arXiv subjects

Yoonjin Lee

Publications and source records attributed to Yoonjin Lee.

13 recordsLinked to original sources

arXiv2025

A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group

We find a non-Hopfian ascending HNN-extension of a finitely presented Hopfian group by providing an explicit construction. This result addresses an analogous question to the one posed by Sapir and Wise, which asks whether there is a non-residually finite ascending HNN-extension of a finitely presented residually finite group. Such an analogy is motivated by Mal'cev's result that every finitely generated residually finite group is Hopfian.

math.GR↗

arXiv2025

Structured Debate Improves Corporate Credit Reasoning in Financial AI

This study investigated LLM-based automation for analyzing non-financial data in corporate credit evaluation. Two systems were developed and compared: a Single-Agent System (SAS), in which one LLM agent infers favorable and adverse repayment signals, and a Popperian Multi-agent Debate System (PMADS), which structures the dual-perspective analysis as adversarial argumentation under the Karl Popper Debate protocol. Evaluation addressed three fronts: (i) work productivity compared with human experts; (ii) perceived report quality and usability, rated by credit risk professionals for system-generated reports; and (iii) reasoning characteristics quantified via reasoning-tree analysis. Both systems drastically reduced task completion time relative to human experts. Professionals rated SAS reports as adequate, while PMADS reports exceeded neutral benchmarks and scored significantly higher in explanatory adequacy, practical applicability, and usability. Reasoning-tree analysis showed PMADS produced deeper, more elaborated structures, whereas SAS yielded single-layered trees. These findings suggest that structured multi-agent debate enhances analytical rigor and perceived usefulness, though at the cost of longer computation time. Overall, the results demonstrate that reasoning-centered automation represents a promising approach for developing useful AI systems in decision-critical financial contexts.

cs.AI↗

arXiv2025

Knowledge-Guided Machine Learning: Illustrating the use of Explainable Boosting Machines to Identify Overshooting Tops in Satellite Imagery

Machine learning (ML) algorithms have emerged in many meteorological applications. However, these algorithms struggle to extrapolate beyond the data they were trained on, i.e., they may adopt faulty strategies that lead to catastrophic failures. These failures are difficult to predict due to the opaque nature of ML algorithms. In high-stakes applications, such as severe weather forecasting, is is crucial to avoid such failures. One approach to address this issue is to develop more interpretable ML algorithms. The primary goal of this work is to illustrate the use of a specific interpretable ML algorithm that has not yet found much use in meteorology, Explainable Boosting Machines (EBMs). We demonstrate that EBMs are particularly suitable to implement human-guided strategies in an ML algorithm. As guiding example, we show how to develop an EBM to detect overshooting tops (OTs) in satellite imagery. EBMs require input features to be scalar. We use techniques from Knowledge-Guided Machine Learning to first extract scalar features from meteorological imagery. For the application of identifying OTs this includes extracting cloud texture from satellite imagery using Gray-Level Co-occurrence Matrices. Once trained, the EBM was examined and minimally altered to more closely match strategies used by domain scientists to identify OTs. The result of our efforts is a fully interpretable ML algorithm developed in a human-machine collaboration that uses human-guided strategies. While the final model does not reach the accuracy of more complex approaches, it performs reasonably well and we hope paves the way for building more interpretable ML algorithms for this and other meteorological applications.

cs.CV↗

arXiv2024

The finitude of tamely ramified pro-$p$ extensions of number fields with cyclic $p$-class groups

Let $p$ be an odd prime and $F$ be a number field whose $p$-class group is cyclic. Let $F_{\{\mathfrak{q}\}}$ be the maximal pro-$p$ extension of $F$ which is unramified outside a single non-$p$-adic prime ideal $\mathfrak{q}$ of $F$. In this work, we study the finitude of the Galois group $G_{\{\mathfrak{q}\}}(F)$ of $F_{\{\mathfrak{q}\}}$ over $F$. We prove that $G_{\{\mathfrak{q}\}}(F)$ is finite for the majority of $\mathfrak{q}$'s such that the generator rank of $G_{\{\mathfrak{q}\}}(F)$ is two, provided that for $p = 3$, $F$ is not a complex quartic field containing the primitive third roots of unity.

math.NT↗

arXiv2022

Tools for Extracting Spatio-Temporal Patterns in Meteorological Image Sequences: From Feature Engineering to Attention-Based Neural Networks

Atmospheric processes involve both space and time. This is why human analysis of atmospheric imagery can often extract more information from animated loops of image sequences than from individual images. Automating such an analysis requires the ability to identify spatio-temporal patterns in image sequences which is a very challenging task, because of the endless possibilities of patterns in both space and time. In this paper we review different concepts and techniques that are useful to extract spatio-temporal context specifically for meteorological applications. In this survey we first motivate the need for these approaches in meteorology using two applications, solar forecasting and detecting convection from satellite imagery. Then we provide an overview of many different concepts and techniques that are helpful for the interpretation of meteorological image sequences, such as (1) feature engineering methods to strengthen the desired signal in the input, using meteorological knowledge, classic image processing, harmonic analysis and topological data analysis (2) explain how different convolution filters (2D/3D/LSTM-convolution) can be utilized strategically in convolutional neural network architectures to find patterns in both space and time (3) discuss the powerful new concept of 'attention' in neural networks and the powerful abilities it brings to the interpretation of image sequences (4) briefly survey strategies from unsupervised, self-supervised and transfer learning to reduce the need for large labeled datasets. We hope that presenting an overview of these tools - many of which are underutilized - will help accelerate progress in this area.

cs.CV↗

arXiv2022

$p$-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on $Γ_1(4)$

For a prime $p\equiv 3$ $(\text{mod }4)$ and $m\ge 2$, Romik raised a question about whether the Taylor coefficients around $\sqrt{-1}$ of the classical Jacobi theta function $θ_3$ eventually vanish modulo $p^m$. This question can be extended to a class of modular forms of half-integral weight on $Γ_1(4)$ and CM points; in this paper, we prove an affirmative answer to it for primes $p\ge5$. Our result is also a generalization of the results of Larson and Smith for modular forms of integral weight on $\mathrm{SL}_2(\mathbb{Z})$.

math.NT↗

arXiv2021

Further improvement on index bounds

In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index bound given by Wan and Wang. As an application, we count the number of all the solutions of some algebraic curves by using our result.

cs.IT↗

arXiv2021

Characterization of $p$-ary functions in terms of association schemes and its applications

We obtain an explicit criterion for $p$-ary functions to produce association schemes in terms of their Walsh spectrum. Employing this characterization, we explicitly find a correlation between $p$-ary bent functions and association schemes; to be more exact, we prove that a $p$-ary bent function induces a $p$-class association scheme if and only if the function is weakly regular. As applications of our main criterion, we construct many infinite families of few-class association schemes arising from $p$-ary functions. Furthermore, we present four classes of $p$-ary two-weight linear codes, which are constructed from the association schemes produced in this paper.

cs.IT↗

arXiv2021

CIRA Guide to Custom Loss Functions for Neural Networks in Environmental Sciences -- Version 1

Neural networks are increasingly used in environmental science applications. Furthermore, neural network models are trained by minimizing a loss function, and it is crucial to choose the loss function very carefully for environmental science applications, as it determines what exactly is being optimized. Standard loss functions do not cover all the needs of the environmental sciences, which makes it important for scientists to be able to develop their own custom loss functions so that they can implement many of the classic performance measures already developed in environmental science, including measures developed for spatial model verification. However, there are very few resources available that cover the basics of custom loss function development comprehensively, and to the best of our knowledge none that focus on the needs of environmental scientists. This document seeks to fill this gap by providing a guide on how to write custom loss functions targeted toward environmental science applications. Topics include the basics of writing custom loss functions, common pitfalls, functions to use in loss functions, examples such as fractions skill score as loss function, how to incorporate physical constraints, discrete and soft discretization, and concepts such as focal, robust, and adaptive loss. While examples are currently provided in this guide for Python with Keras and the TensorFlow backend, the basic concepts also apply to other environments, such as Python with PyTorch. Similarly, while the sample loss functions provided here are from meteorology, these are just examples of how to create custom loss functions. Other fields in the environmental sciences have very similar needs for custom loss functions, e.g., for evaluating spatial forecasts effectively, and the concepts discussed here can be applied there as well. All code samples are provided in a GitHub repository.

cs.LG↗

arXiv2021

New LCD MDS codes of non-Reed-Solomon type

Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on. So far, most of LCD MDS codes have been constructed by employing generalized Reed-Solomon codes. In this paper we construct some classes of new Euclidean LCD MDS codes and Hermitian LCD MDS codes which are not monomially equivalent to Reed-Solomon codes, called LCD MDS codes of non-Reed- Solomon type. Our method is based on the constructions of Beelen et al. (2017) and Roth and Lempel (1989). To the best of our knowledge, this is the first paper on the construction of LCD MDS codes of non-Reed-Solomon type; any LCD MDS code of non- Reed-Solomon type constructed by our method is not monomially equivalent to any LCD code constructed by the method of Carlet et al. (2018).

cs.IT↗

arXiv2020

Binary LCD Codes and Self-orthogonal Codes via Simplicial Complexes

Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary LCD codes and two infinite families of binary self-orthogonal codes. Moreover, we explicitly determine the weight distributions of these codes. We obtain binary LCD codes which have minimum weights two or three, and we also find some self-orthogonal codes meeting the Griesmer bound. As examples, we also present some (almost) {\it optimal} binary self-orthogonal codes and LCD {\it distance optimal} codes.

cs.IT↗

arXiv2012

Construction of quasi-cyclic self-dual codes

There is a one-to-one correspondence between $\ell$-quasi-cyclic codes over a finite field $\mathbb F_q$ and linear codes over a ring $R = \mathbb F_q[Y]/(Y^m-1)$. Using this correspondence, we prove that every $\ell$-quasi-cyclic self-dual code of length $m\ell$ over a finite field $\mathbb F_q$ can be obtained by the {\it building-up} construction, provided that char $(\mathbb F_q)=2$ or $q \equiv 1 \pmod 4$, $m$ is a prime $p$, and $q$ is a primitive element of $\mathbb F_p$. We determine possible weight enumerators of a binary $\ell$-quasi-cyclic self-dual code of length $p\ell$ (with $p$ a prime) in terms of divisibility by $p$. We improve the result of [3] by constructing new binary cubic (i.e., $\ell$-quasi-cyclic codes of length $3\ell$) optimal self-dual codes of lengths $30, 36, 42, 48$ (Type I), 54 and 66. We also find quasi-cyclic optimal self-dual codes of lengths 40, 50, and 60. When $m=5$, we obtain a new 8-quasi-cyclic self-dual $[40, 20, 12]$ code over $\mathbb F_3$ and a new 6-quasi-cyclic self-dual $[30, 15, 10]$ code over $\mathbb F_4$. When $m=7$, we find a new 4-quasi-cyclic self-dual $[28, 14, 9]$ code over $\mathbb F_4$ and a new 6-quasi-cyclic self-dual $[42,21,12]$ code over $\mathbb F_4$.

cs.IT↗

arXiv2012

An Efficient Construction of Self-Dual Codes

We complete the building-up construction for self-dual codes by resolving the open cases over $GF(q)$ with $q \equiv 3 \pmod 4$, and over $\Z_{p^m}$ and Galois rings $\GR(p^m,r)$ with an odd prime $p$ satisfying $p \equiv 3 \pmod 4$ with $r$ odd. We also extend the building-up construction for self-dual codes to finite chain rings. Our building-up construction produces many new interesting self-dual codes. In particular, we construct 945 new extremal self-dual ternary $[32,16,9]$ codes, each of which has a trivial automorphism group. We also obtain many new self-dual codes over $\mathbb Z_9$ of lengths $12, 16, 20$ all with minimum Hamming weight 6, which is the best possible minimum Hamming weight that free self-dual codes over $\Z_9$ of these lengths can attain. From the constructed codes over $\mathbb Z_9$, we reconstruct optimal Type I lattices of dimensions $12, 16, 20,$ and 24 using Construction $A$; this shows that our building-up construction can make a good contribution for finding optimal Type I lattices as well as self-dual codes. We also find new optimal self-dual $[16,8,7]$ codes over GF(7) and new self-dual codes over GF(7) with the best known parameters $[24,12,9]$.

cs.IT↗