Quasinonlocal coupling of nonlocal diffusions

We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with respect to the energy norms induced by the nonlocal diffusion kernels as well as the $L^2$ norm, and it satisfies the maximum principle. A finite difference approximation is used to discretize the coupled system, which inherits the property from the continuous formulation. Furthermore, we design a numerical example which shows the discrepancy between the fully nonlocal and fully local diffusions, whereas the result of the coupled diffusion agrees with that of the fully nonlocal diffusion.Comment: 28 pages, 3 figures, ams.or

Face recognition technologies for evidential evaluation of video traces

Human recognition from video traces is an important task in forensic investigations and evidence evaluations. Compared with other biometric traits, face is one of the most popularly used modalities for human recognition due to the fact that its collection is non-intrusive and requires less cooperation from the subjects. Moreover, face images taken at a long distance can still provide reasonable resolution, while most biometric modalities, such as iris and fingerprint, do not have this merit. In this chapter, we discuss automatic face recognition technologies for evidential evaluations of video traces. We first introduce the general concepts in both forensic and automatic face recognition , then analyse the difficulties in face recognition from videos . We summarise and categorise the approaches for handling different uncontrollable factors in difficult recognition conditions. Finally we discuss some challenges and trends in face recognition research in both forensics and biometrics . Given its merits tested in many deployed systems and great potential in other emerging applications, considerable research and development efforts are expected to be devoted in face recognition in the near future

Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism

The Mori–Zwanzig formalism is applied to derive an equation for the evolution of linear observables of the overdamped Langevin equation. To illustrate the resulting equation and its use in deriving approximate models, a particular benchmark example is studied both numerically and via a formal asymptotic expansion. The example considered demonstrates the importance of memory effects in determining the correct temporal behaviour of such systems

Positive definiteness of the blended force-based quasicontinuum method

The development of consistent and stable quasicontinuum models for multidimensional crystalline solids remains a challenge. For example, proving the stability of the force-based quasicontinuum (QCF) model [M. Dobson and M. Luskin, M2AN Math. Model. Numer. Anal., 42 (2008), pp. 113--139] remains an open problem. In one and two dimensions, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width

Positive definiteness of the blended force-based quasicontinuum method

The development of consistent and stable quasicontinuum models for multidimensional crystalline solids remains a challenge. For example, proving the stability of the force-based quasicontinuum (QCF) model [M. Dobson and M. Luskin, M2AN Math. Model. Numer. Anal., 42 (2008), pp. 113--139] remains an open problem. In one and two dimensions, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width