Mean asymptotic behaviour of radix-rational sequences and dilation equations (Extended version)

The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Ces\`aro means. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence; the coefficients are obtained through some dilation equations. The proofs are based on elementary linear algebra

Fabrication and nanoroughness characterization of specific nanostructures and nanodevice

Nanoroughness is becoming a very important specification for many nanostructures and nanodevices, and its metrology impacts not only the nanodevice properties of interest, but also its material selection and process development. This Ph.D. thesis presents an investigation into fabrication and nanoroughness characterization of nanoscale specimens and MIS (metal-insulator-semiconductor) capacitors with 2 HfO as a high k dielectric. Self-affine curves and Gaussian, non-Gaussian, self-affine as well as complicated rough surfaces were characterized and simulated. The effects of characteristic parameters on the CD (critical dimension) variation and the properties of these rough surfaces were visualized. Compared with experimental investigations, these simulations are flexible, low cost and highly efficient. Relevant conclusions were frequently employed in subsequent investigations. A proposal regarding the thicknesses of the deposited films represented by nominal linewidths and pitch was put forward. The MBE (Molecular Beam Epitaxy) process was introduced and AlGaAs and GaAs were selected to fabricate nanolinewidth and nanopitch specimens on GaAs substrate with nominal linewidths of 2nm, 4nm, 6nm and 8nm, and a nominal pitch of 5nm. HRTEM (High Resolution Transmission Electron Microscopy) image-based characterization of LER/LWR (Line Edge Roughness/Line Width Roughness) in real space and frequency domains demonstrated that the MBE-based process was capable of fabricating the desired nanolinewidth and nanopitch specimens and could be regulated accordingly. MIS capacitors with 2 HfO film as high k dielectric were fabricated, and SEM (Scanning Electron Microscope) image-based nanoroughness characterization, along with measurement of the MIS capacitor electrical properties were performed. It was concluded that the annealing temperature of the deposited 2 HfO film was an important process parameter and 700℃ was an optimal temperature to improve the properties of the MIS capacitor. Also, by quantitative characterization of the relevant nanoroughness, the fabrication process can be further regulated. The uncertainty propagation model of SEM based nanoroughness measurement was presented according to specific requirements of the relevant standards, ISO GPS (Geometric Product Specifications and Verification) and GUM (Guide to the Expression of Uncertainty in Measurement), and the method for implementating uncertainties was evaluated. The case study demonstrated that the total standard uncertainty of the nanoroughness measurement was 0.13nm, while its expanded uncertainty with the coverage factor k as 3 was 0.39nm. They are indispensable parts of LER/LWR measurement results

Spotting Keywords in Offline Handwritten Documents Using Hausdorff Edit Distance

Keyword spotting has become a crucial topic in handwritten document recognition, by enabling content-based retrieval of scanned documents using search terms. With a query keyword, one can search and index the digitized handwriting which in turn facilitates understanding of manuscripts. Common automated techniques address the keyword spotting problem through statistical representations. Structural representations such as graphs apprehend the complex structure of handwriting. However, they are rarely used, particularly for keyword spotting techniques, due to high computational costs. The graph edit distance, a powerful and versatile method for matching any type of labeled graph, has exponential time complexity to calculate the similarities of graphs. Hence, the use of graph edit distance is constrained to small size graphs. The recently developed Hausdorff edit distance algorithm approximates the graph edit distance with quadratic time complexity by efficiently matching local substructures. This dissertation speculates using Hausdorff edit distance could be a promising alternative to other template-based keyword spotting approaches in term of computational time and accuracy. Accordingly, the core contribution of this thesis is investigation and development of a graph-based keyword spotting technique based on the Hausdorff edit distance algorithm. The high representational power of graphs combined with the efficiency of the Hausdorff edit distance for graph matching achieves remarkable speedup as well as accuracy. In a comprehensive experimental evaluation, we demonstrate the solid performance of the proposed graph-based method when compared with state of the art, both, concerning precision and speed. The second contribution of this thesis is a keyword spotting technique which incorporates dynamic time warping and Hausdorff edit distance approaches. The structural representation of graph-based approach combined with statistical geometric features representation compliments each other in order to provide a more accurate system. The proposed system has been extensively evaluated with four types of handwriting graphs and geometric features vectors on benchmark datasets. The experiments demonstrate a performance boost in which outperforms individual systems

Accurate and efficient three-dimensional electrostatics analysis using singular boundary elements and Fast Fourier Transform on Multipole (FFTM)

Ph.DDOCTOR OF PHILOSOPH