Error-correcting code on a cactus:A solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica-symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.

Solvable model for distribution networks on random graphs

We propose a simple model that captures the salient properties of distribution networks, and study the possible occurrence of blackouts, i.e., sudden failings of large portions of such networks. The model is defined on a random graph of finite connectivity. The nodes of the graph represent hubs of the network, while the edges of the graph represent the links of the distribution network. Both, the nodes and the edges carry dynamical two state variables representing the functioning or dysfunctional state of the node or link in question. We describe a dynamical process in which the breakdown of a link or node is triggered when the level of maintenance it receives falls below a given threshold. This form of dynamics can lead to situations of catastrophic breakdown, if levels of maintenance are themselves dependent on the functioning of the net, once maintenance levels locally fall below a critical threshold due to fluctuations. We formulate conditions under which such systems can be analyzed in terms of thermodynamic equilibrium techniques, and under these conditions derive a phase diagram characterizing the collective behavior of the system, given its model parameters. The phase diagram is confirmed qualitatively and quantitatively by simulations on explicit realizations of the graph, thus confirming the validity of our approach. © 2007 The American Physical Society.

A comparison of road accidents in developing countries with special reference to Jamaica

This research was originally undertaken to aid the Jamaican government and the World Bank in making funding decisions relative to improvement of road systems and traffic control in Jamaica. An investigation of the frequency and causes of road accidents and an evaluation of their impact on the Jamaican economy were carried out, and a model system which might be applied was developed. It is believed that the importance of road accident economic and manpower losses to the survival of developing countries, such as Jamaica, cannot be overemphasized. It is suggested that the World Bank, in cooperation with national governments, has a role to play in alleviating this serious problem. Data was collected from such organizations as the Jamaica Ministry of Construction, Police Department, the World Bank, and the World Health Organization. A variety of methodologies were utilized to organize this data in useful and understandable forms. The most important conclusion of this research is that solvable problems in road systems and in traffic control result in the unnecessary loss of useful citizens, in both developed and developing countries. However, a lack of information and understanding regarding the impact of high rates of road accident death and injury on the national economy and stability of a country results in an apparent lack of concern. Having little internal expertise in the field of road accident prevention, developing countries usually hire consultants to help them address this problem. In the case of Jamaica, this practice has resulted in distrust and hard feelings between the Jamaican authorities and major organizations involved in the field. Jamaican officials have found confusing the recommendations of most experts contracted to study traffic safety. The attempts of foreign consultants to utilize a technological approach (the use of coding systems and computers), methods which do not appear cost-effective for Jamaica, have resulted in the expenditure of limited funds for studies which offer no feasible approach to the problem. This funding limitation, which hampers research and road improvement, could be alleviated by such organizations as the World Bank. The causes of high accident rates are many, it was found. Formulation of a plan to address this serious problem must take into account the current failure to appreciate the impact of a high level of road accidents on national economy and stability, inability to find a feasible approach to the problem, and inadequate funding. Such a plan is discussed in detail in the main text of this research.

Nonlinear non-extensive approach for identification of structured information

The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant subspaces are well separated the problem is readily solvable by a linear technique. Otherwise, the linear approach fails to correctly discriminate the required information. Hence, a non-extensive approach is proposed. The resulting nonlinear technique is shown to be suitable for dealing with cases that cannot be tackled by the linear one.