Related papers: Generalized Reduction Procedure: Symplectic and Po…

Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly…

We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and…

In this paper, a generalization of a quadratic manifold approach for the reduction of geometrically nonlinear structural dynamics problems is presented. This generalization is constructed by a linearization of the static force with respect…

In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…

This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian…

Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian…

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…

We construct an analogue of Whittaker reduction for Poisson actions of a semisimple complex Poisson-Lie group G. The reduction takes place along a class of transversal slices to unipotent orbits in G, which are generalizations of the…

We review the prequantization procedure in the context of super symplectic manifolds with a symplectic form which is not necessarily homogeneous. In developing the theory of non homogeneous symplectic forms, there is one surprising result:…

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…

We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic…

Hierarchical Model reduction and Proper Generalized Decomposition both exploit separation of variables to perform a model reduction. After setting the basics, we exemplify these techniques on some standard elliptic problems to highlight…

In this paper we propose a procedure for a noncommutative derived Poisson reduction, in the spirit of the Kontsevich-Rosenberg principle: "a noncommutative structure of some kind on $A$ should give an analogous commutative structure on all…

Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…

This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…

The Cartesian reverse derivative is a categorical generalization of reverse-mode automatic differentiation. We use this operator to generalize several optimization algorithms, including a straightforward generalization of gradient descent…

Compositional generalization is one of the main properties which differentiates lexical learning in humans from state-of-art neural networks. We propose a general framework for building models that can generalize compositionally using the…

This paper studies hamiltonization of nonholonomic systems using geometric tools. By making use of symmetries and suitable first integrals of the system, we explicitly define a global 2-form for which the gauge transformed nonholonomic…