Basic Geometric Constructions

2021 ◽  
pp. 217-226
Author(s):  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Dimensional Space ◽  
Intersection Point ◽  
Important Application ◽  
Geometric Constructions ◽  
Clifford Torus ◽  
The Cost ◽  
Regular Homotopy ◽  
Associated Surfaces

Basic geometric constructions, including tubing, boundary twisting, pushing down intersections, and contraction followed by push-off are presented. These moves are used repeatedly later in the proof. New, detailed pictures illustrating these constructions are provided. The Clifford torus at an intersection point between two surfaces in 4-dimensional space is described. The chapter closes with an important application of some of these moves called the Geometric Casson Lemma. This lemma upgrades algebraically dual spheres to geometrically dual spheres, at the cost of introducing more self-intersections. It is also shown that an immersed Whitney move is a regular homotopy of the associated surfaces.

Determination of Hydraulic Permeability Based on the Measurements of Outflow

2015 ◽  
Vol 3 ◽  
pp. 105-116
Author(s):  
Jozef Kačur ◽  
Jozef Minár
Keyword(s):  
Unsaturated Flow ◽  
Dimensional Space ◽  
A Priori ◽  
Hydraulic Permeability ◽  
Infinite Dimensional ◽  
Tuning Parameters ◽  
Finite Dimensional ◽  
Partially Saturated Porous Media ◽  
The Cost

In this paper we present a method for the determination of the hydraulic permeability for flow in partially saturated porous media. The dependence of hydraulic permeability on effective saturation is not assumed to be a member of any specific finite dimensional class of functions (e.g. vanGenuchten-Mualem, Burdin-Mualem, Brook-Corey). Instead, an infinite dimensional space of functions with limited a priori assumptions (e.g. smoothness, monotonicity) is considered. Consequently, we face a more challenging problem compared to the finite-dimensional case, in which only few tuning parameters need to be determined. We consider the case of 1D unsaturated flow and assume that the data are collected at the outflow of the sample. The hydraulic permeability is determined in an iterative way. We minimize the cost functional reflecting the discrepancy between the measured and computed data. In doing so, we use the Gateaux differential to obtain the direction of the descent.

Cost-Sensitive Sparsity Preserving Projections for Face Recognition

2013 ◽  
Vol 760-762 ◽  
pp. 1615-1620 ◽  
Author(s):  
Xiao Yuan Jing ◽  
Wen Qian Li ◽  
Hao Gao ◽  
Yong Fang Yao ◽  
Jiang Yue Man
Keyword(s):  
Face Recognition ◽  
Sparse Representation ◽  
Dimensional Space ◽  
Recognition Rate ◽  
Recognition Task ◽  
Cost Information ◽  
The Public ◽  
Sparsity Preserving Projection ◽  
Low Dimensional ◽  
The Cost

As one of the most popular research topics, sparse representation (SR) technique has been successfully employed to solve face recognition task. Though current SR based methods prove to achieve high classification accuracy, they implicitly assume that the losses of all misclassifications are the same. However, in many real-world face recognition applications, this assumption may not hold as different misclassifications could lead to different losses. Driven by this concern, in this paper, we propose a cost-sensitive sparsity preserving projections (CSSPP) for face recognition. CSSPP considers the cost information of sparse representation while calculating the sparse structure of the training set. Then, CSSPP employs the sparsity preserving projection method to achieve the projection transform and keeps the sparse structure in the low-dimensional space. Experimental results on the public AR and FRGC face databases are presented to demonstrate that both of the proposed approaches can achieve high recognition rate and low misclassification loss, which validate the efficacy of the proposed approach.

scholarly journals Design of Fractional Order Controllers Using the PM Diagram

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2022
Author(s):  
Santiago Garrido ◽  
Concepción A. Monje ◽  
Fernando Martín ◽  
Luis Moreno
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Dimensional Space ◽  
Color Code ◽  
Graphical Modeling ◽  
Tuning Method ◽  
Graphical Tool ◽  
Rational Systems ◽  
Third Dimension ◽  
The Cost

This work presents a modeling and controller tuning method for non-rational systems. First, a graphical tool is proposed where transfer functions are represented in a four-dimensional space. The magnitude is represented in decibels as the third dimension and a color code is applied to represent the phase in a fourth dimension. This tool, which is called Phase Magnitude (PM) diagram, allows the user to visually obtain the phase and the magnitude that have to be added to a system to meet some control design specifications. The application of the PM diagram to systems with non-rational transfer functions is discussed in this paper. A fractional order Proportional Integral Derivative (PID) controller is computed to control different non-rational systems. The tuning method, based on evolutionary computation concepts, relies on a cost function that defines the behavior in the frequency domain. The cost value is read in the PM diagram to estimate the optimum controller. To validate the contribution of this research, four different non-rational reference systems have been considered. The method proposed here contributes first to a simpler and graphical modeling of these complex systems, and second to provide an effective tool to face the unsolved control problem of these systems.

Study on the Mapping of Streaming Application on Many-Core Architecture

2011 ◽  
Vol 58-60 ◽  
pp. 298-303
Author(s):  
Lei Yu ◽  
Zhi Yong Liu ◽  
Dong Rui Fan ◽  
Yike Ma ◽  
Feng Long Song ◽  
...  
Keyword(s):  
Parallel Processing ◽  
Large Scale ◽  
Mapping Method ◽  
Important Application ◽  
Parallel Method ◽  
Streaming Application ◽  
Scratch Pad Memory ◽  
The Common ◽  
Many Core ◽  
The Cost

Streaming program is an important application of large-scale parallel processing. The common parallel method for streaming program is not suitable for many-core architecture. For the streaming programs, this paper proposes a novel mapping method based on hardwire architecture. The method uses SPM (Scratch-Pad Memory) to transfer the data. Thus, the number of accessing shared Cache is reduced and the cost of communication is also reduced. The experimental results show the effectiveness of the method.

Study on dual peg-in-hole insertion using of constraints formed in the environment

2017 ◽  
Vol 44 (6) ◽  
pp. 730-740 ◽  
Author(s):  
Jianhua Su ◽  
Rui Li ◽  
Hong Qiao ◽  
Jing Xu ◽  
Qinglin Ai ◽  
...  
Keyword(s):  
Configuration Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Force Sensor ◽  
High Dimensional ◽  
Content Type ◽  
Attractive Region ◽  
Low Dimensional ◽  
The Cost ◽  
Yaw Angle

Purpose The purpose of this paper is to develop a dual peg-in-hole insertion strategy. Dual peg-in-hole insertion is the most common task in manufacturing. Most of the previous work develop the insertion strategy in a two- or three-dimensional space, in which they suppose the initial yaw angle is zero and only concern the roll and pitch angles. However, in some case, the yaw angle could not be ignored due to the pose uncertainty of the peg on the gripper. Therefore, there is a need to design the insertion strategy in a higher-dimensional configuration space. Design/methodology/approach In this paper, the authors handle the insertion problem by converting it into several sub-problems based on the attractive region formed by the constraints. The existence of the attractive region in the high-dimensional configuration space is first discussed. Then, the construction of the high-dimensional attractive region with its sub-attractive region in the low-dimensional space is proposed. Therefore, the robotic insertion strategy can be designed in the subspace to eliminate some uncertainties between the dual pegs and dual holes. Findings Dual peg-in-hole insertion is realized without using of force sensors. The proposed strategy is also used to demonstrate the precision dual peg-in-hole insertion, where the clearance between the dual-peg and dual-hole is about 0.02 mm. Practical implications The sensor-less insertion strategy will not increase the cost of the assembly system and also can be used in the dual peg-in-hole insertion. Originality/value The theoretical and experimental analyses for dual peg-in-hole insertion are proposed without using of force sensor.

FluxTracer: A 3D-Partitioning and Radiant Flux Computer Tool to Analyse the Optical Behaviour of Light Collection and Concentration Subsystems Using High Performance Computers

2018 ◽  
Author(s):  
Manuel Blanco ◽  
Evgeny Votyakov ◽  
Chariton Christou ◽  
Costas N. Papanicolas ◽  
Clotilde Corsi ◽  
...  
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Traditional Approach ◽  
Dimensional Space ◽  
Radiant Energy ◽  
Light Collection ◽  
Analysis Tools ◽  
Cost Competitiveness ◽  
The Cost ◽  
High Performance Computers

The light collection and concentration subsystem (LCCS) of any concentrating solar thermal (CST) system is composed of the surfaces that collect and concentrate the sunlight and of the input surfaces of the receivers, or receivers’ envelopes, where the light is concentrated. For all commercial CST technologies the LCCS is, together with the power block, the subsystem that has more influence in the overall performance and cost. Thus, its optimization is critical to increase the cost-competitiveness of these systems. This optimization requires, in many cases, the optimization of the position, geometry and size of a very large number of solar collecting and concentrating surfaces as well as the optimization of the shape and size of the input surfaces of the receivers where the sunlight is concentrated. Because a full optimization requires the exploration of a configuration space with a very large number of dimensions, the traditional approach consist in making many initial assumptions to drastically reduce the number of dimensions of the configuration space to a handful, so that the optimization can be carried out using conventional high-end workstations in a matter of hours. However, to achieve relevant breakthroughs and to substantially increase the cost-competitiveness of CST systems a bolder approach is needed, where sophisticated design and analysis tools, engineered from the start to be used in High Performance Computers (HPC), will be combined with sophisticated optimization strategies targeted to explore and find optimal solutions in very high dimensional configuration spaces. This paper presents the first of a series of such design and analysis tools. The tool, call Flux Tracer, partitions the three-dimensional space in which the LCC subsystem under analysis is immersed into volumetric pixels (voxels) and computes the radiant energy flux that traverses each voxel as a function of time. It integrates the energy density in every voxel overtime, providing detailed information regarding how the radiant energy flows in space in a given LCC subsystem and in a given period of time. This information is the cornerstone of the highly sophisticated computational LCC subsystem optimization framework The Cyprus Institute (CYI) is developing, in collaboration with the Australian National University (ANU), targeted to be used in HPC’s.

scholarly journals Minimum action principle and shape dynamics

2017 ◽  
Vol 14 (130) ◽  
pp. 20170031 ◽  
Author(s):  
Patrice Koehl
Keyword(s):  
Elastic Energy ◽  
Dimensional Space ◽  
Shape Recognition ◽  
Three Dimensional ◽  
The Other ◽  
Success Rates ◽  
Evolutionary Patterns ◽  
The Cost ◽  
Better Than ◽  
Three Dimensional Space

In this paper, we propose a new method for computing a distance between two shapes embedded in three-dimensional space. Instead of comparing directly the geometric properties of the two shapes, we measure the cost of deforming one of the two shapes into the other. The deformation is computed as the geodesic between the two shapes in the space of shapes. The geodesic is found as a minimizer of the Onsager–Machlup action, based on an elastic energy for shapes that we define. Its length is set to be the integral of the action along that path; it defines an intrinsic quasi-metric on the space of shapes. We illustrate applications of our method to geometric morphometrics using three datasets representing bones and teeth of primates. Experiments on these datasets show that the variational quasi-metric we have introduced performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.

Electrochemical Characterization of Synthesized Ni–Co and Ni–Co–Fe Electrodes for Methanol Fuel Cell

2015 ◽  
Vol 12 (1) ◽  
Author(s):  
Subir Paul ◽  
Sk Naimuddin
Keyword(s):  
Fuel Cell ◽  
Electrode Materials ◽  
Electrochemical Impedance ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sem Images ◽  
Cell Potential ◽  
X Ray ◽  
Electrode Reactions ◽  
The Cost

Pt based materials having high electrocatalytic properties are normally used for the electrodes of the fuel cell. But the cost of the material limits the commercialization of alcoholic fuel cell. Non-Pt based metals and alloys as electrode materials for methyl alcohol fuel cells have been investigated with an aim of finding high electrocatalytic surface property for the faster electrode reactions. Electrodes were fabricated by electrodeposition on pure Al foil, from an electrolyte of Ni, Co, and Fe salts. The optimum condition of electrodeposition was found by a series of experiments, varying the chemistry of the electrolyte, pH, temperature, current, and cell potential. Polarization study of the coated Ni–Co or Ni–Co–Fe alloy on pure Al was found to exhibit high exchange current density, indicating an improved electrocatalytic surface with faster charge–discharge reactions at anode and cathode and low overvoltage. Electrochemical impedance studies on the coated and uncoated surface clearly showed that the polarization resistance and impedance were decreased by Ni–Co or N–Co–Fe coating. X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDX), and atomic absorption spectroscopy (AAS) studies confirmed the presence of alloying elements and constituents of the alloy. The morphology of the deposits from scanning electron microscope (SEM) images indicated that the electrode surface was a three-dimensional space which increased the effective surface area for the electrode reactions to take place.

An Improved Augmented Line Segment based Algorithm for the Generation of Rectilinear Steiner Minimum Tree

2017 ◽  
Vol 7 (3) ◽  
pp. 1262 ◽  
Author(s):  
Vani V ◽  
G.R. Prasad
Keyword(s):  
Line Segment ◽  
Vlsi Design ◽  
Intersection Point ◽  
Global Routing ◽  
Good Reduction ◽  
Wire Length ◽  
Line Segments ◽  
Main Application ◽  
The Cost ◽  
Steiner Minimum Tree

An improved Augmented Line Segment Based (ALSB) algorithm for the construction of Rectilinear Steiner Minimum Tree using augmented line segments is proposed. The proposed algorithm works by incrementally increasing the length of line segments drawn from all the points in four directions. The edges are incrementally added to the tree when two line segments intersect. The reduction in cost is obtained by postponing the addition of the edge into the tree when both the edges (upper and lower L-shaped layouts) are of same length or there is no overlap. The improvement is focused on reduction of the cost of the tree and the number of times the line segments are augmented. Instead of increasing the length of line segments by 1, the line segments length are doubled each time until they cross the intersection point between them. The proposed algorithm reduces the wire length and produces good reduction in the number of times the line segments are incremented. Rectilinear Steiner Minimum Tree has the main application in the global routing phase of VLSI design. The proposed improved ALSB algorithm efficiently constructs RSMT for the set of circuits in IBM benchmark.

Acoustic Monitoring of the Great Reed Warbler Using Multiple Microphone Arrays and Robot Audition

2017 ◽  
Vol 29 (1) ◽  
pp. 224-235 ◽  
Author(s):  
Shiho Matsubayashi ◽  
◽  
Reiji Suzuki ◽  
Fumiyuki Saito ◽  
Tatsuyoshi Murate ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Microphone Arrays ◽  
Great Reed Warbler ◽  
Reed Warbler ◽  
Localization Accuracy ◽  
Point Count ◽  
Robot Audition ◽  
Singing Activity ◽  
Point Count Method ◽  
The Cost

[abstFig src='/00290001/21.jpg' width='300' text='Spatial distribution pattern of the observed birds and localized sounds' ] This paper reports the results of our field test of HARKBird, a portable system that consists of robot audition, a laptop PC, and omnidirectional microphone arrays. We assessed its localization accuracy to monitor songs of the great reed warbler (Acrocephalus arundinaceus) in time and two-dimensional space by comparing locational and temporal data collected by human observers and HARKBird. Our analysis revealed that stationarity of the singing individual affected the spatial accuracy. Temporally, HARKBird successfully captured the exact song duration in seconds, which cannot be easily achieved by human observers. The data derived from HARKBird suggest that one of the warbler males dominated the sound space. Given the assumption that the cost of the singing activity is represented by song duration in relation to the total recording session, this particular male paid a higher cost of singing, possibly to win the territory of best quality. Overall, this study demonstrated the high potential of HARKBird as an effective alternative to the point count method to survey bird songs in the field.

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