Spotting Difficult Weakly Correlated Binary Knapsack Problems

In this paper, we examine the possibility of quickly deciding whether or not an instance of a binary knapsack problem is difficult for branch and bound algorithms. We first observe that the distribution of the objective function values is smooth and unimodal. We define a measure of difficulty of solving knapsack problems through branch and bound algorithms, and examine the relationship between the degree of correlation between profit and cost values, the skewness of the distribution of objective function values and the difficulty in solving weakly correlated binary knapsack problems. We see that the even though it is unlikely that an exact relationship exists for individual problem instances, some aggregate relationships may be observed. Key words: Binary Knapsack Problems; Skewness; Computational Experiments.

Robustness of entangled states that are positive under partial transposition

We study robustness of bipartite entangled states that are positive under partial transposition (PPT). It is shown that almost all PPT entangled states are unconditionally robust, in the sense, both inseparability and positivity are preserved under sufficiently small perturbations in its immediate neighborhood. Such unconditionally robust PPT entangled states lie inside an open PPT entangled ball. We construct examples of such balls whose radii are shown to be finite and can be explicitly calculated. This provides a lower bound on the volume of all PPT entangled states. Multipartite generalization of our constructions are also outlined.Comment: Published versio

Enrolment rates are climbing. So what explains the sorry state of India's education sector?

The Annual Status of Education Report (ASER) 2017 will shortly be up for discussion among policy experts. Based on household-based surveys that cover children in the age group 3-16 across almost all rural districts of India, ASER provides estimates of children's schooling status and their ability to do basic reading and arithmetic tasks. Aniruddha Ghosh and Sujan Bandyopadhyay analyse the prior survey findings and conclude that innovative intervention is required over boosting enrolment

Clues for India: looking at the puzzle of total factor productivity and capital flows

While examining previous trends and research on capital flows and total factor productivity, Aniruddha Ghosh and Sujan Bandyopadhyay write that India must be careful to continue to maintain the positive correlation between growth and net foreign capital flows

As scaling effects of research productivity diminish, India must step up R&D investment

Advanced economies may be facing declining returns on research effort. This makes it all the more imperative that the Modi government gets its house, with regard to R&D, in order write Aniruddha Ghosh and Sujan Bandyopadhyay

Quantum dissipation and the virial theorem

In this note, we study the celebrated virial theorem for dissipative systems, both classical and quantum. The classical formulation is discussed and an intriguing effect of the random force (noise) is made explicit in the context of the virial theorem. Subsequently, we derive a generalized virial theorem for a dissipative quantum oscillator, i.e. a quantum oscillator coupled with a quantum heat bath. Such a heat bath is modeled as an infinite collection of independent quantum oscillators with a certain distribution of initial conditions. In this situation, the non-Markovian nature of the quantum noise leads to novel bath-induced terms in the virial theorem. We also consider the case of an electrical circuit with thermal noise and analyze the role of non-Markovian noise in the context of the virial theorem.Comment: v2: Revised version to appear in Physica

Optimal Universal Disentangling Machine for Two Qubit Quantum States

We derive the optimal curve satisfied by the reduction factors, in the case of universal disentangling machine which uses only local operations. Impossibility of constructing a better disentangling machine, by using non-local operations, is discussed.Comment: 15 pages, 2 eps figures, 1 section added, 1 eps figure added, minor corrections, 2 reference numbers correcte

Transition from homogeneous to inhomogeneous limit cycles : Effect of local filtering in coupled oscillators

10 pages, 8 FigsPeer reviewedPublisher PD