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A coprime array of M + N - 1 elements is designed, using product processing (PP), to yield the same beam width as that of a full array of MN elements using conventional beamforming (CBF), while at the same time suppressing the grating lobes. The array gain (AG) for isotropic noise using conventional PP is slightly less than that obtained using CBF, namely, 10log(M + N - 1). It is shown that using the coherent product processing, the coprime array yields an AG equal to that of the full array of MN elements, 10log(MN). The superior gain is often referred to as supergain.

Coprime Sensor Array (CSA) has received a lot of attentions recently due to "coprime" nature of the array configuration, which yields a high resolution using product processing with fewer sensors, similar to that of a uniform liner array (ULA) of a larger aperture using conventional beamforming (CBF), with more sensors. Compared with the ULA, CSA yield higher sidelobes and less detection gain. This paper applies CBF to the CSA and then deconvolution to the CBF beam output, referred to as deconvolved CBF. Simulation results show that deconvolved CBF yields a higher resolution, higher gain and lower sidelobes than the product processing and its extensions.

By using the state space model (Kalman filter model) of the HIV epidemic, in this paper we have developed a general Bayesian procedure to estimate simultaneously the HIV infection distribution, the HIV incubation distribution, the numbers of susceptible people, infective people and AIDS cases. The basic approach is to use the Gibbs sampling method combined with the weighted bootstrap method. We have applied this method to the San Francisco AIDS incidence data from January 1981 to December 1992. The results show clearly that both the probability density function of the HIV infection and the probability density function of the HIV incubation are curves with two peaks. The results of the HIV infection distribution are clearly consistent with the finding by Tan et al. [W.Y. Tan, S.C. Tang, S.R. Lee, Estimation of HIV seroconversion and effects of age in San Francisco homosexual populations, J. Appl. Stat. 25 (1998) 85]. The results of HIV incubation distribution seem to confirm the staged model used by Satten and Longini [G. Satten, I. Longini, Markov chain with measurement error: estimating the `true' course of marker of the progression of human immunodeficiency virus disease, Appl. Stat. 45 (1996) 275].

In this paper we have developed some state space models for the HIV epidemic for populations at risk for AIDS. By using these state space models, we have developed a general Bayesian procedure for estimating simultaneously the unknown parameters and the state variables. The unknown parameters include the immigration and recruitment rates, the death and retirement rates, the incidence of HIV infection ( and hence the HIV infection distribution ) and the incidence of HIV incubation ( and hence the HIV incubation distribution). The state variables are the numbers of susceptible people (S people), HIV-infected people (I people) and AIDS incidence over time. The basic approach is through multi-level Gibbs sampler combined with the weighted bootstrap method. We have applied the methods to the Swiss AIDS homosexual and IV drug data to estimate simultaneously the unknown parameters and the state variables. Our results show that in both populations, both the HIV infection and HIV incubation have multi-peaks indica...

Model of HIV pathogenesis in HIV-infected individuals under very general conditions. In this model, we have considered five different types of CD4(+)T cells, two different types of HIV (M-tropic versus T-tropic) as well as infected and un-infected macrophage. This is a 9-dimensional stochastic process. For this process, we have developed stochastic differential equations for different types of cells. By using these stochastic equations, we have generated some Monte Carlo data to study the stochastic behavior of the HIV pathogenesis and the HIV progression.Through Monte Carlo studies, we have revealed an acute infection stage in the early stage of the HIV infection and have confirmed the basic role played by lymph nodes and some long-lived cells such as macrophage in serving as reservoirs of HIV to escape elimination by the immune system during the long asymptomatic stage of HIV infection. The Monte Carlo results have shown that the HIV heterogeneity and diversity may be a major factor to determine the time period since infection for uninfected T cells to drop to below 200/mm3of blood. The numerical results have also confirmed our previous findings (see [1]) which concluded that the probability distributions of T cells and free HIV can be classified into three periods over time: The latent period, the transition period and the pseudo-steady period.

The objective of our study was to test the hypothesis that subtle brain abnormality can be present in pediatric sickle cell disease (SCD) patients normal by conventional MR imaging (cMRI). We examined 50 SCD patients to identify those patients who were normal by cMRI. Quantitative MR imaging (qMRI) was then used to map spin-lattice relaxation time (T1) in a single slice in brain tissue of all 50 patients and in 52 healthy age-similar controls. We also used a radiofrequency (RF) pulse to saturate blood spins flowing into the T1 map slice, to characterize the effect of blood flow on brain T1. Abnormalities were noted by cMRI in 42% (21/50) of patients, with lacunae in 32%, and encephalo malacia in 20%. Brain T1 in patients normal by cMRI was significantly lower than controls, in caudate, thalamus, and cortex (p < or =0.007), and regression showed that gray matter T1 abnormality was present in caudate and cortex by age 4 (p < or =0.002). In patients abnormal by cMRI, T1 reductions in gray matter were larger and more significant. White matter T1 was not significantly increased except in patients abnormal by cMRI. RF saturation in a slab below the T1 map produced no significant change in T1, compared to RF saturation in a slab above the T1 map, suggesting that inflow of untipped spins in blood does not cause an artifactual shortening of T1. Gray matter T1 abnormality was present in patients normal by cMRI, while white matter T1 abnormality was present only in patients also abnormal by cMRI. These findings suggest that gray matter is selectively vulnerable to damage in pediatric SCD patients and that white matter damage occurs later in the disease process. Our inability to find an effect from saturation of inflowing blood implies that rapid perfusion cannot account for T1 reduction in gray matter.