Model reduction for a class of singularly perturbed stochastic differential equations : Fast variable approximation (Extended Version)

This is an extended version of a paper of the same title accepted to American Control Conference (ACC) 2016

Model reduction for a class of singularly perturbed stochastic differential equations

A class of singularly perturbed stochastic differential equations (SDE) with linear drift and nonlinear diffusion terms is considered. We prove that, on a finite time interval, the trajectories of the slow variables can be well approximated by those of a system with reduced dimension as the singular perturbation parameter becomes small. In particular, we show that when this parameter becomes small the first and second moments of the reduced system's variables closely approximate the first and second moments, respectively, of the slow variables of the singularly perturbed system. Chemical Langevin equations describing the stochastic dynamics of molecular systems with linear propensity functions including both fast and slow reactions fall within the class of SDEs considered here. We therefore illustrate the goodness of our approximation on a simulation example modeling a well known biomolecular system with fast and slow processes.United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0060)National Institute of General Medical Sciences (U.S.) (Grant P50 GMO9879

Trade-offs between retroactivity and noise in connected transcriptional components

At the interconnection of two gene transcriptional components in a biomolecular network, the noise in the downstream component can be reduced by increasing its gene copy number. However, this method of reducing noise increases the load applied to the upstream system, called retroactivity, thereby causing a perturbation in the upstream system. In this work, we quantify the error in the system trajectories caused by perturbations due to retroactivity and noise, and analyze the trade-off between these two perturbations. We model the system as a set of nonlinear chemical Langevin equations and quantify the trade-off by employing contraction theory for stochastic systems.National Science Foundation (U.S.). Division of Computing and Communication Foundations (Award 1058127)United States. Air Force Office of Scientific Research (Award FA9550-12-1-0129

Music Education in Iowa Public Schools

Capstone paper from 2015 spring MPA program. Instructed by Allen Zagoren.Our paper discusses the status of music education programs in Iowa public schools. Music programs are often the first to be cut when school districts have financial difficulties. Therefore, we conducted further research on this topic. Our research includes a short history of music and its importance in education. It is also shown to improve learning and have an effect on the human brain. Throughout the country many schools have dropped or reduced their music programs, mainly due to budget cuts and Common Core requirements. In order to see how Iowa is doing, we sent out surveys to all 338 public school districts and received 91 responses. Our results showed that in Iowa most school districts have retained their music programs and have found ways to keep music alive for their students. It also showed that Iowans are very proud of their music programs and are willing to support them

CFD analysis of blood flow through stenosed arteries

The pathological complications of atherosclerosis, namely heart disease and stroke, remain the leading cause of mortality in the world. Cardiovascular illness is highly prevalent among the American population. One manifesto of cardiovascular disease is Peripheral Artery Disease (PAD) which is caused by atherosclerosis in the arteries. Atherosclerosis is a vascular disease that reduces arterial lumen size through plaque deposition and arterial wall thickening. The flow patterns in the arteries are highly modulating along with the cardiac cycle and a strong function of the waveform created by the heartbeat. In this study, a computational simulation model is developed to analyze blood flow distribution in a femoral artery network based on Navier-Stokes equation. A comparative analysis of blood flow through femoral artery is done based on Newtonian and non-Newtonian blood flow by using Carreau-Yasuda model subjected to a waveform based on a cardiac cycle. The non-Newtonian CFD flow analysis model is use to analyze blood flow distributions in a femoral artery along with the adjacent capillary porous tissue medium. This simulation model is used to analyze the flow and stress field in a healthy and atherosclerosis affected femoral arteries. Velocity, pressure and Wall Shear Stress fields over cardiac cycle are analyzed to demonstrate that adverse flow field created upstream and downstream of the blockage that may cause enhanced growth in size of the blockage

A clinical study of effects of pregnancy on diseases like painful crisis, seizure disorders, hepatopathy, acute anemia and its outcome

Background: The ability of the blood cells to carry oxygen is especially important in pregnancy. Anemia may result in lower amount of oxygen going to the fetus and slowed fetal growth. Because it affects so many organs and body systems, women with the disease are more likely to have complications in pregnancy. The main objective was to study the effects of pregnancy on disease and its outcomes.Methods: It is a hospital based prospective study. The study was conducted at Narayana Medical College Nellore, Andhra Pradesh. The patients admitted in Obstetrics and Gynecology Department were included in the study. The study included total of 45 patients. Detailed history included age, socioeconomic status, address, education and occupation of the patient’s Permission from Institutional Ethics Committee was obtained.Results: Maximum patients were gravida 2-3, and minimum were gravida 4 or more. Maximum numbers of patients were in group 20-25. The patients with preterm birth that is delivery before 37 weeks of pregnancy were 15. Low birth weights were 20 and of still birth and new born death was 4.Conclusions: The present study was carried out in 45 cases and appropriate prenatal care and careful monitoring throughout pregnancy, can have healthy pregnancy with significant improvement in pregnancy outcome