The Role of Cooperative Learning Type Team Assisted Individualization to Improve the Students’ Mathematics Communication Ability in the Subject of Probability Theory

The importance of learning mathematics can not be separated from its role in all aspects of life. Communicating ideas by using mathematics language is even more practical, systematic, and efficient. In order to overcome the difficulties of students who have insufficient understanding of mathematics material, good communications should be built in a learning process. Communication in general can be interpreted as a way to convey a message from the messenger to the receiver to inform opinions or behaviors either directly (oral) or indirectly through the media. In the communication process, we need to think on how to make the message can be understood by others. In order to develop the ability to communicate, people can communicate with a variety of languages including mathematical language. One of the subjects in the Statistics study program which requires mathematics communication ability is the Theory of Probability, which is categorized as a general skill subject that must be taken by all students of mathematics. Improving the students' mathematics communication ability should be hand in hand with the learning process. We can optimize the ability by implementing a learning model which gives chance for the students to discuss and to interact each other so that their mathematics communication ability improved, that is by using cooperative learning type Team Assisted Individualization (TAI). Keywords: Mathematics communication ability, Cooperative learning type  TAI

Coalitional Game Theory for Communication Networks: A Tutorial

Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and autonomic networks, it has become imperative to seek suitable game theoretical tools that allow to analyze and study the behavior and interactions of the nodes in future communication networks. In this context, this tutorial introduces the concepts of cooperative game theory, namely coalitional games, and their potential applications in communication and wireless networks. For this purpose, we classify coalitional games into three categories: Canonical coalitional games, coalition formation games, and coalitional graph games. This new classification represents an application-oriented approach for understanding and analyzing coalitional games. For each class of coalitional games, we present the fundamental components, introduce the key properties, mathematical techniques, and solution concepts, and describe the methodologies for applying these games in several applications drawn from the state-of-the-art research in communications. In a nutshell, this article constitutes a unified treatment of coalitional game theory tailored to the demands of communications and network engineers.Comment: IEEE Signal Processing Magazine, Special Issue on Game Theory, to appear, 2009. IEEE Signal Processing Magazine, Special Issue on Game Theory, to appear, 200

Opinion Behavior Analysis in Social Networks Under the Influence of Coopetitive Media

Both interpersonal communication and media contact are important information sources and play a significant role in shaping public opinions of large populations. In this paper, we investigate how the opinion-forming process evolves over social networks under the media influence. In addition to being affected by the opinions of their connected peers, the media cooperate and/or compete mutually with each other. Networks with mixed cooperative and competitive interactions are said to be coopetitive . In this endeavor, a novel mathematical model of opinion dynamics is introduced, which captures the information diffusion process under consideration, makes use of the community-based network structure, and takes into account personalized biases among individuals in social networks. By employing port-Hamiltonian system theory to analyze the modeled opinion dynamics, we predict how public opinions evolve in the long run through social entities and find applications in political strategy science. A key technical observation is that as a result of the port-Hamiltonian formulation, the mathematical passivity property of individuals’ self-dynamics facilitates the convergence analysis of opinion evolution. We explain how to steer public opinions towards consensus, polarity, or neutrality, and investigate how an autocratic media coalition might emerge regardless of public views. We also assess the role of interpersonal communication and media exposure, which in itself is an essential topic in mathematical sociology

Performance Analysis of Cooperative V2V and V2I Communications under Correlated Fading

Cooperative vehicular networks will play a vital role in the coming years to implement various intelligent transportation-related applications. Both vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications will be needed to reliably disseminate information in a vehicular network. In this regard, a roadside unit (RSU) equipped with multiple antennas can improve the network capacity. While the traditional approaches assume antennas to experience independent fading, we consider a more practical uplink scenario where antennas at the RSU experience correlated fading. In particular, we evaluate the packet error probability for two renowned antenna correlation models, i.e., constant correlation (CC) and exponential correlation (EC). We also consider intermediate cooperative vehicles for reliable communication between the source vehicle and the RSU. Here, we derive closed-form expressions for packet error probability which help quantify the performance variations due to fading parameter, correlation coefficients and the number of intermediate helper vehicles. To evaluate the optimal transmit power in this network scenario, we formulate a Stackelberg game, wherein, the source vehicle is treated as a buyer and the helper vehicles are the sellers. The optimal solutions for the asking price and the transmit power are devised which maximize the utility functions of helper vehicles and the source vehicle, respectively. We verify our mathematical derivations by extensive simulations in MATLAB.Comment: Internet of Vehicles (IoV), Vehicular communication, Antenna correlation, Stackelberg game, Vehicle-to-infrastructure (V2I), Vehicle-to-vehicle (V2V), Game theory, Cooperative vehicular network

Solutions for cooperative games with and without transferable utility

When individuals generate benefits from their cooperation, allocation problems may occur regarding how much of the benefit from the cooperation each individual should take. In many economic situations, defining the contribution of each individual in a fair way is essential. This thesis is on cooperative game theory, a mathematical tool that models and analyses cooperative situations between individuals. Throughout the monograph, allocation rules that are based on the contributions of individuals are studied. The first two parts of this thesis are on the class of transferable utility games, in which benefits from cooperation can be freely transferred between agents. In the first part, allocation rules when the cooperation between agents is restricted by a communication structure are studied. A chapter of this part gives a new characterization of a known allocation rule. In the next chapter, allocation rules are investigated for the class of games in which the underlying communication structure is represented by a circle. The second part of this thesis introduces a new type of restriction on cooperation between players, called quasi-building system, which covers many known structures. The third part of this thesis deals with situations in which benefits from cooperation are not transferable between individuals. This part focuses on when an allocation rule based on contributions of individuals leads to an economically satisfying result