The Multidimensional Perturbation Value

Multidimensional private value auctions

We consider parametric examples of two-bidder private value auctions in which each bidder observes her own private valuation as well as noisy signals about her opponent’s private valuation. In such multidimensional private value auction environments, we show that the revenue equivalence between the first and second price auctions breaks down and there is no definite revenue ranking; while the s...

The value-added of multidimensional poverty measures

We’ve been asked to produce a brief and informal summary of an exchange between ourselves and Martin Ravallion, who is currently Acting Chief Economist and Senior Vice President of the World Bank. All of us agree, as Ravallion pointed out, that poverty is multidimensional. Our exchange concerned whether our group’s efforts to incorporate multiple dimensions into the very definition of who is po...

The Added Value of Multidimensional IRT Models

Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory

In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton’s formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to the quantum field theory, and expound the simplest example, based on a theory due to T. de Donder and H. Weyl. In a second part we explain quickly a work in c...

Singular Value Decomposition for Multidimensional Matrices

Singular Value Decomposition (SVD) is of great significance in theory development of mathematics and statistics. In this paper we propose the SVD for 3-dimensional (3-D) matrices and extend it to the general Multidimensional Matrices (MM). We use the basic operations associated with MM introduced by Solo to define some additional aspects of MM. We achieve SVD for 3-D matrix through these MM ope...