Joseph E. Johnson

University of South Carolina | USC · Department of Physics and Astronomy

This paper reframes Riemannian geometry as a generalized Lie algebra allowing the equations of both RG and then General Relativity to be expressed as commutation relations among fundamental operators. We begin with an Abelian Lie algebra of n operators, X, whose simultaneous eigenvalues, y, define a real n-dimensional space. Then with n new operato...

The ongoing global COVID-19 pandemic has caused more than 440,000 deaths among more than 8 million cases globally by Mid-June, 2020. This pandemic has caused a staggering worldwide socioeconomic impact and loss of lives. This research proposes an innovative technological approach to analyze COVID-19 patient data for new analytical insights via deve...

The Heisenberg Lie algebra (HA) plays an important role in mathematics with Fourier transforms, as well as for the foundations of quantum theory where it expresses the operators of space-time, X, and their commutation rules with the momentum operators, D, that execute infinitesimal translations in X. Yet it is known that space-time is curved and th...

In previous work, the author extended the Poincare Lie algebra to include a four position operator as a natural extension to a large fifteen parameter Lie algebra of operators. We here propose to generalize the metric contained in those structure constants to be the Riemann metric as determined by Einstein's equations from the energy momentum tenso...

The author proved that the continuous general linear (Lie) group in n dimensions can be decomposed into (a) a Markov type Lie group (MTLG) preserving the sum of the components of a vector, and (b) an Abelian Lie scaling group that scales each of the components. For a specific Lie basis, the MTLG generated all continuous Markov transformations (a Li...

In this paper, the authors propose a new method for the propagation of uncertainty through non linear algorithms that may contain conditional statements. The approach is based on bittors, that are bit vectors where bits are expressed in terms of their probability to take value 1 or 0. Provided the logic operations between bittors are defined, the s...

Abstract The continuous general linear group in n dimensions can be decomposed into two Lie groups: (1) an n(n-1) dimensional ‘Markov type’ Lie group that is defined by preserving the sumof the components of a vector, and (2) the n dimensional Abelian Lie group, A(n), of scaling transformations of the coordinates. With the restriction ofthe first L...

The problem is addressed of developing a very general mathematical foundation for networks that permits practical application in the monitoring of large networks such as the internet for both known and unknown attacks, intrusions, worms, viruses, and generally for destructive agents and processes. The PI, under the funding of this grant, has discov...

We present software for deriving innovative metrics describing dominant parts of the internal structure of large networks. The algorithm is sufficiently fast for the network metrics to support real time monitoring of network dynamics. The network connections (connectivity matrix) are mathematically constructed by capturing the appropriate header pa...

We introduce a novel approach to description of networks/graphs. It is based on an analogue physical model which is dynamically evolved. This evolution depends on the connectivity matrix and readily brings out many qualitative features of the graph.

An approach for real-time network monitoring in terms of numerical time-dependant functions of protocol parameters is suggested. Applying complex systems theory for information f{l}ow analysis of networks, the information traffic is described as a trajectory in multi-dimensional parameter-time space with about 10-12 dimensions. The network traffic...

The approach for a network behavior description in terms of numerical time-dependant functions of the protocol parameters is suggested. This provides a basis for application of methods of mathematical and theoretical physics for information flow analysis on network and for extraction of patterns of typical network behavior. The information traffic...

A new approach for the analysis of information flow on a network is suggested using protocol parameters encapsulated in the package headers as functions of time. The minimal number of independent parameters for a complete description of the information flow (phase space dimension of the information flow) is found to be about 10 - 12.

This study presents the frequency and correlates of traumatic injury during sexual assaults for male and female victims. Sexual assaults (6,877 total, 6,213 among females, 664 among males) were reported in South Carolina from October 1991 to September 1994 through the Federal Bureau of Investigation's National Incident Based Reporting System. Sexua...

The general linear group GL(n,R) is decomposed into a Markov-type Lie group and an abelian scale group. The Markov-type Lie group basis is shown to generate all singly stochastic matrices which are continuously connected to the identity when non-negative parameters are used. A basis is found which shows that it in turn contains a Lie subgroup which...

The Hamiltonian of a Dirac particle in an arbitrary electromagnetic field is exactly diagonalized by a unitary transformation generalizing previous work which was restricted to time-dependent fields. A very simple form is found for the covariant Heisenberg equations which manifestly exhibits the classical correspondence. These results are obtained...

The isospin splittings of the ½+ baryon octet are observed empirically to depend upon the (average) sum of charge and hypercharge or equivalently, upon the (average) V3=-1/2(Q+Y) spin component. We construct a simple quark model compatible with this observation and then use this model to predict the 3/2+ decuplet isospin splittings. One obtains dif...

This paper is a continuation of a previous investigation of a proper-time formulation of quantum mechanics based upon an extension of the Poincaré algebra to include a four-vector position operator. The discrete operations of space and time inversion and particle conjugation are studied as groups of automorphisms which must also be supported by the...

Covariant four-vector position operators ${X}^{$\mu${}}$ are proposed, which form a natural operator generalization of the four-position in relativistic classical mechanics. These ${X}^{$\mu${}}$ are defined by specifying commutation relations of the ${X}^{$\mu${}}$ with the Poincar\'e generators ${P}^{$\mu${}}$ and ${M}^{$\mu${}$\nu${}}$, and ther...