Aortic bifurcation angle as an independent risk factor for aortoiliac occlusive disease

Recently, there has been interest in potential geometric risk factors that might result in or exaggerate atherosclerosis. The aortic bifurcation is a complex anatomical area dividing the high pressure blood of the descending abdominal aorta into the lower limbs and pelvis. The distribution of the bifurcation angle and any asymmetry, its relation with age and its possible contribution to the risk of aortoiliac atherosclerosis are presented here. Statistical analysis was performed by SPSS version 11.0 using, Fisher`s exact test, the Pearson and Spearman correlation tests and logistic regression analysis. The p value was set at 0.05. No correlations were found between age, bifurcation angle and angle asymmetry in the Pearson test (p > 0.05). Logistic regression analysis revealed that the bifurcation angle, but not its asymmetry, gender or age, was a significant and independent risk factor for aortoiliac atherosclerosis (model r2 = 0.662, p = 0.027). With additional study these results may have implications regarding risk factors for aortoiliac atherosclerosis. To our knowledge, this study is the first of its kind to indicate the potential of such an important geometric risk factor for atherosclerosis at the aortic bifurcation

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

Precoding for broadcasting with linear network codes

A technique based on linear precoding is introduced for broadcasting on linear networks. The precoding allows the different message components of a broadcast message to be separated and decoded at the desired sink nodes, thus providing a systematic design methodology for broadcasting over a given network with a given linear network code. To achieve a good throughput, however, the network code itself must also be chosen judiciously. Motivated by several recent results on random network codes, we propose a combination of precoding and random linear network codes. This approach does not require a centralized coordination for network code design. One of the advantages of this approach is that by simply changing the precoding matrix (together with associated decoding strategies), different broadcast objectives can be achieved without tampering with the network code, therefore one can manage the network operation by controlling the origin and destination nodes of the network and without manipulating the network interior. Together, random network codes and linear precodings provide a simple yet powerful methodology for broadcast over linear networks

Modeling energy consumption of dual-hop relay based MAC protocols in ad hoc networks

Given that the next and current generation networks will coexist for a considerable period of time, it is important to improve the performance of existing networks. One such improvement recently proposed is to enhance the throughput of ad hoc networks by using dual-hop relay-based transmission schemes. Since in ad hoc networks throughput is normally related to their energy consumption, it is important to examine the impact of using relay-based transmissions on energy consumption. In this paper, we present an analytical energy consumption model for dual-hop relay-based medium access control (MAC) protocols. Based on the recently reported relay-enabled Distributed Coordination Function (rDCF), we have shown the efficacy of the proposed analytical model. This is a generalized model and can be used to predict energy consumption in saturated relay-based ad hoc networks. This model can predict energy consumption in ideal environment and with transmission errors. It is shown that using a relay results in not only better throughput but also better energy efficiency. Copyright (C) 2009 Rizwan Ahmad et al