Artículos de revistas: "Stream graphs"

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Ashrafi-Payaman, Nosratali, Mohammad Reza Kangavari y Amir Mohammad Fander. "A new method for graph stream summarization based on both the structure and concepts". Open Engineering 9, n.º 1 (2 de noviembre de 2019): 500–511. http://dx.doi.org/10.1515/eng-2019-0060.

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AbstractGraph datasets are common in many application domains and for which their graphs are usually massive. One solution to process such massive graphs is summarization. There are two kinds of graphs, stationary and stream. For stationary graphs, a number of summarization algorithms are available while for graph stream there is no a comprehensive summarization method that summarizes a graph stream based on the structure, vertex attributes or both with varying contributions. This is because of challenges of graph stream, which are volume of data and changing of data over time. In this paper, we propose a method based on sliding-window model for which summarizes a graph stream based on a combination of the structure and vertex attributes. We proposed a new structure for summary graphs and also proposed new methods for comparing two summary graphs. To the best of our knowledge, this is the first method that summarizes a graph stream based on both the structure and vertex attributes with varying contributions. Through extensive experiments on real dataset of Amazon co-purchasing products, we have demonstrated the performance of the proposed method.

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Malik, Avinash y David Gregg. "Orchestrating stream graphs using model checking". ACM Transactions on Architecture and Code Optimization 10, n.º 3 (16 de septiembre de 2013): 1–25. http://dx.doi.org/10.1145/2512435.

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Du, Zhihui, Oliver Alvarado Rodriguez, Joseph Patchett y David A. Bader. "Interactive Graph Stream Analytics in Arkouda". Algorithms 14, n.º 8 (21 de julio de 2021): 221. http://dx.doi.org/10.3390/a14080221.

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Data from emerging applications, such as cybersecurity and social networking, can be abstracted as graphs whose edges are updated sequentially in the form of a stream. The challenging problem of interactive graph stream analytics is the quick response of the queries on terabyte and beyond graph stream data from end users. In this paper, a succinct and efficient double index data structure is designed to build the sketch of a graph stream to meet general queries. A single pass stream model, which includes general sketch building, distributed sketch based analysis algorithms and regression based approximation solution generation, is developed, and a typical graph algorithm—triangle counting—is implemented to evaluate the proposed method. Experimental results on power law and normal distribution graph streams show that our method can generate accurate results (mean relative error less than 4%) with a high performance. All our methods and code have been implemented in an open source framework, Arkouda, and are available from our GitHub repository, Bader-Research. This work provides the large and rapidly growing Python community with a powerful way to handle terabyte and beyond graph stream data using their laptops.

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Wang, Ruize, Zhongyu Wei, Piji Li, Qi Zhang y Xuanjing Huang. "Storytelling from an Image Stream Using Scene Graphs". Proceedings of the AAAI Conference on Artificial Intelligence 34, n.º 05 (3 de abril de 2020): 9185–92. http://dx.doi.org/10.1609/aaai.v34i05.6455.

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Visual storytelling aims at generating a story from an image stream. Most existing methods tend to represent images directly with the extracted high-level features, which is not intuitive and difficult to interpret. We argue that translating each image into a graph-based semantic representation, i.e., scene graph, which explicitly encodes the objects and relationships detected within image, would benefit representing and describing images. To this end, we propose a novel graph-based architecture for visual storytelling by modeling the two-level relationships on scene graphs. In particular, on the within-image level, we employ a Graph Convolution Network (GCN) to enrich local fine-grained region representations of objects on scene graphs. To further model the interaction among images, on the cross-images level, a Temporal Convolution Network (TCN) is utilized to refine the region representations along the temporal dimension. Then the relation-aware representations are fed into the Gated Recurrent Unit (GRU) with attention mechanism for story generation. Experiments are conducted on the public visual storytelling dataset. Automatic and human evaluation results indicate that our method achieves state-of-the-art.

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Ni, Xiang, Jing Li, Mo Yu, Wang Zhou y Kun-Lung Wu. "Generalizable Resource Allocation in Stream Processing via Deep Reinforcement Learning". Proceedings of the AAAI Conference on Artificial Intelligence 34, n.º 01 (3 de abril de 2020): 857–64. http://dx.doi.org/10.1609/aaai.v34i01.5431.

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This paper considers the problem of resource allocation in stream processing, where continuous data flows must be processed in real time in a large distributed system. To maximize system throughput, the resource allocation strategy that partitions the computation tasks of a stream processing graph onto computing devices must simultaneously balance workload distribution and minimize communication. Since this problem of graph partitioning is known to be NP-complete yet crucial to practical streaming systems, many heuristic-based algorithms have been developed to find reasonably good solutions. In this paper, we present a graph-aware encoder-decoder framework to learn a generalizable resource allocation strategy that can properly distribute computation tasks of stream processing graphs unobserved from training data. We, for the first time, propose to leverage graph embedding to learn the structural information of the stream processing graphs. Jointly trained with the graph-aware decoder using deep reinforcement learning, our approach can effectively find optimized solutions for unseen graphs. Our experiments show that the proposed model outperforms both METIS, a state-of-the-art graph partitioning algorithm, and an LSTM-based encoder-decoder model, in about 70% of the test cases.

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Declerck, Philippe. "DETECTION OF CHANGES BY OBSERVER IN TIMED EVENT GRAPHS AND TIME STREAM EVENT GRAPHS". IFAC Proceedings Volumes 40, n.º 6 (2007): 49–54. http://dx.doi.org/10.3182/20070613-3-fr-4909.00011.

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7

Llaves, Alejandro, Oscar Corcho, Peter Taylor y Kerry Taylor. "Enabling RDF Stream Processing for Sensor Data Management in the Environmental Domain". International Journal on Semantic Web and Information Systems 12, n.º 4 (octubre de 2016): 1–21. http://dx.doi.org/10.4018/ijswis.2016100101.

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This paper presents a generic approach to integrate environmental sensor data efficiently, allowing the detection of relevant situations and events in near real-time through continuous querying. Data variety is addressed with the use of the Semantic Sensor Network ontology for observation data modelling, and semantic annotations for environmental phenomena. Data velocity is handled by distributing sensor data messaging and serving observations as RDF graphs on query demand. The stream processing engine presented in the paper, morph-streams++, provides adapters for different data formats and distributed processing of streams in a cluster. An evaluation of different configurations for parallelization and semantic annotation parameters proves that the described approach reduces the average latency of message processing in some cases.

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8

Mathieu, Claire y Michel de Rougemont. "Large very dense subgraphs in a stream of edges". Network Science 9, n.º 4 (diciembre de 2021): 403–24. http://dx.doi.org/10.1017/nws.2021.17.

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AbstractWe study the detection and the reconstruction of a large very dense subgraph in a social graph with n nodes and m edges given as a stream of edges, when the graph follows a power law degree distribution, in the regime when $m=O(n. \log n)$ . A subgraph S is very dense if it has $\Omega(|S|^2)$ edges. We uniformly sample the edges with a Reservoir of size $k=O(\sqrt{n}.\log n)$ . Our detection algorithm checks whether the Reservoir has a giant component. We show that if the graph contains a very dense subgraph of size $\Omega(\sqrt{n})$ , then the detection algorithm is almost surely correct. On the other hand, a random graph that follows a power law degree distribution almost surely has no large very dense subgraph, and the detection algorithm is almost surely correct. We define a new model of random graphs which follow a power law degree distribution and have large very dense subgraphs. We then show that on this class of random graphs we can reconstruct a good approximation of the very dense subgraph with high probability. We generalize these results to dynamic graphs defined by sliding windows in a stream of edges.

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Ajwani, Deepak, Shoukat Ali, Kostas Katrinis, Cheng-Hong Li, Alfred J. Park, John P. Morrison y Eugen Schenfeld. "Generating synthetic task graphs for simulating stream computing systems". Journal of Parallel and Distributed Computing 73, n.º 10 (octubre de 2013): 1362–74. http://dx.doi.org/10.1016/j.jpdc.2013.06.002.

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10

Li, Yan, Tingjian Ge y Cindy Chen. "Data stream event prediction based on timing knowledge and state transitions". Proceedings of the VLDB Endowment 13, n.º 10 (junio de 2020): 1779–92. http://dx.doi.org/10.14778/3401960.3401973.

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We study a practical problem of predicting the upcoming events in data streams using a novel approach. Treating event time orders as relationship types between event entities, we build a dynamic knowledge graph and use it to predict future event timing. A unique aspect of this knowledge graph embedding approach for prediction is that we enhance conventional knowledge graphs with the notion of "states"---in what we call the ephemeral state nodes---to characterize the state of a data stream over time. We devise a complete set of methods for learning relevant events, for building the event-order graph stream from the original data stream, for embedding and prediction, and for theoretically bounding the complexity. We evaluate our approach with four real world stream datasets and find that our method results in high precision and recall values for event timing prediction, ranging between 0.7 and nearly 1, significantly outperforming baseline approaches. Moreover, due to our choice of efficient translation-based embedding, the overall throughput that the stream system can handle, including continuous graph building, training, and event predictions, is over one thousand to sixty thousand tuples per second even on a personal computer---which is especially important in resource constrained environments, including edge computing.

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Neumann, Stefan y Pauli Miettinen. "Biclustering and boolean matrix factorization in data streams". Proceedings of the VLDB Endowment 13, n.º 10 (junio de 2020): 1709–22. http://dx.doi.org/10.14778/3401960.3401968.

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We study clustering of bipartite graphs and Boolean matrix factorization in data streams. We consider a streaming setting in which the vertices from the left side of the graph arrive one by one together with all of their incident edges. We provide an algorithm which after one pass over the stream recovers the set of clusters on the right side of the graph using sublinear space; to the best of our knowledge this is the first algorithm with this property. We also show that after a second pass over the stream the left clusters of the bipartite graph can be recovered and we show how to extend our algorithm to solve the Boolean matrix factorization problem (by exploiting the correspondence of Boolean matrices and bipartite graphs). We evaluate an implementation of the algorithm on synthetic data and on real-world data. On real-world datasets the algorithm is orders of magnitudes faster than a static baseline algorithm while providing quality results within a factor 2 of the baseline algorithm. Our algorithm scales linearly in the number of edges in the graph. Finally, we analyze the algorithm theoretically and provide sufficient conditions under which the algorithm recovers a set of planted clusters under a standard random graph model.

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12

Rutten, J. J. M. M. "A tutorial on coinductive stream calculus and signal flow graphs". Theoretical Computer Science 343, n.º 3 (octubre de 2005): 443–81. http://dx.doi.org/10.1016/j.tcs.2005.06.019.

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13

Oh, Sangyun, Hongsik Lee y Jongeun Lee. "Efficient Execution of Stream Graphs on Coarse-Grained Reconfigurable Architectures". IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 36, n.º 12 (diciembre de 2017): 1978–88. http://dx.doi.org/10.1109/tcad.2017.2682645.

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14

Sheshbolouki, Aida y M. Tamer Özsu. "sGrapp: Butterfly Approximation in Streaming Graphs". ACM Transactions on Knowledge Discovery from Data 16, n.º 4 (31 de agosto de 2022): 1–43. http://dx.doi.org/10.1145/3495011.

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We study the fundamental problem of butterfly (i.e., (2,2)-bicliques) counting in bipartite streaming graphs. Similar to triangles in unipartite graphs, enumerating butterflies is crucial in understanding the structure of bipartite graphs. This benefits many applications where studying the cohesion in a graph shaped data is of particular interest. Examples include investigating the structure of computational graphs or input graphs to the algorithms, as well as dynamic phenomena and analytic tasks over complex real graphs. Butterfly counting is computationally expensive, and known techniques do not scale to large graphs; the problem is even harder in streaming graphs. In this article, following a data-driven methodology, we first conduct an empirical analysis to uncover temporal organizing principles of butterflies in real streaming graphs and then we introduce an approximate adaptive window-based algorithm, sGrapp, for counting butterflies as well as its optimized version sGrapp-x. sGrapp is designed to operate efficiently and effectively over any graph stream with any temporal behavior. Experimental studies of sGrapp and sGrapp-x show superior performance in terms of both accuracy and efficiency.

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15

Curzel, J. L., R. Lüders, K. V. O. Fonseca y M. O. Rosa. "Temporal Performance Analysis of Bus Transportation Using Link Streams". Mathematical Problems in Engineering 2019 (11 de febrero de 2019): 1–18. http://dx.doi.org/10.1155/2019/6139379.

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Performance analysis of transport systems usually requires transfer of passengers between trains, cars, or buses, among others. This paper proposes a methodology for modeling and analysis of bus transportation using link streams. Link streams are particular cases of stream graphs whose cliques provide information about available time intervals for connecting buses. These cliques are obtained by algorithms of the literature with good scalability. They are used to quantify performance indicators as transfer time, bunching, congestion, and number of transferred passengers. The results are obtained for real-world data of a bus terminal in the city of Curitiba, Brazil. They reveal important issues regarding transfer delays and available capacity for transport. The proposed performance analysis can be used to support urban planners on planning and improving transport operation.

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Ustaoğlu, Fikret y Yalçın Tepe. "Pazarsuyu Deresi (Giresun, Türkiye) Sediment Kalitesinin Çok Değişkenli İstatistik Yöntemlerle Belirlenmesi". Turkish Journal of Agriculture - Food Science and Technology 6, n.º 3 (19 de marzo de 2018): 304. http://dx.doi.org/10.24925/turjaf.v6i3.304-312.1696.

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The present study, aimed to determine sediment quality of Pazarsuyu Stream, located in the city limit Giresun, Black Sea Region, were carried out between June 2014 and May 2015. The average heavy metal levels of samples taken seasonally from four selected stations were as follow; Cr; 10.64 ppm, Mn; 155.83 ppm, Fe; 8312 ppm, Co; 5.73 ppm, Cu; 17.79 ppm, Zn; 32.74 ppm, Cd; 0.16 ppm, Pb; 19.69 ppm. Additionally, the average sediment organic matter % and pH were found as 6.64 and 5.02, respectively. The obtained data were evaluated statistically by one way ANOVA, Pearson correlation analysis, cluster, and factor analysis. Dot graphs were made by using PAST statistical program. The level of heavy metal pollution in the stream sediment were determined by comparisons of our graphs with sediment quality criteria and the mean heavy metal concentrations of the earth.

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Gao, Junyu, Tianzhu Zhang y Changsheng Xu. "I Know the Relationships: Zero-Shot Action Recognition via Two-Stream Graph Convolutional Networks and Knowledge Graphs". Proceedings of the AAAI Conference on Artificial Intelligence 33 (17 de julio de 2019): 8303–11. http://dx.doi.org/10.1609/aaai.v33i01.33018303.

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Recently, with the ever-growing action categories, zero-shot action recognition (ZSAR) has been achieved by automatically mining the underlying concepts (e.g., actions, attributes) in videos. However, most existing methods only exploit the visual cues of these concepts but ignore external knowledge information for modeling explicit relationships between them. In fact, humans have remarkable ability to transfer knowledge learned from familiar classes to recognize unfamiliar classes. To narrow the knowledge gap between existing methods and humans, we propose an end-to-end ZSAR framework based on a structured knowledge graph, which can jointly model the relationships between action-attribute, action-action, and attribute-attribute. To effectively leverage the knowledge graph, we design a novel Two-Stream Graph Convolutional Network (TS-GCN) consisting of a classifier branch and an instance branch. Specifically, the classifier branch takes the semantic-embedding vectors of all the concepts as input, then generates the classifiers for action categories. The instance branch maps the attribute embeddings and scores of each video instance into an attribute-feature space. Finally, the generated classifiers are evaluated on the attribute features of each video, and a classification loss is adopted for optimizing the whole network. In addition, a self-attention module is utilized to model the temporal information of videos. Extensive experimental results on three realistic action benchmarks Olympic Sports, HMDB51 and UCF101 demonstrate the favorable performance of our proposed framework.

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Ito, Yoshiki, Kenichi Morita, Quan Kong y Tomoaki Yoshinaga. "Multi-Stream Adaptive Graph Convolutional Network Using Inter- and Intra-Body Graphs for Two-Person Interaction Recognition". IEEE Access 9 (2021): 110670–82. http://dx.doi.org/10.1109/access.2021.3102671.

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Tian, Yuanyuan, Yan Liang, Haibin Yang y Jiayu Chen. "Multi-Stream Fusion Network for Skeleton-Based Construction Worker Action Recognition". Sensors 23, n.º 23 (23 de noviembre de 2023): 9350. http://dx.doi.org/10.3390/s23239350.

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The global concern regarding the monitoring of construction workers’ activities necessitates an efficient means of continuous monitoring for timely action recognition at construction sites. This paper introduces a novel approach—the multi-scale graph strategy—to enhance feature extraction in complex networks. At the core of this strategy lies the multi-feature fusion network (MF-Net), which employs multiple scale graphs in distinct network streams to capture both local and global features of crucial joints. This approach extends beyond local relationships to encompass broader connections, including those between the head and foot, as well as interactions like those involving the head and neck. By integrating diverse scale graphs into distinct network streams, we effectively incorporate physically unrelated information, aiding in the extraction of vital local joint contour features. Furthermore, we introduce velocity and acceleration as temporal features, fusing them with spatial features to enhance informational efficacy and the model’s performance. Finally, efficiency-enhancing measures, such as a bottleneck structure and a branch-wise attention block, are implemented to optimize computational resources while enhancing feature discriminability. The significance of this paper lies in improving the management model of the construction industry, ultimately aiming to enhance the health and work efficiency of workers.

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Ustimenko, Vasyl O. y Oleksandr S. Pustovit. "On security of GIS systems with N-tier architecture and family of graph based ciphers". Environmental safety and natural resources 47, n.º 3 (29 de septiembre de 2023): 113–32. http://dx.doi.org/10.32347/2411-4049.2023.3.113-132.

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Discovery of q-regular tree description in terms of an infinite system of quadratic equations over finite field Fq had an impact on Computer Science, theory of graph based cryptographic algorithms in particular. It stimulates the development of new graph based stream ciphers. It turns out that such encryption instruments can be efficiently used in GIS protection systems which use N-Tier Architecture. We observe known encryption algorithms based on the approximations of regular tree, their modifications defined over arithmetical rings and implementations of these ciphers. Additionally new more secure graph based ciphers suitable for GIS protection will be presented.Algorithms are constructed using vertices of bipartite regular graphs D(n,K) defined by a finite commutative ring K with a unit and a non-trivial multiplicative group K*. The partition of such graphs are n-dimensional affine spaces over the ring K. A walk of even length determines the transformation of the transition from the initial to the last vertex from one of the partitions of the graph. Therefore, the affine space Kn can be considered as a space of plaintexts, and walking on the graph is a password that defines the encryption transformation.With certain restrictions on the password the effect when different passwords with K*)2s, s <[(n+5)/2]/2 correspond to different ciphertexts of the selected plaintext with Kn can be achieved.In 2005, such an algorithm in the case of the finite field F127 was implemented for the GIS protection. Since then, the properties of encryption algorithms using D(n, K) graphs (execution speed, mixing properties, degree and density of the polynomial encryption transform) have been thoroughly investigated.The complexity of linearization attacks was evaluated and modifications of these algorithms with the resistance to linearization attacks were found. It turned out that together with D(n, K) graphs, other algebraic graphs with similar properties, such as A(n, K) graphs, can be effectively used.The article considers several solutions to the problem of protecting the geological information system from possible cyberattacks using stream ciphers based on graphs. They have significant advantages compared to the implemented earlier systems.

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Xiang, Xintao, Tiancheng Huang y Donglin Wang. "Learning to Evolve on Dynamic Graphs (Student Abstract)". Proceedings of the AAAI Conference on Artificial Intelligence 36, n.º 11 (28 de junio de 2022): 13091–92. http://dx.doi.org/10.1609/aaai.v36i11.21682.

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Representation learning in dynamic graphs is a challenging problem because the topology of graph and node features vary at different time. This requires the model to be able to effectively capture both graph topology information and temporal information. Most existing works are built on recurrent neural networks (RNNs), which are used to exact temporal information of dynamic graphs, and thus they inherit the same drawbacks of RNNs. In this paper, we propose Learning to Evolve on Dynamic Graphs (LEDG) - a novel algorithm that jointly learns graph information and time information. Specifically, our approach utilizes gradient-based meta-learning to learn updating strategies that have better generalization ability than RNN on snapshots. It is model-agnostic and thus can train any message passing based graph neural network (GNN) on dynamic graphs. To enhance the representation power, we disentangle the embeddings into time embeddings and graph intrinsic embeddings. We conduct experiments on various datasets and down-stream tasks, and the experimental results validate the effectiveness of our method.

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Jiang, Xiaolin, Chengshuo Xu y Rajiv Gupta. "VRGQ". ACM SIGOPS Operating Systems Review 55, n.º 1 (2 de junio de 2021): 11–20. http://dx.doi.org/10.1145/3469379.3469382.

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While much of the research on graph analytics over large power-law graphs has focused on developing algorithms for evaluating a single global graph query, in practice we may be faced with a stream of queries. We observe that, due to their global nature, vertex specific graph queries present an opportunity for sharing work across queries. To take advantage of this opportunity, we have developed the VRGQ framework that accelerates the evaluation of a stream of queries via coarsegrained value reuse. In particular, the results of queries for a small set of source vertices are reused to speedup all future queries. We present a two step algorithm that in its first step initializes the query result based upon value reuse and then in the second step iteratively evaluates the query to convergence. The reused results for a small number of queries are held in a reuse table. Our experiments with best reuse configurations on four power law graphs and thousands of graph queries of five kinds yielded average speedups of 143×, 13.2×, 6.89×, 1.43×, and 1.18×.

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Pan, V. y J. Reif. "The parallel computation of minimum cost paths in graphs by stream contraction". Information Processing Letters 40, n.º 2 (octubre de 1991): 79–83. http://dx.doi.org/10.1016/0020-0190(91)90013-8.

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Fural, Şakir, Serkan Kükrer y İsa Cürebal. "İkizcetepeler Baraj Gölü (Balıkesir) Çökellerindeki Organik Karbon Miktarının Zamansal ve Mekansal Dağılışı". Turkish Journal of Agriculture - Food Science and Technology 7, n.º 12 (15 de diciembre de 2019): 2204. http://dx.doi.org/10.24925/turjaf.v7i12.2204-2208.2966.

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This study was carried out to determine the spatial and temporal changes of organic carbon (OC) concentrations in surface sediment and core samples taken from the base of the İkizcetepeler Dam. Although organic carbon (OC) is an important component of natural life, when found in wetlands over a certain amount, it leads to organic pollution and reduces dissolved oxygen in the environment, putting the life of other living things at risk. Therefore, it is extremely important to determine the spatial and temporal distribution of the amount of OC in wetlands. Within the scope of the study, the data acquired from the titration method on surface and core samples collected were converted into extensional distribution maps and vertical distribution graphs using Arc – Map 10.5 Software. Thus, the amount and distribution of OC were determined, resource identification was facilitated, and risky areas at the base of the dam lake were identified. When all the findings were evaluated, it was determined that the amount of OC reached the highest values was at the sample points where Kille Stream, Koca Stream, and Çınarlı stream mouth and old settlements were located. The highest values according to temporal or spatial distribution were found between 5 – 10 cm slices. This indicates that the OC was transported from the watershed by streams other than Bağırsak Stream and discharged into the dam and that the discharge has increased to its maximum level in recent years and is now on a downward trend. According to the field studies carried out around Ikizcetepeler Dam and data obtained from available literature and analytical procedures, no OC origin pollution was observed in the dam.

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Chen, Chaoyi, Dechao Gao, Yanfeng Zhang, Qiange Wang, Zhenbo Fu, Xuecang Zhang, Junhua Zhu, Yu Gu y Ge Yu. "NeutronStream: A Dynamic GNN Training Framework with Sliding Window for Graph Streams". Proceedings of the VLDB Endowment 17, n.º 3 (noviembre de 2023): 455–68. http://dx.doi.org/10.14778/3632093.3632108.

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Existing Graph Neural Network (GNN) training frameworks have been designed to help developers easily create performant GNN implementations. However, most existing GNN frameworks assume that the input graphs are static, but ignore that most real-world graphs are constantly evolving. Though many dynamic GNN models have emerged to learn from evolving graphs, the training process of these dynamic GNNs is dramatically different from traditional GNNs in that it captures both the spatial and temporal dependencies of graph updates. This poses new challenges for designing dynamic GNN training frameworks. First, the traditional batched training method fails to capture real-time structural evolution information. Second, the time-dependent nature makes parallel training hard to design. Third, it lacks system supports for users to efficiently implement dynamic GNNs. In this paper, we present NeutronStream, a framework for training dynamic GNN models. NeutronStream abstracts the input dynamic graph into a chronologically updated stream of events and processes the stream with an optimized sliding window to incrementally capture the spatial-temporal dependencies of events. Furthermore, NeutronStream provides a parallel execution engine to tackle the sequential event processing challenge to achieve high performance. NeutronStream also integrates a built-in graph storage structure that supports dynamic updates and provides a set of easy-to-use APIs that allow users to express their dynamic GNNs. Our experimental results demonstrate that, compared to state-of-the-art dynamic GNN implementations, NeutronStream achieves speedups ranging from 1.48X to 5.87X and an average accuracy improvement of 3.97%.

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Xu, Chunyan, Rong Liu, Tong Zhang, Zhen Cui, Jian Yang y Chunlong Hu. "Dual-Stream Structured Graph Convolution Network for Skeleton-Based Action Recognition". ACM Transactions on Multimedia Computing, Communications, and Applications 17, n.º 4 (30 de noviembre de 2021): 1–22. http://dx.doi.org/10.1145/3450410.

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In this work, we propose a dual-stream structured graph convolution network ( DS-SGCN ) to solve the skeleton-based action recognition problem. The spatio-temporal coordinates and appearance contexts of the skeletal joints are jointly integrated into the graph convolution learning process on both the video and skeleton modalities. To effectively represent the skeletal graph of discrete joints, we create a structured graph convolution module specifically designed to encode partitioned body parts along with their dynamic interactions in the spatio-temporal sequence. In more detail, we build a set of structured intra-part graphs, each of which can be adopted to represent a distinctive body part (e.g., left arm, right leg, head). The inter-part graph is then constructed to model the dynamic interactions across different body parts; here each node corresponds to an intra-part graph built above, while an edge between two nodes is used to express these internal relationships of human movement. We implement the graph convolution learning on both intra- and inter-part graphs in order to obtain the inherent characteristics and dynamic interactions, respectively, of human action. After integrating the intra- and inter-levels of spatial context/coordinate cues, a convolution filtering process is conducted on time slices to capture these temporal dynamics of human motion. Finally, we fuse two streams of graph convolution responses in order to predict the category information of human action in an end-to-end fashion. Comprehensive experiments on five single/multi-modal benchmark datasets (including NTU RGB+D 60, NTU RGB+D 120, MSR-Daily 3D, N-UCLA, and HDM05) demonstrate that the proposed DS-SGCN framework achieves encouraging performance on the skeleton-based action recognition task.

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Shagapov, V. Sh y E. V. Galiakbarova. "Elements of the theory of forced mixing of oils in tanks". Multiphase Systems 14, n.º 2 (2019): 101–7. http://dx.doi.org/10.21662/mfs2019.2.014.

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To prepare for transportation at the fields, light and heavy oils are mixed with the help of jet mixers, which are injection devices that are installed in the receiving and distributing nozzle inside the tank. The work considers the simplest technological mixing scheme. The basic equations are presented that describe the processes of mixing light and heavy oils in a mixer, in which the light oil stream is the working stream, and the source stream in the heavy oil tank is the injected stream. The characteristic equation of the mixer is obtained. A system of equations is presented that describes the trajectory of the center line of the jet, changes in oil composition and average velocity along the jet. An example of a mixer, which is used in practice in a reservoir of the PBC 2000 type, is considered. Based on the characteristic equation for the known pressure drop of the working and injected flows, as well as the ratio of the sections of the working nozzle and the output section of the mixing chamber, the mixer injection coefficient is found. The calculated graphs of the characteristics of a turbulent flooded jet in an oil field oil storage tank are presented. From the graphs it follows: 1) there is a complete alignment of the concentration of the injected oil mixture with the concentration of heavy oil in the tank; 2) the speed of the jet decreases at a distance of the order of several meters to a value exceeding the minimum fishing speed known from the practice of liquidating bottom sediments. The main role of the mixer when mixing oils is that due to the injection of heavy oil from the reservoir, forced circulation flows are formed that exclude the formation of stagnant zones and the precipitation of solid inactive deposits.

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Min, Seunghwan, Sung Gwan Park, Kunsoo Park, Dora Giammarresi, Giuseppe F. Italiano y Wook-Shin Han. "Symmetric continuous subgraph matching with bidirectional dynamic programming". Proceedings of the VLDB Endowment 14, n.º 8 (abril de 2021): 1298–310. http://dx.doi.org/10.14778/3457390.3457395.

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In many real datasets such as social media streams and cyber data sources, graphs change over time through a graph update stream of edge insertions and deletions. Detecting critical patterns in such dynamic graphs plays an important role in various application domains such as fraud detection, cyber security, and recommendation systems for social networks. Given a dynamic data graph and a query graph, the continuous subgraph matching problem is to find all positive matches for each edge insertion and all negative matches for each edge deletion. The state-of-the-art algorithm TurboFlux uses a spanning tree of a query graph for filtering. However, using the spanning tree may have a low pruning power because it does not take into account all edges of the query graph. In this paper, we present a symmetric and much faster algorithm SymBi which maintains an auxiliary data structure based on a directed acyclic graph instead of a spanning tree, which maintains the intermediate results of bidirectional dynamic programming between the query graph and the dynamic graph. Extensive experiments with real and synthetic datasets show that SymBi outperforms the state-of-the-art algorithm by up to three orders of magnitude in terms of the elapsed time.

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29

Declerck, Philippe y Mohamed Khalid Didi Alaoui. "OPTIMAL CONTROL SYNTHESIS IN INTERVAL DESCRIPTOR SYSTEMS APPLICATION TO TIME STREAM EVENT GRAPHS". IFAC Proceedings Volumes 38, n.º 1 (2005): 13–18. http://dx.doi.org/10.3182/20050703-6-cz-1902.00287.

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30

De Pauw, Wim y Henrique Andrade. "Visualizing Large-Scale Streaming Applications". Information Visualization 8, n.º 2 (22 de enero de 2009): 87–106. http://dx.doi.org/10.1057/ivs.2009.5.

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Stream processing is a new and important computing paradigm. Innovative streaming applications are being developed in areas ranging from scientific applications (for example, environment monitoring), to business intelligence (for example, fraud detection and trend analysis), to financial markets (for example, algorithmic trading systems). In this paper we describe Streamsight, a new visualization tool built to examine, monitor and help understand the dynamic behavior of streaming applications. Streamsight can handle the complex, distributed and large-scale nature of stream processing applications by using hierarchical graphs, multi-perspective visualizations, and de-cluttering strategies. To address the dynamic and adaptive nature of these applications, Streamsight also provides real-time visualization as well as the capability to record and replay. All these features are used for debugging, for performance optimization, and for management of resources, including capacity planning. More than 100 developers, both inside and outside IBM, have been using Streamsight to help design and implement large-scale stream processing applications.

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31

Rice, I. G. "Split Stream Boilers for High-Temperature/High-Pressure Topping Steam Turbine Combined Cycles". Journal of Engineering for Gas Turbines and Power 119, n.º 2 (1 de abril de 1997): 385–94. http://dx.doi.org/10.1115/1.2815586.

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Research and development work on high-temperature and high-pressure (up to 1500°F TIT and 4500 psia) topping steam turbines and associated steam generators for steam power plants as well as combined cycle plants is being carried forward by DOE, EPRI, and independent companies. Aeroderivative gas turbines and heavy-duty gas turbines both will require exhaust gas supplementary firing to achieve high throttle temperatures. This paper presents an analysis and examples of a split stream boiler arrangement for high-temperature and high-pressure topping steam turbine combined cycles. A portion of the gas turbine exhaust flow is run in parallel with a conventional heat recovery steam generator (HRSG). This side stream is supplementary fired opposed to the current practice of full exhaust flow firing. Chemical fuel gas recuperation can be incorporated in the side stream as an option. A significant combined cycle efficiency gain of 2 to 4 percentage points can be realized using this split stream approach. Calculations and graphs show how the DOE goal of 60 percent combined cycle efficiency burning natural gas fuel can be exceeded. The boiler concept is equally applicable to the integrated coal gas fuel combined cycle (IGCC).

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32

Seadawy, Aly R., Syed T. R. Rizvi y Hanadi Zahed. "Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications". Mathematics 11, n.º 5 (21 de febrero de 2023): 1074. http://dx.doi.org/10.3390/math11051074.

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We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solutions, rational kink cross-solutions (RKCs), and homoclinic breather solutions (HBs), and by using the appropriate values for the relevant parameters, their dynamics are visualized in figures. Additionally, two different types of interactions between MSRs and kink waves are analyzed. Furthermore, we examine the stability of the obtained solutions and create a corresponding table. We analyze the stability of these solutions and the movement role of the wave by making graphs as two-dimensional, three-dimensional and density graphs as well as contour visual and stream plots.

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33

Lewiński, Andrzej y Marta Żurek-Mortka. "Analysis and evaluation of the functionality of the mass service system on the basis of customs of truck vehicles". AUTOBUSY – Technika, Eksploatacja, Systemy Transportowe 19, n.º 6 (30 de junio de 2018): 906–10. http://dx.doi.org/10.24136/atest.2018.199.

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Paper discussed the modeling of customs processes for truck vehicles using the Markov processes and mass service theory (queue theory), showing the operation of the notification handling system as a system dependent on random events. The system is characterized as a system with Poisson input stream, exponential service time and many service stations. The results are presented in the form of graphs based on real data received from the customs office

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34

Bok, Kyoungsoo, Jaeyun Jeong, Dojin Choi y Jaesoo Yoo. "Detecting Incremental Frequent Subgraph Patterns in IoT Environments". Sensors 18, n.º 11 (18 de noviembre de 2018): 4020. http://dx.doi.org/10.3390/s18114020.

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As graph stream data are continuously generated in Internet of Things (IoT) environments, many studies on the detection and analysis of changes in graphs have been conducted. In this paper, we propose a method that incrementally detects frequent subgraph patterns by using frequent subgraph pattern information generated in previous sliding window. To reduce the computation cost for subgraph patterns that occur consecutively in a graph stream, the proposed method determines whether subgraph patterns occur within a sliding window. In addition, subgraph patterns that are more meaningful can be detected by recognizing only the patterns that are connected to each other via edges as one pattern. In order to prove the superiority of the proposed method, various performance evaluations were conducted.

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35

Javed, T., B. Ahmed, A. H. Hamid y M. Sajid. "Numerical Analysis of Peristaltic Transport of Casson Fluid for non-zero Reynolds Number in Presence of the Magnetic Field". Nonlinear Engineering 7, n.º 3 (25 de septiembre de 2018): 183–93. http://dx.doi.org/10.1515/nleng-2017-0098.

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Abstract In this study, the peristaltic flow of a Casson fluid in a channel is considered in the presence of an applied magnetic field. Flow is considered in the moving frame of reference with constant velocity along the wave. The developed mathematical model is presented by a set of partial differential equations. A numerical algorithm based on finite element method is implemented to evaluate the numerical solution of the governing partial differential equations in the stream-vorticity formulation. The obtained results are independent of low Reynolds number and long wavelength assumptions, so the effects of non-zero moderate Reynolds number are presented. The expression for the pressure is also calculated implicitly and discussed through graphs. Computed solutions are presented in the form of contours of streamlines and vorticity. Velocity profile and pressure distribution for variation of different involved parameters are also presented through graphs. The investigation shows that the strength of circulation for stream function increases by increasing the Reynolds and Hartmann numbers. Enhancement in longitudinal velocity is noted by increasing the Reynolds number and Casson parameter while increasing Hartmann number reduces the longitudinal velocity. Comparison of the present results with the available results in literature is also included and found in good agreement.

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36

Shin, Kijung, Euiwoong Lee, Jinoh Oh, Mohammad Hammoud y Christos Faloutsos. "CoCoS: Fast and Accurate Distributed Triangle Counting in Graph Streams". ACM Transactions on Knowledge Discovery from Data 15, n.º 3 (12 de abril de 2021): 1–30. http://dx.doi.org/10.1145/3441487.

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Given a graph stream, how can we estimate the number of triangles in it using multiple machines with limited storage? Specifically, how should edges be processed and sampled across the machines for rapid and accurate estimation? The count of triangles (i.e., cliques of size three) has proven useful in numerous applications, including anomaly detection, community detection, and link recommendation. For triangle counting in large and dynamic graphs, recent work has focused largely on streaming algorithms and distributed algorithms but little on their combinations for “the best of both worlds.” In this work, we propose CoCoS , a fast and accurate distributed streaming algorithm for estimating the counts of global triangles (i.e., all triangles) and local triangles incident to each node. Making one pass over the input stream, CoCoS carefully processes and stores the edges across multiple machines so that the redundant use of computational and storage resources is minimized. Compared to baselines, CoCoS is: (a) accurate: giving up to smaller estimation error; (b) fast : up to faster, scaling linearly with the size of the input stream; and (c) theoretically sound : yielding unbiased estimates.

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37

Pavlopoulou, Niki. "Dynamic Diverse Summarisation in Heterogeneous Graph Streams: a Comparison between Thesaurus/Ontology-based and Embeddings-based Approaches". International Journal of Graph Computing 1, n.º 1 (1 de marzo de 2020): 70–94. http://dx.doi.org/10.35708/gc1868-126724.

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Nowadays, there is a lot of attention drawn in smart environments, like Smart Cities and Internet of Things. These environments generate data streams that could be represented as graphs, which can be analysed in real-time to satisfy user or application needs. The challenges involved in these environments, ranging from the dynamism, heterogeneity, continuity, and high-volume of these real-world graph streams create new requirements for graph processing algorithms. We propose a dynamic graph stream summarisation system with the use of embeddings that provides expressive graphs while ensuring high usability and limited resource usage. In this paper, we examine the performance comparison between our embeddings-based approach and an existing thesaurus/ontology-based approach (FACES) that we adapted in a dynamic environment with the use of windows and data fusion. Both approaches use conceptual clustering and top-k scoring that can result in expressive, dynamic graph summaries with limited resources. Evaluations show that sending top-k fused diverse summaries, results in 34% to 92% reduction of forwarded messages and redundancy-awareness with an F-score ranging from 0.80 to 0.95 depending on the k compared to sending all the available information without top-k scoring. Also, the summaries' quality follows the agreement of ideal summaries determined by human judges. The summarisation approaches come with the expense of reduced system performance. The thesaurus/ontology-based approach proved 6 times more latency-heavy and 3 times more memory-heavy compared to the most expensive embeddings-based approach while having lower throughput but provided slightly better quality summaries.

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38

Munawar, Sufian, Ahmer Mehmood, Asif Ali y Najma Saleem. "Unsteady Boundary-Layer Flow over Jerked Plate Moving in a Free Stream of Viscoelastic Fluid". Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/601950.

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This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time0≤τ<∞. Flow properties of the viscoelastic fluid are discussed through graphs.

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39

Alsaedi, A., Naheed Batool, H. Yasmin y T. Hayat. "Convective Heat Transfer Analysis on Prandtl Fluid Model with Peristalsis". Applied Bionics and Biomechanics 10, n.º 4 (2013): 197–208. http://dx.doi.org/10.1155/2013/920276.

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The effects of magnetohydrodynamic (MHD) on peristaltic transport of Prandtl fluid in a symmetric channel have been studied under the assumptions of long wave length and low-Reynolds number. Channel walls are considered compliant in nature. Series solutions of axial velocity, stream function and temperature are given by using regular perturbation technique for small values of Prandtl fluid parameter. The effects of physical parameters on the velocity, streamlines and temperature are examined by plotting graphs.

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40

Karim, Farah, Ioanna Lytra, Christian Mader, Sören Auer y Maria-Esther Vidal. "DESERT: A Continuous SPARQL Query Engine for On-Demand Query Answering". International Journal of Semantic Computing 12, n.º 03 (septiembre de 2018): 373–97. http://dx.doi.org/10.1142/s1793351x18400172.

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The Internet of Things (IoT) has been rapidly adopted in many domains ranging from household appliances e.g. ventilation, lighting, and heating, to industrial manufacturing and transport networks. Despite the, enormous benefits of optimization, monitoring, and maintenance rendered by IoT devices, an ample amount of data is generated continuously. Semantically describing IoT generated data using ontologies enables a precise interpretation of this data. However, ontology-based descriptions tremendously increase the size of IoT data and in presence of repeated sensor measurements, a large amount of the data are duplicates that do not contribute to new insights during query processing or IoT data analytics. In order to ensure that only required ontology-based descriptions are generated, we devise a knowledge-driven approach named DESERT that is able to on-[Formula: see text]emand factoriz[Formula: see text] and [Formula: see text]emantically [Formula: see text]nrich st[Formula: see text]eam da[Formula: see text]a. DESERT resorts to a knowledge graph to describe IoT stream data; it utilizes only the data that is required to answer an input continuous SPARQL query and applies a novel method of data factorization to reduce duplicated measurements in the knowledge graph. The performance of DESERT is empirically studied on a collection of continuous SPARQL queries from SRBench, a benchmark of IoT stream data and continuous SPARQL queries. Furthermore, data streams with various combinations of uniform and varying data stream speeds and streaming window size dimensions are considered in the study. Experimental results suggest that DESERT is capable of speeding up continuous query processing while creates knowledge graphs that include no replications.

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41

Zhao, Yuxuan, Qi Sun, Zhuolun He, Yang Bai y Bei Yu. "AutoGraph: Optimizing DNN Computation Graph for Parallel GPU Kernel Execution". Proceedings of the AAAI Conference on Artificial Intelligence 37, n.º 9 (26 de junio de 2023): 11354–62. http://dx.doi.org/10.1609/aaai.v37i9.26343.

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Deep learning frameworks optimize the computation graphs and intra-operator computations to boost the inference performance on GPUs, while inter-operator parallelism is usually ignored. In this paper, a unified framework, AutoGraph, is proposed to obtain highly optimized computation graphs in favor of parallel executions of GPU kernels. A novel dynamic programming algorithm, combined with backtracking search, is adopted to explore the optimal graph optimization solution, with the fast performance estimation from the mixed critical path cost. Accurate runtime information based on GPU Multi-Stream launched with CUDA Graph is utilized to determine the convergence of the optimization. Experimental results demonstrate that our method achieves up to 3.47x speedup over existing graph optimization methods. Moreover, AutoGraph outperforms state-of-the-art parallel kernel launch frameworks by up to 1.26x.

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42

Akbar, Sobia y Azad Hussain. "The Influences of Squeezed Inviscid Flow between Parallel Plates". Mathematical Problems in Engineering 2021 (22 de abril de 2021): 1–9. http://dx.doi.org/10.1155/2021/6647708.

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Purpose. The main purpose of this study is to investigate the unsteady flow behavior of second-grade inviscid fluid between parallel plates. The effects on the flow are explored through modeling of continuity, momentum, and energy equations. Graphical and tabular exploration has been made to analyze the impact of several influential variables on the dimensionless temperature and velocity profiles. Three-dimensional graphs and stream lines are also mentioned. Design/Approach/Methodology. The governing equations have been metamorphosed into nonlinear ordinary differential equations by using suitable transformation which is the main focus of the study. To approach the solution of the problem numerically, we have used the numerical method such as shooting technique along with Runge–Kutta method is implemented. Findings. The graphs for the squeezing number, Prandtl number, and Eckert number are decreasing by increasing the values of these parameters. The graphs of skin friction coefficient and Nusselt number are increasing by changing the values of both parameters. Originality/Value. The significances of an unsteady squeezed flow of a nonviscous second-grade fluid between parallel plates by using boundary layer phenomenon are discussed.

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43

Malik, Avinash y David Gregg. "Heuristics on Reachability Trees for Bicriteria Scheduling of Stream Graphs on Heterogeneous Multiprocessor Architectures". ACM Transactions on Embedded Computing Systems 14, n.º 2 (25 de marzo de 2015): 1–26. http://dx.doi.org/10.1145/2638553.

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44

Jin, Hai, Changfu Lin, Hanhua Chen y Jiangchuan Liu. "QuickPoint: Efficiently Identifying Densest Sub-Graphs in Online Social Networks for Event Stream Dissemination". IEEE Transactions on Knowledge and Data Engineering 32, n.º 2 (1 de febrero de 2020): 332–46. http://dx.doi.org/10.1109/tkde.2018.2881435.

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45

Buchsbaum, A. L., R. Giancarlo y B. Racz. "New results for finding common neighborhoods in massive graphs in the data stream model". Theoretical Computer Science 407, n.º 1-3 (noviembre de 2008): 302–9. http://dx.doi.org/10.1016/j.tcs.2008.06.056.

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46

Hayat, Tasawar, Zahid Iqbal, Muhammad Qasim y Omar M. Aldossary. "Heat Transfer in a Couple Stress Fluid over a Continuous Moving Surface with Internal Heat Generation and Convective Boundary Conditions". Zeitschrift für Naturforschung A 67, n.º 5 (1 de mayo de 2012): 217–24. http://dx.doi.org/10.5560/zna.2012-0021.

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This investigation reports the boundary layer flow and heat transfer characteristics in a couple stress fluid flow over a continuos moving surface with a parallel free stream. The effects of heat generation in the presence of convective boundary conditions are also investigated. Series solutions for the velocity and temperature distributions are obtained by the homotopy analysis method (HAM). Convergence of obtained series solutions are analyzed. The results are obtained and discussed through graphs for physical parameters of interest.

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47

Sharma, P. Kumar, B. Kumar Sharma y R. C. Chaudhary. "Unsteady free covection oscillatory couette flow through a porous medium with periodic wall temperature". Tamkang Journal of Mathematics 38, n.º 1 (31 de marzo de 2007): 93–102. http://dx.doi.org/10.5556/j.tkjm.38.2007.97.

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This communication investigates the effect of free convection on the heat transfer and the flow through a highly porous medium bounded by two vertical parallel porous plates. It is assume that free stream velocity oscillates in times about a constant mean. Assuming periodic temperature at the moving plate, the approximate solutions for velocity field, emperature field, skin-friction and the rate of heat transfer are obtained and discussed with the help of graphs and tables.

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48

Khan, Ambreen Afsar, Saira Zafar y Atifa Kanwal. "Effect of relaxation and retardation times on dusty Jeffrey fluid in a curved channel with peristalsis". Advances in Mechanical Engineering 13, n.º 6 (junio de 2021): 168781402110284. http://dx.doi.org/10.1177/16878140211028454.

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In recent work, the Jeffrey liquid with uniform dust particles in a symmetric channel is studied. Moving sinusoidal wave is executed on the walls of the channel, which generates peristaltic transport in the fluid. The governing equations for fluid and dust particles have been formulated using stream function. Perturbation method is used to get analytical solution of the problem by using small wave number. Graphical analysis has been carried out for stream function and velocity of fluid and dust particles. Effects of different parameters such as curvature k, relaxation time [Formula: see text], wave number [Formula: see text] and retardation time [Formula: see text] are debated through graphs for both dust particles and fluid. The noteworthy outcomes are fluid velocity, pressure gradient in the region [Formula: see text] and bolus size increases by increasing [Formula: see text]

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49

TRIPATHI, DHARMENDRA. "A MATHEMATICAL MODEL FOR BLOOD FLOW THROUGH INCLINED ARTERIES UNDER THE INFLUENCE OF INCLINED MAGNETIC FIELD". Journal of Mechanics in Medicine and Biology 12, n.º 03 (junio de 2012): 1250033. http://dx.doi.org/10.1142/s0219519411004812.

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A mathematical model is developed to study the characteristics of blood flow through flexible inclined arteries under the influence of an inclined magnetic field. The blood is supposed to be couple stress fluid and the geometry of wall surface of inclined arteries is taken as peristaltic wave. The expressions for axial velocity, volume flow rate, pressure gradient and stream function are obtained under the assumptions of long wavelength and low Reynolds number. The effects of different physical parameters reflecting couple stress parameter, Hartmann number, Reynolds number, Froude number, inclination of channel and inclination of magnetic field on velocity profile, pressure and frictional force are discussed. The stream lines are drawn for various values of emerging parameters and the trapping phenomenon is discussed. The significant features of the blood flow characteristics are analyzed by plotting graphs and discussed numerically in detail.

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50

Bagewadi, C. S. y S. Bhagya. "Steady Plane MHD Flows through Porous Media in the Magnetograph Plane". Mapana - Journal of Sciences 2, n.º 1 (30 de septiembre de 2003): 1–24. http://dx.doi.org/10.12723/mjs.3.1.

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We obtain solutions for steady plane MHD flow through porous media when velocity and magnetic vectors are constantly and variably inclined and the magnitude of the magnetic vector is constant on each individual stream line in the magnetograph plane. It is shown that the path of magnetic and velocity vectors are circles congruency to each other . Also flow analysis is carried out by writing the expression of Legendre transformation in polar co-ordinates. It is shown that solutions obtained agree with the graphs.

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