A Dynamic Model of Differential Human Capital and Criminal Activity

This paper presents a new, dynamic economic model of criminal activity. Individuals are endowed with legal and criminal human capital. Potential incomes in legal and criminal sectors depend on the level of the relevant human capital, the rate of return, and random shocks. Both types of human capital can be enhanced by participating in the relevant sector. Legal human capital can also be enhanced through savings. Each type of human capital is subject to depreciation. Individuals maximize expected discounted lifetime utility, which depends on consumption. In this two-stage dynamic stochastic model, in each period the individual decides in which sector to participate (legal or illegal), and after the realization of income in that period, he decides on the optimal amount of consumption. A particular decision (e.g. participation in the criminal sector) has implications both for future decisions as well as the choices available to the individual in later periods. The model allows analyses of the effects of recessions, neighborhood effects, various imprisonment/rehabilitation scenarios, risk aversion, and time preferences on criminal behavior. It provides new insights, which are different from existing models, and it is able to explain the declining propensity of individuals to commit crimes over time.

A Probability-one Homotopy Algoithm for Non-Smooth Equations and Mixed Complementarity Problems

A probability-one homotopy algorithm for solving nonsmooth equations is described. This algorithm is able to solve problems involving highly nonlinear equations,where the norm of the residual has non-global local minima.The algorithm is based on constructing homotopy mappings that are smooth in the interior of their domains.The algorithm is specialized to solve mixed complementarity problems through the use of MCP functions and associated smoothers.This specialized algorithm includes an option to ensure that all iterates remain feasible.Easily satisfiable sufficient conditions are given to ensure that the homotopy zero curve remains feasible,and global convergence properties for the MCP algorithm are developed.Computational results on the MCPLIB test library demonstrate the effectiveness of the algorithm

An iterative method for generalized set-valued nonlinear mixed quasi-variational inequalities

AbstractThis paper presents an iterative method for solving the generalized nonlinear set-valued mixed quasi-variational inequality, a problem class that was introduced by Huang et al. (Comp. Math. Appl. 40 (2–3) (2000) 205–215). The method incorporates step size controls that enable application to problems where certain set-valued mappings do not always map to nonempty closed bounded sets

ProxECAT: Proxy External Controls Association Test. A new case-control gene region association test using allele frequencies from public controls.

A primary goal of the recent investment in sequencing is to detect novel genetic associations in health and disease improving the development of treatments and playing a critical role in precision medicine. While this investment has resulted in an enormous total number of sequenced genomes, individual studies of complex traits and diseases are often smaller and underpowered to detect rare variant genetic associations. Existing genetic resources such as the Exome Aggregation Consortium (>60,000 exomes) and the Genome Aggregation Database (~140,000 sequenced samples) have the potential to be used as controls in these studies. Fully utilizing these and other existing sequencing resources may increase power and could be especially useful in studies where resources to sequence additional samples are limited. However, to date, these large, publicly available genetic resources remain underutilized, or even misused, in large part due to the lack of statistical methods that can appropriately use this summary level data. Here, we present a new method to incorporate external controls in case-control analysis called ProxECAT (Proxy External Controls Association Test). ProxECAT estimates enrichment of rare variants within a gene region using internally sequenced cases and external controls. We evaluated ProxECAT in simulations and empirical analyses of obesity cases using both low-depth of coverage (7x) whole-genome sequenced controls and ExAC as controls. We find that ProxECAT maintains the expected type I error rate with increased power as the number of external controls increases. With an accompanying R package, ProxECAT enables the use of publicly available allele frequencies as external controls in case-control analysis

Interlaboratory comparison study of Mg/Ca and Sr/Ca measurements in planktonic foraminifera for paleoceanographic research

Thirteen laboratories from the USA and Europe participated in an intercomparison study of Mg/Ca and Sr/Ca measurements in foraminifera. The study included five planktonic species from surface sediments from different geographical regions and water depths. Each of the laboratories followed their own cleaning and analytical procedures and had no specific information about the samples. Analysis of solutions of known Mg/Ca and Sr/Ca ratios showed that the intralaboratory instrumental precision is better than 0.5% for both Mg/Ca and Sr/Ca measurements, regardless whether ICP-OES or ICP-MS is used. The interlaboratory precision on the analysis of standard solutions was about 1.5% and 0.9% for Mg/Ca and Sr/Ca measurements, respectively. These are equivalent to Mg/Ca-based temperature repeatability and reproducibility on the analysis of solutions of ±0.2°C and ±0.5°C, respectively. The analysis of foraminifera suggests an interlaboratory variance of about ±8% (%RSD) for Mg/Ca measurements, which translates to reproducibility of about ±2–3°C. The relatively large range in the reproducibility of foraminiferal analysis is primarily due to relatively poor intralaboratory repeatability (about ±1–2°C) and a bias (about 1°C) due to the application of different cleaning methods by different laboratories. Improving the consistency of cleaning methods among laboratories will, therefore, likely lead to better reproducibility. Even more importantly, the results of this study highlight the need for standards calibration among laboratories as a first step toward improving interlaboratory compatibility

Algorithms for Complementarity Problems and Generalized Equations

Recent improvements in the capabilities of complementarity solvers have led to an increased interest in using the complementarity problem framework to address practical problems arising in mathematical programming, economics, engineering, and the sciences. As a result, increasingly more difficult problems are being proposed that exceed the capabilities of even the best algorithms currently available. There is, therefore, an immediate need to improve the capabilities of complementarity solvers. This thesis addresses this need in two significant ways. First, the thesis proposes and develops a proximal perturbation strategy that enhances the robustness of Newton-based complementarity solvers. This strategy enables algorithms to reliably find solutions even for problems whose natural merit functions have strict local minima that are not solutions. Based upon this strategy, three new algorithms are proposed for solving nonlinear mixed complementarity problems that represent a significant improvement in robustness over previous algorithms. These algorithms have local Q-quadratic convergence behavior, yet depend only on a pseudo-monotonicity assumption to achieve global convergence arbitrary starting points. Using the MCPLIB and GAMSLIB test libraries, we perform extensive computational tests that demonstrate the effectiveness these algorithms on realistic problems. Second, the thesis extends some previously existing algorithms to solve more general problem classes. Specifically, the NE/SQP method of Pang & Gabriel (1993), the semismooth equations approach of De Luca, Facchinei & Kanzow (1995), and the infeasible-interior point method of Wright (1994) are all generalized to the mixed complementarity problems framework. In addition, the pivotal method of Cao & Ferris (1995b), which solves affine variational inequalities, is extended to solve affine generalized equations. To develop this extension, the piecewise-linear homotopy framework of Eaves (1976) is used to generate an algorithm finds a solution in a finite number of iterations under the assumption that the piecewise affine map is coherently oriented

A Homotopy Based Algorithm for Mixed Complementarity Problems

This paper develops an algorithm for solving mixed complementarity problems which is based upon probability one homotopy methods. After the complementarity problem is reformulated as a system of nonsmooth equations, a homotopy method is used to solve a sequence of smooth approximations to this system of equations. The global convergence properties of this approach are considerably stronger than other recent algorithms, depending on very weak assumptions about the problem. To improve efficiency, the homotopy algorithm is embedded in a generalized Newton-method. Keywords: Complementarity problems, homotopy methods, smoothing. 1 Introduction This paper discusses a robust method for solving mixed complementarity problems, which is based upon the probability one homotopy methods of [13, 31, 33]. The idea is to reformulate the mixed complementarity problem as a system of equations, and then solve smooth approximations of this system with a homotopy method. While extremely robust, the homot..