scholarly journals Adaptive cognitive maps for curved surfaces in the 3D world

2021 ◽  
Author(s):  
Misun Kim ◽  
Christian F Doeller
Keyword(s):  
Euclidean Distance ◽  
Flat Surface ◽  
3D Structure ◽  
Distance Estimation ◽  
Cognitive Maps ◽  
Curved Surface ◽  
Spatial Representations ◽  
Curved Surfaces ◽  
Path Distance ◽  
Significant Underestimation

Terrains in a 3D world can be undulating. Yet, most prior research has exclusively investigated spatial representations on a flat surface, leaving a 2D cognitive map as the dominant model in the field. Here, we investigated whether humans represent a curved surface by building a dimension-reduced flattened 2D map or a full 3D map. Participants learned the location of objects positioned on a flat and curved surface in a virtual environment by driving on the surface (Experiment 1), driving and looking vertically (Experiment 2), or flying (Experiment 3). Subsequently, they were asked to retrieve either the path distance or the 3D Euclidean distance between the objects. Path distance estimation was good overall, but we found a significant underestimation bias for the path distance on the curve, suggesting an influence of potential 3D shortcuts, even though participants were only driving on the surface. Euclidean distance estimation was better when participants were exposed more to the global 3D structure of the environment by looking and flying. These results suggest that the representation of the 2D manifold, embedded in a 3D world, is neither purely 2D nor 3D. Rather, it is flexible and dependent on the behavioral experience and demand.

Motion Analysis and Simulation of Complex Curved Surface WEDM System

2008 ◽  
Vol 392-394 ◽  
pp. 151-155
Author(s):  
Tong Wang ◽  
K. Jiang ◽  
Shu Qiang Xie ◽  
Shuang Shuang Hao
Keyword(s):  
Electrical Discharge Machining ◽  
Three Dimensional ◽  
Simulation Method ◽  
Curved Surface ◽  
Polar Coordinates ◽  
Curved Surfaces ◽  
Machining Quality ◽  
Motion Parameters ◽  
Dimensional Graph ◽  
Analysis Of Motion

In this paper, the characteristics and general laws of cutting complex curved surface by wire electrical discharge machining (WEDM) system are studied. Based on analysis of motion parameters the universal mathematical model of polar coordinates is derived. Moreover, the simulation of WEDM system is introduced, which is carried out by using language Visual C++ and the three dimensional graph software OpenGL.This simulation method is helpful in improving machining quality and productivity of complex curved surfaces, and is fundation for establishing CAD/CAPP/CAM technology in WEDM.

Nanofiber curvature with Rho GTPase activity increases mouse embryonic fibroblast random migration velocity

2022 ◽  
Author(s):  
Daniel T Bowers ◽  
Justin L Brown
Keyword(s):  
Stem Cell ◽  
Flat Surface ◽  
Rho Gtpase ◽  
Kinase Inhibitor ◽  
Single Cells ◽  
Stem Cell Differentiation ◽  
Migration Velocity ◽  
Embryonic Cell ◽  
Small Gtpase ◽  
Curved Surface

Abstract Mechanotransduction arises from information encoded in the shape of materials such as curvature. It induces activation of small GTPase signaling affecting cell phenotypes including differentiation. We carried out a set of preliminary experiments to test the hypothesis that curvature (1/radius) would also affect cell motility due to signal pathway crosstalk. High molecular weight poly (methyl methacrylate) straight nanofibers were electrospun with curvature ranging from 41 to 1 μm−1 and collected on a passivated glass substrate. The fiber curvature increased mouse mesenchymal stem cell aspect ratio (P < 0.02) and decreased cell area (P < 0.01). Despite little effect on some motility patterns such as polarity and persistence, we found selected fiber curvatures can increase normalized random fibroblastic mouse embryonic cell (MEF) migration velocity close to 2.5 times compared with a flat surface (P < 0.001). A maximum in the velocity curve occurred near 2.5 μm−1 and may vary with the time since initiation of attachment to the surface (range of 0–20 h). In the middle range of fiber curvatures, the relative relationship to curvature was similar regardless of treatment with Rho-kinase inhibitor (Y27632) or cdc42 inhibitor (ML141), although it was decreased on most curvatures (P < 0.05). However, below a critical curvature threshold MEFs may not be able to distinguish shallow curvature from a flat surface, while still being affected by contact guidance. The preliminary data in this manuscript suggested the large low curvature fibers were interpreted in a manner similar to a non-curved surface. Thus, curvature is a biomaterial construct design parameter that should be considered when specific biological responses are desired. Statement of integration, innovation, and insight  Replacement of damaged or diseased tissues that cannot otherwise regenerate is transforming modern medicine. However, the extent to which we can rationally design materials to affect cellular outcomes remains low. Knowing the effect of material stiffness and diameter on stem cell differentiation, we investigated cell migration and signaling on fibrous scaffolds. By investigating diameters across orders of magnitude (50–2000 nm), we identified a velocity maximum of ~800 nm. Furthermore, the results suggest large fibers may not be interpreted by single cells as a curved surface. This work presents insight into the design of constructs for engineering tissues.

Digital Planimetry With a New Adaptive Calibration Procedure Results in Accurate and Precise Wound Area Measurement at Curved Surfaces

2020 ◽  
pp. 193229682095934
Author(s):  
Piotr Foltynski ◽  
Piotr Ladyzynski
Keyword(s):  
Systematic Error ◽  
Calibration Procedure ◽  
Curved Surface ◽  
Area Measurement ◽  
Curved Surfaces ◽  
Wound Area ◽  
Optical Scanner ◽  
Adaptive Calibration ◽  
Relative Errors ◽  
Commercial Device

Background: The purpose of this study was to determine the accuracy of wound area measurement at a curved surface using a digital planimetry (DP) with the newly proposed adaptive calibration. Methods: Forty wound shapes were printed and placed at the side surfaces of cylinders with diameters of 9.4 and 6.2 cm. Area measurements were carried out using a commercial device SilhouetteMobile (Aranz, New Zealand) and the planimetric app Planimator. Planimetric area measurements were carried out using 2 one-dimensional calibration markers placed above and below the wound shape. The method of adaptive calibration for DP was described. Reference area values of wound shapes were obtained by pixel counting on digital scans made with an optical scanner. Relative errors (REs) and relative differences (RDs) for area measurements were analyzed. Results: The median of REs for the DP with adaptive calibration (DPwAC) was equal to 0.60% and was significantly smaller than the median for the SilhouetteMobile device (SMD) (2.65%), and significantly smaller than the median for the DP (2.23%). The SD of RDs for the DPwAC of 0.87% was considerably lower than for the SMD (6.45%), and for the DP without adaptive calibration (2.51%). The mean of RDs for the DPwAC (0.082%) was not significantly different from zero, which means that the systematic error was not present for the DPwAC. Conclusions: The use of the adaptive calibration in DP to measure the areas at curved surface resulted in a significant increase of accuracy and precision, and removal of systematic error. The DPwAC revealed 4.4 times lower error and 7.4 times higher precision of area measurement at curved surfaces than the SMD.

The three kinds of degree distributions and nash equilibrium on the limiting random network

2019 ◽  
Vol 20 (05) ◽  
pp. 2050033
Author(s):  
Dong Han ◽  
Min Xia
Keyword(s):  
Nash Equilibrium ◽  
Random Network ◽  
Sufficient Conditions ◽  
Curved Surface ◽  
High Dimensional ◽  
Game Model ◽  
Curved Surfaces

A generalized dynamically evolving random network and a game model taking place on the evolving network are presented. We show that there exists a high-dimensional critical curved surface of the parameters related the probabilities of adding or removing vertices or edges such that the evolving network may exhibit three kinds of degree distributions as the time goes to infinity when the parameters belong to the super-critical, critical and sub-critical curved surfaces, respectively. Some sufficient conditions are given for the existence of a regular Nash equilibrium which depends on the three kinds of degree distributions in the game model on the limiting random network.

Distance estimation from cognitive maps

1981 ◽  
Vol 13 (4) ◽  
pp. 526-550 ◽  
Author(s):  
Perry W. Thorndyke
Keyword(s):  
Distance Estimation ◽  
Cognitive Maps

Experimenal analysis of in-plane strain on curved surfaces using transferring techniques

1978 ◽  
Vol 13 (2) ◽  
pp. 121-128 ◽  
Author(s):  
J Buitrago ◽  
A J Durelli ◽  
V J Parks
Keyword(s):  
Rigid Body ◽  
Finite Deformation ◽  
Flat Surface ◽  
Flexible Structures ◽  
Strain Analysis ◽  
Curved Surfaces ◽  
Double Curvature ◽  
Threshold Strain ◽  
Rigid Body Motions ◽  
Inside Out

A new grid-transferring technique is introduced that allows the strain analysis of flat or curved surfaces of single or double curvature. The technique consists of transferring a grid from the structure to a flat surface by means of a thin, adhesive, transparent ribbon. Information is obtained along a strip, or point-by-point when circles or rosettes are used. The technique is specially suitable for the solution of problems of finite deformation of flexible structures, and its threshold strain is about 0.004. As a verification of the new method, strains obtained on a disc under diametral compression are compared with results already given in the literature. As a general example of application, strains on the anticlastic surface of tubes with and without perforation, and turned inside out, are determined. The method is not influenced by rigid-body motions.

scholarly journals Evolution of populations expanding on curved surfaces

2018 ◽  
Author(s):  
Daniel A. Beller ◽  
Kim M. J. Alards ◽  
Francesca Tesser ◽  
Ricardo A. Mosna ◽  
Federico Toschi ◽  
...  
Keyword(s):  
Range Expansion ◽  
Evolutionary Dynamics ◽  
Flat Surface ◽  
Analytical Description ◽  
Relative Increase ◽  
Curved Surfaces ◽  
Complex Environments ◽  
Neutral Genetic Diversity ◽  
Expanding Population ◽  
Dynamics Of Populations

AbstractThe expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure: of the environment shapes the population front and the evolutionary dynamics during such a range expansion is little understood. Here, we investigate the evolutionary dynamics of populations consisting of many selectively neutral genotypes expanding on curved surfaces. Using a combination of individual-based off-lattice simulations, geometrical arguments, and lattice-based stepping-stone simulations, we characterise the effect of individual bumps on an otherwise flat surface. Compared to the case of a range expansion on a flat surface:, we observe a transient relative increase, followed by a decrease, in neutral genetic diversity at the population front. Ill addition, we find that individuals at the sides of the bump have a dramatically increased expected number of descendants, while their neighbours closer to the bump’s centre are far less lucky. Both observations can be explained using an analytical description of straight paths (geodesics) on the curved surface, Complementing previous studies of heterogeneous flat environments, the findings here build our understanding of how complex environments shape the evolutionary dynamics of expanding populations.

Nanostructuring Curved Surfaces Using a Flexible Stamp

2009 ◽  
Author(s):  
Bahador Farshchian ◽  
JaeJong Lee ◽  
Sunggook Park
Keyword(s):  
Hot Embossing ◽  
Curved Surface ◽  
Curved Surfaces ◽  
Pmma Substrate ◽  
Pdms Stamp ◽  
Flat Surfaces ◽  
Force Microscopy ◽  
Atomic Force ◽  
Metallic Object ◽  
Planar Substrates

We report on a simple and effective process that allows direct imprinting of micro- and nanostructures on non-flat surfaces. A thin polydimethylsiloxane (PDMS) stamp having micro/nanogratings was placed between a metallic bar with a trapezoidal cross section or a metallic pellet and a flat polymethyl methacrylate (PMMA) substrate, followed by hot embossing at 200°C. During the hot embossing process, the metallic bar/pellet is pushed into the PMMA sheet forming a millimeter scale channel or a curved surface. Due to the presence of the PDMS stamp between the metallic object and the substrate, micro/nanostructures are produced into the channel or over the curved surface. With this method, we have successfully demonstrated micro- and nanostructures down to 300 nm wide gratings on non-flat substrates, as confirmed by scanning electron microscopy and atomic force microscopy. The process so developed will fill the gap in current micro- and nanofabrication technologies in that most of the technologies allow for patterning only on planar substrates.

scholarly journals α-Probabilistic flexible aggregate nearest neighbor search in road networks using landmark multidimensional scaling

2020 ◽  
Author(s):  
Moonyoung Chung ◽  
Woong-Kee Loh
Keyword(s):  
Multidimensional Scaling ◽  
Shortest Path ◽  
Road Network ◽  
Euclidean Distance ◽  
Nearest Neighbor ◽  
Search Algorithm ◽  
Road Networks ◽  
Path Distance ◽  
Aggregate Nearest Neighbor ◽  
Shortest Path Distance

AbstractIn spatial database and road network applications, the search for the nearest neighbor (NN) from a given query object q is the most fundamental and important problem. Aggregate nearest neighbor (ANN) search is an extension of the NN search with a set of query objects $$Q = \{ q_0, \dots , q_{M-1} \}$$ Q = { q 0 , ⋯ , q M - 1 } and finds the object $$p^*$$ p ∗ that minimizes $$g \{ d(p^*, q_i), q_i \in Q \}$$ g { d ( p ∗ , q i ) , q i ∈ Q } , where g (max or sum) is an aggregate function and d() is a distance function between two objects. Flexible aggregate nearest neighbor (FANN) search is an extension of the ANN search with the introduction of a flexibility factor $$\phi \, (0 < \phi \le 1)$$ ϕ ( 0 < ϕ ≤ 1 ) and finds the object $$p^*$$ p ∗ and the set of query objects $$Q^*_\phi $$ Q ϕ ∗ that minimize $$g \{ d(p^*, q_i), q_i \in Q^*_\phi \}$$ g { d ( p ∗ , q i ) , q i ∈ Q ϕ ∗ } , where $$Q^*_\phi $$ Q ϕ ∗ can be any subset of Q of size $$\phi |Q|$$ ϕ | Q | . This study proposes an efficient $$\alpha $$ α -probabilistic FANN search algorithm in road networks. The state-of-the-art FANN search algorithm in road networks, which is known as IER-$$k\hbox {NN}$$ k NN , used the Euclidean distance based on the two-dimensional coordinates of objects when choosing an R-tree node that most potentially contains $$p^*$$ p ∗ . However, since the Euclidean distance is significantly different from the actual shortest-path distance between objects, IER-$$k\hbox {NN}$$ k NN looks up many unnecessary nodes, thereby incurring many calculations of ‘expensive’ shortest-path distances and eventually performance degradation. The proposed algorithm transforms road network objects into k-dimensional Euclidean space objects while preserving the distances between them as much as possible using landmark multidimensional scaling (LMDS). Since the Euclidean distance after LMDS transformation is very close to the shortest-path distance, the lookup of unnecessary R-tree nodes and the calculation of expensive shortest-path distances are reduced significantly, thereby greatly improving the search performance. As a result of performance comparison experiments conducted for various real road networks and parameters, the proposed algorithm always achieved higher performance than IER-$$k\hbox {NN}$$ k NN ; the performance (execution time) of the proposed algorithm was improved by up to 10.87 times without loss of accuracy.

Structural Optimization of Woven Fabric with Curved Surface

2012 ◽  
Vol 443-444 ◽  
pp. 408-411
Author(s):  
Yan Fang Wang ◽  
Xing Feng Guo
Keyword(s):  
Structural Optimization ◽  
Shear Deformation ◽  
Three Dimensional ◽  
Single Layer ◽  
Woven Fabrics ◽  
Woven Fabric ◽  
Curved Surface ◽  
Theoretical Formula ◽  
Curved Surfaces

The woven fabric with curved surfaces is a kind of single layer woven fabrics, which was produced to smoothly fit three-dimensional solids. The warp or weft of the winding fabric bend were normally made with different lengths, which may result in shear deformation in many cases and accordingly twisting the structure of the fabric after fitted onto the solid. In order to solve the problem mentioned above, a theoretical formula was used to calculate the optimal intervals of the pick-spacing and an improved structure thus was developed in this study.

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