Related papers: Canonical block-oriented model
3D object detection has attracted much attention thanks to the advances in sensors and deep learning methods for point clouds. Current state-of-the-art methods like VoteNet regress direct offset towards object centers and box orientations…
A canonical model, analogous to the one for contraction operators, is introduced for bi-isometries, two commuting isometries on a Hilbert space. This model involves a contractive analytic operator-valued function on the unit disk. Various…
Most elementary numerical schemes found useful for solving classical trajectory problems are {\it canonical transformations}. This fact should be make more widely known among teachers of computational physics and Hamiltonian mechanics. From…
We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type…
The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to…
Many unsteady flows exhibiting complex dynamics are nevertheless characterized by emergent large-scale coherence in space and time. Reduced-order models based on Galerkin projection of the governing equations onto an orthogonal modal basis…
Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization…
The purpose of the present work is to show that an adequate basis for understanding the essentially nonlinear phenomena must also be essentially nonlinear however still simple enough to play the role of a basis. It is shown that such types…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
We discuss the variety of coordinates often used to characterize the coherent state classical limit of an algebraic model. We show selection of appropriate coordinates naturally motivates a procedure to generate a single particle…
We first present a consistent canonical formulation of the general (non-marginal) Oppenheimer-Snyder model. The switching between comoving and stationary observer is achieved by promoting coordinate transformations between dust proper time…
We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of…
Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear…
Many calculi exist for modelling various features of object-oriented languages. Many of them are based on $\lambda$-calculus and focus either on statically typed class-based languages or dynamic prototype-based languages. We formalize…
We describe a new implementation of the Bernstein-Vazirani algorithm which relies on the fact that the polarization states of classical light beams can be cloned. We explore the possibility of computing with waves and discuss a classical…
Models for distributions of shapes contained within images can be widely used in biomedical applications ranging from tumor tracking for targeted radiation therapy to classifying cells in a blood sample. Our focus is on hierarchical…
We identify the canonical contact structure on the link of a simple elliptic or cusp singularity by drawing a Legendrian handlebody diagram of one of its Stein fillings. We also show that the canonical contact structure on the link of a…
We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group…
An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…