Large Scale Computational Problems in Numerical Optimization

Our work under this support broadly falls into five categories: automatic differentiation, sparsity, constraints, parallel computation, and applications. Automatic Differentiation (AD): We developed strong practical methods for computing sparse Jacobian and Hessian matrices which arise frequently in large scale optimization problems [10,35]. In addition, we developed a novel view of "structure" in applied problems along with AD techniques that allowed for the efficient application of sparse AD techniques to dense, but structured, problems. Our AD work included development of freely available MATLAB AD software. Sparsity: We developed new effective and practical techniques for exploiting sparsity when solving a variety of optimization problems. These problems include: bound constrained problems, robust regression problems, the null space problem, and sparse orthogonal factorization. Our sparsity work included development of freely available and published software [38,39]. Constraints: Effectively handling constraints in large scale optimization remains a challenge. We developed a number of new approaches to constrained problems with emphasis on trust region methodologies. Parallel Computation: Our work included the development of specifically parallel techniques for the linear algebra tasks underpinning optimization algorithms. Our work contributed to the nonlinear least-squares problem, nonlinear equations, triangular systems, orthogonalization, and linear programming. Applications: Our optimization work is broadly applicable across numerous application domains. Nevertheless we have specifically worked in several application areas including molecular conformation, molecular energy minimization, computational finance, and bone remodeling

A Subspace, Interior, and Conjugate Gradient Method for Large-scale Bound-constrained Minimization Problems

A subspace adaption of the Coleman-Li trust region and interior method is proposed for solving large-scale bound-constrained minimization problems. This method can be implemented with either sparse Cholesky factorization or conjugate gradient computation. Under reasonable conditions the convergence properties of this subspace trust region method are as strong as those of its full-space version. Computational performance on various large-scale test problems are reported; advantages of our approach are demonstrated. Our experience indicates our proposed method represents an efficient way to solve large-scalebound-constrained minimization problems

An Introduction to the Integrated Community-Engaged Learning and Ethical Reflection Framework (I-CELER)

Cultivating ethical Science, Technology, Engineering, and Mathematics researchers and practitioners requires movement beyond reducing ethical instruction to the rational exploration of moral quandaries via case studies and into the complexity of the ethical issues that students will encounter within their careers. We designed the Integrated Community-Engaged Learning and Ethical Reflection (I-CELER) framework as a means to promote the ethical becoming of future STEM practitioners. This paper provides a synthesis of and rationale for I-CELER for promoting ethical becoming based on scholarly literature from various social science fields, including social anthropology, moral development, and psychology. This paper proceeds in five parts. First, we introduce the state of the art of engineering ethics instruction; argue for the need of a lens that we describe as ethical becoming; and then detail the Specific Aims of the I-CELER approach. Second, we outline the three interrelated components of the project intervention. Third, we detail our convergent mixed methods research design, including its qualitative and quantitative counterparts. Fourth, we provide a brief description of what a course modified to the I-CELER approach might look like. Finally, we close by detailing the potential impact of this study in light of existing ethics education research within STEM

Goserelin, as an ovarian protector during (neo)adjuvant breast cancer chemotherapy, prevents long term altered bone turnover

Background: The Ovarian Protection Trial In Premenopausal Breast Cancer Patients “OPTION” trial (NCT00427245) was a prospective, multicenter, randomised, open label study evaluating the frequency of primary ovarian insufficiency (POI) at 12 months in women randomised to 6–8 cycles of (neo)adjuvant chemotherapy (CT) þ/ goserelin (G). Here we report the results of a secondary endpoint analysis of the effects of CTþ/-G on markers of bone turnover. Methods: Serum for bone alkaline phosphatase (BALP) and urine for N-terminal telopeptide (NTX) were collected at baseline, 6, 12, 18, 24 and 36 months. Changes in median levels of bone turnover markers were evaluated for the overall population, according to age stratification at randomisation (r40 vs 440 years) and with exploratory analysis according to POI rates at 12 months. Results: In the overall population, there was a significant increase in NTX at 6 months compared to baseline in patients treated with CTþG (40.81 vs 57.82 p¼0.0074) with normalisation of levels thereafter. BALP was significantly increased compared to baseline at 6 months and 12 months in those receiving CTþG, but normalised thereafter. BALP remained significantly higher compared to baseline at 12, 24 and 36 months in patients receiving CT, resulting in a significant difference between treatment groups at 36 months (CTþG 5.845 vs CT 8.5 p¼0.0006). These changes were predominantly seen in women 440 years. Women with POI at 12 months showed altered bone formation compared to baseline levels for a longer duration than women who maintained menses. Conclusion: Addition of G to CT increases bone turnover during treatment with normalisation after cessation of treatment suggesting G may offer sufficient ovarian protection against CT induced POI to negate longstanding altered bone turnover associated with POI

The efficient application of automatic differentiation for computing gradients in financial applications

Automatic differentiation (AD) is a practical field of computational mathematics that is of growing interest across many industries, including finance. The use of reverse mode AD is particularly interesting, since it allows for the computation of gradients in the same time required to evaluate the objective function itself. However, it requires excessive memory. This memory requirement can make reverse-mode AD infeasible in some cases (depending on the function complexity and available RAM) and slower than expected in others, due to the use of secondary memory and non-localized memory references. However, it turns out that many complex (expensive) functions in finance exhibit a natural substitution structure. In this paper, we illustrate this structure in computational finance as it arises in calibration and inverse problems, and determine Greeks in a Monte Carlo setting. In these cases, the required memory is a small fraction of that required by reverse-mode AD, but the computing time complexity is the same. In fact, our results indicate a significant realized speedup compared with straight reverse-mode AD

Critical Behavior of the Meissner Transition in the Lattice London Superconductor

We carry out Monte Carlo simulations of the three dimensional (3D) lattice London superconductor in zero applied magnetic field, making a detailed finite size scaling analysis of the Meissner transition. We find that the magnetic penetration length \lambda, and the correlation length \xi, scale as \lambda ~ \xi ~ |t|^{-\nu}, with \nu = 0.66 \pm 0.03, consistent with ordinary 3D XY universality, \nu_XY ~ 2/3. Our results confirm the anomalous scaling dimension of magnetic field correlations at T_c.Comment: 4 pages, 5 ps figure

Sixteen years of Collaborative Learning through Active Sense-making in Physics (CLASP) at UC Davis

This paper describes our large reformed introductory physics course at UC Davis, which bioscience students have been taking since 1996. The central feature of this course is a focus on sense-making by the students during the five hours per week discussion/labs in which the students take part in activities emphasizing peer-peer discussions, argumentation, and presentations of ideas. The course differs in many fundamental ways from traditionally taught introductory physics courses. After discussing the unique features of CLASP and its implementation at UC Davis, various student outcome measures are presented showing increased performance by students who took the CLASP course compared to students who took a traditionally taught introductory physics course. Measures we use include upper-division GPAs, MCAT scores, FCI gains, and MPEX-II scores.Comment: Also submitted to American Journal of Physic