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Penetration depth calculation quantifies the extent of overlap between two objects and is crucial in fields like simulations, the metaverse, and robotics. Recognizing its significance, efforts have been made to accelerate this computation…
We study the optimization of navigational graph queries, i.e., queries which combine recursive and pattern-matching fragments. Current approaches to their evaluation are not effective in practice. Towards addressing this, we present a…
In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the…
Accurately following a geometric desired path in a two-dimensional space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to…
Next-token predictors often appear to develop internal representations of the latent world and its rules. The probabilistic nature of these models suggests a deep connection between the structure of the world and the geometry of probability…
Dimensionality-reduction techniques are a fundamental tool for extracting useful information from high-dimensional data sets. Because secant sets encode manifold geometry, they are a useful tool for designing meaningful data-reduction…
In this paper, we evaluate the accuracy of deep learning approaches on geospatial vector geometry classification tasks. The purpose of this evaluation is to investigate the ability of deep learning models to learn from geometry coordinates…
All modern processors include a set of vector instructions. While this gives a tremendous boost to the performance, it requires a vectorized code that can take advantage of such instructions. As an ideal vectorization is hard to achieve in…
Restricting path tracing to a small number of paths per pixel for performance reasons rarely achieves a satisfactory image quality for scenes of interest. However, path space filtering may dramatically improve the visual quality by sharing…
Graph is a well known data structure to represent the associated relationships in a variety of applications, e.g., data science and machine learning. Despite a wealth of existing efforts on developing graph processing systems for improving…
Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…
Tracking causality (or happened-before relation) between events is useful for many applications such as debugging and recovery from failures. Consider a concurrent system with $n$ threads and $m$ objects. For such systems, either a vector…
Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…
Vessel trajectory clustering, a crucial component of the maritime intelligent transportation systems, provides valuable insights for applications such as anomaly detection and trajectory prediction. This paper presents a comprehensive…
Web pages form a cornerstone of available data for daily human consumption and with the rise of LLM-based search and learning systems a treasure trove of valuable data. The scale of this data and its unstructured format still continue to…
Probabilistic volumetric mapping (PVM) represents a 3D environmental map for an autonomous robotic navigational task. A popular implementation such as Octomap is widely used in the robotics community for such a purpose. The Octomap relies…
Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of…
Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the optimal solutions are fundamentally dependent on the…
Much of the recent improvement in neural networks for computer vision has resulted from discovery of new networks architectures. Most prior work has used the performance of candidate models following limited training to automatically guide…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…