‎two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎levi-civita‎, ‎canonical (zamkovoy)‎, ‎golab and generalized dual‎. ‎their relationship is also analyzed with a special view towards their curvature‎. ‎the particular case of an almost paracosymplectic manifold giv...

We de…ne the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satis…es much more interesting properties than other rules in the literature. F...

Canonical curves are characterized by the vanishing of combinatorial products of g + 1 determinants of the holomorphic abelian differentials. This also implies the characterization of canonical curves in terms of (g − 2)(g − 3)/2 theta identities and the explicit expression of the volume form on the moduli space of canonical curves induced by the Siegel metric. Together with the Mumford form, i...

An efficient and compact canonical form is proposed for the Boolean matching problem under permutation and complementation of variables. In addition an efficient algorithm for computing the proposed canonical form is provided. The efficiency of the algorithm allows it to be applicable to large complex Boolean functions with no limitation on the number of input variables as apposed to previous a...

Paper [1] aimed at providing a unified presentation of neural network architectures. We show in the present comment (i) that the canonical form of recurrent neural networks presented by Nerrand et al. [2] many years ago provides the desired unification, (ii) that what Tsoi and Back call Nerrand's canonical form is not the canonical form presented by Nerrand et al. in [2], and that (iii) contrar...

Paper [1] aimed at providing a unified presentation of neural network architectures. We show in the present comment (i) that the canonical form of recurrent neural networks presented by Nerrand et al. [2] many years ago provides the desired unification, (ii) that what Tsoi and Back call Nerrand's canonical form is not the canonical form presented by Nerrand et al. in [2], and that (iii) contrar...

This paper describes how a commonly used canonical form for linear differential-algebraic equations can be computed using numerical software from the linear algebra package LAPACK. This makes it possible to automate for example observer construction and parameter estimation in linear models generated by a modeling language like Modelica.

The rank/activity restriction on binary resolution is introduced. It accepts only a single derivation tree from a large equivalence class of such trees. The equivalence classes capture all trees that are the same size and differ only by reordering the resolution steps. A proof procedure that combines this restriction with the authors’ minimal restriction of binary resolution computes each minim...