Model order reduction is a mathematical technique to transform nonlinear dynamical models into smaller ones, that are easier to analyze. In this paper we demonstrate how model order reduction can be applied to nonlinear electronic circuits. First we give an introduction to this important topic. For linear time-invariant systems there exist already some well-known techniques, like Truncated Bala...

In computed tomography, a whole scan of the object may be impossible, generally because is larger than scanner field view. Such set up leads to truncated projections. Using differentiated backprojection, reconstruction problem can reduced 1-D problems consisting inversion Hilbert transform. When partly overlaps view, this commonly referred as “one-sided transform.” Our work investigates situati...

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on use proper orthogonal decomposition (POD) to identify a reduced subspace and Galerkin projection evolving dynamics in this space. However, advection-dominated PDEs are represented poorly by methodology since process truncation discards important interactions between higher-order modes...

Incremental truncation is a method for constructing libraries of every one base pair truncation of a segment of DNA. Incremental truncation libraries can be created using a time-dependent nuclease method or through the incorporation of alpha-phosphothioate dNTPs by PCR or by primer extension (THIO(pcr) truncation and THIO(extension) truncation, respectively). Libraries created by the fusion of ...

We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft truncation regime and hard truncation regime, and show that, in the soft truncation regime, truncated power tails behave, in important respects, as if no trunca...

We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-be...

Let A be a complex hyperplane arrangement, and let X be a modular element of arbitrary rank in the intersection lattice of A. We show that projection along X restricts to a fiber bundle projection of the complement of A to the complement of the localization AX of A at X. The fiber is the decone of a realization of the complete principal truncation of the underlying matroid of A along the flat c...

Artefacts can result when reconstructing a dynamic image sequence from inconsistent single photon emission computed tomography (SPECT) projection data acquired by a slowly rotating gantry. The artefacts can lead to biases in kinetic parameters estimated from time-activity curves generated by overlaying volumes of interest on the images. Insufficient sampling and truncation of projections by con...

This paper introduces a method of region-of-interest (ROI) reconstruction from truncated 3D X-ray projections, consisting of a waveletbased regularized iterative reconstruction procedure that, under appropriate conditions, converges within the ROI to an exact or highly accurate solution. ROI tomography is motivated by the goal to reduce the overall radiation exposure when primarily the reconstr...

In a dedicated cardiac single photon emission computed tomography (SPECT) system, the detectors are focused on the heart and the background is truncated in the projections. Reconstruction using truncated data results in biased images, leading to inaccurate kinetic parameter estimates. This paper has developed a closed-form kinetic parameter estimation solution to the dynamic emission imaging pr...