In this paper, we consider the problem of formally verifying the safety of an autonomous robot equipped with a Neural Network (NN) controller that processes LiDAR images to produce control actions. Given a workspace that is characterized by a set of polytopic obstacles, our objective is to compute the set of safe initial conditions such that a robot trajectory starting from these initial conditions is guaranteed to avoid the obstacles. Our approach is to construct a finite state abstraction of the system and use standard reachability analysis over the finite state abstraction to compute the set of the safe initial states. The first technical problem in computing the finite state abstraction is to mathematically model the imaging function that maps the robot position to the LiDAR image. To that end, we introduce the notion of imaging-adapted sets as partitions of the workspace in which the imaging function is guaranteed to be affine. Based on this notion, and resting on efficient algorithms in the literature of computational geometry, we develop a polynomialtime algorithm to partition the workspace into imaging-adapted sets along with computing the corresponding affine imaging functions. Given this workspace partitioning, a discrete-time linear dynamics of the robot, and a pre-trained NN controller with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge is to analyze the behavior of the neural network. To that end, and thanks to the ReLU functions being piecewise linear functions, we utilize a Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible segments of different ReLUs. SMC solvers then use a Boolean satisfiability solver and a convex programming solver and decompose the problem into smaller subproblems. At each iteration, the Boolean satisfiability solver searches for a candidate assignment for the different ReLU segments while completely abstracting the robot dynamics. Convex programming is then used to check the feasibility of the proposed ReLU phases against the dynamic and imagining constraints, or generate succinct explanations for their infeasibility to reduce the search space. To accelerate this process, we develop a pre-processing algorithm that could rapidly prune the space feasible ReLU segments. Finally, we demonstrate the efficiency of the proposed algorithms using numerical simulations with increasing complexity of the neural network controller.
Quantification of left ventricular (LV) volume, ejection fraction and myocardial mass from multi-slice multi-phase cine MRI requires accurate segmentation of the LV in many images. We propose a stack attention-based convolutional neural network (CNN) approach for fully automatic segmentation from short-axis cine MR images. Methods: To extract the relevant spatiotemporal image features, we introduce two kinds of stack methods, spatial stack model and temporal stack model, combining the target image with its neighboring images as the input of a CNN. A stack attention mechanism is proposed to weigh neighboring image slices in order to extract the relevant features using the target image as a guide. Based on stack attention and standard U-Net, a novel Stack Attention U-Net (SAUN) is proposed and trained to perform the semantic segmentation task. A loss function combining cross-entropy and Dice is used to train SAUN. The performance of the proposed method was evaluated on an internal and a public dataset using technical metrics including Dice, Hausdorff distance (HD), and mean contour distance (MCD), as well as clinical parameters, including left ventricular ejection fraction (LVEF) and myocardial mass (LVM). In addition, the results of SAUN were compared to previously presented CNN methods, including U-Net and SegNet. Results: The spatial stack attention model resulted in better segmentation results than the temporal stack model. On the internal dataset comprising of 167 post-myocardial infarction patients and 57 healthy volunteers, our method achieved a mean Dice of 0.91, HD of 3.37 mm, and MCD of 1.08 mm. Evaluation on the publicly available ACDC dataset demonstrated good generalization performance, yielding a Dice of 0.92, HD of 9.4 mm, and MCD of 0.74 mm on end-diastolic images, and a Dice of 0.89, HD of 7.1 mm and MCD of 1.03 mm on end-systolic images. The Pearson correlation coefficient of LVEF and LVM between automatically and manually derived results were higher than 0.98 in both datasets. Conclusion:We developed a CNN with a stack attention mechanism to automatically segment the LV chamber and myocardium from the multi-slice short-axis cine MRI. The experimental results demonstrate that the proposed approach exceeds existing state-of-the-art segmentation methods and verify its potential clinical applicability.
Heterogeneous microprocessors integrate a CPU and GPU on the same chip, providing fast CPU-GPU communication and enabling cores to compute on data "in place." This permits exploiting a finer granularity of parallelism on the integrated GPUs, and enables the use of GPUs for accelerating more complex and irregular codes. One challenge, however, is exposing enough parallelism such that both the CPU and GPU are effectively utilized to achieve maximum gain. In this article, we propose exploiting nested parallelism for integrated CPU-GPU chips. We look for loop structures in which one or more regular data parallel loops are nested within a parallel outer loop that can contain irregular code (e.g., with control divergence). By scheduling the outer loop on multiple CPU cores, multiple dynamic instances of the inner regular loop(s) can be scheduled on the GPU cores. This boosts GPU utilization and parallelizes the outer loop. We find that such nested MIMD-SIMD parallelization provides greater levels of parallelism for integrated CPU-GPU chips, and additionally there is ample opportunity to perform such parallelization in OpenMP programs. Our results show nested MIMD-SIMD parallelization provides a 16.1x and 8.67x speedup over sequential execution on a simulator and a physical machine, respectively. Our technique beats CPU-only parallelization by 4.13x and 2.40x, respectively, and GPU-only parallelization by 2.74x and 2.26x, respectively. Compared to the next-best scheme (either CPU-or GPU-only parallelization) per benchmark, our approach provides a 1.46x and 1.23x speedup for the simulator and physical machine, respectively.
Predicting protein complexes from protein-protein interaction (PPI) network is of great significance to recognize the structure and function of cells. A protein may interact with different proteins under different time or conditions. Existing approaches only utilize static PPI network data that may lose much temporal biological information. First, this article proposed a novel method that combines gene expression data at different time points with traditional static PPI network to construct different dynamic subnetworks. Second, to further filter out the data noise, the semantic similarity based on gene ontology is regarded as the network weight together with the principal component analysis, which is introduced to deal with the weight computing by three traditional methods. Third, after building a dynamic PPI network, a predicting protein complexes algorithm based on "core-attachment" structural feature is applied to detect complexes from each dynamic subnetworks. Finally, it is revealed from the experimental results that our method proposed in this article performs well on detecting protein complexes from dynamic weighted PPI networks.
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