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Mobile robots equipped with multiple light detection and ranging (LiDARs) and capable of recognizing their surroundings are increasing due to the minitualization and cost reduction of LiDAR. This paper proposes a target-less extrinsic calibration method of multiple LiDARs with non-overlapping field of view (FoV). The proposed method uses accumulated point clouds of floor plane and objects while in motion. It enables accurate calibration with challenging configuration of LiDARs that directed towards the floor plane, caused by biased feature values. Additionally, the method includes a noise removal module that considers the scanning pattern to address bleeding points, which are noises of significant source of error in point cloud alignment using high-density LiDARs. Evaluations through simulation demonstrate that the proposed method achieved higher accuracy extrinsic calibration with two and four LiDARs than conventional methods, regardless type of objects. Furthermore, the experiments using a real mobile robot has shown that our proposed noise removal module can eliminate noise more precisely than conventional methods, and the estimated extrinsic parameters have successfully created consistent 3D maps., Comment: 8pages, 10figures

In a recent paper [{\em F. Bernal, J. Mor\'on-Vidal and J.A. Acebr\'on, Comp.$\&$ Math. App. 146:294-308 (2023)}] an hybrid supercomputing algorithm for elliptic equations has been put forward. The idea is that the interfacial nodal solutions solve a linear system, whose coefficients are expectations of functionals of stochastic differential equations confined within patches of about subdomain size. Compared to standard substructuring techniques such as the Schur complement method for the skeleton, the hybrid approach renders an explicit and sparse shrunken matrix -- hence suitable for being substructured again. The ultimate goal is to push strong scalability beyond the state of the art, by leveraging the scope for parallelisation of stochastic calculus. Here, we present a major revamping of that framework, based on the insight of embedding the domain in a cover of overlapping circles (in two dimensions). This allows for efficient Fourier interpolation along the interfaces (now circumferences) and -- crucially -- for the evaluation of most of the interfacial system entries as the solution of small boundary value problems on a circle. This is both extremely efficient (as they can be solved in parallel and by the pseudospectral method) and free of Monte Carlo error. Stochastic numerics are only needed on the relatively few circles intersecting the domain boundary. In sum, the new formulation is significantly faster, simpler and more accurate, while retaining all of the advantageous properties of PDDSparse. Numerical experiments are included for the purpose of illustration.

Recent studies have experimentally shown that we can achieve in non-Euclidean metric space effective and efficient graph embedding, which aims to obtain the vertices' representations reflecting the graph's structure in the metric space. Specifically, graph embedding in hyperbolic space has experimentally succeeded in embedding graphs with hierarchical-tree structure, e.g., data in natural languages, social networks, and knowledge bases. However, recent theoretical analyses have shown a much higher upper bound on non-Euclidean graph embedding's generalization error than Euclidean one's, where a high generalization error indicates that the incompleteness and noise in the data can significantly damage learning performance. It implies that the existing bound cannot guarantee the success of graph embedding in non-Euclidean metric space in a practical training data size, which can prevent non-Euclidean graph embedding's application in real problems. This paper provides a novel upper bound of graph embedding's generalization error by evaluating the local Rademacher complexity of the model as a function set of the distances of representation couples. Our bound clarifies that the performance of graph embedding in non-Euclidean metric space, including hyperbolic space, is better than the existing upper bounds suggest. Specifically, our new upper bound is polynomial in the metric space's geometric radius $R$ and can be $O(\frac{1}{S})$ at the fastest, where $S$ is the training data size. Our bound is significantly tighter and faster than the existing one, which can be exponential to $R$ and $O(\frac{1}{\sqrt{S}})$ at the fastest. Specific calculations on example cases show that graph embedding in non-Euclidean metric space can outperform that in Euclidean space with much smaller training data than the existing bound has suggested.

A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver for multiple right-hand sides using block GCR method with the factorization in lower precision as a preconditioner, which achieves mixed precision arithmetic, and then the Schur complement will be factorized in higher precision. In this algorithm, essential procedure is decomposition of the matrix into a union of moderate and hard parts, which is realized by LDU-factorization in lower precision with symmetric pivoting and threshold postponing technique., Comment: 12 pages, 4 figures, submitted to proceedings of ECCOMAS Congress 2022

We address the problem of predicting when a disease will develop, i.e., medical event time (MET), from a patient's electronic health record (EHR). The MET of non-communicable diseases like diabetes is highly correlated to cumulative health conditions, more specifically, how much time the patient spent with specific health conditions in the past. The common time-series representation is indirect in extracting such information from EHR because it focuses on detailed dependencies between values in successive observations, not cumulative information. We propose a novel data representation for EHR called cumulative stay-time representation (CTR), which directly models such cumulative health conditions. We derive a trainable construction of CTR based on neural networks that has the flexibility to fit the target data and scalability to handle high-dimensional EHR. Numerical experiments using synthetic and real-world datasets demonstrate that CTR alone achieves a high prediction performance, and it enhances the performance of existing models when combined with them., Comment: To be published in IJCAI-22

Hyperbolic ordinal embedding (HOE) represents entities as points in hyperbolic space so that they agree as well as possible with given constraints in the form of entity i is more similar to entity j than to entity k. It has been experimentally shown that HOE can obtain representations of hierarchical data such as a knowledge base and a citation network effectively, owing to hyperbolic space's exponential growth property. However, its theoretical analysis has been limited to ideal noiseless settings, and its generalization error in compensation for hyperbolic space's exponential representation ability has not been guaranteed. The difficulty is that existing generalization error bound derivations for ordinal embedding based on the Gramian matrix do not work in HOE, since hyperbolic space is not inner-product space. In this paper, through our novel characterization of HOE with decomposed Lorentz Gramian matrices, we provide a generalization error bound of HOE for the first time, which is at most exponential with respect to the embedding space's radius. Our comparison between the bounds of HOE and Euclidean ordinal embedding shows that HOE's generalization error is reasonable as a cost for its exponential representation ability.

PageRank is a well-known centrality measure for the web used in search engines, representing the importance of each web page. In this paper, we follow the line of recent research on the development of distributed algorithms for computation of PageRank, where each page computes its own PageRank value by interacting with pages connected over hyperlinks. Our approach is novel in that it is based on a reinterpretation of PageRank, which leads us to a set of algorithms with exponential convergence rates. We first employ gossip-type randomization for the page selections in the update iterations. Then, the algorithms are generalized to deterministic ones, allowing simultaneous updates by multiple pages. Finally, based on these algorithms, we propose a clustering-based scheme, in which groups of pages make updates by locally interacting among themselves many times to expedite the convergence. In comparison with other existing techniques, significant advantages can be exhibited in their convergence performance, as demonstrated via numerical examples using real web data, and also in the limited amount of communication required among pages., Comment: 16 pages, 8 figures

We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence of a weak solution based on it. Furthermore, we also consider an alternating iteration method and show that it is nothing but an alternating minimizing method of the total energy. The convergence of a monolithic formulation and the alternating iteration method are numerically studied with the finite element method., Comment: 12 pages

This paper proposes a method for modeling event sequences with ambiguous timestamps, a time-discounting convolution. Unlike in ordinary time series, time intervals are not constant, small time-shifts have no significant effect, and inputting timestamps or time durations into a model is not effective. The criteria that we require for the modeling are providing robustness against time-shifts or timestamps uncertainty as well as maintaining the essential capabilities of time-series models, i.e., forgetting meaningless past information and handling infinite sequences. The proposed method handles them with a convolutional mechanism across time with specific parameterizations, which efficiently represents the event dependencies in a time-shift invariant manner while discounting the effect of past events, and a dynamic pooling mechanism, which provides robustness against the uncertainty in timestamps and enhances the time-discounting capability by dynamically changing the pooling window size. In our learning algorithm, the decaying and dynamic pooling mechanisms play critical roles in handling infinite and variable length sequences. Numerical experiments on real-world event sequences with ambiguous timestamps and ordinary time series demonstrated the advantages of our method., Comment: 18th IEEE International Conference on Data Mining (ICDM 2018)