Related papers: Generalized iterated-sums signatures
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a central, and our motivating example. It leads to features of…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In…
We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance we prove a…
We investigate a signed version of the Hammersley process, a discrete process on words related to a property of integer sequences called heapability (Byers et al., ANALCO 2011). The specific version that we investigate corresponds to a…
The 'signature method' refers to a collection of feature extraction techniques for multivariate time series, derived from the theory of controlled differential equations. There is a great deal of flexibility as to how this method can be…
We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack,…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
In this paper, we investigate the invertibility of generalized g-Bessel multipliers. We show that for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame…
In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard…
We consider Gauss sums associated to functions $T\to \mathbb R/\mathbb Z$ which satisfy some sort of quadratic property and investigate their elementary properties. These properties and a Gauss sum formula from the nineteenth century due to…
The signature of a membrane is a sequence of tensors whose entries are iterated integrals. We study algebraic properties of membrane signatures, with a focus on signature matrices of polynomial and piecewise bilinear membranes. Generalizing…
We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on surfaces, modular forms and multiplicities in…
The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper halfplane, eventually multiplied by $z^{s-1}$, along geodesics connecting two cusps. This setting generalizes simultaneously the…
Controlled ordinary differential equations driven by continuous bounded variation curves can be considered a continuous time analogue of recurrent neural networks for the construction of expressive features of the input curves. We ask up to…
It is known that a certain invariant subring $R$ has finite $F$-representation type. Thus, we can write the $R$-module ${}^eR$ as a finite direct sum of finitely many $R$-modules. In such a decomposition of ${}^eR$, we pay attention to the…
In this paper, some more properties of the generalized principal pivot transform are derived. Necessary and sufficient conditions for the equality between Moore-Penrose inverse of a generalized principal pivot transform and its…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…