The aim of this work is to give an alternative presentation for the multiplicative fragment of Yetter’s cyclic linear logic. The new presentation is inspired by the calculus of structures, and has the interesting feature of avoiding the cyclic rule. The main point in this work is to show how cyclicity can be substituted by deepness, i.e. the possibility of applying an inference rule at any poin...

We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear heat equation with multiplicative white noise. Then we settle this question by proving that solutions to the linear equation have negative moments of all orders. Supported by NSA...

We investigate several fragments of multiplicative linear logic, in a natural deduction setting and with the aim of a better understanding of the par connective. We study, first, a pre-tensorial calculus, which is strengthened then in the standard tensorial fragment. The addition of a further pre-tensorial connective yields (a natural deduction version of) Full Intuitionistic Linear Logic. A fu...

The language of modern mechanics is calculus on manifolds, and exterior calculus is an important part of that. It consists of objects like differential forms, general tensors and vector fields on manifolds, and operators that act on these. While the smooth exterior calculus has a long history going back to Cartan, Lie, Grassmann, Hodge, de Rham and many others, the need for a discrete calculus ...

The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing empty premises.

In this paper, a novel variational model with strict convexity for removing multiplicative noise from images is proposed and studied. Firstly, by applying maximum likelihood estimation method and the Bayesian formulation, the variational model is derived. Then, we use an alternating minimization algorithm to find out the minimizer of the objective function, and prove the existence of the minimi...

In this article, a class of second order differential equations on [0, 1], driven by a γ-Hölder continuous function for any value of γ ∈ (0, 1) and with multiplicative noise, is considered. We first show how to solve this equation in a pathwise manner, thanks to Young integration techniques. We then study the differentiability of the solution with respect to the driving process and consider the...

Abstract. This paper presents a mathematical view of aspects of physics, showing how the forms of gauge theory, Hamiltonian mechanics and quantum mechanics arise from a non-commutative framework for calculus and differential geometry. This work is motivated by discrete calculus, as it is shown that classical discrete calculus embeds in a non-commutative context. It is shown how various processe...