Realistic representation of objects requires models which can synthesize the image of an object under all possible viewing conditions. We propose to learn these models from examples. Methods for learning surface geometry and albedo from one or more images under fixed posed and varying lighting conditions are described. Singular value decomposition (SVD) is used to determine shape, albedo, and l...

The integrability of the one-dimensional long range supersymmetric t-J model has previously been established for both open systems and those closed by periodic boundary conditions through explicit construction of its integrals of motion. Recently the system has been extended to include the effect of magnetic flux, which gives rise to a closed chain with twisted boundary conditions. While the t-...

We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of th...

Abstract. In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case appearing as a special case of this larger framework. Then, depending on the rationality of the Kovalewski exponents, the different models, both in th...

Abstract. We show that for each weakly majorizing measure there is a natural metric with respect to which sample paths of stochastic processes are Hölder continuous and their Hölder norm satisfies a strong integrability condition. We call such metric a minorizing metric. The class of minorizing metrics is minimal among all metrics assuring sample Hölder continuity of processes satisfying certai...

Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A definition of quantum integrability in terms of canonical transformations is proposed which includes systems which have fewer commuting integrals of motion th...

In this short note we revisit the gain of integrability property of the gain part of the Boltzmann collision operator. This property implies the W l,r k regularity propagation for solutions of the associated space homogeneous initial value problem. We present a new method to prove the gain of integrability that simplifies the technicalities of previous approaches by avoiding the argument of gai...

The integrability of a system of two symmetrically coupled higherorder nonlinear Schrödinger equations is tested by means of the singularity analysis. It is proven that the system passes the Painlevé test for integrability only in ten distinct cases, of which two are new. For one of the new cases, a Lax pair and a multi-field generalization are obtained; for the other one, the equations of the ...

We covered Riemann integrals in the first three weeks in MA502 this semester (Chapter 11 in [1]). This report explores a necessary and sufficient condition for determining Riemann integrability of f(x) solely from its properties. This condition is known as Lebesgue’s criterion and elucidating the proof of this condition is the aim of this report. This report revisits the concepts learnt in MA50...