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Más que minería de procesos y predicción de comportamientos. = Un nuevo enfoque.<= span style=3D'mso-bookmark:_Hlk532635351'>

 

 

More than mining processes and prediction of behaviors. A new approach.

 

 

Lázaro Luis Acosta Quintana.[1], Orlenys López Pintado.[2] , Yasser Vázquez Alfonso. [3]& Velasteguí López Efraín= [4].

 

Recibido: 13-12-201= 7 / Revisado: 07-02-2018 Aceptado: 05-03-2018/ Publicado: 01-04-2018=

 

Abstract.

As a result of the boom and technological advancement of computing, the limita= tion in the manual analysis of the data has increased. On a daily basis, informa= tion systems store large amounts of respective events to the processes they represent. This situation motivated researchers to look for new alternative= s. As a result, process mining arises, with a great impact on the organization= al world.  This discipline aims to ext= ract non-trivial information, in processes of a varied domain of applications. In this branch, several techniques have been developed to model, extend and monitor processes. One of the key achievements of process mining is the Aud= it 2.0 model. Unifying most of the results obtained in this discipline, Audit = 2.0 substantially changes the role of auditors. However, the scarce results in = some areas of process mining limit the implementation of this strategy.  For example, in predicting behaviors, b= eing one of the least exploited areas within the discipline. The fundamental motivation of the research focuses precisely on this problem. The study foc= uses on the limitations of predicting behavior. In that sense, the first stage is devoted to the general analysis of process mining. It shows the imbalance between the fundamental stages of this branch and the isolated stages. Fina= lly, a critical analysis of various machine learning techniques is performed that can be used in the problems de tected.

 

Keywords: Process Mining, Auditing 2.0, = Predicting Behaviors, Machine Learning

Resumen.=

Consecuentemente con el auge y av= ance tecnológico de la computación,<= span style=3D'letter-spacing:-1.0pt'> ha aumentado la limitación en el análisis manual de los datos. Diariamente, los sistemas de información almacenan grandes cantidades de eventos respectivos a los proce= sos que representan. Esta situación, motivó a los investigadores para buscar nu= evas alternativas. Como resultado surge la minería de procesos, con un gran impa= cto en el mundo organizacional. Esta disciplina, tiene como objetivo extraer información no trivial, en procesos de un variado dominio de aplicaciones. = En esta rama, diversas técnicas han sido desarrolladas para modelar, extender y monitorear procesos. Uno de los logros fundamentales de la minería de proce= sos lo constituye el modelo Auditoría 2.0. Unificando la mayoría de los resulta= dos obtenidos en esta disciplina, Auditoría 2.0 cambia sustancialmente el rol de los auditores. No obstante, los= resultados escasos en algunas áreas = de la minería de procesos, limitan la<= span style=3D'letter-spacing:.45pt'> puesta en práctica de esta estrategia. Por ejemplo, en la predicción de c= omportamientos, siendo una de las áreas menos explotada dentro de la disciplina. La motivación fundamental de la investigación se enfoca precisamente en esta problemática. El estudio realizado, se centra en las limitaciones de la predicción de comportamientos. En ese sentido, la primera etapa está dedicada al análisis general de la minería de procesos. Se demuestra, = el desequilibrio existente entre las etapas fundamentales de esta rama y las etapas aisladas. Finalme= nte, se realiza un análisis crítico de variadas técnicas de aprendizaje de máquinas= que pueden ser utilizadas en la problemática detectada.

&nb= sp;

Palabras Claves: Minería de Procesos, Auditoría 2.0, Pre= dicción de Comportamientos, Aprendizaj= e de Máquinas.

Introducción.

1. Minería de Procesos: Etapas Fundamentales y Trabajos Relacionados.

 

La minería de procesos es una discipli= na en crecimiento dentro de la ciencia de la computación. Su objetivo, se enfo= ca en la extracción de conocimiento sobre procesos de un variado dominio de aplicaciones. En la actualidad, el crecimiento de la informatización ha provocado que las organizaciones almacenen grandes cantidades de datos diariamente. Esto imposibilita el análisis de los procesos sin la utilizaci= ón de herramientas automatizadas. Como resultado, de manera general se detectan desviaciones basadas en suposiciones y no en los datos, siendo estos los que representan el comportamiento ocurrido. En ese sentido, la minería de proce= sos es una solución efectiva, ofreciendo técnicas de modelación y mejora de procesos de manera automática. Los resultados obtenidos es esta área han te= nido tanto impacto que en el ańo 2012 se plasmaron varios de los retos fundament= ales y paradigmas que rigen la minería de procesos en un manifiesto (Van der Aalst et al, 2011).

 

Lanzado por un grupo de expertos conoc= ido como IEEE Task Force on Process Mining, dicho manifiesto constituye uno de los documentos fundamentales de esta disciplina. Además, es un estándar soportado por 53 organizaciones y bajo la contribución de 77 especialistas en el tema. Todas las técnicas de minería = de procesos asumen que es posible recuperar los eventos secuencialmente de un = log[5]. = Cada evento representa una actividad[6] q= ue fue ejecutada en una de las ocurrencias (instancias) del proceso en cuestió= n. Comúnmente, los registros de eventos incorporan información asociada a los eventos o las instancias, variando en función del proceso. Los atributos utilizados con más frecuencia son: persona o dispositivo que ejecuta la actividad, fecha de ocurrencia, estado en que se encuentra la actividad (iniciada, sus<= span style=3D'letter-spacing:.3pt'>pendida, terminada, etc.), entre otros. Teniendo en cuenta esta información, los datos pueden ser analizados desde diferentes perspectivas (Van der Aalst, 2011).

 

La perspectiva de control de flujo: Analiza el orden y relación entre las actividades. Tiene co= mo objetivo caracterizar el proceso intentando representar todas las posibles secuencias de actividades.

 

La perspectiva organizacional: Se centra en los actores involucrados y sus relaciones con las actividades. Su objetivo es estructurar el conocimiento obtenido atendiendo a roles o para obtener el grafo social.

 

La perspectiva de los casos: Se refiere a los atributos de las instancias. Aun cuando esta representa una ejecución del proceso, puede enriquecerse con información que la caracterice, atendiendo a datos generales de dicha ejecución.

 

La perspectiva del tiempo: Utiliza la información relacionada con los tiempos de ocurrencia y frecuencias de los eventos. Tiene como objetivo detectar posib= les cuellos de botella, así como intentar predecir la duración de los futuros eventos.

 <= /o:p>

Tradicionalmente, las diferentes técni= cas de minería de procesos toman como punto de entrada un registro de eventos. = A su vez, según sus características, dividen en tres etapas fundamentales esta disciplina (Van der Aalst, 2011) descubrimiento de modelos, chequeo de correspondencia y extensión de modelos. Estas etapas interactúan entre sí con, el objetivo de obtener modelos que representen en la medida de lo posible la realidad de l= os procesos. Para ello, se deben tener en cuenta las 4 dimensiones utilizadas = para evaluar modelos (Adriansyah et al, 2015., Buijs et al, 2012., Dongen et al, 2014., Pintado, 2015., Rozinat y Van der Aalst, 2008 & Van der Aalst et al, 2010)

 

Completitud: Mide cuánto del comportamiento ocurrido en el proceso es representado por el mod= elo obtenido. Un modelo completo debe ser capaz de reproducir todo el comportamiento observado en el log.

 

Simplicidad: Esta dimensión se centra en determinar de todos los modelos que reproduzcan el comportamiento del proceso, el que sea estructuralmente más simple.

 

Precisión: Evalúa el modelo atendiendo a cuánto del comportamiento representado no ocurre realmente en el proceso. Tiene como objetivo evitar modelos muy generales, = en ese sentido, serán penalizados modelos que reflejen comportamiento no obser= vado en el registro de eventos.

 

Generalización: Determina cuánto del comportamiento no ocurrido, pero que puede ser correcto, debe ser representado, evitando modelos demasi= ado precisos.

 

El principal desafío de los algoritmos= de descubrimiento, radica en detectar las diferentes relaciones entre las actividades del proceso, teniendo en cuenta los principales patrones estructurales (Medeiros, 2006). En esta área se han realizado numerosas investigaciones, dando lugar a disimiles algoritmos para descubrir modelos = de variadas características. Algunas investigaciones asumen condiciones como completitud y ausencia de ruidos en los registros de eventos, muy difíciles= de lograr en entornos reales (Weerdt, Backer, Vanthienen & = Baesens, 2012). Entre estos, se encuentra el algoritmo Alpha (Van der Aalst, Weij= ters & Maruster, 2004), siendo uno de los pioner= os en esta rama.

 

Varias investigaciones se centran en la utilización de heurísticas para el descubrimiento de modelos. Por ejemplo, = el algoritmo Heuristic Miner<= /span> (Burattin A. and Sperduti,= 2010., Greco et al, 2006., Weijters y Ribeiro, 2011 &a= mp; Weijters et al, 2006), que es capaz de lidiar con reg= istros de eventos con ruido, no obstante, falla al determinar tareas duplicadas y = no recupera el patrón selección no libre. Sin embargo, el Heuristic Miner se encuentra entre los de mayor aceptació= n en esta ´área. Otro algoritmo que emplea heurísticas es el Genetic Miner (Bratosin, 20= 11., MEDEIROS et al, 2007., Medeiros, 2006 & Turner, 2009), es robusto ante ruidos y es capaz de recuperar todos los patrones estructurales más comunes= .

 

Al igual que el H= euristic Miner, este algoritmo ha servido de guía para o= tras investigaciones posteriores. Un resultado relacionado (Pintado, 2015) inten= ta aprovechar las ventajas de ambos y eliminar sus limitaciones, mostrando una nueva estrategia para obtener modelos robustos. El algoritmo Evolutionary Tree Miner (Buijs et al, 2012 = & Buijs, 2014), es una técnica reciente relacionada con= los algoritmos genéticos, el cual obtiene resultados considerables utilizando alineamientos entre el log y el modelo (Buijs e= t al, 2012). Los algoritmos mencionados relacionan estrechamente las tres etapas = fundamentales de la minería de procesos. En sus enfoques utilizan técnicas que evalúan modelos, luego, basándose en los resultados obtenidos, construyen ex- tensi= ones hasta lograr el modelo final como resultado del algoritmo. Esto permite la obtención de modelos con índices de calidad elevados.

 

Desde otra perspectiva, se encuentra el algoritmo Inductive Miner<= /span> (Leemans S., Fahland D. &a= mp; Van der Aalst, 2013), que utiliza teoría de grafos para la obtención del modelo. En su versión inicial, presenta problemas para detect= ar ciclos complejos, tareas invisibles y no construye el patrón selección no libre. No obstante, en su extensión (Leemans, 2= 014), se tienen en cuenta los efectos de las secuencias de eventos incompletas pa= ra intentar solucionar los problemas anteriores. Otro resultado (Leemans S., Fahland D. &a= mp; Van der Aalst, 2015), utiliza la información relacionada = con los tiempos de ejecución de los eventos, para diferenciar tareas concurrent= es de tareas intercaladas.

 

1.1.    Trabajos aislados.

Aunque no incluidas, existen diversas técnicas que contribuyen y se relacionan estrechamente con las tres etapas fundamentales de la minería de procesos. Entre ellas, las técnicas de agrupamiento, que a pesar de no se propias de esta disciplina, han sido aplicadas con diversos objetivos. El principal, ha sido contribuir al descubrimiento de modelos, intentando solucionar el problema de los llamados modelos espagueti (Van der Aalst, 2011). En ese sentido, se han realizado diversas investigaciones, algunas proponen determ= inar la similitud de las trazas (instancias) atendiendo a la frecuencia de ocurrencia de sus actividades (Song M., Gu¨nther C. & Van der= Aalst, 2008). No obstante, este enfoque no es eficaz en presencia de ciclos comple= jos, construcciones de selección no libre y tareas invisibles. Otros resultados = Chandra J y Van der Aalst= (2009), asumen que las actividades son letras y las instancias son palabras. Luego, utilizan esta información para determinar la similitud de las trazas basánd= ose en patrones. Otra investigación relacionada (Chandra J y Van der Aalst, 2009), determina la similitu= d de dos trazas basándose en la cantidad mínima de cambios que se necesitan para= igualarlas. Aunque generalmente se utiliza el agrupamiento de trazas como soporte para = el descubrimiento de modelos, existen otros enfoques. Por ejemplo, el agrupami= ento puede ser utilizado para detectar desviaciones en el proceso (Hompes, s/f). Otra variante puede ser, utilizar el agrupamiento en combinación con las reglas propuestas en DecSerFlow (Chesani et al.2007), permitiendo analizar el p= roceso con otro enfoque. Además, el agrupamiento de trazas puede ser utilizado des= de la perspectiva del tiempo. Un ejemplo de ello (Luengo D y Sepu´lveda M., 2011), utiliza los tiempos de ejecución de los eventos para agrupar des= de esta perspectiva.

 

Otro grupo de técnicas se definen bajo= el nombre de soporte operacional. Una gama relativamente nueva dentro de esta = disciplina que es de gran interés para el análisis de procesos. Dividiéndose en tres etapas: detección, predicción y recomendación de comportamientos, el soporte operacional es una de las áreas de investigación menos explotada en la mine= ría de procesos. Las técnicas descritas previamente, son utilizadas en el análisis= de trazas finalizadas[7] o casos históricos. A diferencia, los resultados en esta área se cent= ran en el análisis de trazas no finalizadas[8] o casos actuales.

 

La figura 1 muestra una comparación en= tre ambos enfoques, teniendo en cuenta las técnicas de soporte operacional y las etapas clásicas de minería de procesos. Nótese que, la detección, predicció= n y recomendación de comportamientos, están orientadas al trabajo con casos act= uales. Sin embargo, la detección también es aplicable a las trazas finalizadas. Por otro lado, las técnicas de descubrimiento, chequeo y extensión de modelos e= stán destinadas al trabajo con casos históricos. Es importante seńalar que, el soporte operacional, a pesar de utilizar modelos de procesos en la mayoría = de los casos, tiene como objetivo el análisis de trazas. Esto ocurre, debido a= que las técnicas de esta área no contribuyen directamente a la modelación. No obstante, pudiese considerarse que el soporte operacional está estrechamente relacionado con la extensión de modelos. El soporte operacional, en conjunto con las etapas fundamentales de la minería de procesos dan lugar al modelo Auditoría 2.0 (Van Aalst et al, 2010), como nueva estrategia para la audito= ria de procesos.

 

 

Figura 1. Comparación de la utilización de las diferentes técnicas de minería de procesos en casos actuales y casos históricos. (Tomada de: Van der Aalst et al. 2010).

 

2.  <= /span>Modelo Auditoría 2.0.

 

El modelo Auditoría 2.0, presentado en= el ańo 2010 por van der Aaslt= y colaboradores, cambia drásticamente el rol de los auditores. Típicamente,= el trabajo de los analistas ha estado limitado, debido a los grandes volúmenes= de datos almacenados. Con la utilización de esta nueva estrategia de auditoría, las elevadas cantidades de eventos registrados no son una limitante. En consecuencia, posibilita la extracción de conocimiento a mayor escala. En Auditoría 2.0, las diferentes funcionalidades aparecen divididas, debido a = las fuentes de datos para las cuales están dirigidas. En un primer grupo se encuentran las técnicas de descubrimiento, chequeo y extensión de modelos, utilizadas a partir de los datos históricos. Luego, a estas técnicas contri= buye la comparación entre modelos reales y modelos ideales.

 

De esta forma, a partir de los casos históricos, se pueden detectar violaciones o inconsistencias en el proceso. Además de detectar violaciones, los modelos pueden ser evaluados con otros objetivos. Por ejemplo, si el modelo que se obtiene debe ser descriptivo, en este caso una traza no representada por el mismo no necesariamente sería una violación. En ese sentido, el modelo podría no estar correctamente construi= do.

 

Basándose en el conocimiento adquirido= a partir de las trazas finalizadas, y enfocadas en los casos actuales, se encuentran las técnicas de soporte operacional. En este punto, orientadas al funcionamiento en tiempo real, dichas técnicas habilitan a los auditores pa= ra el análisis de procesos desde otro enfoque. Aunque el modelo Auditoría 2.0 propone utilizar la mayoría de las técnicas de minería de procesos, fuese conveniente adicionar otros enfoques. Por ejemplo, el agrupamiento de datos, con el objetivo de detectar desviaciones, así como obtener varios modelos q= ue se relacionen en lugar de un único modelo. Otra posible extensión, tendría lugar vinculando otras disciplinas como minería de datos con el objetivo de mejorar las técnicas de soporte operacional (De Leoni M. y Van der Aalst, 2014)

 

3.   Predicción de Comportamientos: Análisis Crítico y Trabajos Relacionados.

 

Los resultados obtenidos hasta el momento en la predicción de comportamientos, = se basan fundamentalmente en la utilización de análisis estadísticos. Entre el= los, destaca una investigación realizada por (Van der Aalst et al. 2011), en la cual se propone una estrategia general para el soporte operacional. En ese caso, se analiza la duración de los eventos y su tiempo de espera antes de comenzar.= Con ello, se extiende un modelo que será utilizado para predecir comportamiento= s. Otras investigaciones (Van der Aalst, Pesic y Minseok, 2010., V= an der Aalst, Schonenberg y = Song, 2011), trabajan igualmente desde la perspectiva= del tiempo utilizando datos estadísticos y modelos de procesos básicos.

 

En ninguna de las investigaciones mencionadas se analiza la influencia de los atributos de los eventos, así como la influencia de las posibles secuencias= de los mismos. Por ejemplo, un modelo de procesos debe tener cierto nivel de generalización, permitiendo comportamientos no reflejados en los datos (pero que pudieran ser correctos).  En ese sentido, una predicción puede indicar la ocurrencia de un evento determinad= o. Sin embargo, para la secuencia de eventos ocurrida puede que esta predicción sea improbable.

 

Un caso similar ocurre cuando el evento que se predice, representa un comportamiento reflejado por el proceso. No obstante, debido al análisis de= las frecuencias de ejecución de los eventos, puede ocurrir que la probabilidad = con la que se estima dicha predicción sea incorrecta. Igualmente ocurre con la predicción de atributos, en este caso, lo que sucede comúnmente es que se estiman los valores utilizando métodos puramente estadísticos. Esto imposib= ilita el análisis de los atributos según las secuencias de eventos ocurridas. Otra variante a utilizar sería representar el proceso utilizando arboles de prefijos, de esta forma solo serían consideradas las secuencias de eventos ocurridas. En comparación con las técnicas mencionadas, este enfoque brinda mayor precisión en las predicciones, no obstante, se pierde la capacidad de generalización. Además, persiste la problemática mencionada con respecto a = la influencia de las secuencias de eventos y los atributos. =

 

Recientemente, una investigación realizada por van der Aalst y colaboradores (Nakatumba, = Westergaard & Van der Aalst, 2012), propone un meta-mod= elo para el soporte operacional. Dicho enfoque puede resultar útil para general= izar estrategias que permitan diagnosticar, comparar, predecir y recomendar comportamientos.  No obstante, dada= la naturaleza de dicha investigación, continúan las limitaciones detectadas.

 

Según el análisis realizado, el principal reto a la hora de realizar predicciones, radica en la utilización de técnicas capaces extraer conocimiento de los da= tos de cada suceso. Además, que permitan analizar la influencia de los mismos en las diferentes etapas del proceso. Esta problemática constituye uno de los principales desafíos planteados en el manifiesto de minería de procesos.

 

4. Aprendizaje de Máquinas: Basamentos Fundamentales y Técnicas de Interés.=

 

El aprendizaje, al igual que la inteligencia, tiene diferentes concepciones se= gún el área de la ciencia en la que se analiza. Del aprendizaje de máquinas o aprendizaje automático, específicamente, se puede decir que tiene grandes similitudes con el aprendizaje de los animales. Existe un gran número de técnicas de esta disciplina que tienen sus basamentos en descubrimientos de carácter biológico, creando a partir de ellos modelos computacionales.  De igual manera, se puede considerar qu= e los resultados obtenidos por los investigadores del aprendizaje automático, pue= den aportar a las teorías del aprendizaje animal. Desde el punto de vista de la computación, se puede decir que una máquina aprende cuando cambia su estructura, programa o información, debido a cambios en el entorno que estu= dia. Similarmente, se dice que una máquina ha aprendido cuando ha sido capaz de estructurar la información, detectando las relaciones significativas. Con e= llo, debe poder analizar nuevos datos basándose en el conocimiento obtenido. En muchas ocasiones, el campo del aprendizaje automático se solapa con el de la minería de datos y la estadística.

 

En un inicio, se pudiese considerar la creación de programas de computado- ras= , ya diseńados y optimizados para resolver las tareas concretas que se necesiten= . De esta forma, se evitaría la utilización del aprendizaje automático, sustituyéndolo por algoritmos que resuelvan la misma problemática sin la necesidad de inducir conocimiento. No obstante, existen varias razones para rechazar esta hipótesis, demostrando la necesidad del aprendizaje de máquin= as, a continuación, se describen algunas:

1.      Las grandes cantidades de datos almacenados respectivos a las problemáticas que se estudian, pueden imposibilitar su análisis de forma manual. Debido a ello, sería complejo diseńar programas desconociendo total o parcialmente el problema a resolver= . En ese sentido, las computadoras poseen capacidades que les permiten analizar grandes volúmenes de información en menor tiempo. Además, existen varias técnicas de aprendizaje automático diseńadas para aprender a medida que los datos son obtenidos.

<= ![if !supportLists]>2.      Algunas tareas no pueden ser definidas de forma precisa, excepto, atendiendo a ejemplos de entrada y sal= ida. Sin embargo, se desconocen las relaciones entre los datos. En esos casos, convienen técnicas capaces de analizar la información y modificar su estruc= tura interna para representar el conocimiento.

<= ![if !supportLists]>3.      Las condiciones del ambiente do= nde se desarrolla la problemática pueden cambiar constantemente. En ese sentido, l= as técnicas de aprendizaje automático pueden adaptarse a nuevas condiciones reduciendo la necesidad de rediseńar los programas.

4.      Nuevos conocimientos son obteni= dos constantemente acerca de las tareas a resolver. El rediseńo de los sistemas= en esos casos sería una solución poco práctica.  No obstante, el aprendizaje de máquinas puede estar habilitado para = manejar dichos cambios sin necesidad de rediseńo.

 

Teniendo en cuenta la tipología de los datos de entrada, los algoritmos de aprendizaje automático se dividen en va= rios grupos. A continuación, se describen de manera general los fundamentales (H= arrington, 2012 & Nilsson, 1996)

 

Aprendizaje supervisado: Se refiere a = los algoritmos que parten de ejemplos en forma de tuplas, = refiriéndos cada una a los datos de la entrada y su correspondiente salida. El objetivo= de estas técnicas es obtener funciones o estructuras que establezcan una correspondencia entras las entradas y las salidas deseadas. Esta gama, a su vez, se divide en dos grupos: clasificación y predicción de valores numéric= os (también conocido como regresión).

 

Aprendizaje no supervisado: El aprendizaje se lleva a cabo a partir ejemplos formados solamente por datos de entrada, para los cuales se desconocen sus categorías. Los algoritmos de esta área intentan reconocer patrones dentro = de los datos, con el objetivo de etiquetarlos y poder etiquetar nuevas entrada= s. Entre estas técnicas se encuentran algoritmos de agrupamiento, algoritmos p= ara encontrar reglas de asociación y conjuntos de datos frecuentes.<= /span>

 

Atendiendo a los dos grupos descritos,= se realizó un estudio de las técnicas pertenecientes a cada uno, que se prevé pueden ser utilizadas en la predicción de comportamientos. Lo que resta de = esta sección, se dedicó al análisis crítico de las estructuras y algoritmos identificados.

 

4.1. Aprendizaje Supervisado. Clasificación.

 <= /span>

Las técnicas= de clasificación tienen lugar cuando la variable a predecir (variable objetivo= ) es de tipo nominal, aunque una variable nominal puede ser mapeada a una variab= le discreta. En ese sentido, se espera que un clasificador una vez ter- minado= su aprendizaje, sea capaz de asociar a una entrada su variable objetivo correspondiente. Además, debe ser capaz de generalizar los comportamientos presentes en los datos. La mayoría de las técnicas de esta gama, cuentan con dos etapas: una etapa de entrenamiento y una etapa de predicción de nuevos valores. En la primera etapa, un conjunto de datos es suministrado al algoritmo, para ser utilizados en el proceso de aprendizaje. Es importante seńalar que, dichos datos deben reflejar de manera general todo el espacio = de entrada, de lo contrario, la estructura puede no aprender correctamente. Algunos de = los clasificadores más comunes son los ´arboles de decisión, el método k-nn conocido como k vecinos más cercanos (del inglés K= nearest neighbours), las = redes neuronales y las máquinas de soporte vectorial.

 <= /o:p>

Los arboles = de decisión (Harrington, 2012., Nilsson, 1996 & Shwartz y Shai, 2014), son estructuras que dividen los datos de entrada atendiendo a sus atributos, hasta llegar a un estado final o decisión. Formalmente, se puede decir que cada nodo representa un estado, mientras que los arcos representa= n posibles decisiones dado un estado. Los nodos hoja, particularmente, se refieren al resultado final del conjunto de decisiones tomadas. Bajo este principio, los algoritmos que construyen árboles de decisión realizan cortes secuencialmente en los datos, hasta llegar al valo= r de la variable objetivo. En cada estado, las divisiones en la información se realizan teniendo en cuenta el concepto entropía, basándose en los atributo= s.

 

De esta forma, el árbol se construye eligiendo primero aquellos atributos que contengan mayor cantidad de información. Una vez finalizado el proceso de entrenamiento, la estructura resultante puede ser utilizada tanto para predecir como para tom= ar decisiones. Los árboles de decisión pueden ser construidos utilizando atributos tanto discretos como continuos. No obstante, el resultado de una predicción siemp= re es nominal, de ahí que se encuentre en el grupo de los clasificadores. Una = de las mayores ventajas de los árboles de decisión, es su facilidad de compren= sión por los humanos, convirtiéndolos en un paradigma en la toma de decisiones. Además, pueden tratar de forma consistente con datos que presenten ruidos o= atributos irrelevantes. También, se destaca que su construcción es computacionalmente factible. Sin embargo, es necesario seńalar que esta estructura es propensa= a sobreajuste[9] (comúnmente se utiliza= el término en ingles overfitting).

 

El algoritmo k-<= span class=3DSpellE>nn (Harrington et al, 2014), a diferencia de los árboles de decisión, no construye una estructura en concreto, aunque pueden utilizarse estructuras = de datos para su optimización. El objetivo de esta técnica es clasificar un nu= evo valor, para el cual se desconoce a qué grupo pertenece. Para ello, el algor= itmo se basa en los k vecinos más cercanos al él, donde la distancia se mide en = base a los valores de sus atributos. Este enfoque se basa en la premisa de que, = si los k elementos más cercanos al ejemplo a predecir se encuentran en su mayoría = en un grupo determinado, es probable que el caso a predecir también pertenezca= a esta categoría. El valor seleccionado de k, supone en esta técnica, cambios= en cuanto a la generalización-especificación, el crecimiento de k es directame= nte proporcional a la capacidad de generalización. Una extensión de este algori= tmo puede ser la utilización de distancias ponderadas, dando mayor peso a los elementos más cercanos. El algoritmo k-nn, pese= a que realiza la clasificación con altos valores de precisión y es robusto ante r= uidos, es computacionalmente costoso y no recomendado para grandes volúmenes de da= tos.

 

Una amplia gama = de algoritmos y estructuras se encuentran bajo el nombre de redes neuronales artificiales, constituyendo un paradigma en el aprendizaje computacional. Basadas en las características del sistema nervioso animal, las redes neuro= nales están compuestas por un conjunto de nodos, interconectados estructuralmente= por aristas de pesos ajustables.  Diver= sos tipos de redes neuronales han sido diseńadas, diferenciándose entre sí tant= o en estructura como en mecanismos de entrenamiento. Entre las redes más básicas= se encuentran Adaline y Perceptrón (Harrington, 20= 12 & Ben Krose et al, 1993), las cuales no son capaces de resolver problemas no lineales. Por otro lado, el Perceptrón Multicapa (Ben Krose et al, 1993 & <= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se= rif'>Nilsson, 1996), en conjunto con el método de entrenamiento propagación hacia atrás (del inglés back= propagation), es capaz de aproximar relaciones no lineales entre datos de entrada y salid= a. Esta red se ha convertido en una de las arquitecturas más utilizadas actualmente. Las redes neuronales son robustas ante datos que presenten rui= dos. Además, es importante seńalar que son capaces de ajustar su estructura inte= rna para representar la in- formación. De esta forma, no es necesario conocer d= etalladamente las relaciones entre los datos. No obstante, algunos parámetros importantes deben ser seleccionados por el usuario, por ejemplo: cantidad de capas ocul= tas, cantidad de nodos por capa, umbrales, etc. En ese sentido, el diseńo de red= es neuronales ha sido apoyado por la utilización de algoritmos evolutivos, para la obtenc= ión de valores que arrojen resultados satisfactorios. La limitación fundamental= en la utilización de redes neuronales radica en el alto coste computacional requerido para su entrenamiento. Sin embargo, esta gama de técnicas continúa siendo utilizada e investigada debido a su capacidad de aprendizaje.

 

Las máquinas de soporte vectorial (And= rew, 2013. & Zhang, 2001), son un conjunto de algoritmos utilizados para problemas de clasificación.  Un ele= vado número de investigadores consideran esta técnica como uno de los mejores clasificadores. Una máquina de soporte vectorial, intenta dado un conjunto = de datos de entrada obtener un modelo de predicción, basándose en la obtención= de un conjunto de hiperplanos[10] = que los dividan. La manera más simple de realizar una separación es utilizando = una recta o un hiperplano N-dimensional, no obstante, en la mayoría de los casos esto no es posible.  Esta problemát= ica trae como consecuencia un elevado coste computacional para este tipo de algoritmos. Como solución, se plantea la utilización de funciones Kernel para proyectar la información a un espacio de características de mayor dimensión. Las máquinas de soporte vectorial constituyen un mecanismo aceptado en sustitución de clasificadores como las redes neurona- les. En ese sentido, cabe seńalar que el entrenamiento de es= tos algoritmos es muy eficiente. Sin embargo, se necesitan definir parámetros c= omo la función Kernel.

 

Pese a que todas las técnicas analizad= as tienen ventajas y desventajas, existe una limitación en común: la problemát= ica conocida como clasificación desequilibrada. Considérese, una situación donde algunas clasificaciones estén representadas por cantidades de elementos pot= encialmente menores que el resto. Cuan- do esto ocurre, de manera general los clasificadores presentan problemas para etiquetar las entradas pertenecient= es a estos grupos. Diversas investigaciones han sido realizadas para intentar solucionar esta problemática. De los resulta- dos obtenidos, uno de los que= ha tenido mayor impacto es el meta-algoritmo AdaBoost (Harrington, 2012 & Shwartz & Shai, 2014).

 

Utilizando múltiples clasificadores de= un mismo tipo, dicho algoritmo los entrena secuencialmente, teniendo en cuenta= en cada momento los errores detectados en el entrenamiento anterior. Finalment= e, en presencia de un caso de entrada desconocido, ´este es sometido a cada un= o de los clasificadores, donde cada clasificador influye en el resultado final s= egún haya sido su error en el entrenamiento.

 

4.2. Aprendizaje Supervisado. Regresión.

 

Al igual que el enfoque de clasificaci= ón, la regresión se encuentra en el área de los algoritmos que utilizan aprendi= zaje supervisado. Esta variante, es utilizada cuando la variable a predecir es numérica y continua, a diferencia de las técnicas de clasificación. El méto= do de regresión lineal (Harrington, 2012 & Montgomery, 2015) es comúnmente utilizado en esta área. La regresión lineal tiene como objetivo modelar las relaciones existentes entre los atributos del caso de análisis y la variabl= e a predecir. Para lograr este resultado, se plantea una ecuación que contiene = los atributos multiplicados por coeficientes.

 

Los algoritmos de regresión intentan determinar los valores de dichos coeficientes. La limitación fundamental de estas técnicas, es que, pese a que reducen el error global, los errores loc= ales influyen notablemente en las predicciones. Una forma de resolver esto es so= brecargando en la función los datos cercanos a los de interés, de esta forma, se logra = una predicción más precisa (Harrin= gton, 2012). No obstante, tiene como desventaja, que para cada predicción debemos aplicar el algoritmo de regresión, lo que aumenta considerablemente el costo computacional.  En ocasiones, la va= riable a predecir muestra cambios considerables en algunos segmentos dentro del espacio de valores. En ese sentido, convendría utilizar el método de regres= ión segmentada (Oosterbaan et al,1990), que plantea analizar los datos por intervalos. Este enfoque mejora los resultados en comparación con la regresión lineal clásica. Otra problemática ocurre cuando las características de los datos, no permiten encontrar una ecuación lineal= que los represente. Debido a ello, varias investigaciones han sido llevadas a c= abo utilizando regresiones no lineales. En muchos casos, los métodos de regresi= ón son factibles, dado su bajo costo computacional. Además, atendiendo a las características de los datos, existen varios métodos de regresión que pueden ser seleccionados, aumentando el alcance de dicha técnica.

 

En entornos reales, es común encontrar situaciones en las que no se puedan determinar claramente las ecuaciones que las representen. En ese sentido, existe una variante de regresión que puede= ser de utilidad, conocida como regresión basada en árboles (Buja A. & Lee, = 2001 & Harrington, 2012).

 

Lo que propone dicha estrategia, es dividir los datos consecutivamente, hasta lograr que cada división pueda ser representada con un modelo de regresión lineal. Luego, llevar a cabo el entrenamiento para cada división obtenida. Finalmente, la estructura constr= uida, funcionaría de forma similar a los árboles de decisión analizados en el apartado anterior, con la diferencia de que las hojas contendrán modelos de regresión lineal. Esta nueva variante, eleva el costo computacional en comparación con el uso de regresión lineal solamente. Sin embargo, habilita dichas técnicas para analizar datos con relaciones complejas entre sus variables.

 

4.3. Aprendizaje no Supervisado.

 

En muchas situaciones reales, a difere= ncia de los casos analizados previamente, no se tiene una variable respuesta para los datos de entrada. En estos casos, en lugar de clasificar o predecir val= ores numéricos, lo que se busca comúnmente es extraer información útil, por ejem= plo: posibles agrupamientos.  El objetiv= o de estas técnicas es encontrar subconjuntos dentro del espacio de entrada, minimizando las diferencias entre elementos pertenecientes a un mismo grupo= . La similitud entre dos elementos de la entrada es computada mediante una funci= ón de distancia atendiendo a los valores de sus atributos. Diversos algoritmos= han sido desarrollados para automatizar este procedimiento.  Uno de los más conocidos es el algoritm= o K-Means (Alsabti et al,1997= ., Harrington, 2012., Morissette y Chartier, 2013.= & Shwartz y Shai, 2014) el cual divide los datos = de entrada en K subgrupos, tomando K como parámetro. La principal dificultad p= ara utilizar este algoritmo, es que para entornos reales difícilmente se conoce= el número ´óptimo de K. Sin embargo, algunas investigaciones han sido llevadas= a cabo para determinar métricas que aseguren una buena selección de K (Pham, Dimov & Nguyen,= 2005)

 

El algoritmo basado en encadenamiento = (Shwartz S. & Shai, 2014), es otra variante clásic= a para realizar agrupamientos. A diferencia del algoritmo K-m= eans, tiene en cuenta las distancias internas y ex- ternas de los grupos. Dicho algoritmo propone analizar iterativamente el espacio de entrada, uniendo ca= da vez los dos grupos más cercanos en un nuevo grupo.

 

Diferentes métricas de distancia pueden ser utilizadas: basándose en la distancia mínima, distancia máxima y distan= cia promedio. Al igual que K-means, se puede contar= con un parámetro K, el cual determinaría la finalización del algoritmo una vez obtenidos K grupos. No obstante, existe otra variante utilizando un umbral,= que se obtiene teniendo en cuenta la distancia máxima entre dos elementos del espacio de entrada. En este caso, el algoritmo une dos grupos siempre que no sobrepasen el umbral.

 

Existe otra estrategia que propone agr= upar en dos etapas. La primera etapa utiliza una red neuronal conocida como SOM = (del inglés Self-Organizing Map= ) (Richard et al, 1999., Vesanto & AlhoniemI, 2000 & Yin, 2008), para reducir el esp= acio de entrada en un número menor de prototipos que lo represente de manera apr= oximada. Luego, los prototipos obtenidos son agrupados utilizado alguno de los algoritmos de agrupamiento analizados previamente.  Esta estrategia tiene como ventaja, que= puede ser utilizada en grandes volúmenes de datos, minimizando el coste computaci= onal.  Una posible extensión de esta propuesta= , consiste en utilizar funciones de densidad para agrupar utilizando solamente la prim= era etapa (Cabanes G, & Bennani, 2010)

 

En el ámbito de las redes neuronales existe una problemática conocida como Dilema de la Estabilidad y Plasticidad del Aprendizaje. La plasticidad se refiere a la capacidad de una red de aprender nuevos patrones, mientras que la estabilidad permite a una red entrenada poder retener los conocimientos aprendidos. Diseńar redes que cum= plan con una de estas características es sencillo, el principal reto consiste en= la creación de redes que cumplan ambos objetivos. En las redes más comunes, co= mo Perceptrón Multicapa, Adaline y SOM, el aprender nuevas características puede suponer el olvido del conocimiento ya obtenido= , de ahí una limitación considerable. En ese sentido, una nueva gama de redes neuronales ha sido desarrollada bajo el nombre de Teoría de la Resonancia Adaptativa (ART, del inglés Adaptive Resonance Theory). Este m= odelo de redes se encuentra en el grupo conocido como redes de aprendizaje competiti= vo, al igual que la red SOM. Estas redes poseen variantes de aprendizaje supervisado (Carpenter A., Grossberg S. & Reynolds J.,1991), y no supervisado (Carpente= r & Stephen, 1987., Carpenter & Stephen, = 1990., Carpenter & Stephen, 1991 & Grossberg<= span style=3D'letter-spacing:1.0pt'> S.1987).

 

Basándose en las propuestas básicas de estas redes, se han obtenido variantes que utilizan lógica difusa (Carpenter A, & Grossberg ,1992. & Carpenter A, & Grossberg, 1991), con el objetivo de brindar mayor realismo. Además, como característi= ca fundamental se tiene que crean su propia clasificación de lo que aprenden. = El principal impacto de las redes ART radica en su capacidad de utilización en tiempo real. Esto viene da- do porque la red es capaz de detectar nuevas características en los datos, lo que supone una nueva clasificación, sin ll= evar al olvido del conocimiento previamente obtenido. A diferencia de los algori= tmos de agrupamiento analizados, utilizando las redes de la familia ART, se pued= en desarrollar técnicas orientadas a agrupar en tiempo real, sin necesidad de nuevos entrenamientos.  Sin embargo, persi= ste la problemática general en el diseńo de redes neuronales, la elección de los parámetros correctos, dígase umbrales, cantidad de capas, etc.

 

Conclusiones.<= o:p>

ˇ      =    El estudio realizado, en su propósito de analizar el estado actual de las técn= icas de predicción de comportamientos, fue divido en 4 etapas lógicas. La primera parte de la investigación, se dedicó a la minería de procesos, demostrando = su impacto en el mundo organizacional.  Se analizaron las principales etapas en que se divide esta disciplina, así como algunos trabajos aislados. Por ejemplo, el agrupamiento de trazas y el sopo= rte operacional, que pudiesen considerarse como etapas independientes. La inter= acción de las diferentes técnicas de esta rama da lugar al modelo Auditoría 2.0. E= sto cambia drásticamente la forma de trabajo de los auditores, consolidando la aplicabilidad de la minería de procesos. Específicamente, la predicción de comportamientos, juega un papel fundamental dentro del modelo Auditoría 2.0, analizando los procesos desde una perspectiva en línea. De esta parte de la investigación, es importante seńalar, que la predicción es una de las áreas= de investigación menos explotada dentro de la disciplina. A su vez, los result= ados obtenidos no logran establecer la predicción de comportamientos como paradi= gma en la auditoría de procesos. Además, la carencia de investigaciones relacionadas en los últimos ańos ha contribuido al estancamiento de este en= foque. Finalizando, en concordancia con los investigadores reconocidos en el área,= se concluye con uno de los principales retos de la minería de procesos: vincul= ar disciplinas externas a la predicción de comportamientos.<= /p>

 

ˇ      =    Atendiendo a la problemática detectada, se realizó un estudio de las técnicas de la ra= ma aprendizaje automático, que puedan ser utilizadas en la predicción de comportamientos.  Centrándose específicamente en las técnicas de aprendizaje supervisado y no supervisado= , se analizan parcialmente estos grupos, teniendo en cuenta los algoritmos y estructuras de interés. Atendiendo a las características de estas técnicas = se concluye, que es de vital importancia su utilización en la predicción de comportamientos. Además, se estima que la combinación del aprendizaje automático y la predicción de comportamientos, puede aportar nuevas funcionalidades y enfoques en la auditoría de procesos.

ˇ      =    Diversas líneas de investigación pueden ser identificadas a partir del estudio realizado. Pudiese ser de interés, tanto la aplicación de otras técnicas de esta disciplina, así como otras disciplinas. Además, los resultados que se obtengan a partir de esta investigación, pueden arrojar nuevas teorías en el soporte operacional en general, dígase detección, predicción y recomendació= n de comportamientos.

 

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Anne Rozinat, AK Alves De Medeiros, Christian  W  Gu¨nther,  AJMM  Weijters= , and Wil  MP Van der Aalst, Towards an evaluation framework for process mining algorithms, BPM Center Report BPM-07-06, BPMcenter. org 123 (2007), 142.

Anne = Rozinat and Wil MP van der Aalst, Conformance checking of processes basedon<= span style=3D'letter-spacing:.6pt'> monitoring real behavior, Information Systems 3= 3 (2008), no. 1, 64–95.

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Wil Van Der Aalst, Arya Adriansyah, Ana Karla Alves De Medeiros, Franco Arcieri,= Thomas Baier, Tobias Blickle, Jagadeesh Chandr= a Bose, Peter van den Brand, Ronald Brandtjen, J= oos Buijs, et al., Process mining manifesto, International Con- ference on Business Process Management, Springer, 2011, pp. 169–194.

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=  

=  

=  

=  

=  

= Para citar el artículo indexado.

=  

=  

= Acosta L., López O., Vázquez Y. & Velasteguí E.  (2018).  Más que minería de procesos y predicción= de comportamientos. Un nuevo enfoque. = Revista electrónica Ciencia Digital 2(2), 8-28. Recuperado desde: = http://cienciadigital.org/revistacienciadigital2= /index.php/CienciaDigital/article/view/70/65

=  

 

 

 

artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Ciencia Digital.

 

El articulo queda en propiedad de la revista y, por tanto, su publicación parc= ial y/o total en otro medio tiene que ser autorizado por el director de la Revista Ciencia Digital.

 

 

 

 



[1] Departamento de Informá= tica, Universidad Agraria de La Habana, Mayabeque, cubaluis92aq@unah.edu.cu

[2] Institute of Computer Science, University of Tartu, Tartu, Estonia,<= span lang=3DEN-US style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font-famil= y:"Times New Roman",serif; mso-ansi-language:EN-US'> orlenyslopez@gmail.com

[3] Facultad de Turismo, Universidad de La Habana, La Habana, Cuba yalfos1@gmail.com

[4] Universidad Técnica de Cotopaxi Ext. La Maná, Latacunga, Ecuador, luis.velastegui7838@utc.edu.ec

[5] Estándar utilizado en la minería de procesos para el almacenamiento de la información.

[6] Se corresponde con un paso b= ien definido dentro del proceso en que se ejecuta.

[7]El análisis de trazas finaliz= adas, suele identificarse con el nombre de fuera análisis de línea (del inglés offline).<= /o:p>

[8] El análisis de trazas no finalizadas, también aparece bajo el nombre de análisis en línea (del inglés online).

[9]Es el resultado de sobreentre= nar un algoritmo de aprendizaje con ciertos datos para los cuales se conoce su resultado, perdiendo la capacidad de generalización.=

[10] Un hiperplano, en geometría,= es una extensión del concepto plano.

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////////////////////////////////////////////////////vYFP//////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAAAAAAAAD///8AAAD///////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////+9gU////+9gU+9gU////+9 gU////+9gU+9gU+9gU////////////+9gU////+9gU////////+9gU+9gU////////+9gU////+9 gU+9gU////+9gU////+9gU////+9gU////+9gU+9gU////+9gU+9gU+9gU+9gU////+9gU////// //+9gU////+9gU////////+9gU+9gU////////+9gU////+9gU+9gU////+9gU////+9gU+9gU+9 gU+9gU////+9gU////+9gU+9gU+9gU////+9gU////////+9gU////+9gU////////+9gU+9gU// //////+9gU////+9gU////+9gU+9gU////+9gU////+9gU+9gU////+9gU////+9gU+9gU+9gU// 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/////////////////////////////////////wAAAAAAAAAA////AAAA//////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////AAAA AAAAAAD///8AAAD///////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////8AAAAAAAAAAP///wAAAP////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////wAAAAAAAAAA ////AAAA//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////AAAAAAAAAAD///8AAAD///////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////8AAAAAAAAAAP///wAA AP////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////wAAAAAAAAAA////AAAA//////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////AAAAAAAAAAD///8AAAD///// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////8AAAAAAAAAAP///wAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////wAAAAAAAAAA////AAAA//////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////AAAAAAAAAAD///8AAAD///////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////8AAAAAAAAAAP///wAAAP////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////wAA AAAAAAAA////AAAA//////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////AAAAAAAA////////////////////////////////////AAAA//////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////AAAAAAAAAAD///8AAAD///////////////////////// //////////////////////////////////////////////////////////////////////////// //////8AAAD///8AAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAD///8AAAAA AAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAD/ //8AAAD///////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////8AAAAAAAAA AP///wAAAP////////////////////////////////////////////////////////////////// /////////////////////////////////////wAAAAAAAP///wAAAAAAAAAAAP///wAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAP///////wAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAA AAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////wAAAAAAAAAA////AAAA//////////////////////////////// ////////////////////////////////////////////////////////////////////////AAAA ////AAAA////AAAA////////////////////////////////////////////////AAAA//////// ////////////////////////////////AAAAAAAA////AAAA//////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////AAAAAAAAAAD///8A AAD///////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////8AAAAAAAAAAP///wAAAP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAP////////////////////// /////////////////////////////////////wAAAP////////////////////////////////// /////wAAAP///////////////////////////////////wAAAP////////////////////////// /////////////////////////////////////////////////////////wAAAP////////////// /////////////////////////////////////////////////////////////////////wAAAP// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////wAAAAAAAAAA////AAAA//// //////////////////////////////////////////////////////////////////////////// ////////////////////////AAAAAAAAAAAA////AAAAAAAAAAAAAAAA////AAAAAAAA////AAAA AAAA////AAAAAAAAAAAAAAAA////////AAAAAAAA////AAAAAAAAAAAAAAAA////AAAAAAAA//// ////AAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAA//////////// ////////AAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAA////AAAA////////////AAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAA////AAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAA 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////AAAAAAAAAAD///8AAAD///////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////8A AAAAAAAAAP///wAAAP////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////wAAAAAAAAAA////AAAA//////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////AAAAAAAA AAD///8AAAD///////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////8AAAAAAAAAAP///wAAAP////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////wAAAAAAAAAA//// AAAA//////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////AAAAAAAAAAD///8AAAD///////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAAAAAAAAAP///wAAAP// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////wAAAAAAAAAA////AAAA//////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////AAAAAAAAAAD///8AAAD///////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////8AAAAAAAAAAP///wAAAP////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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AAAA////AAAA//////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////AAAAAAAAAAD///8AAAD///////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////8AAAAAAAAAAP// /wAAAP////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////wAAAAAAAAAA////AAAA//////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////AAAAAAAAAAD///8AAAD/ //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAAAAAAAAAP///wAAAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAAAAAAAA////AAAA//////// //////////////////////////////////////////////////////////////////////////// ////////////////////vYFPvYFPvYFPvYFPvYFPvYFPvYFPvYFPvYFPvYFPvYFPvYFPvYFPvYFP 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////8AAAAAAAAAAP///wAAAP////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /wAAAAAAAAAA////AAAA//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////AAAAAAAAAAD///8AAAD///////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////8AAAAA AAAAAP///wAAAP////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////wAAAAAAAAAA////AAAA//////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////AAAAAAAAAAD/ //8AAAD///////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////8AAAAAAAD///////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////8AAAAAAAD///////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////8AAAAAAAAAAP///wAAAP////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////wAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAA AAAAAAAAAP///////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAAAAAP///wAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////////wAAAAAAAP///wAAAAAAAAAA AP///////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////wAAAAAAAAAAAAAAAP///////wAA AAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAAAAAP///wAAAAAAAAAA AP////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////8AAAAAAAD///8AAAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///8A AAD///8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAD///8AAAAAAAAA AAAAAAAAAAAAAAAAAAD///8AAAAAAAD///////////////8AAAD///8AAAAAAAAAAAAAAAD///// //8AAAAAAAAAAAAAAAD///8AAAAAAAAAAAD///8AAAAAAAAAAAAAAAD///////////8AAAAAAAD/ //8AAAAAAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAD///8AAAD///8AAAAAAAD///////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////8AAAAAAAAAAP///wAAAP////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //8AAAAAAAAAAP///wAAAP////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////wAAAAAAAAAA////AAAA//////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////AAAAAAAA//////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAAAAAA//////////////////////// ////////////////////////////////////////////////////////AAAA//////////////// AAAAAAAA//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////AAAA AAAAAAD///8AAAD///////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////8AAAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///// //8AAAD///8AAAAAAAAAAAAAAAAAAAAAAAD///////8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAAA 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////wAAAAAAAAAA////AAAA//////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////AAAAAAAAAAD///8AAAD///// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////8AAAAAAAAAAP///wAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////wAA AAAAAAAA////AAAA//////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////8AAAAAAAAA AP///wAAAP////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////wAAAAAAAAAA////AAAA//////////////////////////////// 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www.cienciadigital.org

                                                                      =                                                  ISSN: 2602-8085

                        Vol. 2, N°2, p. 8-= 28, Abril - Junio, 2018 =

 

EDUCACIÓN DEL FUTURO                                =                                                                    =                         Página 21<= /span> de 21<= /span>

 

 

 

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