We consider combining multiple biomarkers to improve diagnostic accuracy. Su and Liu derived the linear combinations that maximize the area under the receiver operating characteristic (ROC) curves. These linear combinations, however, may have unsatisfactory low sensitivity over a certain range of desired specificity. In this paper, we consider maximizing sensitivity over a range of specificity. We first present a simpler proof for Su and Liu's main theorem and further investigate some other optimal properties of their linear combinations. We then derive alternative linear combinations that have higher sensitivity over a range of high (or low) specificity. The methods are illustrated using data from a study evaluating biomarkers for coronary heart disease.

Summary With advanced information technologies and industrial intelligence, Industry 4.0 has been witnessing a large scale digital transformation. Intelligent transportation plays an important role in the new era and the classic vehicle routing problem (VRP), which is a typical problem in providing intelligent transportation, has been drawing more attention in recent years. In this article, we study multidepot VRP (MDVRP) that considers the management of the vehicles and the optimization of the routes among multiple depots, making the VRP variant more meaningful. In addressing the time efficiency and depot cooperation challenges, we apply the artificial bee colony (ABC) algorithm to the MDVRP. To begin with, we degrade MDVRP to single‐depot VRP by introducing depot clustering. Then we modify the ABC algorithm for single‐depot VRP to generate solutions for each depot. Finally, we propose a coevolution strategy in depot combination to generate a complete solution of the MDVRP. We conduct extensive experiments with different parameters and compare our algorithm with a greedy algorithm and a genetic algorithm (GA). The results show that the ABC algorithm has a good performance and achieve up to 70% advantage over the greedy algorithm and 3% advantage over the GA.

Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process, under the assumption that the process has bounded information loss and induces causal dependencies whose strength is above a fixed (but otherwise arbitrary) threshold. Our method is based on a quantum algorithm whose complexity scales polynomially in the total number of input/output systems, in the dimension of the systems involved in each interaction, and in the inverse of the chosen threshold for the strength of the causal dependencies. Under additional assumptions, we also provide a second algorithm that has lower complexity and requires only local state preparation and local measurements. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography. Similarly, they can be used to identify useful communication channels in quantum networks, and to test the internal structure of uncharacterized quantum circuits.

This paper attempts to develop an efficient route planning algorithm to guide the operations of the multi-helicopter search and rescue in emergency. Route planning model of multi-helicopter cooperative search and rescue activity was established first, based on preference ordering of search and rescue objectives, as well as behavioral model of rescue helicopter and on-board detector. Given the route planning model, a multi-helicopter search and rescue route planning general algorithm was developed. The operation mechanism of ant colony algorithm was improved by introducing cooperative modes and the pheromone updating mechanism into existing methods. Furthermore, two cooperative search and rescue modes were studied: one is Overall Cooperative Search and Rescue Mode (OCSARM), in which many ants search and rescue the same region all together; the other is Blocking Cooperative Search and Rescue Mode (BCSARM), which partitions the region into small blocks and appoints helicopter with corresponding performance capabilities. Simulated experiments were developed to test the operability of proposed multi-helicopter search and rescue route planning algorithm. The comparison with existing algorithm shows that the algorithm proposed in this paper reduces computational complexity and evidently enhances algorithm efficiency. Results also indicate that this algorithm not only has the capability of comparing efficiency of two search and rescue modes in different mission requirements but also helps select search and rescue modes before rescue operation.