arXiv subjects

Paul-Louis Delacour

Publications and source records attributed to Paul-Louis Delacour.

3 recordsLinked to original sources

arXiv2026

Mixed-integer flow formulations for motion planning and decision-making of networked multi-agent systems

This work investigates the use of flow-based connectivity maintenance constraints in mixed-integer linear programming (MILP) trajectory planning and decision-making models for networked multi-agent systems (MAS). We integrate flow-based encodings for standard and k-hop connectivity into MILP multi-vehicle maneuvering models that are widely used alongside receding horizon planning strategies. Their necessity and sufficiency is demonstrated, guaranteeing full coverage of potential network topologies. The flow formulation for standard connectivity decreases the growth of the required inequality constraints from exponential to polynomial w.r.t. the size of the MAS when compared to the state-of-the-art subtour elimination (SEC) method. The flow-based k-hop connectivity constraints decrease the number of required binary variables and decouple its growth from the number of hops. However, the impact of these formulations in performance is not straightforward due to the introduction of a substantial number of continuous flow optimization variables and, in the case of k-hop connectivity, additional inequality constraints. We investigate this trade-off through a statistical evaluation of costs and optimization times using a conventional branch-and-bound commercial solver and trials performed with randomized environments for increasingly larger MAS. The results show that the flow formulation outperforms SEC in standard connectivity problems, enabling the solutions to be computed for larger MAS considering the imposed optimization time limit. The reduction in number of binary variables enabled by the k-hop flow formulations decreases the theoretical worst-case number of iterations required by the branch-and-bound algorithm to compute the global optimal solution. Our results show that this advantage did not translate into improvements in the average performance when compared to the baseline.

cs.MA↗

arXiv2026

Phase Transition of Eigenvalues of Covariances from the Spiked Mixture Model in High-dimensional Regimes

The spiked mixture model (SMM) has been introduced as a probabilistic model that generalizes the single-spike (Wishart) model to a mixture model form. With applications ranging from imaging mass spectrometry in the life sciences to hyperspectral imaging in computer vision, it is crucial to understand under which circumstances its signals can be recovered from noisy measurements. The highly multiplexed nature of these measurement types furthermore necessitates such analysis to hold in highdimensional settings. In this paper, we prove that the extreme eigenvalues of the covariance matrix from the SMM exhibit a phase transition in high-dimensional regimes. We show that this phase transition, and thus signal recovery by extreme eigenvalues, depends on several interacting factors: the correlation between spikes (i.e., how similar in content underlying signals are), the energy parameters (i.e., the absolute strength of each underlying signal), and the mixture probabilities (i.e., how likely it is to encounter each underlying signal). This work provides sharp information-theoretic bounds on the parameters needed to detect one or more spikes from extreme eigenvalues of the SMM covariance matrix, and these guarantees could potentially impact any application of the SMM. Understanding this interplay could serve as a tool for driving experimental design in analytical chemistry and life sciences.

math.PR↗

arXiv2025

Signal Recovery Using a Spiked Mixture Model

We introduce the spiked mixture model (SMM) to address the problem of estimating a set of signals from many randomly scaled and noisy observations. Subsequently, we design a novel expectation-maximization (EM) algorithm to recover all parameters of the SMM. Numerical experiments show that in low signal-to-noise ratio regimes, and for data types where the SMM is relevant, SMM surpasses the more traditional Gaussian mixture model (GMM) in terms of signal recovery performance. The broad relevance of the SMM and its corresponding EM recovery algorithm is demonstrated by applying the technique to different data types. The first case study is a biomedical research application, utilizing an imaging mass spectrometry dataset to explore the molecular content of a rat brain tissue section at micrometer scale. The second case study demonstrates SMM performance in a computer vision application, segmenting a hyperspectral imaging dataset into underlying patterns. While the measurement modalities differ substantially, in both case studies SMM is shown to recover signals that were missed by traditional methods such as k-means clustering and GMM.

stat.ML↗