6 research outputs found
Myhill's work in recursion theory
AbstractIn this paper we discuss the following contributions to recursion theory made by John Myhill: (1) two sets are recursively isomorphic iff they are one-one equivalent; (2) two sets are recursively isomorphic iff they are recursively equivalent and their complements are also recursively equivalent; (3) every two creative sets are recursively isomorphic; (4) the recursive analogue of the Cantor–Bernstein theorem; (5) the notion of a combinatorial function and its use in the theory of recursive equivalence types
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
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