An algebraic curve is defined as the zero set of a multivariate polynomial. We consider the problem of fitting an algebraic curve to a set of vectors given an additional set of vectors labelled as interior or exterior to the curve. The problem of fitting a linear curve in this way is shown to lend itself to a support vector representation, allowing non-linear curves and high dimensional surface...

This article is concerned with the problem of data fitting where the model is nonlinear in the free parameters, using the Huber M-estimator. Under the assumption that there are significant errors in all the variables, an efficient algorithm is developed. Some numerical examples are given.

We present a differential geometric approach for cylindrical anatomical surface reconstruction from 3D volumetric data that may have missing slices or discontinuities. We extract planar boundaries from the 2D image slices, and parameterize them by an indexed set of curves. Under the SRVF framework, the curves are represented as invariant elements of a nonlinear shape space. Differently from sta...

In most event history models, the effect of a covariate on the hazard is assumed to have a log-linear functional form. For continuous covariates, this assumption is often violated as the effect is highly nonlinear. Assuming a log-linear functional form when the nonlinear form applies causes specification errors leading to erroneous statistical conclusions. Scholars can, instead of ignoring the ...

The longitudinal relaxation time, T(1), can be estimated from two or more spoiled gradient recalled echo images (SPGR) acquired with different flip angles and/or repetition times (TRs). The function relating signal intensity to flip angle and TR is nonlinear; however, a linear form proposed 30 years ago is currently widely used. Here we show that this linear method provides T(1) estimates that ...

Cortical sensory neurons are commonly characterized using the receptive field, the linear dependence of their response on the stimulus. In primary auditory cortex neurons can be characterized by their spectrotemporal receptive fields, the spectral and temporal features of a sound that linearly drive a neuron. However, receptive fields do not capture the fact that the response of a cortical neur...

We study the existence, uniqueness and stability properties of solutions to the integral equation q,=Q[q] with q,(-)=l, q,()=0. Here Q[u](x)=f K(x-y)g(y,u(y))dy is defined on functions bounded between 0 and 1, K is a probability density function and g(x,u)=[s(x)u +u]/[l+s(x)u2+ o(x)(1-u)2] according to a population genetics model. The hypotheses on g are based on the biological assumption that ...

This article presents a damage detection method for prestressed reinforced concrete (PRC) elements based on free vibration tests and nonlinear damping identification. Integrated static and dynamic experiments were carried out on three precast PRC beam specimens. The static loading induced different levels of damage to the beams. At each damage level, impulsive loading was applied to the beams a...