An Efficient Geometric Search Algorithm of Pandemic Boundary Detection

We consider a scenario where the pandemic infection rate is inversely proportional to the power of the distance between the infected region and the non-infected region. In our study, we analyze the case where the exponent of the distance is 2, which is in accordance with Reilly’s law of retail gravitation. One can test for infection but such tests are costly so one seeks to determine the region of infection while performing few tests. Our goal is to find a boundary region of minimal size that contains all infected areas. We discuss efficient algorithms and provide the asymptotic bound of the testing cost and simulation results for this problem.

FFRob: Leveraging symbolic planning for efficient task and motion planning

Mobile manipulation problems involving many objects are challenging to solve due to the high dimensionality and multi-modality of their hybrid configuration spaces. Planners that perform a purely geometric search are prohibitively slow for solving these problems because they are unable to factor the configuration space. Symbolic task planners can efficiently construct plans involving many variables but cannot represent the geometric and kinematic constraints required in manipulation. We present the FFRob algorithm for solving task and motion planning problems. First, we introduce extended action specification (EAS) as a general purpose planning representation that supports arbitrary predicates as conditions. We adapt existing heuristic search ideas for solving strips planning problems, particularly delete-relaxations, to solve EAS problem instances. We then apply the EAS representation and planners to manipulation problems resulting in FFRob. FFRob iteratively discretizes task and motion planning problems using batch sampling of manipulation primitives and a multi-query roadmap structure that can be conditionalized to evaluate reachability under different placements of movable objects. This structure enables the EAS planner to efficiently compute heuristics that incorporate geometric and kinematic planning constraints to give a tight estimate of the distance to the goal. Additionally, we show FFRob is probabilistically complete and has a finite expected runtime. Finally, we empirically demonstrate FFRob’s effectiveness on complex and diverse task and motion planning tasks including rearrangement planning and navigation among movable objects.

Finding defectives on a line by random docking and interval group tests

Suppose that some of the [Formula: see text] elements of a totally ordered structure is defective, and several repair robots are at our disposal. They can dock at a random element, move at unit speed or leave, and send each other signals if there is no defective between them. We show that, by using only two robots that obey simple rules, the defective can be localized in [Formula: see text] time, which is also optimal. A variation of our strategy needs three robots but has a more predictable behavior. The model is motivated by a conjectured DNA repair mechanism, and it combines group testing with geometric search.

An Adaptive Geometric Search Algorithm for Macromolecular Scaffold Selection

A wide variety of protein and peptidomimetic design tasks require matching functional three-dimensional motifs to potential oligomeric scaffolds. Enzyme design, for example, aims to graft active-site patterns typically consisting of 3 to 15 residues onto new protein surfaces. Identifying suitable proteins capable of scaffolding such active-site engraftment requires costly searches to identify protein folds that can provide the correct positioning of side chains to host the desired active site. Other examples of biodesign tasks that require simpler fast exact geometric searches of potential side chain positioning include mimicking binding hotspots, design of metal binding clusters and the design of modular hydrogen binding networks for specificity. In these applications the speed and scaling of geometric search limits downstream design to small patterns. Here we present an adaptive algorithm to searching for side chain take-off angles compatible with an arbitrarily specified functional pattern that enjoys substantive performance improvements over previous methods. We demonstrate this method in both genetically encoded (protein) and synthetic (peptidomimetic) design scenarios. Examples of using this method with the Rosetta framework for protein design are provided but our implementation is compatible with multiple protein design frameworks and is freely available as a set of python scripts (https://github.com/JiangTian/adaptive-geometric-search-for-protein-design).