A New General Incremental Algorithm for Conic Section

2014 ◽  
Author(s):  
E. Banissi ◽  
M.K. Golipour
Keyword(s):  
Incremental Algorithm ◽  
Conic Section

2. Note on the Hodograph

1869 ◽  
Vol 6 ◽  
pp. 221-226
Author(s):  
Tait
Keyword(s):  
Fixed Point ◽  
Single Particle ◽  
Analytical Methods ◽  
Present Note ◽  
Conic Section ◽  
Real Importance

The object of the present Note is to show, by a few examples (of which, however, the last is the only one of any real importance), how easily the geometrical ideas supplied by Hamilton's beautiful invention of the Hodograph enable us to dispense with analytical processes in the establishment of some of the fundamental propositions connected with the motion of a single particle, besides many others which are merely curious; and also how they help us to understand the full bearing of some of the analytical methods. Some of the simplest of such geometrical investigations are given in “Tait and Steele's Dynamics of a Particle,” and will not be reproduced here; though a few of the results will be assumed,—as, for instance, that when the acceleration is directed to a fixed point, and varies inversely as the square of the distance from it, the hodograph is a circle, and the path a conic section, of which the point is a focus.

scholarly journals Discovering the Giant Nest Architecture of Grass-Cutting Ants, Atta capiguara (Hymenoptera, Formicidae)

2017 ◽  
Author(s):  
Luiz Carlos Forti ◽  
Ana Paula Protti de Andrade ◽  
Roberto da Silva Camargo ◽  
Nadia Caldato ◽  
Aldenise Alves Moreira
Keyword(s):  
Main Part ◽  
Ground Level ◽  
Conic Section ◽  
Nest Architecture ◽  
Cerrado Biome ◽  
Loose Soil ◽  
Internal Structures ◽  
Length Width ◽  
Typical Shape

Atta capiguara is a grass-cutting ant species frequently found in Cerrado biome. However, little is known about the giant nest architecture of this ant. In this study, we investigated the architecture of three A. capiguara nests from the fragment of cerrado in Botucatu, São Paulo, Brazil. Casts were made of the nests by filling them with cement to permit better visualization of internal structures such as chambers and tunnels. After excavation, the depth and dimensions (length, width, and height) of the chambers were measured. The results showed the typical shape of Atta capiguara nests consisting of mounds of loose soil with unique features resembling a conic section. The fungus chambers were found outside the apparent main part of the nest and were spaced apart and distributed laterally at ground level. The waste chambers were located beneath the largest mound of loose soil. Both the fungus and waste chambers exhibited a sectoral distribution. Our study contributes to a better understanding of the so far unknown nest architecture of the grass-cutting ant A. capiguara.

scholarly journals TRAFFIC LIGHT DETECTION USING CONIC SECTION GEOMETRY

2016 ◽  
Vol III-1 ◽  
pp. 191-200
Author(s):  
S. Hosseinyalmdary ◽  
A. Yilmaz
Keyword(s):  
Prior Knowledge ◽  
Pose Estimation ◽  
Open Problem ◽  
Autonomous Vehicles ◽  
Conic Section ◽  
Traffic Light ◽  
Light Detection ◽  
State Recognition ◽  
Traffic Lights ◽  
Stereo Cameras

Traffic lights detection and their state recognition is a crucial task that autonomous vehicles must reliably fulfill. Despite scientific endeavors, it still is an open problem due to the variations of traffic lights and their perception in image form. Unlike previous studies, this paper investigates the use of inaccurate and publicly available GIS databases such as OpenStreetMap. In addition, we are the first to exploit conic section geometry to improve the shape cue of the traffic lights in images. Conic section also enables us to estimate the pose of the traffic lights with respect to the camera. Our approach can detect multiple traffic lights in the scene, it also is able to detect the traffic lights in the absence of prior knowledge, and detect the traffics lights as far as 70 meters. The proposed approach has been evaluated for different scenarios and the results show that the use of stereo cameras significantly improves the accuracy of the traffic lights detection and pose estimation.

scholarly journals Incremental Method of Generating Decision Implication Canonical Basis

2021 ◽  
Author(s):  
Shaoxia Zhang ◽  
Deyu Li ◽  
Yanhui Zhai
Keyword(s):  
Formal Concept Analysis ◽  
Canonical Basis ◽  
Concept Analysis ◽  
Experimental Results ◽  
Incremental Algorithm ◽  
Compact Representation ◽  
Formal Concept ◽  
Practical Applications ◽  
Incremental Method ◽  
Elementary Representation

Abstract Decision implication is an elementary representation of decision knowledge in formal concept analysis. Decision implication canonical basis (DICB), a set of decision implications with completeness and nonredundancy, is the most compact representation of decision implications. The method based on true premises (MBTP) for DICB generation is the most efficient one at present. In practical applications, however, data is always changing dynamically, and MBTP has to re-generate inefficiently the whole DICB. This paper proposes an incremental algorithm for DICB generation, which obtains a new DICB just by modifying and updating the existing one. Experimental results verify that when the samples in data are much more than condition attributes, which is actually a general case in practical applications, the incremental algorithm is significantly superior to MBTP. Furthermore, we conclude that, even for the data in which samples is less than condition attributes, when new samples are continually added into data, the incremental algorithm must be also more efficient than MBTP, because the incremental algorithm just needs to modify the existing DICB, which is only a part of work of MBTP.

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