Approximate factorization of multivariate polynomials using singular value decomposition

We describe the design, implementation and experimental evaluation of new algorithms for computing the approximate factorization of multivariate polynomials with complex coefficients that contain numerical noise. Our algorithms are based on a generalization of the differential forms introduced by W. Ruppert and S. Gao to many variables, and use singular value decomposition or structured total least squares approximation and Gauss–Newton optimization to numerically compute the approximate multivariate factors. We demonstrate on a large set of benchmark polynomials that our algorithms efficiently yield approximate factorizations within the coefficient noise even when the relative error in the input is substantial (10⁻³).     

Solders development and application process for a micro chip-camera

Nowadays, micro components have to fulfill rising optical requirements for different scientific and industrial fields like astronomy, medicine or multimedia. For this purpose, advanced miniaturized chip-cameras are produced for the microsystems engineering market. The assembly and joining technologies play a very important role in the production of these micro components. Several challenges are associated with the joining of chip-cameras. In this study, the application of the soldering technology has been considered in order to face these challenges. Two joining technologies have been investigated: active soldering and transient liquid phase (TLP) bonding. Both soldering processes have shown a big potential for hybrid microsystems joining in previous studies. For both processes, soldering alloys and parameters have been conceived in order to fulfill the joining requirements of the micro camera components. For instance, the joining temperature represents a major challenge because the chip-camera consists of a plastic material, polymethyl methacrylate (PMMA). Therefore, particular attention has been directed to the soldering as well as to the coating temperature. The experimental investigations concerning the solders application through physical vapor deposition (PVD) have been supported by finite element method (FEM) simulations. The analysis of  the temperature distribution in the micro components during the coating process was the focus of  the calculations. Possible undesirable local overheated areas of the chip-camera components can be detected through simulation.

---

Structured document storage and refined declarative and navigational access mechanisms in HyperStorM

The combination of SGML and database technology allows to refine both declarative and navigational access mechanisms for structured document collection: with regard to declarative access, the user can formulate complex information needs without knowing a query language, the respective document type definition (DTD) or the underlying modelling. Navigational access is eased by hyperlink-rendition mechanisms going beyond plain link-integrity checking. With our approach, the database-internal representation of documents is configurable. It allows for an efficient implementation of operations, because DTD knowledge is not needed for document structure recognition. We show how the number of method invocations and the cost of parsing can be significantly reduced. Edited by Y.C. Tay. Received April 22, 1996 / Accepted March 16, 1997     

Model Checking Games for the Quantitative μ-Calculus

We investigate quantitative extensions of modal logic and the modal μ-calculus, and study the question whether the tight connection between logic and games can be lifted from the qualitative logics to their quantitative counterparts. It turns out that, if the quantitative μ-calculus is defined in an appropriate way respecting the duality properties between the logical operators, then its model checking problem can indeed be characterised by a quantitative variant of parity games. However, these quantitative games have quite different properties than their classical counterparts, in particular they are, in general, not positionally determined. The correspondence between the logic and the games goes both ways: the value of a formula on a quantitative transition system coincides with the value of the associated quantitative game, and conversely, the values of quantitative parity games are definable in the quantitative μ-calculus.     

Parametric G n blending of curves and surfaces

We introduce a simple blending method for parametric curves and surfaces that produces families of parametrically defined, G ⁿ –continuous blending curves and surfaces. The method depends essentially on the parameterizations of the curves/surfaces to be blended. Hence, the flexibility of the method relies on the existence of suitable parameter transformations of the given curves/surfaces. The feasibility of the blending method is shown by several examples. The shape of the blend curve/surface can be changed in a predictable way with the aid of two design parameters (thumb weight and balance).     

Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata

Although topology optimization is well established in most engineering fields, it is still in its infancy concerning highly non-linear structural applications like vehicular crashworthiness. One of the approaches recently proposed and based on Hybrid Cellular Automata is modified here such that it can be applied for the first time to thin-walled structures. Classical methods based on voxel techniques, i.e., on solid three-dimensional volume elements, cannot derive structures made from thin metal sheets where the main energy absorption mode is related to plastic buckling, folding and failure. Because the main components of car structures are made from such thin-walled beams and panels, a special approach using SFE CONCEPT was developed, which is presented in this paper.     

Online segmentation of time series based on polynomial least-squares approximations

The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based on a least-squares approximation of time series in sliding and/or growing time windows utilizing a basis of orthogonal polynomials. This allows the definition of fast update steps for the approximating polynomial, where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window. The coefficients of the orthogonal expansion of the approximating polynomial-obtained by means of the update steps-can be interpreted as optimal (in the least-squares sense) estimators for average, slope, curvature, change of curvature, etc., of the signal in the time window considered. These coefficients, as well as the approximation error, may be used in a very intuitive way to define segmentation criteria. The properties of SwiftSeg are evaluated by means of some artificial and real benchmark time series. It is compared to three different offline and online techniques to assess its accuracy and runtime. It is shown that SwiftSeg-which is suitable for many data streaming applications-offers high accuracy at very low computational costs.     

Adaptive training of video sets for image recognition on mobile phones

We present an enhancement towards adaptive video training for PhoneGuide, a digital museum guidance system for ordinary camera-equipped mobile phones. It enables museum visitors to identify exhibits by capturing photos of them. In this article, a combined solution of object recognition and pervasive tracking is extended to a client–server-system for improving data acquisition and for supporting scale-invariant object recognition. A static as well as a dynamic training technique are presented that preprocess the collected object data differently and apply two types of neural networks (NN) for classification. Furthermore, the system enables a temporal adaptation for ensuring a continuous data acquisition to improve the recognition rate over time. A formal field experiment reveals current recognition rates and indicates the practicability of both methods under realistic conditions in a museum.

---