TLA+ Proofs

TLA+ is a specification language based on standard set theory and temporal logic that has constructs for hierarchical proofs. We describe how to write TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's mutual exclusion algorithm as a simple example to describe the features of TLAPS and show how it and the Toolbox (an IDE for TLA+) help users to manage large, complex proofs.Comment: A shorter version of this article appeared in the proceedings of the conference Formal Methods 2012 (FM 2012, Paris, France, Springer LNCS 7436, pp. 147-154

ShapeFit and ShapeKick for Robust, Scalable Structure from Motion

We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers. When pairwise directions represent scaled relative positions between pairs of views (estimated for instance with epipolar geometry) our method can be used for location recovery, that is the determination of relative pose up to a single unknown scale. For this task, our method yields performance comparable to the state-of-the-art with an order of magnitude speed-up. Our proposed numerical framework is flexible in that it accommodates other approaches to location recovery and can be used to speed up other methods. These properties are demonstrated by extensively testing against state-of-the-art methods for location recovery on 13 large, irregular collections of images of real scenes in addition to simulated data with ground truth

A Realistic Model under which the Genetic Code is Optimal

The genetic code has a high level of error robustness. Using values of hydrophobicity scales as a proxy for amino acid character, and the Mean Square measure as a function quantifying error robustness, a value can be obtained for a genetic code which reflects the error robustness of that code. By comparing this value with a distribution of values belonging to codes generated by random permutations of amino acid assignments, the level of error robustness of a genetic code can be quantified. We present a calculation in which the standard genetic code is shown to be optimal. We obtain this result by (1) using recently updated values of polar requirement as input; (2) fixing seven assignments (Ile, Trp, His, Phe, Tyr, Arg, and Leu) based on aptamer considerations; and (3) using known biosynthetic relations of the 20 amino acids. This last point is reflected in an approach of subdivision (restricting the random reallocation of assignments to amino acid subgroups, the set of 20 being divided in four such subgroups). The three approaches to explain robustness of the code (specific selection for robustness, amino acid-RNA interactions leading to assignments, or a slow growth process of assignment patterns) are reexamined in light of our findings. We offer a comprehensive hypothesis, stressing the importance of biosynthetic relations, with the code evolving from an early stage with just glycine and alanine, via intermediate stages, towards 64 codons carrying todays meaning.Comment: 22 pages, 3 figures, 4 tables Journal of Molecular Evolution, July 201

Dynamics simulation of human box delivering task

Thesis (M.S.) University of Alaska Fairbanks, 2018The dynamic optimization of a box delivery motion is a complex task. The key component is to achieve an optimized motion associated with the box weight, delivering speed, and location. This thesis addresses one solution for determining the optimal delivery of a box. The delivering task is divided into five subtasks: lifting, transition step, carrying, transition step, and unloading. Each task is simulated independently with appropriate boundary conditions so that they can be stitched together to render a complete delivering task. Each task is formulated as an optimization problem. The design variables are joint angle profiles. For lifting and carrying task, the objective function is the dynamic effort. The unloading task is a byproduct of the lifting task, but done in reverse, starting with holding the box and ending with it at its final position. In contrast, for transition task, the objective function is the combination of dynamic effort and joint discomfort. The various joint parameters are analyzed consisting of joint torque, joint angles, and ground reactive forces. A viable optimization motion is generated from the simulation results. It is also empirically validated. This research holds significance for professions containing heavy box lifting and delivering tasks and would like to reduce the chance of injury.Chapter 1 Introduction -- Chapter 2 Skeletal Human Modeling -- Chapter 3 Kinematics and Dynamics -- Chapter 4 Lifting Simulation -- Chapter 5 Carrying Simulation -- Chapter 6 Delivering Simulation -- Chapter 7 Conclusion and Future Research -- Reference