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Online social networks (OSNs) are increasinglyused by different sectors of societywith the purpose of informing and influencing people. These sectors are: govemments, political parties, non-govemmental organizations, suppliers ofgoods and services, etc. Theywish they could predict the extent ofthe spread of information and the influence theytransmit through these networks. Currently there are many m athem atical models that allow us to predict the scope of these propagations, many ofwhich are based on Linear Threshold Nlodel (L TM) or lndependent Cascad e Model (ICM). In this document we present Lucy Nlodel, a new predictive mathematical model that incorporates several elements that have not been considered or taken into account in the base models orín their derived models, but which are present in real life and affect the extent of propagation of messages on online social networks. These new elements are the following: We distinguish three classes of messages: pure.ly informative messages; messages that are intended to influence appealing to people's emotions and feelings; and messages that are intended to influence by appealing to personal interests and conveniences. We argue that the intensity of the relationship between individua Is (tie-strength) depends on the relevan ce and affinitybetween them . Toe probabilitythat the message is received byan individual is directlyproportional to this relationship intensity. Also, we consider that a message with greater im portance is more likely to spread among people than a message with less importance. Finally, we maintain that individuals are informad or influenced (activated) after exceeding a threshold, which depends on the type and importance ofthe message and the relevance or affinity, as the case may be, between individuals. On the other hand, we determine a way to quantify the affinity between nodes and the strength of the relations hip between nodes, and we link this to the probabilitythat a node receives a message. To validate the results of LM, we performed laboratorytests of LM, L TM, ICM and WCM with a Facebook network tracked of an anonymous user. These results have been comparad with empirical tests ofinformation propagation and influence on the Facebook platform in the network of the same anonymous user. LM represents the message propagation process in a finer way and its results are notab(y closer to the empirical results in comparison with the results that were obtained with the models L TM, ICM and WCM. In order to study the behavior of LM, we carry out additional laboratorytests, modifying its parameters and using a synthetic (artificial) Power-Law network and two real networks (Facebook and YouTube). LM is suitable to be used in different spheres of human activity, for example: 1- lt will allow to know more preciselythe different sectors of society about the impact produced bythe messages that they publish in the OSNs. 2- lt can be incorporated into the maximization models ofinfluence propagation in social networks. 3- lt can be used in models that predict the loss of customers in mobile telephone services. 4. lt can also be used in systems that simulate the spread of informatics virus es in computer networks, cell phone networks and online social networks. ; Las redes sociales online (OSNs) son cada vez más utilizadas por diferentes sectores de la sociedad, y tienen el propósito de informar e influir a la gente. Estos sectores son, entre otros: gobiernos, partidos políticos, organizaciones no gubernamentales, proveedores de bienes y servicios, etc. A ellos les sería muy útil poder pronosticar el alcance de la propagación de la información y de la influencia que transmiten a través de las redes sociales. Actualmente existen muchos modelos matemáticos utilizados en trabajos científicos, que pronostican el alcance de esas propagaciones, muchos de los cuales se basan, a su vez, en uno de siguientes modelos referentes: Linear Threshold Model (L TM) y lndependent Casca de Model (ICM). En este documento presentamos Lucy Model (LM), un nuevo modelo matemático predictor, que incorpora varios elementos que no han sido tomados en cuenta en los modelos base ni en sus modelos derivados, pero que están presentes en la vida real y afectan el alcance de la propagación de mensajes en redes sociales online. Estos nuevos elementos son los siguientes: Nosotros distinguimos tres clases de mensajes: mensajes meramente informativos; mensajes que tienen la intensión de influir apelando a las emociones y sentimientos de la gente; y mensajes que tienen la intensión de influir apelando a las conveniencias e intereses personales. Nosotros planteamos que la intensidad de la relación entre individuos (tie-strength) depende de la relevancia yde la afinidad entre ellos. La probabilidad de que el mensaje sea recibido por un individuo es directamente proporcional a esta intensidad de relación. También, nosotros consideramos que un mensaje con mayor importancia tiene más probabilidad de propagarse entre la gente que un mensaje con menos importancia. Finalmente, nosotros sostenemos que los individuos son informados o influenciados (activados) luego de superar un umbral, el cual depende de la clase e importancia de mensaje yde la relevancia o afinidad, según el caso, entre individuos. Por otro lado, determinamos una forma de cuantificar la afinidad entre nodos y la fortaleza de la relación entre nodos, y esta la ligamos a la probabilidad de que un nodo reciba un mensaje. Para validar los resultados de LM, realizamos pruebas de laboratorio de LM, L TM, ICM yWCM con una red Facebook rastreada de un usuario anónimo. Estos resultados los comparamos con pruebas empíricas de propagación de información e influencia en la plataforma Facebook en la red del mismo usuario anónimo. LM representa el proceso de propagación de mensajes de manera más fina y sus resultados son notablemente más cercanos a los resultados empíricos en comparación con los resultados que se obtuvieron con los modelos L TM, ICM y WCM. Con el propósito de estudiar el comportamiento de LM, llevamos a cabo pruebas de laboratorio adicionales, modificando sus parámetros y utilizando una red sintética (artificial) Power-Law y dos redes sociales reales: YouTube y la red social Facebook de un específico usuario. LM es adecuado para ser utilizado en diferentes ámbitos de la actividad humana, por ejemplo: 1- Permitirá conocer de una forma más precisa a los diferentes sectores de la sociedad el impacto que producen los mensajes que ellos publican en las OSNs. 2- Puede ser incorporado en los modelos de maximización de propagación de influencia en redes sociales. 3- Puede ser utilizado en los modelos que pronostican la pérdida de clientes en los servicios de telefonía móvil. 4. También se puede utilizar en los sistemas que simulan la propagación de virus informático en las redes de computadores, redes de telefonía celular y redes sociales online. ; Postprint (published version)

Online social networks (OSNs) are increasinglyused by different sectors of societywith the purpose of informing and influencing people. These sectors are: govemments, political parties, non-govemmental organizations, suppliers ofgoods and services, etc. Theywish they could predict the extent ofthe spread of information and the influence theytransmit through these networks. Currently there are many m athem atical models that allow us to predict the scope of these propagations, many ofwhich are based on Linear Threshold Nlodel (L TM) or lndependent Cascad e Model (ICM). In this document we present Lucy Nlodel, a new predictive mathematical model that incorporates several elements that have not been considered or taken into account in the base models orín their derived models, but which are present in real life and affect the extent of propagation of messages on online social networks. These new elements are the following: We distinguish three classes of messages: pure.ly informative messages; messages that are intended to influence appealing to people's emotions and feelings; and messages that are intended to influence by appealing to personal interests and conveniences. We argue that the intensity of the relationship between individua Is (tie-strength) depends on the relevan ce and affinitybetween them . Toe probabilitythat the message is received byan individual is directlyproportional to this relationship intensity. Also, we consider that a message with greater im portance is more likely to spread among people than a message with less importance. Finally, we maintain that individuals are informad or influenced (activated) after exceeding a threshold, which depends on the type and importance ofthe message and the relevance or affinity, as the case may be, between individuals. On the other hand, we determine a way to quantify the affinity between nodes and the strength of the relations hip between nodes, and we link this to the probabilitythat a node receives a message. To validate the results of LM, we performed ...

"The final publication is available at Springer via http://dx.doi.org/10.1007/s10588-013-9156-z ; We present a new mathematical model that predicts the number of users informed and influenced by messages that are propagated in an online social network. Our model is based on a new way of quantifying the tie-strength, which in turn considers the affinity and relevance between nodes. We could verify that the messages to inform and influence, as well as their importance, produce different propagation behaviors in an online social network. We carried out laboratory tests with our model and with the baseline models Linear Threshold and Independent Cascade, which are currently used in many scientific works. The results were evaluated by comparing them with empirical data. The tests show conclusively that the predictions of our model are notably more accurate and precise than the predictions of the baseline models. Our model can contribute to the development of models that maximize the propagation of messages; to predict the spread of viruses in computer networks, mobile telephony and online social networks. ; This work was carried out by the financing of the Ecuadorian government of President Rafael Correa D. and by FLAMINGO, a Network of Excellence project (318488) supported by the European Commission under the Seventh Framework Program and the project TEC2015-71329-C2-2-R (MINECO/FEDER) from Ministerio de Economía y Competitividad. R.M.O-G. thanks Dr. Joan Serrat Fernández, Dr. Xavier Muñoz and Dr. Josep Fàbrega, professors at the University Polytechnic of Catalonia. Similarly, Dr. Esteban Samaniego Alvarado and PhD student Vladimiro Tobar Solano, professors at Universidad de Cuenca, and the PhD student Lucía Mendez Tapia for the accomplishment of this work. ; Peer Reviewed ; Postprint (author's final draft)