This paper develops object-oriented data analysis (OODA) statistical methods that are novel and complementary to existing methods of analysis of human brain scan connectomes, defined as graphs representing brain anatomical or functional connectivity. OODA is an emerging field where classical statistical approaches (e.g., hypothesis testing, regression, estimation, and confidence intervals) are ...

We investigate the mis-match in the classical interpretation of certain distribution-fitting problems as maximum-likelihood (ML) estimation problems in the particular case of the I-divergence. The general relation between Bregman divergences and exponential families shown by Banerjee et al. [8] enables to consider distribution-fitting problems based on Bregman divergences as ML problems based o...

Increasingly, fractals are being incorporated into pharmacokinetic models to describe transport and chemical kinetic processes occurring in confined and heterogeneous spaces. However, fractal compartmental models lead to differential equations with power-law time-dependent kinetic rate coefficients that currently are not accommodated by common commercial software programs. This paper describes ...

In this chapter, we discuss fitting probability laws to data. Many families of probability laws depend on a small number of parameters; for example, the Poisson family depends on the parameter λ (the mean number of counts), and the Gaussian family depends on two parameters, μ and σ . Unless the values of parameters are known in advance, they must be estimated from data in order to fit the proba...

Large-scale simulations of plastic deformation and phase transformations in alloys require reliable classical interatomic potentials. We construct an embedded-atom method potential for niobium as the first step in alloy potential development. Optimization of the potential parameters to a well-converged set of density-functional theory DFT forces, energies, and stresses produces a reliable and t...

teraction, global-to-local deformations, shape statistics, setting low-level parameters, and incorporating new forces or energy terms. However, incorporating expert knowledge to automatically guide deformations can not be easily and elegantly achieved using the classical deformable model low-level energy-based fitting mechanisms. In this chapter we review Deformable Organisms, a decision-making...

Changing the data representation from the classical time delay histogram to the phasor representation provides a global view of the fluorescence decay at each pixel of an image. In the phasor representation we can easily recognize the presence of different molecular species in a pixel or the occurrence of fluorescence resonance energy transfer. The analysis of the fluorescence lifetime imaging ...

Although algebraic or so called “implicit polynomial” curves/surfaces have been studied rather extensively for several decades, to the best of our knowledge, a dynamic formulation of them, similar to active contours, has not been done yet. This paper proposes to use implicit polynomial functions instead of signed distance functions in classical level set formulation and shows potential of such ...

We consider the problem of multiple fitting of linearly parametrized curves, that arises in many computer vision problems such as road scene analysis. Data extracted from images usually contain non-Gaussian noise and outliers, which makes classical estimation methods ineffective. In this paper, we first introduce a family of robust probability density functions which appears to be well-suited t...