3D TOPOLOGICAL SUPPORT IN SPATIAL DATABASES: AN OVERVIEW

The storage of spatial data that consists of spatial and non-spatial properties requires a database management system that possesses spatial functions that can cater to the spatial characteristics of data. These characteristics include the geometrical shape, topological and positional information. Parallel to how geometries describe the shape of an object, topological information is also an important spatial property which describes how the geometries in a space are related to each other. This information describes the connectivity, containment and adjacencies of spatial objects which are the foundation for more complex analysis such as navigation, data reconstruction, spatial queries and others. However, the topological support provided by spatial databases varies. This paper provided an overview on the current implementations of topological support in spatial databases such as ArcGIS, QGIS, PostgreSQL and others. The native topology in most spatial databases was found to be 2D topology maintained by 2D topology rules with limited representation of 3D topological relationships. Consequently, 3D objects represented by 2D topology had to be decomposed into objects of lower dimensions. Approaches to implement additional topological support for spatial databases included the use of topological data models, data structures, operators, and rules. 3D applications such as 3D cadastre required more detailed representations of topological information which required a more comprehensive 3D topological data model. Nonetheless, comprehensive preservation of topological information also mandates voluminous storage and higher computational efficiency. Thus, the appropriate 3D topological support should be provided in spatial databases to accurately represent 3D objects and meet 3D analysis requirements.

Prospects for $$ {B}_c^{+} $$→ τ +ντ at FCC-ee

This paper presents the prospects for a precise measurement of the branching fraction of the leptonic $$ {B}_c^{+} $$ B c + → τ+ντ decay at the Future Circular Collider (FCC-ee) running at the Z -pole. A detailed description of the simulation and analysis framework is provided. To select signal candidates, two Boosted Decision Tree algorithms are employed and optimised. The first stage suppresses inclusive $$ b\overline{b} $$ b b ¯ , $$ c\overline{c} $$ c c ¯ , and $$ q\overline{q} $$ q q ¯ backgrounds using event-based topological information. A second stage utilises the properties of the hadronic τ+→ π+π+π−$$ \overline{\nu} $$ ν ¯ τ decay to further suppress these backgrounds, and is also found to achieve high rejection for the B+→ τ+ντ background. The number of $$ {B}_c^{+} $$ B c + → τ+ντ candidates is estimated for various Tera-Z scenarios, and the potential precision of signal yield and branching fraction measurements evaluated. The phenomenological impact of such measurements on various New Physics scenarios is also explored.

Spatiotemporal Graph Indicators for Air Traffic Complexity Analysis

There has been extensive research in formalising air traffic complexity, but existing works focus mainly on a metric to tie down the peak air traffic controllers workload rather than a dynamic approach to complexity that could guide both strategical, pre-tactical and tactical actions for a smooth flow of aircraft. In this paper, aircraft interdependencies are formalized using graph theory and four complexity indicators are described, which combine spatiotemporal topological information with the severity of the interdependencies. These indicators can be used to predict the dynamic evolution of complexity, by not giving one single score, but measuring complexity in a time window. Results show that these indicators can capture complex spatiotemporal areas in a sector and give a detailed and nuanced view of sector complexity.

TopoResNet: A Hybrid Deep Learning Architecture and Its Application to Skin Lesion Classification

The application of artificial intelligence (AI) to various medical subfields has been a popular topic of research in recent years. In particular, deep learning has been widely used and has proven effective in many cases. Topological data analysis (TDA)—a rising field at the intersection of mathematics, statistics, and computer science—offers new insights into data. In this work, we develop a novel deep learning architecture that we call TopoResNet that integrates topological information into the residual neural network architecture. To demonstrate TopoResNet, we apply it to a skin lesion classification problem. We find that TopoResNet improves the accuracy and the stability of the training process.

Graph convolutional networks: analysis, improvements and results

A graph can represent a complex organization of data in which dependencies exist between multiple entities or activities. Such complex structures create challenges for machine learning algorithms, particularly when combined with the high dimensionality of data in current applications. Graph convolutional networks were introduced to adopt concepts from deep convolutional networks (i.e. the convolutional operations/layers) that have shown good results. In this context, we propose two major enhancements to two of the existing graph convolutional network frameworks: (1) topological information enrichment through clustering coefficients; and (2) structural redesign of the network through the addition of dense layers. Furthermore, we propose minor enhancements using convex combinations of activation functions and hyper-parameter optimization. We present extensive results on four state-of-art benchmark datasets. We show that our approach achieves competitive results for three of the datasets and state-of-the-art results for the fourth dataset while having lower computational costs compared to competing methods.

Robust Data-Driven Leak Localization in Water Distribution Networks Using Pressure Measurements and Topological Information

This article presents a new data-driven method for locating leaks in water distribution networks (WDNs). It is triggered after a leak has been detected in the WDN. The proposed approach is based on the use of inlet pressure and flow measurements, other pressure measurements available at some selected inner nodes of the WDN, and the topological information of the network. A reduced-order model structure is used to calculate non-leak pressure estimations at sensed inner nodes. Residuals are generated using the comparison between these estimations and leak pressure measurements. In a leak scenario, it is possible to determine the relative incidence of a leak in a node by using the network topology and what it means to correlate the probable leaking nodes with the available residual information. Topological information and residual information can be integrated into a likelihood index used to determine the most probable leak node in the WDN at a given instant k or, through applying the Bayes’ rule, in a time horizon. The likelihood index is based on a new incidence factor that considers the most probable path of water from reservoirs to pressure sensors and potential leak nodes. In addition, a pressure sensor validation method based on pressure residuals that allows the detection of sensor faults is proposed.

Time-topology analysis

Many real-world networks have been evolving, and are finely modeled as temporal graphs from the viewpoint of the graph theory. A temporal graph is informative, and always contains two types of information, i.e., the temporal information and topological information, where the temporal information reflects the time when the relationships are established, and the topological information focuses on the structure of the graph. In this paper, we perform time-topology analysis on temporal graphs to extract useful information. Firstly, a new metric named T-cohesiveness is proposed to evaluate the cohesiveness of a temporal subgraph. It defines the cohesiveness of a temporal subgraph from the time and topology dimensions jointly. Specifically, given a temporal graph G s = ( Vs , ε Es ), cohesiveness in the time dimension reflects whether the connections in G s happen in a short period of time, while cohesiveness in the topology dimension indicates whether the vertices in V s are densely connected and have few connections with vertices out of G s . Then, T-cohesiveness is utilized to perform time-topology analysis on temporal graphs, and two time-topology analysis methods are proposed. In detail, T-cohesiveness evolution tracking traces the evolution of the T-cohesiveness of a subgraph, and combo searching finds out all the subgraphs that contain the query vertex and have T-cohesiveness larger than a given threshold. Moreover, a pruning strategy is proposed to improve the efficiency of combo searching. Experimental results confirm the efficiency of the proposed time-topology analysis methods and the pruning strategy.

TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State

We present ToloMEo (TOpoLogical netwOrk Maximum Entropy Optimization), a program implemented in C and Python that exploits a maximum entropy algorithm to evaluate network topological information. ToloMEo can study any system defined on a connected network where nodes can assume N discrete values by approximating the system probability distribution with a Pottz Hamiltonian on a graph. The software computes entropy through a thermodynamic integration from the mean-field solution to the final distribution. The nature of the algorithm guarantees that the evaluated entropy is variational (i.e., it always provides an upper bound to the exact entropy). The program also performs machine learning, inferring the system’s behavior providing the probability of unknown states of the network. These features make our method very general and applicable to a broad class of problems. Here, we focus on three different cases of study: (i) an agent-based model of a minimal ecosystem defined on a square lattice, where we show how topological entropy captures a crossover between hunting behaviors; (ii) an example of image processing, where starting from discretized pictures of cell populations we extract information about the ordering and interactions between cell types and reconstruct the most likely positions of cells when data are missing; and (iii) an application to recurrent neural networks, in which we measure the information stored in different realizations of the Hopfield model, extending our method to describe dynamical out-of-equilibrium processes.