arXiv subjects
Publications and source records attributed to Jingwei Lu.
We prove the Virasoro constraints for the relative Gromov--Witten theory of all smooth projective effective orbifold curves, allowing relative conditions at ordinary points. The absolute Jiang--Tseng Virasoro conjecture for smooth projective effective orbifold curves follows as a corollary.
We investigate power series satisfying the exponential concentration property, and show that suitable modifications of hypergeometric series respect this property. As a geometric application, we prove that the quantum period of a Fano manifold possesses the same property, whenever the manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients.
In the classic sparsity-driven problems, the fundamental L-1 penalty method has been shown to have good performance in reconstructing signals for a wide range of problems. However this performance relies on a good choice of penalty weight which is often found from empirical experiments. We propose an algorithm called the Laplacian variational automatic relevance determination (Lap-VARD) that takes this penalty weight as a parameter of a prior Laplace distribution. Optimization of this parameter using an automatic relevance determination framework results in a balance between the sparsity and accuracy of signal reconstruction. Our algorithm is implemented in a transmission tomography model with sparsity constraint in wavelet domain.
We propose a flat, analytic, mixed-size placement algorithm ePlace-3D for three-dimension integrated circuits (3D-ICs) using nonlinear optimization. Our contributions are (1) electrostatics based 3D density function with globally uniform smoothness (2) 3D numerical solution with improved spectral formulation (3) 3D nonlinear pre-conditioner for convergence acceleration (4) interleaved 2D-3D placement for efficiency enhancement. Our placer outperforms the leading work mPL6-3D and NTUplace3-3D with 6.44% and 37.15% shorter wirelength, 9.11% and 10.27% fewer 3D vertical interconnects (VI) on average of IBM-PLACE circuits. Validation on the large-scale modern mixed-size (MMS) 3D circuits shows high performance and scalability.
We propose a flat nonlinear placement algorithm FFTPL using fast Fourier transform for density equalization. The placement instance is modeled as an electrostatic system with the analogy of density cost to the potential energy. A well-defined Poisson's equation is proposed for gradient and cost computation. Our placer outperforms state-of-the-art placers with better solution quality and efficiency.