Random Access Game in Fading Channels with Capture: Equilibria and Braess-like Paradoxes

The Nash equilibrium point of the transmission probabilities in a slotted ALOHA system with selfish nodes is analyzed. The system consists of a finite number of heterogeneous nodes, each trying to minimize its average transmission probability (or power investment) selfishly while meeting its average throughput demand over the shared wireless channel to a common base station (BS). We use a game-theoretic approach to analyze the network under two reception models: one is called power capture, the other is called signal to interference plus noise ratio (SINR) capture. It is shown that, in some situations, Braess-like paradoxes may occur. That is, the performance of the system may become worse instead of better when channel state information (CSI) is available at the selfish nodes. In particular, for homogeneous nodes, we analytically present that Braess-like paradoxes occur in the power capture model, and in the SINR capture model with the capture ratio larger than one and the noise to signal ratio sufficiently small.Comment: 30 pages, 5 figure

Classification of modules of the intermediate series over Ramond N=2 superconformal algebras

In this paper, we first discuss the structure of the Ramond N=2 superconformal algebras. Then we also classify the modules of the intermediate series over Ramond N=2 superconformal algebra.Comment: 17 Pages. LaTeX. We simplify some computations in Section 2, and correct some misprints in Section

Approaching the Ground State of Frustrated A-site Spinels: A Combined Magnetization and Polarized Neutron Scattering Study

We re-investigate the magnetically frustrated, {\it diamond-lattice-antiferromagnet} spinels FeAl$_2$O$_4$ and MnAl$_2$O$_4$ using magnetization measurements and diffuse scattering of polarized neutrons. In FeAl$_2$O$_4$, macroscopic measurements evidence a "cusp" in zero field-cooled susceptibility around 13~K. Dynamic magnetic susceptibility and {\it memory effect} experiments provide results that do not conform with a canonical spin-glass scenario in this material. Through polarized neutron scattering studies, absence of long-range magnetic order down to 4~K is confirmed in FeAl$_2$O$_4$. By modeling the powder averaged differential magnetic neutron scattering cross-section, we estimate that the spin-spin correlations in this compound extend up to the third nearest-neighbour shell. The estimated value of the Land\'{e} $g$ factor points towards orbital contributions from Fe$^{2+}$. This is also supported by a Curie-Weiss analysis of the magnetic susceptibility. MnAl$_2$O$_4$, on the contrary, undergoes a magnetic phase transition into a long-range ordered state below $\approx$ 40~K, which is confirmed by macroscopic measurements and polarized neutron diffraction. However, the polarized neutron studies reveal the existence of prominent spin-fluctuations co-existing with long-range antiferromagnetic order. The magnetic diffuse intensity suggests a similar short range order as in FeAl$_2$O$_4$. Results of the present work supports the importance of spin-spin correlations in understanding magnetic response of frustrated magnets like $A$-site spinels which have predominant short-range spin correlations reminiscent of the "spin liquid" state.Comment: 10 pages, 10 figures, double-column, accepted in Phys. Rev. B, 201