Interacting Agents in Social Networks: The Idea of Self and Influence Spaces

We study the evolution of social clusters, in an analogy with physical spin systems, and in detail show the importance of the concept of the "self" of each agent with quantifiable variable attributes. We investigate the effective influence space around each agent with respect to each attribute, which allows the cutoff of the Hamiltonian dictating the time evolution and suggest that equations similar to those in general relativity for geodesics in distorted space may be relevant in such a context too. We perform in a simple small-world toy system simulations with weight factors for different couplings between agents and their attributes and spin-type flips in either direction from consideration of a utility function, and observe chaotic, highly aperiodic behavior, with also the possibility of punctuated equilibrium-like phenomena. In a realistic large system, because of the very large number of parameters available, we suggest that it would probably almost always be necessary to reduce the problem to simpler systems with a manageable set of coupling matrices, using assumptions of fuzziness or symmetry or some other consideration

Nonextensive Entropy, Prior PDFs and Spontaneous Symmetry Breaking

We show that using nonextensive entropy can lead to spontaneous symmetry breaking when a parameter changes its value from that applicable for a symmetric domain, as in field theory. We give the physical reasons and also show that even for symmetric Dirichlet priors, such a defnition of the entropy and the parameter value can lead to asymmetry when entropy is maximized.Comment: Some typos and confusing lines have been fixe

Quantum Control with Level Set Method

We examine the relevance of Level Set Methods (LSM)in coherent control quantum systems where the objective is to retain or attain a particular expectation value of a given measurable. The differences with the usual applications of LSM, where continuous closed interfaces are involved, and the quantum case, where we may have a discrete number of points to deal with, are noted. The question of optimization in this new context is also clarified. Simple examples with symmetric and asymmetric multidimensional potentials are briefly considered

Optimal Control of Quantum Systems and a Generalized Level Set Method

We study the application of a generalized form of the level set method used in classical physical contexts to quantum optimal control situations. The set of OCT equations needed to keep the expectation value of an observable constant is first discussed and the dimensionality of the actual parameter space carefully considered. Then we see how concepts of level set methods emerge that may help solve the inverse problem associated with designing the control Hamiltonian with greater speed. The formal equations and the algorithm are presented

Quantum Indeterminism and First Passage Random Walks in Hilbert Space

We propose a new model for a measurement of a characteristic of a microscopic quantum state by a large system that selects stochastically the different eigenstates with appropriate quantum weights. Unlike previous works which formulate a modified Schr\"odinger equation or an explicit modified Hamiltonian, or more complicated mechanisms for reduction and decoherence to introduce transition to classical stochasticity, we propose the novel use of couplings to the environment, and random walks in the product Hilbert space of the combined system, with first passage stopping rules, which seem intuitively simple, as quantum weights and related stochasticity is a commonality that must be preserved under the widest range of applications, independent of the measured quantity and the specific properties of the measuring device.Comment: model extended and partly rewritten for clarity and rigou

Quantum Optimal Control and Level Sets

We investigate how the concepts of optimal control of measurables of a system with a time dependent Hamiltonian may be mixed with the level set technique to keep the desired entity invariant. We derive sets of equations for this purpose and also algorithms for numerical use. The notion of constancy of measurables in this context is also examined to make the techniques more useful in real-life situation where some variability of the measurable may be tolerable

Interactions Among Agent Variables and Evolution of Social Clusters

In this paper, we first review some basic concepts associated with a model for social interaction previously proposed by us. Each agent is seen as an array of variables that can be found in different states. The agents are then allowed to interact and form groups based on their variables. We discuss how spin-glass type physics may be appropriate for our model. Several types of variables and costs associated with flipping the variables are discussed. Then some simple graphs are presented to understand the formation of various levels of identities within social clusters. In the end, we analyze events from the French revolution and the Russian revolution to to understand how different variables and identities interact within a hierarchical social structure.Comment: The paper was written as mostly a review of a model developed 2002 onwards by the author in some personal papers, and submitted to a journal in Jan 2009 when the author was at Princeton. It is still being refereed. The author has now left Princeton. minor revisio

Entangled Quantum Networks

We present some results from simulation of a network of nodes connected by c-NOT gates with nearest neighbors. Though initially we begin with pure states of varying boundary conditions, the updating with time quickly involves a complicated entanglement involving all or most nodes. As a normal c-NOT gate, though unitary for a single pair of nodes, seems to be not so when used in a network in a naive way, we use a manifestly unitary form of the transition matrix with c?-NOT gates, which invert the phase as well as flipping the qubit. This leads to complete entanglement of the net, but with variable coefficients for the different components of the superposition. It is interesting to note that by a simple logical back projection the original input state can be recovered in most cases. We also prove that it is not possible for a sequence of unitary operators working on a net to make it move from an aperiodic regime to a periodic one, unlike some classical cases where phase-locking happens in course of evolution. However, we show that it is possible to introduce by hand periodic orbits to sets of initial states, which may be useful in forming dynamic pattern recognition systems.Comment: 10 pages; pdf problem solved; more explanations adde

Agent Components and the Emergence of Altruism in Social Interaction Networks

We discuss a special aspect of agents placed in a social network. If an agent can be seen as comprising many components, the expressions and interactions among these components may be crucial. We discuss the role of patterns within the environment as a mode of expression of these components. The stability and identity of an agent is derived as a function of component and component-pattern identity. The agent is then placed in a specific social network within the environment, and the enigmatic case of altruism is explained in terms of interacting component identities

A Spin Glass Model of Human Logic Systems

In this paper, we discuss different models for human logic systems and describe a game with nature. Godel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking. We start by saying that although an agent is rational, the axioms defining different agent's logic systems need not be the same although they might have a large degree of overlap. This can be seen as each agent being coupled to a higher dimensional world by means of his perception where the couplings produce slightly different projections of the higher dimensional world to each agent. The different projections would produce slightly different concepts about the "world" to each agent and hence create a slightly differing set of axioms that each agent would use to act logically. Then we place the agents in an interacting logical network, where these axioms can be treated as spins that can be flipped as agents interact with each other and with the environment in which they are placed. Agents, who would share a common material world that they wish to use or change by using different or conflicting sets of axioms will try to flip the other agent's axioms (This can be seen by observing that as one agent acts to interact with his world as followed by his axiom, another agent's world changes as well, and the change might be contradictory to the second agent's "axioms" or "optimal world". We define an equation that allows an axiom to be flipped into an "anti axiom (the opposite or conflicting axiom)" as agents interact. All agents share an "existence" axiom by means of which they strive to perpetuate themselves or the network.Comment: accepted as short talk at eccs 05. Supersedes nlin/021101