a b s t r a c tA physically concise polynomial-time iterative-cum-non-iterative algorithm is presented to solve the linear program (LP) Min c t x subject to Ax = b, x ≥ 0. The iterative part -a variation of Karmarkar projective transformation algorithm -is essentially due to Barnes only to the extent of detection of basic variables of the LP taking advantage of monotonic convergence. It involves much less number of iterations than those in the Karmarkar projective transformation algorithm. The shrunk linear system containing only the basic variables of the solution vector x resulting from Ax = b is then solved in the mathematically non-iterative part. The solution is then tested for optimality and is usually more accurate because of reduced computation and has less computational and storage complexity due to smaller order of the system. The computational complexity of the combination of these two parts of the algorithm is polynomial-time O(n 3 ). The boundedness of the solution, multiple solutions, and no-solution (inconsistency) cases are discussed. The effect of degeneracy of the primal linear program and/or its dual on the uniqueness of the optimal solution is mentioned. The algorithm including optimality test is implemented in Matlab which is found to be useful for solving many real-world problems.

Abstract-Predicting the outcomes of social interactions between humans is notoriously difficult. Variations within the experiences, beliefs, and actions of individual humans (and even within a particular given human from one situation to the next) render accurate predictions of the outcome of individual interactions problematic at best. However, it is somewhat easier to make predictions regarding the expected outcome of interactions involving large groups of humans over an extended period. This paper presents a series of studies where simple social interactions between humans of different personality types were modeled over a long term, and where the behavior patterns of individuals within the population were allowed to change. The results of these studies provide predictions for how groups of humans would likely behave in similar situations.Index Terms-Agent-based simulation, evolutionary modeling, predictive modeling, social interactions.