For the de Rham mapping cone cochain complex induced by a smooth closed 2-form, we explicitly write down the associated mapping cone Thom form in the sense of Mathai-Quillen. Our construction uses the mapping cone covariant derivative, carrying the extra information brought by the 2-form. Our main tool is the Berezin integral. As the main result, we show that this Thom form is closed with respect to the mapping cone differentiation, its integration along the fiber is 1, and it satisfies the transgression formula.
The norm operator method, which was recently proposed as a new formulation of the boson expansion theory (BET), is used to show that the subspace mapping is properly derived from the whole space mapping. This derivation requires the appropriate renormalization of the contribution of phonons that are not adopted as boson excitations in the subspace mapping. This was impossible with conventional BETs (which ignore these contributions), and is only made possible for the first time by the norm operator method, which treats these contributions appropriately. We also correct the confusion in the claims of conventional BETs. Namely, contrary to conventional claims, we show that when the phonon excitations not adopted as boson excitations make no contribution at all, the subspace mapping is obtained simply by discarding those excitations. Furthermore, we demonstrate that the Park operator, which had been considered effective only in the whole space mapping, is also effective in the subspace mapping. These findings provide a clear criterion for verifying the applicability of the boson expansion theory to large-amplitude collective motions and offer a new perspective on a microscopic foundation of the interacting boson model (IBM).
Dominik Kulmer, Maximilian Leitenstern, Marcel Weinmann
et al.
Accurate localization is a critical component of mobile autonomous systems, especially in Global Navigation Satellite Systems (GNSS)-denied environments where traditional methods fail. In such scenarios, environmental sensing is essential for reliable operation. However, approaches such as LiDAR odometry and Simultaneous Localization and Mapping (SLAM) suffer from drift over long distances, especially in the absence of loop closures. Map-based localization offers a robust alternative, but the challenge lies in creating and georeferencing maps without GNSS support. To address this issue, we propose a method for creating georeferenced maps without GNSS by using publicly available data, such as building footprints and surface models derived from sparse aerial scans. Our approach integrates these data with onboard LiDAR scans to produce dense, accurate, georeferenced 3D point cloud maps. By combining an Iterative Closest Point (ICP) scan-to-scan and scan-to-map matching strategy, we achieve high local consistency without suffering from long-term drift. Thus, we eliminate the reliance on GNSS for the creation of georeferenced maps. The results demonstrate that LiDAR-only mapping can produce accurate georeferenced point cloud maps when augmented with existing map priors.
3D Gaussian splatting (3DGS) has recently demonstrated promising advancements in RGB-D online dense mapping. Nevertheless, existing methods excessively rely on per-pixel depth cues to perform map densification, which leads to significant redundancy and increased sensitivity to depth noise. Additionally, explicitly storing 3D Gaussian parameters of room-scale scene poses a significant storage challenge. In this paper, we introduce OG-Mapping, which leverages the robust scene structural representation capability of sparse octrees, combined with structured 3D Gaussian representations, to achieve efficient and robust online dense mapping. Moreover, OG-Mapping employs an anchor-based progressive map refinement strategy to recover the scene structures at multiple levels of detail. Instead of maintaining a small number of active keyframes with a fixed keyframe window as previous approaches do, a dynamic keyframe window is employed to allow OG-Mapping to better tackle false local minima and forgetting issues. Experimental results demonstrate that OG-Mapping delivers more robust and superior realism mapping results than existing Gaussian-based RGB-D online mapping methods with a compact model, and no additional post-processing is required.
In this paper we give an example of duoidal $\infty$-categories. We introduce map $\mathcal{O}$-monoidales in an $\mathcal{O}$-monoidal $(\infty,2)$-category for an $\infty$-operad $\mathcal{O}^{\otimes}$. We show that the endomorphism mapping $\infty$-category of a map $\mathcal{O}$-monoidale is a coCartesian $(Δ^{\rm op},\mathcal{O})$-duoidal $\infty$-category. After that, we introduce a convolution product on the mapping $\infty$-category from an $\mathcal{O}$-comonoidale to an $\mathcal{O}$-monoidale. We show that the $\mathcal{O}$-monoidal structure on the duoidal endomorphism mapping $\infty$-category of a map $\mathcal{O}$-monoidale is equivalent to the convolution product on the mapping $\infty$-category from the dual $\mathcal{O}$-comonoidale to the map $\mathcal{O}$-monoidale.
Hiroshi Seno, Toshiya Kojima, Masatoshi Yamazaki
et al.
Catheter ablation has limited therapeutic efficacy against non-paroxysmal atrial fibrillation (AF), and electrophysiological studies using mapping catheters have been applied to evaluate the AF substrate. However, many of these approaches rely on detecting excitation timing from electrograms (ECGs), potentially compromising their effectiveness in complex AF scenarios. Herein, we introduce Deep-learning-based Electrode Action Potential Mapping (DEAP Mapping), a deep learning model designed to reconstruct membrane potential images from annotation-free unipolar ECG signals. We conducted ex vivo experiments using porcine hearts (N = 6) to evaluate the accuracy of DEAP Mapping by simultaneously performing fluorescence measurement of membrane potentials and measurements of epicardial unipolar ECGs. Membrane potentials estimated via DEAP Mapping were compared with those measured via optical mapping. We assessed the clinical applicability of DEAP Mapping by comparing the DEAP Mapping's estimations from clinically measured catheter electrode signals with those from established electrode-mapping techniques. DEAP Mapping accurately estimated conduction delays and blocks in ex vivo experiments. Phase variance analysis, an AF substrate evaluation method, revealed that the substrate identified from optical mapping closely resembled that identified from DEAP Mapping estimations (structural similarity index of >0.8). In clinical evaluations, DEAP Mapping estimation observed several conduction delays and blocks that were not observed with existing methods, indicating that DEAP Mapping can estimate excitation patterns with higher spatiotemporal resolution. DEAP Mapping has a potential to derive detailed changes in membrane potential from intra-operative catheter electrode signals, offering enhanced visualisation of the AF substrate from the estimated membrane potentials.
Large-scale multi-session LiDAR mapping is essential for a wide range of applications, including surveying, autonomous driving, crowdsourced mapping, and multi-agent navigation. However, existing approaches often struggle with data redundancy, robustness, and accuracy in complex environments. To address these challenges, we present MS-Mapping, an novel multi-session LiDAR mapping system that employs an incremental mapping scheme for robust and accurate map assembly in large-scale environments. Our approach introduces three key innovations: 1) A distribution-aware keyframe selection method that captures the subtle contributions of each point cloud frame to the map by analyzing the similarity of map distributions. This method effectively reduces data redundancy and pose graph size, while enhancing graph optimization speed; 2) An uncertainty model that automatically performs least-squares adjustments according to the covariance matrix during graph optimization, improving mapping precision, robustness, and flexibility without the need for scene-specific parameter tuning. This uncertainty model enables our system to monitor pose uncertainty and avoid ill-posed optimizations, thereby increasing adaptability to diverse and challenging environments. 3) To ensure fair evaluation, we redesign baseline comparisons and the evaluation benchmark. Direct assessment of map accuracy demonstrates the superiority of the proposed MS-Mapping algorithm compared to state-of-the-art methods. In addition to employing public datasets such as Urban-Nav, FusionPortable, and Newer College, we conducted extensive experiments on such a large \SI{855}{m}$\times$\SI{636}{m} ground truth map, collecting over \SI{20}{km} of indoor and outdoor data across more than ten sequences...
Małgorzata Busko, Monika Balawejder, Oleksandra Kovalyshyn
et al.
Abstract Since the early days, cadastral data represent the geographic extent of the past, current, and future rights and interests in real property. Thus, these data are extremely important for the proper development of statehood and society. The article analyses the process of formation of the real estate cadastre in two countries – Poland and Ukraine – from the time of its establishment to the present. Both countries were in the past (and Ukraine still is) victims of various historical events that deprived them of statehood, stability and opportunities for development; therefore, it affected the development of the cadastre and its accessibility to all stakeholders. The authors attempt to answer the question of if and how geographic location and historical conditions can affect the quality and availability of open cadastral data (OCD). After all, our perception of reality is a direct result of processes originating in history. This paper contains comparisons between a post-Soviet (Ukraine) and a post-communist country (Poland) and their path from early cadastral maps to OCD.
Abstract. Unmanned Aerial Systems (UAS) are increasingly used in different applications, including 3D urban modelling, cadastral mapping, urban planning, GIS information system and other fields because of their advantages. As a consequence, UAS equipment is constantly developed to provide more accurate results in a more reliable mode. This paper aims to evaluate the performances of a low-cost UAS system, namely DJI Phantom 4 Pro v2 equipped with a TeoKIT GNSS PPK (post-processing kinematic) module for cadastral mapping purposes. Two fights (oblique and nadir) over a residential area at 60 m height were performed and some 100 ground points were used to derive RMSE accuracies. Comparison between GNSS-aided with PPK processing and indirect georeferencing processes are performed. Given a mobile laser scanner (MLS) point cloud as ground truth, comparison with UAS point clouds and manually digitized features are also performed and reported.
Uno de los documentos de Naciones Unidas, que sirve como guía para mejorar la gestión del territorio, es el Marco para la Administración Efectiva de la Tierra. El mismo incluye aspectos relacionados al catastro territorial, registro de la propiedad, urbanismo, valoración de suelo, etc. Actualmente, se observa la necesidad de documentar, registrar y reconocer las relaciones de las personas con el territorio. Tales acciones, son indispensables para alcanzar el cumplimiento de los Objetivos del Desarrollo Sostenible enunciados en la Agenda 2030 de Naciones Unidas. Los Catastros Territoriales son una herramienta primordial en todo sistema de administración del suelo, conformando uno de los pilares fundamentales en la registración de la compleja trama de derechos y restricciones que relacionan al ser humano con el medio que habita. También a nivel internacional, la Federación Internacional de Agrimensores ha elaborado y aprobado una visión para el desarrollo de los sistemas catastrales, el mismo es conocido como “Catastro 2014”. Tal documento, define el término de “objetos territoriales legales” y aconseja su registración en los sistemas catastrales. En Argentina, los lineamientos impartidos por el documento señalado en el párrafo precedente, han sido incorporados por la Ley Nacional de Catastro N° 26.209, promulgada en enero del año 2007. En el presente trabajo, se analiza si los Catastro Territorial de Argentina cuentan con un marco normativo nacional suficiente que permita generar la información requerida para la administración efectiva de la tierra y la implementación de políticas destinadas a alcanzar los Objetivos del Desarrollo Sostenible.
The concepts of institutions and institutional approaches are studied. On the basis of institutional approaches to the planning of sustainable use and protection of agricultural lands of individual land uses, a system of institutes was formed, which include: the Institute of Land Management, the Institute of Land Monitoring, the Institute of the State Land Cadastre, the Institute of Local Self-Government, and the Institute of Local Traditions. The importance and effectiveness of these institutions, namely as systems and their relevance, are substantiated. The tools of these institutes, which allow for planning the sustainable use and protection of agricultural lands of individual land uses, as well as their implementation, have been analysed.
The institute of land management and its tools, such as land management schemes and technical and economic justifications for the use and protection of lands of administrative territorial units, territories of territorial communities, and complex plans for the spatial development of the territory of the territorial community, are analysed in detail. The need to introduce a tool of land management regulations to expand the possibilities of the institute of land management in planning the use of territories located outside of settlements is justified. The importance of the institution of land monitoring is substantiated and the urgency of creating and implementing an automated land monitoring system is emphasized. The current state of the Institute of the State Land Cadastre was investigated and the expediency of expanding the list of objects of the State Land Cadastre by adding "agricultural land use" was substantiated. It was found that the significance of the institution of local self-government in the context of planning the sustainable use and protection of agricultural lands of individual land uses increases due to the expansion of the powers of local authorities in the process of decentralization of power. The need to take into account local agricultural traditions when planning the sustainable use and protection of agricultural lands of individual land uses has been confirmed.
Key words: institutions, institutional approaches, agricultural land, land use, sustainable use and protection of agricultural land, land management, State Land Cadastre, local self-government.
Constructing a high-quality dense map in real-time is essential for robotics, AR/VR, and digital twins applications. As Neural Radiance Field (NeRF) greatly improves the mapping performance, in this paper, we propose a NeRF-based mapping method that enables higher-quality reconstruction and real-time capability even on edge computers. Specifically, we propose a novel hierarchical hybrid representation that leverages implicit multiresolution hash encoding aided by explicit octree SDF priors, describing the scene at different levels of detail. This representation allows for fast scene geometry initialization and makes scene geometry easier to learn. Besides, we present a coverage-maximizing keyframe selection strategy to address the forgetting issue and enhance mapping quality, particularly in marginal areas. To the best of our knowledge, our method is the first to achieve high-quality NeRF-based mapping on edge computers of handheld devices and quadrotors in real-time. Experiments demonstrate that our method outperforms existing NeRF-based mapping methods in geometry accuracy, texture realism, and time consumption. The code will be released at: https://github.com/SYSU-STAR/H2-Mapping
Marcelo Crespo, Alexander Follmann, C. Butsch
et al.
ABSTRACT International Retirement Migration (IRM) is a growing phenomenon in the Global South. Using the example of the city of Cotacachi in the Ecuadorian Andes, this paper analyzes the spatio-temporal growth of the properties acquired by foreign retirees. We have developed a multi-temporal map that visualizes the spatio-temporal patterns of foreign-owned real estate properties and explains them in the historical context of land tenure. As no official spatial data is available for foreign-owned properties in Cotacachi, the mapping was developed based on data triangulation from remote sensing, participatory mapping, document analysis (e.g. a cadastral database), and semi-structured interviews with key stakeholders. With this origin approach, the map reveals a significant growth in the number of properties and the size of the land acquired by foreigners particularly since the 2008 United States’ housing crisis. Most of the foreign-owned properties are located at the urban fringe and have been built on former colonial hacienda lands in direct proximity to existing indigenous communities.
: The development, in recent decades, of specific GIS and remote sensing techniques, facilitates the spatial analysis of the pastoral space and provides access to a huge volume of geospatial data. In this context, the purpose of the research is the mapping of the grasslands of Arad county and their analysis in correlation with the altitude and slope of the terrain. For Arad county, the grassland areas were identified and mapped, as follows: the Corine Land Cover database, 2018 edition, on a medium scale, was completed on the basis of orthophotoplans and cadastral plans at a scale of 1:10000, a process that obtained representation of grasslands on a large scale. The calculations show that 12% of the area of Arad county belongs to grasslands. The overlay analysis allowed the study of grasslands in correlation with other environmental factors, which can influence the floristic composition or their spatio-temporal dynamics. Thus, 89% of the grassland areas are located between 80.8 and 300 m altitude and 96% are located on slopes with an inclination below 15º. The application of GIS techniques in the research of grasslands in a given territory, offers the possibility of a holistic approach or for particular cases.
Urban gardening is becoming increasingly popular. Air pollution, which is a major concern in cities might, however, threaten food safety and thus must be assessed. Health risks arise particularly from toxic persistent organic pollutants such as Polycyclic Aromatic Hydrocarbons (PAHs) which are formed by incomplete combustion. A first assessment of crop contamination in two different atmospheric environments in the urban area of Nice reveals a predominance of light PAHs. These pollutants present in the gaseous phase, seem to bioaccumulate while heavy PAHs are absent in vegetation. By understanding the PAH sources and their behavior in the atmosphere but also by analyzing the spatial and temporal data since the European directive in 2004, a link between concentrations found in vegetables grown in experimental gardens and PAH cadastral emission data is presented. The first results could be used as a possible guidance for urban agriculture.
The article analyzes the management processes based on the institutional approach to agricultural land use management and finds that so far there have been no changes in priorities in these processes, due to the crisis situation in such land use. It is substantiated that institutional support for the development of highly efficient and environmentally friendly agricultural land use is achieved through management processes aimed at the formation, full functionality and legitimacy of such institutions as: Institute of Land Management, Institute of State Land Cadastre, Institute of Land Valuation, Institute of Land Use Monitoring that complement and characterize each other. In this regard, the institutional framework for reforming land relations in terms of a deeper understanding of management phenomena, processes to ensure the implementation of social, economic and environmental values in society and ensure systemic development of land use should be changed. As the main tools for achieving highly efficient and environmentally friendly agricultural land use, public authorities should first of all produce universally binding socially necessary clearly defined requirements, norms, rules and regulations and monitor their strict implementation by economic entities. It is proved that the chosen approach reflects the needs of society in this area.
Key words: state regulation, land use institutions, land management regulations, highly efficient agricultural land use, environmentally friendly agricultural land use.
Y. Dorosh, А. Tarnopolskyi, R. Kharytonenko
et al.
It is emphasized that the issue of establishing the boundaries of the territories of territorial communities currently remains relevant in Ukraine and presents new challenges caused by the state of war. The sequence (stages) of land management works related to establishing the boundaries of the territories of territorial communities is proposed. It is assumed that in the post-war period, the boundaries of the territories of territorial communities may be limited in their establishment, if these boundaries were located in the area of military (combat) operations or were under temporary occupation, encirclement (blockade).
Attention is focused on the difficulties associated with the financial capacity of territorial communities in ordering work on the development of land management projects to establish the boundaries of these communities in the event of a return to peaceful life. The existence of disputes regarding the common borders between certain adjacent territorial communities made it necessary to introduce the possibility of partially establishing the borders of the territories of territorial communities in relation to crossing the border.
Ways of improving the process of establishing the boundaries of the territories of territorial communities and adapting it to the conditions of the state of war and the post-war period are proposed, through the examples of post-war boundary establishment in foreign countries. Proposals will be made regarding amendments to the land legislation related to the definition of the boundaries of the territories of territorial communities as a whole, as well as individual parts thereof.
Keywords: administrative-territorial unit, boundary of the territory of the territorial community, State land cadastre, land management
To evaluate how the CIM contributes to improving public services and the quality of life of citizens, studies conducted by some authors have analyzed the international standard ISO 37120 - Sustainable cities and communities - Indicators for
city services and quality of life and City Information Modeling (CIM) data that can be used to obtain useful data for ISO indicators 37120. The CIM paradigm, understood as an approach to a global model of the city, must absolutely be formed
by the incorporation of BIM models of buildings that have a geographical insertion in the reference system in use. In this way all the data relating to the cities will be available and attached to the georeferenced representations of the buildings present
in the CIM database.
GEOMATICS AND ROBOTICS: A WINNING COMBINATION TOWARDS THE AUTOMATION OF THE SURVEY
The discipline of Geomatics itself is experiencing a phase of profound innovation, resulting from an ever greater integration with technologies and methods developed, among others, in the field of Robotics and of IT.
Let $M$ be a closed orientable manifold. We introduce two numerical invariants, called filling volumes, on the mapping class group $\mathrm{MCG}(M)$ of $M$, which are defined in terms of filling norms on the space of singular boundaries on $M$, both with real and with integral coefficients. We show that filling volumes are length functions on $\mathrm{MCG}(M)$, we prove that the real filling volume of a mapping class $f$ is equal to the simplicial volume of the corresponding mapping torus $E_f$, while the integral filling volume of $f$ is not smaller than the stable integral simplicial volume of $E_f$. We discuss several vanishing and non-vanishing results for the filling volumes. As applications, we show that the hyperbolic volume of $3$-dimensional mapping tori is not subadditive with respect to their monodromy, and that the real and the integral filling norms on integral boundaries are often non-biLipschitz equivalent.