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We define the Laplacian on an arbitrary set with a not necessarily symmetric weight function and discuss the Dirichlet problem and other classical topics in this setting.
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)
In this paper we propose a method for blind signal decomposition that does not require the independence or stationarity of the sources. We define suitable quotients of linear combinations of the images of the mixtures in a given frame and we show experimentally that such quotients can be used to recursively extract three sources from only two measurements.… (More)
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 , . 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)
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)
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  and Singular .
In this paper we use the notion of slice monogenic functions  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  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)
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 , and the key tools are a new resolvent operator and a new eigenvalue problem.
In this paper we prove a new representation formula for slice regular functions, which shows that the value of a slice regular function f at a point q = x + yI can be recovered by the values of f at the points q + yJ and q + yK for any choice of imaginary units I, J, K. This result allows us to extend the known properties of slice regular functions defined… (More)