BACKGROUND AND PURPOSE Brain tumor cellularity has been assessed by using apparent diffusion coefficient (ADC). However, the ADC value might be influenced by both perfusion and true molecular diffusion, and the perfusion effect on ADC can limit the reliability of ADC in the characterization of tumor cellularity, especially, in hypervascular brain tumors. In contrast, the IVIM technique estimate...

Network data arise in a wide variety of applications. Although descriptive statistics for networks abound in the literature, the science of fitting statistical models to complex network data is still in its infancy. The models considered in this article are based on exponential families; therefore, we refer to them as exponential random graph models (ERGMs). Although ERGMs are easy to postulate...

This paper is concerned with multidimensional exponential fitting modified Runge-Kutta-Nyström (MEFMRKN) methods for the system of oscillatory second-order differential equations q ′′(t) +Mq(t) = f (q(t)), where M is a d × d symmetric and positive semi-definite matrix and f (q) is the negative gradient of a potential scalar U(q). We formulate MEFMRKN methods and show clearly the relationship be...

We study a class of explicit or implicit multistep integration formulas for solving N X N systems of ordinary differential equations. The coefficients of these formulas are diagonal matrices of order N, depending on a diagonal matrix of parameters Q of the same order. By definition, the formulas considered here are exact with respect to y = Dy + 4>(x, y) provided Q — hD, h is the integration st...

This study compares the capability of two different mathematical forms of the so-called softening variable to describe strain-induced stress softening observed within cyclic uniaxial tension of the human thoracic aorta. Specifically, the softening variable, which serves as the stress reduction factor, was considered to be tangent hyperbolic-based and error function-based. The mechanical respons...

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...