Livelihood Diversification and Women Empowerment Through Self-Help Micro Credit Programme: Evidence from Jammu and Kashmir.

In the paper an attempt has been made to analyze the process of livelihood diversification and women empowerment through women self-help groups (WSHGs) and micro credit and its impact under Integrated Watershed Development Project (IWDP), Hills-II, Jammu and Kashmir; to find out difficulties in operationalizing micro income generating activities (MIGAs) through WSHGs and micro credit; and to suggest policy recommendations to make the programme of micro enterprise development through WSHGs and micro credit a success. The study reveals that through creation of WSHGs, 250 beneficiaries have been trained, out of which 50 percent have taken up MIGAs on sustainable basis and started earning up to Rs. 500 per month in Ramnagar Sub-watershed. The scheme of inter-loaning has also been introduced and members of WSHGs gets loan up to Rs. 5000. Through opening of saving accounts in nationalized banks, monthly savings of WSHGs have increased up to Rs. 1000. All these have resulted in increased income and improved livelihoods of the beneficiaries. New WSHGs should be formed through which new high potential MIGAs needs to be promoted. The system of revolving fund/mutual fund groups should also be promoted. The extent of beneficiaries’ willingness to contribute towards the cost of any MIGA is a ‘litmus test’ of their interest and commitment. Efforts should be made to evolve cost-sharing mechanism to ensure sustainability. The members of the WSHGs should be imparted training related to technical, financial, and marketing aspects, for which reputed local NGOs should be roped in. Exposure visits and training programmes should also be organized on regular interval to give WSHGs the opportunities to learn and express themselves in public and to improve their self-confidence.Livelihood Diversification, Women Empowerment, Self-Help Groups, Micro Credit

List decoding group homomorphisms between supersolvable groups

We show that the set of homomorphisms between two supersolvable groups can be locally list decoded up to the minimum distance of the code, extending the results of Dinur et al who studied the case where the groups are abelian. Moreover, when specialized to the abelian case, our proof is more streamlined and gives a better constant in the exponent of the list size. The constant is improved from about 3.5 million to 105.Comment: 11 page

Approximate Graph Coloring by Semidefinite Programming

We consider the problem of coloring k-colorable graphs with the fewest possible colors. We present a randomized polynomial time algorithm that colors a 3-colorable graph on $n$ vertices with min O(Delta^{1/3} log^{1/2} Delta log n), O(n^{1/4} log^{1/2} n) colors where Delta is the maximum degree of any vertex. Besides giving the best known approximation ratio in terms of n, this marks the first non-trivial approximation result as a function of the maximum degree Delta. This result can be generalized to k-colorable graphs to obtain a coloring using min O(Delta^{1-2/k} log^{1/2} Delta log n), O(n^{1-3/(k+1)} log^{1/2} n) colors. Our results are inspired by the recent work of Goemans and Williamson who used an algorithm for semidefinite optimization problems, which generalize linear programs, to obtain improved approximations for the MAX CUT and MAX 2-SAT problems. An intriguing outcome of our work is a duality relationship established between the value of the optimum solution to our semidefinite program and the Lovasz theta-function. We show lower bounds on the gap between the optimum solution of our semidefinite program and the actual chromatic number; by duality this also demonstrates interesting new facts about the theta-function