相关论文: A normal form algorithm for the Brieskorn lattice
The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for these ensembles the BDD problem is NP-hard in the worst case.…
The pseudo likelihood method of Besag(1974), has remained a popular method for estimating Markov random field on a very large lattice, despite various documented deficiencies. This is partly because it remains the only computationally…
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…
We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest…
We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.
We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinement of the zero sets of multivariable Alexander polynomials. In particular we identify…
We calculate the eta-invariant for the odd signature operator relative to a specific submersion metric on the Milnor fibration of a quasihomogeneous hypersurface singularity using certain global boundary conditions in terms of the data of…
We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…
We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an…
We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones. The minimum degrees of polynomials…
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the…
We introduce spectral Hirzebruch-Milnor classes for singular hypersurfaces. These can be identified with Steenbrink spectra in the isolated singularity case, and may be viewed as their global analogues in general. Their definition uses…
A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Non-ideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and…
A few years ago Kramer and Laubenbacher introduced a discrete notion of homotopy for simplicial complexes. In this paper, we compute the discrete fundamental group of the order complex of the Boolean lattice. As it turns out, it is…
In this work we employ a recently proposed bifurcation analysis technique, the deflated continuation algorithm, to compute steady-state solitary waveforms in a one-component, two dimensional nonlinear Schr\"odinger equation with a parabolic…
We study a simple nonlinear model defined on the cubic lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the…
The most singular residues of the standard meromorphic family of trilinear conformally invariant forms on $\mathcal C^\infty_c(\mathbb R^d)$ are computed. Their expression involves covariant bidifferential operators (generalized Rankin…
We introduce and analyze parallelizable algorithms to compress and accurately reconstruct finite simplicial complexes that have non-trivial automorphisms. The compressed data -- called a complex of groups -- amounts to a functor from (the…
In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and…