STOCHASTIC FLOWS OF MAPPINGS

In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.

A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system

We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.

Molecular phylogeny,biogeography and character evolution of the montane genus Incarvillea Juss.(Bignoniaceae)

The complex orogeny of the Himalaya and the Qinghai-Tibet Plateau(QTP)fosters habitat fragmentation that drives morphological differentiation of mountain plant species.Consequently,determining phylogenetic relationships between plant subgenera using morphological characters is unreliable.Therefore,we used both molecular phylogeny and historical biogeographic analysis to infer the ancestral states of several vegetative and reproductive characters of the montane genus Incarvillea.We determined the taxonomic position of the genus Incarvillea within its family and inferred the biogeographical origin of taxa through Bayesian inference(BI),maximum likelihood(ML)and maximum parsimony(MP)analyses using three molecular data sets(trnL-trnF sequences,nr ITS sequences,and a data set of combined sequences)derived from 81%of the total species of the genus Incarvillea.Within the genus-level phylogenetic framework,we examined the character evolution of 10 key morphological characters,and inferred the ancestral area and biogeographical history of the genus.Our analyses revealed that the genus Incarvillea is monophyletic and originated in Central Asia during mid-Oligocene ca.29.42 Ma.The earliest diverging lineages were subsequently split into theWestern Himalaya and Sino-Himalaya during the early Miocene ca.21.12 Ma.These lineages resulted in five re-circumscribed subgenera(Amphicome,Olgaea,Niedzwedzkia,Incarvillea,and Pteroscleris).Moreover,character mapping revealed the ancestral character states of the genus Incarvillea(e.g.,suffruticose habit,cylindrical capsule shape,subligneous capsule texture,absence of capsule wing,and loculicidal capsule dehiscence)that are retained at the earliest diverging ancestral nodes across the genus.Our phylogenetic tree of the genus Incarvillea differs from previously proposed phylogenies,thereby recommending the placement of the subgenus Niedzwedzkia close to the subgenus Incarvillea and maintaining two main divergent lineages.

Adaptive sampling for generalized probabilistic roadmaps

In this paper, an adaptive sampling strategy is presented for the generalized sampling-based motion plan- ner, generalized probabilistic roadmap （GPRM）. These planners are designed to account for stochastic map and model uncertainty and provide a feedback solution to the motion planning problem. Intelligently sampling in this framework can result in large speedups when compared to naive uniform sampling. By using the information of transition probabilities, encoded in these generalized planners, the proposed strategy biases sampling to improve the efficiency of sampling, and increase the overall success probability of GPRM. The strategy is used to solve the motion planning problem of a fully actuated point robot and a 3-DOF fixed-base manipulator on several maps of varying difficulty levels, and results show that the strategy helps solve the problem efficiently, while simultaneously increasing the success probability of the solution. Results also indicate that these rewards increase with an increase in map complexity.

Denoising Stochastic Progressive Photon Mapping Renderings Using a Multi-Residual Network

Stochastic progressive photon mapping(SPPM)is one of the important global illumination methods in computer graphics.It can simulate caustics and specular-diffuse-specular lighting effects efficiently.However,as a biased method,it always suffers from both bias and variance with limited iterations,and the bias and the variance bring multi-scale noises into SPPM renderings.Recent learning-based methods have shown great advantages on denoising unbiased Monte Carlo(MC)methods,but have not been leveraged for biased ones.In this paper,we present the first learning-based method specially designed for denoising-biased SPPM renderings.Firstly,to avoid conflicting denoising constraints,the radiance of final images is decomposed into two components:caustic and global.These two components are then denoised separately via a two-network framework.In each network,we employ a novel multi-residual block with two sizes of filters,which significantly improves the model’s capabilities,and makes it more suitable for multi-scale noises on both low-frequency and high-frequency areas.We also present a series of photon-related auxiliary features,to better handle noises while preserving illumination details,especially caustics.Compared with other state-of-the-art learning-based denoising methods that we apply to this problem,our method shows a higher denoising quality,which could efficiently denoise multi-scale noises while keeping sharp illuminations.