We present here a vector calculus on weighted networks following the guidelines of Differential Geometry. The key to develop an efficient calculus on weighted networks which mimetizes the calculus in the smooth case is an adequate construction of the tangent space at each vertex. This allows to consider discrete vector fields, inner products and general metrics. Then, we obtain discrete version...

We give a graph theoretical criterion on Multiplicative Additive Linear Logic (MALL) cut-free proof structures that exactly characterizes those whose interpretation is a hyperclique in Ehrhard’s hypercoherent spaces. This criterion is strictly weaker than the one given by Hughes and van Glabbeek characterizing proof nets (i.e. desequentialized sequent calculus proofs). We thus also give the fir...

We give a graph theoretical criterion on multiplicative additive linear logic (MALL) cut-free proof structures that exactly characterizes those whose interpretation is a hyperclique in Ehrhard’s hypercoherent spaces. This criterion is strictly weaker than the one given by Hughes and van Glabbeek characterizing proof nets (i.e. desequentialized sequent calculus proofs). We thus also give the fir...

In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the c...

Multiplicative linear logic [6, 7] is a formal calculus for reasoning about resources, which is similar to traditional logic, except that resources cannot be duplicated or neglected in the way that propositions can. A central problem in logic is determining when two proofs should be considered equivalent. In this paper, we describe a scheme for interpreting proofs in multiplicative linear logic...

We propose a multiplicative speci cation of a discrete choice model that renders choice probabilities independent of the scale of the utility. The scale can thus be random with unspeci ed distribution. The model mostly outperforms the classical additive formulation over a range of stated choice data sets. In some cases, the improvement in likelihood is greater than that obtained from adding obs...