Journal articles: 'Spatial and geometric constraints'

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Campeotto, F., A. Dal Palù, A. Dovier, F. Fioretto, and E. Pontelli. "A Constraint Solver for Flexible Protein Model." Journal of Artificial Intelligence Research 48 (December 30, 2013): 953–1000. http://dx.doi.org/10.1613/jair.4193.

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This paper proposes the formalization and implementation of a novel class of constraints aimed at modeling problems related to placement of multi-body systems in the 3-dimensional space. Each multi-body is a system composed of body elements, connected by joint relationships and constrained by geometric properties. The emphasis of this investigation is the use of multi-body systems to model native conformations of protein structures---where each body represents an entity of the protein (e.g., an amino acid, a small peptide) and the geometric constraints are related to the spatial properties of the composing atoms. The paper explores the use of the proposed class of constraints to support a variety of different structural analysis of proteins, such as loop modeling and structure prediction. The declarative nature of a constraint-based encoding provides elaboration tolerance and the ability to make use of any additional knowledge in the analysis studies. The filtering capabilities of the proposed constraints also allow to control the number of representative solutions that are withdrawn from the conformational space of the protein, by means of criteria driven by uniform distribution sampling principles. In this scenario it is possible to select the desired degree of precision and/or number of solutions. The filtering component automatically excludes configurations that violate the spatial and geometric properties of the composing multi-body system. The paper illustrates the implementation of a constraint solver based on the multi-body perspective and its empirical evaluation on protein structure analysis problems.

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Wu, Chi-haur, and Chi-cheng Jou. "Design of a Controlled Spatial Curve Trajectory for Robot Manipulations." Journal of Dynamic Systems, Measurement, and Control 113, no. 2 (June 1, 1991): 248–58. http://dx.doi.org/10.1115/1.2896372.

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For integrating different constraints from robot’s tasks, such as geometry, kinematics, and dynamics, with trajectory planning and robot motion control, a two-layer robot trajectory planning structure is proposed. The structure decomposes the trajectory planning problem into path geometry planning and motion speed planning. By separating speed planning from path geometry planning, two different problems can be solved. The first problem is to incorporate geometric changes of a robot task into both translational and orientational path plannings. By solving it, various spatial curve paths can be planned and the difficulty of predicting rotational motions in the Cartesian space can be removed. The second problem is to incorporate motion constraints into the trajectory planning, such as the constraint of maintaining a desired constant robot speed along any planned geometric path. Through the proposed structure, different robot motion requirements along various spatial curves can be controlled by different speed control functions. To demonstrate the proposed scheme, examples are given.

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Wang, Yao, Shixing Yang, Tao Zhou, and Na Li. "Geometric Optimization of Distributed MIMO Radar Systems With Spatial Distance Constraints." IEEE Access 8 (2020): 199227–41. http://dx.doi.org/10.1109/access.2020.3034591.

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Rosenberg, S. S., E. E. Kelland, E. Tokar, A. R. De La Torre, and J. R. Chan. "The geometric and spatial constraints of the microenvironment induce oligodendrocyte differentiation." Proceedings of the National Academy of Sciences 105, no. 38 (September 11, 2008): 14662–67. http://dx.doi.org/10.1073/pnas.0805640105.

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Sapidis, N. S. "Geometric modeling of spatial constraints: objectives, methods and solid-modeling requirements." Computing 79, no. 2-4 (March 7, 2007): 337–52. http://dx.doi.org/10.1007/s00607-006-0210-2.

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Wang, Wei, Xinyao Tang, and Ying Li. "Optimization and Estimation Algorithm of Vehicle Spatial Form Based on Monocular Traffic Camera." Transportation Research Record: Journal of the Transportation Research Board 2676, no. 3 (October 23, 2021): 360–70. http://dx.doi.org/10.1177/03611981211051347.

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Accurate and rapid acquisition of vehicle spatial form is of great importance in the fields of intelligent transportation and autonomous driving. However, given the limitations of projective geometry, it is difficult to obtain the 3-D structure of vehicles using monocular cameras. The purpose of this paper is, therefore, to estimate the vehicle spatial form using monocular traffic cameras. Firstly, we establish the camera calibration model of the road scene, and jointly construct the geometric constraint model of the vehicle spatial form by vanishing points. Secondly, the contour and edge constraints of the vehicle are obtained based on Mask R-CNN. Then, based on these constraints, the error constraint function is constructed to calculate the projection error of the vehicle spatial form. Finally, a particle swarm optimization algorithm is used to iteratively optimize the parameters in the constraint space to obtain accurate vehicle spatial form information. Experiments are carried on the BrnoCompSpeed data set and the home-made data set. The experimental results show that the processing time of a single frame is less than 0.5 s and the average accuracy is higher than 94%. Moreover, the proposed algorithm has good robustness to the issue of vehicle occlusion and queuing in the scene, which outperforms existing methods.

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Gorti, Sreenivasa Rao, Salal Humair, Ram D. Sriram, Sarosh Talukdar, and Sesh Murthy. "Solving constraint satisfaction problems using ATeams." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 10, no. 1 (January 1996): 1–19. http://dx.doi.org/10.1017/s0890060400001256.

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AbstractThis paper presents an approach to solving constraint satisfaction problems using Asynchronous Teams of autonomous agents (ATeams). The focus for the constraint satisfaction problem is derived from an effort to support spatial layout generation in a conceptual design framework. The constraint specification allows a high-level representation and manipulation of qualitative geometric information. We present a computational technique based on ATeams to instantiate solutions to the constraint satisfaction problem. The technique uses a search for a solution in numerical space. This permits us to handle both qualitative relationships and numerical constraints in a unified framework. We show that simple knowledge, about human spatial reasoning and about the nature of arithmetic operators can be hierarchically encapsulated and exploited efficiently in the search. An example illustrates the generality of the approach for conceptual design. We also present empirical studies that contrast the efficiency of ATeams with a search based on genetic algorithms. Based on these preliminary results, we argue that the ATeams approach elegantly handles arbitrary sets of constraints, is computationally efficient, and hence merits further investigation.

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Werkhoven, Peter, and Jan J. Koenderink. "Visual Size Invariance Does Not Apply to Geometric Angle and Speed of Rotation." Perception 22, no. 2 (February 1993): 177–84. http://dx.doi.org/10.1068/p220177.

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The ability of humans to visually estimate geometric angle and speed of rotation was examined as a function of the spatial scale of the stimuli. Both properties are objectively invariant at different spatial scales, but the results of experiments show that the judgement of acute geometric angles as well as that of speed of rotation varies strongly and monotonically with the scale of presentation. If the image is magnified, the perceived geometric angle and the perceived speed of rotation increase. If the image is reduced in size, they decrease. This result imposes strong constraints on perceptual theories.

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Wang, Naige, Guohua Cao, Lu Yan, and Lei Wang. "Modeling and Control for a Multi-Rope Parallel Suspension Lifting System under Spatial Distributed Tensions and Multiple Constraints." Symmetry 10, no. 9 (September 18, 2018): 412. http://dx.doi.org/10.3390/sym10090412.

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The modeling and control of the multi-rope parallel suspension lifting system (MPSLS) are investigated in the presence of different and spatial distributed tensions; unknown boundary disturbances; and multiple constraints, including time varying geometric constraint, input saturation, and output constraint. To describe the system dynamics more accurately, the MPSLS is modelled by a set of partial differential equations and ordinary differential equations (PDEs-ODEs) with multiple constraints, which is a nonhomogeneous and coupled PDEs-ODEs, and makes its control more difficult. Adaptive boundary control is a recommended method for position regulation and vibration degradation of the MPSLS, where adaptation laws and a boundary disturbance observer are formulated to handle system uncertainties. The system stability is rigorously proved by using Lyapunov’s direct method, and the position and vibration eventually diminish to a bounded neighborhood of origin. The original PDEs-ODEs are solved by finite difference method, and the multiple constraints problem is processed simultaneously. Finally, the performance of the proposed control is demonstrated by both the results of ADAMS simulation and numerical calculation.

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Catenacci Volpi, Nicola, and Daniel Polani. "Space Emerges from What We Know—Spatial Categorisations Induced by Information Constraints." Entropy 22, no. 10 (October 19, 2020): 1179. http://dx.doi.org/10.3390/e22101179.

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Seeking goals carried out by agents with a level of competency requires an “understanding” of the structure of their world. While abstract formal descriptions of a world structure in terms of geometric axioms can be formulated in principle, it is not likely that this is the representation that is actually employed by biological organisms or that should be used by biologically plausible models. Instead, we operate by the assumption that biological organisms are constrained in their information processing capacities, which in the past has led to a number of insightful hypotheses and models for biologically plausible behaviour generation. Here we use this approach to study various types of spatial categorizations that emerge through such informational constraints imposed on embodied agents. We will see that geometrically-rich spatial representations emerge when agents employ a trade-off between the minimisation of the Shannon information used to describe locations within the environment and the reduction of the location error generated by the resulting approximate spatial description. In addition, agents do not always need to construct these representations from the ground up, but they can obtain them by refining less precise spatial descriptions constructed previously. Importantly, we find that these can be optimal at both steps of refinement, as guaranteed by the successive refinement principle from information theory. Finally, clusters induced by these spatial representations via the information bottleneck method are able to reflect the environment’s topology without relying on an explicit geometric description of the environment’s structure. Our findings suggest that the fundamental geometric notions possessed by natural agents do not need to be part of their a priori knowledge but could emerge as a byproduct of the pressure to process information parsimoniously.

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Ananthasuresh, G. K., and S. N. Kramer. "Analysis and Optimal Synthesis of the RSCR Spatial Mechanisms." Journal of Mechanical Design 116, no. 1 (March 1, 1994): 174–81. http://dx.doi.org/10.1115/1.2919342.

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A closed form solution of the analysis of the RSCR (Revolute-Spherical-Cylindrical-Revolute) spatial mechanism is presented in this paper. This work is based on the geometric characteristics of the mechanism involving the following three cases: the cone, the cylinder, and the one-sheet hyperboloid. These cases derive their names from the nature of the locus of the slider of the linkage as viewed from the output side. Each case is then treated separately to develop a closed form, geometry based analysis technique. These analysis modules are then used to optimally synthesize the mechanism for function, path and motion generation problems satisfying precision conditions within prescribed accuracy limits. The Selective Precision Synthesis technique is employed to formulate the nonlinear inequality constraints. These constraints along with an objective function and other constraints are solved using the Generalized Reduced Gradient method of optimization. In addition, mobility charts are used to aid the designer in making a judicious choice for the initial design point before invoking the optimization method. Numerical examples are presented to validate the theory. This new closed form method of analysis that is based on geometric characteristics is computationally less intensive than other available techniques for spatial mechanism analysis and helps in the visualization of the physical mechanism; something that is not possible with most vector and matrix methods.

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Wu, Xiaomeng, Jun Shimamura, Taiga Yoshida, Hidehisa Nagano, Kunio Kashino, Takahito Kawanishi, Kaoru Hiramatsu, Takayuki Kurozumi, and Tetsuya Kinebuchi. "[Invited Paper] Spatial Verification via Pairwise Geometric Constraints and 3D View-Directional Voting." ITE Transactions on Media Technology and Applications 4, no. 3 (2016): 239–50. http://dx.doi.org/10.3169/mta.4.239.

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Chen, Yidi, Renwen Chen, Hao Liu, Jiapeng Guo, Yujie Wang, and Junyi Zhang. "Research on Configuration Constraints of Airborne Bistatic SARs." Sensors 22, no. 17 (August 30, 2022): 6534. http://dx.doi.org/10.3390/s22176534.

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Based on the analysis of the airborne bistatic synthetic aperture radar (SAR) imaging geometric mode, an extended nonlinear chirp scaling algorithm is employed to simulate and verify the imaging effect of the bistatic SARs. A gradient theory-based two-dimensional resolution bistatic SAR model is proposed, and the constraints of the multi-platform flight trajectory parameters meeting the imaging accuracy of the bistatic SAR are analyzed. Finally, through the bistatic SAR imaging simulation of cooperative flight trajectories under various situations, the spatial configuration constraint envelope between the flight vehicles to achieve the optimal resolution is revealed. The results of this paper will provide a theoretical reference for the SAR application in formation flight control.

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Zhang, Yan Hua, Xiu Ju Du, and Bai Yong Zhang. "Synthesis and Analysis of 4-DOF Parallel Manipulators of Computer Aided Geometry Approach." Advanced Materials Research 912-914 (April 2014): 1010–16. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.1010.

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A novel computer aided geometry approach for type synthesis and analysis of new spatial 4-DOF parallel manipulators is put forward, and create the computer simulation mechanisms of parallel manipulators using the geometric constraints and dimension driving techniques in CAD software, Based on the computer simulation mechanisms of parallel manipulators, several new spatial 4-DOF parallel manipulators are synthesized, the kinematic characteristics of the moving platforms are analyzed by computer simulation. The results of computer simulation prove that the computer aided geometric approach for solving type synthesis and kinematic analysis is not only fairly quick and straightforward, but also has the advantages of accuracy.

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Jung, Woonhyung, Janghun Hyeon, and Nakju Doh. "Robust Cuboid Modeling from Noisy and Incomplete 3D Point Clouds Using Gaussian Mixture Model." Remote Sensing 14, no. 19 (October 9, 2022): 5035. http://dx.doi.org/10.3390/rs14195035.

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A cuboid is a geometric primitive characterized by six planes with spatial constraints, such as orthogonality and parallelism. These characteristics uniquely define a cuboid. Therefore, previous modeling schemes have used these characteristics as hard constraints, which narrowed the solution space for estimating the parameters of a cuboid. However, under high noise and occlusion conditions, a narrowed solution space may contain only false or no solutions, which is called an over-constraint. In this paper, we propose a robust cuboid modeling method for point clouds under high noise and occlusion conditions. The proposed method estimates the parameters of a cuboid using soft constraints, which, unlike hard constraints, do not limit the solution space. For this purpose, a cuboid is represented as a Gaussian mixture model (GMM). The point distribution of each cuboid surface owing to noise is assumed to be a Gaussian model. Because each Gaussian model is a face of a cuboid, the GMM shares the cuboid parameters and satisfies the spatial constraints, regardless of the occlusion. To avoid an over-constraint in the optimization, only soft constraints are employed, which is the expectation of the GMM. Subsequently, the soft constraints are maximized using analytic partial derivatives. The proposed method was evaluated using both synthetic and real data. The synthetic data were hierarchically designed to test the performance under various noise and occlusion conditions. Subsequently, we used real data, which are more dynamic than synthetic data and may not follow the Gaussian assumption. The real data are acquired by light detection and ranging-based simultaneous localization and mapping with actual boxes arbitrarily located in an indoor space. The experimental results indicated that the proposed method outperforms a previous cuboid modeling method in terms of robustness.

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Li, Chunfeng, Xiping Xu, Zhen Ren, and Siyuan Liu. "Research on Calibration Method of Line-Structured Light Based on Multiple Geometric Constraints." Applied Sciences 13, no. 10 (May 13, 2023): 5998. http://dx.doi.org/10.3390/app13105998.

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Line-structured light calibration is an important step in the process of the visual measurement of structured light, and in the calibration process, the light plane equation is fitted by the camera coordinates of the data points on the light plane. There is error in solving the spatial coordinates of the data points, and the existing methods generally cannot effectively find the deviation points in the fitted data points, which leads to deviation when solving the parameters of the light plane equation. To correct the error caused by the deviation point in the calibration, this paper established a calibration method based on geometric constraints. In the method, the first constraint was that all fit points involved in the fitting had a certain consistency, and a part of the error points could be filtered by the distance from the data point to the light plane. In order to further improve the calibration accuracy, the laser was moved on a linear guide, the optimized objective function was established by the second geometric constraint, and the constraint was the relationship that the light plane at each position was parallel. In the experiment, a high-precision gauge block was used as the measured object, and the measurement results could be obtained. The calibration method can improve the calibration accuracy according to the experimental results.

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Smart, Philip D., Alia I. Abdelmoty, and Baher El-Geresy. "Spatial Reasoning with Place Information on the Semantic Web." International Journal on Artificial Intelligence Tools 23, no. 05 (October 2014): 1450011. http://dx.doi.org/10.1142/s0218213014500110.

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Geographical referencing of data and resources on the Web has become prevalent. Discovering and linking this information poses eminent research challenges to the geospatial semantic web, with regards to the representation and manipulation of information on geographic places. Towards addressing these challenges, this work explores the potential of the current semantic web languages and tools. In particular, an integrated logical framework of rules and ontologies, using current W3C standards, is assessed for modeling geospatial ontologies of place and for encoding both symbolic and geometric references to place locations. Spatial reasoning is incorporated in the framework to facilitate the deduction of implicit spatial relations and for expressing spatial integrity constraints. The logical framework is extended with geo-computation engines that offer more effective manipulation of geometric information. Example data sets mined from web resources are used to demonstrate and evaluate the framework, offering insights to its potentials and limitations.

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Laurie, Henri, and John A. Silander. "Geometric constraints and spatial pattern of species richness: critique of range-based null models." Diversity and Distributions 8, no. 6 (November 2002): 351–64. http://dx.doi.org/10.1046/j.1472-4642.2002.00160.x.

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Jiang, San, Wanshou Jiang, Lelin Li, Lizhe Wang, and Wei Huang. "Reliable and Efficient UAV Image Matching via Geometric Constraints Structured by Delaunay Triangulation." Remote Sensing 12, no. 20 (October 16, 2020): 3390. http://dx.doi.org/10.3390/rs12203390.

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Outlier removal is a crucial step in local feature-based unmanned aerial vehicle (UAV) image matching. Inspired by our previous work, this paper proposes a method for reliable and efficient outlier removal in UAV image matching. The inputs of the method are only two images without any other auxiliary data. The core idea is to design local geometric constraints within the neighboring structure via the Delaunay triangulation and use a two-stage method for outlier removal and match refinement. In the filter stage, initial matches are first organized as the Delaunay triangulation (DT) and its corresponding graph, and their dissimilarity scores are computed from the affine-invariant spatial angular order (SAO), which is used to achieve hierarchical outlier removal. In addition, by using the triangle constraint between the refined Delaunay triangulation and its corresponding graph, missed inliers are resumed from match expansion. In the verification stage, retained matches are refined using the RANSAC-based global geometric constraint. Therefore, the two-stage algorithm is termed DTSAO-RANSAC. Finally, using four datasets, DTSAO-RANSAC is comprehensively analyzed and compared with other methods in feature matching and image orientation tests. The experimental results demonstrate that compared with the LO-RANSAC algorithm, DTSAO-RANSAC can achieve efficient outlier removal with speedup ratios ranging from 4 to 16 and, it can provide reliable matching results for image orientation of UAV datasets.

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Foertsch, Tobias C., Alex T. Davis, Roman Popov, Clemens von Bojničić-Kninski, Felix E. Held, Svetlana B. Tsogoeva, Felix F. Loeffler, and Alexander Nesterov-Mueller. "Spatial Modes of Laser-Induced Mass Transfer in Micro-Gaps." Applied Sciences 9, no. 7 (March 28, 2019): 1303. http://dx.doi.org/10.3390/app9071303.

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We have observed the concentric deposition patterns of small molecules transferred by means of laser-induced forward transfer (LIFT). The patterns comprised different parts whose presence changed with the experimental constraints in a mode-like fashion. In experiments, we studied this previously unknown phenomenon and derived model assumptions for its emergence. We identified aerosol micro-flow and geometric confinement as the mechanism behind the mass transfer and the cause of the concentric patterns. We validated our model using a simulation.

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Han, Feiyan, Zhitao Hu, Longlong He, Xianlong Peng, Manzhi Yang, and Chuanwei Zhang. "Solution of Spatial Transformation Relationship of Similar Ruled Surfaces Based on Registration of Divided Regions." Machines 10, no. 10 (October 19, 2022): 956. http://dx.doi.org/10.3390/machines10100956.

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Since the geometric transformation relationship of similar surfaces with complex features, such as local deformation and curvature changes, is hard to be solved through global registration, this paper proposes a method for solving the spatial transformation relationship of similar ruled surfaces based on registration of divided regions. First, an adaptive region division algorithm is proposed to divide similar surfaces, and then, an improved registration algorithm is proposed by adding two constraints which are the curvature feature and differential geometric features of point clouds. Through this improved registration algorithm, the geometric transformation relationship of each sub-region can be solved, and then the spatial geometric transformation relationship of the overall similar surface can be established. Moreover, the improved registration algorithm can ensure that the differential geometric properties of corresponding points are similar after registration, which may provide a basis for mapping and reuse of process knowledge between corresponding points on similar surfaces. Finally, two similar ruled surface blades are taken as examples for simulation verification, the results show that the maximum registration error of each sub-region is 0.025 mm, which is within the allowable error range, and the registration speed of the proposed algorithm is better than the S-ICP algorithm. This proves that the method in this paper is feasible and effective.

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YANG, LU. "SOLVING SPATIAL CONSTRAINTS WITH GLOBAL DISTANCE COORDINATE SYSTEM." International Journal of Computational Geometry & Applications 16, no. 05n06 (December 2006): 533–47. http://dx.doi.org/10.1142/s0218195906002178.

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A systematic approach making use of distance geometry to solve spatial constraints is introduced. We demonstrate how to create the constraint equations by means of a relevant distance coordinate system. A short program is made (in Maple) which implements the algorithm producing automatically a complete set of constraint equations for a given point-plane configuration. The point-line-plane configurations are converted into point-plane ones beforehand.

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Komyak, Vladimir, Valentina Komyak, Kazim Kazimov, Alexander Pankratov, and Alexander Danilin. "APPROACH TO THE EVALUATION OF FILLING BY PEOPLE OF MOBILE MEANS AT EMERGENCY EVACUATION FROM BUILDINGS." Journal of Automation and Information sciences 3 (May 1, 2021): 78–90. http://dx.doi.org/10.34229/1028-0979-2021-3-7.

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The tasks of geometric design (of arrangement, cutting, coverage, partitioning) consist in optimization display of geometric information about objects in accordance with a given quality criterion and limitations. Geometric information about a geometric object consists of three components: spatial shape, metric shape parameters, placement parameters, and which, as a rule, is involves in the synthesis of complex systems. The configuration space of geometric objects is based on the formalization of the concept of geometric information. The mapping of objects into their configuration space according to a given set of constraints defines the spatial configuration of geometric objects. The article introduces the concept of a spatial configuration of placement, with the help of which a new model of placement of complex objects is constructed, representing the union of three loosely coupled ellipses, of which one (main) allows continuous translations and rotations, and two of auxiliary ellipses can rotate within acceptable limits (with respect to the angle of rotation of main ellipse) and relative to the points of their “gluing”. As a result of solving the optimization problem, not only the arrangement configuration of such objects is synthesized, but also the spatial form of each of them. Computer modeling of the optimization of the placement of the complex objects considered in the work was carried out and the effectiveness of the proposed approach was shown by comparing the location configurations for objects with a changing spatial shape and with constant shape parameters. Consideration of the parameters of the placement of objects, as well as additional parameters that allow us to synthesize new spatial forms of objects, as independent variables will allow us to offer new mathematical models and optimization methods for the synthesis of spatial configurations. A further direction can also be considered the development of new approaches to modeling the movement of flows of people, robots, to get upper bounds for filling areas with objects. All this increases the range of tasks to be solved according to their functional capabilities and can be used, for example, when dividing the compartments of vehicles for transporting goods and storing them, in pattern recognition systems, in robotics, etc.

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Gao, Xiao-Shan, Christoph M. Hoffmann, and Wei-Qiang Yang. "Solving spatial basic geometric constraint configurations with locus intersection." Computer-Aided Design 36, no. 2 (February 2004): 111–22. http://dx.doi.org/10.1016/s0010-4485(03)00056-3.

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Xie, Yong-Hua, Zhao-Fei Xu, and Hans Burkhardt. "Spatial geometric constraints histogram descriptors based on curvature mesh graph for 3D pollen particles recognition." Chinese Physics B 23, no. 6 (May 30, 2014): 060701. http://dx.doi.org/10.1088/1674-1056/23/6/060701.

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Jiang, Xinwei, Xin Song, Yongshan Zhang, Junjun Jiang, Junbin Gao, and Zhihua Cai. "Laplacian Regularized Spatial-Aware Collaborative Graph for Discriminant Analysis of Hyperspectral Imagery." Remote Sensing 11, no. 1 (December 25, 2018): 29. http://dx.doi.org/10.3390/rs11010029.

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Dimensionality Reduction (DR) models are of significance to extract low-dimensional features for Hyperspectral Images (HSIs) data analysis where there exist lots of noisy and redundant spectral features. Among many DR techniques, the Graph-Embedding Discriminant Analysis framework has demonstrated its effectiveness for HSI feature reduction. Based on this framework, many representation based models are developed to learn the similarity graphs, but most of these methods ignore the spatial information, resulting in unsatisfactory performance of DR models. In this paper, we firstly propose a novel supervised DR algorithm termed Spatial-aware Collaborative Graph for Discriminant Analysis (SaCGDA) by introducing a simple but efficient spatial constraint into Collaborative Graph-based Discriminate Analysis (CGDA) which is inspired by recently developed Spatial-aware Collaborative Representation (SaCR). In order to make the representation of samples on the data manifold smoother, i.e., similar pixels share similar representations, we further add the spectral Laplacian regularization and propose the Laplacian regularized SaCGDA (LapSaCGDA), where the two spectral and spatial constraints can exploit the intrinsic geometric structures embedded in HSIs efficiently. Experiments on three HSIs data sets verify that the proposed SaCGDA and LapSaCGDA outperform other state-of-the-art methods.

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DINIZ-FILHO, J. A. F., and N. M. TÔRRES. "Rapoport effect in South American Carnivora (Mammalia): null models under geometric and phylogenetic constraints." Brazilian Journal of Biology 62, no. 3 (August 2002): 437–44. http://dx.doi.org/10.1590/s1519-69842002000300006.

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Rapoport effect predicts that species geographic range sizes will increase toward higher latitudes, probably reflecting adaptations to extreme climatic conditions that increase species tolerance. Recently, studies about spatial patterns in species richness and geographic range size may be associated with the geometry of species' ranges. In this context, null models can be used to search for the causal mechanisms associated with these patterns. In this paper, we analyzed Rapoport effect using a null model to evaluate how phylogenetic structure and geometric constraints simultaneously affect latitudinal extents of 40 species of South American terrestrial Carnivora. The latitudinal extents of Carnivora tended to decrease toward Southern latitudes, in the opposite direction expected under a simple Rapoport effect, but in accordance to geometric expectations of position of midpoints in the continent. Using 5000 simulations, it was possible to show that the null regression coefficients of latitudinal extents against midpoints are positively biased, reflecting the geometric constraints in the latitudinal extents. The results were equivalent in phylogenetic and non-phylogenetic analyses. The observed regression coefficient was significantly smaller (line is less inclined) than expected by chance alone, demonstrating that the geometric constraints in the latitudinal extents exist even after controlling for phylogenetic structure in data using eigenvector regressions. This suggests that the "spirit" of Rapoport effect (sensu Lyons & Willig, 1997) could be maintained, i.e., that latitudinal extents in Southern region of the continent are relatively larger than those in Northern regions, even after controlling for phylogenetic effects.

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Fattah, Abbas, and Sunil K. Agrawal. "Design and simulation of a class of spatial reactionless manipulators." Robotica 23, no. 1 (January 2005): 75–81. http://dx.doi.org/10.1017/s0263574704000670.

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For conventional designs of robots, manipulator motions result in forces and moments on the base. These forces and moments may cause undesirable translation and rotation of the base. The objective of this paper is to systematically analyze the fundamentals of reactionless robots. Based on this analysis, a design of one distinct class of spatial robot is proposed. The design is achieved through appropriate choices of geometric and inertial parameters. Due to the underlying conservation laws, the trajectory must satisfy additional constraints. We illustrate the reactionless feature of this robot through computer simulations. We are also fabricating reactionless robots to illustrate the underlying concepts.

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Ćirić, Dragana. "Relational logics and diagrams: 'No-scale conditions'." SAJ - Serbian Architectural Journal 8, no. 3 (2016): 388–425. http://dx.doi.org/10.5937/saj1603388q.

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The paper investigates logics of relational thinking and connectivity, rendering particular correspondences between the elements of representation and the things represented in drawings, diagrams, maps, or notations, which either deny notions of scale, or work at all scales without belonging to any specific one of them. They include ratios and proportions (static and dynamic, geometric, arithmetic and harmonic progressions) expressing symmetry and self-similarity principles in spatial-metric terms, but also principles of nonlinearity and complexity by symmetry-breakings within non-metric systems. The first part explains geometric and numeric relational figures/sets as taken for "principles of beauty and primary aesthetic quality of all things" in classical philosophy, science, and architecture. These progressions are guided by certain rules or their combinations (codes and algorithms) based on principles of regularity, usually directly spatially reflected. Conversely, configurations representing the main subject of the following sections, could be spatially independent, transformable, and unpredictable, escaping regular extensive definitions. Their forms are presented through transitions from scalable to no-scale conditions showing initial symmetry breakings and abstractions, through complex forms of dynamic modulations and variations of matter, ending with some of the relational diagrammatic and topological ways of architectural data-processing outside of the spatial constraints and parameters - all through diagrams as ultimate tools of relational thinking and inference.

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Zhao, T. S., J. S. Dai, and Z. Huang. "Geometric synthesis of spatial parallel manipulators with fewer than six degrees of freedom." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216, no. 12 (December 1, 2002): 1175–85. http://dx.doi.org/10.1243/095440602321029418.

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Manipulators with fewer than six degrees of freedom meet specific tasks and have the advantage of reducing structural complexity, design redundancy and cost. In order to construct parallel manipulators for given tasks, this paper develops an algebraic approach to type synthesis of spatial parallel mechanisms with fewer than six degrees of freedom based on the screw theory. With the proposed steps (i.e. describing restraining screws, identifying basic kinematic pair (KP) screws reciprocal to the restraining screws, linearly transforming the basic KP screws to obtain equivalent serial limbs and allocating the serial limbs) new parallel mechanisms can be constructed. The approach converts a mechanism design into a screw algebra operation, in which screws describe kinematic pairs and constraints between links. As examples, synthesis procedures of parallel mechanisms with four degrees of freedom are given, from which five novel parallel mechanisms result.

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Sato, Rai, Yuto Izumi, and Sungyoung Kim. "Room-aware portable Auditory Augmented Reality: Real-time spatial audio generation with geometric data analysis." Journal of the Acoustical Society of America 154, no. 4_supplement (October 1, 2023): A281. http://dx.doi.org/10.1121/10.0023527.

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This study proposes an innovative and practical approach to spatial acoustic rendering for Auditory Augmented Reality (AAR) in small room usage. AAR aims to enhance user experiences by overlaying spatially appropriate sounds in the real environment, creating the illusion that virtual sounds coexist in the physical world. However, current technological constraints in hardware and AAR rendering present challenges in creating a truly immersive sensation of “being there.” To address these challenges, we present a dynamic processing framework for a typical mobile AAR setting. This framework combines a game-audio engine with 3-D visual computation both specialized for real-time processing, providing a plausible spatial impression with lightweight computation. The process involves capturing room information by the Light Detection And Ranging (LiDAR) sensor mounted on the device, followed by estimating its dominant acoustic materials. The generated data will be used to compute dynamic early reflections and late reverberation. Early reflections are calculated up to the fourth reflection using the image source method, considering the acoustic materials. Late reverberation is generated using the Feedback Delay Network (FDN), with room frequency characteristics and spatial directivity varying relative to the listener's position. All components will be represented in fifth-order Ambisonics and binauralized with head-tracking. Notably, this dynamic rendering method could be light enough to handle all processing on a single mobile device.

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Zhang, Qingwang, and Yingying Zhu. "Aligning Geometric Spatial Layout in Cross-View Geo-Localization via Feature Recombination." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 7 (March 24, 2024): 7251–59. http://dx.doi.org/10.1609/aaai.v38i7.28554.

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Cross-view geo-localization holds significant potential for various applications, but drastic differences in viewpoints and visual appearances between cross-view images make this task extremely challenging. Recent works have made notable progress in cross-view geo-localization. However, existing methods either ignore the correspondence between geometric spatial layout in cross-view images or require high costs or strict constraints to achieve such alignment. In response to these challenges, we propose a Feature Recombination Module (FRM) that explicitly establishes the geometric spatial layout correspondences between two views. Unlike existing methods, FRM aligns geometric spatial layout by directly recombining features, avoiding image preprocessing, and introducing no additional computational and parameter costs. This effectively reduces ambiguities caused by geometric misalignments between ground-level and aerial-level images. Furthermore, it is not sensitive to frameworks and applies to both CNN-based and Transformer-based architectures. Additionally, as part of the training procedure, we also introduce a novel weighted (B+1)-tuple loss (WBL) as optimization objective. Compared to the widely used weighted soft margin ranking loss, this innovative loss enhances convergence speed and final performance. Based on the two core components (FRM and WBL), we develop an end-to-end network architecture (FRGeo) to address these limitations from a different perspective. Extensive experiments show that our proposed FRGeo not only achieves state-of-the-art performance on cross-view geo-localization benchmarks, including CVUSA, CVACT, and VIGOR, but also is significantly superior or competitive in terms of computational complexity and trainable parameters. Our project homepage is at https://zqwlearning.github.io/FRGeo.

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Davies, Richard G., C. David L. Orme, David Storch, Valerie A. Olson, Gavin H. Thomas, Simon G. Ross, Tzung-Su Ding, et al. "Topography, energy and the global distribution of bird species richness." Proceedings of the Royal Society B: Biological Sciences 274, no. 1614 (February 20, 2007): 1189–97. http://dx.doi.org/10.1098/rspb.2006.0061.

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A major goal of ecology is to determine the causes of the latitudinal gradient in global distribution of species richness. Current evidence points to either energy availability or habitat heterogeneity as the most likely environmental drivers in terrestrial systems, but their relative importance is controversial in the absence of analyses of global (rather than continental or regional) extent. Here we use data on the global distribution of extant continental and continental island bird species to test the explanatory power of energy availability and habitat heterogeneity while simultaneously addressing issues of spatial resolution, spatial autocorrelation, geometric constraints upon species' range dynamics, and the impact of human populations and historical glacial ice-cover. At the finest resolution (1°), topographical variability and temperature are identified as the most important global predictors of avian species richness in multi-predictor models. Topographical variability is most important in single-predictor models, followed by productive energy. Adjusting for null expectations based on geometric constraints on species richness improves overall model fit but has negligible impact on tests of environmental predictors. Conclusions concerning the relative importance of environmental predictors of species richness cannot be extrapolated from one biogeographic realm to others or the globe. Rather a global perspective confirms the primary importance of mountain ranges in high-energy areas.

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Phan, Thanh Trong, and Doan Van Thang. "Joint Spatial Geometric and Max-margin Classifier Constraints for Facial Expression Recognition Using Nonnegative Matrix Factorization." International Journal of Machine Learning and Networked Collaborative Engineering 03, no. 03 (December 10, 2019): 125–34. http://dx.doi.org/10.30991/ijmlnce.2019v03i03.001.

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Rangel, Thiago Fernando L. V. B., and José Alexandre F. Diniz-Filho. "An evolutionary tolerance model explaining spatial patterns in species richness under environmental gradients and geometric constraints." Ecography 28, no. 2 (April 2005): 253–63. http://dx.doi.org/10.1111/j.0906-7590.2005.04038.x.

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Liu, Yuwei, Pan Ou, Xinqi Xu, and Junhua Sun. "Multi-line structured light binocular vision stereo matching method via coarse-to-fine spatial geometric constraints." Optics & Laser Technology 176 (September 2024): 110950. http://dx.doi.org/10.1016/j.optlastec.2024.110950.

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Feppon, Florian, Grégoire Allaire, and Charles Dapogny. "A variational formulation for computing shape derivatives of geometric constraints along rays." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 1 (January 2020): 181–228. http://dx.doi.org/10.1051/m2an/2019056.

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In the formulation of shape optimization problems, multiple geometric constraint functionals involve the signed distance function to the optimized shape Ω. The numerical evaluation of their shape derivatives requires to integrate some quantities along the normal rays to Ω, a challenging operation to implement, which is usually achieved thanks to the method of characteristics. The goal of the present paper is to propose an alternative, variational approach for this purpose. Our method amounts, in full generality, to compute integral quantities along the characteristic curves of a given velocity field without requiring the explicit knowledge of these curves on the spatial discretization; it rather relies on a variational problem which can be solved conveniently by the finite element method. The well-posedness of this problem is established thanks to a detailed analysis of weighted graph spaces of the advection operator β ⋅ ∇ associated to a C1 velocity field β. One novelty of our approach is the ability to handle velocity fields with possibly unbounded divergence: we do not assume div(β) ∈ L∞. Our working assumptions are fulfilled in the context of shape optimization of C2 domains Ω, where the velocity field β = ∇dΩ is an extension of the unit outward normal vector to the optimized shape. The efficiency of our variational method with respect to the direct integration of numerical quantities along rays is evaluated on several numerical examples. Classical albeit important implementation issues such as the calculation of a shape’s curvature and the detection of its skeleton are discussed. Finally, we demonstrate the convenience and potential of our method when it comes to enforcing maximum and minimum thickness constraints in structural shape optimization.

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Rangel, T. F. L. V. B., and J. A. F. Diniz-filho. "Worldwide patterns in species richness of falconiformes: analytical null models, geometric constraints, and the mid-domain effect." Brazilian Journal of Biology 64, no. 2 (May 2004): 209–308. http://dx.doi.org/10.1590/s1519-69842004000200016.

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Recently, the hypothesis that the geographic distribution of species could be influenced by the shape of the domain edges, the so-called Mid-Domain Effect (MDE), has been included as one of the five credible hypotheses for explaining spatial gradients in species richness, despite all the unsuccessful current attempts to prove empirically the validity of MDE. We used data on spatial worldwide distributions of Falconiformes to evaluate the validity of MDE assumptions, incorporated into two different sorts of null models at a global level and separately across five domains/landmasses. Species richness values predicted by the null models of the MDE and those values predicted by Net Primary Productivity, a surrogate variable expressing the effect of available energy, were compared in order to evaluate which hypothesis better predicts the observed values. Our tests showed that MDE continues to lack empirical support, regardless of its current acceptability, and so, does not deserve to be classified as one possible explanation of species richness gradients.

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Zhou, Biao, Deockhyeon Ahn, Jungpyo Lee, Chao Sun, Sabbir Ahmed, and Youngok Kim. "A Passive Tracking System Based on Geometric Constraints in Adaptive Wireless Sensor Networks." Sensors 18, no. 10 (September 29, 2018): 3276. http://dx.doi.org/10.3390/s18103276.

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Target tracking technologies in wireless sensor network (WSNs) environments fall into two categories: active and passive schemes. Unlike with the active positioning schemes, in which the targets are required to hold cooperative devices, the research on passive tracking, i.e., tracking device-free targets, has recently showed promise. In the WSN, device-free targets can be tracked by sensing radio frequency tomography (RFT) on the line-of-sight links (LOSLs). In this paper, we propose a passive tracking scheme exploiting both adaptive-networking LOSL webs and geometric constraint methodology for tracking single targets, as well as multiple targets. Regarding fundamental knowledge, we firstly explore the spatial diversity technique for RFT detection in realistic situations. Then, we analyze the power consumption of the WSN and propose an adaptive networking scheme for the purpose of energy conservation. Instead of maintaining a fixed LOSL density, the proposed scheme can adaptively adjust the networking level to save energy while guaranteeing tracking accuracy. The effectiveness of the proposed scheme is evaluated with computer simulations. According to the results, it is observed that the proposed scheme can sufficiently reduce power consumption, while providing qualified tracking performance.

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Schütte, Ole M., Ingo Mey, Jörg Enderlein, Filip Savić, Burkhard Geil, Andreas Janshoff, and Claudia Steinem. "Size and mobility of lipid domains tuned by geometrical constraints." Proceedings of the National Academy of Sciences 114, no. 30 (July 10, 2017): E6064—E6071. http://dx.doi.org/10.1073/pnas.1704199114.

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In the plasma membrane of eukaryotic cells, proteins and lipids are organized in clusters, the latter ones often called lipid domains or “lipid rafts.” Recent findings highlight the dynamic nature of such domains and the key role of membrane geometry and spatial boundaries. In this study, we used porous substrates with different pore radii to address precisely the extent of the geometric constraint, permitting us to modulate and investigate the size and mobility of lipid domains in phase-separated continuous pore-spanning membranes (PSMs). Fluorescence video microscopy revealed two types of liquid-ordered (lo) domains in the freestanding parts of the PSMs: (i) immobile domains that were attached to the pore rims and (ii) mobile, round-shapedlodomains within the center of the PSMs. Analysis of the diffusion of the mobilelodomains by video microscopy and particle tracking showed that the domains’ mobility is slowed down by orders of magnitude compared with the unrestricted case. We attribute the reduced mobility to the geometric confinement of the PSM, because the drag force is increased substantially due to hydrodynamic effects generated by the presence of these boundaries. Our system can serve as an experimental test bed for diffusion of 2D objects in confined geometry. The impact of hydrodynamics on the mobility of enclosed lipid domains can have great implications for the formation and lateral transport of signaling platforms.

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FREITAS, PAULO P., SUSANA CARDOSO, RICARDO FERREIRA, VERÓNICA C. MARTINS, ANDRÉ GUEDES, FILIPE A. CARDOSO, JOANA LOUREIRO, RITA MACEDO, RUI C. CHAVES, and JOSÉ AMARAL. "OPTIMIZATION AND INTEGRATION OF MAGNETORESISTIVE SENSORS." SPIN 01, no. 01 (June 2011): 71–91. http://dx.doi.org/10.1142/s2010324711000070.

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This paper addresses challenging issues related to the integration of magnetoresistive (MR) sensors in applications such as magnetic field mapping, magnetic bead detection in microfluidic channels, or biochips. Although sharing the same technological principle for detection (magnetoresistance effect), each application has unique specifications in terms of noise, sensitivity, spatial resolution, electrical robustness or geometric constraints. These differences are of high impact for manufacturing, because some strategies used for sensor optimization compromise the freedom for device architecture.

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Rashidifard, Mahtab, Jérémie Giraud, Mark Lindsay, Mark Jessell, and Vitaliy Ogarko. "Constraining 3D geometric gravity inversion with a 2D reflection seismic profile using a generalized level set approach: application to the eastern Yilgarn Craton." Solid Earth 12, no. 10 (October 22, 2021): 2387–406. http://dx.doi.org/10.5194/se-12-2387-2021.

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Abstract. One of the main tasks in 3D geological modeling is the boundary parametrization of the subsurface from geological observations and geophysical inversions. Several approaches have been developed for geometric inversion and joint inversion of geophysical datasets. However, the robust, quantitative integration of models and datasets with different spatial coverage, resolution, and levels of sparsity remains challenging. One promising approach for recovering the boundary of the geological units is the utilization of a level set inversion method with potential field data. We focus on constraining 3D geometric gravity inversion with sparse lower-uncertainty information from a 2D seismic section. We use a level set approach to recover the geometry of geological bodies using two synthetic examples and data from the geologically complex Yamarna Terrane (Yilgarn Craton, Western Australia). In this study, a 2D seismic section has been used for constraining the location of rock unit boundaries being solved during the 3D gravity geometric inversion. The proposed work is the first we know of that automates the process of adding spatially distributed constraints to the 3D level set inversion. In many hard-rock geoscientific investigations, seismic data are sparse, and our results indicate that unit boundaries from gravity inversion can be much better constrained with seismic information even though they are sparsely distributed within the model. Thus, we conclude that it has the potential to bring the state of the art a step further towards building a 3D geological model incorporating several sources of information in similar regions of investigation.

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Camacho-Sanchez, Miguel, Melissa T. R. Hawkins, Fred Tuh Yit Yu, Jesus E. Maldonado, and Jennifer A. Leonard. "Endemism and diversity of small mammals along two neighboring Bornean mountains." PeerJ 7 (October 8, 2019): e7858. http://dx.doi.org/10.7717/peerj.7858.

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Mountains offer replicated units with large biotic and abiotic gradients in a reduced spatial scale. This transforms them into well-suited scenarios to evaluate biogeographic theories. Mountain biogeography is a hot topic of research and many theories have been proposed to describe the changes in biodiversity with elevation. Geometric constraints, which predict the highest diversity to occur in mid-elevations, have been a focal part of this discussion. Despite this, there is no general theory to explain these patterns, probably because of the interaction among different predictors with the local effects of historical factors. We characterize the diversity of small non-volant mammals across the elevational gradient on Mount (Mt.) Kinabalu (4,095 m) and Mt. Tambuyukon (2,579 m), two neighboring mountains in Borneo, Malaysia. We documented a decrease in species richness with elevation which deviates from expectations of the geometric constraints and suggests that spatial factors (e.g., larger diversity in larger areas) are important. The lowland small mammal community was replaced in higher elevations (from above ~1,900 m) with montane communities consisting mainly of high elevation Borneo endemics. The positive correlation we find between elevation and endemism is concordant with a hypothesis that predicts higher endemism with topographical isolation. This supports lineage history and geographic history could be important drivers of species diversity in this region.

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Wang, M., Y. Ye, M. Sun, X. Tan, and L. Li. "ROBUST REGISTRATION FOR OPTICAL AND SAR IMAGES BASED ON SPATIAL GEOMETRIC CONSTRAINT AND STRUCTURE FEATURES." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-1-2020 (August 3, 2020): 117–24. http://dx.doi.org/10.5194/isprs-annals-v-1-2020-117-2020.

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Abstract. Automatic registration of optical and synthetic aperture radar (SAR) images is a challenging task due to significant geometric deformation and radiometric differences between two images. To address this issue, this paper proposes an automatic registration method for optical and SAR images based on spatial geometric constraint and structure features. Firstly, the Harris detector with a block strategy is used to extract evenly distributed feature points in the images. Subsequently, a local geometric correction is performed by using the Rational Function Model, which eliminates the rotation and scale differences between optical and SAR images. Secondly, orientated gradient information of images is used to construct a geometric structural feature descriptor. Then, the feature descriptor is transformed into the frequency domain, and the three-dimensional (3-D) phase correlation is used as the similarity metric to achieve correspondences by employing a template matching scheme. Finally, mismatches are eliminated based on spatial geometric constraint relationship between images, followed by a process of geometric correction to achieve the image registration. Experimental results with multiple high-resolution optical and SAR images show that the proposed method can achieve reliable registration accuracy, and outperforms the state of the art methods.

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Wang, Jinghua, Ziyu Xu, Xiyu Zheng, and Ziwei Liu. "A Fuzzy Logic Path Planning Algorithm Based on Geometric Landmarks and Kinetic Constraints." Information Technology and Control 51, no. 3 (September 23, 2022): 499–514. http://dx.doi.org/10.5755/j01.itc.51.3.30016.

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This paper mainly focuses on the path planning of mobile robots in complex two-dimensional terrain. It proposes a fuzzy rule-based path planning algorithm for multiple guide points by changing the spatial point-taking method and combining Dijkstra's algorithm and fuzzy logic algorithm. The planning process of this algorithm divide into three stages. The first stage identifies the edge points of the forbidden area by designing the search space, marks the feasible area widths of the edge points in X and Y directions, and marks their midpoints. The second stage uses Dijkstra's algorithm that does the road map sorting on these marked points and the starting and ending points and takes the lowest cost sequence as the search road map. In the third stage, using a fuzzy logic system to search these road signs one by one until the endpoint area is searched. The simulation results show that this algorithm can solve the complex environment that traditional fuzzy inference algorithms cannot plan. Compared with the graph search algorithm, this algorithm dramatically reduces the planning time and provides more flexible turning angles. This algorithm can better consider the robot's size and the relationship between speed and turning angles while estimating the motion state at each step compared with the sampling algorithm. This algorithm will extend to group path planning and dynamic environment planning in subsequent studies.

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Rodrigues, Priscila M., Cicero C. de Escobar, Luiz Alberto Oliveira Rocha, Liércio André Isoldi, and Elizaldo Domingues dos Santos. "Geometry Evaluation of Heat Transfer by Mixed Convention in Driven Cavities with Two Inserted Fins." Defect and Diffusion Forum 396 (August 2019): 164–73. http://dx.doi.org/10.4028/www.scientific.net/ddf.396.164.

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In this work, a numerical study of a flow with heat transfer by mixed convection are carried out. The objective is the geometric evaluation through the application of the Construtal Design and the exhaustive search method. The behavior of a lid-driven cavity with stable stratification subjected to an incompressible, laminar and two-dimensional flow is investigated. The cavity has two rectangular fins inserted in the lower surface. The problem is subject to three constrains: three geometric constraints: the area of the cavity, two fin areas. The investigated geometry has three degrees of freedom: the ratio between height and cavity length (H/L) and the ratio between height and length of each fin (H1/L1 and H2/L2). The effect of the fin geometry over spatial-averaged Nusselt (NuH) is investigated for Reynolds number (ReH) = 400 and Richardson (Ri) = 0.1. The conservation equations of mass, momentum and energy are tackled with Finite Volume Method (FVM) through the use of commercial software FLUENT. The results showed that the lower H2/L2 ratios resulted in higher NuH values. An increase in NuH value of approximately 49% between the worst and the best geometrical configuration was found, thus highlighting the importance of geometric evaluation on this kind of problem. It is concluded that for the problem addressed the best behavior is obtained when the fins have a small insertion into the cavity, thus avoiding the restriction of the main vortex flow. The results found highlight the importance of the geometric evaluation for the purpose of theoretical recommendation on the geometric configurations that lead to the best thermal performance.

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Zirnstein, E. J., P. Swaczyna, M. A. Dayeh, and J. Heerikhuisen. "Constraints on the IBEX Ribbon’s Origin from Its Evolution over a Solar Cycle." Astrophysical Journal 949, no. 2 (May 25, 2023): 45. http://dx.doi.org/10.3847/1538-4357/acc577.

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Abstract In 2009, the Interstellar Boundary Explorer (IBEX) discovered a narrow “ribbon” of energetic neutral atom emissions across the sky with properties correlated with the solar wind latitudinal structure and the interstellar magnetic field draped around the heliosphere. It is widely believed that the ribbon is formed from the escape of heliospheric ENAs into the local interstellar medium and their eventual return as secondary ENAs. However, there is no consensus on the rate of pitch angle scattering of these PUIs before they become secondary ENAs. We test two opposing limits of scattering rates (“weak” versus “strong”) by solving a time-dependent model of the ribbon that evolves with the solar cycle, and we compare them to IBEX observations over 2009–2019. First, we find that both models qualitatively reproduce the evolution of IBEX fluxes for most of the data set, with a few exceptions, although the strong (or “spatial retention”) scattering model greatly underestimates the observed fluxes. Regardless, time dependence of fluxes cannot distinguish these models. Second, the ribbon’s geometric properties, i.e., its center and radius, are significantly different between the models. The spatial retention model reproduces the observed ribbon centers as a function of energy and time slightly better than the weak scattering model, and the spatial retention model reproduces the observed ribbon radius over energy and time almost perfectly, whereas the weak scattering model compares poorly. Our analysis favors the spatial retention mechanism as the source of the IBEX ribbon, but it requires modification to increase the flux of ENAs observed at 1 au.

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KAUSHAL, R. S. "POSSIBILITY OF A GEOMETRIC CONSTRAINT IN THE SCHRÖDINGER QUANTUM MECHANICS." Modern Physics Letters A 15, no. 21 (July 10, 2000): 1391–97. http://dx.doi.org/10.1142/s0217732300001869.

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Within the framework of some straightforward mathematical terms it is argued that there exists a space-invariant in the Schrödinger quantum mechanics (SQM). As an alternative to the geometric features of localized nature dictated by the prescribed boundary conditions in a potential problem in SQM, this spatial invariant is expected to account for some global geometric features of the quantum system.

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Totu, Vlad, and Cătălin Alexandru. "Study Concerning the Effect of the Bushings' Deformability on the Static Behavior of the Rear Axle Guiding Linkages." Applied Mechanics and Materials 245 (December 2012): 132–37. http://dx.doi.org/10.4028/www.scientific.net/amm.245.132.

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In this paper, we attempt to study the influence of the bushings (compliant joints) on the static behavior of the guiding system used for the rear axle of the vehicles. In fact, we are interested to determine the difference in behavior between the compliant model (with bushings) and the rigid model (bushings modeled as spherical joints) of the axle guiding mechanism. The static model, in which the car body is attached to ground, is a constrained, multi-body spatial mechanical system, in which the bodies are connected through geometric constraints, compliant joints, and force elements. The external loading is made by vertical forces applied to the wheels, in stationary regime. The study is made for the general groups of guiding mechanisms, with M=1 and M=2 degrees of mobility, by using the MBS (Multi-Body Systems) environment ADAMS of MSC Software.

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Humayun, Mohammad Ali, Hayati Yassin, and Pg Emeroylariffion Abas. "Spatial position constraint for unsupervised learning of speech representations." PeerJ Computer Science 7 (July 21, 2021): e650. http://dx.doi.org/10.7717/peerj-cs.650.

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The success of supervised learning techniques for automatic speech processing does not always extend to problems with limited annotated speech. Unsupervised representation learning aims at utilizing unlabelled data to learn a transformation that makes speech easily distinguishable for classification tasks, whereby deep auto-encoder variants have been most successful in finding such representations. This paper proposes a novel mechanism to incorporate geometric position of speech samples within the global structure of an unlabelled feature set. Regression to the geometric position is also added as an additional constraint for the representation learning auto-encoder. The representation learnt by the proposed model has been evaluated over a supervised classification task for limited vocabulary keyword spotting, with the proposed representation outperforming the commonly used cepstral features by about 9% in terms of classification accuracy, despite using a limited amount of labels during supervision. Furthermore, a small keyword dataset has been collected for Kadazan, an indigenous, low-resourced Southeast Asian language. Analysis for the Kadazan dataset also confirms the superiority of the proposed representation for limited annotation. The results are significant as they confirm that the proposed method can learn unsupervised speech representations effectively for classification tasks with scarce labelled data.

Journal articles on the topic 'Spatial and geometric constraints'

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