Multiscale Visual Drilldown for the Analysis of Large Ensembles of Multi-Body Protein Complexes

When studying multi-body protein complexes, biochemists use computational tools that can suggest hundreds or thousands of their possible spatial configurations. However, it is not feasible to experimentally verify more than only a very small subset of them. In this paper, we propose a novel multiscale visual drilldown approach that was designed in tight collaboration with proteomic experts, enabling a systematic exploration of the configuration space. Our approach takes advantage of the hierarchical structure of the data - from the whole ensemble of protein complex configurations to the individual configurations, their contact interfaces, and the interacting amino acids. Our new solution is based on interactively linked 2D and 3D views for individual hierarchy levels. At each level, we offer a set of selection and filtering operations that enable the user to narrow down the number of configurations that need to be manually scrutinized. Furthermore, we offer a dedicated filter interface, which provides the users with an overview of the applied filtering operations and enables them to examine their impact on the explored ensemble. This way, we maintain the history of the exploration process and thus enable the user to return to an earlier point of the exploration. We demonstrate the effectiveness of our approach on two case studies conducted by collaborating proteomic experts.

Running-time Analysis of Ant System Algorithms with Upper-bound Comparison

Running-time analysis of ant colony optimization (ACO) is crucial for understanding the power of the algorithm in computation. This paper conducts a running-time analysis of ant system algorithms (AS) as a kind of ACO for traveling salesman problems (TSP). The authors model the AS algorithm as an absorbing Markov chain through jointly representing the best-so-far solutions and pheromone matrix as a discrete stochastic status per iteration. The running-time of AS can be evaluated by the expected first-hitting time (FHT), the least number of iterations needed to attain the global optimal solution on average. The authors derive upper bounds of the expected FHT of two classical AS algorithms (i.e., ant quantity system and ant-cycle system) for TSP. They further take regular-polygon TSP (RTSP) as a case study and obtain numerical results by calculating six RTSP instances. The RTSP is a special but real-world TSP where the constraint of triangle inequality is stringently imposed. The numerical results derived from the comparison of the running time of the two AS algorithms verify our theoretical findings.