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

Symmetrization, quantum images and measurement

We argue that symmetrization of an incoming microstate with similar states in a sea of microstates contained in a macroscopic detector can produce an effective image, which does not contradict the no-cloning theorem, and such a combinatorial set can then be used with first passage random walk interactions suggested in an earlier work to give the right quantum mechanical weight for measured eigenvalues

Spin-glass-like Dynamics of Social Networks

In this work we study spin-glass (SG) like behavior in the dynamics of multiple agents in a social or economic context using interactions which are similar to the physical case. The different preferences shown by individual agents are represented by orientations of spin-like variables. Because of limited resources, each agent tries to maximize her total utility function, giving a prescription for the dynamics of the system similar to the evolution resulting from the optimization of the interaction of a SG. The coupling between agents for different attributes may be positive or negative, as in a physical SG system, forming "frustrations" from the ensuing conflicts, with the system trying to find an overall equilibrium, but in vain, so that we observe oscillations. The couplings are provided by matrices corresponding to each attribute and each agent, which are allowed to have some fixed bias, indicating the unchangeable component of the make up of the agents from genetic factors or lasting environmental influences, and also contain a random part from environmental noise, i.e. the cumulative stochastic effect of lumped factors not explicitly accounted for in the model.Comment: To be presented at WEHIA, 200

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

Neural Networks with c-NOT Gated Nodes

We try to design a quantum neural network with qubits instead of classical neurons with deterministic states, and also with quantum operators replacing teh classical action potentials. With our choice of gates interconnecting teh neural lattice, it appears that the state of the system behaves in ways reflecting both the strengths of coupling between neurons as well as initial conditions. We find that depending whether there is a threshold for emission from excited to ground state, the system shows either aperiodic oscillations or coherent ones with periodicity depending on the strength of coupling.Comment: 4 pages 6 figures; minor corrections made; clearer explanations added; Engineering Applications of Artificial Intelligence, online Nov 1, 200

Level Set Method for Quantum Control of Dipole Moment

We investigate the level set method (LSM) in a specific quantum context; namely the dipole transition moment for a system with a nontrivial Morse potential. We draw equal moment sets in the two-dimensional space of two important parameters of the potential, namely the depth of the potential and its width. Another variable is introduced as a scale and we see "motions" of the level sets normal to the contours, as in classical contexts such as fluid dynamics or in epitaxial crystal growth. Presumably interpolating the level sets normally by smooth functions such as splines may give a fairly accurate method of combining the variables to keep the dipole moment invariant

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

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

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