Recovery and Characterization of Orbital Angular Momentum Modes with Ghost Diffraction Holography

Orbital angular momentum (OAM) of optical vortex beams has been regarded as an independent physical dimension of light with predominant information-carrying potential. However, the presence of scattering environment and turbulent atmosphere scrambles the helical wavefront and destroys the orthogonality of modes in vortex beam propagation. Here, we propose and experimentally demonstrate a new basis for the recovery of the OAM mode using a holographic ghost diffraction scheme. The technique utilizes the speckle field generated from a rotating diffuser for optical vortex mode encoding, and the fourth-order correlation of the speckle field for the efficient recovery of the associated modes. Furthermore, we successfully demonstrate the complex-field recovery of OAM modes by the adoption of a holography scheme in combination with the ghost diffraction system. We evaluate the feasibility of the approach by simulation and followed by experimental demonstration for the recovery of various sequentially encoded OAM modes. Finally, the efficacy of the recovered modes was quantitatively analyzed by an OAM mode analysis utilizing orthogonal projection scheme.

RPnet: A Reverse Projection Based Neural Network for Coarse-graining Metastable Conformational States for Protein Dynamics

Markov State Model (MSM) is a powerful tool for modeling the long timescale dynamics based on numerous short molecular dynamics (MD) simulation trajectories, which makes it a useful tool for elucidating the conformational changes of biological macromolecules. By partitioning the phase space into discretized states and estimate the probabilities of inter-state transitions based on short MD trajectories, one can construct a kinetic network model that could be used to extrapolate long time kinetics if the Markovian condition is met. However, meeting the Markovian condition often requires hundreds or even thousands of states (microstates), which greatly hinders the comprehension of conformational dynamics of complex biomolecules. Kinetic lumping algorithms can coarse grain numerous microstates into a handful of metastable states (macrostates), which would greatly facilitate the elucidation of biological mechanisms. In this work, we have developed a reverse projection based neural network (RPnet) method to lump microstates into macrostates, by making use of a physics-based loss function based on the projection operator framework of conformational dynamics. By recognizing that microstate and macrostate transition modes can be related through a projection process, we have developed a reverse projection scheme to directly compare the microstate and macrostate dynamics. Based on this reverse projection scheme, we designed a loss function that allows effectively assess the quality of a given kinetic lumping. We then make use of a neural network to efficiently minimize this loss function to obtain an optimized set of macrostates. We have demonstrated the power of our RPnet in analyzing the dynamics of a numerical 2D potential, alanine dipeptide, and the clamp opening of an RNA polymerase. In all these systems, we have illustrated that our method could yield comparable or better results than competing methods in terms of state partitioning and reproduction of slow dynamics. We expect that our RPnet holds promise in analyzing conformational dynamics of biological macromolecules.

Existence of solutions for functional boundary value problems at resonance on the half-line

By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.