Related papers: On Compatibility of Discrete Relations
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the…
This article presents a unified theory for analysis of components in discrete data, and compares the methods with techniques such as independent component analysis, non-negative matrix factorisation and latent Dirichlet allocation. The main…
For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Groebner bases provide a systematic way of doing this. The algebraic…
The behavior and architecture of large scale discrete state systems found in computer software and hardware can be specified and analyzed using a particular class of primitive recursive functions. This paper begins with an illustration of…
This work presents a first time accurate calculation of the magnetic dipole hyperfine structure constants for the ground state and some low-lying excited states of Pb$^+$. By comparing different levels of approximation with experimental…
The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight…
This paper describes a Buchberger-style algorithm to compute a Groebner basis of a polynomial ideal, allowing for a selection strategy based on "signatures". We explain how three recent algorithms can be viewed as different strategies for…
This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model. This model provides a unified approach for a variety of applications such as dynamic programming, solving sparse…
We address the challenge of identifying all real positive steady states in chemical reaction networks (CRNs) governed by mass-action kinetics. Traditional numerical methods often require specific initial guesses and may fail to find all the…
Experiences with the implementation of strong Gr\"obner bases respectively standard bases for polynomial rings over principal ideal rings are explained: different strategies for creating the pair set, methods to avoid coefficient growth and…
Signature-based algorithms are a popular kind of algorithms for computing Groebner basis, including the famous F5 algorithm, F5C, extended F5, G2V and the GVW algorithm. In this paper, an efficient method is proposed to solve the…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Groebner bases via Buchberger's Algorithm.
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…
This paper discusses the letter entitled "Network analysis of the state space of discrete dynamical systems" by A. Shreim et al. [Physical Review Letters, 98, 198701 (2007)]. We found that some theoretical analyses are wrong and the…
The understanding of the behaviour of systems of identical composite bosons has progressed significantly in connection with the analysis of the entanglement between constituents and the development of coboson theory. The basis of these…
By employing the (de)homogenization technique in a relatively extensive setting, this note studies in detail the relation between non-homogeneous Gr\"obner bases and homogeneous Gr\"obner bases. As a consequence, a general principle of…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…