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.     

Integrated design and control for robust performance: Application to an MSMPR crystallizer

The interplay of different types of performance constraints in an integrated design and control problem is studied by means of a case study. This integrated problem is based on a recent method for robust process design [M. Mönnigmann, W. Marquardt, Normal vectors on manifolds of critical points for parametric robustness of equilibrium solutions of ODE systems, J. Nonlinear Sci. 12 (2002) 85–112; M. Mönnigmann, W. Marquardt, Steady state process optimization with guaranteed robust stability and feasibility, AIChE J. 49 (12) (2003) 3110–3126; M. Mönnigmann, W. Marquardt, Steady state process optimization with guaranteed robust stability and flexibility: application to HDA reaction section, Ind. Eng. Chem. Res. 44 (2005) 2737–2753; W. Marquardt, M. Mönnigmann, Constructive nonlinear dynamics in process systems engineering, Comput. Chem. Eng. 29 (2005) 1265–1275; M. Mönnigmann, Constructive nonlinear dynamics methods for the design of chemical engineering processes, Ph.D. Thesis, RWTH Aachen University, 2003]. The design is found by means of a steady-state optimization problem accounting for process economics and performance requirements. In particular, the latter are represented by constraints which guarantee a user-specified performance of the design in spite of parametric uncertainties. For the first time, two types of dynamic performance constraints are used simultaneously within the adopted framework. These are constraints on time-domain performance indicators as well as on the asymptotic dynamic process behavior. Furthermore, the effect of uncertainty in both, design and model parameters, is accounted for. A key strength of the suggested framework is the direct quantification of the trade-offs between economics and dynamic performance requirements for a selection of uncertainty scenarios. A series of different integrated design and control problems are formulated and solved for a continuous mixed-suspension mixed-product removal (MSMPR) crystallizer. The process exhibits a complex nonlinear behavior and represents a challenging example. The results of the case study allow an in depth understanding of the interactions of design and control for the underlying process.     

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.     

Some remarks on static-feedback linearization for time-varying systems

This work summarizes some results about static state feedback linearization for time-varying systems. Three different necessary and sufficient conditions are stated in this paper. The first condition is the one by [Sluis, W. M. (1993). A necessary condition for dynamic feedback linearization. Systems & Control Letters, 21, 277–283]. The second and the third are the generalizations of known results due respectively to [Aranda-Bricaire, E., Moog, C. H., Pomet, J. B. (1995). A linear algebraic framework for dynamic feedback linearization. IEEE Transactions on Automatic Control, 40, 127–132] and to [Jakubczyk, B., Respondek, W. (1980). On linearization of control systems. Bulletin del’Academie Polonaise des Sciences. Serie des Sciences Mathematiques, 28, 517–522]. The proofs of the second and third conditions are established by showing the equivalence between these three conditions. The results are re-stated in the infinite dimensional geometric approach of [Fliess, M., Lévine J., Martin, P., Rouchon, P. (1999). A Lie–Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922–937].     

Mixed Discontinuous Galerkin Methods for Darcy Flow

We consider a family of mixed finite element discretizations of the Darcy flow equations using totally discontinuous elements (both for the pressure and the flux variable). Instead of using a jump stabilization as it is usually done for discontinuos Galerkin (DG) methods (see e.g. D.N. Arnold et al. SIAM J. Numer. Anal.39, 1749–1779 (2002) and B. Cockburn, G.E. Karniadakis and C.-W. Shu, DG methods: Theory, computation and applications, (Springer, Berlin, 2000) and the references therein) we use the stabilization introduced in A. Masud and T.J.R. Hughes, Meth. Appl. Mech. Eng.191, 4341–4370 (2002) and T.J.R. Hughes, A. Masud, and J. Wan, (in preparation). We show that such stabilization works for discontinuous elements as well, provided both the pressure and the flux are approximated by local polynomials of degree ≥ 1, without any need for additional jump terms. Surprisingly enough, after the elimination of the flux variable, the stabilization of A. Masud and T.J.R. Hughes, Meth. Appl. Mech. Eng.191, 4341–4370 (2002) and T.J.R. Hughes, A. Masud, and J. Wan, (in preparation) turns out to be in some cases a sort of jump stabilization itself, and in other cases a stable combination of two originally unstable DG methods (namely, Bassi-Rebay F. Bassi and S. Rebay, Proceedings of the Conference ‘‘Numerical methods for fluid dynamics V’‘, Clarendon Press, Oxford (1995) and Baumann–Oden Comput. Meth. Appl. Mech. Eng.175, 311–341 (1999).This revised version was published online in July 2005 with corrected volume and issue numbers.     

LSC Verification for UML Models with Unbounded Creation and Destruction

The approaches to automatic formal verification of UML models known up to now require a finite bound on the number of objects existing at each point in time. In [W. Damm, B. Westphal, Live and let die: LSC-based verification of UML-models, Science of of Computer Programming 55 (2005) 117–159] we have observed that the class of hardware systems with replicated components studied by McMillan [K.L. McMillan, A methodology for hardware verification using compositional model checking, Science of Computer Programming 37 (2000) 279–309] is equivalent to the class of systems where the only source of infiniteness is unbounded creation and destruction of objects, i.e. where all data-types except for object identities are finite. Exploiting the symmetry of UML models induced by objects being instances of classes, the restriction to finite bounds can be overcome applying [K.L. McMillan, A methodology for hardware verification using compositional model checking, Science of Computer Programming 37 (2000) 279–309].In this paper we report on experiences from an evaluation of this approach within the UML Verifi- cation Environment (UVE) [I. Schinz, T. Toben, C. Mrugalla and B. Westphal, The Rhapsody UML Verification Environment, in: J.R. Cuellar and Z. Liu, editors, Proceedings SEFM 2004 (2004), pp. 174–183], a state-of-the-art tool for formal verification of UML models using Live Sequence Charts (LSC) [W. Damm, D. Harel, LSCs: Breathing Life into Message Sequence Charts, Formal Methods in System Design 19 (2001) 45–80] for requirements specification.     

Clustering rows and/or columns of a two-way contingency table and a related distribution theory

The row-wise multiple comparison procedure proposed in Hirotsu [Hirotsu, C., 1977. Multiple comparisons and clustering rows in a contingency table. Quality 7, 27–33 (in Japanese); Hirotsu, C., 1983. Defining the pattern of association in two-way contingency tables. Biometrika 70, 579–589] has been verified to be useful for clustering rows and/or columns of a contingency table in several applications. Although the method improved the preceding work there was still a gap between the squared distance between the two clusters of rows and the largest root of a Wishart matrix as a reference statistic for evaluating the significance of the clustering. In this paper we extend the squared distance to a generalized squared distance among any number of rows or clusters of rows and dissolves the loss of power in the process of the clustering procedure. If there is a natural ordering in columns we define an order sensitive squared distance and then the reference distribution becomes that of the largest root of a non-orthogonal Wishart matrix, which is very difficult to handle. We therefore propose a very nice χ²-approximation which improves the usual normal approximation in Anderson [Anderson, T.W., 2003. An Introduction to Multivariate Statistical Analysis. 3rd ed. Wiley Intersciences, New York] and also the first χ²-approximation introduced in Hirotsu [Hirotsu, C., 1991. An approach to comparing treatments based on repeated measures. Biometrika 75, 583–594]. A two-way table reported by Guttman [Guttman, L., 1971. Measurement as structural theory. Psychometrika 36, 329–347] and analyzed by Greenacre [Greenacre, M.J., 1988. Clustering the rows and columns of a contingency table. Journal of Classification 5, 39–51] is reanalyzed and a very nice interpretation of the data has been obtained.     

Generalized projection method for a variational inequality system with different mapping in Banach spaces

The approximate solution of a system for variational inequality with different mapping in Hilbert spaces has been studied, based on the convergence of projection methods. However, little research has been done in Banach space. The primary reason is that projection mapping lacks preferable properties in Banach space. In this paper, we introduce generalized projection methods. By using these methods, the results presented in this paper have extended the main results of Chang et al.’s and Huang and Noor’s recent works [S.S. Chang, H.W. Joseph Lee, C.K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329–334; Zhenyu Huang, Muhammad Aslam Noor, An explicit projection method for a system of nonlinear variational inequalities with different (γ,r)-cocoercive mappings, Appl. Math. Comput. 190 (2007) 356–361] from Hilbert spaces to Banach space.     

Focus points and convergent process operators: a proof strategy for protocol verification

We present a method for efficiently providing algebraic correctness proofs for communication systems. It is described in the setting of μCRL [J.F. Groote, A. Ponse, The syntax and semantics of μCRL, in: A. Ponse, C. Verhoef, S.F.M. van Vlijmen (Eds.), Algebra of Communicating Processes, Workshops in Computing, Springer, Berlin, 1994, pp. 26–62] which is, roughly, ACP [J.C.M. Baeten, W.P. Weijland, Process Algebra, Cambridge Tracts in Theoretical Computer Science, vol. 18, Cambridge University Press, Cambridge 1990, J.A. Bergstra, J.W. Klop, The algebra of recursively defined processes and the algebra of regular processes, in: Proceedings of the 11th ICALP, Antwerp, Lecture Notes in Computer Science, vol. 172, Springer, Berlin, 1984, pp. 82–95] extended with a formal treatment of the interaction between data and processes. The method incorporates assertional methods, such as invariants and simulations, in an algebraic framework, and centers around the idea that the state spaces of distributed systems are structured as a number of cones with focus points. As a result, it reduces a large part of algebraic protocol verification to the checking of a number of elementary facts concerning data parameters occurring in implementation and specification. The resulting method has been applied to various non-trivial case studies of which a number have been verified mechanically with the theorem checker PVS. In this paper the strategy is illustrated by several small examples and one larger example, the Concurrent Alternating Bit Protocol (CABP).     

A Compact Linear Translation for Bounded Model Checking

We present a syntactic scheme for translating future-time LTL bounded model checking problems into propositional satisfiability problems. The scheme is similar in principle to the Separated Normal Form encoding proposed in [Frisch, A., D. Sheridan and T. Walsh, A fixpoint based encoding for bounded model checking, in: M.D. Aagaard and J.W. O'Leary, editors, Formal Methods in Computer-Aided Design; 4th International Conference, FMCAD 2002, Lecture Notes in Computer Science 2517 (2002), pp. 238–254] and extended to past time in [Cimatti, A., M. Roveri and D. Sheridan, Bounded verification of past LTL, in: A.J. Hu and A.K. Martin, editors, Proceedings of the 5th International Conference on Formal Methods in Computer Aided Design (FMCAD 2004), Lecture Notes in Computer Science (2004)]: an initial phase involves putting LTL formulae into a normal form based on linear-time fixpoint characterisations of temporal operators.As with [Cimatti, A., M. Roveri and D. Sheridan, Bounded verification of past LTL, in: A.J. Hu and A.K. Martin, editors, Proceedings of the 5th International Conference on Formal Methods in Computer Aided Design (FMCAD 2004), Lecture Notes in Computer Science (2004)] and [Latvala, T., A. Biere, K. Heljanko and T. Junttila, Simple bounded LTL model checking, in: Formal Methods in Computer-Aided Design; 5th International Conference, FMCAD 2004, Lecture Notes in Computer Science 3312 (2004), pp. 186–200], the size of propositional formulae produced is linear in the model checking bound, but the constant of proportionality appears to be lower.A denotational approach is taken in the presentation which is significantly more rigorous than that in [Frisch, A., D. Sheridan and T. Walsh, A fixpoint based encoding for bounded model checking, in: M.D. Aagaard and J.W. O'Leary, editors, Formal Methods in Computer-Aided Design; 4th International Conference, FMCAD 2002, Lecture Notes in Computer Science 2517 (2002), pp. 238–254] and [Cimatti, A., M. Roveri and D. Sheridan, Bounded verification of past LTL, in: A.J. Hu and A.K. Martin, editors, Proceedings of the 5th International Conference on Formal Methods in Computer Aided Design (FMCAD 2004), Lecture Notes in Computer Science (2004)], and which provides an elegant alternative way of viewing fixpoint based translations in [Latvala, T., A. Biere, K. Heljanko and T. Junttila, Simple bounded LTL model checking, in: Formal Methods in Computer-Aided Design; 5th International Conference, FMCAD 2004, Lecture Notes in Computer Science 3312 (2004), pp. 186–200] and [Biere, A., A. Cimatti, E. M. Clarke, O. Strichman and Y. Zhu, Bounded model checking, Advances in Computers 58 (2003)].     

Sensor and actuator fault isolation by structured partial PCA with nonlinear extensions

Partial PCA based on principal component analysis (PCA) with ideas borrowed from parity relations is a useful method in fault isolation (J. Gertler, W. Li, Y. Huang, T.J. McAvoy, Isolation enhanced principal component analysis, AIChE Journal 45(2) (1999) 323–334). By performing PCA on subsets of variables, a set of structured residuals can be obtained in the same way as structured parity relations. The structured residuals are utilized in composing an isolation scheme for sensor and actuator faults, according to a properly designed incidence matrix. To overcome the limitations of PCA, nonlinear approaches based on generalized PCA (GPCA) and nonlinear PCA (NPCA) are proposed. The nonlinear methods are demonstrated on an artificial 2×2 system while simulation studies on the Tennessee Eastman process illustrate the linear method and some extensions.     

An accurate and reliable solution procedure for the EOQ model with deteriorating items under supplier credits linked to the ordering quantity

The inventory problem consists of two parts: (1) the modelling and (2) the solution procedure. The modelling can provide insight to solve the inventory problem and the solution procedure involves the implementation of the inventory model. Basically, the modelling and the solution procedure to the inventory problem are equally important. Chang et al.’s inventory model [Chang, C. T., Ouyang, L. Y., & Teng, J. T (2003). An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. Applied Mathematical Modelling, 27, 983–996] is correct and interesting. However, they ignore the explorations of the functional behaviors of the annual total relevant cost to locate the optimal solutions such that proofs of their solution procedures are not perfect from the viewpoint of logic. The main purposes of this paper are to provide accurate and reliable solution procedures to improve [Chang, C. T., Ouyang, L. Y., & Teng, J. T (2003). An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. Applied Mathematical Modelling, 27, 983–996].     

On global stabilization of Burgers’ equation by boundary control

Although often referred to as a one-dimensional “cartoon” of Navier–Stokes equation because it does not exhibit turbulence, the Burgers equation is a natural first step towards developing methods for control of flows. Recent references include Burns and Kang [Nonlinear Dynamics 2 (1991) 235–262], Choi et al. [J. Fluid Mech. 253 (1993) 509–543], Ito and Kang [SIAM J. Control Optim. 32 (1994) 831–854], Ito and Yan [J. Math. Anal. Appl. 227 (1998) 271–299], Byrnes et al. [J. Dynam. Control Systems 4 (1998) 457–519] and Van Ly et al. [Numer. Funct. Anal. Optim. 18 (1997) 143–188]. While these papers have achieved tremendous progress in local stabilization and global analysis of attractors, the problem of global asymptotic stabilization has remained open. This problem is non-trivial because for large initial conditions the quadratic (convective) term – which is negligible in a linear/local analysis – dominates the dynamics. We derive nonlinear boundary control laws that achieve global asymptotic stability. We consider both the viscous and the inviscid Burgers’ equation, using both Neumann and Dirichlet boundary control. We also study the case where the viscosity parameter is uncertain, as well as the case of stochastic Burgers’ equation. For some of the control laws that would require the measurement in the interior of the domain, we develop the observer-based versions.     

Unfair Problems and Randomized Algorithms for Metrical Task Systems

Borodin, Linial, and Saks introduced a general model for online systems calledmetrical task systems(1992,J. Assoc. Comput. Mach.39(4), 745–763). In this paper, the unfair two state problem, a natural generalization of the two state metrical task system problem, is studied. A randomized algorithm for this problem is presented, and it is shown that this algorithm is optimal. Using the analysis of the unfair two state problem, a proof of a decomposition theorem similar to that of Blum, Karloff, Rabani, and Saks (1992, “Proc. 33rd Symposium on Foundations of Computer Science,” pp. 197–207) is presented. This theorem allows one to design divide and conquer algorithms for specific metrical task systems. Our theorem gives the same bounds asymptotically, but it has less restrictive boundary conditions.     

Sturm–Liouville problems with discontinuities at two points

In this paper we extend some spectral properties of regular Sturm–Liouville problems to those which consist of a Sturm–Liouville equation with piecewise continuous potentials together with eigenparameter-dependent boundary conditions and four supplementary transmission conditions. By modifying some techniques of [C.T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977) 293–308; E. Tunç, O.Sh. Muhtarov, Fundamental solutions and eigenvalues of one boundary-value problem with transmission conditions, Appl. Math. Comput. 157 (2004) 347–355; O.Sh. Mukhtarov, E. Tunç, Eigenvalue problems for Sturm–Liouville equations with transmission conditions, Israel J. Math. 144 (2004) 367–380] and [O.Sh. Mukhtarov, M. Kadakal, F.Ş. Muhtarov, Eigenvalues and normalized eigenfunctions of discontinuous Sturm–Liouville problem with transmission conditions, Rep. Math. Phys. 54 (2004) 41–56], we give an operator-theoretic formulation for the considered problem and obtain asymptotic formulae for the eigenvalues and eigenfunctions.     

Modeling of high-affinity binding of the novel atrial anti-arrhythmic agent, vernakalant, to Kv1.5 channels

Vernakalant (RSD1235) is an investigational drug that converts atrial fibrillation rapidly and safely in patients intravenously [Roy et al., J. Am. Coll. Cardiol. 44 (2004) 2355–2361; Roy et al., Circulation 117 (2008) 1518–1525] and maintains sinus rhythm when given orally [Savelieva et al., Europace 10 (2008) 647–665]. Here, modeling using AutoDock4 allowed exploration of potential binding modes of vernakalant to the open-state of the Kv1.5 channel structure. Point mutations were made in the channel model based on earlier patch-clamp studies [Eldstrom et al., Mol. Pharmacol. 72 (2007) 1522–1534] and the docking simulations re-run to evaluate the ability of the docking software to predict changes in drug–channel interactions. Each AutoDock run predicted a binding conformation with an associated value for free energy of binding (FEB) in kcal/mol and an estimated inhibitory concentration (K_i). The most favored conformation had a FEB of −7.12 kcal/mol and a predicted K_i of 6.08 μM (the IC50 for vernakalant is 13.8 μM; [Eldstrom et al., Mol. Pharmacol. 72 (2007) 1522–1534]). This conformation makes contact with all four T480 residues and appears to be clearly positioned to block the channel pore.     

Regression output from a remote analysis server

This paper is concerned with the problem of balancing the competing objectives of allowing statistical analysis of confidential data while maintaining standards of privacy and confidentiality. Remote analysis servers have been proposed as a way to address this problem by delivering results of statistical analyses without giving the analyst any direct access to data. Several national statistical agencies operate remote analysis servers [Australian Bureau of Statistics Remote Access Data Laboratory (RADL), <www.abs.gov.au>; Luxembourg Income Study, <www.lisproject.org>].Remote analysis servers are not free from disclosure risk, and current implementations address this risk by “confidentialising” the underlying data and/or by denying some queries. In this paper we explore the alternative solution of “confidentialising” the output of a server so that no confidential information is revealed or can be inferred.In this paper we review results on remote analysis servers, and provide a list of measures for confidentialising the output from a single regression query to a remote server as developed by Sparks et al. [R. Sparks, C. Carter, J. Donnelly, J. Duncan, C.M. O’Keefe, L. Ryan, A framework for performing statistical analyses of unit record health data without violating either privacy or confidentiality of individuals, in: Proceedings of the 55th Session of the International Statistical Institute, Sydney, 2005; R. Sparks, C. Carter, J. Donnelly, C.M. O’Keefe, J. Duncan, T. Keighley, D. McAullay, Remote access methods for exploratory data analysis and statistical modelling: privacy-preserving Analytics^™, Comput. Meth. Prog. Biomed. 91 (2008) 208–222.] We provide a fully worked example, and compare the confidentialised output from the query with the output from a traditional statistical package. Finally, we provide a comparison the confidentialised regression diagnostics with the synthetic regression diagnostics generated by the alternative method of Reiter [J.P. Reiter, Model diagnostics for remote-access regression servers, Statistics and Computing 13 (2003) 371–380].     

Block preconditioners with circulant blocks for general linear systems

Block preconditioner with circulant blocks (BPCB) has been used for solving linear systems with block Toeplitz structure since 1992 [R. Chan, X. Jin, A family of block preconditioners for block systems, SIAM J. Sci. Statist. Comput. (13) (1992) 1218–1235]. In this new paper, we use BPCBs to general linear systems (with no block structure usually). The BPCBs are constructed by partitioning a general matrix into a block matrix with blocks of the same size and then applying T. Chan’s optimal circulant preconditioner [T. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput. (9) (1988) 766–771] to each block. These BPCBs can be viewed as a generalization of T. Chan’s preconditioner. It is well-known that the optimal circulant preconditioner works well for solving some structured systems such as Toeplitz systems by using the preconditioned conjugate gradient (PCG) method, but it is usually not efficient for solving general linear systems. Unlike T. Chan’s preconditioner, BPCBs used here are efficient for solving some general linear systems by the PCG method. Several basic properties of BPCBs are studied. The relations of the block partition with the cost per iteration and the convergence rate of the PCG method are discussed. Numerical tests are given to compare the cost of the PCG method with different BPCBs.