The number conn counts matchings X on {1, 2, . . . , 2n}, which are partitions into n two-element blocks, such that the crossing graph of X is connected. Similarly, cron counts matchings whose crossing graph has no isolated vertex. (If it has no edge, Catalan numbers arise.) We apply generating functions techniques and prove, using a more generally applicable criterion, that the sequences (conn...

Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false. Given a finite simple graph G, its independence complex IG is defined as the simplicial complex whose vertices are the vertices of G an...

We consider the solution of nonlinear programs in the case where derivatives of the objective function and nonlinear constraints are unavailable. To solve such problems, we propose an adaptation of a method due to Conn, Gould, Sartenaer, and Toint that proceeds by approximately minimizing a succession of linearly constrained augmented Lagrangians. Our modification is to use a 3 derivative-free ...

The generalization capability and training time of conventional neural networks depend on their architecture. In conventional neural networks, we have to define the architecture prior to training but in constructive neural network (CoNN) algorithms the network architecture is constructed during the training process. This paper presents an overview of CoNN algorithms that constructing feedforwar...

In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted Conn) contained between the families (widely described in literature) of Darboux Baire 1 functions (DB1) and connectivity ...