QCDgrid: A Grid Resource for Quantum Chromodynamics

Quantum Chromodynamics (QCD) is an application area that requires access to large supercomputing resources and generates large amounts of raw data. The UK's national lattice QCD collaboration UKQCD currently stores and requires access to around five Tbytes of data, a figure that is growing dramatically as the collaboration's purpose built supercomputing system, QCDOC [P.A. Boyle, D. Chen, N.H. Christ, M. Clark, S.D. Cohen, C. Cristian, Z. Dong, A. Gara, B. Joo, C. Jung, C. Kim, L. Levkova, X. Liao, G. Liu, R.D. Mawhinney, S. Ohta, K. Petrov, T. Wettig and A. Yamaguchi, “Hardware and software status of QCDOC, arXiv: hep-lat/0309096”, Nuclear Physics. B, Proceedings Supplement, Vol. 838, pp. 129–130, 2004. See: http://www.ph.ed.ac.uk/ukqcd/community/qcdoc/; P.A. Boyle, D. Chen, N.H. Christ, M.A. Clark, S.D. Cohen, C. Cristian, Z. Dong, A. Gara, B. Joo, C. Jung, C. Kim, L.A. Levkova, X. Liao, R.D. Mawhinney, S. Ohta, K. Petrov, T. Wettig and A. Yamaguchi, “Overview of the QCDSP and QCDOC computers”, IBM Journal of Research and Development, Vol. 49, No. 2/3, p. 351, 2005] came into full production service towards the end of 2004. This data is stored on QCDgrid, a data Grid currently composed of seven storage elements at five separate UK sites.     

Weaker convergence for Newton's method under Hölder differentiability

We use more precise majorizing sequences than in earlier studies such as [J. Appell, E. De Pascale, J.V. Lysenko, and P.P. Zabrejko, New results on Newton–Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18 (1997), pp. 1–17; I.K. Argyros, Concerning the ‘terra incognita’ between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005), pp. 179–194; F. Cianciaruso, A further journey in the ‘terra incognita’ of the Newton–Kantorovich method, Nonlinear Funct. Anal. Appl. 15 (2010), pp. 173–183; F. Cianciaruso and E. De Pascale, Newton–Kantorovich approximations when the derivative is Hölderian: Old and new results, Numer. Funct. Anal. Optim. 24 (2003), pp. 713–723; F. Cianciaruso, E. De Pascale, and P.P. Zabrejko, Some remarks on the Newton–Kantorovich approximations, Atti Sem. Mat. Fis. Univ. Modena 48 (2000), pp. 207–215; E. De Pascale and P.P. Zabrejko, Convergence of the Newton–Kantorovich method under Vertgeim conditions: A new improvement, Z. Anal. Anwendvugen 17 (1998), pp. 271–280; J.A. Ezquerro and M.A. Hernández, On the R-order of convergence of Newton's method under mild differentiability conditions, J. Comput. Appl. Math. 197 (2006), pp. 53–61; J.V. Lysenko, Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations (in Russian), Dokl. Akad. Nauk BSSR 38 (1994), pp. 20–24; P.D. Proinov, New general convergence theory for iterative processes and its applications to Newton–Kantorovich type theorems, J. Complexity 26 (2010), pp. 3–42; J. Rokne, Newton's method under mild differentiability conditions with error analysis, Numer. Math. 18 (1971/72), pp. 401–412; B.A. Vertgeim, On conditions for the applicability of Newton's method, (in Russian), Dokl. Akad. N., SSSR 110 (1956), pp. 719–722; B.A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957), pp. 166–169 (in Russian); English transl.: Amer. Math. Soc. Transl. 16 (1960), pp. 378–382; P.P. Zabrejko and D.F. Nguen, The majorant method in the theory of Newton–Kantorovich approximations and the Pták error estimates, Numer. Funct. Anal. Optim. 9 (1987), pp. 671–684; A.I. Zinc?enko, Some approximate methods of solving equations with non-differentiable operators (Ukrainian), Dopovidi Akad. Nauk Ukraïn. RSR (1963), pp. 156–161] to provide a semilocal convergence analysis for Newton's method under Hölder differentiability conditions. Our sufficient convergence conditions are also weaker even in the Lipschitz differentiability case. Moreover, the results are obtained under the same or less computational cost. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.     

Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

In this work, we combine (i) NURBS-based isogeometric analysis, (ii) residual-driven turbulence modeling and iii) weak imposition of no-slip and no-penetration Dirichlet boundary conditions on unstretched meshes to compute wall-bounded turbulent flows. While the first two ingredients were shown to be successful for turbulence computations at medium-to-high Reynolds number [I. Akkerman, Y. Bazilevs, V. M. Calo, T. J. R. Hughes, S. Hulshoff, The role of continuity in residual-based variational multiscale modeling of turbulence, Comput. Mech. 41 (2008) 371–378; Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, G. Scovazzi, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197 (2007) 173–201], it is the weak imposition of no-slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher Reynolds number [Y. Bazilevs, T.J.R. Hughes. Weak imposition of Dirichlet boundary conditions in fluid mechanics, Comput. Fluids 36 (2007) 12–26; Y. Bazilevs, C. Michler, V.M. Calo, T.J.R. Hughes, Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4853–4862]. These three ingredients form a basis of a possible practical strategy for computing engineering flows, somewhere between RANS and LES in complexity. We demonstrate this by solving two challenging incompressible turbulent benchmark problems: channel flow at friction-velocity Reynolds number 2003 and flow in a planar asymmetric diffuser. We observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data. This lends some credence to the proposed approach, which we believe may become a viable engineering tool.     

A DAFT DL_POLY distributed memory adaptation of the Smoothed Particle Mesh Ewald method

The Smoothed Particle Mesh Ewald method [U. Essmann, L. Perera, M.L. Berkowtz, T. Darden, H. Lee, L.G. Pedersen, J. Chem. Phys. 103 (1995) 8577] for calculating long ranged forces in molecular simulation has been adapted for the parallel molecular dynamics code DL_POLY_3 [I.T. Todorov, W. Smith, Philos. Trans. Roy. Soc. London 362 (2004) 1835], making use of a novel 3D Fast Fourier Transform (DAFT) [I.J. Bush, The Daresbury Advanced Fourier transform, Daresbury Laboratory, 1999] that perfectly matches the Domain Decomposition (DD) parallelisation strategy [W. Smith, Comput. Phys. Comm. 62 (1991) 229; M.R.S. Pinches, D. Tildesley, W. Smith, Mol. Sim. 6 (1991) 51; D. Rapaport, Comput. Phys. Comm. 62 (1991) 217] of the DL_POLY_3 code. In this article we describe software adaptations undertaken to import this functionality and provide a review of its performance.     

Comparison of computational approaches for predicting the effects of missense mutations on p53 function

We applied our recently developed kinetic computational mutagenesis (KCM) approach [L.T. Chong, W.C. Swope, J.W. Pitera, V.S. Pande, Kinetic computational alanine scanning: application to p53 oligomerization, J. Mol. Biol. 357 (3) (2006) 1039–1049] along with the MM-GBSA approach [J. Srinivasan, T.E. Cheatham 3rd, P. Cieplak, P.A. Kollman, D.A. Case, Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate-DNA helices, J. Am. Chem. Soc. 120 (37) (1998) 9401–9409; P.A. Kollman, I. Massova, C.M. Reyes, B. Kuhn, S. Huo, L.T. Chong, M. Lee, T. Lee, Y. Duan, W. Wang, O. Donini, P. Cieplak, J. Srinivasan, D.A. Case, T.E. Cheatham 3rd., Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models, Acc. Chem. Res. 33 (12) (2000) 889–897] to evaluate the effects of all possible missense mutations on dimerization of the oligomerization domain (residues 326–355) of tumor suppressor p53. The true positive and true negative rates for KCM are comparable (within 5%) to those of MM-GBSA, although MM-GBSA is much less computationally intensive when it is applied to a single energy-minimized configuration per mutant dimer. The potential advantage of KCM is that it can be used to directly examine the kinetic effects of mutations.     

Book reviews

CALCULUS AND THE COMPUTER (An Approach to problem solving) by T. V. Fossum and R. W. Gatterdam, 1980, pub. by Scott, Forrseman & Co., Glenview, Illinois, 217pp+Index. $6.95 (only U.S. Price available).

KNOWLEDGE BASED PROGRAM CONSTRUCTION, by David R. Barstow, The Computer Science Library, Programming Languages Series No. 6. North-Holland, 1979. $10.

NUMERICAL ANALYSIS OF SEMICONDUCTOR DEVICES. Proceedings of the NASECODE 1 Conference held at Trinity College, Dublin, from 27th-29th June 1979, edited by B.T. Browne and J. J. H. Miller, pub. by Boole Press Ltd., P.O. Box No. 5, 51 Sandycove Road, Dunlaoghaire, Co. Dublin, Ireland, August 1979, XII + 303 pages, Cloth £20 (U.S. $42) ISBN 0-906783-003.     

New shape-based auroral oval segmentation driven by LLS-RHT

A new method that exploits shape to localize the auroral oval in satellite imagery is introduced. The core of the method is driven by the linear least-squares (LLS) randomized Hough transform (RHT). The LLS-RHT is a new fast variant of the RHT suitable when not all necessary conditions of the RHT can be satisfied. The method is also compared with the three existing methods for aurora localization, namely the histogram-based k-means [C.C. Hung, G. Germany, K-means and iterative selection algorithms in image segmentation, IEEE Southeastcon 2003 (Session 1: Software Development)], adaptive thresholding [X. Li, R. Ramachandran, M. He, S. Movva, J.A. Rushing, S.J. Graves, W. Lyatsky, A. Tan, G.A. Germany, Comparing different thresholding algorithms for segmenting auroras, in: Proceedings of the International Conference on Information Technology: Coding and Computing, vol. 6, 2004, pp. 594-601], and pulse-coupled neural network-based [G.A. Germany, G.K. Parks, H. Ranganath, R. Elsen, P.G. Richards, W. Swift, J.F. Spann, M. Brittnacher, Analysis of auroral morphology: substorm precursor and onset on January 10, 1997, Geophys. Res. Lett. 25 (15) (1998) 3042-3046] methods. The methodologies and their performance on real image data are both considered in the comparison. These images include complications such as random noise, low contrast, and moderate levels of key obscuring phenomena.     

Response to the comments on "Fundamental limits of reconstruction-based superresolution algorithms under local translation"

Wang and Feng (IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 5, p 846, May 2006) pointed out that the deduction in (Z. Lin and H. Y. Shum, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, Jan. 2004) overlooked the validity of the perturbation theorem used in (Z. Lin and H. Y. Shum, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, Jan. 2004). In this paper, we show that, when the perturbation theorem is invalid, the probability of successful superresolution is very low. Therefore, we only have to derive the limits under the condition that validates the perturbation theorem, as done in (Z. Lin and H. Y. Shum, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, Jan. 2004).     

A counterexample of a theorem by Tsolas et al. and an independentresult by Zaborszky et al. [with reply]

Recent results on the composition of the stability boundary by N.A. Tsolas et al. (IEEE Trans. Circuits Syst., vol.CAS-32, no.10, pp.1041-9, Oct. 1985) and J. Zaborszky et al. (Proc. IFAC Symp. Power Syst. Power Plant. Contr., Beijing, China, Aug. 1986, pp.597-603) claimed that it consisted of the stable manifolds of index-one unstable equilibria and their closures. A counterexample shows the potential existence of additional structures within the boundary. This finding invalidates numerous theorems published in the literature. The author concedes that the counterexample to the theorem in the paper by N.A. Tsolas et al. is unassailable and identifies the error in his proof     

Comparison of computational approaches for predicting the effects of missense mutations on p53 function

We applied our recently developed kinetic computational mutagenesis (KCM) approach [L.T. Chong, W.C. Swope, J.W. Pitera, V.S. Pande, Kinetic computational alanine scanning: application to p53 oligomerization, J. Mol. Biol. 357 (3) (2006) 1039–1049] along with the MM-GBSA approach [J. Srinivasan, T.E. Cheatham 3rd, P. Cieplak, P.A. Kollman, D.A. Case, Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate-DNA helices, J. Am. Chem. Soc. 120 (37) (1998) 9401–9409; P.A. Kollman, I. Massova, C.M. Reyes, B. Kuhn, S. Huo, L.T. Chong, M. Lee, T. Lee, Y. Duan, W. Wang, O. Donini, P. Cieplak, J. Srinivasan, D.A. Case, T.E. Cheatham 3rd., Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models, Acc. Chem. Res. 33 (12) (2000) 889–897] to evaluate the effects of all possible missense mutations on dimerization of the oligomerization domain (residues 326–355) of tumor suppressor p53. The true positive and true negative rates for KCM are comparable (within 5%) to those of MM-GBSA, although MM-GBSA is much less computationally intensive when it is applied to a single energy-minimized configuration per mutant dimer. The potential advantage of KCM is that it can be used to directly examine the kinetic effects of mutations.     

On the estimation of the general parameter

In this paper, we first discuss the origin, developments and various thoughts by several researchers on the generalized linear regression estimator (GREG) due to Deville and Särndal [Deville, J.C., Särndal, C.E., 1992. Calibration estimators in survey sampling. J. Amer. Statist. Assoc. 87, 376-382]. Then, the problem of estimation of the general parameter of interest considered by Rao [Rao, J.N.K., 1994. Estimating totals and distribution functions using auxiliary information at the estimation stage. J. Official Statist. 10 (2), 153-165], and Singh [Singh, S., 2001. Generalized calibration approach for estimating the variance in survey sampling. Ann. Inst. Statist. Math. 53 (2), 404-417; Singh, S., 2004. Golden and Silver Jubilee Year-2003 of the linear regression estimators. In: Proceedings of the Joint Statistical Meeting, Toronto (Available on the CD), 4382-4380; Singh, S., 2006. Survey statisticians celebrate Golden Jubilee Year-2003 of the linear regression estimator. Metrika 1-18] is further investigated. In addition to that it is shown that the Farrell and Singh [Farrell, P.J., Singh, S., 2005. Model-assisted higher order calibration of estimators of variance. Australian & New Zealand J. Statist. 47 (3), 375-383] estimators are also a special case of the proposed methodology. Interestingly, it has been noted that the single model assisted calibration constraint studied by Farrell and Singh [Farrell, P.J., Singh, S., 2002. Re-calibration of higher order calibration weights. Presented at Statistical Society of Canada conference, Hamilton (Available on CD); Farrell, P.J., Singh, S., 2005. Model-assisted higher order calibration of estimators of variance. Australian & New Zealand J. Statist. 47 (3), 375-383] and Wu [Wu, C., 2003. Optimal calibration estimators in survey sampling. Biometrika 90, 937-951] is not helpful for calibrating the Sen [Sen, A.R., 1953. On the estimate of the variance in sampling with varying probabilities. J. Indian Soc. Agril. Statist. 5, 119-127] and Yates and Grundy [Yates, F., Grundy, P.M., 1953. Selection without replacement from within strata with probability proportional to size. J. Roy. Statist. Soc. Ser. 15, 253-261] estimator of the variance of the linear regression estimator under the optimal designs of Godambe and Joshi [Godambe, V.P., Joshi, V.M., 1965. Admissibility and Bayes estimation in sampling finite populations—I. Ann. Math. Statist. 36, 1707-1722]. Three new estimators of the variance of the proposed linear regression type estimator of the general parameters of interest are introduced and compared with each other. The newly proposed two-dimensional linear regression models are found to be useful, unlike a simulation based on a couple of thousands of random samples, in comparing the estimators of variance. The use of knowledge of the model parameters in assisting the estimators of variance has been found to be beneficial. The most attractive feature is that it has been shown theoretically that the proposed method of calibration always remains more efficient than the GREG estimator.     

Book Reviews

Book reviewed in this article:
Title : Cognition and Computers-Studies in Learning Authors : R. W. Lawler, J. B. H. du Boulay, M. Hughes and H. MacLeod
Title : Never mind the technology think of the information Authors : Godfrey Wace
Title : Computer Appreciation Author : Bob Dingle
Title : Programming in microProlog made simple Authors : P. H. Hepburn
Title : Children, Computers and the Curriculum Authors : J. J. Wellington
Title : Computers and Modern Language Studies Authors : K. C. Cameron, W. S. Dodd & S. P. Q. Rahtz     

An extension of Harrington''''s noncupping theorem

(i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a < b such that for any c.e. w, w x implies a ∪ w b ∪ x.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping relative to x for each c.e. degree x.By a tree method, we prove that every high c.e. degree has e.a.c. property by extending Harrington's anti-cupping theorem.     

Taylor polynomial solution of hyperbolic type partial differential equations with constant coefficients

The purpose of this study is to give a Taylor polynomial approximation for the solution of hyperbolic type partial differential equations with constant coefficients. The technique used is an improved Taylor matrix method, which has been given for solving ordinary differential, integral and integro-differential equations [M. Gülsu and M. Sezer, A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. Math. 82(5) (2005), pp. 629–642; M. Gülsu and M. Sezer, On the solution of the Riccati equation by the Taylor matrix method, Appl. Math. Comput. 188 (2007), pp. 446–449; A. Karamete and M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79(9) (2002), pp. 987–1000; N. Kurt and M. Çevik, Polynomial solution of the single degree of freedom system by Taylor matrix method, Mech. Res. Commun. 35 (2008), pp. 530–536; N. Kurt and M. Sezer, Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients, J. Franklin Inst. 345 (2008), pp. 839–850; ?. Nas, S. Yalçinba?, and M. Sezer, A method for approximate solution of the high-order linear Fredholm integro-differential equations, Int. J. Math. Edu. Sci. Technol. 27(6) (1996), pp. 821–834; M. Sezer, Taylor polynomial solution of Volterra integral equations, Int. J. Math. Edu. Sci. Technol. 25(5) (1994), pp. 625–633; M. Sezer, A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. Edu. Sci. Technol. 27(6) (1996), pp. 821–834; M. Sezer, M. Gülsu, and B. Tanay, A matrix method for solving high-order linear difference equations with mixed argument using hybrid Legendre and Taylor polynomials, J. Franklin Inst. 343 (2006), pp. 647–659; S. Yalçinba?, Taylor polynomial solutions of nonlinear Volterra–Fredholm integral equation, Appl. Math. Comput. 127 (2002), pp. 196–206; S. Yalçinba? and M. Sezer, The approximate solution of high-order linear Volterra–Fredholm integro-differential equations in terms of Taylor polynomials, Appl. Math. Comput. 112 (2000), pp. 291–308]. Some numerical examples, which consist of initial and boundary conditions, are given to illustrate the reliability and efficiency of the method. Also, the results obtained are compared by the known results; the error analysis is performed and the accuracy of the solution is shown.     

The discoveries of continuations

We give a brief account of the discoveries of continuations and related concepts by A. van Wijngaarden, A. W. Mazurkiewicz, F. L. Morris, C. P. Wadsworth, J. H. Morris, M. J. Fischer, and S. K. Abdali.     

Book Reviews

F.R.A.Hopgood, D.A.Duce, J.R.Gallop, D.'Csutcliffe Introduction to the Graphical Kernel System (GKS)
G.Enderle, K.Kansy, G.Pfaff Computer Graphics Programming.
Reviewer: Ken Brodlie Department of Computer Studies University of Leeds     

Fuzzy set-valued Gaussian processes and Brownian motions

Gaussian processes and Brownian motion are concepts and tools in modelling important uncertain systems in many areas. In view of uncertainty complexity in many real-world problems, we extend these tools to the case where stochastic processes can take on fuzzy sets as values. In this paper, we discuss fuzzy set-valued Gaussian processes based on the results of [S. Li, Y. Ogura, V. Kreinovich, Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables, Kluwer Academic Publishers, Dordrecht, 2002; S. Li, Y. Ogura, H.T. Nguyen, Gaussian processes and martingales for fuzzy valued variables with continuous parameter, Inform. Sci. 133 (2001) 7–21; S. Li, Y. Ogura, F.N. Proske, M.L. Puri, Central limit theorems for generalized set-valued random variables, J. Math. Anal. Appl. 285 (2003) 250–263; N.N. Lyashenko, On limit theorems for sums of independent compact random subsets in the Euclidean space, J. Soviet Math. 20 (1982) 2187–2196] and [M.L. Puri, D.A. Ralescu, The concept of normality for fuzzy random variables, Ann. Probab. 13 (1985) 1373–1379]. We also introduce the concept of fuzzy set-valued Brownian motion, and then prove several properties of such processes.     

Monte Carlo methods for computing the capacitance of the unit cube

It is well known that there is no analytic expression for the electrical capacitance of the unit cube. However, there are several Monte Carlo methods that have been used to numerically estimate this capacitance to high accuracy. These include a Brownian dynamics algorithm [H.-X. Zhou, A. Szabo, J.F. Douglas, J.B. Hubbard, A Brownian dynamics algorithm for calculating the hydrodynamic friction and the electrostatic capacitance of an arbitrarily shaped object, J. Chem. Phys. 100 (5) (1994) 3821–3826] coupled to the “walk on spheres” (WOS) method [M.E. Müller, Some continuous Monte Carlo methods for the Dirichlet problem, Ann. Math. Stat. 27 (1956) 569–589]; the Green’s function first-passage (GFFP) algorithm [J.A. Given, J.B. Hubbard, J.F. Douglas, A first-passage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules, J. Chem. Phys. 106 (9) (1997) 3721–3771]; an error-controlling Brownian dynamics algorithm [C.-O. Hwang, M. Mascagni, Capacitance of the unit cube, J. Korean Phys. Soc. 42 (2003) L1–L4]; an extrapolation technique coupled to the WOS method [C.-O. Hwang, Extrapolation technique in the “walk on spheres” method for the capacitance of the unit cube, J. Korean Phys. Soc. 44 (2) (2004) 469–470]; the “walk on planes” (WOP) method [M.L. Mansfield, J.F. Douglas, E.J. Garboczi, Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects, Phys. Rev. E 64 (6) (2001) 061401:1–061401:16; C.-O. Hwang, M. Mascagni, Electrical capacitance of the unit cube, J. Appl. Phys. 95 (7) (2004) 3798–3802]; and the random “walk on the boundary” (WOB) method [M. Mascagni, N.A. Simonov, The random walk on the boundary method for calculating capacitance, J. Comp. Phys. 195 (2004) 465–473]. Monte Carlo methods are convenient and efficient for problems whose solution includes singularities. In the calculation of the unit cube capacitance, there are edge and corner singularities in the charge density distribution. In this paper, we review the above Monte Carlo methods for computing the electrical capacitance of a cube and compare their effectiveness. We also provide a new result. We will focus our attention particularly on two Monte Carlo methods: WOP [M.L. Mansfield, J.F. Douglas, E.J. Garboczi, Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects, Phys. Rev. E 64 (6) (2001) 061401:1–061401:16; C.-O. Hwang, M. Mascagni, Electrical capacitance of the unit cube, J. Appl. Phys. 95 (7) (2004) 3798–3802; C.-O. Hwang, T. Won, Edge charge singularity of conductors, J. Korean Phys. Soc. 45 (2004) S551–S553] and the random WOB [M. Mascagni, N.A. Simonov, The random walk on the boundary method for calculating capacitance, J. Comp. Phys. 195 (2004) 465–473] methods.     

On the convergence of Newton-type methods using recurrent functions

We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Newton-type methods. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases [X. Chen, On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms, Ann. Inst. Statist. Math. 42 (1990), pp. 387–401; X. Chen and T. Yamamoto, Convergence domains of certain iterative methods for solving nonlinear equations, Numer. Funct. Anal. Optim. 10 (1989), pp. 37–48; Y. Chen and D. Cai, Inexact overlapped block Broyden methods for solving nonlinear equations, Appl. Math. Comput. 136 (2003), pp. 215–228; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in Nonlinear Functional Analysis and Applications, L.B. Rall, ed., Academic Press, New York, 1971, pp. 425–472; P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, Springer-Verlag, Berlin, 2004; P. Deuflhard and G. Heindl, Affine invariant convergence theorems for Newton's method and extensions to related methods, SIAM J. Numer. Anal. 16 (1979), pp. 1–10; Z. Huang, A note of Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993), pp. 211–217; L.V. Kantorovich and G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982; D. Li and M. Fukushima, Globally Convergent Broyden-like Methods for Semismooth Equations and Applications to VIP, NCP and MCP, Optimization and Numerical Algebra (Nanjing, 1999), Ann. Oper. Res. 103 (2001), pp. 71–97; C. Ma, A smoothing Broyden-like method for the mixed complementarity problems, Math. Comput. Modelling 41 (2005), pp. 523–538; G.J. Miel, Unified error analysis for Newton-type methods, Numer. Math. 33 (1979), pp. 391–396; G.J. Miel, Majorizing sequences and error bounds for iterative methods, Math. Comp. 34 (1980), pp. 185–202; I. Moret, A note on Newton type iterative methods, Computing 33 (1984), pp. 65–73; F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985), pp. 71–84; W.C. Rheinboldt, A unified convergence theory for a class of iterative processes, SIAM J. Numer. Anal. 5 (1968), pp. 42–63; T. Yamamoto, A convergence theorem for Newton-like methods in Banach spaces, Numer. Math. 51 (1987), pp. 545–557; P.P. Zabrejko and D.F. Nguen, The majorant method in the theory of Newton–Kantorovich approximations and the Pták error estimates, Numer. Funct. Anal. Optim. 9 (1987), pp. 671–684; A.I. Zin[cbreve]enko, Some approximate methods of solving equations with non-differentiable operators, (Ukrainian), Dopovidi Akad. Nauk Ukraïn. RSR (1963), pp. 156–161]. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar-type, and a differential equation are also provided in this study.     

RFRCDB-siRNA: improved design of siRNAs by random forest regression model coupled with database searching

Although the observations concerning the factors which influence the siRNA efficacy give clues to the mechanism of RNAi, the quantitative prediction of the siRNA efficacy is still a challenge task. In this paper, we introduced a novel non-linear regression method: random forest regression (RFR), to quantitatively estimate siRNAs efficacy values. Compared with an alternative machine learning regression algorithm, support vector machine regression (SVR) and four other score-based algorithms [A. Reynolds, D. Leake, Q. Boese, S. Scaringe, W.S. Marshall, A. Khvorova, Rational siRNA design for RNA interference, Nat. Biotechnol. 22 (2004) 326-330; K. Ui-Tei, Y. Naito, F. Takahashi, T. Haraguchi, H. Ohki-Hamazaki, A. Juni, R. Ueda, K. Saigo, Guidelines for the selection of highly effective siRNA sequences for mammalian and chick RNA interference, Nucleic Acids Res. 32 (2004) 936-948; A.C. Hsieh, R. Bo, J. Manola, F. Vazquez, O. Bare, A. Khvorova, S. Scaringe, W.R. Sellers, A library of siRNA duplexes targeting the phosphoinositide 3-kinase pathway: determinants of gene silencing for use in cell-based screens, Nucleic Acids Res. 32 (2004) 893-901; M. Amarzguioui, H. Prydz, An algorithm for selection of functional siRNA sequences, Biochem. Biophys. Res. Commun. 316 (2004) 1050-1058) our RFR model achieved the best performance of all. A web-server, RFRCDB-siRNA (http://www.bioinf.seu.edu.cn/siRNA/index.htm), has been developed. RFRCDB-siRNA consists of two modules: a siRNA-centric database and a RFR prediction system. RFRCDB-siRNA works as follows: (1) Instead of directly predicting the gene silencing activity of siRNAs, the service takes these siRNAs as queries to search against the siRNA-centric database. The matched sequences with the exceeding the user defined functionality value threshold are kept. (2) The mismatched sequences are then processed into the RFR prediction system for further analysis.