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2021 ◽  
Vol 17 (4) ◽  
pp. 1-26
Author(s):  
Guy Even ◽  
Reut Levi ◽  
Moti Medina ◽  
Adi Rosén

We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space, and randomness complexities of such samplers. In the standard approach, the whole graph is chosen randomly according to the randomized evolving process, stored in full, and then queries on the sampled graph are answered by simply accessing the stored graph. This may require prohibitive amounts of time, space, and random bits, especially when only a small number of queries are actually issued. Instead, we propose a setting where one generates parts of the sampled graph on-the-fly, in response to queries, and therefore requires amounts of time, space, and random bits that are a function of the actual number of queries. Yet, the responses to the queries correspond to a graph sampled from the distribution in question. Within this framework, we focus on two random graph models: the Barabási-Albert Preferential Attachment model (BA-graphs) ( Science , 286 (5439):509–512) (for the special case of out-degree 1) and the random recursive tree model ( Theory of Probability and Mathematical Statistics , (51):1–28). We give on-the-fly generation algorithms for both models. With probability 1-1/poly( n ), each and every query is answered in polylog( n ) time, and the increase in space and the number of random bits consumed by any single query are both polylog( n ), where n denotes the number of vertices in the graph. Our work thus proposes a new approach for the access to huge graphs sampled from a given distribution, and our results show that, although the BA random graph model is defined by a sequential process, efficient random access to the graph’s nodes is possible. In addition to the conceptual contribution, efficient on-the-fly generation of random graphs can serve as a tool for the efficient simulation of sublinear algorithms over large BA-graphs, and the efficient estimation of their on such graphs.


Author(s):  
M. W. Jahn ◽  
P. E. Bradley

Abstract. To simulate environmental processes, noise, flooding in cities as well as the behaviour of buildings and infrastructure, ‘watertight’ volumetric models are a measuring prerequisite. They ensure topologically consistent 3D models and allow the definition of proper topological operations. However, in many existing city or other geo-information models, topologically unchecked boundary representations are used to store spatial entities. In order to obtain consistent topological models, including their ‘fillings’, in this paper, a triangulation combined with overlay and path-finding methods is presented by climbing up the dimension, beginning with the wireframe model. The algorithms developed for this task are presented, whereby using the philosophy of graph databases and the Property Graph Model. Examples to illustrate the algorithms are given, and experiments are performed on a data-set from Erfurt, Thuringia (Germany), providing complex geometries of buildings. The heavy influence of double precision arithmetic on the results, in particular the positional and angular precision, is discussed in the end.


Author(s):  
Lianyue Feng ◽  
Helian Xu ◽  
Gang Wu ◽  
Wenting Zhang

2021 ◽  
Vol 2021 (10) ◽  
pp. 1217-1223
Author(s):  
A. A. Tyrymov

2021 ◽  
Vol 8 (10) ◽  
Author(s):  
Xue Gong ◽  
Desmond J. Higham ◽  
Konstantinos Zygalakis

We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph model. We focus on two existing spectral approaches that build and analyse Laplacian-style matrices via the minimization of frustration and trophic incoherence. These algorithms aim to reveal directed periodic and linear hierarchies, respectively. We show that reordering nodes using the two algorithms, or mapping them onto a specified lattice, is associated with new classes of directed random graph models. Using this random graph setting, we are able to compare the two algorithms on a given network and quantify which structure is more likely to be present. We illustrate the approach on synthetic and real networks, and discuss practical implementation issues.


Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1204
Author(s):  
Adèle Helena Ribeiro ◽  
Maciel Calebe Vidal ◽  
João Ricardo Sato ◽  
André Fujita

Graphs/networks have become a powerful analytical approach for data modeling. Besides, with the advances in sensor technology, dynamic time-evolving data have become more common. In this context, one point of interest is a better understanding of the information flow within and between networks. Thus, we aim to infer Granger causality (G-causality) between networks’ time series. In this case, the straightforward application of the well-established vector autoregressive model is not feasible. Consequently, we require a theoretical framework for modeling time-varying graphs. One possibility would be to consider a mathematical graph model with time-varying parameters (assumed to be random variables) that generates the network. Suppose we identify G-causality between the graph models’ parameters. In that case, we could use it to define a G-causality between graphs. Here, we show that even if the model is unknown, the spectral radius is a reasonable estimate of some random graph model parameters. We illustrate our proposal’s application to study the relationship between brain hemispheres of controls and children diagnosed with Autism Spectrum Disorder (ASD). We show that the G-causality intensity from the brain’s right to the left hemisphere is different between ASD and controls.


2021 ◽  
Author(s):  
Dian Jin

<div>As a highly dynamic operating process, flight activity requires a lot of attention from pilots. Thus, it’s quite imperative to give research to their visual attention. Traditional research methods mostly based on qualitative analysis, or hypothetical model, and seldom put context information into their model. However, the underlying knowledge (tacit knowledge) hidden in the different performances of pilot’s attention allocation is context related, and is hard to express by experts, thus it is difficult to use those traditional methods to construct an interaction system. In this paper, we mined attention pattern with scene context to achieve the quantitative analysis of tacit knowledge of pilots during flight tasks, and use the method of data mining as well as attribute graph model to construct visual cognitive graph(s). The attribute graph model was adopted to construct visual cognitive graphs which associate the obtained visual information within the flight context. Based on the model, the attention pattern with scene context was mined to achieve the quantitative analysis of tacit knowledge of pilots during flight tasks. Besides, three physical quantities derived from graph theory was introduced to describe the tacit knowledge, which can be used directly to construct an interaction system: first, key information, which shown as central node in the graph we built, reveals the most important information during flight mission within context; second, relevant information, which contains several nodes that was closely connected and strongly impact the central node, reveals the factors affecting the key information; third, bridge information based on betweenness centrality, which can be regard as the important information bridge(s), reveals the process of decision making. Our work can be directly used to train novice pilots, to guide the interface design, and to construct the adaptive interaction system.</div>


2021 ◽  
Author(s):  
Dian Jin

<div>As a highly dynamic operating process, flight activity requires a lot of attention from pilots. Thus, it’s quite imperative to give research to their visual attention. Traditional research methods mostly based on qualitative analysis, or hypothetical model, and seldom put context information into their model. However, the underlying knowledge (tacit knowledge) hidden in the different performances of pilot’s attention allocation is context related, and is hard to express by experts, thus it is difficult to use those traditional methods to construct an interaction system. In this paper, we mined attention pattern with scene context to achieve the quantitative analysis of tacit knowledge of pilots during flight tasks, and use the method of data mining as well as attribute graph model to construct visual cognitive graph(s). The attribute graph model was adopted to construct visual cognitive graphs which associate the obtained visual information within the flight context. Based on the model, the attention pattern with scene context was mined to achieve the quantitative analysis of tacit knowledge of pilots during flight tasks. Besides, three physical quantities derived from graph theory was introduced to describe the tacit knowledge, which can be used directly to construct an interaction system: first, key information, which shown as central node in the graph we built, reveals the most important information during flight mission within context; second, relevant information, which contains several nodes that was closely connected and strongly impact the central node, reveals the factors affecting the key information; third, bridge information based on betweenness centrality, which can be regard as the important information bridge(s), reveals the process of decision making. Our work can be directly used to train novice pilots, to guide the interface design, and to construct the adaptive interaction system.</div>


Semantic Web ◽  
2021 ◽  
pp. 1-23
Author(s):  
Steven J. Baskauf ◽  
Jessica K. Baskauf

The W3C Generating RDF from Tabular Data on the Web Recommendation provides a mechanism for mapping CSV-formatted data to any RDF graph model. Since the Wikibase data model used by Wikidata can be expressed as RDF, this Recommendation can be used to document tabular snapshots of parts of the Wikidata knowledge graph in a simple form that is easy for humans and applications to read. Those snapshots can be used to document how subgraphs of Wikidata have changed over time and can be compared with the current state of Wikidata using its Query Service to detect vandalism and value added through community contributions.


2022 ◽  
Vol 16 (2) ◽  
pp. 1-31
Author(s):  
Lucas Santos De Oliveira ◽  
Pedro O. S. Vaz-De-Melo ◽  
Aline Carneiro Viana

The pervasiveness of smartphones has shaped our lives, social norms, and the structure that dictates human behavior. They now directly influence how individuals demand resources or interact with network services. From this scenario, identifying key locations in cities is fundamental for the investigation of human mobility and also for the understanding of social problems. In this context, we propose the first graph-based methodology in the literature to quantify the power of Point-of-Interests (POIs) over its vicinity by means of user mobility trajectories. Different from literature, we consider the flow of people in our analysis, instead of the number of neighbor POIs or their structural locations in the city. Thus, we modeled POI’s visits using the multiflow graph model where each POI is a node and the transitions of users among POIs are a weighted direct edge. Using this multiflow graph model, we compute the attract, support, and independence powers . The attract power and support power measure how many visits a POI gathers from and disseminate over its neighborhood, respectively. Moreover, the independence power captures the capacity of a POI to receive visitors independently from other POIs. We tested our methodology on well-known university campus mobility datasets and validated on Location-Based Social Networks (LBSNs) datasets from various cities around the world. Our findings show that in university campus: (i) buildings have low support power and attract power ; (ii) people tend to move over a few buildings and spend most of their time in the same building; and (iii) there is a slight dependence among buildings, even those with high independence power receive user visits from other buildings on campus. Globally, we reveal that (i) our metrics capture places that impact the number of visits in their neighborhood; (ii) cities in the same continent have similar independence patterns; and (iii) places with a high number of visitation and city central areas are the regions with the highest degree of independence.


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