This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the introduction of statistics. We show that density distribution has its fundamental limitation -- high-density bias, irrespective of the algorithms used to perform clustering. Existing density-based clustering algorithms have employed different algorithmic means to counter the effect of the high-density bias with some success, but the fundamental limitation of using density distribution remains an obstacle to discovering clusters of arbitrary shapes, sizes and densities. Using the mass distribution as a better foundation, we propose a new algorithm which maximizes the total mass of all clusters, called mass-maximization clustering (MMC). The algorithm can be easily changed to maximize the total density of all clusters in order to examine the fundamental limitation of using density distribution versus mass distribution. The key advantage of the MMC over the density-maximization clustering is that the maximization is conducted without a bias towards dense clusters.

Mammographic breast density is a well-established risk factor for breast cancer. Recently there has been interest in breast MRI as an adjunct to mammography, as this modality provides an orthogonal and highly quantitative assessment of breast tissue. However, its 3D nature poses analytic challenges related to delineating and aggregating complex structures across slices. Here, we applied an in-house machine-learning algorithm to assess breast density on normal breasts in three MRI datasets. Breast density was consistent across different datasets (0.104 - 0.114). Analysis across different age groups also demonstrated strong consistency across datasets and confirmed a trend of decreasing density with age as reported in previous studies. MR breast density was correlated with mammographic breast density, although some notable differences suggest that certain breast density components are captured only on MRI. Future work will determine how to integrate MR breast density with current tools to improve future breast cancer risk prediction.

This paper proposes a framework for multi-robot systems to perform simultaneous learning and coverage of a domain of interest characterized by an unknown and potentially time-varying density function. To overcome the limitations of Gaussian Process (GP) regression, we employ Random Feature GP (RFGP) and its online variant (O-RFGP) which enables online and incremental inference. By integrating these with Voronoi-based coverage control and Upper Confidence Bound (UCB) sampling strategy, a team of robots can adaptively focus on important regions while refining the learned spatial field for efficient coverage. The incremental update mechanism of O-RFGP naturally supports time-varying environments, allowing efficient adaptation without retaining historical data. Furthermore, to the best of our knowledge, we provide the first theoretical analysis of online learning and coverage through a regret-based formulation, establishing asymptotic no-regret guarantees in the time-invariant setting. The effectiveness of the proposed framework is demonstrated through simulations with both time-invariant and time-varying density functions, along with a physical experiment with a time-varying density function.

The geodesy of irregularly shaped small bodies presents fundamental challenges for gravitational field modeling, particularly as deep space exploration missions increasingly target asteroids and comets. Traditional approaches suffer from critical limitations: spherical harmonics diverge within the Brillouin sphere where spacecraft typically operate, polyhedral models assume unrealistic homogeneous density distributions, and existing machine learning methods like GeodesyNets and Physics-Informed Neural Networks (PINN-GM) require extensive computational resources and training time. This work introduces Mascon-Cubes, a novel self-supervised learning approach that formulates gravity inversion as a direct optimization problem over a regular 3D grid of point masses (mascons). Unlike implicit neural representations, MasconCubes explicitly model mass distributions while leveraging known asteroid shape information to constrain the solution space. Comprehensive evaluation on diverse asteroid models including Bennu, Eros, Itokawa, and synthetic planetesimals demonstrates that MasconCubes achieve superior performance across multiple metrics. Most notably, MasconCubes demonstrate computational efficiency advantages with training times approximately 40 times faster than GeodesyNets while maintaining physical interpretability through explicit mass distributions. These results establish MasconCubes as a promising approach for mission-critical gravitational modeling applications requiring high accuracy, computational efficiency, and physical insight into internal mass distributions of irregular celestial bodies.

We use a support vector regressor based on a projected quantum kernel method to predict the density structure of 1D fermionic systems of interest in quantum chemistry and quantum matter. The kernel is built on with the observables of a quantum reservoir implementable with interacting Rydberg atoms. Training and test data of the fermionic system are generated using a Density Functional Theory approach. We test the performance of the method for several Hamiltonian parameters, finding a general common behavior of the error as a function of measurement time. At sufficiently large measurement times, we find that the method outperforms the classical linear kernel method and can be competitive with the radial basis function method.

Neural network-based methods for solving Mean-Field Games (MFGs) equilibria have garnered significant attention for their effectiveness in high-dimensional problems. However, many algorithms struggle with ensuring that the evolution of the density distribution adheres to the required mathematical constraints. This paper investigates a neural network approach to solving MFGs equilibria through a stochastic process perspective. It integrates process-regularized Normalizing Flow (NF) frameworks with state-policy-connected time-series neural networks to address McKean-Vlasov-type Forward-Backward Stochastic Differential Equation (MKV FBSDE) fixed-point problems, equivalent to MFGs equilibria.

Nowadays, Social Networks have become an essential communication tools producing a large amount of information about their users and their interactions, which can be analysed with Data Mining methods. In the last years, Social Networks are being used to radicalise people. In this paper, we study the performance of a set of indicators and their respective metrics, devoted to assess the risk of radicalisation of a precise individual on three different datasets. Keyword-based metrics, even though depending on the written language, performs well when measuring frustration, perception of discrimination as well as declaration of negative and positive ideas about Western society and Jihadism, respectively. However, metrics based on frequent habits such as writing ellipses are not well enough to characterise a user in risk of radicalisation. The paper presents a detailed description of both, the set of indicators used to asses the radicalisation in Social Networks and the set of datasets used to evaluate them. Finally, an experimental study over these datasets are carried out to evaluate the performance of the metrics considered.

Learning models of complex spatial density functions, representing the steady-state density of mobile nodes moving on a two-dimensional terrain, can assist in network design and optimization problems, e.g., by accelerating the computation of the density function during a parameter sweep. We address the question of applicability for off-the-shelf mixture density network models for the description of mobile node density over a disk. We propose the use of M\"obius distributions to retain symmetric spatial relations, yet be flexible enough to capture changes as one radially traverses the disk. The mixture models for M\"obius versus Gaussian distributions are compared and the benefits of choosing M\"obius distributions become evident, yet we also observe that learning mixtures of M\"obius distributions is a fragile process, when using current tools, compared to learning mixtures of Gaussians.

Proximity operations to small bodies, such as asteroids and comets, demand high levels of autonomy to achieve cost-effective, safe, and reliable Guidance, Navigation and Control (GNC) solutions. Enabling autonomous GNC capabilities in the vicinity of these targets is thus vital for future space applications. However, the highly non-linear and uncertain environment characterizing their vicinity poses unique challenges that need to be assessed to grant robustness against unknown shapes and gravity fields. In this paper, a pipeline designed to generate variable density gravity field models is proposed, allowing the generation of a coherent set of scenarios that can be used for design, validation, and testing of GNC algorithms. The proposed approach consists in processing a polyhedral shape model of the body with a given density distribution to compute the coefficients of the spherical harmonics expansion associated with the gravity field. To validate the approach, several comparison are conducted against analytical solutions, literature results, and higher fidelity models, across a diverse set of targets with varying morphological and physical properties. Simulation results demonstrate the effectiveness of the methodology, showing good performances in terms of modeling accuracy and computational efficiency. This research presents a faster and more robust framework for generating environmental models to be used in simulation and hardware-in-the-loop testing of onboard GNC algorithms.

This paper introduces a decentralized state-dependent Markov chain synthesis (DSMC) algorithm for finite-state Markov chains. We present a state-dependent consensus protocol that achieves exponential convergence under mild technical conditions, without relying on any connectivity assumptions regarding the dynamic network topology. Utilizing the proposed consensus protocol, we develop the DSMC algorithm, updating the Markov matrix based on the current state while ensuring the convergence conditions of the consensus protocol. This result establishes the desired steady-state distribution for the resulting Markov chain, ensuring exponential convergence from all initial distributions while adhering to transition constraints and minimizing state transitions. The DSMC's performance is demonstrated through a probabilistic swarm guidance example, which interprets the spatial distribution of a swarm comprising a large number of mobile agents as a probability distribution and utilizes the Markov chain to compute transition probabilities between states. Simulation results demonstrate faster convergence for the DSMC based algorithm when compared to the previous Markov chain based swarm guidance algorithms.