Project Narrative: Categorical approach to agent interaction

I am pursuing a category-theoretic model for the study of interaction. In particular I will consider the following sort of system: a network of interacting entities (or agents), such that each entity is an instantiation of a given type of structure and each interaction follows some mathematically prescribed rules. This research applies to a wide variety of systems found in the natural world and in technology. Indeed, the nervous system, human society, hierarchical protein materials, computers and networks, and complex organizations such as businesses and militaries are all systems that can be modeled in this way. It also has direct application to problems of information integration and distributed intelligence. Statement of objectives As stated in the introduction (Section 1.1), I am pursuing a mathematical model for the study of interaction. In particular I will consider the following sort of system: a network of individuals entities (or agents), each of which is an instantiation of a given type of structure, wherein these entities interact in a prescribed manner. Such systems are ubiquitous in the natural world and in technology. Indeed, the nervous system, human society, hierarchical protein materials, computers and networks, and complex organizations such as businesses and militaries are very different systems that can all be modeled in this way. Understanding these interactions and their exchanged semantics is important for fusing dynamic information from distributed agents. This research will include two main aspects. The first is a detailed look at individual interactions, in which two agents are tasked with developing a richer medium for communicating with each other. To begin this requires carefully formulating the structure of the information which get passed between agents, the way such information is received, and the sense in which the agents are modified by successful receipt of new information. The second is an investigation of the relationship between small-scale interactions and their global aggregates. For example, given a complete understanding of the stimulus-response pattern for each neuron and of the connection pattern of neurons, I will provide a formula for predicting the stimulus-response pattern of the whole system. I will discuss these two themes in order: In Section 2.1, I will propose a category-theoretic “communication protocol” by which agents can discuss and learn from one another, and in Section 2.2, I will outline an approach to modeling the relationship between individual interactions and their results in aggregate.