Monotone approximation of aggregation operators using least squares splines

The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.

Monotonicity preserving approximation of multivariate scattered data

This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming problem. Estimation of the unknown Lipschitz constant from the data by sample splitting and cross-validation is described. Extension of the method for locally Lipschitz functions is presented.

Identification of general aggregation operators by Lipschitz approximation

Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction and aver aging. The choice of aggregation operators suitable for a particular problem is frequently done by fitting the parameters of the operator to the observed data. This paper examines fitting general aggregation operators by using a new method of Lipschitz approximation.

Multi-wavelets from B-spline super-functions with approximation order

Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p−1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix H_f; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.

Shape preserving approximation using least squares splines

Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.

Using Choquet integrals for kNN approximation and classification

k-nearest neighbors (kNN) is a popular method for function approximation and classification. One drawback of this method is that the nearest neighbors can be all located on one side of the point in question x. An alternative natural neighbors method is expensive for more than three variables. In this paper we propose the use of the discrete Choquet integral for combining the values of the nearest neighbors so that redundant information is canceled out. We design a fuzzy measure based on location of the nearest neighbors, which favors neighbors located all around x.

A sex difference in the cortisol response to tail docking and ACTH develops between 1 and 8 weeks of age in lambs

It is important to understand factors that may influence responses to stress, as these factors may also influence vulnerability to pathologies that can develop when stress responses are excessive or prolonged. It is clear that, in adults, the sex of an individual can influence the cortisol response to stress in a stressor specific manner. Nevertheless, the stage of development at which these sex differences emerge is unknown. We tested the hypothesis that there are sex differences in the cortisol response to tail docking and ACTH in lambs of 1 and 8 weeks of age. We also established cortisol responses in males when tail docking was imposed alone and in combination with castration at these ages. In experiment 1, 1 and 8 week old male and female lambs were subjected to sham handling, tail docking or, in males, a combination of tail docking and castration. In experiment 2, we administered ACTH (1.0 IU/kg) to male and female lambs at 1 and 8 weeks of age. There were significant cortisol responses to all treatments at both ages. Sex differences in the cortisol responses to tail docking and ACTH developed between 1 and 8 weeks of age, with females having greater responses than males. The data suggest that the mechanism for the sex difference in response to tail docking may involve the adrenal glands. At both ages, in males, the cortisol response to the combined treatment of tail docking and castration was significantly greater than that for tail docking alone.

A pseudosymmetric cell adhesion regulatory domain in the β7 tail of the integrin α4β7 that interacts with focal adhesion kinase and src

The β7 integrins α4β7 and Eβ7 play key roles in forming the gut-associated lymphoid tissue, and contribute to chronic inflammation. The α4β7 integrin-mediated adhesion of activated lymphocytes is largely due to a transient increase in avidity from ligand-induced clustering of α4β7 at the cell-surface. Here, we report that L and D enantiomers of a cell-permeable peptide YDRREY encompassing residues 735-740 of the cytoplasmic tail of the β7 subunit inhibit the adhesion of T cells to β7 integrin ligands. The YDRREY peptide abrogated mucosal addressin cell adhesion molecule-1-induced clustering of α4β7 on the surface of activated T cells. A mutated form of the YDRREY peptide carrying either single or double conservative mutations at Tyr⁷³⁵Phe and Tyr⁷⁴⁰Phe was unable to inhibit T cell adhesion, suggesting that both tandem tyrosines are critical for activity. The YDRREY peptide was bound and phosphorylated by focal adhesion kinase and src, which may serve to sequester cytoskeletal proteins to the cytoplasmic domain of 4β7. The quasi-palindromic sequence YDRREY within the β7 cytoplasmic tail constitutes a cell adhesion regulatory domain that modulates the interaction of β7-expressing leukocytes with their endothelial and epithelial ligands. Cell-permeable peptidomimetics based on this motif have utility as anti-inflammatory reagents for the treatment of chronic inflammatory disease.

A fresh look at the validity of the diffusion approximation for modeling fluorescence spectroscopy in biological tissue

Fluorescence has become a widely used technique for applications in noninvasive diagnostic tissue spectroscopy. The standard model used for characterizing fluorescence photon transport in biological tissue is based on the diffusion approximation. On the premise that the total energy of excitation and fluorescent photon flows must be conserved, we derive the widely used diffusion equations in fluorescence spectroscopy and show that there must be an additional term to account for the transport of fluorescent photons. The significance of this additional term in modeling fluorescence spectroscopy in biological tissue is assessed.