Related papers: Slim normal Bases and Basefield Transforms

The notion of regular cell complexes plays a central role in topological combinatorics because of its close relationship with posets. A generalization, called totally normal cellular stratified spaces, was introduced by the third author by…

We show that each number of the form, the square root of s for s not a perfect square, is simply normal to the base 2. The argument uses some elementary ideas from the calculus of finite differences.

Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial…

The search for a highly discriminating and easily computable invariant to distinguish graphs remains a challenging research topic. Here we focus on cospectral graphs whose complements are also cospectral (generalized cospectral), and on…

A new way of computing scattering amplitudes in a certain very important QFT (N=4 SYM) has recently been developed, in which an algebraic structure called the positive Grassmannian plays a very important role. The mathematics of the…

An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…

Let $V$ be a finite dimensional vector space over a field $\mathrm{k}$ of characteristic $0$. Let $A$ be a linear mapping of $V$ into itself. This paper gives a normal form for $A$, which gives a better description of the structure of $A$…

Switching is an operation on a graph that does not change the spectrum of the adjacency matrix, thus producing cospectral graphs. An important activity in the field of spectral graph theory is the characterization of graphs by their…

In this paper we study the possibility of constructing two-field models from one-field models. The idea is to start with a given one-field model and use the deformation procedure to generate another one-field model, and then couple the two…

When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…

In this paper, we consider whether existence of a sums-of-squares formula depends on the base field. We reformulate the question of existence as a question in algebraic geometry. We show that, for large enough p, existence of…

The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…

We show that in supersymmetric theories, knowing the soft theorem for a single particle in a supermultiplet allows one to immediately determine soft theorems for the remainder of the supermultiplet. While soft theorems in supersymmetric…

Splint is a decomposition of root system into union of root systems. Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching…

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…

A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes…

For a smooth family of exact forms on a smooth manifold, an algorithm for computing a primitive family smoothly dependent on parameters is given. The algorithm is presented in the context of a diagram chasing argument in the \v{C}ech-de…

The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…

Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths.…

An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vector field is based on a differential geometric setting in…