Given two n-bit (cyclic) binary strings, A and B, represented on a circle (necklace instances). Let each sequence have the same number k of 1’s. We are interested in computing the cyclic swap distance between A and B, i.e., the minimum number of swaps needed to convert A to B, minimized over all rotations of B. We show that, given the compressed representation of A and B, this distance may be c...

Using the reduced form framework with inter-dependent default correlation, we perform valuation of credit default swap with counterparty risk. The inter-dependent default risk structure between the protection buyer, protection seller and the reference entity in a credit default swap are characterized by their correlated default intensities, where the default intensity of one party increases whe...

We give the optimal decomposition of a universal two-qubit circuit using Heisenberg exchange interactions and single qubit rotations. Tuning the strength and duration of the Heisenberg exchange allows one to implement SWAP gates. Our optimal circuit is constructed from only three SWAP gates and six single qubit gates. We show that three SWAP gates are not only sufficient, but necessary. Since s...

The Ministry of Health and Family Welfare (MOHFW) of the Government of Bangladesh embarked on a sector-wide approach (SWAp) modality for the health, nutrition and population (HNP) sector in 1998. This programmatic shift initiated a different set of planning disciplines and practices along with institutional changes in the MOHFW. Over the years, the SWAp modality has evolved in Bangladesh as the...