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Membrane particles such as proteins and lipids organize into zones that perform unique functions. Here, I introduce a topological and category-theoretic framework to represent particle and zone intra-scale interactions and inter-scale…

A new family of combined subdivision schemes with one tension parameter is proposed by the interpolatory and approximating subdivision schemes. The displacement vectors between the points of interpolatory and approximating subdivision…

We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an…

This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence…

Two numerical methods are proposed for detection of coupling between multiple time series generated by deterministic nonlinear systems. The first detects interdependence or the existence of coupling between time series. The second…

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…

The four-dimensional nonlinear model is extended to include the inter-channel stimulated Raman scattering, enabling accurate prediction of dual-polarization four-dimensional modulation formats and probabilistically shaped constellations in…

Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic…

This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to…

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Particle filters provide Monte Carlo approximations of intractable quantities such as point-wise evaluations of the likelihood in state space models. In many scenarios, the interest lies in the comparison of these quantities as some…

In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…

It is crucially important to estimate unknown parameters in earth system models by integrating observation and numerical simulation. For many applications in earth system sciences, an optimization method which allows parameters to…

The ability to understand and solve high-dimensional inference problems is essential for modern data science. This article examines high-dimensional inference problems through the lens of information theory and focuses on the standard…

The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…

We introduce a new nonlinear model for classification, in which we model the joint distribution of response variable, y, and covariates, x, non-parametrically using Dirichlet process mixtures. We keep the relationship between y and x linear…

Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…

In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper,…