Related papers: Aggregation-fragmentation model of robust concentr…
With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering…
The generator coordinate method of a microscopic cluster model is developed to treat the resonance and scattering of nuclear clusters with complex scaling. We consistently derive the formulation of the complex scaling for the microscopic…
Rapid solidification experiments on thin film aluminum samples reveal the presence of lattice orientation gradients within crystallizing grains. To study this phenomenon, a single-component phase-field crystal (PFC) model that captures the…
Classically, Bayesian clustering interprets each component of a mixture model as a cluster. The inferred clustering posterior is highly sensitive to any inaccuracies in the kernel within each component. As this kernel is made more flexible,…
We consider the gelation of particles which are permanently connected by random crosslinks, drawn from an ensemble of finite-dimensional continuum percolation. To average over the randomness, we apply the replica trick, and interpret the…
In many cellular signaling pathways, key components form clusters at the cell membrane. Although much work has focused on the mechanisms behind such cluster formation, the implications for downstream signaling remain poorly understood.…
The onset of star formation is set by the collapse of filaments in the interstellar medium. From a theoretical point of view, an isolated cylindrical filament forms cores via the edge effect. Due to the self-gravity of a filament, the…
Gas-phase oxygen-rich iron oxide clusters Fe(O2)n+ (n=1-6), are produced in a molecular beam apparatus. Their stability and structure are investigated by measuring the fragmentation cross sections from collision-induced-dissociation…
The inclusion of a fragmentation mechanism in population balance equations introduces complex interactions that make the analytical or even computational treatment much more difficult than for the pure aggregation case. This is specially…
We study the flocking and pattern formations of active particles with a Vicsek-like model that includes a configuration dependent noise term. In particular, we couple the strength of the noise with both the local density and orientation of…
We establish the exponential clustering of correlation functions for the high-temperature Gibbs states of Bose-Hubbard type models. To overcome the technical difficulties arising from the unboundedness of bosonic operators, we develop the…
Transformers have emerged as a powerful neural network architecture capable of tackling a wide range of learning tasks. In this work, we provide a theoretical analysis of their ability to automatically extract structure from data in an…
Mass segregation stands as one of the most robust features of the dynamical evolution of self-gravitating star clusters. In this paper we formulate parametrised models of mass segregated star clusters in virial equilibrium. To this purpose…
There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
Fine-grained clustering is a practical yet challenging task, whose essence lies in capturing the subtle differences between instances of different classes. Such subtle differences can be easily disrupted by data augmentation or be…
A review is given on the studies of formation of light clusters and heavier fragments in heavy-ion collisions at incident energies from several tens of MeV/nucleon to several hundred MeV/nucleon, focusing on dynamical aspects and on…
Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…
Traditional clustering methods are limited when dealing with huge and heterogeneous groups of gene expression data, which motivates the development of bi-clustering methods. Bi-clustering methods are used to mine bi-clusters whose subsets…
In this project we are interested in performing clustering of observations such that the cluster membership is influenced by a set of predictors. To that end, we employ the Bayesian nonparameteric Common Atoms Model, which is a nested…