Related papers: Generalized Ideals and Co-Granular Rough Sets
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…
Significant efforts have been devoted in the last decade towards improving the predictivity of coarse-grained models in molecular dynamics simulations and providing a rigorous justification of their use, through a combination of theoretical…
In this paper, we formulate a new generalized reference kernel hoping to improve the original base kernel using a set of reference vectors. Depending on the selected reference vectors, our formulation shows similarities to approximate…
Fractional Gaussian fields provide a rich class of spatial models and have a long history of applications in multiple branches of science. However, estimation and inference for fractional Gaussian fields present significant challenges. This…
We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…
Approximate lattices of locally compact groups were first studied in a seminal monograph of Yves Meyer and were subsequently used in the theory of aperiodic order to model objects such as Pisot numbers, quasi-cristals or aperiodic tilings.…
Parallel transport as dictated by a gauge field determines a collection of local reference systems. Comparing local reference systems in overlapping regions leads to an ensemble of algebras of relational kinematical observables for gauge…
This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…
Coreference resolution is an intermediate step for text understanding. It is used in tasks and domains for which we do not necessarily have coreference annotated corpora. Therefore, generalization is of special importance for coreference…
We develop the basic theory of derived quasi-coherent ideals for stacks relative to a given derived algebraic context. We compare different notions of adic completeness with respect to derived ideals, define and compare formal spectra and…
Coarse-grained (CG) modeling has gained significant attention in recent years due to its wide applicability in enhancing the spatiotemporal scales of molecular simulations. While CG simulations, often performed with Hamiltonian mechanics,…
In this paper, we intend the concept of rough cubic Pythagorean fuzzy ideals in the semigroup. By using this notion, we discuss lower approximation and upper approximation of cubic Pythagorean fuzzy left (right) ideals, bi-ideals, interior…
We examine non-dual relational extensions of rough set approximations and find an extension which satisfies surprisingly many of the usual rough set properties. We then use this definition to give an explanation for an observation made by…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
Recently there has been developed a reformulation of General Relativity - referred to as {\it the null surface version of GR} - where instead of the metric field as the basic variable of the theory, families of three-surfaces in a…
Many word clouds provide no semantics to the word placement, but use a random layout optimized solely for aesthetic purposes. We propose a novel approach to model word significance and word affinity within a document, and in comparison to a…
In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…
This paper studies expansions of bounded distributive lattices equipped with a Galois connection. We introduce GC-frames and canonical frames for these algebras. The complex algebras of GC-frames are defined in terms of rough set…
When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of…