Identifying Half-Twists Using Randomized Algorithm Methods

Since the braid group was discovered by E. Artin, the question of its conjugacy problem has been solved by Garside and Birman, Ko and Lee. However, the solutions given thus far are difficult to compute with a computer, since the number of operations needed is extremely large. Meanwhile, random algorithms used to solve difficult problems such as primality of a number were developed, and the random practical methods have become an important tool. We give a random algorithm, along with a conjecture of how to improve its convergence speed, in order to identify elements in the braid group, which are conjugated to its generators for a given power. These elements of the braid group, the half-twists, are important in themselves, as they are the key players in some geometrical and algebraical methods, the building blocks of quasipositive braids and they construct endless sets of generators for the group.Comment: 18 pages, 4 Postscript figures; Last proof read corrections before printing - Paper accepted for publicatio

Job creation and labor reform in Latin America

This paper studies the effects of labor-regulation reform using data for 10,396 firms from 14 Latin American countries. Firms are asked both how many permanent workers they would have hired and how many they would have terminated if labor regulations were made more flexible. I find that making labor regulations more flexible would lead to an average net increase of 2.08 percent in total employment. Firms with fewer than 20 employees would benefit the most, with average gains in net employment of 4.27 percent. Countries with more regulated labor markets would experience larger gains in total employment. These larger gains in total employment, however, would be achieved through higher rates of hiring and higher rates of termination. These results may explain why there is substantial opposition to labor reforms despite the predicted gains in efficiency and total employment.Labor Markets,Labor Policies,Labor Management and Relations,Labor Standards,Work&Working Conditions

Conceptual Foundations of the Balanced Scorecard

David Norton and I introduced the Balanced Scorecard in a 1992 Harvard Business Review article (Kaplan & Norton, 1992). The article was based on a multi-company research project to study performance measurement in companies whose intangible assets played a central role in value creation (Nolan Norton Institute, 1991). Norton and I believed that if companies were to improve the management of their intangible assets, they had to integrate the measurement of intangible assets into their management systems. After publication of the 1992 HBR article, several companies quickly adopted the Balanced Scorecard giving us deeper and broader insights into its power and potential. During the next 15 years, as it was adopted by thousands of private, public, and nonprofit enterprises around the world, we extended and broadened the concept into a management tool for describing, communicating and implementing strategy. This paper describes the roots and motivation for the original Balanced Scorecard article as well as the subsequent innovations that connected it to a larger management literature.