Without geospatial data management, today’s challenges in big data applications such as earth observation, geographic information system/building information modeling (GIS/BIM) integration, and 3D/4D city planning cannot be solved. Furthermore, geospatial data management plays a connecting role between data acquisition, data modelling, data visualization, and data analysis. It enables the continuous availability of geospatial data and the replicability of geospatial data analysis. In the first part of this article, five milestones of geospatial data management research are presented that were achieved during the last decade. The first one reflects advancements in BIM/GIS integration at data, process, and application levels. The second milestone presents theoretical progress by introducing topology as a key concept of geospatial data management. In the third milestone, 3D/4D geospatial data management is described as a key concept for city modelling, including subsurface models. Progress in modelling and visualization of massive geospatial features on web platforms is the fourth milestone which includes discrete global grid systems as an alternative geospatial reference framework. The intensive use of geosensor data sources is the fifth milestone which opens the way to parallel data storage platforms supporting data analysis on geosensors. In the second part of this article, five future directions of geospatial data management research are presented that have the potential to become key research fields of geospatial data management in the next decade. Geo-data science will have the task to extract knowledge from unstructured and structured geospatial data and to bridge the gap between modern information technology concepts and the geo-related sciences. Topology is presented as a powerful and general concept to analyze GIS and BIM data structures and spatial relations that will be of great importance in emerging applications such as smart cities and digital twins. Data-streaming libraries and “in-situ” geo-computing on objects executed directly on the sensors will revolutionize geo-information science and bridge geo-computing with geospatial data management. Advanced geospatial data visualization on web platforms will enable the representation of dynamically changing geospatial features or moving objects’ trajectories. Finally, geospatial data management will support big geospatial data analysis, and graph databases are expected to experience a revival on top of parallel and distributed data stores supporting big geospatial data analysis.

A new methodology is presented for estimating age distribution and survival functions of an urban building stock. This allows for a random sample of the undemolished stock together with a complete inventory count of the demolished part to create a Kaplan–Meier estimator for the survival function. This method can be applied to any building stock with difficult access to data. A demonstration of this method is applied to a sample of German urban stock and used to illustrate the data-collection process, the survival analysis and an estimate of the dynamics. Findings from this sample indicate a slower dynamic in the residential part in comparison with the non-residential part, which is related to seemingly different survival functions. Another finding is that the percentage of undemolished buildings seems much lower for older buildings than for the younger structures. Through a Weibull fit, little future change in this survival pattern is estimated. The estimates obtained in this preliminary study challenge many assumptions of service life, economic life and effective life time. It is found that the effective life time of building stocks is much higher than generally assumed, and possibly independent of their age. For recent buildings, the implication is whether the existing service life or economic life approaches are adequate to understand and plan for a potentially higher survival rate. Nous présentons ici une nouvelle méthodologie pour l'estimation de la répartition des âges et des fonctions de survie d'un parc de bâtiments urbains. A partir d'un échantillon aléatoire du parc non démoli et d'un inventaire complet de la partie démolie, cette méthodologie permet la création d'un estimateur Kaplan–Meier pour la fonction de survie. La méthode peut être appliquée à tout parc de bâtiments pour lequel les données sont difficiles à obtenir. Une démonstration est appliquée à un échantillon de parc urbain allemand et permet d'illustrer le processus de collecte de données, l'analyse de survie ainsi qu'une estimation de la dynamique. L'analyse de cet échantillon révèle une dynamique plus lente dans la partie résidentielle par rapport à la partie non résidentielle et qui est associée à des fonctions de survie apparemment différentes. Une autre conclusion est que le pourcentage des bâtiments non démolis est bien plus faible pour les bâtiments anciens que pour les structures plus récentes. Une régression de Weibull permet de prédire la faible évolution de ce modèle de survie à terme. Les estimations obtenues dans cette étude préliminaire remettent en cause bon nombre d'hypothèses sur les durées de vie utile, économique et effective. La durée de vie utile des parcs de bâtiments apparaît ainsi bien plus longue que l'on croît habituellement et pourrait être indépendante de l'âge. Pour les bâtiments récents, l'étude suggère que l'on est en droit de s'interroger quant à la pertinence des démarches actuelles appuyées sur la durée de vie utile ou économique pour comprendre et prévoir des mesures de relèvement du taux de survie. Mots clés: répartition des âges, parc de bâtiments, conservation, taux de démolition, planification, gestion de biens, durée de vie utile, analyse de survie, tissu urbain

An effective p-adic encoding of dendrograms is presented through an explicit embedding into the Bruhat–Tits tree for a p-adic number field. This field depends on the number of children of a vertex and is a finite extension of the field of p-adic numbers. It is shown that fixing p-adic representatives of the residue field allows a natural way of encoding strings by identifying a given alphabet with such representatives. A simple p-adic hierarchic classification algorithm is derived for p-adic numbers, and is applied to strings over finite alphabets. Examples of DNA coding are presented and discussed. Finally, new geometric and combinatorial invariants of time series of p-adic dendrograms are developed.

A class of heat operators over non-archimedean local fields acting on \(L_2\)-function spaces on holed discs in the local field are developed and seen as being operators previously introduced by Zúñiga-Galindo, and if the underlying trees are regular, they are associated here with certain finite Kronecker product graphs. \(L_2\)-spaces and integral operators invariant under the action of a finite group acting on a holed disc are studied, and then applied to Mumford curves. It is found that the spectral gap in families of Mumford curves can become arbitrarily small.

For a finite graph, a spectral curve is constructed as the zero set of a two-variate polynomial with integer coefficients coming from p-adic diffusion on the graph. It is shown that certain spectral curves can distinguish non-isomorphic pairs of isospectral graphs, and can even reconstruct the graph. This allows the graph reconstruction from the spectrum of the associated p-adic Laplacian operator. As an application to p-adic geometry, it is shown that the reduction graph of a Mumford curve and the product reduction graph of a p-adic analytic torus can be recovered from the spectrum of such operators.