In this article children's musical improvisation is investigated through the "reflexive interaction" paradigm. We used a particular system, the MIROR-Impro, implemented in the framework of the MIROR project (EC-FP7), which is able to reply to the child playing a keyboard by a "reflexive" output, mirroring (with repetitions and variations) her/his inputs. The study was conducted in a public prim...

In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Gröbner basis of Z[x]-lattices, regular and coherent difference ascending chains, and partial characters over Z[x]-lattices, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, and perfect a...

Emergence has a long and controversial history. In this paper we briefly review the primary strands of the debate, paying attention to its use in the fields of philosophy of science and mind, social science and systems theory including the theory of complex systems. We argue that it is important to recognize why emergence in social systems is fundamentally different from other natural systems. ...

We study the cohomology of reflexive rank 2 sheaves on smooth projective threefolds. Applications are given to the moduli space of reflexive sheaves.

Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.