Related papers: Study of a general growth model
General regression and classification models are constructed as linear combinations of simple rules derived from the data. Each rule consists of a conjunction of a small number of simple statements concerning the values of individual input…
We discuss the space-time determinantal random field which arises for the PNG model in one dimension and resembles the one for Dyson's Brownian motion. The information of interest for growth processes is carried by the edge statistics of…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…
A hypothesis of singleness of the growth equation for biological objects on different organizational levels and dimensional analysis are used in order to substantiate Schmalhausen's model of ontogenetic growth (the mass of a growing…
Reconstructing the missing parts of a curve has been the subject of much computational research, with applications in image inpainting, object synthesis, etc. Different approaches for solving that problem are typically based on processes…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the…
Learning curves model a classifier's test error as a function of the number of training samples. Prior works show that learning curves can be used to select model parameters and extrapolate performance. We investigate how to use learning…
We investigate the relationship among characteristic curves on developable surfaces. In case parameter curves coincide with these curves, we show that the base curve of a developable surface could be either a plane curve, a circular helix,…
We study entire holomorphic curves in the algebraic torus, and show that they can be characterized by the ``growth rate'' of their derivatives.
This paper explores the generalization loss of linear regression in variably parameterized families of models, both under-parameterized and over-parameterized. We show that the generalization curve can have an arbitrary number of peaks, and…
Principal curves are natural generalizations of principal lines arising as first principal components in the Principal Component Analysis. They can be characterized from a stochastic point of view as so-called self-consistent curves based…
The paper considers mediation analysis with longitudinal data under latent growth curve models within a counterfactual framework. Estimators and their standard errors are derived for natural direct and indirect effects when the mediator,…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
Mathematical method based on a direct or indirect analysis of growth rates is described. It is shown how simple assumptions and a relatively easy analysis can be used to describe mathematically complicated trends and to predict growth. Only…
In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution…
Over the past years several authors have used the approach of generalized modeling to study the dynamics of food chains and food webs. Generalized models come close to the efficiency of random matrix models, while being as directly…
We discuss explicit solutions of the logistic model with variable parameters. Classical data on the sunflower seeds growth are revisited as a simple application of the logistic model with periodic coefficients. Some applications to related…