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Obstacle avoidance of polytopic obstacles by polytopic robots is a challenging problem in optimization-based control and trajectory planning. Many existing methods rely on smooth geometric approximations, such as hyperspheres or ellipsoids,…
The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…
The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…
It is well known that the convex hull of $\{(x,y,xy)\}$, where $(x,y)$ is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti {\em et al.\,}(2010) and Miller {\em et al.\,}(2011)…
Bi-Directional Grid Constrained (BGC) stochastic processes (BGCSP) are constrained It\^{o} diffusions with the property that the further they drift away from the origin, the more resistance to movement in that direction they undergo. We…
Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear…
In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying…
Ensuring constraint satisfaction is a key requirement for safety-critical systems, which include most robotic platforms. For example, constraints can be used for modeling joint position/velocity/torque limits and collision avoidance.…
Neural networks are often used to process information from image-based sensors to produce control actions. While they are effective for this task, the complex nature of neural networks makes their output difficult to verify and predict,…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…
Large-scale neutrino observatories operate under unavoidable detector deadtime and signal pile-up, leading to systematic inefficiencies in conventional coincidence-based trigger systems. Such triggers typically rely on binary temporal…
In co-manipulative continuum robots (CCRs), multiple continuum arms cooperate by grasping a common flexible object, forming a closed-chain deformable mechanical system. The closed-chain coupling induces strong dynamic interactions and…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
Boundary representation (B-rep) of geometric models is a fundamental format in Computer-Aided Design (CAD). However, automatically generating valid and high-quality B-rep models remains challenging due to the complex interdependence between…
Graph Spectral Clustering methods (GSC) allow representing clusters of diverse shapes, densities, etc. However, the results of such algorithms, when applied e.g. to text documents, are hard to explain to the user, especially due to…
Topology diagrams are widely seen in power system applications, but their automatic generation is often easier said than done. When facing power transmission systems with strongly-meshed structures, existing approaches can hardly produce…
Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by…
Reservoir Computing (RC) models, a subclass of recurrent neural networks, are distinguished by their fixed, non-trainable input layer and dynamically coupled reservoir, with only the static readout layer being trained. This design…
Generalized subtour elimination constraints (GSECs) are widely used in state-of-the-art exact algorithms for vehicle routing and network design problems, as their right-hand sides often capture problem-specific feasibility conditions of…