Derivative-based methods are developed for uncertainty quantification (UQ) in largescale ocean state estimation. The estimation system is based on the adjoint method for solving a least-squares optimization problem, whereby the state-of-the-art MIT general circulation model (MITgcm) is fit to observations. The UQ framework is applied to quantify Drake Passage transport uncertainties in a global...

A synthesis of results of the recently introduced paradigm of multi-adjoint logic programming is presented. These results range from a proof theory together with some (quasi)completeness results to general termination results, and from the neural-like implementation of its fix-point semantics to the more general biresiduated multi-adjoint logic programming and its relationship with other approa...

[1] As the incidence of groundwater contamination continues to grow, a number of inverse modeling methods have been developed to address forensic groundwater problems. In this work the geostatistical approach to inverse modeling is extended to allow for the recovery of the antecedent distribution of a contaminant at a given point back in time, which is critical to the assessment of historical e...

Introduction This paper ( 2 ) is the second part of [2]. We want to study microlocally the solutions of a self-adjoint system of semi-classical pseudo-differential operators using normal forms. In our paper [2], we studied the case where the principal symbol (called the dispersion matrix) is a real symmetric matrix. We will consider here the case where the dispersion matrix Hclass is complex He...

Hessenberg decomposition is the basic tool used in computational linear algebra to approximate the eigenvalues of a matrix. In this article, we generalize Hessenberg decomposition to continuous matrix fields over topological spaces. This works in great generality: the space is only required to be normal and to have finite covering dimension. As applications, we derive some new structure results...

Let g(z; x) denote the diagonal Green's matrix of a self-adjoint m m matrix-valued Schrr odinger operator H = ? d 2 dx 2 Im + Q(x) in L 2 (R) m , m 2 N. One of the principal results proven in this paper states that for a xed x 0 2 R and all z 2 C + , g(z; x 0) and g 0 (z; x 0) uniquely determine the matrix-valued m m potential Q(x) for a.e. x 2 R. We also prove the following local version of th...

Let g(z, x) denote the diagonal Green's matrix of a self-adjoint m × m matrix-valued Schrödinger operator H = − d 2 dx 2 Im + Q(x) in L 2 (R) m , m ∈ N. One of the principal results proven in this paper states that for a fixed x 0 ∈ R and all z ∈ C + , g(z, x 0) and g ′ (z, x 0) uniquely determine the matrix-valued m × m potential Q(x) for a.e. x ∈ R. We also prove the following local version o...

We examine the equivalence between the Konishi anomaly equations and the matrix model loop equations in N = 1 gauge theories, the mass deformation of N = 4 supersymmetric Yang-Mills. We perform the superfunctional integral of two adjoint chiral superfields to obtain an effective N = 1 theory of the third adjoint chiral superfield. By choosing an appropriate holomorphic variation, the Konishi an...

Multi-adjoint logic programming represents a very recent, extremely flexible attempt for introducing fuzzy logic into logic programming. In this setting, the execution of a goal w.r.t. a given program is done in two separate phases. During the operational one, admissible steps are systematically applied in a similar way to classical resolution steps in pure logic programming, thus returning a c...