidad” de La Habana p e d r o . s o t o l o n g o @ i n f o m e d . i l d . c up e d r o . s o t o l o n g o @ i n f o m e d . i l d . c u
    2. 2. 22 Objetivos de esta mañanaObjetivos de esta mañana  Introducir los conceptos de laIntroducir los conceptos de la teoría general de sistemas,teoría general de sistemas, Sistemas Dinámicos, Teoría deSistemas Dinámicos, Teoría de Complejidad Computacional yComplejidad Computacional y AplicadaAplicada  Destacar el carácterDestacar el carácter transdisciplinario (no inter-transdisciplinario (no inter- disciplinario) de la complejidaddisciplinario) de la complejidad  Convocatoria para la creación deConvocatoria para la creación de "medios de comunicación Proyecto"medios de comunicación Proyecto Genoma" (Si hay tiempo)Genoma" (Si hay tiempo)
    3. 3. 33 Primeros ConceptosPrimeros Conceptos DataesferaDataesfera  lugar conceptual en el que todos los datoslugar conceptual en el que todos los datos existen en todos los formatosexisten en todos los formatos  La dataesfera es accesible para todas lasLa dataesfera es accesible para todas las personas en diversos gradospersonas en diversos grados  DatosDatos  AnálisisAnálisis  la informaciónla información  Información = "Lo que nos ayuda a tomarInformación = "Lo que nos ayuda a tomar una decisión"una decisión"  "Sistemas" y "sub-sistemas" en la"Sistemas" y "sub-sistemas" en la Dataesfera funcionan para procesar datos,Dataesfera funcionan para procesar datos, ayudar en el análisis y generar informaciónayudar en el análisis y generar información
    4. 4. 44 Teoría General de SistemasTeoría General de Sistemas  Definición:Definición: "... un sistema es una configuración de partes"... un sistema es una configuración de partes conectadas y unidas por una red de relaciones“conectadas y unidas por una red de relaciones“  La perspectiva analítica y el énfasis se desplazaLa perspectiva analítica y el énfasis se desplaza de las partes a la organización de y a lasde las partes a la organización de y a las relaciones entre las partes (ejemplo: variables /relaciones entre las partes (ejemplo: variables / agentes / entidades)agentes / entidades)  Reconocimiento de que las interacciones no sonReconocimiento de que las interacciones no son estáticas, sino dinámicasestáticas, sino dinámicas
    5. 5. 55 Atributos de TGSAtributos de TGS 1. Compuesta de variables, i.e., elementos que pueden ser definidos o descritos, por separado. 2. Sub-variables. Árbol-a-rama-a- hoja-a-célula 3. Existen relaciones horizontales entre las variables y … 4. …relaciones verticales (i.e, jerárquicas)
    6. 6. 66 Atributos de TSGAtributos de TSG 3. Un sistema tiene límites  Conceptual  jurídico: las empresas, la jurisdicción  geográfica  Cultural 4. Un sistema tiene metas auto-definidas o con una definición impuesta por el observador / investigador  Gana dinero  Proporcionar al grupo seguridad, felicidad, procreación
    7. 7. 77 Atributos de TSGAtributos de TSG 5. Un sistema aprende de los cambios en sus variables o ambiente
    8. 8. 88 El Periódico como sistemaEl Periódico como sistema Variable/agentsVariable/agents Editorial Publicidad ProducciónCirculación Administración El sistema tiene variables / agentes / entidades
    9. 9. 99 El Periódico como sistemaEl Periódico como sistema Editorial Publicidad ProducciónCirculación Administración Variables are related to other variables …y generalmente en una relación que puede medirse. Circulación
    10. 10. 1010 ““Environmental” ModelsEnvironmental” Models Biosphere Species Sub-Species Organism Organs Tissue Cell Chromosome Gene
    11. 11. 1111 El periódico como un sistemaEl periódico como un sistema-- ScalingScaling Un sistema - y el análisis del sistema(s) - pueden ser "a escala" Datasphere Medios de comun. Periódicos Editorial Deportes Futbol Equipo local Concepto alto Baja Concepto Escalabilida d
    12. 12. 1212 Ejemplo de la herramienta deEjemplo de la herramienta de modelado de simulación SimVenturemodelado de simulación SimVenture “Calidad de la experiencia” “Tráfico total”
    13. 13. 1313 Valor de los Sistemas de PensamientoValor de los Sistemas de Pensamiento  Exige definir y enfocarse exactamente en el sistema del que se está hablando  Exige la consideración del nivel de análisis, es decir, el "zooming" de niveles de enfoque  Exige la definición de variables y, a continuación, la importancia relativa de las variables  Exige el examen de las relaciones entre las variables
    14. 14. 1414 TGS como base para modelos deTGS como base para modelos de simulación y análisis de la complejidadsimulación y análisis de la complejidad  TGS como base para modelos de simulación y análisis de la complejidad
    15. 15. 1515 Resumen  Datasphere oDatasphere o DataesferaDataesfera  DatosDatos  AnálisisAnálisis  InformaciónInformación  SistemasSistemas – Límites de Sistemas losLímites de Sistemas los – Los variables/agentes /entidadesLos variables/agentes /entidades – Relaciones entre variablesRelaciones entre variables – Objetivos del SistemaObjetivos del Sistema – ““Feedback (bucle) / "aprendizaje"Feedback (bucle) / "aprendizaje"  Preparación para modelado de simulaciónPreparación para modelado de simulación y Teoría de la Complejidad y Complejidady Teoría de la Complejidad y Complejidad AplicadaAplicada
    16. 16. 1616 Herramientas para la ComplejidadHerramientas para la Complejidad Complejidad y AplicadaComplejidad y Aplicada  Complejidad - como los fractales,Complejidad - como los fractales, las estadísticas y SIG - es unlas estadísticas y SIG - es un "transdisciplinario" método"transdisciplinario" método analíticoanalítico
    17. 17. 1717 Herramientas para la ComplejidadHerramientas para la Complejidad Complejidad y AplicadaComplejidad y Aplicada  FractalesFractales == A figuraA figura geométricageométrica que seque se repite en virtud de varios niveles de aumento,repite en virtud de varios niveles de aumento, una formauna forma irregularirregular que aparece en todas lasque aparece en todas las escalasescalas dede longitudlongitud, por ejemplo, un, por ejemplo, un helechohelecho
    18. 18. 1818 Transdiscipline Tools : SIGTransdiscipline Tools : SIG  SIG:SIG: SSistemas deistemas de IInformaciónnformación GGeográficaeográfica
    19. 19. 1919 Fractales y RedesFractales y Redes
    20. 20. 2020 Análisis visual de la Complejidad y RedAnálisis visual de la Complejidad y Red diagramasdiagramas
    21. 21. 2121 Recursos en línea: Complejidad yRecursos en línea: Complejidad y Análisis de Redes SocialesAnálisis de Redes Sociales  Complejidad y Redes SocialesComplejidad y Redes Sociales BlogBlog El objetivo de este blog es ofrecer un foro para laEl objetivo de este blog es ofrecer un foro para la discusión de los temas interrelacionados de ladiscusión de los temas interrelacionados de la red de análisisred de análisis yy teoría de sistemas complejos.teoría de sistemas complejos. http://ComplexityYSocialNetBlog-Esp.notlong.comhttp://ComplexityYSocialNetBlog-Esp.notlong.com  Análisis de redes socialesAnálisis de redes sociales Análisis de redes sociales se basa en el supuestoAnálisis de redes sociales se basa en el supuesto de la importancia de las relaciones entre lasde la importancia de las relaciones entre las unidades que interactúan.unidades que interactúan. http://www.iq.harvard.edu/blog/netgovhttp://www.iq.harvard.edu/blog/netgov
    22. 22. 2222 Red ejemplos gráficosRed ejemplos gráficos
    23. 23. 2323 Social Network Analysis graphicsSocial Network Analysis graphics
    24. 24. 2424 Herramientas para la Complejidad YHerramientas para la Complejidad Y Complejidad AplicadaComplejidad Aplicada  Complejidad - como los fractales, lasComplejidad - como los fractales, las estadísticas y SIG - es unestadísticas y SIG - es un "transdisciplinario" método analítico"transdisciplinario" método analítico  Red de análisisRed de análisis ((Social Network AnalysisSocial Network Analysis))  Leyes de PotenciaLeyes de Potencia – GeografíaGeografía – BiologíaBiología – Forense de contabilidadForense de contabilidad ((la Ley de Benfordla Ley de Benford:: Benford’s LawBenford’s Law)) – UrbanizaciónUrbanización
    25. 25. 2525 Análisis de la Leyes de PotenciaAnálisis de la Leyes de Potencia  Leyes de Potencia: una relaciónLeyes de Potencia: una relación matemática entre los aspectos de unmatemática entre los aspectos de un tipo - tamaño de las piedras en untipo - tamaño de las piedras en un montón de rocas - o dos cantidades.montón de rocas - o dos cantidades. Si una cantidad es la frecuencia de un caso, la relación esSi una cantidad es la frecuencia de un caso, la relación es una facultad de derecho de distribución, y la disminución deuna facultad de derecho de distribución, y la disminución de las frecuencias muy lentamente como el tamaño del eventolas frecuencias muy lentamente como el tamaño del evento aumenta.aumenta.  Otros tipos de relacionesOtros tipos de relaciones – de la tasade la tasa – metabólica de una especie y su masa corporalmetabólica de una especie y su masa corporal (llamada la ley de Kleiber)(llamada la ley de Kleiber) – Tamaño de una ciudad y el número deTamaño de una ciudad y el número de patentes que producepatentes que produce..
    26. 26. 2626 Leyes de Potencia BiologíaLeyes de Potencia Biología The “mouse-elephant” plot has the exponent 7/6. Source: http://www.bionik.tu-berlin.de/institut/xtutor1.htm
    27. 27. 2727 Geography-Global Islands’ Area Power LawsGeography-Global Islands’ Area Power Laws Source: Global Islands Power Laws.xlsx
    28. 28. 2828 Contabilidad Forense - la Ley deContabilidad Forense - la Ley de BenfordBenford Source: http://paul.kedrosky.com/archives/2008/12/19/bernie_vs_benfo.html Could you have applied Benford's Law to the distribution of most significant digit in the monthly series of Madoff returns, spotted something awry, and turned him in?
    29. 29. 2929 Leyes de PotenciazonaLeyes de Potenciazona urbanaurbana
    30. 30. 3030 Leyes de Potenciazona urbanaLeyes de Potenciazona urbana Source: 2007 Growth, innovation, scaling, and the pace of life in cities. Luís M. A. Bettencourt, José Lobo, Dirk Helbing, Christian Kühnert, and Geoffrey B. West PNAS 104(17):7301-7306 The slope of Power Law plots do not always have to go up
    31. 31. 3131 Inversa Ley de PotenciaInversa Ley de Potencia 20% de casos = 80% de total cuantidad 80% de total casos = 20%
    32. 32. 3232 Lista de los periódicos del mundo en circulaciónLista de los periódicos del mundo en circulación (000s)(000s) ley de potencia inversa 59 diarios necesario para 80% de total
    33. 33. 3333 Clasificación jerárquica de la circulaciónClasificación jerárquica de la circulación mundial de periódicosmundial de periódicos 3 periódicos representan el 20% del total de la circulación
    34. 34. 3434 Clasificación jerárquica de la circulaciónClasificación jerárquica de la circulación mundial de periódicosmundial de periódicos 3 periódicos representan el 20% del total de la circulación
    35. 35. 3535 ResumenResumen  Ver los fenómenos como sistemasVer los fenómenos como sistemas  Utilice la teoría general de sistemas paraUtilice la teoría general de sistemas para pensar en los fenómenospensar en los fenómenos  Definir las relaciones entre variables y laDefinir las relaciones entre variables y la manera de medir las relacionesmanera de medir las relaciones  Aplicar métodos cuantitativos yAplicar métodos cuantitativos y cualitativos para entender cualquiercualitativos para entender cualquier fenómenofenómeno  Buscar colegas de otras disciplinas conBuscar colegas de otras disciplinas con otras metodologías. Pruebe sus métodos.otras metodologías. Pruebe sus métodos.
    36. 36. 3636 Gracias. 11 NuevosNuevos métodos paramétodos para lala investigacióninvestigación de lade la comunicacióncomunicación social y lossocial y los mediosmedios dede comunicacióncomunicación Prof. Tom JohnsonProf. Tom Johnson Instituto de Periodismo AnalíticoInstituto de Periodismo Analítico Santa Fe, Nuevo Mexico USASanta Fe, Nuevo Mexico USA t o m @ j t j o h n s o n . c o mt o m @ j t j o h n s o n . c o m Prof. Pedro SotolongoProf. Pedro Sotolongo Presidente Fundador de la Cátedra“Presidente Fundador de la Cátedra“ de Complejidad” de La Habanade Complejidad” de La Habana p e d r o . s o t o l o n g o @ i n f o m e d . i l d . c up e d r o . s o t o l o n g o @ i n f o m e d . i l d . c u GraciasGracias
    37. 37. 3737 IFIF time available….time available….  Tom can introduce News MediaTom can introduce News Media Genome ProjectGenome Project
    38. 38. 3838 ““Environmental” ModelsEnvironmental” Models Biosphere Species Sub-Species Organism Organs Tissue Cell Chromosome Gene
    39. 39. 3939 Genes y cancerGenes y cancer 26 de julio de 2007, 9:33 PM CT UM investigadores identificar los genes implicados en el cáncer de mama Los científicos observaron que el gen, FOXP3, suprime el crecimiento tumoral. FOXP3 se encuentra en el cromosoma X, lo que significa una única mutación puede silenciar el gen de manera eficaz. Esto es inusual, ya que sólo uno de otros genes asociados con el cáncer se ha encontrado en el cromosoma X.
    40. 40. 4040 ““Environmental” ModelsEnvironmental” Models DATASPHEREBiosphere Species Sub-Species Organism Organs Tissue Cell Chromosome Gene Ley-Medicina-Periodismo T-e-P-Transmision Diarios Editorial-Producion- Distribution-Propaganda National Advertising-Local Specific Cities/Zones Ad type (auto, etc.)
    41. 41. 4141 ““Proyecto Genoma de MediosProyecto Genoma de Medios Informativos”Informativos”  Objectives:Objectives: – Develop methods to “map the genome”Develop methods to “map the genome” of media institutionsof media institutions – Develop methods to conduct an autopsyDevelop methods to conduct an autopsy of media institutions that have recentlyof media institutions that have recently dieddied – Do this by looking at methods fromDo this by looking at methods from other disciplinesother disciplines
    42. 42. 4242 ““Proyecto Genoma de MediosProyecto Genoma de Medios Informativos”Informativos” – ArticulateArticulate initialinitial mission statementmission statement  Identify tools to conduct “condition of the institution”Identify tools to conduct “condition of the institution” analysis (autopsy?) of existing mediaanalysis (autopsy?) of existing media – Create int’l database of media organizationCreate int’l database of media organization variablesvariables – Create platform for collaboration on analysisCreate platform for collaboration on analysis – Share knowledge of analytic tools fromShare knowledge of analytic tools from multiple disciplinesmultiple disciplines – Share evolution of methods and findingsShare evolution of methods and findings
    43. 43. 4343 ““Proyecto Genoma de MediosProyecto Genoma de Medios Informativos”Informativos”  Project processProject process – Create Web 2.0 website with …Create Web 2.0 website with …  Methods for creating “standards” forMethods for creating “standards” for metadata and data qualitymetadata and data quality  Web site objectivesWeb site objectives  Data source sitesData source sites  Analytic tool sitesAnalytic tool sites  Project management sub-sets andProject management sub-sets and collaboration toolscollaboration tools
    44. 44. 4444 Proyecto Genoma de MediosProyecto Genoma de Medios InformativosInformativos – Define/create databaseDefine/create database  MetadataMetadata –Trans-lingual definitions/code tagsTrans-lingual definitions/code tags  Who can submit/verify/edit data?Who can submit/verify/edit data?  Evaluation methods of data quality?Evaluation methods of data quality?
    45. 45. 4545 Clickstream Data Yields High-Resolution Maps ofClickstream Data Yields High-Resolution Maps of ScienceScience
    46. 46. 4646 Gracias. 11 NuevosNuevos métodos paramétodos para lala investigacióninvestigación de lade la comunicacióncomunicación social y lossocial y los mediosmedios dede comunicacióncomunicación Prof. Tom JohnsonProf. Tom Johnson Instituto de Periodismo AnalíticoInstituto de Periodismo Analítico Santa Fe, Nuevo Mexico USASanta Fe, Nuevo Mexico USA t o m @ j t j o h n s o n . c o mt o m @ j t j o h n s o n . c o m Prof. Pedro SotolongoProf. Pedro Sotolongo Presidente Fundador de la Cátedra“Presidente Fundador de la Cátedra“ de Complejidad” de La Habanade Complejidad” de La Habana p e d r o . s o t o l o n g o @ i n f o m e d . i l d . c up e d r o . s o t o l o n g o @ i n f o m e d . i l d . c u GraciasGracias

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