| 1. |
- Besselink, Bart, et al.
(author)
-
A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control
- 2013
-
In: Journal of Sound and Vibration. - : Elsevier BV. - 0022-460X .- 1095-8568. ; 332:19, s. 4403-4422
-
Research review (peer-reviewed)abstract
- In this paper, popular model reduction techniques from the fields of structural dynamics, numerical mathematics and systems and control are reviewed and compared. The motivation for such a comparison stems from the fact that the model reduction techniques in these fields have been developed fairly independently. In addition, the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique, on the basis of the desired objectives and properties of the model reduction problem. In particular, a detailed review is given on mode displacement techniques, moment matching methods and balanced truncation, whereas important extensions are outlined briefly. In addition, a qualitative comparison of these methods is presented, hereby focusing both on theoretical and computational aspects. Finally, the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example.
|
|
| 2. |
- Jarlebring, Elias, et al.
(author)
-
Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations
- 2009
-
In: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 431:3-4, s. 369-380
-
Journal article (peer-reviewed)abstract
- Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called matrix pencil methods, the general ideas used as well as the proofs differ considerably. Moreover, the available theory hardly reveals the relations between the different methods. In this work, a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem: the polynomial two-parameter eigenvalue problem, of which the quadratic two-parameter eigenvalue problem is a special case. This framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods. We also recognize a few new matrix pencil variants to determine DDE stability. Finally, the recognition of the new types of eigenvalue problem opens a door to efficient computation of DDE stability. (C) 2009 Elsevier Inc. All rights reserved.
|
|
| 3. |
- Koskela, Antti, et al.
(author)
-
Krylov approximation of linear odes with polynomial parameterization
- 2016
-
In: SIAM Journal on Matrix Analysis and Applications. - : Society for Industrial and Applied Mathematics Publications. - 0895-4798 .- 1095-7162. ; 37:2, s. 519-538
-
Journal article (peer-reviewed)abstract
- We propose a new numerical method to solve linear ordinary differential equations of the type δu/δt (t, ϵ) = A(ϵ) u(t,ϵ), where A: C → Cn×n is a matrix polynomial with large and sparse matrix coefficients. The algorithm computes an explicit parameterization of approximations of u(t, ϵ) such that approximations for many different values of ϵ and t can be obtained with a very small additional computational effort. The derivation of the algorithm is based on a reformulation of the parameterization as a linear parameter-free ordinary differential equation and on approximating the product of the matrix exponential and a vector with a Krylov method. The Krylov approximation is generated with Arnoldi's method and the structure of the coefficient matrix turns out to be independent of the truncation parameter so that it can also be interpreted as Arnoldi's method applied to an infinite dimensional matrix. We prove the super linear convergence of the algorithm and provide a posteriori error estimates to be used as termination criteria. The behavior of the algorithm is illustrated with examples stemming from spatial discretizations of partial differential equations.
|
|
| 4. |
- Merlo, Domenico Franco, et al.
(author)
-
Micronuclei in Cord Blood Lymphocytes and Associations with Biomarkers of Exposure to Carcinogens and Hormonally Active Factors, Gene Polymorphisms, and Gene Expression : The NewGeneris Cohort
- 2014
-
In: Journal of Environmental Health Perspectives. - : Environmental Health Perspectives. - 0091-6765 .- 1552-9924. ; 122:2, s. 193-200
-
Journal article (peer-reviewed)abstract
- Background: Leukemia incidence has increased in recent decades among European children, -suggesting that early-life environmental exposures play an important role in disease development. Objectives: We investigated the hypothesis that childhood susceptibility may increase as a result of in utero exposure to carcinogens and hormonally acting factors. Using cord blood samples from the NewGeneris cohort, we examined associations between a range of biomarkers of carcinogen exposure and hormonally acting factors with micronuclei (MN) frequency as a proxy measure of cancer risk. Associations with gene expression and genotype were also explored. Methods: DNA and protein adducts, gene expression profiles, circulating hormonally acting factors, and GWAS (genome-wide association study) data were investigated in relation to genomic damage measured by MN frequency in lymphocytes from 623 newborns enrolled between 2006 and 2010 across Europe. Results: Malondialdehyde DNA adducts (M(1)dG) were associated with increased MN frequency in binucleated lymphocytes (MNBN), and exposure to androgenic, estrogenic, and dioxin-like compounds was associated with MN frequency in mononucleated lymphocytes (MNMONO), although no monotonic exposure-outcome relationship was observed. Lower frequencies of MNBN were associated with a 1-unit increase expression of PDCD11, LATS2, TRIM13, CD28, SMC1A, IL7R, and NIPBL genes. Gene expression was significantly higher in association with the highest versus lowest category of bulky and M(1)dG-DNA adducts for five and six genes, respectively. Gene expression levels were significantly lower for 11 genes in association with the highest versus lowest category of plasma AR CALUX (R) (chemically activated luciferase expression for androgens) (8 genes), ER alpha CALUX (R) (for estrogens) (2 genes), and DR CALUX (R) (for dioxins). Several SNPs (single-nucleotide polymorphisms) on chromosome 11 near FOLH1 significantly modified associations between androgen activity and MNBN frequency. Polymorphisms in EPHX1/ 2 and CYP2E1 were associated with MNBN. Conclusion: We measured in utero exposure to selected environmental carcinogens and circulating hormonally acting factors and detected associations with MN frequency in newborns circulating T lymphocytes. The results highlight mechanisms that may contribute to carcinogen-induced leukemia and require further research.
|
|
