Marijuana Legislation: Identifying the Impact on the Oral Healthcare Provider

Objectives/Aims: Since the mid-2000s, the United States has seen a surge in legislation involving the legalization of marijuana, both recreationally and medicinally. The relaxed laws translated into an increase of marijuana consumption and thereby a potential increase in the number of patients a provider will see that are cannabis users. The purpose of this review is to illustrate how the providers begin to see pathologies related to cannabis use more frequently, and how they will need to be prepared for ways this can be addressed. Additionally, oral healthcare providers will face ethical dilemmas and legal challenges when treating patients and their ability to give informed consent. Methods: Research reviewed in this paper was compiled from scholarly articles and peer-reviewed journals, including PubMed and CINAHL, published within the last five years. Studies were analyzed on the impact legalization and decriminalization laws have had on marijuana use. Additional research reviewed numerous pathologies related to marijuana use in the dental cavity. Results: Based on current proposals, it is expected that 40 states will legalize marijuana by the end of 2020. Studies conducted in states such as Oregon, Colorado and Alaska have shown an increase in marijuana usage since legalization has occurred. Research reviewed showed multiple conditions related to marijuana use. Periodontitis, xerostomia, oral cancer, and staining are several of the associated pathologies. Conclusion: Research suggests an anticipated increase of marijuana users in states that will soon pass legalization. Studies have also shown that there is a higher prevalence of pathologies of the oral cavity in cannabis users versus non cannabis users. The oral healthcare provider will treat more pathologies related to cannabis use and deal with the legal challenges presented to them surrounding informed consent.https://scholarscompass.vcu.edu/denh_student/1016/thumbnail.jp

New versions of iterative splitting methods for the momentum equation

[EN] In this paper we propose some modifications in the schemes for the iterative splitting techniques defined in Geiser (2009) for partial differential equations and introduce the parallel version of these modified algorithms. Theoretical results related to the order of the iterative splitting for these schemes are obtained. In the numerical experiments we compare the obtained results by applying iterative methods to approximate the solutions of the nonlinear systems obtained from the discretization of the splitting techniques to the mixed convection-diffusion Burgers' equation and a momentum equation that models a viscous flow. The differential equations in each splitting interval are solved by the back-Euler-Newton algorithm using sparse matrices. (C) 2016 Elsevier B.V. All rights reserved.This work has been supported by Ministerio de Economía y Competitividad de España MTM2014-52016-02-2-PGeiser, J.; Hueso Pagoaga, JL.; Martínez Molada, E. (2017). New versions of iterative splitting methods for the momentum equation. Journal of Computational and Applied Mathematics. 309:359-370. https://doi.org/10.1016/j.cam.2016.06.002S35937030

Using Burdens of Proof to Allocate the Risk of Error when Assessing Developmental Maturity of Youthful Offenders

Behavioral and neuroscientific research provides a relatively clear window into the timing of developmental maturity from adolescence to early adulthood. We know with considerable confidence that, on average, sixteen-year-olds are less developmentally mature than nineteen-year-olds, who are less developmentally mature than twenty-three-year-olds, who are less developmentally mature than twenty-six-year-olds. However, in the context of a given case, the question presented might be whether a particular seventeen-year-old defendant convicted of murder is “developmentally mature enough” that a sentence of life without parole can be constitutionally imposed on him or her. While developmental maturity can be accurately measured in group data, it cannot be assessed in individuals with confidence. This fact is an instance of a fundamental disconnect that occurs at the intersection of science and law between what scientists study and what courts ordinarily need to know. Scientists typically study phenomena at the group or population level, whereas courts usually need to determine whether a particular case is an instance of some known phenomenon. This is called the group to individual (G2i) problem. Although the G2i problem cannot be fully resolved, it can be managed by using the base-rate data available in the research literature to set the burden of proof. Setting the burden of proof is a classic mechanism for allocating the risks of making a mistake. Two factors in particular inform judgments about allocating risk of error, with the first being the likelihood or frequency of the fact in question and the second being the costs associated with the error. The rarer the fact and the larger the cost of a mistake, the greater the burden of proof should be. The latter factor, the costs associated with error, lies behind the traditional burdens of proof of preponderance of evidence and proof beyond a reasonable doubt in civil and criminal cases, respectively. In contrast, while the former factor, the frequency of the fact in question, is used regularly in areas of applied science, it has generally not informed allocations of burdens of proof in court. This Article sets forth a framework of shifting burdens of proof grounded in the research literature that can be employed to allocate the risk of error when assessing developmental maturity in the sentencing of offenders across the age spectrum

Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations

[EN] This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection-diffusion-reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive ideas. Based on shifting the time-steps with additional adaptive time-ranges, we could embedded the adaptive techniques into the splitting approach. The numerical analysis of the adapted iterative splitting schemes is considered and we develop the underlying error estimates for the application of the adaptive schemes. The performance of the method with respect to the accuracy and the acceleration is evaluated in different numerical experiments. We test the benefits of the adaptive splitting approach on highly nonlinear Burgers' and Maxwell-Stefan diffusion equations.This research was funded by German Academic Exchange Service grant number 91588469. We acknowledge support by the DFG Open Access Publication Funds of the Ruhr-Universität of Bochum, Germany and by Ministerio de Economía y Competitividad, Spain, under grant PGC2018-095896-B-C21-C22.Geiser, J.; Hueso, JL.; Martínez Molada, E. (2020). Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations. Mathematics. 8(3):1-22. https://doi.org/10.3390/math8030302S12283Auzinger, W., & Herfort, W. (2014). Local error structures and order conditions in terms of Lie elements for exponential splitting schemes. Opuscula Mathematica, 34(2), 243. doi:10.7494/opmath.2014.34.2.243Auzinger, W., Koch, O., & Quell, M. (2016). Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions. Numerical Algorithms, 75(1), 261-283. doi:10.1007/s11075-016-0206-8Descombes, S., & Massot, M. (2004). Operator splitting for nonlinear reaction-diffusion systems with an entropic structure : singular perturbation and order reduction. Numerische Mathematik, 97(4), 667-698. doi:10.1007/s00211-003-0496-3Descombes, S., Dumont, T., Louvet, V., & Massot, M. (2007). On the local and global errors of splitting approximations of reaction–diffusion equations with high spatial gradients. International Journal of Computer Mathematics, 84(6), 749-765. doi:10.1080/00207160701458716McLachlan, R. I., & Quispel, G. R. W. (2002). Splitting methods. Acta Numerica, 11, 341-434. doi:10.1017/s0962492902000053Trotter, H. F. (1959). On the product of semi-groups of operators. Proceedings of the American Mathematical Society, 10(4), 545-545. doi:10.1090/s0002-9939-1959-0108732-6Strang, G. (1968). On the Construction and Comparison of Difference Schemes. SIAM Journal on Numerical Analysis, 5(3), 506-517. doi:10.1137/0705041Jahnke, T., & Lubich, C. (2000). Bit Numerical Mathematics, 40(4), 735-744. doi:10.1023/a:1022396519656Nevanlinna, O. (1989). Remarks on Picard-Lindelöf iteration. BIT, 29(2), 328-346. doi:10.1007/bf01952687Farago, I., & Geiser, J. (2007). Iterative operator-splitting methods for linear problems. International Journal of Computational Science and Engineering, 3(4), 255. doi:10.1504/ijcse.2007.018264DESCOMBES, S., DUARTE, M., DUMONT, T., LOUVET, V., & MASSOT, M. (2011). ADAPTIVE TIME SPLITTING METHOD FOR MULTI-SCALE EVOLUTIONARY PARTIAL DIFFERENTIAL EQUATIONS. Confluentes Mathematici, 03(03), 413-443. doi:10.1142/s1793744211000412Geiser, J. (2008). Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations. Journal of Computational and Applied Mathematics, 217(1), 227-242. doi:10.1016/j.cam.2007.06.028Dimov, I., Farago, I., Havasi, A., & Zlatev, Z. (2008). Different splitting techniques with application to air pollution models. International Journal of Environment and Pollution, 32(2), 174. doi:10.1504/ijep.2008.017102Karlsen, K. H., Lie, K.-A., Natvig, J. ., Nordhaug, H. ., & Dahle, H. . (2001). Operator Splitting Methods for Systems of Convection–Diffusion Equations: Nonlinear Error Mechanisms and Correction Strategies. Journal of Computational Physics, 173(2), 636-663. doi:10.1006/jcph.2001.6901Geiser, J. (2010). Iterative operator-splitting methods for nonlinear differential equations and applications. Numerical Methods for Partial Differential Equations, 27(5), 1026-1054. doi:10.1002/num.20568Geiser, J., & Wu, Y. H. (2015). Iterative solvers for the Maxwell–Stefan diffusion equations: Methods and applications in plasma and particle transport. Cogent Mathematics, 2(1), 1092913. doi:10.1080/23311835.2015.1092913Geiser, J., Hueso, J. L., & Martínez, E. (2017). New versions of iterative splitting methods for the momentum equation. Journal of Computational and Applied Mathematics, 309, 359-370. doi:10.1016/j.cam.2016.06.002Boudin, L., Grec, B., & Salvarani, F. (2012). A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations. Discrete & Continuous Dynamical Systems - B, 17(5), 1427-1440. doi:10.3934/dcdsb.2012.17.1427Duncan, J. B., & Toor, H. L. (1962). An experimental study of three component gas diffusion. AIChE Journal, 8(1), 38-41. doi:10.1002/aic.69008011

Serial and Parallel Iterative Splitting Methods: Algorithms and Applications to Fractional Convection-Diffusion Equations

[EN] The benefits and properties of iterative splitting methods, which are based on serial versions, have been studied in recent years, this work, we extend the iterative splitting methods to novel classes of parallel versions to solve nonlinear fractional convection-diffusion equations. For such interesting partial differential examples with higher dimensional, fractional, and nonlinear terms, we could apply the parallel iterative splitting methods, which allow for accelerating the solver methods and reduce the computational time. Here, we could apply the benefits of the higher accuracy of the iterative splitting methods. We present a novel parallel iterative splitting method, which is based on the multi-splitting methods, The flexibilisation with multisplitting methods allows for decomposing large scale operator equations. In combination with iterative splitting methods, which use characteristics of waveform-relaxation (WR) methods, we could embed the relaxation behavior and deal better with the nonlinearities of the operators. We consider the convergence results of the parallel iterative splitting methods, reformulating the underlying methods with a summation of the individual convergence results of the WR methods. We discuss the numerical convergence of the serial and parallel iterative splitting methods with respect to the synchronous and asynchronous treatments. Furthermore, we present different numerical applications of fluid and phase field problems in order to validate the benefit of the parallel versions.This research was partially supported by Ministerio de Economia y Competitividad, Spain, under grant PGC2018-095896-B-C21-C22 and German Academic Exchange Service grant number 91588469.Geiser, J.; Martínez Molada, E.; Hueso, JL. (2020). Serial and Parallel Iterative Splitting Methods: Algorithms and Applications to Fractional Convection-Diffusion Equations. Mathematics. 8(11):1-42. https://doi.org/10.3390/math8111950S142811Farago, I., & Geiser, J. (2007). Iterative operator-splitting methods for linear problems. International Journal of Computational Science and Engineering, 3(4), 255. doi:10.1504/ijcse.2007.018264Frommer, A., & Szyld, D. B. (2000). On asynchronous iterations. Journal of Computational and Applied Mathematics, 123(1-2), 201-216. doi:10.1016/s0377-0427(00)00409-xO’Leary, D. P., & White, R. E. (1985). Multi-Splittings of Matrices and Parallel Solution of Linear Systems. SIAM Journal on Algebraic Discrete Methods, 6(4), 630-640. doi:10.1137/0606062White, R. E. (1986). Parallel Algorithms for Nonlinear Problems. SIAM Journal on Algebraic Discrete Methods, 7(1), 137-149. doi:10.1137/0607017Geiser, J. (2016). Picard’s iterative method for nonlinear multicomponent transport equations. 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(1998). Physical and geometrical interpretation of fractional operators. Journal of the Franklin Institute, 335(6), 1077-1086. doi:10.1016/s0016-0032(97)00048-3El-Nabulsi, R. A. (2009). Fractional Dirac operators and deformed field theory on Clifford algebra. Chaos, Solitons & Fractals, 42(5), 2614-2622. doi:10.1016/j.chaos.2009.04.002Kanney, J. F., Miller, C. T., & Kelley, C. T. (2003). Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems. Advances in Water Resources, 26(3), 247-261. doi:10.1016/s0309-1708(02)00162-8Geiser, J., Hueso, J. L., & Martínez, E. (2020). Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations. Mathematics, 8(3), 302. doi:10.3390/math8030302Meerschaert, M. M., Scheffler, H.-P., & Tadjeran, C. (2006). Finite difference methods for two-dimensional fractional dispersion equation. 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Performance of a diagnostic algorithm for fibrotic hypersensitivity pneumonitis. A case-control study.

The differential diagnosis fibrotic hypersensitivity pneumonitis (HP) versus idiopathic pulmonary fibrosis (IPF) is important but challenging. Recent diagnostic guidelines for HP emphasize including multidisciplinary discussion (MDD) in the diagnostic process, however MDD is not comprehensively available. We aimed to establish the diagnostic accuracy and prognostic validity of a previously proposed HP diagnostic algorithm that foregoes MDD. We tested the algorithm in patients with an MDD diagnosis of fibrotic HP or IPF (case control study) and determined diagnostic test performances for diagnostic confidences of ≥ 90% and ≥ 70%. Prognostic validity was established using Cox proportional hazards models. Thirty-one patients with fibrotic HP and 50 IPF patients were included. The algorithm-derived ≥ 90% confidence level for HP had high specificity (0.94, 95% confidence interval [CI] 0.83-0.99), but low sensitivity (0.35 [95%CI 0.19-0.55], J-index 0.29). Test performance was improved for the ≥ 70% confidence level (J-index 0.64) with a specificity of 0.90 (95%CI 0.78-0.97), and a sensitivity of 0.74 (95%CI 0.55-0.88). MDD fibrotic HP diagnosis was strongly associated with lower risk of death (adjusted hazard ratio [HR] 0.10 [0.01-0.92], p = 0.04), whereas the algorithm-derived ≥ 70% and ≥ 90% confidence diagnoses were not significantly associated with survival (adjusted HR 0.37 [0.07-1.80], p = 0.22, and adjusted HR 0.41 [0.05-3.25], p = 0.39, respectively). The algorithm-derived ≥ 70% diagnostic confidence had satisfactory test performance for MDD-HP diagnosis, with insufficient sensitivity for ≥ 90% confidence. The lowest risk of death in the MDD-derived HP diagnosis validates the reference standard and suggests that a diagnostic algorithm not including MDD, might not replace the latter