Papers Continued fraction
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Unsupervised Discovery of Formulas for Mathematical Constants
Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not e…
Continued fractionscientific discoveryThe Ramanujan Library -- Automated Discovery on the Hypergraph of Integer Relations
Fundamental mathematical constants appear in nearly every field of science, from physics to biology. Formulas that connect different constants often bring great insight by hinting at connections between previously dispar…
Continued fractionAlgorithm-assisted discovery of an intrinsic order among mathematical constants
In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As com…
Continued fractionMathematical ProofsAutomated Search for Conjectures on Mathematical Constants using Analysis of Integer Sequences
Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas h…
Continued fractionCircuit Model Reduction with Scaled Relative Graphs
Continued fractions are classical representations of complex objects (for example, real numbers) as sums and inverses of simpler objects (for example, integers). The analogy in linear circuit theory is a chain of series/…
Continued fractionmodelSemantic Preserving Bijective Mappings of Mathematical Formulae between Document Preparation Systems and Computer Algebra Systems
Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NI…
Continued fractionMathMultiple regression techniques for modeling dates of first performances of Shakespeare-era plays
The date of the first performance of a play of Shakespeare's time must usually be guessed with reference to multiple indirect external sources, or to some aspect of the content or style of the play. Identifying these dat…
Continued fractionregressionLearning to extrapolate using continued fractions: Predicting the critical temperature of superconductor materials
In the field of Artificial Intelligence (AI) and Machine Learning (ML), the approximation of unknown target functions $y=f(\mathbf{x})$ using limited instances $S={(\mathbf{x^{(i)}},y^{(i)})}$, where $\mathbf{x^{(i)}} \i…
Continued fractionregressionQuasi-Equivalence of Width and Depth of Neural Networks
While classic studies proved that wide networks allow universal approximation, recent research and successes of deep learning demonstrate the power of deep networks. Based on a symmetric consideration, we investigate if …
ClassificationContinued fractionGeneral ClassificationThe Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants
Fundamental mathematical constants like $e$ and $\pi$ are ubiquitous in diverse fields of science, from abstract mathematics to physics, biology and chemistry. For centuries, new formulas relating fundamental constants h…
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