PI-BA Bundle Adjustment Acceleration on Embedded FPGAs with Co-observation Optimization

Bundle adjustment (BA) is a fundamental optimization technique used in many crucial applications, including 3D scene reconstruction, robotic localization, camera calibration, autonomous driving, space exploration, street view map generation etc. Essentially, BA is a joint non-linear optimization problem, and one which can consume a significant amount of time and power, especially for large optimization problems. Previous approaches of optimizing BA performance heavily rely on parallel processing or distributed computing, which trade higher power consumption for higher performance. In this paper we propose {\pi}-BA, the first hardware-software co-designed BA engine on an embedded FPGA-SoC that exploits custom hardware for higher performance and power efficiency. Specifically, based on our key observation that not all points appear on all images in a BA problem, we designed and implemented a Co-Observation Optimization technique to accelerate BA operations with optimized usage of memory and computation resources. Experimental results confirm that {\pi}-BA outperforms the existing software implementations in terms of performance and power consumption.Comment: in Proceedings of IEEE FCCM 201

Polarization modes of gravitational waves in generalized Proca theory

In this paper, we study polarization modes of gravitational waves in generalized Proca theory in the homogeneous and isotropic Minkowski background. The results show that the polarizations of gravitational waves depend on the parameter space of this gravity theory and can be divided into quite rich cases by parameters. In some parameter space, it only allows two tensor modes, i.e., the $+$ and $\times$ modes. In some parameter space, besides tensor modes, it also allows one scalar mode, or two vector (vector-$x$ and vector-$y$) modes, or both one scalar mode and two vector modes. The scalar mode is a mixture mode of a breathing mode and a longitudinal mode, or just a pure breathing mode. Interestingly, it is found that the amplitude of the vector modes is related to the speed of the tensor modes. This allows us to give the upper bound of the amplitude of the vector modes by detecting the speed of the tensor modes. Specifically, if the speed of tensor modes is strictly equal to the speed of light, then the amplitude of vector modes is zero.Comment: v2: 28 pages, 1 figure, 2 tables, improved versio

Polarization modes of gravitational waves in general modified gravity: General metric theory and general scalar-tensor theory

In this paper, we establish a unified parameterized framework for analyzing the polarization modes of gravitational waves in the general metric theory (gravity is only described by the metric) and the general scalar-tensor theory (gravity is described by the metric and an additional scalar field). Specifically, we study the polarization modes of gravitational waves in the most general metric theory and general scalar-tensor theory that satisfy the following conditions: (1) Spacetime is four-dimensional; (2) The theory satisfies the principle of least action; (3) The theory is generally covariant; (4) The action describing a free particle is $\int ds$. We find that the polarization modes of gravitational waves in the theory satisfying the above conditions depends on the selection of parameters in the framework, and the theory allows for up to all six polarization modes. Once we have established our framework, the analysis of the polarization modes of gravitational waves in specific theories will depend on determining the corresponding parameters within our framework. In our analysis, we also find that the polarization modes of gravitational waves in the general metric theory and the general scalar-tensor theory that satisfy the conditions also have some interesting universal properties.Comment: v3: 38 pages, 1 figure, 2 tables, typos correcte

Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

The paper by Liu (2010) introduces a method termed the canonical least-squares Monte Carlo (CLM) which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX) puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities