相关论文: Integrating Space, Time, Version and Scale Using A…
We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…
Models trained on semantically related datasets and tasks exhibit comparable inter-sample relations within their latent spaces. We investigate in this study the aggregation of such latent spaces to create a unified space encompassing the…
When the focus is on the relationships or interactions between entities, graphs offer an intuitive model for many real-world data. Such graphs are usually large and change over time, thus, requiring models and strategies that explore their…
Efficiently computing spatio-textual queries has become increasingly important in various applications that need to quickly retrieve geolocated entities associated with textual information, such as in location-based services and social…
The Alexandrov topology affords a well-known semantics of modal necessity and possibility. This paper develops an Alexandrov topological semantics of intuitionistic propositional modal logic internally in any elementary topos. This is done…
Spatial-temporal data, fundamental to many intelligent applications, reveals dependencies indicating causal links between present measurements at specific locations and historical data at the same or other locations. Within this context,…
Understanding large amounts of spatiotemporal data from particle-based simulations, such as molecular dynamics, often relies on the computation and analysis of aggregate measures. These, however, by virtue of aggregation, hide structural…
The efficiency of contemporary algebraic topology is not optimal since the category of topological spaces can be made more algebraic by introducing a profoundly new (-1)-dimensional topological space as a topological join unit. Thereby…
In spacetime dimensions of 4 (i.e., 3+1) and higher, topological orders exhibit spatially extended excitations like loops and membranes, which support diverse topological data characterizing braiding, fusion, and shrinking processes,…
Predicting spatio-temporal traffic flow presents significant challenges due to complex interactions between spatial and temporal factors. Existing approaches often address these dimensions in isolation, neglecting their critical…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
In enterprise datasets, documents are rarely pure. They are not just text, nor just numbers; they are a complex amalgam of narrative and structure. Current Retrieval-Augmented Generation (RAG) systems have attempted to address this…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
Existing Multivariate Time Series Anomaly Detection (MTSAD) frameworks increasingly rely on integrating Graph Neural Networks (GNNs) with sequence models to capture complex spatio-temporal dependencies. However, less attention is paid to…
Spatial-temporal (ST) graph modeling, such as traffic speed forecasting and taxi demand prediction, is an important task in deep learning area. However, for the nodes in graph, their ST patterns can vary greatly in difficulties for…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
In this paper, we employ graph theory to establish a connection between the Time Series Expansion (TSE) and Proper Generalized Decomposition (PGD) methods. Using the concept of a directed graph, we demonstrate how one can transition from…
Spatial data is ubiquitous. Massive amounts of data are generated every day from a plethora of sources such as billions of GPS-enabled devices (e.g., cell phones, cars, and sensors), consumer-based applications (e.g., Uber and Strava), and…