A comprehensive heuristic analysis of the Pollard's Rho Method (PRM) is given. The analysis is based on ultimate periods and tails distribution of sequences. If $n$ is the composite number to be factored, then an improved version of PRM is developed which has an expected run time of $O(\sqrt[8]{n}\ln n)$ on a multi-core architecture which utilized a clever way of evaluating polynomials.

Mini-bioreactor systems enabling automatized operation of numerous parallel cultivations have been used to accelerate and optimize bioprocess development. As implementation of fed-batch conditions, multiple options of process control and sample analysis are possible, these systems represent valuable screening tools for large-scale production. However, the dynamic behavior of cultivations has not yet been considered regarding data evaluation and decision making during high-throughput screening in mini-bioreactors. In this study, the characterization of Saccharomyces cerevisiae AH22 secreting recombinant endopolygalacturonase is performed in 48 parallel fed-batch cultivations regarding 16 experimental conditions. Automated parallel process control, frequent sampling and analysis were implemented. Data-driven multivariate methods were developed to allow for fast, automated decision making as well as online predictive data analysis regarding endopolygalacturonase production. Using dynamic process information, a cultivation with abnormal behavior could be detected by principal component analysis as well as two clusters of similarly behaving cultivations, later classified according to the feeding rate. By decision tree analysis, cultivation conditions leading to an optimal recombinant product formation could be identified automatically. The developed method is easily adaptable and suitable for automatized process development reducing the experimental times and costs.

Autonomous driving systems are increasingly becoming a necessary trend towards building smart cities of the future. Numerous proposals have been presented in recent years to tackle particular aspects of the working pipeline towards creating a functional end-to-end system, such as object detection, tracking, path planning, sentiment or intent detection. Nevertheless, few efforts have been made to systematically compile all of these systems into a single proposal that effectively considers the real challenges these systems will have on the road, such as real-time computation, hardware capabilities, etc. This paper has reviewed various techniques towards proposing our own end-to-end autonomous vehicle system, considering the latest state on the art on computer vision, DSs, path planning, and parallelization.

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters. A higher-order scheme is used to discretize geometry of the structure as well as the relevant physical quantities. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss-Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve computational efficiency, a Chebyshev approximation approach is applied to a fast calculation of the Green function that needs evaluation thousands of times. In addition, OpenMP parallel technique is used to the formation of influence coefficient matrix, which significantly reduces CPU time. Finally, computations are performed on wave exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates good performance of the present method.

Fluidic larger-scale integration (LSI) resides at the heart of comprehensive sample-to-answer automation and parallelization of assay panels for frequent and ubiquitous bioanalytical testing in decentralized the point-of-use / point-of-care settings. This paper develops a novel “digital twin” strategy with an emphasis on rotational, centrifugo-pneumatic flow control. The underlying model systematically connects retention rates of rotationally actuated valves as a key element of LSI to experimental input parameters; for the first time, the concept of band widths in frequency space as the decisive quantity characterizing operationally robustness is introduced, a set of quantitative performance metrics guiding algorithmic optimization of disc layouts is defined, and the engineering principles of advanced, logical flow control and timing are elucidated. Overall, the digital twin enables efficient design for automating multiplexed bioassay protocols on such “Lab-on-a-Disc” (LoaD) systems featuring high packing density, reliability, configurability, modularity and manufacturability to eventually minimize cost, time and risk of development and production.