Related papers: An Algebraic Framework for Discrete Tomography: Re…
It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…
We present a computational algebra solution to reverse engineering the network structure of discrete dynamical systems from data. We use monomial ideals to determine dependencies between variables that encode constraints on the possible…
Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple…
We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourer-finite-element-methods in weighted functions spaces. Closed Hilbert complexes and commuting projectors are used through…
The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…
This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three…
The importance of the first-class constraint algebra of general relativity is not limited just by its self-contained description of the gauge nature of spacetime, but it also provides conditions to properly evolve the geometry by selecting…
We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…
The discrete tomography of B-type and F-type icosahedral model sets is investigated, with an emphasis on reconstruction and uniqueness problems. These are motivated by the request of materials science for the unique reconstruction of…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
We study free dg-Lie algebroids over arbitrary derived schemes, and compute their universal enveloping and jet algebras. We also introduce derived twisted connections, and relate them with lifts on twisted square zero extensions. This…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…
The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
In this paper, time-independent Hamiltonian systems are investigated via a Lie-group/algebra formalism. The (unknown) solution linked with the Hamiltonian is considered to be a Lie-group transformation of the initial data, where the group…