Neural Networks with Finite Width Action Potentials
The paper was done as an assigned Princeton university project. It is being withdrawn since it needs to be changed and updated substantially.
cond-mat.dis-nn↗
arXiv subjects
Fariel Shafee
Publications and source records attributed to Fariel Shafee.
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.
physics.soc-ph↗
Organization and Complexity in a Nested Hierarchical Spin-Glass like Social Space
In this paper, we mathematically formulate the interaction and dynamics of a hierarchical complex social system where each agent is seen as an array of many variables. The formation of identities and modifications can be studied by using interaction physics in an energy landscape. The spin glass Hamiltonian is modified to suit our needs in light of complexity. The expression of variables subject to weights and topology is considered. Interactions within the same hierarchy level as well as the effect of one hierarchy level on another are studied. The effect of having many variables associated with a single agent brings about interesting dynamics. The persistence of the identity units subject to stiffness, continuous changes and also sudden reorganizations is discussed.
physics.soc-ph↗
The Problem of Quantum Measurement and Entangled States: Interactions Among States and Formation of Detector Images
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of variables within a complex system. Then we discuss a model for quantum measurement proposed by us, in which the quantum system is allowed to interact with its image created within the detector, followed by a first passage random walk in the Hilbert space. Definitions and ideas from the first part are used in the context of the model. In the end, we discuss the puzzling question of entanglement. We propose how borrowing concepts from our model for quantum measurement may enable us to formulate a hidden variable scenario that does not violate Bell's inequality.
quant-ph↗
Generalized Entropy from Mixing: Thermodynamics, Mutual Information and Symmetry Breaking
We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy configurations unlike Shannon entropy. We discuss how, beginning with quantum entanglement of microsystems with one another and with the environment, one can obtain classical stochasticity for our form of entropy.
cond-mat.stat-mech↗
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.
nlin.AO↗
Network of Perceptions
The role of perception in conscious behavior and decision-making is examined. The effect of spatial and temporal stochasticity in the acquisition of beliefs is discussed. The idea of an agent as a locally strongly coupled group of states leads to the creation of energy minima in an interaction potential landscape. The interaction of such agent states and environment states acting at different levels of complexity and scale, subject to stochastically expressed interaction interfaces, may lead to asymmetry in perceptions. Agents possessing different perception related beliefs are then connected in a social network.
nlin.AO↗
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 Schrödinger 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.
quant-ph↗
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.
cond-mat.stat-mech↗
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.
nlin.AO↗
Generalized Entropy with Clustering and Quantum Entangled States
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one for completely independent units. We comment on the relevance of such an approach for variable-size microsystems such as in a liquid. We then indicate how the entanglement and purity of a two-unit compound state can depend on their entanglement with the environment. We consider entropies of Tsallis, which is used in many different real- life contexts, and also our new generalization, which takes into account correlated clustering in a more transparent way, and is just as amenable mathematically as that of Tsallis, and show how both purity and entangle- ment can appear naturally together in a measure of mutual information in such a generalized picture of the entropy, with values differing from the Shannon type of entropy. This opens up the possibility of using such an entropy in a quantum context for relevant systems, where interactions between microsystems makes clustering and correlations a non-ignorable characteristic.
cond-mat.dis-nn↗
Oligo-parametric Hierarchical Structure of Complex Systems
We investigate the possible origin of hierarchical structures in complex systems describable in terms of a finite and small number of parameters which control the behavioral pattern at each level of organization. We argue that the limitation on the number of important parameters at each stage is a reflection of the fact that Thom's classification of catastrophes, i.e., qualitative changes, involve only a few parameters. In addition, we also point out that even in systems with a large number of components, only a few may be of statistically great significance, just as in Zipf's law the quantitative measure of the important collections is inversely proportional to the rank. We then consider the concept of relative degeneracies coming from change of resolving power, at various scales, which too would vindicate the procedure of coarse-graining in building up hierarchical organizations. We suggest that, similar to the group-theoretical annihilation of dangling tensor indices due to symmetry to minimize energy, even in more inexact contexts such as in biology and the social sciences, similar attempts by the system to reduce frustration may lead to cluster formation, which are semi-closed, and let leakage interactions come into play at larger scales.
nlin.AO↗
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.
physics.soc-ph↗
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.
quant-ph↗
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.
physics.soc-ph↗
Energy Level Sets for the Morse Potential
In continuation of our previous work investigating the possibility of the use of the Level Set Method in quantum control, we here present some numerical results for a Morse potential. We find that a proper treatment of the Morse potential eigenfunctions and eigenvalues for the case of a system with a small number of bound energy levels, the anharmonic perturbative approximation is actually invalid. We, therefore, use a Runge-Kutta integration method that gives more plausible results. We also calculate the dipole moment for the transitions between the two levels with our eigenfunctions and find that there is a critical depth of the potential. Finally we find the level sets giving equal expectation values of the energy, and comment on the unitary operators needed to make transitions from any level set to another.
quant-ph↗
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.
quant-ph↗
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.
quant-ph↗