Increasing power for voxel-wise genome-wide association studies : the random field theory, least square kernel machines and fast permutation procedures

Imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains. Although imaging genetics has attracted growing attention and interest, most brain-wide genome-wide association studies focus on voxel-wise single-locus approaches, without taking advantage of the spatial information in images or combining the effect of multiple genetic variants. In this paper we present a fast implementation of voxel- and cluster-wise inferences based on the random field theory to fully use the spatial information in images. The approach is combined with a multi-locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms (SNP) with imaging traits. A fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p-value estimates based on parametric tail approximation. We explored the relation between 448,294 single nucleotide polymorphisms and 18,043 genes in 31,662 voxels of the entire brain across 740 elderly subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. We find method to be more sensitive compared with voxel-wise single-locus approaches. A number of genes were identified as having significant associations with volumetric changes. The most associated gene was GRIN2B, which encodes the N-methyl-d-aspartate (NMDA) glutamate receptor NR2B subunit and affects both the parietal and temporal lobes in human brains. Its role in Alzheimer's disease has been widely acknowledged and studied, suggesting the validity of the approach. The various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains

Critical manifolds and stability in Hamiltonian systems with non-holonomic constraints

We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained Hamiltonian system, which comprises the non-holonomic mechanical system as a dynamical subsystem on an invariant manifold. The embedding system possesses a completely natural structure in the context of symplectic geometry, and using it in order to understand properties of the subsystem has compelling advantages. We discuss generic geometric and topological properties of the critical sets of both embedding and physical system, using Conley-Zehnder theory and by relating the Morse-Witten complexes of the 'free' and constrained system to one another. Furthermore, we give a qualitative discussion of the stability of motion in the vicinity of the critical set. We point out key relations to sub-Riemannian geometry, and a potential computational application.Comment: LaTeX, 52 pages. Sections 2 and 3 improved, Section 5 adde

LIO-PPF: Fast LiDAR-Inertial Odometry via Incremental Plane Pre-Fitting and Skeleton Tracking

As a crucial infrastructure of intelligent mobile robots, LiDAR-Inertial odometry (LIO) provides the basic capability of state estimation by tracking LiDAR scans. The high-accuracy tracking generally involves the kNN search, which is used with minimizing the point-to-plane distance. The cost for this, however, is maintaining a large local map and performing kNN plane fit for each point. In this work, we reduce both time and space complexity of LIO by saving these unnecessary costs. Technically, we design a plane pre-fitting (PPF) pipeline to track the basic skeleton of the 3D scene. In PPF, planes are not fitted individually for each scan, let alone for each point, but are updated incrementally as the scene 'flows'. Unlike kNN, the PPF is more robust to noisy and non-strict planes with our iterative Principal Component Analyse (iPCA) refinement. Moreover, a simple yet effective sandwich layer is introduced to eliminate false point-to-plane matches. Our method was extensively tested on a total number of 22 sequences across 5 open datasets, and evaluated in 3 existing state-of-the-art LIO systems. By contrast, LIO-PPF can consume only 36% of the original local map size to achieve up to 4x faster residual computing and 1.92x overall FPS, while maintaining the same level of accuracy. We fully open source our implementation at https://github.com/xingyuuchen/LIO-PPF.Comment: IROS 202

Synergy of stereo cloud top height and ORAC optimal estimation cloud retrieval: evaluation and application to AATSR

In this paper we evaluate the retrievals of cloud top height when stereo derived heights are combined with the radiometric cloud top heights retrieved from the ORAC (Optimal Retrieval of Aerosol and Cloud) algorithm. This is performed in a mathematically rigorous way using the ORAC optimal estimation retrieval framework, which includes the facility to use independent a priori information. Key to the use of a priori information is a characterisation of their associated uncertainty. This paper demonstrates the improvements that are possible using this approach and also considers their impact on the microphysical cloud parameters retrieved. The AATSR instrument has two views and three thermal channels so is well placed to demonstrate the synergy of the two techniques. The stereo retrieval is able to improve the accuracy of the retrieved cloud top height when compared to collocated Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), particularly in the presence of boundary layer inversions and high clouds. The impact on the microphysical properties of the cloud such as optical depth and effective radius was evaluated and found to be very small with the biggest differences occurring over bright land surfaces and for high clouds. Overall the cost of the retrievals increased indicating a poorer radiative fit of radiances to the cloud model, which currently uses a single layer cloud model. Best results and improved fit to the radiances may be obtained in the future if a multi-layer model is used