A new algorithm for fast generalized DFTs

We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups $G$. The new algorithm uses $O(|G|^{\omega/2 + o(1)})$ operations to compute the generalized DFT over finite groups of Lie type, including the linear, orthogonal, and symplectic families and their variants, as well as all finite simple groups of Lie type. Here $\omega$ is the exponent of matrix multiplication, so the exponent $\omega/2$ is optimal if $\omega = 2$. Previously, "exponent one" algorithms were known for supersolvable groups and the symmetric and alternating groups. No exponent one algorithms were known (even under the assumption $\omega = 2$) for families of linear groups of fixed dimension, and indeed the previous best-known algorithm for $SL_2(F_q)$ had exponent $4/3$ despite being the focus of significant effort. We unconditionally achieve exponent at most $1.19$ for this group, and exponent one if $\omega = 2$. Our algorithm also yields an improved exponent for computing the generalized DFT over general finite groups $G$, which beats the longstanding previous best upper bound, for any $\omega$. In particular, assuming $\omega = 2$, we achieve exponent $\sqrt{2}$, while the previous best was $3/2$

Dimensional verification and correction of five-axis numerically controlled milling tool paths

A system of algorithms is presented for material removal simulation, automatic dimensional verification and integrated error correction of numerically controlled (NC) milling tool paths. Several different approaches to these problems have been proposed including direct solid modeling, discrete vector intersection, and spatial partitioning. However, each of these methods suffer inherent restrictions that limit their practical application. This dissertation presents a discrete dexel NC verification algorithm based on a spatial partitioning technique (dexel representation) which incorporates the advantages of the discrete vector intersection approach. Hence, real-time animated five-axis milling simulation is supported by efficient regularized Boolean set operations, and dimensional milling errors are verified simultaneously with the simulation process. Based on intermediate dimensional verification results, a reduction of intersection volume algorithm is developed to eliminate detected gouges on the part surface. In addition, a technique for detection and elimination of unexpected collisions between the tool assembly and the workpiece is developed. These combined algorithms automatically correct tool paths to avoid gouges and collisions resulting in tool paths that are ready for immediate industrial application. A major disadvantage of dexel-based spatial partitioning, as originally proposed, is view dependency, i.e., dexels are constructed along a specific viewing vector so reconstruction of dexels is required for each new viewing direction. To overcome this problem, a contour display method is developed to transform dexel-based objects into a set of parallel planar contours thus enabling dynamic viewing transformations. In summary, this dissertation describes a unique hybrid approach to NC milling verification which provides for efficient, accurate and automatic assessment and correction of five-axis milling tool paths

Determination of image quality for added noise as a function of spatial frequency

The noise in color images which is referred to as chromatic noise represents a distribution within three spectral bands and contributes to chromatic and achromatic visual effects. The chromatic noise depends very strongly on the spatial frequency response of the visual system. Therefore, this study characterizes the variation in perceived chromatic noise level and generates the noise field to add to the color image samples. From these degraded images, we found that noise in low spatial frequencies is much more disturbing than in the medium and high spatial frequency regions. The perceived quality scales of the modulated chromatic noise images were compared to the subjective quality factor (S.Q.F.) scales. By using category analysis, this quality scale yields the S.Q.F. rating, and determines the dependence of the spatial frequency content of chromatic noise and achromatic effect

Pharmaceutical Data Protection Law and Policy and Their Effects on the Right to Medicines : a Comparative Analysis

To examine the compatibility between data protection and the right to access medicines in the current data protection regimes, this study examines the concept of data protection in current legal regimes, examine exclusive data protection regime, discusses the impact of the right to medicines on data protection regime, finally provide sound legal reform and recommendations to improve the protection of pharmaceutical data. In its entirety, this research aims at researching the protection regime of pharmaceutical data from top to bottom; therefore, this research conducts a comprehensive analysis within three dimensions of protections: first, the international dimension represented by TRIPS, second; the regional dimension represented by NAFTA, and CAFTA and other regional agreements and; third, the national dimension represented by Israel and India. Another attempt of this research is to explore the entire exceptions of data exclusivity. The research reviews the exceptions provided under Article 39.3 of the TRIPS. In addition, the compulsory license scheme is another possible ground to exclude data exclusivity although it provides under the patent regime; therefore it also examined. The thesis will explore the three major sources of WTO documents, 2001 WTO DohaDeclaration, 2003 Doha Decision and 2005 Amendment to analyze current trends and pattern of exceptions of data exclusivity, within the international as well as the national system. This research also provides an overview of human rights instruments to justify its call for the reconciliation of the protection of pharmaceuticals data with the right to health and medicines. In the last chapter, the case of Taiwan shows how a state like Taiwan is making such reconciliation a reality