Stationary Map Research Articles

Coarse-to-Fine Hybrid 3D Mapping System With Co-Calibrated Omnidirectional Camera and Non-Repetitive LiDAR

This letter presents a novel 3D mapping robot with an omnidirectional field-of-view (FoV) sensor suite composed of a non-repetitive LiDAR and an omnidirectional camera. Thanks to the non-repetitive scanning nature of the LiDAR, an automatic targetless co-calibration method is proposed to simultaneously calibrate the intrinsic parameters for the omnidirectional camera and the extrinsic parameters for the camera and LiDAR, which is crucial for the required step in bringing color and texture information to the point clouds in surveying and mapping tasks. Comparisons and analyses are made to target-based intrinsic calibration and mutual information (MI)-based extrinsic calibration, respectively. With this co-calibrated sensor suite, the hybrid mapping robot integrates both the odometry-based mapping mode and stationary mapping mode. Meanwhile, we proposed a new workflow to achieve coarse-to-fine mapping, including efficient and coarse mapping in a global environment with odometry-based mapping mode; planning for viewpoints in the region-of-interest (ROI) based on the coarse map (relies on the previous work [1]); navigating to each viewpoint and performing finer and more precise stationary scanning and mapping of the ROI. The fine map is stitched with the global coarse map, which provides a more efficient and precise result than the conventional stationary approaches and the emerging odometry-based approaches, respectively.

AERO: Design Space Exploration Framework for Resource-Constrained CNN Mapping on Tile-Based Accelerators

Analog In-Memory Compute (AIMC) arrays can store weights and perform matrix-vector multiplication operations for Deep Convolutional Neural Networks (CNNs). A number of recent efforts have integrated AIMC arrays into hybrid digital-analog accelerators in a multi-layer parallel manner to achieve energy efficiency and high throughput. Multi-layer parallelism on large-scale tile-based architectures need efficient mapping support at the processing element (PE)-level ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , digital or analog processing elements) and tile-level. To find the most efficient architectures, fast and accurate design space exploration (DSE) support is required. In this paper, a novel DSE framework, AERO, is presented to characterize a CNN inference workload executing on hybrid tile-based architectures that supports multi-layer parallelism. Three characteristics can be seen in our DSE framework: (1) It presents a hierarchical Tile/PE-level mapping exploration strategy including inter-layer interaction, and allowing layer fusion/splitting configurations for PE-level mapping optimization. (2) It unlocks different Performance, Power and Area (PPA) exploration points under both sufficient and limited resource constraints, while limited resource case is not considered in prior works of multi-layer parallel architectures. The impact of weight loading and weight stationary mapping are analyzed for better insights into hybrid tile-based architectures. (3) It incorporates a detailed PPA model that supports a broad range of hybrid digital and analog units in a tile. Experimental case-studies are performed for realistic and relevant benchmarks such as MLP, CNNs (Lenet-5, Resnet-18,-34,-50 and −101).

Stationary Mapping Based Generalized Monitoring Scheme for Industrial Processes With Mixed Operational Stages

Stationary Mapping Based Generalized Monitoring Scheme for Industrial Processes With Mixed Operational Stages

Chaos in conservative discrete-time systems subjected to parameter drift.

Based on the example of a paradigmatic area preserving low-dimensional mapping subjected to different scenarios of parameter drifts, we illustrate that the dynamics can best be understood by following ensembles of initial conditions corresponding to the tori of the initial system. When such ensembles are followed, snapshot tori are obtained, which change their location and shape. Within a time-dependent snapshot chaotic sea, we demonstrate the existence of snapshot stable and unstable foliations. Two easily visualizable conditions for torus breakup are found: one in relation to a discontinuity of the map and the other to a specific snapshot stable manifold, indicating that points of the torus are going to become subjected to strong stretching. In a more general setup, the latter can be formulated in terms of the so-called stable pseudo-foliation, which is shown to be able to extend beyond the instantaneous chaotic sea. The average distance of nearby point pairs initiated on an original torus crosses over into an exponential growth when the snapshot torus breaks up according to the second condition. As a consequence of the strongly non-monotonous change of phase portraits in maps, the exponential regime is found to split up into shorter periods characterized by different finite-time Lyapunov exponents. In scenarios with plateau ending, the divided phase space of the plateau might lead to the Lyapunov exponent averaged over the ensemble of a torus being much smaller than that of the stationary map of the plateau.

The Stationary Point Set Map in General Parametric Optimization Problems

The present paper shows how the linear independence constraint qualification (LICQ) can be combined with some conditions put on the first-order and second-order derivatives of the objective function and the constraint functions to ensure the Robinson stability and the Lipschitz-like property of the stationary point set map of a general C2-smooth parametric constrained optimization problem. So, a part of the results in two preceding papers of the authors [J. Optim. Theory Appl. 180 (2019), 91–116 (Part 1); 117–139 (Part 2)], which were obtained for a problem with just one inequality constraint, now has an adequate extension for problems having finitely many equality and inequality constraints. Our main tool is an estimate of B. S. Mordukhovich and R. T. Rockafellar [SIAM J. Optim. 22 (2012), 953–986; Theorem 3.3] for a second-order partial subdifferential of a composite function. The obtained results are illustrated by three examples.

Characterizations of local upper Lipschitz property of perturbed solutions to nonlinear second-order cone programs

We characterize the local upper Lipschitz property of the stationary point mapping and the Karush–Kuhn–Tucker (KKT) mapping for a nonlinear second-order cone programming problem using the graphical derivative criterion. We demonstrate that the second-order sufficient condition and the strict constraint qualification are sufficient for the local upper Lipschitz property of the stationary point mapping and are both sufficient and necessary for the local upper Lipschitz property of the KKT mapping.

Multi-directional adjacent wave subtraction and shifted time point mapping algorithms and their application to defect visualization in a space tank liner

We propose the multi-directional adjacent wave subtraction (MAWS), shifted time point (STP) mapping and variable time window amplitude (VTWA) mapping algorithms for crack visualization based on our finding that the processing direction of the adjacent wave subtraction with respect to crack orientation can dramatically affect crack visibility. The proposed MAWS, STP and VTWA mapping algorithms were implemented in a laser ultrasonic propagation imaging system and were applied in a nondestructive evaluation of an Al-alloy tank liner for space applications. A crack and void on the fusion zone of a weld were more effectively visualized using the proposed algorithms, and the crack could be visualized regardless of its orientation. The multi-directional processing results of the anomalous wave propagation imaging were visualized as video clips. The STP mapping algorithm, which maps the number of shifted time points to minimize the difference between adjacent waves, was developed to enhance the crack visualization capability of the system. Additionally, the multi-directional VTWA mapping algorithm performed data projection using the residuals of MAWS processing and provided stationary mapping results of crack-induced anomalous waves. The presented results demonstrate that the proposed visualization algorithms are promising techniques that do not overlook unknown crack orientations.

A Hölder continuity of symphonic maps into the spheres

In the paper Nakauchi and Takenaka (Ric Mat 60:219–235, 2011) the second author introduced a stationary map for the functional of the \(L^2\)-norm of the pullbacks of metrics. We call it a symphonic map. In our previous paper Misawa and Nakauchi (Nonlinear Anal 75:5971–5974, 2012), we verify a Holder continuity of locally minimizing symphonic maps into the Euclidean space. In this paper we show a Holder continuity of symphonic maps from domains of \(\mathbb {R}^4\) into the spheres.

Harmonic maps from Riemann surfaces into complex Finsler manifolds

Given a smooth map from a compact Riemann surface to a complex manifold equipped with a strongly pseudoconvex complex Finsler metric, we define the [Formula: see text]-energy of the map, whose absolute minimum is attained by a holomorphic map. A harmonic map is then defined to be a stationary map of the [Formula: see text]-energy functional. We prove that with each harmonic map is associated a holomorphic quadratic differential on the domain, which vanishes if the map is weakly conformal. Also, under the condition that the metric be weakly Kähler, we determine the second variation of the functional, and prove that any [Formula: see text]-energy minimizing harmonic map from the Riemann sphere to a weakly Kähler Finsler manifold of positive curvature is either holomorphic or anti-holomorphic.

Математические основы теории познания на основе экспериментов

В статье рассматриваются математические предпосылки для разработки теории познания, использующей информацию о реальных экспериментах, проводимых над реальными объектами с помощью формально-технологических аналогов машин Тьюринга. Такие аналоги, получившие название «универсальных синтезаторов-анализаторов объектов», теоретически позволяют выполнять синтез и анализ самых разнообразных конструкций (в том числе объектов, полученных путем соединения конечного числа исходных более мелких объектов, так называемых элементов базы) по различным алгоритмам в рамках некоторых ограничений, накладываемых алгоритмическими системами, названными формальными технологиями. Эти алгоритмические системы оказываются весьма близкими по своей формальной структуре и сути к структурам алгебраических систем Мальцева. Формальная близость таких алгоритмических систем позволяет, во-первых, выдвинуть гипотезу об алгоритмической основе практически всех окружающих нас понятных или непонятных (пока) нам физических процессов, что в какой-то степени объясняет широкую применимость математики к объяснению самых различных особенностей окружающего нас мира; во-вторых, она же позволяет сформулировать и доказать ряд теорем (называемых утверждениями), касающихся особенностей и ключевых характеристик алгоритмов познания в одномерных, двухмерных и трехмерных средах для различных формальных технологических систем, включая так называемую «теорему об эффективности накопленных знаний». Теорема (утверждение) оказывается применимой к очень широкому классу технологий, использующих в качестве операции анализа предикат равенства двух объектов. В статье приводятся и доказываются утверждения о существовании алгоритмов познания с различными наборами технологических операций типа синтеза и декомпозиции, а также с различными наборами операций анализа, включая предикат равенства, операцию «случайного стационарного отображения» (механизм действия которой неизвестен, а потому близок к концепции оракулов в машинах Тьюринга), операции определения формы объектов и др. Приводится структура соответствующего автоматически действующего устройства, названного «познавателем».

Symphonic join of maps between the spheres

In the previous papers Nakauchi and Takenaka (2011) and Kawai and Nakauchi (2011), the first author introduced a stationary map for the functional of L2-norm of pullbacks of metrics. We call it a symphonic map. In this paper using the argument of Xu and Yang (1993) (see also Smith (1975) and Ding (1988)), we give a notion of the symphonic join of two symphonic maps between the standard spheres.

Soil Moisture Assessment over an Alpine Hillslope with Significant Soil Heterogeneity

We strive to assess soil water content on a well‐studied slow‐moving hillslope in Austria. In doing so, we employ time lapse mapping of bulk electrical conductivity using a geophysical electromagnetic induction system operated at low induction numbers. This information is complemented by the acquisition of soil samples for gravimetric water content analysis during one survey campaign. Simple visual soil sample analysis reveals that the upper material in the survey area is a spatially highly variable mixture of predominately sandy, silty, clayey and organic materials. Due to this heterogeneity, classical approaches of mapping soil moisture on the basis of stationary mapping of electrical conductivity variations are not successful. Also the time‐lapse approach does not allow ruling out some of the ambiguity inherent to the linkage of bulk electrical conductivity to soil water content. However, indication is found that time‐lapse measurements may have supportive capabilities to identify regions of low precipitation infiltration due to high soil saturation. Furthermore, the relationship between the mean electrical conductivity averaged over a full vegetation period and an already available ecological moisture map produced by vegetation analysis is found to resemble closely the relationship observed between gravimetric soil water content and electrical conductivity during the time of sample collection except for highly organic soils. This leads us to the assumption that the relative soil moisture distribution is temporarily stable except for those areas characterized by highly organic soils.

A Hölder continuity of minimizing symphonic maps

In the paper Nakauchi and Takenaka (2011) [3] the second author introduced a stationary map for the functional of the L2-norm of the pullbacks of metrics. We call it a symphonic map. In this paper, using Morrey’s argument, we give a regularity of (locally) minimizing symphonic maps into the Euclidean space.

Stationary map coloring

Nous etudions un processus de Poisson planaire et sa partition de Voronoi associee. Nous montrons qu’il existe une coloration a six couleurs de cette partition satisfaisant les deux proprietes suivantes : la coloration est une fonction deterministe du processus de Poisson. Par ailleurs, elle commute avec les isometries du plan. Une partie de la preuve consiste a montrer que le “6-core” de la triangulation de Delaunay associee est vide. Des generalisations, extensions et problemes ouverts sont discutes.

Connectivity analysis of one-dimensional ad-hoc networks

Application and communication protocols in dynamic ad-hoc networks are exposed to physical limitations imposed by the connectivity relations that result from mobility. Motivated by vehicular freeway scenarios, this paper analyzes a number of important connectivity metrics for instantaneous snapshots of stochastic geographic movement patterns: (1) The single-hop connectivity number, corresponding to the number of single-hop neighbors of a mobile node; (2) the multi-hop connectivity number, expressing the number of nodes reachable via multi-hop paths of arbitrary hop-count; (3) the connectivity distance, expressing the geographic distance that a message can be propagated in the network on multi-hop paths; (4) the connectivity hops, which corresponds to the number of hops that are necessary to reach all nodes in the connected network. The paper develops analytic expressions for the distributions and moments of these random variables for general stationary MAP processes on a one dimensional space. The numerical results compare bursty vehicular traffic with independent movement scenarios described by a Poisson process, illustrate in examples the impact of a random communication range, and demonstrate the usefulness of MAP processes via comparison with vehicular simulation traces.

Invariant colorings of random planar maps

AbstractWe show that every locally finite random graph embedded in the plane with an isometry-invariant distribution can be five-colored in an invariant and deterministic way, under some non-triviality assumption and a mild assumption on the tail of edge lengths. The assumptions hold for any Voronoi map on a point process that has no non-trivial symmetries almost surely, hence we improve and generalize previous results on six-coloring the Voronoi map on a Poisson point process (see Angel, Benjamini, Gurel-Gurevich, Mayerovitch and Peled [Stationary map coloring. Preprint, 2008]).

THE ENTROPY OF STATIONARY SOLUTIONS' MAP OF CELLULAR NEURAL NETWORKS

In this paper, the entropy of the stationary solutions' map of one-dimensional Cellular Neural Networks with threshold is restudied. Under certain parameters, the map is topological conjugate to a Beruonulli shift of certain symbolic space. Further, the topological entropy of the map can be obtained explicitly as a spacial devil-staircase function.

A weighted Poincar� inequality and removable singularities for harmonic maps

We give a sufficient condition on a closed subset Σ⊂Rn for the weighted Poincare inequality (1.5) below to be valid. As an application, we prove that, for any 2≤p<n and any such closed subset Σ⊂Rn, if u∈C1(Ω ∖ Σ, N) ∩ W1,p (Ω, N) is a stationary p-harmonic map such that ∫Ω|Du|p(x) dx is sufficiently small, then u∈C1(Ω, N). This extends previously known removal singularity theorems for p-harmonic maps.

Control of electron transfer in disordered DNA under the impact of viscous damping and an external periodic field

We investigate the influence of energetic disorder, viscous damping and an external field on the electron transfer (ET) in DNA. The double helix structure of the λ-form of DNA is modeled by a steric oscillator network. In the context of the base-pair picture two different kinds of modes representing twist motions of the base pairs and H-bond distortions are coupled to the electron amplitude. Through the nonlinear interaction between the electronic and the vibrational degrees of freedom localized stationary states in the form of standing electron-vibron breathers are produced which we derive with a stationary map method. We show that in the presence of additional energetic disorder the degree of localization of such breathers is enhanced. It is demonstrated how an applied electric field initiates the long-range coherent motion of breathers along the bases of a DNA strand. These moving electron-vibron breathers, absorbing energy from the applied field, sustain energetic losses due to the viscous friction caused by the aqueous solvent as well as the impact of a moderate amount of energetic disorder. Moreover, it is illustrated that with the choice of the amplitude and frequency of the external field, the breather can be steered to a desired lattice position achieving control of the ET.

全方位視覚センサを用いたロバストな環境マップ生成と自己位置推定

Generation of a stationary environmental map is one of important tasks for robot navigation. Under the assumption of a known motion of a robot, environmental maps of a real scene are successfully generated by monitoring azimuth changes in an image. However, it is difficult to observe the exact motion parameters of the robot because of measurement error of the encoder of the robot. Therefore, observational errors in the generated environmental map accumulated in long movements of the robot. Furthermore, the exact stationary map generation is difficult because of ambiguity of correspondence caused by occlusion.In this paper, we propose a method to generate a stationary environmental map and estimate the egomotion of a robot, recursively, by using an omnidirectional image sensor. And the method can find mismatching and bring to right correspondence by evaluating estimation error of each objects location.