Neil V. Budko

This work demonstrates that applying a fixed-effect multiple linear regression model to an overparameterized dataset is mathematically equivalent to fitting a hyper-curve parameterized by a single scalar. This reformulation shifts the focus from global coefficients to individual predictors, allowing each to be modeled as a function of a common parameter. We prove that this overparameterized linear framework can yield exact predictions even when the underlying data contains nonlinear dependencies that violate classical linear assumptions. By employing parameterization in terms of the dependent variable and a monomial basis, we validate this approach on both synthetic and experimental datasets. Our results show that the hyper-curve perspective provides a robust framework for regularizing problems with noisy predictors and offers a systematic method for identifying and removing ‘improper’ predictors that degrade model generalizability.

We propose to use diurnal temperature variations for nondestructive monitoring of growing tubers and investigate the feasibility by numerically simulating the data collected with a grid of passive thermal sensors placed in the ground and sampled at regular time intervals. A qualitative linear imaging algorithm that produces an approximate projected view of the tubers is proposed and an effective inversion method is applied to recover the volume fraction of tubers. In particular, it is shown that a correlation-based cost functional outperforms the usual least-squares metric, although, requiring additional steps to deal with the non-uniqueness of the solution.

The vigor of potato plants, defined as the canopy area at the end of the exponential growth stage, depends on the origin and physiological state of the seed tuber. Experiments carried out with six potato varieties in three test fields over three years show that there is a 73%-90% correlation in the vigor of the plants from the same seedlot grown in different test fields. However, these correlations are not always observed on the level of individual varieties and vanish or become negative when the seed tubers and young plants experience environmental stress. A comprehensive study of the association between the vigor and the seed tuber biochemistry has revealed that, while 50%-70% of the variation in the plant vigor is explained by the tuber data, the vigor is dominated by the potato genotype. Analysis of individual predictors, such as the abundance of a particular metabolite, indicates that the vigor enhancing properties of the seed tubers differ between genotypes. Variety-specific models show that, for some varieties, up to 30% of the vigor variation within the variety is explained by and can be predicted from the tuber biochemistry, whereas, for other varieties, the association between the tuber composition and the vigor is much weaker.

Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting problems can be formulated as a low-dimensional phase-space conservation law and solved either explicitly or with simple iterative methods. In particular, we consider: non-interacting populations with unbounded and logistic growth, populations with randomized and biased migration, populations competing for a resource, coexisting species, and populations with phase-space interactions. The method provides an alternative to Monte Carlo simulations and may be useful in the fast analysis of biological data and/or removal of deterministic trends.

The charging of insulating samples degrades the quality and complicates the interpretation of images in scanning electron microscopy and is important in other applications, such as particle detectors. In this paper we analyze this nontrivial phenomenon on different time scales employing the drift-diffusion-reaction approach augmented with the trapping rate equations and a realistic semi-empirical source function describing the pulsed nature of the electron beam. We consider both the fast processes following the impact of a single primary electron, the slower dynamics resulting from the continuous bombardment of a sample, and the eventual approach to the steady-state regime.