Limiting Behavior of Delayed Sums of φ-Mixing under a Non-Identical Distribution Setup

We present an integral test to determine the limiting behavior of delayed sums under a non-identical distribution setup for φ-mixing sequence, and deduce Chover-type laws of the iterated logarithm for them. These complement and extend the results of Vasudeva and Divanji and Chen et al.

Implementing Delay Multiply and Sum Beamformer on a Hybrid CPU-GPU Platform for Medical Ultrasound Imaging Using Open MP and CUDA

Anovel beamforming algorithmnamed Delay Multiply and Sum(DMAS),which excels at enhancing the resolution and contrast of ultrasonic image,has recently been proposed.However,there are nested loops in this algorithm,so the calculation complexity is higher compared to the Delay and Sum(DAS)beamformer which is widely used in industry.Thus,we proposed a simple vector-based method to lower its complexity.The key point is to transform the nested loops into several vector operations,which can be efficiently implemented on many parallel platforms,such as Graphics Processing Units(GPUs),and multi-core Central Processing Units(CPUs).Consequently,we considered to implement this algorithm on such a platform.In order to maximize the use of computing power,we use the GPUs andmulti-core CPUs inmixture.The platform used in our test is a low cost Personal Computer(PC),where a GPU and a multi-core CPU are installed.The results show that the hybrid use of a CPU and a GPU can get a significant performance improvement in comparison with using a GPU or using amulti-core CPU alone.The performance of the hybrid system is increased by about 47%–63%compared to a single GPU.When 32 elements are used in receiving,the fame rate basically can reach 30 fps.In the best case,the frame rate can be increased to 40 fps.

A Type of General Forward-Backward Stochastic Differential Equations and Applications

The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.