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Autonomous exploration for mapping unknown large scale environments is a fundamental challenge in robotics, with efficiency in time, stability against map corruption and computational resources being crucial. This paper presents a novel…
The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…
A distance-approximation algorithm for a graph property $\mathcal{P}$ in the adjacency-matrix model is given an approximation parameter $\epsilon \in (0,1)$ and query access to the adjacency matrix of a graph $G=(V,E)$. It is required to…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Temperature Accelerated Sliced Sampling (TASS) is an efficient method to compute high dimensional free energy landscapes. The original TASS method employs the Weighted Histogram Analysis Method (WHAM) which is an iterative post-processing…
New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented. By illuminating the way these metrics balance density and geometry in the underlying data, we clarify their key parameters and…
State-of-the-art approaches in computer vision heavily rely on sufficiently large training datasets. For real-world applications, obtaining such a dataset is usually a tedious task. In this paper, we present a fully automated pipeline to…
ATLAS is a constraint-guided generation framework for structured engineering artifacts whose outputs must satisfy explicit schemas, domain rules, and audit requirements. Rather than treating a large language model as a standalone generator,…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
This article introduces an approach to facilitate cooperative exploration and mapping of large-scale, near-ground, underground, or indoor spaces via a novel integration framework for locally-dense agent map data. The effort targets limited…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
The paper formalizes a version of parallel online directed acyclic graph (DAG) exploration, general enough to be readily mapped to many computational scenarios. In both the offline and online versions, vertices are weighted with the work…
Density map is an effective visualization technique for depicting the scalar field distribution in 2D space. Conventional methods for constructing density maps are mainly based on Euclidean distance, limiting their applicability in urban…
In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
Topographic feature maps are low dimensional representations of data, that preserve spatial dependencies. Current methods of training such maps (e.g. self organizing maps - SOM, generative topographic maps) require centralized control and…