Related papers: Inhomogeneous K-function for germ-grain models
This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries.…
The fundamental functional summary statistics used for studying spatial point patterns are developed for marked homogeneous and inhomogeneous point processes on the surface of a sphere. These are extended to point processes on the surface…
For a contraction $C_0$-semigroup on a separable Hilbert space, the decay rate is estimated by using the weak Poincar\'e inequalities for the symmetric and anti-symmetric part of the generator. As applications, non-exponential convergence…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
Biological tissue consists of various molecules. Instead of focusing on a particular molecule, we consider the Shannon entropy which is calculated from the abundance of different molecules at each spot in the tissue. The spatial…
Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and…
Kink model is developed to analyze the data where the regression function is twostage linear but intersects at an unknown threshold. In quantile regression with longitudinal data, previous work assumed that the unknown threshold parameters…
The goal of this paper is to establish a complete Khintchine-Groshev type theorem in both homogeneous and inhomogeneous setting, on analytic nondegenerate manifolds over a local field of positive characteristic. The dual form of Diophantine…
In this paper the study of a nonlocal second order Cahn-Hilliard-type singularly perturbed family of functions is undertaken. The kernels considered include those leading to Gagliardo fractional seminorms for gradients. Using Gamma…
We present an extension to the iterative Boltzmann inversion method to generate coarse-grained models with three-body intramolecular potentials that can reproduce correlations in structural distribution functions. The coarse-grained…
We establish precise bounds on cumulants for a rather general class of non-linear geometric functionals satisfying the stabilization property under a simple, stationary (marked) point process admitting fast decay of its correlation…
Analyzing point patterns with linear structures has recently been of interest in e.g. neuroscience and geography. To detect anisotropy in such cases, we introduce a functional summary statistic, called the cylindrical $K$-function, since it…
We derive an improved mean-field approximation for k-body annihilation reactions kA --> inert, for hard-core diffusing particles on a line, annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping and annihilation…
In this paper we investigate the gamma-relative differentiation by the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. With the help of this we give some definitions of…
In homogenization theory, mathematical models at the macro level are constructed based on the solution of auxiliary cell problems at the micro level within a single periodicity cell. These problems are formulated using asymptotic expansions…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the…
We propose a coarse-grained theoretical model to capture the aging of microfluidic devices under different conditions including constant applied flow rate and constant applied pressure gradient. Microfluidic devices that sort cells by their…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
This paper discusses an abstract Kramer sampling theorem for functions within a reproducing kernel Hilbert space (RKHS) of vector valued holomorphic functions. Additionally, we extend the concept of quasi Lagrange-type interpolation for…