In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation. We obtain an explicit characterization of the structure of these measures, which ref...

linTAP is a tableau prover for the multiplicative and exponential fragment M?LL of Girards linear logic. It proves the validity of a given formula by constructing an analytic tableau and ensures the linear validity using prefix unification. We present the tableau calculus used by linTAP, an algorithm for prefix unification in linear logic, the linTAP implementation, and some experimental result...

We introduce a canonical structure of a commutative associative filtered algebra with the unit on polynomial smooth valuations and study its properties. The induced structure on the subalgebra of translation invariant smooth valuations has especially nice properties (it is the structure of the Frobenius algebra). We also present some applications.

Context dependent rules are an obstacle to cut elimination. A generalised sequent style formulation using deep inferences is helpful and may indeed be essential. First this is shown for a substructural, multiplicative, pure propositional calculus. Then we consider the extra problems induced by non-logical axioms and extend the results to additive connectives and quantifiers.

We introduce proof nets and sequent calculus for the multiplicative fragment of non-commutative logic, which is an extension of both linear logic and cyclic linear logic. The two main technical novelties are a third switching position for the non-commutative disjunction, and the structure of order variety.

Interaction nets are graph rewriting systems which are a generalisation of proof nets for classical linear logic. The linear chemical abstract machine (CHAM) is a term rewriting system which corresponds to classical linear logic, via the Curry-Howard isomorphism. We can obtain a textual calculus for interaction nets which is surprisingly similar to linear CHAM based on the multiplicative fragme...

Learning temporal dependencies between variables over continuous time is an important and challenging task. Continuous-time Bayesian networks effectively model such processes but are limited by the number of conditional intensity matrices, which grows exponentially in the number of parents per variable. We develop a partition-based representation using regression trees and forests whose paramet...

Let X be a compact Hausdorff space. We denote by C(X) the multiplicative semigroup of all continuous real-valued functions on X. Milgram [2] has shown that C(X) as a semigroup determines X. In this paper we investigate the set %(X) of all continuous positive nontrivial2 multiplicative functionals on C(X), where C(X) has the topology of uniform convergence. If multiplication is defined pointwise...

Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the stochastic equations defining such processes, involving infinitely divisible stochastic integrals. Causal evolution laws are also given. This gives the first ge...