Related papers: Generalized iterated-sums signatures
In this paper we provide for parsing with respect to grammars expressed in a general TFS-based formalism, a restriction of ALE. Our motivation being the design of an abstract (WAM-like) machine for the formalism, we consider parsing as a…
In this paper we find the number of different signatures of $P(3,1), P(5,1)$ and $P(7,1)$ upto switching isomorphism, where $P(n, k)$ denotes the generalised Petersen graph, $2k < n$. We also count the number of non-isomorphic signatures on…
Text summarization systems have made significant progress in recent years, but typically generate summaries in one single step. However, the one-shot summarization setting is sometimes inadequate, as the generated summary may contain…
We give explicit expressions for the Fourier coefficients of Eisenstein series twisted by Dirichlet characters and modular symbols on $\Gamma_0(N)$ in the case where $N$ is prime and equal to the conductor of the Dirichlet character. We…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
In this paper we deal with the generalized Gamma processes and their compositions. For the compositions of two or more than two generalized Gamma processes we give, when possible, the explicit law whereas, in the other cases the…
The paper studies how to compute irreducible characters of the generalized symmetric group $C_k\wr{S}_n$ by iterative algorithms. After reproving the Ariki-Koike version of the Murnaghan-Nakayama rule by vertex algebraic methods, we…
Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded…
Recently it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of…
For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the…
We study a set of generalized V-line transforms, namely longitudinal, mixed, and transverse V-line transforms, of a symmetric $m$-tensor field in $\mathbb{R}^2$. The goal of this article is to recover a symmetric $m$-tensor field…
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…
We present a fit-for-purpose introduction to tensors and their operations. It is envisaged to help the reader become acquainted with its underpinning concepts for the study of path signatures. The text includes exercises, solutions and many…
This paper gives a plethysm formula on the characteristic map of the induced linear characters from the unipotent upper-triangular matrices $U_n(\mathbb F_q)$ to $GL_n(\mathbb F_q)$, the general linear group over finite field $\mathbb F_q$.…
Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…
We introduce a use of the \(M\)-cover (or \(M\)-layer) transform for machine learning. The method replicates a model \(M\) times, but instead of coupling the copies through parameter averaging or an explicit attractive force, as in…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
In this paper we consider the iteration of infinitely many signed exponentials with the same base but the signs may vary. We show that for every base in an explicit interval this iteration converges for any sequence of signs and all the…
We present a new sum rule for Clebsch-Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is obtained from an integral involving Gegenbauer ultraspherical polynomials. A…
We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that…