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We propose a degree-based coarse graining approach that not just accelerates the evaluation of dynamics on complex networks, but also satisfies the consistency conditions for both equilibrium statistical distributions and nonequilibrium…
Cell cortex contraction is essential for shaping cells, enabling movement, ensuring proper division, maintaining tissue integrity, guiding development, and responding to mechanical signals - all critical for the life and health of…
We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our…
Clustering is often presumed to lead to enhanced agglomeration between cohesive grains due to the reduced relative velocities of particles within a cluster. Our discrete-particle simulations on gravity-driven, gas-solid flows of cohesive…
Star-forming regions presenting a density gradient experience a higher star formation rate than if they were of uniform density. We refer to the ratio between the star formation rate of a spherical centrally-concentrated gas clump and the…
Clustering of molecules on biological membranes is a widely observed phenomenon. In some cases, such as the clustering of Ras proteins on the membranes of mammalian cells, proper cell signaling is critically dependent on the maintenance of…
Molecule generation is a challenging open problem in cheminformatics. Currently, deep generative approaches addressing the challenge belong to two broad categories, differing in how molecules are represented. One approach encodes molecular…
Nanoparticles introduced in living cells are capable of strongly promoting the aggregation of peptides and proteins. We use here molecular dynamics simulations to characterise in detail the process by which nanoparticle surfaces catalyse…
Coarse-grained (CG) molecular dynamics (MD) simulations can simulate large molecular complexes over extended timescales by reducing degrees of freedom. A critical step in CG modeling is the selection of the CG mapping algorithm, which…
The goal of lifetime clustering is to develop an inductive model that maps subjects into $K$ clusters according to their underlying (unobserved) lifetime distribution. We introduce a neural-network based lifetime clustering model that can…
Numerical simulations of Diffusion-Limited and Reaction-Limited Cluster-Cluster Aggregation processes of identical particles are performed in a two-dimensional box. It is shown that, for concentrations larger than a characteristic gel…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
In the framework of model-based clustering, a model allowing several latent class variables is proposed. This model assumes that the distribution of the observed data can be factorized into several independent blocks of variables. Each…
Ample experimental evidence has been accumulated demonstrating that the formation of monodispersed colloids proceeds through a more complex mechanism, than the generally excepted diffusional "burst nucleation" process. Instead, the…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
As a response to ligand binding, transmembrane cell receptors often enhance their clustering, or oligomerization, during the signalling process. Here we present a statistical mechanical model which combines the aspects of clustering and…
Eukaryotic cells sense chemical gradients to decide where and when to move. Clusters of cells can sense gradients more accurately than individual cells by integrating measurements of the concentration made across the cluster. Is this…
In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
We develop a model in two dimensions to characterise the growth rate of a tracer gradient mixed by a statistically homogeneous flow with rapid temporal variations. % % The model is based on the orientation dynamics of the passive-tracer…