Circumcentered reflections method for wavelet feasibility problems

We introduce a two-stage global-then-local search method for solving feasibility problems. The approach pairs the advantageous global tendency of the Douglas–Rachford method to find a basin of attraction for a fixed point, together with the local tendency of the circumcentered reflections method to perform faster within such a basin. We experimentally demonstrate the success of the method for solving nonconvex problems in the context of wavelet construction formulated as a feasibility problem. References F. J. Aragón Artacho, R. Campoy, and M. K. Tam. The Douglas–Rachford algorithm for convex and nonconvex feasibility problems. Math. Meth. Oper. Res. 91 (2020), pp. 201–240. doi: 10.1007/s00186-019-00691-9 R. Behling, J. Y. Bello Cruz, and L.-R. Santos. Circumcentering the Douglas–Rachford method. Numer. Algor. 78.3 (2018), pp. 759–776. doi: 10.1007/s11075-017-0399-5 R. Behling, J. Y. Bello-Cruz, and L.-R. Santos. On the linear convergence of the circumcentered-reflection method. Oper. Res. Lett. 46.2 (2018), pp. 159–162. issn: 0167-6377. doi: 10.1016/j.orl.2017.11.018 J. M. Borwein, S. B. Lindstrom, B. Sims, A. Schneider, and M. P. Skerritt. Dynamics of the Douglas–Rachford method for ellipses and p-spheres. Set-Val. Var. Anal. 26 (2018), pp. 385–403. doi: 10.1007/s11228-017-0457-0 J. M. Borwein and B. Sims. The Douglas–Rachford algorithm in the absence of convexity. Fixed-point algorithms for inverse problems in science and engineering. Springer, 2011, pp. 93–109. doi: 10.1007/978-1-4419-9569-8_6 I. Daubechies. Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41.7 (1988), pp. 909–996. doi: 10.1002/cpa.3160410705 N. D. Dizon, J. A. Hogan, and J. D. Lakey. Optimization in the construction of nearly cardinal and nearly symmetric wavelets. In: 13th International conference on Sampling Theory and Applications (SampTA). 2019, pp. 1–4. doi: 10.1109/SampTA45681.2019.9030889 N. D. Dizon, J. A. Hogan, and S. B. Lindstrom. Circumcentering reflection methods for nonconvex feasibility problems. arXiv preprint arXiv:1910.04384 (2019). url: https://arxiv.org/abs/1910.04384 D. J. Franklin. Projection algorithms for non-separable wavelets and Clifford Fourier analysis. PhD thesis. University of Newcastle, 2018. doi: 1959.13/1395028. D. J. Franklin, J. A. Hogan, and M. K. Tam. A Douglas–Rachford construction of non-separable continuous compactly supported multidimensional wavelets. arXiv preprint arXiv:2006.03302 (2020). url: https://arxiv.org/abs/2006.03302 D. J. Franklin, J. A. Hogan, and M. K. Tam. Higher-dimensional wavelets and the Douglas–Rachford algorithm. 13th International conference on Sampling Theory and Applications (SampTA). 2019, pp. 1–4. doi: 10.1109/SampTA45681.2019.9030823 B. P. Lamichhane, S. B. Lindstrom, and B. Sims. Application of projection algorithms to differential equations: Boundary value problems. ANZIAM J. 61.1 (2019), pp. 23–46. doi: 10.1017/S1446181118000391 S. B. Lindstrom and B. Sims. Survey: Sixty years of Douglas–Rachford. J. Aust. Math. Soc. 110 (2020), 1–38. doi: 10.1017/S1446788719000570 S. B. Lindstrom, B. Sims, and M. P. Skerritt. Computing intersections of implicitly specified plane curves. J. Nonlin. Convex Anal. 18.3 (2017), pp. 347–359. url: http://www.yokohamapublishers.jp/online2/jncav18-3 S. G. Mallat. Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans. Amer. Math. Soc. 315.1 (1989), pp. 69–87. doi: 10.1090/S0002-9947-1989-1008470-5 Y. Meyer. Wavelets and operators. Cambridge University Press, 1993. doi: 10.1017/CBO9780511623820 G. Pierra. Decomposition through formalization in a product space. Math. Program. 28 (1984), pp. 96–115. doi: 10.1007/BF02612715

Facing sampling techniques as an optimal design problem

Summary The aim of this paper is to investigate and discuss the common points shared, in their line of development, by both Sampling Theory and Design of Experiments. In fact, Sampling Theory adopts the main optimality criterion of the Optimal Design of Experiments, the minimization of variance, i.e. D-optimality. There is also an approach based on c-optimality, as far as ratio estimates are concerned, in Design of Experiments, and the A-optimality involved in a proposed Sampling technique. It is pointed out that the L2 norm is mainly applied as a distance measure.

Use of Discrete Element Modelling to Evaluate the Parameters of the Sampling Theory in the Feed Grade Sampler of a Sulphide Gold Plant

Cross-stream cutters are widely used in the mining and resources industry to obtain representative samples of particulate flows. Discrete element modelling (DEM) and analysis can be used to investigate influences of operational parameters, sampler design and material physical properties in the generation of the Increment Extraction Error (IEE), which when present, results in a frequently biased, non-representative sample. The study investigates the practicality of the rules and recommendations proposed by Dr. Pierre Gy that were developed and established as principles for the correct extraction of samples in industrial sampling equipment. Results validate Pierre Gy’s sampling theory using DEM in a cross-stream cutter of a sulphide gold plant. Importantly, the outcomes indicate that careful consideration must be given to physical ore properties and, consequently, that sampling systems should be developed specifically to each application.

An evidence-based data science perspective on the prediction of heart failure readmissions

The prevention of unplanned 30-day readmissions of patients discharged with a diagnosis of heart failure (HF) remains a profound challenge among hospital enterprises. Despite the many models and indices developed to predict which HF patients will readmit for any unplanned cause within 30 days, predictive success has been meager. Using simulations of HF readmission models and the diagnostics most often used to evaluate them (C-statistics, ROC curves), we demonstrate common factors that have contributed to the lack of predictive success among studies. We reveal a greater need for precision and alternative metrics such as partial C-statistics and precision-recall curves and demonstrate via simulations how those tools can be used to better gauge predictive success. We suggest how studies can improve their applicability to hospitals and call for a greater understanding of the uncertainty underlying 30-day all-cause HF readmission. Finally, using insights from sampling theory, we suggest a novel uncertainty-based perspective for predicting readmissions and non-readmissions.

No Evidence of Loss Aversion Disappearance and Reversal in Walasek and Stewart (2015)

Loss aversion—the idea that losses loom larger than equivalent gains—is one of the most important ideas in Behavioral Economics. In an influential article published in the Journal of Experimental Psychology: General, Walasek and Stewart (2015) test an implication of decision by sampling theory: Loss aversion can disappear, and even reverse, depending on the distribution of gains and losses people have encountered. In this manuscript, we show that the pattern of results reported in Walasek and Stewart (2015) should not be taken as evidence that loss aversion can disappear and reverse, or that decision by sampling is the origin of loss aversion. It emerges because the estimates of loss aversion are computed on different lotteries in different conditions. In other words, the experimental paradigm violates measurement invariance, and is thus invalid. We show that analyzing only the subset of lotteries that are common across conditions eliminates the pattern of results. We note that other recently published articles use similar experimental designs, and we discuss general implications for empirical examinations of utility functions.