A novel 3D shape classification scheme, based on collaborative representation learning, is investigated in this work. A data-driven feature-extraction procedure, taking the form of a simple projection operator, is in the core of our methodology. Provided a shape database, a graph encapsulating the structural relationships among all the available shapes, is first constructed and then employed in...

This paper introduces a quasi-interpolation operator for scalarand vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator gives optimal estimates of the best approximation error in any Lp-norm assuming regularity in the fractional Sobolev spaces W r,p, where p ∈ [1,∞] and the smoothness index r can be arbitraril...

Evolutionary programming (EP) has been successfully applied to many parameter optimization problems. We propose a mean mutation operator, consisting of a linear combination of Gaussian and Cauchy mutations. Preliminary results indicate that both the adaptive and non-adaptive versions of the mean mutation operator are capable of producing solutions that are as good as, or better than those produ...

We propose a new shape analysis approach based on the non-local analysis of local shape variations. Our method relies on a novel description of shape variations, called Local Probing Field (LPF), which describes how a local probing operator transforms a pattern onto the shape. By carefully optimizing the position and orientation of each descriptor, we are able to capture shape similarities and ...

In this paper we introduce a median operator between two sets of interpretations (worlds) in a finite propositional language. Our definition is based on morphological operations and Hausdorff distance. It provides a result which lies “halfway” between both sets and accounts for the “extension” or “shape” of the sets. We prove several interesting properties of this operator and compare it with f...

The commercially available systems for EC inspection usually use only the phase and amplitude information. After the detection (with amplitude and phase thresholds), the defects are sized using calibration curves and the phase information. Such a system is not foolproof, usually because ofincorrect or spurious defect detection. Therefore, in practice the classification made by the system is usu...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

We prove R-sectoriality or, equivalently, Lp-maximal regularity for a class of operators on cylindrical domains of the form Rn−k × V , where V ⊂ Rk is a domain with compact boundary, Rk, or a half-space. Instead of extensive localization procedures, we present an elegant approach via operator valued multiplier theory, which takes advantage of the cylindrical shape of both, the domain and the op...