Related papers: The method of creative microscoping
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of…
We propose an abstraction-based multi-document summarization framework that can construct new sentences by exploring more fine-grained syntactic units than sentences, namely, noun/verb phrases. Different from existing abstraction-based…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
We analyze the differential equations produced by the method of creative telescoping applied to a hyperexponential term in two variables. We show that equations of low order have high degree, and that higher order equations have lower…
In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are…
In this article a new method of generating sums of like powers is presented.
The essence of good creative writing is calibrated surprise: when constraints from all relevant dimensions act together, the feasible solution space collapses into a narrow region, and the surviving choices look least predictable from an…
A summation is a shift-invariant ${\rm R}$-module homomorphism from a submodule of ${\rm R}[[\sigma]]$ to ${\rm R}$ or another ring. [11] formalized a method for extending a summation to a larger domain by telescoping. In this paper, we…
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
We describe a technique that can be used for the fusion of multiple sources of information as well as for the evaluation and selection of alternatives under multi-criteria. Three important properties contribute to the uniqueness of the…
This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
Reconstruction of the fundamental supersymmetric theory and its breaking mechanism will require high-precision tools. Here a brief introduction to SPA, the Supersymmetry Parameter Analysis (SPA) Convention and Project, is presented which is…
Latent-space optimization methods for counterfactual explanations - framed as minimal semantic perturbations that change model predictions - inherit the ambiguity of Wachter et al.'s objective: the choice of distance metric dictates whether…
We describe a new way to construct finite geometric objects. For every k we obtain a symmetric configuration E(k-1) with k points on a line. In particular, we have a constructive existence proof for such configurations. The method is very…
Generating synthetic variants of a document is often posed as text-to-text transformation. We propose an alternate LLM based method that first decomposes a document into semantic frames and then generates text using this interim sparse…
The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a…
We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between…