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Euclidean movement minimization

2015 Journal of combinatorial optimization
We consider a class of optimization problems called movement minimization on euclidean plane.  ...  By minimum movement, we mean either the sum of all movements (Sum) or the maximum movement (Max). We obtain several approximation algorithms and some hardness results for these four problems.  ...  In Sum, the goal is to minimize the sum of the movements of all robots, or formally to minimize m i=1 |p * i − p i | 2 . This parameter roughly measures the total energy consumed by the robots.  ...

Motor Compositionality and Timing: Combined Geometrical and Optimization Approaches [chapter]

Tamar Flash, Matan Karklinsky, Ronit Fuchs, Alain Berthoz, Daniel Bennequin, Yaron Meirovitch
2018 Springer Tracts in Advanced Robotics
Human movements were shown to optimize different costs. Specifically, hand trajectories were found to maximize motion smoothness by minimizing jerk.  ...  The kinematic features and internal movement timing were accounted for by the mixture of geometries model using a combination of Euclidean, affine and equi-affine geometries.  ...  Bright found a specific spiral for which constant equi-affine speed yields minimal jerk and other spirals for which constant Euclidean or fullaffine speed profiles yield minimal jerk trajectories.  ...

Vowel-related tongue movements in speech: Straight or curved paths? (L)

Anders Löfqvist
2011 Journal of the Acoustical Society of America
To assess the movement path, the movement magnitude was calculated in two ways, as a straight line, the Euclidean distance, and as the actual path, obtained by summing the individual Euclidean distances  ...  The ratio between the path and the Euclidean distance is 1 when the movement is a straight line and greater than 1 when the path is curved.  ...  One prediction, based on minimization of effort, is that the movement will be very close to a straight line.  ...

Exploring environments by hand or foot: Time-based heuristics for encoding distance in movement space

Susan J. Lederman, Roberta L. Klatzky, April Collins, Jackie Wardell
1987 Journal of Experimental Psychology. Learning, Memory and Cognition
With manipulatory exploration, slower movements increased length distortion, but duration effects proved secondary to effects of spatial extent.  ...  The studies establish length distortion as a general phenomenon in movement space and identify its major causes as spatial rather than temporal.  ...  There was also an effect of movement speed, such that length distortion was minimal for fast rates of movement and greatest for slow rates.  ...

Least-cost transportation networks predict spatial interaction of invasion vectors

D. Andrew R. Drake, Nicholas E. Mandrak
2010 Ecological Applications
To determine possible model improvements resulting from inclusion of network travel, spatialinteraction models were constructed using standard Euclidean (e.g., straight-line) distance measures and also  ...  To date, spatial-interaction models that predict the movement of humans as vectors of biotic transfer have not incorporated patterns of human movement through transportation networks.  ...  routes between i and j to minimize travel time given relative impedance.  ...

Exploring environments by hand or foot: Time-based heuristics for encoding distance in movement space

Susan J. Lederman, Roberta L. Klatzky, April Collins, Jackie Wardell
1987 Journal of Experimental Psychology. Learning, Memory and Cognition
With manipulatory exploration, slower movements increased length distortion, but duration effects proved secondary to effects of spatial extent.  ...  The studies establish length distortion as a general phenomenon in movement space and identify its major causes as spatial rather than temporal.  ...  There was also an effect of movement speed, such that length distortion was minimal for fast rates of movement and greatest for slow rates.  ...

Computational techniques for non-Euclidean planar spatial data applied to migrant flows [chapter]

Michael Worboys, Keith Mason, Jenny Lingham
1998 Innovations In GIS 5
The paper presents some background to interaction analysis and non-Euclidean techniques.  ...  This paper describes the development of an approach to spatial analysis in the setting of a non-Euclidean space.  ...  In the finite case, the minimal neighbourhoods of locations exist and correspond to the minimal open sets.  ...

Recognition of Elementary Upper Limb Movements in an Activity of Daily Living Using Data from Wrist Mounted Accelerometers

Dwaipayan Biswas, Andy Cranny, Nayaab Gupta, Koushik Maharatna, Steffen Ortmann
2014 2014 IEEE International Conference on Healthcare Informatics
movement types using Euclidean distance classifier.  ...  selected from a ranked set of 30 features, using Euclidean and Mahalonobis distance as the metric.  ...  II RECOGNITION ACCURACIES (%) FOR EACH ARM MOVEMENT WITH EUCLIDEAN (EUC) AND MAHALONOBIS (MAH) DISTANCE CLASSIFIER.  ...

A realistic outdoor urban pedestrian mobility model

Ryan Vogt, Ioanis Nikolaidis, Pawel Gburzynski
2012 Simulation modelling practice and theory
Most significantly, existing models are not representative of actual human movement.  ...  : centrality bias significantly affects network simulation results in non-grid-based urban centres, whereas the pathfinding metric affects results more in grid-based urban centres; distance decay has minimal  ...  minimizes Euclidean distance travelled).  ...

Learning to be Lazy: Exploiting Redundancy in a Novel Task to Minimize Movement-Related Effort

R. Ranganathan, A. Adewuyi, F. A. Mussa-Ivaldi
2013 Journal of Neuroscience
One hypothesis is that redundancy may be resolved by minimizing movement-related costs.  ...  Furthermore, postures chosen also depended upon the information content of visual feedback, with precise visual feedback resulting in postures that minimized movement-related costs.  ...  The Euclidean error was quantified by the Euclidean distance between the center of the target and the cursor at the end of the movement.  ...

Path planning on a compressed terrain

Daniel M. Tracy, W. Randolph Franklin, Barbara Cutler, Franklin T. Luk, Marcus Andrade
2008 Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems - GIS '08
Next, we compute a path that a smuggler would take to minimize detection by an observer, path length, and uphill movement.  ...  The smuggler is allowed the full range of Euclidean motion on the 2-dimensional plane, unlike alternate path planning schemes that strictly avoid obstacles.  ...  An algorithm was developed that minimizes path cost, as measured by path length plus penalties for uphill movement and observer detection, while also permitting the range of Euclidean motion, rather than  ...

Constant Affine Velocity Predicts the 13 Power Law of Planar Motion Perception and Generation

FRANK E. POLLICK, GUILLERMO SAPIRO
1997 Vision Research
Numerous studies have shown that the power of 1/3 is important in relating Euclidean velocity to radius of curvature (R) in the generation and perception of planar movement.  ...  Possible reasons for the appearance of affine transformations in the generation and perception of planar movement are discussed. Copyright 0 1996 Elsevier Science Ltd  ...  Simplest here refers to minimal order (number of derivatives).  ...

Using Optimal Transport Theory to Estimate Transition Probabilities in Metapopulation Dynamics

J.M. Nichols, J.A. Spendelow, J.D. Nichols
2017 Ecological Modelling
The theory of optimal transport provides such a constraint in the form of a cost function, to be minimized in expectation over the space of possible transition matrices.  ...  It is shown that by choosing the squared Euclidean distance as the cost, the estimated transition probabilities compare favorably to those obtained via maximum likelihood with marked individuals.  ...  The cost function is taken as the squared Euclidean distance, hence the resulting paths minimize the total system kinetic energy. SE(P XY (x i , y j )) = P XY .  ...

Configuration Space Metrics [article]

Hong Jun Jeon, Anca Diana Dragan
2018 arXiv   pre-print
In this paper, we analyze the effect of the metric on robot behavior, examining both Euclidean, as well as non-Euclidean metrics -- metrics that make certain joints cheaper, or that correlate different  ...  What is efficient under a Euclidean metric might not necessarily look the most efficient or natural to a person observing the robot.  ...  Expensive Elbow: Expensive elbow metrics minimize movement in the elbow. Fig. 5 (5th column) gives a simple example.  ...

Cluster Analysis of Diffusion Tensor Fields with Application to the Segmentation of the Corpus Callosum

Safa Elsheikh, Andrew Fish, Roma Chakrabarti, Diwei Zhou
2016 Procedia Computer Science
Cholesky, root Euclidean and log Euclidean).  ...  Then we applied the adapted Hartigan's K-means, using Euclidean, Cholesky, root Euclidean and log Euclidean metrics along with Procrustes and Riemannian metrics (which need numerical solutions for mean  ...  Both Hartigan's method and Lloyd's algorithm aim to find a partition of a data set that minimizes the WCSS, but they use different methods to reduce the WCSS.  ...
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