Gauging of Lorentz Group WZW Model by its Null Subgroup

We consider the standard vector gauging of Lorentz group $SO(3,1)$ WZW model by its non-semisimple null Euclidean subgroup in two dimensions $E(2)$. The resultant effective action of the theory is seen to describe a one dimensional bosonic field in the presence of external charge that we interpret it as a Liouville field. Gauging a boosted $SO(3)$ subgroup, we find that in the limit of the large boost, the theory can be interpreted as an interacting Toda theory. We also take the generalized non-standard bilinear form for $SO(3,1)$ and gauge both $SO(3)$ and $E(2)$ subgroups and discuss the resultant theories.Comment: 11 pages, LaTeX fil

Rate-Constrained Wireless Networks with Fading Channels: Interference-Limited and Noise-Limited Regimes

A network of $n$ wireless communication links is considered in a Rayleigh fading environment. It is assumed that each link can be active and transmit with a constant power $P$ or remain silent. The objective is to maximize the number of active links such that each active link can transmit with a constant rate $\lambda$. An upper bound is derived that shows the number of active links scales at most like $\frac{1}{\lambda} \log n$. To obtain a lower bound, a decentralized link activation strategy is described and analyzed. It is shown that for small values of $\lambda$, the number of supported links by this strategy meets the upper bound; however, as $\lambda$ grows, this number becomes far below the upper bound. To shrink the gap between the upper bound and the achievability result, a modified link activation strategy is proposed and analyzed based on some results from random graph theory. It is shown that this modified strategy performs very close to the optimum. Specifically, this strategy is \emph{asymptotically almost surely} optimum when $\lambda$ approaches $\infty$ or 0. It turns out the optimality results are obtained in an interference-limited regime. It is demonstrated that, by proper selection of the algorithm parameters, the proposed scheme also allows the network to operate in a noise-limited regime in which the transmission rates can be adjusted by the transmission powers. The price for this flexibility is a decrease in the throughput scaling law by a multiplicative factor of $\log \log n$.Comment: Submitted to IEEE Trans. Information Theor

Exactly solvable models through the generalized empty interval method, for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E^{\mathbf a}_n(t)$'s, the expectation value of the product of certain linear combination of the number operators on $n$ consecutive sites at time $t$. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of $E^{\mathbf a}_n(t)$'s are closed, are given.Comment: 18 pages, LaTeX2e, no figure

THRESHOLD EFFECTS OF REAL INTEREST RATE ON INVESTMENT OF THE PRIVATE SECTOR IN IRAN: TESTING STIEGLITZ'S THEORY

In this paper, Stieglitz’s theory regarding the threshold effects of real interest rate on investment of Iran's private sector during 1973-2008 is experimentally examined. The study showed that although the real interest rate directly affects on private investment in Iran, an increase of more than 2 percent in the real interest rate will reduce the private sector's investment. In other words, Stieglitz’s argument about a one-threshold level (close to zero) of the real interest rate is confirmed in Iran. Paying attention to the rate of inflation and threshold limit of influence of interest rate on monetary policies is considered the most important proposals of the present researchPrivate sector's investment, Real interest rate, Threshold effects

On the Exceptional Gauged WZW Theories

We consider two different versions of gauged WZW theories with the exceptional groups and gauged with any of theirs null subgroups. By constructing suitable automorphism, we establish the equivalence of these two theories. On the other hand our automorphism, relates the two dual irreducible Riemannian globally symmetric spaces with different characters based on the corresponding exceptional Lie groups.Comment: 5 pages, LaTeX fil

On the Capacity Region of Multi-Antenna Gaussian Broadcast Channels with Estimation Error

In this paper we consider the effect of channel estimation error on the capacity region of MIMO Gaussian broadcast channels. It is assumed that the receivers and the transmitter have (the same) estimates of the channel coefficients (i.e., the feedback channel is noiseless). We obtain an achievable rate region based on the dirty paper coding scheme. We show that this region is given by the capacity region of a dual multi-access channel with a noise covariance that depends on the transmit power. We explore this duality to give the asymptotic behavior of the sum-rate for a system with a large number of user, i.e., n rarr infin. It is shown that as long as the estimation error is of fixed (w.r.t n) variance, the sum-capacity is of order M log log n, where M is the number of antennas deployed at the transmitter. We further obtain the sum-rate loss due to the estimation error. Finally, we consider a training-based scheme for block fading MISO Gaussian broadcast channels. We find the optimum length of the training interval as well as the optimum power used for training in order to maximize the achievable sum-rate

Characterization of Rate Region in Interference Channels with Constrained Power

In this paper, an $n$-user Gaussian interference channel, where the power of the transmitters are subject to some upper-bounds is studied. We obtain a closed-form expression for the rate region of such a channel based on the Perron-Frobenius theorem. While the boundary of the rate region for the case of unconstrained power is a well-established result, this is the first result for the case of constrained power. We extend this result to the time-varying channels and obtain a closed-form solution for the rate region of such channels.Comment: 21 Pages, The Conference Version is Submitted to IEEE International Symposium on Information Theory (ISIT2007