Analysis of modified degree six chordal rings and traditional chordal rings degree six interconnection network

Chordal rings are attractive network interconnection due to their short diameters especially when the degree was increased. Chordal rings were related to find the shortest path in a ring structured. This paper presents an analysis of modified degree six chordal rings (CHRm6) and chordal rings degree six (CR6) or commonly known as traditional chordal rings degree six (CR6). This analysis includes the structures, tree visualization, paths, formulations and geometrical representation. The comparison of diameters was made between theoretical and ideal graphs for these two methods. We tested and compared for a large number of nodes. CHRm6 gives shortest diameters for even and odd source node

Energy-Efficient NoC for Best-Effort Communication

A Network-on-Chip (NoC) is an energy-efficient on-chip communication architecture forMulti-Processor System-on-Chip (MPSoC) architectures. In an earlier paper we proposed a energy-efficient reconfigurable circuit-switched NoC to reduce the energy consumption compared to a packetswitched NoC. In this paper we investigate a chordal slotted ring and a bus architecture that can be used to handle the best-effort traffic in the system and configure the circuitswitched network. Both architectures are compared on their latency behavior and power consumption. At the same clock frequency, the chordal ring has the major benefit of a lower latency and higher throughput. But the bus has a lower overall power consumption at the same frequency. However, if we tune the frequency of the network to meet the throughput requirements of control network, we see that the ring consumes less energy per transported bit

A coupled mitral valve -- left ventricle model with fluid-structure interaction

Understanding the interaction between the valves and walls of the heart is important in assessing and subsequently treating heart dysfunction. With advancements in cardiac imaging, nonlinear mechanics and computational techniques, it is now possible to explore the mechanics of valve-heart interactions using anatomically and physiologically realistic models. This study presents an integrated model of the mitral valve (MV) coupled to the left ventricle (LV), with the geometry derived from in vivo clinical magnetic resonance images. Numerical simulations using this coupled MV-LV model are developed using an immersed boundary/finite element method. The model incorporates detailed valvular features, left ventricular contraction, nonlinear soft tissue mechanics, and fluid-mediated interactions between the MV and LV wall. We use the model to simulate the cardiac function from diastole to systole, and investigate how myocardial active relaxation function affects the LV pump function. The results of the new model agree with in vivo measurements, and demonstrate that the diastolic filling pressure increases significantly with impaired myocardial active relaxation to maintain the normal cardiac output. The coupled model has the potential to advance fundamental knowledge of mechanisms underlying MV-LV interaction, and help in risk stratification and optimization of therapies for heart diseases.Comment: 25 pages, 6 figure

Exploiting chordal structure in polynomial ideals: a Gr\"obner bases approach

Chordal structure and bounded treewidth allow for efficient computation in numerical linear algebra, graphical models, constraint satisfaction and many other areas. In this paper, we begin the study of how to exploit chordal structure in computational algebraic geometry, and in particular, for solving polynomial systems. The structure of a system of polynomial equations can be described in terms of a graph. By carefully exploiting the properties of this graph (in particular, its chordal completions), more efficient algorithms can be developed. To this end, we develop a new technique, which we refer to as chordal elimination, that relies on elimination theory and Gr\"obner bases. By maintaining graph structure throughout the process, chordal elimination can outperform standard Gr\"obner basis algorithms in many cases. The reason is that all computations are done on "smaller" rings, of size equal to the treewidth of the graph. In particular, for a restricted class of ideals, the computational complexity is linear in the number of variables. Chordal structure arises in many relevant applications. We demonstrate the suitability of our methods in examples from graph colorings, cryptography, sensor localization and differential equations.Comment: 40 pages, 5 figure

A coupled mitral valve - left ventricle model with fluid-structure interaction

Understanding the interaction between the valves and walls of the heart is important in assessing and subsequently treating heart dysfunction. This study presents an integrated model of the mitral valve (MV) coupled to the left ventricle (LV), with the geometry derived from in vivo clinical magnetic resonance images. Numerical simulations using this coupled MV–LV model are developed using an immersed boundary/finite element method. The model incorporates detailed valvular features, left ventricular contraction, nonlinear soft tissue mechanics, and fluid-mediated interactions between the MV and LV wall. We use the model to simulate cardiac function from diastole to systole. Numerically predicted LV pump function agrees well with in vivo data of the imaged healthy volunteer, including the peak aortic flow rate, the systolic ejection duration, and the LV ejection fraction. In vivo MV dynamics are qualitatively captured. We further demonstrate that the diastolic filling pressure increases significantly with impaired myocardial active relaxation to maintain a normal cardiac output. This is consistent with clinical observations. The coupled model has the potential to advance our fundamental knowledge of mechanisms underlying MV–LV interaction, and help in risk stratification and optimisation of therapies for heart diseases