Browsing by Subject "ODE"
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Item HxC scaling algorithm applied to first and second order ordinary differential equations(2016-12) Wang, Chunqi; Bryant, Michael DavidA scaling algorithm for the Hybrid eXtreme Computer (HxC) was developed, and the operation of the entire HxC was simulated in MATLAB environment. The HxC will solve Ordinary Differential Equations (ODEs) in a more efficient way. The computer consists of both analog and digital components and is based on a previously designed hybrid integrator. The ODEs are integrated by analog integrators assisted by digital, and results are represented and stored in analog and digital. To represent nonlinear functions as analog voltages, a Taylor Series approach is employed which rapidly repositions the expansion operating points. The analog integrator of HxC integrates the ODE as a voltage. The Taylor Series function approximators use Digital to Analog Converter (DAC) R2R ladders to implement multiplications of the Taylor Series coefficients by states, which are analog integrator voltages. Simulations are presented of the HxC solving first and second order ODEs.Item Lurking Pathway Prediction And Pathway ODE Model Dynamic Analysis(2013-11-18) Zhang, RengjingSignaling pathway analysis is so important to study the causes of diseases and the treatment of drugs. Finding the lurking pathway from ligand to signature is a significant issue in studying the mechanism of how the cell response to the stimulation signal. However, recent literature based pathway analysis methods can only tell about highly differentially expressed pathways related to the experiment data, which may tell nothing about our interested specific ligand and signature. In this paper, we designed an approach to successfully detect the most reliable pathways for specific ligand and signature by solving multi-objective optimization problem on the bridge connecting two signaling pathways where the ligand and sig- nature locate. The pathway bridge consisted of enriched looping patterns refined the complicated entire protein interactions network with 39031 links, which made the approach time-saving. The approach was further applied to study the mod- ulator mechanism of the signal molecule, receptor, intermediate transfer proteins, transcription factor, and signature. With preliminary studied pathways, we then employed Ordinary Differential Equations(ODE) to modeling and dynamic analysis the signaling transduction. The biological reactions were represented in terms of differential equations, and the solu- tions to the group of equations were further be optimized to fit the RPPA experiment data. In order to find the potential signaling paths in specific disease and discovery the best therapy, coefficient variation analysis, system robustness study and system outcomes changes to perturbations were also utilized. Our approach successfully predicted the lurking pathway for the signal molecule T GF ?1 and the nova protein OC I AD2 in cancer microenviroment: T GF ?1 ?T GF ?R1 ? SM AD2/3 ? SM AD4/AR ? OC I AD2, and this result was verified by literature. Better than recent pathway analysis tool, our predicted pathway also took care of significant but relatively less regulated proteins in the transduction pro- cess. And by modeling the CCL2 pathway in MTB infected cells, J N K , cM Y C and P LC showed as the most significant modules. Hence, the drug treatments inhibit- ing J N K , cM Y C and P LC would effectively obstruct the increasing of MMPs and further prevent the Mtb infections.