Related papers: Lavaurs algorithm for cubic symmetric polynomials
We consider the symmetries of coincidence site lattices of 3-dimensional cubic lattices. This includes the discussion of the symmetry groups and the Bravais classes of the CSLs. We derive various criteria and necessary conditions for…
We describe a locally connected model of the boundary of the cubic connectedness locus. The model is obtained by constructing a decomposition of the space of critical portraits and collapsing elements of the decomposition into points. This…
We study the dynamics of template iterations, consisting of arbitrary compositions of functions chosen from a finite set of polynomials. In particular, we focus on templates using complex unicritical maps in the family $\{ z^d + c, c \in…
We provide a model for an open invariant neighborhood of any orbit in a symplectic manifold endowed with a canonical proper symmetry. Our results generalize the constructions of Marle and Guillemin and Sternberg for canonical symmetries…
We study asymptotic dynamics in networks of coupled quadratic nodes. While single map complex quadratic iterations have been studied over the past century, considering ensembles of such functions, organized as coupled nodes in a network,…
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…
We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and…
We construct new knot polynomials. Let $V$ be the standard solid torus in 3-space and let $pr$ be its standard projection onto an annulus. Let $M$ be the space of all smooth oriented knots in $V$ such that the restriction of $pr$ is an…
The LC method described in this work seeks to approximate the roots of polynomial equations in one variable. This book allows you to explore the LC method, which uses geometric structures of Lines L and Circumferences C in the plane of…
We consider the polynomial algebra $\mathbb{C}[\mathbf{z}]:=\mathbb{C}[z_1,\,z_2,\,z_3]$ and the polynomial $f:=z_1^3+z_2^3+z_3^3+3qz_1z_2z_3$, where $q\in \mathbb{C}$. Our aim is to compute the Hochschild homology and cohomology of the…
In this article, for degree $d\geq 1$, we construct an embedding $\Phi_d $ of the connectedness locus $\mathcal{M}_{d+1}$ of the polynomials $z^{d+1}+c$ into the connectedness locus of degree $2d+1$ bicritical odd polynomials.
Given any rational map $f$, there is a lamination by Riemann surfaces associated to $f$. Such laminations were constructed in general by Lyubich and Minsky. In this paper, we classify laminations associated to quadratic polynomials with…
Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit constructions of higher order symmetries and the structure…
The Hamiltonian symmetry reduction of the geodesics system on a symmetric space of negative curvature by the maximal compact subgroup of the isometry group is investigated at an arbitrary value of the momentum map. Restricting to regular…
In this paper we show the existence of a closed, embedded $\lambda$-hypersurfaces $\Sigma \subset \mathbb{R}^{2n}$. The hypersurface is diffeomorhic to $\mathbb{S}^{n-1} \times \mathbb{S}^{n-1} \times \mathbb{S}^1$ and exhibits $SO(n)…
We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D…
It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an…
Given a matrix $D$ describing the pairwise dissimilarities of a data set, a common task is to embed the data points into Euclidean space. The classical multidimensional scaling (cMDS) algorithm is a widespread method to do this. However,…
The coupled nonlinear space fractional Ginzburg-Landau (CNLSFGL) equations with the fractional Laplacian have been widely used to model the dynamical processes in a fractal media with fractional dispersion. Due to the existence of…
We give a classification of quadratic harmonic morphisms between Euclidean spaces (Theorem 2.4) after proving a Rank Lemma. We also find a correspondence between umbilical (Definition 2.7) quadratic harmonic morphisms and Clifford systems.…