Given two univalent harmonic mappings f1 and f2 on D, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for f3 = (1−s)f1+sf2 to lift to a minimal surface for s ∈ [0, 1]. We then construct such mappings from Enneper’s surface to Scherk’s singularly periodic surface, Sckerk’s doubly periodic surface to the catenoid, and ...

Abstract We study the problem of recovering an unknown signal $${\varvec{x}}$$ x given measurements obtained from a generalized linear model with Gaussian sensing matrix. Two popular solutions are based on estimator $$\hat{\varvec{x}}^\mathrm{L}$$ ^</mml:m...

In this paper, we propose a novel algorithm to design multiclass kernels based on an iterative combination of weak kernels in a schema inspired from the boosting framework. Our solution has a complexity linear with the training set size. We evaluate our method for classification on a toy example by integrating our multi-class kernel into a kNN classifier and comparing our results with a referen...

In this paper, Linear Discriminant Analysis (LDA) is investigated with respect to the combination of different acoustic features for automatic speech recognition. It is shown that the combination of acoustic features using LDA does not consistently lead to improvements in word error rate. A detailed analysis of the recognition results on the Verbmobil (VM II) and on the English portion of the E...

A family of subsets of [n] is positive linear combination free if the characteristic vector of neither edge is the positive linear combination of the characteristic vectors of some other ones. We construct a positive linear combination free family which contains (1−o(1))2 subsets of [n] and we give tight bounds on the o(1)2 term. The problem was posed by the late Levon Khachatrian and the resul...

A vital aspect of the classification based model construction process is calibration scoring function. One weaknesses that it does not take into account information about relative positions recognized objects in feature space. To alleviate this limitation, paper, we propose a novel concept calculating function on distance object from decision boundary and its to class centroid. An important pro...