Limited memory switched Broyden method for faster image deblurring

Iterative methods have gained a solid reputation for efficient image restoration, for both spatially invariant and spatially variant blurs. This paper shows how a "strap-on" quasi-Newton Broyden method can further accelerate the convergence of these iterative methods with little extra overhead

On degeneracy in linear complementarity problems

AbstractLet M be an n×n matrix and q an nth order vector. Then the linear complementarity problem LCP(q, M) is defined as follows: determine x⩾0 such that w=Mx+q⩾0 and xTw=0. A vector x which satisfies these conditions is called a solution of the problem, and a solution for which xi=wi=0 for at least one value of i is termed degenerate. If the solutions of LCP(q, M) are nondegenerate and their number is odd (even), we say that the solution set has odd (even) parity, and Murty has shown that this parity is determined uniquely by M. In this paper the idea of parity is extended to degenerate solutions and, through these, to solution sets containing both degenerate and nondegenerate solutions. These results are then used to give a generalization of Lemke's method and to analyse the stability of certain degenerate solutions of linear complementarity problems

Implementation of different computational variations of biconjugate residual methods

AbstractIn this paper, we describe the derivation of the biconjugate residual (BCR) method from the general framework of the Block-CG algorithm; we then introduce different versions of BCR and test their numerical performance

Numerical Computation of p-values with myFitter

Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are, however, many realistic situations where Wilks' theorem does not apply. In particular, no simple formula exists for the comparison of models that are not nested, in the sense that one model can be obtained from the other by fixing some of its parameters. In this paper I present methods for efficient numerical computations of p-values, which work for both nested and non-nested models and do not rely on additional approximations. These methods have been implemented in a publicly available C++ framework for maximum likelihood fits called myFitter and have recently been applied in a global analysis of the Standard Model with a fourth generation of fermions

Kaon Condensation in a Nambu--Jona-Lasinio (NJL) Model at High Density

We demonstrate a fully self-consistent microscopic realization of a kaon-condensed colour-flavour locked state (CFLK0) within the context of a mean-field NJL model at high density. The properties of this state are shown to be consistent with the QCD low-energy effective theory once the proper gauge neutrality conditions are satisfied, and a simple matching procedure is used to compute the pion decay constant, which agrees with the perturbative QCD result. The NJL model is used to compare the energies of the CFLK0 state to the parity even CFL state, and to determine locations of the metal/insulator transition to a phase with gapless fermionic excitations in the presence of a non-zero hypercharge chemical potential and a non-zero strange quark mass. The transition points are compared with results derived previously via effective theories and with partially self-consistent NJL calculations. We find that the qualitative physics does not change, but that the transitions are slightly lower.Comment: 21 pages, ReVTeX4. Clarified discussion and minor change

Numerical study of metastable states in Ising spin glasses

We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all non-paramagnetic stationary points of the free energy are organized into pairs, consisting in a minimum and a saddle of order one, which coalesce in the thermodynamic limit. Within the annealed approximation, the entropic contribution of these states, that is the complexity, is compatible with the supersymmetry-breaking calculation performed in [A.J. Bray and M.A. Moore, J. Phys. C, 13 L469 (1980)]. This result indicates that the supersymmetry is spontaneously broken in the Sherrington-Kirkpatrick model

Combination preconditioning of saddle point systems for positive definiteness

Amongst recent contributions to preconditioning methods for saddle point systems, standard iterative methods in nonstandard inner products have been usefully employed. Krzyzanowski (Numer. Linear Algebra Appl. 2011; 18:123–140) identified a two-parameter family of preconditioners in this context and Stoll and Wathen (SIAM J. Matrix Anal. Appl. 2008; 30:582–608) introduced combination preconditioning, where two preconditioners, self-adjoint with respect to different inner products, can lead to further preconditioners and associated bilinear forms or inner products. Preconditioners that render the preconditioned saddle point matrix nonsymmetric but self-adjoint with respect to a nonstandard inner product always allow a MINRES-type method (W-PMINRES) to be applied in the relevant inner product. If the preconditioned matrix is also positive definite with respect to the inner product a more efficient CG-like method (W-PCG) can be reliably used. We establish eigenvalue expressions for Krzyzanowski preconditioners and show that for a specific choice of parameters, although the Krzyzanowski preconditioned saddle point matrix is self-adjoint with respect to an inner product, it is never positive definite. We provide explicit expressions for the combination of certain preconditioners and prove the rather counterintuitive result that the combination of two specific preconditioners for which only W-PMINRES can be reliably used leads to a preconditioner for which, for certain parameter choices, W-PCG is reliably applicable. That is, combining two indefinite preconditioners can lead to a positive definite preconditioner. This combination preconditioner outperforms either of the two preconditioners from which it is formed for a number of test problems

The detection of globular clusters in galaxies as a data mining problem

We present an application of self-adaptive supervised learning classifiers derived from the Machine Learning paradigm, to the identification of candidate Globular Clusters in deep, wide-field, single band HST images. Several methods provided by the DAME (Data Mining & Exploration) web application, were tested and compared on the NGC1399 HST data described in Paolillo 2011. The best results were obtained using a Multi Layer Perceptron with Quasi Newton learning rule which achieved a classification accuracy of 98.3%, with a completeness of 97.8% and 1.6% of contamination. An extensive set of experiments revealed that the use of accurate structural parameters (effective radius, central surface brightness) does improve the final result, but only by 5%. It is also shown that the method is capable to retrieve also extreme sources (for instance, very extended objects) which are missed by more traditional approaches.Comment: Accepted 2011 December 12; Received 2011 November 28; in original form 2011 October 1

Multifactorial disease risk calculator: risk prediction for multifactorial disease pedigrees

Construction of multifactorial disease models from epidemiological findings and their application to disease pedigrees for risk prediction is nontrivial for all but the simplest of cases. Multifactorial Disease Risk Calculator is a web tool facilitating this. It provides a user-friendly interface, extending a reported methodology based on a liability-threshold model. Multifactorial disease models incorporating all the following features in combination are handled: quantitative risk factors (including polygenic scores), categorical risk factors (including major genetic risk loci), stratified age of onset curves, and the partition of the population variance in disease liability into genetic, shared, and unique environment effects. It allows the application of such models to disease pedigrees. Pedigree-related outputs are (i) individual disease risk for pedigree members, (ii) n year risk for unaffected pedigree members, and (iii) the disease pedigree's joint liability distribution. Risk prediction for each pedigree member is based on using the constructed disease model to appropriately weigh evidence on disease risk available from personal attributes and family history. Evidence is used to construct the disease pedigree's joint liability distribution. From this, lifetime and n year risk can be predicted. Example disease models and pedigrees are provided at the website and are used in accompanying tutorials to illustrate the features available. The website is built on an R package which provides the functionality for pedigree validation, disease model construction, and risk prediction. Website: http://grass.cgs.hku.hk:3838/mdrc/current

Enhancing structure relaxations for first-principles codes: an approximate Hessian approach

We present a method for improving the speed of geometry relaxation by using a harmonic approximation for the interaction potential between nearest neighbor atoms to construct an initial Hessian estimate. The model is quite robust, and yields approximately a 30% or better reduction in the number of calculations compared to an optimized diagonal initialization. Convergence with this initializer approaches the speed of a converged BFGS Hessian, therefore it is close to the best that can be achieved. Hessian preconditioning is discussed, and it is found that a compromise between an average condition number and a narrow distribution in eigenvalues produces the best optimization.Comment: 9 pages, 3 figures, added references, expanded optimization sectio