The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical scatterers. To model this, we consider two optically random media, with the second medium obtained by shifting the first medium in some local region. We derive the radiative transfer equation for the cross-correlation of the wave fields in the media. Then we derive its diffusion approximation. In both the radiative transfer and the diffusion regimes, we relate the correlation of speckle patterns to the solutions of the radiative transfer and the diffusion equations. We present numerical simulations based on our model which are in agreement with recent experimental measurements.

In this paper, we study smooth complex projective varieties X such that some exterior power ⋀^rT_X of the tangent bundle is strictly nef. We prove that such varieties are rationally connected. We also classify the following two cases. If T_X is strictly nef, then X isomorphic to the projective space P^n. If ⋀^2T_X is strictly nef and if X has dimension at least 3, then X is either isomorphic to P^n or a quadric Q^n.

The aim of this paper is to provide a fast and efficient procedure for (real-time) target identification in imaging based on matching on a dictionary of precomputed generalized polarization tensors (GPTs). The approach is based on some important properties of the GPTs and new invariants. A new shape representation is given and numerically tested in the presence of measurement noise. The stability and resolution of the proposed identification algorithm is numerically quantified. We compare the proposed GPT-based shape representation with a moment-based one.

Let (X, g) be a compact Riemannian manifold with quasi-positive Riemannian scalar curvature. If there exists a complex structure J compatible with g, then the Kodaira dimension of (X, J) is equal to −∞ and the canonical bundle KX is not pseudo-effective. We also introduce the complex Yamabe number λc(X) for compact complex manifold X, and show that if λ_c(X) is greater than 0, then κ(X) is equal to −∞; moreover, if X is also spin, then the Hirzebruch A-hat genus \hat{A}(X) is zero.

In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric ω such that (T_X,ω) is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective manifold X is rationally connected, then there exists a uniformly RC-positive complex Finsler metric on T_X .