Academic literature on the topic 'RANSAC connectivity field'

Graph theory is the principal field of mathematics. In this manuscript, we have discussed the toroidal polyhex graph. Some new indices such as reduced reciprocal randic, arithmetic geometric, SK, SK1, SK2 indices, First Zagrab, the general sum-connectivity, SCIλ, and the forgotten index have been used. We have computed the closed form of topological indices of toroidal polyhex graph via M-Polynomial.

Abstract Grid implementation is a principal unit in electrical and electronic engineering but it depends on the domain of these projects. For example, depending on the grid and the signal processing in that fields of electronic and electrical engineering, such as more abstract mathematics in signal conversion and e-transmission theory griding, etc. Provides transmission through grid nodes. Graph theory is very useful in research fields. As topological indices, there are more actual numbers associated with chemical composition complaints connected to the chemical grid with physical and chemical properties and reactions. In this paper, we expand the work to interconnected grid and examine the first Zagreb, the second Zagreb, Randic, sum-connectivity, harmonic, geometric, and atom bond connectivity exponents of hierarchical hypercube network based on vertex-edge and edge-vertex degree.

The article is aimed at demonstrating the practical application of graph theory as a subsection of the theoretical foundations of computer science in solving one of the interdisciplinary problems — describing the structure of the cadmium sulfide molecule using methods and indices of chemoinformatics. The article presents the results of calculations of the atom-bond connectivity index (ABC), of the geometric and arithmetic index GA, of the generalized Randic index, GA5 and ABC4, of the Zagreb indices for the chemical graph of cadmium sulfide (CdS). Topological indices for cadmium sulfide are considered for the first time, although the task of calculating these indices is not new in itself. The relevance of the results is emphasized by the fact that cadmium sulfide is widely used in various fields, such as optoelectronics, photodetectors, photoresistors, etc.

<abstract><p>Zagreb indices are well-known and historical indices that are very useful to calculate the properties of compounds. In the last few years, various kinds of Zagreb and Randic indices are investigated and defined to fulfil the demands of various engineering applications. Phenylenes are a class of conjugated hydrocarbons composed of a special arrangement of six- and four-membered rings. This special chain, produced by zeroth-order Markov process has been commonly appeared in the field of pharmacology and materials. Here, we compute the expected values of a multiplicative versions of the geometric arithmetic and atomic bond connectivity indices for these special hydrocarbons. Moreover, we make comparisons in the form of explicit formulae and numerical tables between the expected values of these indices in the random polyphenyl $ \mathbb{P}_n $ and spiro $ \mathbb{S}_n $ chains.</p></abstract>

We have multiple real numbers that describe chemical descriptors in the field of Graph theory. These descriptors constitute the entire structure of a graph, which possesses an actual chemical structure. Among these, the main focus of topological indices is that they are associated with many non-identical physiochemical properties of chemical compounds. Also, the biological properties of chemical compounds can be established by the topological indices. In this analysis, we compute the Reciprocal Randic index〖(R〗^(-1)), Reduced Reciprocal Randic index(〖RR〗^(-1)), Atom-bond Connectivity index(ABC) and the geometric arithmetic index(GA) of thorn graphs are obtained theoretically.

Fracture and fracture network modelling is a multi-disciplinary research area. Although the literature in general is significant, many research challenges remain. The complex geometry and topology of realistic fracture networks largely determine the static and dynamic mechanical properties of rock. In applications to hot dry rock geothermal reservoirs it is not possible to observe or measure fractures directly on any scale and the only data available are indirect measurements, such as seismic activity generated by hydraulic fracture stimulation. The lack of direct data and the complexities of the fracture characteristics make fracture network prediction and modelling in these applications very difficult. The ultimate purpose of the fracture and fracture network models is to evaluate the response of the fracture system to stress regimes and fluid flow. As understanding of the effective factors in the geometrical modelling of fractures and consequently topological properties of fracture networks increases, more accurate and hence more reliable results can be achieved from associated analyses. For flow modelling in geothermal reservoirs, the critical component of a fracture model is the connectivity of the fractures as this determines the technical feasibility of heat production and is the single most significant factor in converting a heat resource to a reserve. The ability to model this component effectively and to understand the associated system is severely constrained by the lack of direct data. In simulations, the connectivity of a fracture network can be controlled to a limited extent by adjusting the fracture and fracture network parameters (e.g., locations, orientations) of the defining distribution functions. In practical applications connectivity is a response of the system not a variable. It is essential to pursue modelling methods that maximise the extraction of information from the available data so as to achieve the highest possible accuracy in the modelling. Although the evaluation of fracture connectivity is an active research area, widely reported in the literature, almost all connectivity measures are based on degraded representations of the fracture network i.e., lattice-based. The loss of fracture connectivity information caused by using discrete representations is significant even when very high resolutions (assuming they are feasible) are used. This is basically due to the fact that the aperture dimensions of fractures are several magnitudes smaller than their lengths. If discretisation is necessary, then a better approach would be to retain all connectivity information between fractures, i.e. for connectivity information to remain invariant to the resolution of the discretisation. Such a method would provide more reliable evaluation of connectivity. This thesis covers the modelling of fracture networks, the characterisation (particularly connectivity) of fracture networks and applications.
Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 2014