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Weighted inter-rater agreement measures for ordinal outcomes
No full texthttp://dx.doi.org/10.1017/S000497271200033
Stationary Markovian arrival processes: Results and open problems
No full textWe consider two classes of irreducible Markovian arrival processes specified by the matrices and : the Markov-modulated Poisson process (MMPP) and the Markov-switched Poisson process (MSPP). The former exhibits a diagonal matrix D while the latter exhibits a diagonal matrix C. For these two classes we consider the following four statements: (I) the counting process is overdispersed; (II) the hazard rate of the event-stationary interarrival time is nonincreasing; (III) the squared coefficient of variation of the event-stationary process is greater than or equal to one; (IV) there is a stochastic order showing that the time-stationary interarrival time dominates the event-stationary interarrival time. For general MSPPs and order two MMPPs, we show that (I)–(IV) hold. Then for general MMPPs, it is easy to establish (I), while (II) is shown to be false by a counter-example. For general simple point processes, (III) follows from (IV). For MMPPs, we conjecture that (IV) and thus (III) hold. We also carry out some numerical experiments that fail to disprove this conjecture. Importantly, modelling folklore has often treated MMPPs as “bursty”, and implicitly assumed that (III) holds. However, to the best of our knowledge, proving this is still an open problem.
doi: https://doi.org/10.1017/S144618112200001
On the probability of ventricular fibrillation due to electric shock
Get PDFWhen exposed to a specified electrical shock, theprobability that a randomly chosen individual will undergofatal ventricular fibrillation can be regarded as a functionof random variation in the human population along twodimensions. The first dimension is the individual's bodyimpedance characteristic: for this, we introduce a newtwo-parameter model that improves on the simplerone-parameter model used in previous work. The seconddimension is the individual's current tolerance: we codifysome curves used in previous practice. We also considermethods of solving the resulting shock circuit and show thatthe fixed-point iteration method can give incorrect results
Weak imposition of boundary conditions for the gauge formulation of the incompressible Navier–Stokes equations
Get PDFThe projection method was first introduced by Chorin [Bull. AMS 73 (1967), pp. 928–931] and Temam [Arch. Rat. Mech. Anal. 33 (1969), pp. 377–385] as a computationally efficient numerical method to solve the incompressible Navier–Stokes equations. Despite its success in decoupling the computations of velocity and pressure, it suffers from inaccurate numerical boundary layers. As an effort to resolve this inaccuracy, E and Liu [Int. J. Numer. Meth. Fluids 34 (2000), pp. 701–710] proposed the gauge method, which is a reformulation of the Navier–Stokes equations in terms of an auxiliary vector field and a gauge variable. This method utilizes the freedom of choosing a boundary condition for the gauge variable to reduce the numerical coupling between the considered variables. Nevertheless, the computational implementation of the boundary conditions for the auxiliary vector field is difficult in the context of finite elements since they involve either the normal or tangential derivative of the gauge variable. In order to circumvent this issue, we propose a weak formulation of the boundary conditions based on the symmetric Nitsche method. Computational results are presented to illustrate the accuracy of the proposed method.
References
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D. L. Brown, R. Cortez, and M. L. Minion. Accurate projection methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 168.2 (2001), pp. 464–499. doi: 10.1006/jcph.2001.6715
A. J. Chorin. The numerical solution of the Navier–Stokes equations for an incompressible fluid. Bull. Amer. Math. Soc. 73 (1967), pp. 928–931. doi: 10.1090/s0002-9904-1967-11853-6 on p. C100).
W. E and J.-G. Liu. Gauge finite element method for incompressible flows. Int. J. Numer. Meth. Fluids 34 (2000), pp. 701–710. doi: 10.1002/1097-0363(20001230)34:8<701::AID-FLD76>3.0.CO;2-B
W. E and J.-G. Liu. Projection method I: Convergence and numerical boundary layers. SIAM J. Numer. Anal. 32 (1995), pp. 1017–1057. doi: 10.1137/0732047
W. Ef and J.-G. Liu. Gauge method for viscous incompressible flows. Commun. Math. Sci. 1.2 (2003), pp. 317–332. doi: 10.4310/CMS.2003.v1.n2.a6
A. Ern and J.-L. Guermond. Theory and practice of finite elements. Vol. 159. Applied mathematical sciences. Springer, 2004. doi: 10.1007/978-1-4757-4355-5
P. Hansbo. Nitsche’s method for interface problems in computational mechanics. GAMM-Mitteilungen 28.2 (2005), pp. 183–206. doi: 10.1002/gamm.201490018
W. Layton, N. Mays, M. Neda, and C. Trenchea. Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier–Stokes equations. Math. Model. Numer. Anal. 48.3 (2014), pp. 765–793. doi: 10.1051/m2an/2013120
A. Logg, K.-A. Mardal, and G. Wells. Automated solution of differential equations by the finite element method: The FEniCS book. Vol. 84. Lecture notes in computational science and engineering. Springer, 2012. doi: 10.1007/978-3-642-23099-8
R. Mekhlouf, A. Baggag, and L. Remaki. Assessment of Nitsche’s method for Dirichlet boundary conditions treatment. J. Fluid Flow, Heat Mass Trans. 4.1 (2017), pp. 54–63. doi: 10.11159/jffhmt.2017.007
J. Nitsche. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Semin. Univ. Hambg. Vol. 36. Springer. 1971, pp. 9–15. doi: 10.1007/BF02995904
R. H. Nochetto and J.-H. Pyo. The gauge-Uzawa finite element method. Part I: The Navier–Stokes equations. SIAM J. Numer. Anal. 43.3 (2005), pp. 1043–1068. doi: 10.1137/040609756
J.-H. Pyo. Error estimates for the second order semi-discrete stabilized gauge-Uzawa method for the Navier–Stokes equations. Int. J. Numer. Anal. Mod. 10.1 (2013). url: https://www.global-sci.org/intro/article_detail/ijnam/557.html
L. Ridgway Scott. Introduction to automated modeling with FEniCS. Computational Modeling Initiative, 2018. url: https://www.cminit.company/publications
R. Temam. Sur l’approximation de la solution des équations de Navier–Stokes par la méthode des pas fractionnaires (II). Arch. Rat. Mech. Anal. 33.5 (1969), pp. 377–385. doi: 10.1007/BF00247696
C. Wang and J.-G. Liu. Convergence of gauge method for incompressible flow. Math. Comput. 69 (2000), pp. 1385–1407. doi: 10.1090/S0025-5718-00-01248-5
K. Wiratama. A comparison of projection and gauge methods for numerical incompressible fluid dynamics. Masters thesis. Australian National University, Oct. 2019
H. Zhang. Application of projection methods to the numerical solution of the incompressible Navier Stokes equations. Honours thesis. Australian National University, Oct. 201
Reconstruction of tubular structures from 2.5D point clouds: A mesophotic gorgonian coral case study
Get PDFA method for the surface reconstruction of 3D tubular branched structures characterized by low informative point clouds (i.e., 2.5D) is proposed. These specific clouds can arise when using photogrammetry techniques on complex subjects in challenging scanning environments (e.g., underwater gorgonian coral at mesophotic depths). The core idea behind the proposed Sphere Skeleton Approach (SSA) is to approximate the assumed tubular shapes via merged spheres having variable radii and centered in the points of the medial skeleton. To assess the generality and robustness of the proposed SSA, additional experiments have been conducted on 2.5D point clouds that were synthetically generated from 3D model benchmarks. Hausdorff distances between the target and the reconstructed 3D models are used to quantitatively compare the SSA performances to a classical meshing algorithm. Early results highlight the capability to outperform existing approaches in reconstructing objects from 2.5D clouds.
References
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M. Berger, A. Tagliasacchi, L. M. Seversky, P. Alliez, G. Guennebaud, J. A. Levine, A. Sharf, and C. T. Silva. A survey of surface reconstruction from point clouds. Comput. Graph. Forum. Vol. 36. 1. 2017, pp. 301–329. doi: 10.1111/cgf.12802
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J. F. Blinn. A generalization of algebraic surface drawing. ACM Trans. Graph. 1.3 (1982), pp. 235–256. doi: 10.1145/357306.357310
P. Cignoni, M. Callieri, M. Corsini, M. Dellepiane, F. Ganovelli, and G. Ranzuglia. Meshlab: an open-source mesh processing tool. Eurographics Italian Chapter Conference. Ed. by V. Scarano,
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H. Huang, S. Wu, D. Cohen-Or, M. Gong, H. Zhang, G. Li, and B. Chen. L1-medial skeleton of point cloud. ACM Trans. Graph. 32.4 (2013), pp. 1–8. doi: 10.1145/2461912.2461913
Y.-H. Jin and W.-H. Lee. Fast cylinder shape matching using random sample consensus in large scale point cloud. Appl. Sci. 9.5 (2019), p. 974. doi: 10.3390/app9050974
L. Liu, D. Ceylan, C. Lin, W. Wang, and N. J. Mitra. Image-based reconstruction of wire art. ACM Trans. Graph. 36.4 (2017), pp. 1–11. doi: 10.1145/3072959.3073682
B. B. Mandelbrot. The fractal geometry of nature. Vol. 1. W. H. Freeman New York, 1982. url: https://www.nhbs.com/the-fractal-geometry-of-nature-book
J. Mei, L. Zhang, S. Wu, Z. Wang, and L. Zhang. 3D tree modeling from incomplete point clouds via optimization and L1-MST. Int. J. Geo. Inf. Sci. 31.5 (2017), pp. 999–1021. doi: 10.1080/13658816.2016.1264075
S. J. Rowley, T. E. Roberts, R. R. Coleman, H. L. Spalding, E. Joseph, and M. K. L. Dorricott. Pohnpei, Federated States of Micronesia. Mesophotic Coral Ecosystems. Springer, 2019, pp. 301–320. doi: 10.1007/978-3-319-92735-0_17
K. Siddiqi, J. Zhang, D. Macrini, A. Shokoufandeh, S. Bouix, and S. Dickinson. Retrieving articulated 3-D models using medial surfaces. Machine Vis. Appl. 19.4 (2008), pp. 261–275. doi: 10.1007/s00138-007-0097-8
Sketchfab. 2021. url: https://sketchfab.com/
L. Wasserman. Topological data analysis. Ann. Rev. Stat. Appl. 5 (2018), pp. 501–532. doi: 10.1146/annurev-statistics-031017-10004
Cubes in finite fields and related permutations
No full texthttp://dx.doi.org/10.1017/S000497271200033
On transcendental continued fractions in fields of formal power series over finite fields
No full texthttp://dx.doi.org/10.1017/S000497271200033
Modelling diversity in abstract algebra textbooks
No full texthttp://dx.doi.org/10.1017/S000497271200033