"Improved FCM algorithm for Clustering on Web Usage Mining"

In this paper we present clustering method is very sensitive to the initial center values, requirements on the data set too high, and cannot handle noisy data the proposal method is using information entropy to initialize the cluster centers and introduce weighting parameters to adjust the location of cluster centers and noise problems.The navigation datasets which are sequential in nature, Clustering web data is finding the groups which share common interests and behavior by analyzing the data collected in the web servers, this improves clustering on web data efficiently using improved fuzzy c-means(FCM) clustering. Web usage mining is the application of data mining techniques to web log data repositories. It is used in finding the user access patterns from web access log. Web data Clusters are formed using on MSNBC web navigation dataset.Comment: ISSN(Online):1694-0814. http://www.ijcsi.org/papers/IJCSI-8-1-42-45.pd

Particle creation in the oscillatory phase of inflaton

A thermal squeezed state representation of inflaton is constructed for a flat Friedmann-Robertson-Walker background metric and the phenomenon of particle creation is examined during the oscillatory phase of inflaton, in the semiclassical theory of gravity. An approximate solution to the semiclassical Einstein equation is obtained in thermal squeezed state formalism by perturbatively and is found obey the same power-law expansion as that of classical Einstein equation. In addition to that the solution shows oscillatory in nature except on a particular condition. It is also noted that, the coherently oscillating nonclassical inflaton, in thermal squeezed vacuum state, thermal squeezed state and thermal coherent state, suffer particle production and the created particles exhibit oscillatory behavior. The present study can account for the post inflation particle creation due to thermal and quantum effects of inflaton in a flat FRW universe.Comment: 11 page

Rigorous construction of a Spin Foam Model for Lorentzian BF theory and Gravity: The foundations

Spin foam models for gravity or BF theory can be constructed by path integral formulation of the classical discrete models formulated on simplicial manifolds. Using this, we discuss the rigorous construction of Lorentzian spin foam models for gravity and BF theory based on the Gelfand-Naimark theory of the representations of SL(2,C). First we construct the simplex amplitude for the BF SL(2,C) model. Next we discuss the implementation of the Barrett-Crane constraints on this model to derive the spin foam model for gravity. The non-trivial constraints are the cross simplicity constraints which state that the sum of the bivectors associated to any two triangles of a quantum tetrahedron is simple. We do not complete the construction of the model, but ultimately we derive an equation corresponding to the cross simplicity constraints that the Lorentzian spin foam model of gravity has to satisfy. In the appendix we give a simple derivation of the Clebsch-Gordan coefficients for SL(2,C).Comment: 18 pages, many figures. Version3: Serious changes to title, abstract, introduction, equation(3.5) and conclusio

Ashtekar Formulation with Temporal Foliations

This article has been withdrawn.Comment: This article has been withdrawn as it is incomplet

Spin Foams for the Real, Complex Orthogonal Groups in 4D and the bivector scalar product reality constraint

The Barrett-Crane model for the SO(4,C) general relativity is systematically derived. This procedure makes rigorous the calculation of the Barrett-Crane intertwiners from the Barrett-Crane constraints of both real and complex Riemannian general relativity. The reality of the scalar products of the complex bivectors associated with the triangles of a flat four simplex is equivalent to the reality of the associated flat geometry. Spin foam models in 4D for the real and complex orthogonal gauge groups are discussed in a unified manner from the point of view of the bivector scalar product reality constraints. Many relevant issues are discussed and generalizations of the ideas are introduced. The asymptotic limit of the SO(4,C) general relativity is discussed. The asymptotic limit is controlled by the SO(4,C) Regge calculus which unifies the Regge calculus theories for all the real general relativity cases. The spin network functionals for the 3+1 formulation of the spin foams are discussed. The field theory over group formulation for the Barrett-Crane models is discussed briefly. I introduce the idea of a mixed Lorentzian Barrett-Crane model which mixes the intertwiners for the Lorentzian Barrett-Crane models. A mixed propagator is calculated. I also introduce a multi-signature spin foam model for real general relativity which is made by splicing together the four simplex amplitudes for the various signatures. Further research that is to be done is listed and discussed.Comment: Title has been changed. Many important changes has been made from the previous version. The systematic derivation of the spin foam models of SO(4,C) general relativity has been explained using picture equations. The details of the reality constraints has been modified. Additional sections has been introduced. One of them deals with the asymptotic limit of the spin foams with new results. English has been improved, sections edited and reorganize

Reality Conditions for Spin Foams

An idea of reality conditions in the context of spin foams (Barrett-Crane models) is developed. The square of areas are the most elementary observables in the case of spin foams. This observation implies that simplest reality conditions in the context of the Barrett-Crane models is that the all possible scalar products of the bivectors associated to the triangles of a four simplex be real. The continuum generalization of this is the area metric reality constraint: the area metric is real iff a non-degenerate metric is real or imaginary. Classical real general relativity (all signatures) can be extracted from complex general relativity by imposing the area metric reality constraint. The Plebanski theory can be modified by adding a Lagrange multiplier to impose the area metric reality condition to derive classical real general relativity. I discuss the SO(4,C) BF model and SO(4,C) Barrett-Crane model. It appears that the spin foam models in 4D for all the signatures are the projections of the SO(4,C) spin foam model using the reality constraints on the bivectors.Comment: 39 Pages, Presented at Loop05 conferenc

A Systematic Derivation of the Riemannian Barrett-Crane Intertwiner

The Barrett-Crane intertwiner for the Riemannian general relativity is systematically derived by solving the quantum Barrett-Crane constraints corresponding to a tetrahedron (except for the non-degeneracy condition). It was shown by Reisenberger that the Barrett-Crane intertwiner is the unique solution. The systematic derivation can be considered as an alternative proof of the uniqueness. The new element in the derivation is the rigorous imposition of the cross-simplicity constraint.Comment: 10 page

Spin Foams for the SO(4,C) BF theory and the SO(4,C) General Relativity

The Spin Foam Model for the SO(4,C) BF theory is discussed. The Barrett-Crane intertwiner for the SO(4,C) general relativity is systematically derived. The SO(4,C) Barret-Crane interwiner is unique. The propagators of the SO(4,C) Barrett-Crane model are discussed. The asymptotic limit of the SO(4,C) general relativity is discussed. The asymptotic limit is controlled by the SO(4,C) Regge calculus.Comment: 26 pages, 16 figure equation

The Area Metric Reality Constraint in Classical General Relativity

A classical foundation for an idea of reality condition in the context of spin foams (Barrett-Crane models) is developed. I extract classical real general relativity (all signatures) from complex general relativity by imposing the area metric reality constraint; the area metric is real iff a non-degenerate metric is real or imaginary. First I review the Plebanski theory of complex general relativity starting from a complex vectorial action. Then I modify the theory by adding a Lagrange multiplier to impose the area metric reality condition and derive classical real general relativity. I investigate two types of action: Complex and Real. All the non-trivial solutions of the field equations of the theory with the complex action correspond to real general relativity. Half the non-trivial solutions of the field equations of the theory with the real action correspond to real general relativity. Discretization of the area metric reality constraint in the context of Barrett-Crane theory is discussed. In the context of Barrett-Crane theory the area metric reality condition is equivalent to the condition that the scalar products of the bivectors associated to the triangles of a four simplex be real. The Plebanski formalism for the degenerate case and Palatini formalism are also briefly discussed by including the area metric reality condition.Comment: The title has been changed. A new section on the simplicial discretization of the area metric reality constraint and GR actions has been introduced. Certain errors in field equations has been corrected. English has been improved, sections edited and reorganize

A Note on the Asymptotic Limit of the Four Simplex

Recently the asymptotic limit of the Barrett-Crane models has been studied by Barrett and Steele. Here by a direct study, I show that we can extract the bivectors which satisfy the essential Barrett-Crane constraints from the asymptotic limit. Because of this the Schlaffi identity is implied by the asymptotic limit, rather than to be imposed as a constraint.Comment: 4 page