Related papers: Smooth Geometry of Diffusion Algebras
Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation.…
Diffusion models have achieved state-of-the-art performance, demonstrating remarkable generalisation capabilities across diverse domains. However, the mechanisms underpinning these strong capabilities remain only partially understood. A…
We study the diffusion front for a natural two-dimensional model where many particles starting at the origin diffuse independently. It turns out that this model can be described using properties of near-critical percolation, and provides a…
We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.
In this paper we study the Hilbert scheme of smooth, linearly normal, special scrolls under suitable assumptions on degree, genus and speciality.
We aim at giving a rigorous proof of the state-ments on the smoothness and the dimension of Severi varieties wherethere are gaps in the proofs in some standard literature. The method isa mixture of algebraic and analytic methods.
This paper gives direct derivations of the differential equations and likelihood formulas of diffusion models assuming only knowledge of Gaussian distributions. A VAE analysis derives both forward and backward stochastic differential…
This paper discusses the variation of sendograph distances under some algebra operations.
In this paper we study the the Gauss image problem, which is a generalization of the Aleksandrov problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we…
We revisit the modeling of ion-neutral (or ambipolar) diffusion with two fluid smoothed particle hydrodynamics, as discussed by Hosking & Whitworth. Some parts of the technique are optimized to testify the pioneer works on behavior of the…
In the present work, we explore homogenization techniques for a class of switching diffusion processes whose drift and diffusion coefficients, and jump intensities are smooth, spatially periodic functions; we assume full coupling between…
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
Associated to a differential BV algebra are two differential graded Lie algebras: we call one classical and the other, which contains a formal h-bar parameter, quantum. The classical dgLa is always smooth formal. In this paper, we give…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…
In this paper, we develop a geometric approach to study derived tame finite dimensional associative algebras, based on the theory of non-commutative nodal curves.
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
The diffeomorphism symmetry of general relativity leads in the canonical formulation to constraints, which encode the dynamics of the theory. These constraints satisfy a complicated algebra, known as Dirac's hypersurface deformation…
Looking for the universal covering of the smooth non-commutative torus leads to a curve of associative multiplications on the space $\Cal O_M'(\Bbb R^{2n})\cong \Cal O_C(\Bbb R^{2n})$ of Laurent Schwartz which is smooth in the deformation…