Search results for: graph storage structure
9936 Characterising Stable Model by Extended Labelled Dependency Graph
Authors: Asraful Islam
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Extended dependency graph (EDG) is a state-of-the-art isomorphic graph to represent normal logic programs (NLPs) that can characterize the consistency of NLPs by graph analysis. To construct the vertices and arcs of an EDG, additional renaming atoms and rules besides those the given program provides are used, resulting in higher space complexity compared to the corresponding traditional dependency graph (TDG). In this article, we propose an extended labeled dependency graph (ELDG) to represent an NLP that shares an equal number of nodes and arcs with TDG and prove that it is isomorphic to the domain program. The number of nodes and arcs used in the underlying dependency graphs are formulated to compare the space complexity. Results show that ELDG uses less memory to store nodes, arcs, and cycles compared to EDG. To exhibit the desirability of ELDG, firstly, the stable models of the kernel form of NLP are characterized by the admissible coloring of ELDG; secondly, a relation of the stable models of a kernel program with the handles of the minimal, odd cycles appearing in the corresponding ELDG has been established; thirdly, to our best knowledge, for the first time an inverse transformation from a dependency graph to the representing NLP w.r.t. ELDG has been defined that enables transferring analytical results from the graph to the program straightforwardly.Keywords: normal logic program, isomorphism of graph, extended labelled dependency graph, inverse graph transforma-tion, graph colouring
Procedia PDF Downloads 2159935 Reductions of Control Flow Graphs
Authors: Robert Gold
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Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modelled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyse the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.Keywords: control flow graph, graph reduction, software engineering, software applications
Procedia PDF Downloads 5529934 Introduction to Paired Domination Polynomial of a Graph
Authors: Puttaswamy, Anwar Alwardi, Nayaka S. R.
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One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs.Keywords: domination polynomial, paired dominating set, paired domination number, paired domination polynomial
Procedia PDF Downloads 2329933 Graph-Oriented Summary for Optimized Resource Description Framework Graphs Streams Processing
Authors: Amadou Fall Dia, Maurras Ulbricht Togbe, Aliou Boly, Zakia Kazi Aoul, Elisabeth Metais
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Existing RDF (Resource Description Framework) Stream Processing (RSP) systems allow continuous processing of RDF data issued from different application domains such as weather station measuring phenomena, geolocation, IoT applications, drinking water distribution management, and so on. However, processing window phase often expires before finishing the entire session and RSP systems immediately delete data streams after each processed window. Such mechanism does not allow optimized exploitation of the RDF data streams as the most relevant and pertinent information of the data is often not used in a due time and almost impossible to be exploited for further analyzes. It should be better to keep the most informative part of data within streams while minimizing the memory storage space. In this work, we propose an RDF graph summarization system based on an explicit and implicit expressed needs through three main approaches: (1) an approach for user queries (SPARQL) in order to extract their needs and group them into a more global query, (2) an extension of the closeness centrality measure issued from Social Network Analysis (SNA) to determine the most informative parts of the graph and (3) an RDF graph summarization technique combining extracted user query needs and the extended centrality measure. Experiments and evaluations show efficient results in terms of memory space storage and the most expected approximate query results on summarized graphs compared to the source ones.Keywords: centrality measures, RDF graphs summary, RDF graphs stream, SPARQL query
Procedia PDF Downloads 2039932 Eccentric Connectivity Index, First and Second Zagreb Indices of Corona Graph
Authors: A. Kulandai Therese
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The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics.In this paper, we present the explicit eccentric connectivity index, first and second Zagreb indices for a Corona graph and sub division-related corona graphs.Keywords: corona graph, degree, eccentricity, eccentric connectivity index, first zagreb index, second zagreb index, subdivision graphs
Procedia PDF Downloads 3429931 Multi-Stream Graph Attention Network for Recommendation with Knowledge Graph
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In recent years, Graph neural network has been widely used in knowledge graph recommendation. The existing recommendation methods based on graph neural network extract information from knowledge graph through entity and relation, which may not be efficient in the way of information extraction. In order to better propose useful entity information for the current recommendation task in the knowledge graph, we propose an end-to-end Neural network Model based on multi-stream graph attentional Mechanism (MSGAT), which can effectively integrate the knowledge graph into the recommendation system by evaluating the importance of entities from both users and items. Specifically, we use the attention mechanism from the user's perspective to distil the domain nodes information of the predicted item in the knowledge graph, to enhance the user's information on items, and generate the feature representation of the predicted item. Due to user history, click items can reflect the user's interest distribution, we propose a multi-stream attention mechanism, based on the user's preference for entities and relationships, and the similarity between items to be predicted and entities, aggregate user history click item's neighborhood entity information in the knowledge graph and generate the user's feature representation. We evaluate our model on three real recommendation datasets: Movielens-1M (ML-1M), LFM-1B 2015 (LFM-1B), and Amazon-Book (AZ-book). Experimental results show that compared with the most advanced models, our proposed model can better capture the entity information in the knowledge graph, which proves the validity and accuracy of the model.Keywords: graph attention network, knowledge graph, recommendation, information propagation
Procedia PDF Downloads 1199930 Evaluation of SDS (Software Defined Storage) Controller (CorpHD) for Various Storage Demands
Authors: Shreya Bokare, Sanjay Pawar, Shika Nema
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Growth in cloud applications is generating the tremendous amount of data, building load on traditional storage management systems. Software Defined Storage (SDS) is a new storage management concept becoming popular to handle this large amount of data. CoprHD is one of the open source SDS controller, available for experimentation and development in the storage industry. In this paper, the storage management techniques provided by CoprHD to manage heterogeneous storage platforms are experimented and analyzed. Various storage management parameters such as time to provision, storage capacity measurement, and heterogeneity are experimentally evaluated along with the theoretical expression to prove the completeness of CoprHD controller for storage management.Keywords: software defined storage, SDS, CoprHD, open source, SMI-S simulator, clarion, Symmetrix
Procedia PDF Downloads 3139929 Graph Codes - 2D Projections of Multimedia Feature Graphs for Fast and Effective Retrieval
Authors: Stefan Wagenpfeil, Felix Engel, Paul McKevitt, Matthias Hemmje
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Multimedia Indexing and Retrieval is generally designed and implemented by employing feature graphs. These graphs typically contain a significant number of nodes and edges to reflect the level of detail in feature detection. A higher level of detail increases the effectiveness of the results but also leads to more complex graph structures. However, graph-traversal-based algorithms for similarity are quite inefficient and computation intensive, especially for large data structures. To deliver fast and effective retrieval, an efficient similarity algorithm, particularly for large graphs, is mandatory. Hence, in this paper, we define a graph-projection into a 2D space (Graph Code) as well as the corresponding algorithms for indexing and retrieval. We show that calculations in this space can be performed more efficiently than graph-traversals due to a simpler processing model and a high level of parallelization. In consequence, we prove that the effectiveness of retrieval also increases substantially, as Graph Codes facilitate more levels of detail in feature fusion. Thus, Graph Codes provide a significant increase in efficiency and effectiveness (especially for Multimedia indexing and retrieval) and can be applied to images, videos, audio, and text information.Keywords: indexing, retrieval, multimedia, graph algorithm, graph code
Procedia PDF Downloads 1629928 Construction of Graph Signal Modulations via Graph Fourier Transform and Its Applications
Authors: Xianwei Zheng, Yuan Yan Tang
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Classical window Fourier transform has been widely used in signal processing, image processing, machine learning and pattern recognition. The related Gabor transform is powerful enough to capture the texture information of any given dataset. Recently, in the emerging field of graph signal processing, researchers devoting themselves to develop a graph signal processing theory to handle the so-called graph signals. Among the new developing theory, windowed graph Fourier transform has been constructed to establish a time-frequency analysis framework of graph signals. The windowed graph Fourier transform is defined by using the translation and modulation operators of graph signals, following the similar calculations in classical windowed Fourier transform. Specifically, the translation and modulation operators of graph signals are defined by using the Laplacian eigenvectors as follows. For a given graph signal, its translation is defined by a similar manner as its definition in classical signal processing. Specifically, the translation operator can be defined by using the Fourier atoms; the graph signal translation is defined similarly by using the Laplacian eigenvectors. The modulation of the graph can also be established by using the Laplacian eigenvectors. The windowed graph Fourier transform based on these two operators has been applied to obtain time-frequency representations of graph signals. Fundamentally, the modulation operator is defined similarly to the classical modulation by multiplying a graph signal with the entries in each Fourier atom. However, a single Laplacian eigenvector entry cannot play a similar role as the Fourier atom. This definition ignored the relationship between the translation and modulation operators. In this paper, a new definition of the modulation operator is proposed and thus another time-frequency framework for graph signal is constructed. Specifically, the relationship between the translation and modulation operations can be established by the Fourier transform. Specifically, for any signal, the Fourier transform of its translation is the modulation of its Fourier transform. Thus, the modulation of any signal can be defined as the inverse Fourier transform of the translation of its Fourier transform. Therefore, similarly, the graph modulation of any graph signal can be defined as the inverse graph Fourier transform of the translation of its graph Fourier. The novel definition of the graph modulation operator established a relationship of the translation and modulation operations. The new modulation operation and the original translation operation are applied to construct a new framework of graph signal time-frequency analysis. Furthermore, a windowed graph Fourier frame theory is developed. Necessary and sufficient conditions for constructing windowed graph Fourier frames, tight frames and dual frames are presented in this paper. The novel graph signal time-frequency analysis framework is applied to signals defined on well-known graphs, e.g. Minnesota road graph and random graphs. Experimental results show that the novel framework captures new features of graph signals.Keywords: graph signals, windowed graph Fourier transform, windowed graph Fourier frames, vertex frequency analysis
Procedia PDF Downloads 3429927 On Chromaticity of Wheels
Authors: Zainab Yasir Abed Al-Rekaby, Abdul Jalil M. Khalaf
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Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.Keywords: chromatic polynomial, chromatically equivalent, chromatically unique, wheel
Procedia PDF Downloads 4319926 MhAGCN: Multi-Head Attention Graph Convolutional Network for Web Services Classification
Authors: Bing Li, Zhi Li, Yilong Yang
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Web classification can promote the quality of service discovery and management in the service repository. It is widely used to locate developers desired services. Although traditional classification methods based on supervised learning models can achieve classification tasks, developers need to manually mark web services, and the quality of these tags may not be enough to establish an accurate classifier for service classification. With the doubling of the number of web services, the manual tagging method has become unrealistic. In recent years, the attention mechanism has made remarkable progress in the field of deep learning, and its huge potential has been fully demonstrated in various fields. This paper designs a multi-head attention graph convolutional network (MHAGCN) service classification method, which can assign different weights to the neighborhood nodes without complicated matrix operations or relying on understanding the entire graph structure. The framework combines the advantages of the attention mechanism and graph convolutional neural network. It can classify web services through automatic feature extraction. The comprehensive experimental results on a real dataset not only show the superior performance of the proposed model over the existing models but also demonstrate its potentially good interpretability for graph analysis.Keywords: attention mechanism, graph convolutional network, interpretability, service classification, service discovery
Procedia PDF Downloads 1369925 Challenges in Multi-Cloud Storage Systems for Mobile Devices
Authors: Rajeev Kumar Bedi, Jaswinder Singh, Sunil Kumar Gupta
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The demand for cloud storage is increasing because users want continuous access their data. Cloud Storage revolutionized the way how users access their data. A lot of cloud storage service providers are available as DropBox, G Drive, and providing limited free storage and for extra storage; users have to pay money, which will act as a burden on users. To avoid the issue of limited free storage, the concept of Multi Cloud Storage introduced. In this paper, we will discuss the limitations of existing Multi Cloud Storage systems for mobile devices.Keywords: cloud storage, data privacy, data security, multi cloud storage, mobile devices
Procedia PDF Downloads 7009924 Hybrid Approximate Structural-Semantic Frequent Subgraph Mining
Authors: Montaceur Zaghdoud, Mohamed Moussaoui, Jalel Akaichi
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Frequent subgraph mining refers usually to graph matching and it is widely used in when analyzing big data with large graphs. A lot of research works dealt with structural exact or inexact graph matching but a little attention is paid to semantic matching when graph vertices and/or edges are attributed and typed. Therefore, it seems very interesting to integrate background knowledge into the analysis and that extracted frequent subgraphs should become more pruned by applying a new semantic filter instead of using only structural similarity in graph matching process. Consequently, this paper focuses on developing a new hybrid approximate structuralsemantic graph matching to discover a set of frequent subgraphs. It uses simultaneously an approximate structural similarity function based on graph edit distance function and a possibilistic vertices similarity function based on affinity function. Both structural and semantic filters contribute together to prune extracted frequent set. Indeed, new hybrid structural-semantic frequent subgraph mining approach searches will be suitable to be applied to several application such as community detection in social networks.Keywords: approximate graph matching, hybrid frequent subgraph mining, graph mining, possibility theory
Procedia PDF Downloads 4049923 Evolutions of Structural Properties of Native Phospho Casein (NPC) Powder during Storage
Authors: Sarah Nasser, Anne Moreau, Alain Hedoux, Romain Jeantet, Guillaume Delaplace
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Background: Spray dryed powders containing some caseins are commonly produced in dairy industry. It is widely admitted that the structure of casein evolves during powder storage, inducing a loss of solubility. However few studies evaluate accurately the destabilization mechanisms at molecular and mesoscopic level, in particular for Native Phospho Casein powder (NPC). Consequently, at the state of the art, it is very difficult to assess which secondary structure change or crosslinks initiate insolubility during storage. To address this issue, controlled ageing conditions have been applied to a NPC powder (which was obtained by spray drying a concentrate containing a higher content of casein (90%), whey protein (8%) and lactose (few %)). Evolution of structure and loss of solubility, with the effects of temperature and time of storage were systematically reported. Methods: FTIR spectroscopy, Raman and Circular Dichroism were used to monitor changes of secondary structure in dry powder and in solution after rehydration. Besides, proteomic tools and electrophoresis have been performed after varying storage conditions for evaluating aggregation and post translational modifications, like lactosylation or phosphorylation. Finally, Tof Sims and MEB were used to follow in parallel evolution of structure in surface and skin formation due to storage. Results + conclusion: These results highlight the important role of storage temperature in the stability of NPC. It is shown that this is not lactosylation at the heart of formation of aggregates, as advanced in others publications This is almost the rise of multitude post translational modifications (chemical cross link), added to disulphide bridges (physical cross link) wich contribute to the destabilisation of structure and aggregation of casein. A relative quantification of each kind of cross link, source of aggregates, is proposed. In addition, it has been proved that migration of lipids and formation of skin in surface during the ageing also explains the evolution of structure casein and thus the alterations of functional properties of NPC powder.Keywords: casein, cross link, powder, storage
Procedia PDF Downloads 3799922 A Study of Chromatic Uniqueness of W14
Authors: Zainab Yasir Al-Rekaby, Abdul Jalil M. Khalaf
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Coloring the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W14 is chromatically unique.Keywords: chromatic polynomial, chromatically Equivalent, chromatically unique, wheel
Procedia PDF Downloads 4149921 GRCNN: Graph Recognition Convolutional Neural Network for Synthesizing Programs from Flow Charts
Authors: Lin Cheng, Zijiang Yang
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Program synthesis is the task to automatically generate programs based on user specification. In this paper, we present a framework that synthesizes programs from flow charts that serve as accurate and intuitive specification. In order doing so, we propose a deep neural network called GRCNN that recognizes graph structure from its image. GRCNN is trained end-to-end, which can predict edge and node information of the flow chart simultaneously. Experiments show that the accuracy rate to synthesize a program is 66.4%, and the accuracy rates to recognize edge and node are 94.1% and 67.9%, respectively. On average, it takes about 60 milliseconds to synthesize a program.Keywords: program synthesis, flow chart, specification, graph recognition, CNN
Procedia PDF Downloads 1209920 A Graph-Based Retrieval Model for Passage Search
Authors: Junjie Zhong, Kai Hong, Lei Wang
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Passage Retrieval (PR) plays an important role in many Natural Language Processing (NLP) tasks. Traditional efficient retrieval models relying on exact term-matching, such as TF-IDF or BM25, have nowadays been exceeded by pre-trained language models which match by semantics. Though they gain effectiveness, deep language models often require large memory as well as time cost. To tackle the trade-off between efficiency and effectiveness in PR, this paper proposes Graph Passage Retriever (GraphPR), a graph-based model inspired by the development of graph learning techniques. Different from existing works, GraphPR is end-to-end and integrates both term-matching information and semantics. GraphPR constructs a passage-level graph from BM25 retrieval results and trains a GCN-like model on the graph with graph-based objectives. Passages were regarded as nodes in the constructed graph and were embedded in dense vectors. PR can then be implemented using embeddings and a fast vector-similarity search. Experiments on a variety of real-world retrieval datasets show that the proposed model outperforms related models in several evaluation metrics (e.g., mean reciprocal rank, accuracy, F1-scores) while maintaining a relatively low query latency and memory usage.Keywords: efficiency, effectiveness, graph learning, language model, passage retrieval, term-matching model
Procedia PDF Downloads 1549919 BodeACD: Buffer Overflow Vulnerabilities Detecting Based on Abstract Syntax Tree, Control Flow Graph, and Data Dependency Graph
Authors: Xinghang Lv, Tao Peng, Jia Chen, Junping Liu, Xinrong Hu, Ruhan He, Minghua Jiang, Wenli Cao
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As one of the most dangerous vulnerabilities, effective detection of buffer overflow vulnerabilities is extremely necessary. Traditional detection methods are not accurate enough and consume more resources to meet complex and enormous code environment at present. In order to resolve the above problems, we propose the method for Buffer overflow detection based on Abstract syntax tree, Control flow graph, and Data dependency graph (BodeACD) in C/C++ programs with source code. Firstly, BodeACD constructs the function samples of buffer overflow that are available on Github, then represents them as code representation sequences, which fuse control flow, data dependency, and syntax structure of source code to reduce information loss during code representation. Finally, BodeACD learns vulnerability patterns for vulnerability detection through deep learning. The results of the experiments show that BodeACD has increased the precision and recall by 6.3% and 8.5% respectively compared with the latest methods, which can effectively improve vulnerability detection and reduce False-positive rate and False-negative rate.Keywords: vulnerability detection, abstract syntax tree, control flow graph, data dependency graph, code representation, deep learning
Procedia PDF Downloads 1709918 The K-Distance Neighborhood Polynomial of a Graph
Authors: Soner Nandappa D., Ahmed Mohammed Naji
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In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented.Keywords: vertex degrees, distance in graphs, graph operation, Nk-polynomials
Procedia PDF Downloads 5519917 A Summary-Based Text Classification Model for Graph Attention Networks
Authors: Shuo Liu
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In Chinese text classification tasks, redundant words and phrases can interfere with the formation of extracted and analyzed text information, leading to a decrease in the accuracy of the classification model. To reduce irrelevant elements, extract and utilize text content information more efficiently and improve the accuracy of text classification models. In this paper, the text in the corpus is first extracted using the TextRank algorithm for abstraction, the words in the abstract are used as nodes to construct a text graph, and then the graph attention network (GAT) is used to complete the task of classifying the text. Testing on a Chinese dataset from the network, the classification accuracy was improved over the direct method of generating graph structures using text.Keywords: Chinese natural language processing, text classification, abstract extraction, graph attention network
Procedia PDF Downloads 1029916 A Graph Library Development Based on the Service-Oriented Architecture: Used for Representation of the Biological Systems in the Computer Algorithms
Authors: Mehrshad Khosraviani, Sepehr Najjarpour
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Considering the usage of graph-based approaches in systems and synthetic biology, and the various types of the graphs employed by them, a comprehensive graph library based on the three-tier architecture (3TA) was previously introduced for full representation of the biological systems. Although proposing a 3TA-based graph library, three following reasons motivated us to redesign the graph library based on the service-oriented architecture (SOA): (1) Maintaining the accuracy of the data related to an input graph (including its edges, its vertices, its topology, etc.) without involving the end user: Since, in the case of using 3TA, the library files are available to the end users, they may be utilized incorrectly, and consequently, the invalid graph data will be provided to the computer algorithms. However, considering the usage of the SOA, the operation of the graph registration is specified as a service by encapsulation of the library files. In other words, overall control operations needed for registration of the valid data will be the responsibility of the services. (2) Partitioning of the library product into some different parts: Considering 3TA, a whole library product was provided in general. While here, the product can be divided into smaller ones, such as an AND/OR graph drawing service, and each one can be provided individually. As a result, the end user will be able to select any parts of the library product, instead of all features, to add it to a project. (3) Reduction of the complexities: While using 3TA, several other libraries must be needed to add for connecting to the database, responsibility of the provision of the needed library resources in the SOA-based graph library is entrusted with the services by themselves. Therefore, the end user who wants to use the graph library is not involved with its complexity. In the end, in order to make the library easier to control in the system, and to restrict the end user from accessing the files, it was preferred to use the service-oriented architecture (SOA) over the three-tier architecture (3TA) and to redevelop the previously proposed graph library based on it.Keywords: Bio-Design Automation, Biological System, Graph Library, Service-Oriented Architecture, Systems and Synthetic Biology
Procedia PDF Downloads 3119915 An Overview of Thermal Storage Techniques for Solar Thermal Applications
Authors: Talha Shafiq
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The traditional electricity operation in solar thermal plants is designed to operate on a single path initiating at power plant and executes at the consumer. Due to lack of energy storage facilities during this operation, a decrease in the efficiency is often observed with the power plant performance. This paper reviews the significance of energy storage in supply design and elaborates various methods that can be adopted in this regard which are equally cost effective and environmental friendly. Moreover, various parameters in thermal storage technique are also critically analyzed to clarify the pros and cons in this facility. Discussing the different thermal storage system, their technical and economical evaluation has also been reviewed.Keywords: thermal energy storage, sensible heat storage, latent heat storage, thermochemical heat storage
Procedia PDF Downloads 5659914 Normalized Laplacian Eigenvalues of Graphs
Authors: Shaowei Sun
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Let G be a graph with vertex set V(G)={v_1,v_2,...,v_n} and edge set E(G). For any vertex v belong to V(G), let d_v denote the degree of v. The normalized Laplacian matrix of the graph G is the matrix where the non-diagonal (i,j)-th entry is -1/(d_id_j) when vertex i is adjacent to vertex j and 0 when they are not adjacent, and the diagonal (i,i)-th entry is the di. In this paper, we discuss some bounds on the largest and the second smallest normalized Laplacian eigenvalue of trees and graphs. As following, we found some new bounds on the second smallest normalized Laplacian eigenvalue of tree T in terms of graph parameters. Moreover, we use Sage to give some conjectures on the second largest and the third smallest normalized eigenvalues of graph.Keywords: graph, normalized Laplacian eigenvalues, normalized Laplacian matrix, tree
Procedia PDF Downloads 3289913 Designing ZIF67 Derivatives Using Ammonia-Based Fluorine Complex as Structure-Directing Agent for Energy Storage Applications
Authors: Lu-Yin Lin
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The morphology of electroactive material is highly related to energy storage ability. Structure-directing agent (SDA) can design electroactive materials with favorable surface properties. Zeolitic imidazolate framework 67 (ZIF67) is one of the potential electroactive materials for energy storage devices. The SDA concept is less applied to designing ZIF67 derivatives in previous studies. An in-situ technique with ammonium fluoride (NH₄F) as SDA is proposed to produce a ZIF67 derivative with highly improved energy storage ability. Attracted by the effective in-situ technique, the NH₄F, ammonium bifluoride (NH₄HF₂), and ammonium tetrafluoroborate (NH₄BF₄) are first used as SDA to synthesize ZIF67 derivatives in one-step solution process as electroactive material of energy storage devices. The mechanisms of forming ZIF67 derivatives synthesized with different SDAs are discussed to explain the SDA effects on physical and electrochemical properties. The largest specific capacitance (CF) of 1527.0 Fg-¹ and the capacity of 296.9 mAhg-¹ are obtained for the ZIF67 derivative prepared using NH₄BF₄ as SDA. The energy storage device composed of the optimal ZIF67 derivative and carbon electrodes presents a maximum energy density of 15.1 Whkg-¹ at the power density of 857 Wkg-¹. The CF retention of 90% and Coulombic efficiency larger than 98% are also obtained after 5000 cycles.Keywords: ammonium bifluoride, ammonium tetrafluoroborate, energy storage device, one-step solution process, structure-directing agent, zeolitic imidazolate framework 67
Procedia PDF Downloads 799912 The Second Smallest Eigenvalue of Complete Tripartite Hypergraph
Authors: Alfi Y. Zakiyyah, Hanni Garminia, M. Salman, A. N. Irawati
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In the terminology of the hypergraph, there is a relation with the terminology graph. In the theory of graph, the edges connected two vertices. In otherwise, in hypergraph, the edges can connect more than two vertices. There is representation matrix of a graph such as adjacency matrix, Laplacian matrix, and incidence matrix. The adjacency matrix is symmetry matrix so that all eigenvalues is real. This matrix is a nonnegative matrix. The all diagonal entry from adjacency matrix is zero so that the trace is zero. Another representation matrix of the graph is the Laplacian matrix. Laplacian matrix is symmetry matrix and semidefinite positive so that all eigenvalues are real and non-negative. According to the spectral study in the graph, some that result is generalized to hypergraph. A hypergraph can be represented by a matrix such as adjacency, incidence, and Laplacian matrix. Throughout for this term, we use Laplacian matrix to represent a complete tripartite hypergraph. The aim from this research is to determine second smallest eigenvalues from this matrix and find a relation this eigenvalue with the connectivity of that hypergraph.Keywords: connectivity, graph, hypergraph, Laplacian matrix
Procedia PDF Downloads 4909911 On Chvátal’s Conjecture for the Hamiltonicity of 1-Tough Graphs and Their Complements
Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su
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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.Keywords: complement, degree sum, hamiltonian, tough
Procedia PDF Downloads 2899910 Attempt to Reuse Used-PCs as Distributed Storage
Authors: Toshiya Kawato, Shin-ichi Motomura, Masayuki Higashino, Takao Kawamura
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Storage for storing data is indispensable. If a storage capacity becomes insufficient, we can increase its capacity by adding new disks. It is, however, difficult to add a new disk when a budget is not enough. On the other hand, there are many unused idle resources such as used personal computers despite those use value. In order to solve those problems, used personal computers can be reused as storage. In this paper, we attempt to reuse used-PCs as a distributed storage. First, we list up the characteristics of used-PCs and design a storage system that utilizes its characteristics. Next, we experimentally implement an auto-construction system that automatically constructs a distributed storage environment in used-PCs.Keywords: distributed storage, used personal computer, idle resource, auto construction
Procedia PDF Downloads 2529909 Computational Chemical-Composition of Carbohydrates in the Context of Healthcare Informatics
Authors: S. Chandrasekaran, S. Nandita, M. Shivathmika, Srikrishnan Shivakumar
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The objective of the research work is to analyze the computational chemical-composition of carbohydrates in the context of healthcare informatics. The computation involves the representation of complex chemical molecular structure of carbohydrate using graph theory and in a deployable Chemical Markup Language (CML). The parallel molecular structure of the chemical molecules with or without other adulterants for the sake of business profit can be analyzed in terms of robustness and derivatization measures. The rural healthcare program should create awareness in malnutrition to reduce ill-effect of decomposition and help the consumers to know the level of such energy storage mixtures in a quantitative way. The earlier works were based on the empirical and wet data which can vary from time to time but cannot be made to reuse the results of mining. The work is carried out on the quantitative computational chemistry on carbohydrates to provide a safe and secure right to food act and its regulations.Keywords: carbohydrates, chemical-composition, chemical markup, robustness, food safety
Procedia PDF Downloads 3749908 Enhancing Knowledge Graph Convolutional Networks with Structural Adaptive Receptive Fields for Improved Node Representation and Information Aggregation
Authors: Zheng Zhihao
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Recently, Knowledge Graph Framework Network (KGCN) has developed powerful capabilities in knowledge representation and reasoning tasks. However, traditional KGCN often uses a fixed weight mechanism when aggregating information, failing to make full use of rich structural information, resulting in a certain expression ability of node representation, and easily causing over-smoothing problems. In order to solve these challenges, the paper proposes an new graph neural network model called KGCN-STAR (Knowledge Graph Convolutional Network with Structural Adaptive Receptive Fields). This model dynamically adjusts the perception of each node by introducing a structural adaptive receptive field. wild range, and a subgraph aggregator is designed to capture local structural information more effectively. Experimental results show that KGCN-STAR shows significant performance improvement on multiple knowledge graph data sets, especially showing considerable capabilities in the task of representation learning of complex structures.Keywords: knowledge graph, graph neural networks, structural adaptive receptive fields, information aggregation
Procedia PDF Downloads 349907 Some Conjectures and Programs about Computing the Detour Index of Molecular Graphs of Nanotubes
Authors: Shokofeh Ebrtahimi
Abstract:
Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G.Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena.[1] The pioneers of the chemical graph theory are Alexandru Balaban, Ante Graovac, Ivan Gutman, Haruo Hosoya, Milan Randić and Nenad TrinajstićLet G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new program for computing the detour index of molecular graphs of nanotubes by heptagons is determineded. Some Conjectures about detour index of Molecular graphs of nanotubes is included.Keywords: chemical graph, detour matrix, Detour index, carbon nanotube
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