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This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a node, and every social interaction is represented by a segment connecting two nodes. Early work in family interactions,… (More)

- Fabrizio Colombo, Irene Sabadini, Daniele C Struppa
- 2008

In this paper we offer a new definition of monogenicity for functions defined on R n+1 with values in the Clifford algebra R n following an idea inspired by the recent papers [6], [7]. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra R n. We will prove a Cauchy… (More)

- W W Adams, P Loustaunau, V P Palamodov, D C Struppa
- 1995

In this paper we prove that the projective dimension of Mn = R 4 =hAni is 2n ? 1, where R is the ring of polynomials in 4n variables with complex coeecients, and hAni is the module generated by the columns of a 44n matrix which arises as the Fourier transform of the matrix of diierential operators associated with the regularity condition for a function of n… (More)

This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer algebra packages such as CoCoA [5] and Singular [9].

- Fabrizio Colombo, Irene Sabadini, Daniele C Struppa
- 2007

In this paper we use the notion of slice monogenic functions [2] to define a new functional calculus for an n-tuple T of not necessarily commuting operators. This calculus is different from the one discussed in [5] and it allows the explicit construction of the eigenvalue equation for the n-tuple T based on a new notion of spectrum for T. Our functional… (More)

- W W Adams, C A Berenstein, P Loustaunau, I Sabadini, D C Struppa
- 2007

We employ a classical idea of Ehrenpreis, together with a new algebraic result, to give a new proof that regular functions of several quaternionic variables cannot have compact singularities. As a byproduct we characterize those inhomogeneous Cauchy{ Fueter systems which admit solutions on convex sets. Our method readily extends to the case of monogenic… (More)

- Fabrizio Colombo, Graziano Gentili, Irene Sabadini, Daniele C Struppa
- 2008

In this paper we develop a functional calculus for bounded operators defined on quater-nionic Banach spaces. This calculus is based on the notion of slice-regularity, see [4], and the key tools are a new resolvent operator and a new eigenvalue problem.

The problem of reconstructing and identifying intracellular protein signaling and biochemical networks is of critical importance in biology. We propose a mathematical approach called augmented sparse reconstruction for the identification of links among nodes of ordinary differential equation (ODE) networks, given a small set of observed trajectories with… (More)

- W W Adams, C A Berenstein, P Loustaunau, I Sabadini, D C Struppa
- 1995

We prove that regular functions of one quaternionic variable which satisfy a large class of diierential equations cannot have compact singularities. This result is equivalent to the fact that a large family of 8 4 matrices has torsion-free cokernel. The result (obvious in the complex case) easily extends to Cliiord algebras. 1. Introduction The classical… (More)