Tree Graph Representation Research Articles

A novel design methodology for fixed-shaft hybrid powertrain with a single-motor

Hybrid power configuration has two kinds of power sources, how to design the configuration to couple the energy of the two power sources is an important part of the development of hybrid power technology. In the systematic design scheme of hybrid power, most scholars focus on the design of planetary gear hybrid power configuration, but lack of systematic design scheme of fixed-shaft hybrid power configuration. In this paper, based on the equivalent tree graph method, the fixed-shaft hybrid configuration is transformed into the corresponding tree graph representation, and all possible configurations are generated by the combination of the trunk, branches and leaves. Add the corresponding design constraints, use Matlab to realize automatic generation and screening, and finally obtain the required configuration after specification. The configuration is verified in the Simulink & Amesim co-simulation environment. The results show that the proposed single-motor fixed-shaft hybrid power configuration has certain advantages in economy compared with the traditional P2 and P3 configurations, and its dynamic performance is the same as that of P2 configurations and superior to P3 configurations.

A Mathematical Analysis of HDV Genotypes: From Molecules to Cells.

Hepatitis D virus (HDV) is classified according to eight genotypes. The various genotypes are included in the HDVdb database, where each HDV sequence is specified by its genotype. In this contribution, a mathematical analysis is performed on RNA sequences in HDVdb. The RNA folding predicted structures of the Genbank HDV genome sequences in HDVdb are classified according to their coarse-grain tree-graph representation. The analysis allows discarding in a simple and efficient way the vast majority of the sequences that exhibit a rod-like structure, which is important for the virus replication, to attempt to discover other biological functions by structure consideration. After the filtering, there remain only a small number of sequences that can be checked for their additional stem-loops besides the main one that is known to be responsible for virus replication. It is found that a few sequences contain an additional stem-loop that is responsible for RNA editing or other possible functions. These few sequences are grouped into two main classes, one that is well-known experimentally belonging to genotype 3 for patients from South America associated with RNA editing, and the other that is not known at present belonging to genotype 7 for patients from Cameroon. The possibility that another function besides virus replication reminiscent of the editing mechanism in HDV genotype 3 exists in HDV genotype 7 has not been explored before and is predicted by eigenvalue analysis. Finally, when comparing native and shuffled sequences, it is shown that HDV sequences belonging to all genotypes are accentuated in their mutational robustness and thermodynamic stability as compared to other viruses that were subjected to such an analysis.

A Mathematical Analysis of RNA Structural Motifs in Viruses

RNA stem-loop structures play an important role in almost every step of the viral replication cycle. In this contribution, a mathematical analysis is performed on a large dataset of RNA secondary structure elements in the coding regions of viruses by using topological indices that capture the Laplacian eigenvalues of the associated RNA graph representations and thereby enable structural classification, supplemented by folding energy and mutational robustness. The application of such an analysis for viral RNA structural motifs is described, being able to extract structural categories such as stem-loop structures of different sizes according to the tree-graph representation of the RNA structure, in our attempt to find novel functional motifs. While the analysis is carried on a large dataset of viral RNA structures, it can be applied more generally to other data that involve RNA secondary structures in biological agents.

Investigating exploratory search activities based on the stratagem level in digital libraries

In this paper we present the results of a user study on exploratory search activities in a social science digital library. We conducted a user study with 32 participants with a social sciences background -- 16 postdoctoral researchers and 16 students -- who were asked to solve a task on searching related work to a given topic. The exploratory search task was performed in a 10-minutes time slot. The use of certain search activities is measured and compared to gaze data recorded with an eye tracking device. We use a novel tree graph representation to visualise the users' search patterns and introduce a way to combine multiple search session trees. The tree graph representation is capable to create one single tree for multiple users and to identify common search patterns. In addition, the information behaviour of students and postdoctoral researchers is being compared. The results show that search activities on the stratagem level are frequently utilised by both user groups. The most heavily used search activities were keyword search, followed by browsing through references and citations, and author searching. The eye tracking results showed an intense examination of documents metadata, especially on the level of citations and references. When comparing the group of students and postdoctoral researchers we found significant differences regarding gaze data on the area of the journal name of the seed document. In general, we found a tendency of the postdoctoral researchers to examine the metadata records more intensively with regards to dwell time and the number of fixations.

Comparative analysis of N-hydroxy-2,6-bis (p-chlorophenyl)-3-isopropylpiperidin-4-one semicarbazone and N-hydroxy-2,6-bis (p-chlorophenyl)-3-isopropylpiperidin-4-one thiosemicarbazone by graceful tree graph, non-graceful graph and cliques representation of graph with the data spectrum

Comparative analysis of N-hydroxy-2,6-bis (p-chlorophenyl)-3-isopropylpiperidin-4-one semicarbazone and N-hydroxy-2,6-bis (p-chlorophenyl)-3-isopropylpiperidin-4-one thiosemicarbazone by graceful tree graph, non-graceful graph and cliques representation of graph with the data spectrum

Comparative analysis of N-hydroxy-2,6-bis (p-chlorophenyl)-3-isopropylpiperidin-4-one semicarbazone and N-hydroxy-2,6-bis (p-chlorophenyl)-3-isopropylpiperidin-4-one thiosemicarbazone by graceful tree graph, non-graceful graph and cliques representation of graph with the data spectrum

In this paper, the graph theory has been developed into an extensive and popular branch of mathematics, which in turn has been applied to many problems in semicarbazone and thiosemicarbazone compounds. The compounds such as N-hydroxy-2,6-bis(pchlorophenyl)-3-isopropylpiperidin-4-one semicarbazone and N-hydroxy-2,6-bis(p-chlorophenyl)-3-isopropylpiperidin-4-one thiosemicarbazone have been synthesised and characterised on the basis of elemental analysis such as 1H NMR and 13C NMR. Several open problems that have gained respect with the help of graph theory, which can be recorded through simple, finite, connected and undirected group. The compounds which have been synthesised can be split into four sub groups. Each subset has been defined such as alkyl by graceful tree graph, N-hydroxy ring and phenyl compounds by non-graceful graph and semicarbazone and thiosemicarbazone by cliques representations of graph. The compound has been represented mathematically in terms of −p vertices and −q cliques. A complete picturisation of the compounds by combining all the subgroups together has been schematically icono-graphed.

Design and Implementation of an Improved Routing Algorithm using Frequent Item Set Mining

This paper presents how routers can manage large amount of data packets as routers exchange information with each other to find the best possible route to a destination thus graphs represent a more general class of structures than sets, sequences, lattices and trees. Since on web heavy range of information is represented by a graph as in social networks so modelling a sophisticated network by statistical analysis requires efficiency in routing packets within an autonomous system hence this approach here focuses on how routers can upgrade their configuration to exactly route the frequently occuring data packets within a homogeneous network. General Terms RTB-FP–Tree graph representation of a homogeneous network, improved algorithm and network statistics based forwarding table.

Theoretical and Experimental Exploration of the Energy Landscape of LiI

The prediction of the existence and stability of (meta)-stable phases in a chemical system is realized via a two-step process: identification of structure candidates through global exploration of the classical empirical energy landscape, followed by a local optimization of the candidates on ab-initio level employing a heuristic algorithm. From the computed energy/volume curves, one can then calculate the thermodynamically stable phase at a given pressure and the transition pressures among the phases. In order to gain insight into the kinetic stability of the structure candidates, one computes estimates of the energy and enthalpy barriers around the structures with the so-called threshold algorithm, yielding a tree graph representation of the chemical system. In this work we perform a theoretical and experimental study of the LiI energy landscape. We determine the structure candidates, construct the tree graph representation and compute the abinitio energy/volume curves for the hypothetical structures. We find that the thermodynamically preferred modifications at standard pressure should exhibit the rock salt and the wurtzite structure, respectively. In order to validate our predictions by experiments, we have employed the newly developed ´Low-Temperature - Atomic Beam Deposition` (LT-ABD) technique, which allows to disperse the components of the desired product at an atomic level and in an appropriate ratio. After depositing LiI at T = 77 K, the first crystallization occurs at T » 173 K in the wurtzite-type structure followed by a transition to the more stable rock salt-type structure at T » 273 K. At room temperature only the cubic phase remains.

Spectral Decomposition for the Search and Analysis of RNA Secondary Structure

Scales in RNA, based on geometrical considerations, can be exploited for the analysis and prediction of RNA structures. By using spectral decomposition, geometric information that relates to a given RNA fold can be reduced to a single positive scalar number, the second eigenvalue of the Laplacian matrix corresponding to the tree-graph representation of the RNA secondary structure. Along with the free energy of the structure, being the most important scalar number in the prediction of RNA folding by energy minimization methods, the second eigenvalue of the Laplacian matrix can be used as an effective signature for locating a target folded structure given a set of RNA folds. Furthermore, the second eigenvector of the Laplacian matrix can be used to partition large RNA structures into smaller fragments. An illustrative example is given for the use of the second eigenvalue to predict mutations that may cause structural rearrangements, thereby disrupting stable motifs.

A tree obscured by vines: horizontal gene transfer and the median tree method of estimating species phylogeny.

A phylogeny is a tree graph representation of genealogical relationships between biological objects. It is of general interest to estimate the phylogeny of whole organisms (species trees) using bio-molecular sequences. When multiple sequences are available for each organism such as with whole genome data, individual phylogenies estimated by each molecule (gene trees) may not be concordant. The lack of concordance may be due to actual biological mechanisms such as horizontal transfer of the molecules. Here, we present a new phylogeny estimation method designed to estimate the species tree despite such horizontal transfer. It uses the idea that horizontal transfer distorts distance relationships between pairs of species but a median estimate of the distances is robust to such distortions. We demonstrate the utility of our method using a simulation study.

Configuration synthesis of machining centers without tool change arms

The purpose of this paper is to generate all possible configurations of machining centers without tool change arms. The topology and motion characteristics of machining centers are discussed first. And, the tree-graph representation is applied for describing the topology structures of machining centers based on defined coordinate systems. Then, by applying the techniques of generalization and theory of graphs, generalized tree graphs and atlas of tree graphs are obtained. Finally, a methodology is presented for synthesizing the mechanisms of machining centers with required topology and motion characteristics. Machining centers without tool change arms up to seven links are synthesized. As the results, the mechanisms of machining centers with 6 and 7 links have 2 and 13 design configurations, respectively. Furthermore, the result of this paper provides a systematic approach for synthesizing spatial open-type mechanisms with motion requirements.

Tree graph representation of hamiltonian paths

Paths along faces of a polyhedron can be assimilated to paths along the branches of a tree graph. This paper shows the pruned trees corresponding to all Hamiltonian paths of regular polyhedra enumerated by the author in a previous paper [1].

Computational Complexity of Coherent Systems and the Reliability Polynomial

There are three general methods for system reliability evaluation, namely; (1) inclusion–exclusion, (2) sum of disjoint products, and (3) pivoting. Of these, only pivoting can be applied directly to a logic tree or network graph representation without first finding minimal path (or cut) sets. Domination theory provides the basis for selecting optimal pivoting strategies. Simple proofs of domination-theory results for coherent systems are given, based on the reliability polynomial. These results are related to the problem of finding efficient strategies for computing coherent system reliability. The original results for undirected networks are due to Satyanarayana and Chang [5] (cf. [1]). Many of the original set theoretic results are due to Huseby [3]. However, he does not use the reliability polynomial to prove his results.