Approximation of Bayesian inverse problems for PDEs

Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at the level of probability measures. The stability which results from this well posedness may be used as the basis for quantifying the approximation, in finite dimensional spaces, of inverse problems for functions. This paper contains a theory which utilizes this stability property to estimate the distance between the true and approximate posterior distributions, in the Hellinger metric, in terms of error estimates for approximation of the underlying forward problem. This is potentially useful as it allows for the transfer of estimates from the numerical analysis of forward problems into estimates for the solution of the related inverse problem. It is noteworthy that, when the prior is a Gaussian random field model, controlling differences in the Hellinger metric leads to control on the differences between expected values of polynomially bounded functions and operators, including the mean and covariance operator. The ideas are applied to some non-Gaussian inverse problems where the goal is determination of the initial condition for the Stokes or Navier–Stokes equation from Lagrangian and Eulerian observations, respectively

Prescribing Change for Minority Students: Diagnosing Inequalities in Science Education in the Clark County School District

Promoting entry of underrepresented minority groups into the allied health professions is paramount to developing a balanced workforce that reflects the needs of an evolving populace. Currently, significant underrepresentation of racial minority groups in health and science related fields correlates with data showing an overrepresentation of black and Latino students in Title 1 (at-risk and low-income) schools. Data suggest that students who are exposed to “higher quality” science education, such as “hands on” experiences, have increased interest in pursuing a health or science related career. These findings prompt the hypothesis that Title 1 schools face inequalities in their science education when compared to Non-Title 1 schools. The study presented herein utilizes surveys targeted to Clark County School District high school science teachers to analyze variation in science education between Title 1 and Non-Title 1 high schools. These surveys reveal that Title 1 schools perform significantly fewer biology experiments than Non-Title 1 schools. In addition, this study indicates a correlation between lower socioeconomic status and the absence of a school science club. Science clubs are important outlets for mentorship and further exposure to science education, especially for minority students of low socioeconomic backgrounds. These results may provide the basis for legislative action to improve minority students’ access to health/science programs. Future retrospective and/or prospective studies may determine how secondary science education influences such factors as college acceptance rate, percentage of college matriculates declaring majors in science related fields, and ultimately, rates of entry into healthcare fields

A Constrained Approach to Multiscale Stochastic Simulation of\ud Chemically Reacting Systems

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper we introduce a multiscale methodology suitable to address this problem. It is based on the Conditional Stochastic Simulation Algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the Constrained Multiscale Algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems

Effects of Nostalgia on Responses to Negative Feedback

Nostalgia is a bittersweet emotion evoked by memories of cherished personal experiences. Though nostalgia is a self-focused emotion, it has many interpersonal effects as well. Feeling nostalgia increases feelings of social connectedness and self esteem, and may protect against negative effects of existential threat (Wildschut et al., 2006). However, less is known about the extent to which nostalgia relates to anger and aggression. We hypothesized that nostalgia would buffer against the effect of negative feedback on feelings of anger and motivation to aggress. Undergraduate students wrote about a nostalgic or objective memory, and then received negative feedback about another personal writing project. Participants reported their feelings of anger, then had the opportunity to punish the individual who gave them negative feedback by administering loud noise blasts in a competitive game. We discuss the results and real-world implications of these findings.https://scholarscompass.vcu.edu/uresposters/1283/thumbnail.jp

Deep spectroscopy of z~1 6C radio galaxies - II. Breaking the redshift-radio power degeneracy

The results of a spectroscopic analysis of 3CR and 6C radio galaxies at redshift z~1 are contrasted with the properties of lower redshift radio galaxies, chosen to be matched in radio luminosity to the 6C sources studied at z~1, thus enabling the P-z degeneracy to be broken. Partial rank correlations and principal component analysis have been used to determine which of z and P are the critical parameters underlying the observed variation of the ionization state andd kinematics of the emission line gas. [OII]/H-beta is shown to be a useful ionization mechanism diagnostic. Statistical analysis of the data shows that the ionization state of the emission line gas is strongly correlated with radio power, once the effects of other parameters are removed. No dependence of ionization state on z is observed, implying that the ionization state of the emission line gas is solely a function of the AGN properties rather than the hostt galaxy and/or environment. Statistical analysis of the kinematic properties of the emission line gas shows that these are strongly correlated independently withh both P and z. The correlation with redshift is the stronger of the two, suggesting that host galaxy composition or environment may play a role in producing the less extreme gas kinematics observed in the emission line regions of low redshift galaxies. For both the ionization and kinematic properties of thee galaxies, the independent correlations observed with radio size are strongest. Radio source age is a determining factor for the extended emission line regions.Comment: 10 pages, 5 figures, accepted for publication in MNRA

Cockpit in the Systems Engineering Lenses

The commercial transport aircraft of today vary greatly from early aircraft in regards to how they are controlled and the feedback provided from the machine to the human operator. Automation has improved operational precision and efficiency but at the cost of providing less feedback. Pilots are the last line of defense and current technology cannot provide the human ability to solve novel problems for which no computer logic can be written. The automated cockpits of today have may sub-components that interact in a manner often opaque and unpredictable when a sensor or sub-component fails or even in situations where no failure occurs but an unexpected result comes from the normal interaction of system components. This system complexity means the most rigorous pre-deployment testing may not predict an undesirable outcome when system parts interact as designed. Different stakeholders in the design and operations process have different and sometimes competing objectives. The components of the commercial aviation system and their numerous interactions means that examining each component individually is difficult. Evaluating all the hard and soft elements requires a systems analysis approach to provide the best outcome when working with human-automation co-existing systems