Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.Comment: Provisionally accepted to appear in IEEE Transactions on Automatic Contro

Computational linear algebra over finite fields

We present here algorithms for efficient computation of linear algebra problems over finite fields

MOfinder: A Novel Algorithm for Detecting Overlapping Modules from Protein-Protein Interaction Network

Since organism development and many critical cell biology processes are organized in modular patterns, many algorithms have been proposed to detect modules. In this study, a new method, MOfinder, was developed to detect overlapping modules in a protein-protein interaction (PPI) network. We demonstrate that our method is more accurate than other 5 methods. Then, we applied MOfinder to yeast and human PPI network and explored the overlapping information. Using the overlapping modules of human PPI network, we constructed the module-module communication network. Functional annotation showed that the immune-related and cancer-related proteins were always together and present in the same modules, which offer some clues for immune therapy for cancer. Our study around overlapping modules suggests a new perspective on the analysis of PPI network and improves our understanding of disease

Vector Form Implementation in Three-Phase Power Flow Analysis Based on Power Injection Rectangular Coordinate

This paper aims to propose the vector form implementation into three-phase power flow analysis. The developed algorithm is based on Newton-Raphson method with voltage is represented in rectangular coordinate. The Python programming language and its mathematical libraries are used in this works. Three-phase power flow analysis in vector form utilizes sparse matrix ordering algorithm, so the elements of the coefficient correction matrix can be rearranged easily. This method was used to solve three-phase power flow for balance or unbalance network in two actual distribution system feeders in Lampung, i.e. 119 nodes and 191 nodes. Comparison with traditional Newton-Raphson method (non-vector) shows the vector form is able to solve computation up to eight times faster than non-vector

GPU-Resident Sparse Direct Linear Solvers for Alternating Current Optimal Power Flow Analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs