Searching for incomplete self orthogonal latin squares : a targeted and parallel approach

The primary purpose of this dissertation is in the search for new methods in which to search for Incomplete Self Orthogonal Latin Squares. As such a full understanding of the structures involved must be examined, starting from basic Latin Squares. The structures will be explained and built upon in order to cover Mutually Orthogonal Latin Squares, Frame Latin Squares and Self Orthogonal Latin Squares. In addition the related structure Orthogonal Arrays, will be explained as they relate to Incomplete Self Orthogonal Latin Squares. This paper also dedicates time to explaining basic search methods and optimizations that can be done. The two search methods of focus are the backtracking algorithm and heuristic searches. In our 6nal method the two will work together to achieve an improved result. The methods currently being used to search in parallel are also provided, along with the necessary backup to there structure. The main research of this paper is focused on the search for Incomplete Self Orthogonal Squares. This is done by breaking down the problem into four separate areas of the square. By separating the blocks it enables us to work on a smaller problem while eliminating many incorrect solutions. The solution methodology is broken up into three steps and systematically solving the individual areas of the square. By taking advantage of the properties of squares to constrain our search as much as possible we succeeded in reducing the total search time significantly. Unfortunately, even with our improvement in the overall search time, no open incomplete self orthogonal latin square problems could be solved. Full results and comparisons to existing methods are provided

Patient-Specific Implants in Musculoskeletal (Orthopedic) Surgery

Most of the treatments in medicine are patient specific, aren’t they? So why should we bother with individualizing implants if we adapt our therapy to patients anyway? Looking at the neighboring field of oncologic treatment, you would not question the fact that individualization of tumor therapy with personalized antibodies has led to the thriving of this field in terms of success in patient survival and positive responses to alternatives for conventional treatments. Regarding the latest cutting-edge developments in orthopedic surgery and biotechnology, including new imaging techniques and 3D-printing of bone substitutes as well as implants, we do have an armamentarium available to stimulate the race for innovation in medicine. This Special Issue of Journal of Personalized Medicine will gather all relevant new and developed techniques already in clinical practice. Examples include the developments in revision arthroplasty and tumor (pelvic replacement) surgery to recreate individual defects, individualized implants for primary arthroplasty to establish physiological joint kinematics, and personalized implants in fracture treatment, to name but a few

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing