Public Health, Biological & Social Sciences

• The big impact of small groups on college drinking, B.G. Fitzpatrick, J.W. Martinez, E.J. Polidan, E. Angelis (2015)
  College drinking is a problem with severe academic, health, and safety consequences. The underlying social processes that lead to increased drinking activity are not well understood. Social Norms Theory is an approach to analysis and intervention based on the notion that students’ misperceptions about the drinking culture on campus lead to increases in alcohol use. In this paper we develop an agent-based simulation model, implemented in MATLAB, to examine college drinking. Students’ drinking behaviors are governed by their identity (and how others perceive it) as well as peer influences, as they interact in small groups over the course of a drinking event. Our simulation results provide some insight into the potential effectiveness of interventions such as social norms marketing campaigns.

• Forecasting the effect of the Amethyst Initiative on college drinking, B.G. Fitzpatrick, R.A. Scribner, A.S. Ackleh, and N. Simonsen (2012)
  Background: A number of college presidents have endorsed the Amethyst Initiative, a call to consider lowering the minimum legal drinking age (MLDA). Our objective is to forecast the effect of the Amethyst Initiative on college drinking. Methods: A system model of college drinking simulates MLDA changes through (i) a decrease in heavy episodic drinking (HED) because of the lower likelihood of students drinking in unsupervised settings where they model irresponsible drinking (misperception), and (ii) an increase in overall drinking among currently underage students because of increased social availability of alcohol (wetness). Results: For the proportion of HEDs on campus, effects of large decreases in misperception of responsible drinking behavior were more than offset by modest increases in wetness. Conclusions: For the effect of lowering the MLDA, it appears that increases in social availability of alcohol have a stronger impact on drinking behavior than decreases in misperceptions.

• Heavy episodic drinking on college campuses: does changing the legal drinking age make a difference? J.W Rasul, R.G Rommel, G.M. Jacquez, B.G. Fitzpatrick, A.S. Ackleh, N.  Simonson, and R.A. Scribner (2011)
  Objective: This article extends the compartmental model previously developed by Scribner et al. in the context of college drinking to a mathematical model of the consequences of lowering the legal drinking age. Method: Using data available from 32 U.S. campuses, the analyses separate underage and legal age drinking groups into an eight-compartment model with different alcohol availability (wetness) for the underage and legal age groups. The model evaluates the likelihood that underage students will incorrectly perceive normative drinking levels to be higher than they actually are (i.e., misperception) and adjust their drinking accordingly by varying the interaction between underage students in social and heavy episodic drinking compartments. Results: The results evaluate the total heavy episodic drinker population and its dependence on the difference in misperception, as well as its dependence on underage wetness, legal age wetness, and drinking age. Conclusions: Results suggest that an unrealistically extreme combination of high wetness and low enforcement would be needed for the policies related to lowering the drinking age to be effective.

• A systems approach to college drinking: Development of a deterministic model for testing alcohol control policies, R. Scribner, A. Ackleh, B.G. Fitzpatrick, and  G.M. Jacquez (2009)
  Objective: The misuse and abuse of alcohol among college students remain persistent problems. Using a systems approach to understand the dynamics of student drinking behavior and thus forecasting the impact of campus policy to address the problem represents a novel approach. Toward this end, the successful development of a predictive mathematical model of college drinking would represent a significant advance for prevention efforts. Method: A deterministic, compartmental model of college drinking was developed, incorporating three processes: (1) individual factors, (2) social interactions, and (3) social norms. The model quantifies these processes in terms of the movement of students between drinking compartments characterized by five styles of college drinking: abstainers, light drinkers, moderate drinkers, problem drinkers, and heavy episodic drinkers. Predictions from the model were first compared with actual campus-level data and then used to predict the effects of several simulated interventions to address heavy episodic drinking. Results: First, the model provides a reasonable fit of actual drinking styles of students attending Social Norms Marketing Research Project campuses varying by “wetness” and by drinking styles of matriculating students. Second, the model predicts that a combination of simulated interventions targeting heavy episodic drinkers at a moderately “dry” campus would extinguish heavy episodic drinkers, replacing them with light and moderate drinkers. Instituting the same combination of simulated interventions at a moderately “wet” campus would result in only a moderate reduction in heavy episodic drinkers (i.e., 50% to 35%). Conclusions: A simple, five-state compartmental model adequately predicted the actual drinking patterns of students from a variety of campuses surveyed in the Social Norms Marketing Research Project study. The model predicted the impact on drinking patterns of several simulated interventions to address heavy episodic drinking on various types of campuses.

• Ecosystem modeling of college drinking: Parameter estimation and comparing models to data, A.S. Ackleh, B.G. Fitzpatrick, R.A. Scribner, N.  Simonson, and J.J. Thibodeaux (2009)
  Recently we developed a model composed of five impulsive differential equations that describes the changes in drinking patterns (that persist at epidemic level) amongst college students. Many of the model parameters cannot be measured directly from data; thus, an inverse problem approach, which chooses the set of parameters that results in the “best” model to data fit, is crucial for using this model as a predictive tool. The purpose of this paper is to present the procedure and results of an unconventional approach to parameter estimation that we developed after more common approaches were unsuccessful for our specific problem. The results show that our model provides a good fit to survey data for 32 campuses. Using these parameter estimates, we examined the effect of two hypothetical intervention policies: 1) reducing environmental wetness, and 2) penalizing students who are caught drinking. The results suggest that reducing campus wetness may be a very effective way of reducing heavy episodic (binge) drinking on a college campus, while a policy that penalizes students who drink is not nearly as effective.

• Statistical considerations and techniques for understanding physiological data, modeling and treatments, B.G. Fitzpatrick (2008)
  Comparing models with data always forces us to deal with uncertainty. This uncertainty may take many different forms and involve multiple scales of resolution in the model and in the experiment. In this paper, we discuss issues surrounding the development of deterministic dynamic models of mean behavior and the associated statistical models of the difference between model and experiment. We touch on a variety of topics, including basic exploratory data analysis, confidence bounds and model reduction hypothesis tests. Tools ranging from nonlinear regression to time series to Bayesian decision theory are presented.

• Numerical analysis and simulation of resource-exploration models, B.G. Fitzpatrick (2005)
  In this paper, we examine models for exploration and consumption of resources. The fundamental feature of the models is the jump-process nature of the exploration for and discovery of the resource. Several models have been proposed and analyzed in the literature. Here we provide numerical schemes, convergence properties, and some new models that provide risk-averse policies to avoid depletion of the resource.

• Statistical tests of fit in estimation problems for structured population modeling, H.T. Banks and B.G. Fitzpatrick (1995)
  In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.

• Estimation of growth rate distributions in size structured population modeling, H.T. Banks and B.G. Fitzpatrick (1992)
  We propose models for size-structured populations which allow growth rates to vary with individuals (growth rate distribution across all possible individual growth rates). A theoretical framework for the estimation of the growth rate distribution from data of sized population densities is developed. Numerical examples are presented to demonstrate feasibility of the ideas

Engineering & Physical Sciences

• Convergence and error bounds of adaptive filtering under model structure and regressor uncertainties, B.G. Fitzpatrick, G.G. Yin, L.Y. Wang (2012)
  Adaptive filtering algorithms are investigated when system models are subject to model structure errors and regressor signal perturbations. System models for practical applications are often approximations of high-order or nonlinear systems, introducing model structure uncertainties. Measurement and actuation errors cause signal perturbations, which in turn lead to uncertainties in regressors of adaptive filtering algorithms. Employing ordinary differential equation (ODE) methodologies, we show that convergence properties and estimation bias can be characterized by certain differential inclusions. Conditions to ensure algorithm convergence and bounds on estimation bias are derived. These findings yield better understanding of the robustness of adaptive algorithms against structural and signal uncertainties.

• Robustness, weak stability, and stability in distribution of adaptive filtering algorithms under model mismatch, B.G. Fitzpatrick, G.G. Yin, Y.L. Wang (2012)
  This work is concerned with robustness, convergence, and stability of adaptive filtering (AF) type algorithms in the presence of model mismatch. The algorithms under consideration are recursive and have inherent multiscale structure. They can be considered as dynamic systems, in which the “state” changes much more slowly than the perturbing noise. Beyond the existing results on adaptive algorithms, model mismatch significantly affects convergence properties of AF algorithms, raising issues of algorithm robustness. Weak convergence and weak stability (i.e., recurrence) under model mismatch are derived. Based on the limiting stochastic differential equations of suitably scaled iterates, stability in distribution is established. Then algorithms with decreasing step sizes and their convergence properties are examined. When input signals are large, identification bias due to model mismatch will become large and unacceptable. Methods for reducing such bias are introduced when the identified models are used in regulation problems.

• Stochastic game approach to air operations, W.M. EcEneaney, B.G. Fitzpatrick, and I. Lauko (2004)
  A command and control (C²) problem for military air operations is addressed. Specifically, we consider C² problems for air vehicles against ground-based targets and defensive systems. The problem is viewed as a stochastic game. We restrict our attention to the C² level where the problem may consist of a few unmanned combat air vehicles (UCAVs) or aircraft (or possibly teams of vehicles), less than say, a half-dozen enemy surface-to-air missile air defense units (SAMs), a few enemy assets (viewed as targets from our standpoint), and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some targets are mapped out and possible SAM sites that are unavoidably part of the situation are known. One may then employ a discrete stochastic game problem formulation to determine which of these SAMs should optimally be engaged (if any), and by what series of air vehicle operations. We provide analysis, numerical implementation, and simulation for full state-feedback and measurement feedback control within this C² context. Sensitivity to parameter uncertainty is discussed. Some insight into the structure of optimal and near-optimal strategies for C² is obtained. The analysis is extended to the case of observations which may be affected by adversarial inputs. A heuristic based on risk-sensitive control is applied, and it is found that this produces improved results over more standard approaches.

• Dispersion modeling and simulation in subsurface contaminant transport, J.V. Butera, B.G. Fitzpatrick, and C.J. Wypasek (1998)
  In this paper, we examine three separate approaches to analyze the spatial dispersion of a subsurface contaminant. These methods are contrasted against traditional models to demonstrate their feasibility and usefulness. Lastly, numerical simulations illustrate the effectiveness of these approaches.

• Smart material structures: Modeling, estimation and control, H.T. Banks, R.C. Smith, and Y.L. Wang (1995)
  The monograph is devoted to the study of smart material systems, a term containing systems known in the literature as controllable, adaptive, compliant, intelligent.

• Well posedness for damped second order systems with unbounded input operators, H.T. Banks, K. Ito, and Y.L. Wang (1995) [Downloaded from NCSU CRSC Technical Reports page and converted to PDF: crsc-tr93-10.]
  We consider damped second order in time systems such as those arising in structures with piezoceramic actuators and sensors. These systems are naturally formulated as abstract second order systems with unbounded nonhomogeneous term. Existence, uniqueness and continuous dependence of solutions in a weak or variational setting are given. A semigroup formulation is presented and conditions under which the variational solutions and semigroup solutions are the same are discussed.

• Approximation and parameter identification for damped second order systems with unbounded input operators, H.T. Banks, D.J. Inman, J.C. Slater, Y.L. Wang (1994)  [Downloaded from NCSU CRSC Technical Reports page and converted to PDF: crsc-tr93-9.]
  We consider a class of parameter estimation problems motivated by smart structures i.e. structures with integrated piezoelectric actuators and sensors. Problems involving damped second order partial differential equations with unbounded input coefficients are discussed in the context of a variational formulation. Theoretical, computational and experimental aspects of a smart structural system are successfully considered here, illustrating the importance of the proposed procedure in providing accurate models for identification and control. Approximation techniques are introduced and convergence arguments are presented rigorously. Numerical results of parameter estimation procedures are given and experimental data are used to test our computational results.

• A PDE-based methodology for modeling, parameter estimation and feedback control in structural and structural acoustic systems, H.T. Banks, D.E. Brown, V.L. Metcalf, R.J. Silcox, R.C. Smith, and Y.L. Wang (1994) [Downloaded from NCSU CRSC and converted to PDF: crsc-tr94-1]
  A problem of continued interest concerns the control of vibrations in a flexible structure and the related problem of reducing structure-borne noise in structural acoustic systems. In both cases, piezoceramic patches bonded to the structures have been successfully used as control actuators. Through the application of a controlling voltage, the patches can be used to reduce structural vibrations which in turn leads to methods for reducing structure-borne noise. A PDE-based methodology for modeling, estimating physical parameters, and implementing a feedback control scheme for problems of this type is discussed. While the illustrating example is a circular plate, the methodology is sufficiently general so as to be applicable in a variety of structural and structural acoustic systems.

• Vibration suppression with approximating finite dimensional compensator for distributed systems, H.T. Banks, R.C. Smith, and Y.L. Wang (1994)
  Based on a distributed parameter model for vibrations, an approximate finite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the effectiveness of this design.

• Computational methods for identification and feedback control in structures with piezoceramic actuators and sensors, H.T. Banks, K. Ito, Y.L. Wang (1993) [Downloaded from NCSU CRSC and converted to PDF: crsc-tr92-2]
  In this note we give fundamental existence, uniqueness, and continuous dependence results (well-posedness) for a variational formulation of a class of damped second order partial differential equations with unbounded input or control coefficients. Included as special cases in this class are structures with piezoceramic actuators. We then consider approximation techniques leading to computational methods in the context of both parameter estimation and feedback control problems for these systems. Rigorous convergence results for parameter estimates and feedback gains are presented.

• Numerical methods for an optimal investment-consumption model, B.G. Fitzpatrick and W.H. Fleming (1991)
  Some stochastic control problems are considered which arise in an optimal investment-consumption context. These problems have the common feature that the optimal cost function, which satisfies a dynamic programming differential equation, is a concave function of the state. The purpose is to find good numerical approximations to the optimal cost function, as well as optimal investment and consumption policies, and to prove convergence of these approximations as the step size tends to zero. The special linear-concave structure of the problems results in stronger convergence than for more general classes of optimal stochastic control problems. The stronger convergence is obtained by partial differential equation viscosity solution methods rather than by the probabilistic-weak convergence techniques. It is expected that the methods developed with be applicable to wider classes of problems with linear-concave structure.

• Bayesian analysis in inverse problems, B.G. Fitzpatrick (1991)
  In this paper, we consider some statistical aspects of inverse problems, using Bayesian analysis, particularly estimation and hypothesis-testing questions for parameter-dependent differential equations. We relate Bayesian maximum likelihood Io Tikhonv regularization, and we apply the expectation-minimization(E-M) algorithm to the problem of setting regularization levels. Further, we compare Bayesian results with those of a classical statistical approach, through consistency and asymptotic normality. A numerical example illustrates the application of Bayesian techniques. In many cases one is interested in parameters which are infinite dimensional (e.g. functions). Bayesian techniques offer a sound theoretical and computational paradigm, through probability measures on Banach space. We develop a framework for infinite dimensional Bayesian analysis, including convergence of approximations required to perform inference tasks computationally.

• Statistical tests for model comparison in parameter estimation problems for distributed parameter systems, H.T. Banks and B.G. Fitzpatrick (1990)
  In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.

• The identification of a distributed parameter model for a flexible structure, H.T. Banks, S.S. Gates, I.G. Rosen, and Y. Wang (1988)
  We develop a computational method for the estimation of parameters in a distributed model for a flexible structure. The structure consists of a cantilevered beam with a thruster and linear accelerometer at the free end. The thruster is fed by a pressurized hose whose horizontal motion affects the transverse vibration of the beam. We use the Euler-Bernoulli theory to model the vibration of the beam and treat the hose-thruster assembly as a lumped or point-mass-dashpot-spring system at the tip. Using measurements of linear acceleration at the tip, we estimate the hose parameters (mass, stiffness, damping) and a Voigt-Kelvin viscoelastic structural damping parameter for the beam using a least-squares fit to the data. We consider spline based approximation to the hybrid system. Theoretical convergence results and numerical studies with both simulation and actual experimental data obtained from the structure are discussed.