Noncommutative gravity, a `no strings attached' quantum-classical duality, and the cosmological constant puzzle

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the `weakly quantum, strongly gravitational' dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the `strongly quantum, weakly gravitational' dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.Comment: 7 pages. Second Prize in Gravity Research Foundation Essay Competition, 2008. Two paragraphs added to original essay to enhance clarity. To appear in Gen. Rel. Gra

A characterization of the central shell-focusing singularity in spherical gravitational collapse

We give a characterization of the central shell-focusing curvature singularity that can form in the spherical gravitational collapse of a bounded matter distribution obeying the dominant energy condition. This characterization is based on the limiting behaviour of the mass function in the neighbourhood of the singularity. Depending on the rate of growth of the mass as a function of the area radius R, the singularity may be either covered or naked. The singularity is naked if this growth rate is slower than R, covered if it is faster than R, and either naked or covered if the growth rate is same as R.Comment: 12 pages, Latex, significantly revised version, including change of title. Revised version to appear in Classical and Quantum Gravit

Collective Oscillations of Strongly Correlated One-Dimensional Bosons on a Lattice

We study the dipole oscillations of strongly correlated 1D bosons, in the hard-core limit, on a lattice, by an exact numerical approach. We show that far from the regime where a Mott insulator appears in the system, damping is always present and increases for larger initial displacements of the trap, causing dramatic changes in the momentum distribution, $n_k$. When a Mott insulator sets in the middle of the trap, the center of mass barely moves after an initial displacement, and $n_k$ remains very similar to the one in the ground state. We also study changes introduced by the damping in the natural orbital occupations, and the revival of the center of mass oscillations after long times.Comment: 4 pages, 5 figures, published versio

Edge-Cloud Synergy: Unleashing the Potential of Parallel Processing for Big Data Analytics

If an edge-node orchestrator can partition Big Data tasks of variable computational complexity between the edge and cloud resources, major reductions in total task completion times can be achieved even at low Wide Area Network (WAN) speeds. The percentage time savings are greater with increasing task computational complexity and higher WAN speeds are required for low-complexity tasks. We demonstrate from numerical simulations that low-complexity tasks can benefit either by task partitioning between an edge node and multiple cloud servers. The orchestrator can also achieve greater time benefits by rerouting Big Data tasks directly to a single cloud resource if the balance of parameters (WAN speed and the ratio between edge and cloud processing speeds) is favourable

On kinetic energy stabilized superconductivity in cuprates

The possibility of kinetic energy driven superconductivity in cuprates as was recently found in the $tJ$ model is discussed. We argue that the violation of the virial theorem implied by this result is serious and means that the description of superconductivity within the $tJ$ model is pathological.Comment: 3 pages, v2 includes additional reference