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16 pages, 1256 KiB

Open AccessArticle

Investigating Models for the Transcription of Mathematical Formulas in Images

by Christian Feichter and Tim Schlippe

Appl. Sci. 2024, 14(3), 1140; https://doi.org/10.3390/app14031140 - 29 Jan 2024

Cited by 5 | Viewed by 3001

The automated transcription of mathematical formulas represents a complex challenge that is of great importance for digital processing and comprehensibility of mathematical content. Consequently, our goal was to analyze state-of-the-art approaches for the transcription of printed mathematical formulas on images into spoken English text. We focused on two approaches: (1) The combination of mathematical expression recognition (MER) models and natural language processing (NLP) models to convert formula images first into LaTeX code and then into text, and (2) the direct conversion of formula images into text using vision-language (VL) models. Since no dataset with printed mathematical formulas and corresponding English transcriptions existed, we created a new dataset, Formula2Text, for fine-tuning and evaluating our systems. Our best system for (1) combines the MER model LaTeX-OCR and the NLP model BART-Base, achieving a translation error rate of 36.14% compared with our reference transcriptions. In the task of converting LaTeX code to text, BART-Base, T5-Base, and FLAN-T5-Base even outperformed ChatGPT, GPT-3.5 Turbo, and GPT-4. For (2), the best VL model, TrOCR, achieves a translation error rate of 42.09%. This demonstrates that VL models, predominantly employed for classical image captioning tasks, possess significant potential for the transcription of mathematical formulas in images. Full article

(This article belongs to the Special Issue Deep Learning and Technology-Assisted Education)

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14 pages, 341 KiB

Open AccessArticle

A Novel Dynamical Regulation of mRNA Distribution by Cross-Talking Pathways

by Qiwen Sun, Zhaohang Cai and Chunjuan Zhu

Mathematics 2022, 10(9), 1515; https://doi.org/10.3390/math10091515 - 2 May 2022

Cited by 4 | Viewed by 1712

Abstract

In this paper, we use a similar approach to the one proposed by Chen and Jiao to calculate the mathematical formulas of the generating function

V (z, t)

and the mass function

P_{m} (t)

of a cross-talking [...] Read more.

In this paper, we use a similar approach to the one proposed by Chen and Jiao to calculate the mathematical formulas of the generating function

V (z, t)

and the mass function

P_{m} (t)

of a cross-talking pathways model in large parameter regions. Together with kinetic rates from yeast and mouse genes, our numerical examples reveal novel bimodal mRNA distributions for intermediate times, whereby the mode of distribution

P_{m} (t)

displays unimodality with the peak at

m = 0

for initial and long times, which has not been obtained in previous works. Such regulation of mRNA distribution exactly matches the transcriptional dynamics for the osmosensitive genes in Saccharomyces cerevisiae, which has not been generated by those models with one single pathway or feedback loops. This paper may provide us with a novel observation on transcriptional distribution dynamics regulated by multiple signaling pathways in response to environmental changes and genetic perturbations. Full article

(This article belongs to the Special Issue Difference and Differential Equations and Applications)

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12 pages, 4042 KiB

Open AccessProceeding Paper

Ad Oculos. Images, Imagination and Abstract Thinking

by Alessandra Cirafici

Proceedings 2017, 1(9), 945; https://doi.org/10.3390/proceedings1090945 - 14 Mar 2018

Cited by 1 | Viewed by 2526

Abstract

The unusual edition of Elements of Euclid released for publishing in 1847 by Oliver Byrne offers the occasion to suggest a few elements for discussion on the uniqueness of the ‘representation’ of geometric-mathematical thinking—and more in general of the abstract thinking—enshrined in its ‘nature of a pure imaginative vision able to connect the intelligible with the tangible’. The purpose is, thus, a reasoning on images and communicative artefacts, that, when articulated, provide different variations of the idea of ‘transcription’ of complex theoretical structures from one language (that of abstract logic) to another (that of sensory experience), with a view to facilitate, ease and make more accurate the noetic process. Images able over time to facilitate the understanding of complex and abstract theoretical principles—since able to show them in an extremely concrete way, ad oculos,—and which at some points could reveal the horizons of art interpretation to inscrutable and figurative meaningless formulas. Full article

(This article belongs to the Proceedings of Proceedings of the International and Interdisciplinary Conference IMMAGINI? Brixen, Italy, 27–28 November 2017.)

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