In recent years, Light Detection and Ranging (LiDAR) has been drawing extensive attention both in academia and industry because of the increasing demand for autonomous vehicles. LiDAR is believed to be the crucial sensor for autonomous driving and flying, as it can provide high-density point clouds with accurate three-dimensional information. This review presents an extensive overview of Microelectronechanical Systems (MEMS) scanning mirrors specifically for applications in LiDAR systems. MEMS mirror-based laser scanners have unrivalled advantages in terms of size, speed and cost over other types of laser scanners, making them ideal for LiDAR in a wide range of applications. A figure of merit (FoM) is defined for MEMS mirrors in LiDAR scanners in terms of aperture size, field of view (FoV) and resonant frequency. Various MEMS mirrors based on different actuation mechanisms are compared using the FoM. Finally, a preliminary assessment of off-the-shelf MEMS scanned LiDAR systems is given.
As more and more neuroanatomical data are made available through efforts such as NeuroMorpho.Org and FlyCircuit.org, the need to develop computational tools to facilitate automatic knowledge discovery from such large datasets becomes more urgent. One fundamental question is how best to compare neuron structures, for instance to organize and classify large collection of neurons. We aim to develop a flexible yet powerful framework to support comparison and classification of large collection of neuron structures efficiently. Specifically we propose to use a topological persistence-based feature vectorization framework. Existing methods to vectorize a neuron (i.e, convert a neuron to a feature vector so as to support efficient comparison and/or searching) typically rely on statistics or summaries of morphometric information, such as the average or maximum local torque angle or partition asymmetry. These simple summaries have limited power in encoding global tree structures. Based on the concept of topological persistence recently developed in the field of computational topology, we vectorize each neuron structure into a simple yet informative summary. In particular, each type of information of interest can be represented as a descriptor function defined on the neuron tree, which is then mapped to a simple persistence-signature. Our framework can encode both local and global tree structure, as well as other information of interest (electrophysiological or dynamical measures), by considering multiple descriptor functions on the neuron. The resulting persistence-based signature is potentially more informative than simple statistical summaries (such as average/mean/max) of morphometric quantities—Indeed, we show that using a certain descriptor function will give a persistence-based signature containing strictly more information than the classical Sholl analysis. At the same time, our framework retains the efficiency associated with treating neurons as points in a simple Euclidean feature space, which would be important for constructing efficient searching or indexing structures over them. We present preliminary experimental results to demonstrate the effectiveness of our persistence-based neuronal feature vectorization framework.
A new algorithm for computing a comprehensive Gröbner system of a parametric polynomial ideal over k [U ][X] is presented. This algorithm generates fewer branches (segments) compared to Suzuki and Sato's algorithm as well as Nabeshima's algorithm, resulting in considerable efficiency. As a result, the algorithm is able to compute comprehensive Gröb-ner systems of parametric polynomial ideals arising from applications which have been beyond the reach of other well known algorithms. The starting point of the new algorithm is Weispfenning's algorithm with a key insight by Suzuki and Sato who proposed computing first a Gröbner basis of an ideal over k[U, X] before performing any branches based on parametric constraints. Based on Kalkbrener's results about stability and specialization of Gröbner basis of ideals, the proposed algorithm exploits the result that along any branch in a tree corresponding to a comprehensive Gröb-ner system, it is only necessary to consider one polynomial for each nondivisible leading power product in k(U ) [X] with the condition that the product of their leading coefficients is not 0; other branches correspond to the cases where this product is 0. In addition, for dealing with a disequality parametric constraint, a probabilistic check is employed for radical membership test of an ideal of parametric constraints. This is in contrast to a general expensive check based on Rabinovitch's trick using a new variable as in Nabeshima's algorithm. The proposed algorithm has been implemented in Magma and experimented with a number of examples from different applications. Its performance (vis a vie number of branches and execution timings) has been compared with the Suzuki-Sato's algorithm and Nabeshima's speed-up algorithm. The algorithm has been successfully used to solve the famous P3P problem from computer vision.
Highlights d An integrated platform that resolves, registers, and quantifies single-neuron morphology d The pipeline facilitates high-resolution, scalable single neuron anatomy in mouse brain d Cortical axo-axonic interneurons consist of multiple morphological subtypes d AAC subtypes differ in laminar position and dendritic and axonal arborization patterns
An algorithm to generate a minimal comprehensive Gröbner basis of a parametric polynomial system from an arbitrary faithful comprehensive Gröbner system is presented. A basis of a parametric polynomial ideal is a comprehensive Gröbner basis if and only if for every specialization of parameters in a given field, the specialization of the basis is a Gröbner basis of the associated specialized polynomial ideal. The key idea used in ensuring minimality is that of a polynomial being essential with respect to a comprehensive Gröbner basis. The essentiality check is performed by determining whether a polynomial can be covered for various specializations by other polynomials in the associated branches in a comprehensive Gröbner system. The algorithm has been implemented and successfully tried on many examples from the literature. Keywordscomprehensive Gröbner basis, minimal comprehensive Gröbner basis, parametric polynomial system, specialization of polynomial systems, essentiality.
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