Spatial CSMA: A Distributed Scheduling Algorithm for the SIR Model with Time-varying Channels

Recent work has shown that adaptive CSMA algorithms can achieve throughput optimality. However, these adaptive CSMA algorithms assume a rather simplistic model for the wireless medium. Specifically, the interference is typically modelled by a conflict graph, and the channels are assumed to be static. In this work, we propose a distributed and adaptive CSMA algorithm under a more realistic signal-to-interference ratio (SIR) based interference model, with time-varying channels. We prove that our algorithm is throughput optimal under this generalized model. Further, we augment our proposed algorithm by using a parallel update technique. Numerical results show that our algorithm outperforms the conflict graph based algorithms, in terms of supportable throughput and the rate of convergence to steady-state.Comment: This work has been presented at National Conference on Communication, 2015, held at IIT Bombay, Mumbai, Indi

Equivariant cobordism of schemes

We study the equivariant cobordism theory of schemes for action of linear algebraic groups. We compare the equivariant cobordism theory for the action of a linear algebraic groups with similar groups for the action of tori and deduce some consequences for the cycle class map of the classifying space of an algebraic groups.Comment: This revised version supercedes arxiv:1006:317

Gersten Conjecture For Equivariant K-theory And Applications

For a reductive group scheme over a regular semi-local ring, we prove an equivarinat version of the Gersten conjecture. We draw some interesting consequences for the representation rings of such reductive group schemes. We also prove the rigidity for the equivariant K-theory of reductive group schemes over a henselian local ring. This is then used to compute the equivariant K-theory of algebraically closed fields

The Phases of QCD in Heavy Ion Collisions and Compact Stars

I review arguments for the existence of a critical point in the QCD phase diagram as a function of temperature and baryon chemical potential. I describe how heavy ion collision experiments at the SPS and RHIC can discover the tell-tale signatures of such a critical point, thus mapping this region of the QCD phase diagram. I then review the phenomena expected in cold dense quark matter: color superconductivity and color-flavor locking. I close with a snapshot of ongoing explorations of the implications of recent developments in our understanding of cold dense quark matter for the physics of compact stars.Comment: 29 pages. 4 figures. latex with aipproc. References added and corrected. One version of this review is to appear in the Comments of Nuclear and Particle Physics section of Comments on Modern Physics. Other versions were contributed to the proceedings of the Conference on Intersections of Nuclear and Particle Physics, Quebec, May 2000 and to the proceedings of the 40th Zakopane School of Theoretical Physics, June 200