Accurate and fast estimation of probability density functions is crucial for satisfactory computational performance in many scientiic problems. When the type of density is known a priori, then the problem becomes statistical estimation of parameters from the observed values. In the non-parametric case, usual estimators make use of kernel functions. If X j ; j = 1; 2; : : : ; n is a sequence of ...

In [2] we presented a Definite Integral Table Lookup (the DITLU) for parametric functions, including a minimal prototype implementation demonstrating its capabilities. In this paper we present a possible application of a DITLU, which would extend its utility for a modest investment of effort. The naive algorithm for indefinite integration of rational functions (see e.g. [12, 2.10]) can be imple...

Weighted finite automata (WFA) are an extension of finite automata that can be used to compute real functions and parametric WFA (PWFA) are a multidimensional variant of WFA. This paper shows that each PWFA computable set is computable by a PWFA that has an alphabet cardinality of two. Further we show that real polynomials with solely rational coefficients can be computed by PWFA that do not us...

Axon diameter is an important neuroanatomical characteristic of the nervous system that alters in the course of neurological disorders such as multiple sclerosis. Axon diameters vary, even within a fiber bundle, and are not normally distributed. An accurate distribution function is therefore beneficial, either to describe axon diameters that are obtained from a direct measurement technique (e.g...

A sequence of prices and demands are rationalizable if there exists a concave, continuous and monotone utility function such that the demands are the maximizers of the utility function over the budget set corresponding to the price. Afriat [1] presented necessary and sufficient conditions for a finite sequence to be rationalizable. Varian [30] and later Blundell et al. [5, 6] continued this lin...

This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in the case of one function. We also make an extensive study of an example for which we give an expression of a generic (and under some conditions, a relative) B...

Consider linear systems whose input data are linear functions of uncertain parameters varying within given intervals. We are interested in an explicit description of the so-called AE parametric solution sets (where all universally quantified parameters precede all existentially quantified ones) by a set of inequalities not involving the parameters. This work presents how to obtain explicit desc...

Growth is a key cellular phenotype relevant in areas ranging from microbiology to cancer biology. Hence, quantitative measures of growth must be accurately estimated. Historically, many parametric models have been proposed, reviewed in ([1]). However, in our experience, growth curves rarely follow these idealistic behaviours. In practice, non-parametric models, in which curves are simply smooth...

Functional principal component analysis (FPCA) is a popular approach in functional data analysis to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). Most existing FPCA approaches use a set of flexible basis functions such as B-spline basis to represent the FPCs, and control the smoothness...

MOTIVATION A mass spectrum produced via tandem mass spectrometry can be tentatively matched to a peptide sequence via database search. Here, we address the problem of assigning a posterior error probability (PEP) to a given peptide-spectrum match (PSM). This problem is considerably more dif.cult than the related problem of estimating the error rate associated with a large collection of PSMs. Ex...