Related papers: Refracting profiles and generalized holodiagrams
The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency…
Under ray-optical light transport, the classical ray serves as a linear and local "point query" of light's behaviour. Linearity and locality are crucial to the formulation of sophisticated path tracing and sampling techniques, that enable…
We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…
In this paper, we develop a theoretical analysis to efficiently handle superpositions of waves with concentrated wavevector and frequency spectra, allowing an easy analytical description of fields with interesting transverse profiles.…
We introduce jacobian graphs, which are explicit families of regular graphs that are spectrally indistinguishable from random graphs, but whose local structure is very different from that of random graphs. The construction relies on the…
We show that the Poincar\'e lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincar\'e lemma for transversal crystals of level…
We describe a classical thermodynamic model that reproduces the main features of the solid hydrogen phase diagram. In particular, we show how the general structure types that are found by electronic structure calculations and the quantum…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
The notion of quantum algebras is merged with that of Lie systems in order to establish a new formalism called Poisson-Hopf algebra deformations of Lie systems. The procedure can be naturally applied to Lie systems endowed with a symplectic…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of connection. Using connections,…
The one-dimensional system of particles with a $1/x^2$ repulsive potential is known as the Calogero-Moser system. Its classical version can be generalised by substituting the coupling constants with additional degrees of freedom, which span…
The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization…
We develop the method of the hamiltonian reduction of affine Lie superalgebras to obtain explicit and general expressions both for the classical and the quantum extended superconformal algebras. By performing the gauge transformation which…
Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large. Underpinning the traditional rules for the refraction of an…
We describe a bigraded generalization of the Weil algebra, of its basis and of the characteristic homomorphism which besides ordinary characteristic classes also maps on Donaldson invariants.
This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
The aim of this paper is to introduce the notion of restricted Hom- Lie superalgebras. This class of algebras is a generalization of both restricted Hom-Lie algebras and restricted Lie superalgebras. In this paper, we present a way to…
The generic singularities and bifurcations are classified for one-parameter families of curves with frames in a space form, the Euclidean space, the elliptic space or the hyperbolic space via projective geometry. Two kinds of frames are…