Overview • Goals/ motivation: find patterns in large datasets: – (A) Sensor data – (B) network/graph data • Solutions: self-similarity and power laws • Discussion MSU, 2005 Applications of sensors/streams • 'Smart house': monitoring temperature, humidity etc

We address the definitions and synthesis of stochastic processes which possess warped scaling laws that depart from power law behaviors in a controlled manner. We define warped infinitely divisible cascading (IDC) noise, motion and random walk. We provide a theoretical derivation of the scaling behavior of the moments of their increments. We provide numerical simulations of a warped log-Normal ...

Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and ...

Direct numerical simulation (DNS) can be used to extract information implicit in the equations of fluid-particle motion. We have investigated the lift-off of a single particle and many particles in pressure driven flows by 2D DNS (N.A. Patankar, Huang, Ko & Joseph 2001a, Ko, N.A. Patankar & Joseph 2001, Joseph, & Ocando 2001, Choi & Joseph 2001, N.A. Patankar, Ko, Choi & Joseph 2001b). We show ...

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Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power laws derived from general arguments and the singular behaviour of solutions of nonlinear hyperbolic differential equations are in excellent agreement with the ...