Towards solving generic cosmological singularity problem

The big bounce transition of the quantum FRW model in the setting of loop quantum cosmology is presented. We determine the physical self-adjoint Hamiltonian generating the dynamics. It is used to define, via the Stone theorem, an evolution operator. We examine properties of expectation values of physical observables in the process of the quantum big bounce transition. The dispersion of observables are studied in the context of the Heisenberg uncertainty principle. We suggest that the real nature of the bounce may become known only after we quantize the Belinskii-Khalatnikov-Lifshitz scenario, which concerns the generic cosmological singularity.Comment: 4 pages, no figures; talk presented at the Multiverse and Fundamental Cosmology Conference, 10-14 September, 2012, Szczecin, Poland; to be published in the AIP Conference Proceedings Serie

Probing the cosmological singularity with a particle

We examine the transition of a particle across the singularity of the compactified Milne (CM) space. Quantization of the phase space of a particle and testing the quantum stability of its dynamics are consistent to one another. One type of transition of a quantum particle is described by a quantum state that is continuous at the singularity. It indicates the existence of a deterministic link between the propagation of a particle before and after crossing the singularity. Regularization of the CM space leads to the dynamics similar to the dynamics in the de Sitter space. The CM space is a promising model to describe the cosmological singularity deserving further investigation by making use of strings and membranes.Comment: 19 pages, 7 figures, revtex4, added references, version accepted for publication in Class. Quantum Gra

Combinatorial Channel Signature Modulation for Wireless ad-hoc Networks

In this paper we introduce a novel modulation and multiplexing method which facilitates highly efficient and simultaneous communication between multiple terminals in wireless ad-hoc networks. We term this method Combinatorial Channel Signature Modulation (CCSM). The CCSM method is particularly efficient in situations where communicating nodes operate in highly time dispersive environments. This is all achieved with a minimal MAC layer overhead, since all users are allowed to transmit and receive at the same time/frequency (full simultaneous duplex). The CCSM method has its roots in sparse modelling and the receiver is based on compressive sampling techniques. Towards this end, we develop a new low complexity algorithm termed Group Subspace Pursuit. Our analysis suggests that CCSM at least doubles the throughput when compared to the state-of-the art.Comment: 6 pages, 7 figures, to appear in IEEE International Conference on Communications ICC 201