1,134 research outputs found

### 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

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