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Masaki Nakagawa

Publications and source records attributed to Masaki Nakagawa.

At least 19 recordsLinked to original sources
arXiv2025

Statistical properties of homoclinic bursting: an approach using infinite-modal maps toward predicting extreme events

Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps arising from homoclinic bursting to predict extreme events. The numerical investigation presents bifurcation diagrams, Lyapunov exponents, height probability distributions, and interevent interval probability distributions for infinite-modal maps. The theoretical analysis derives analytical formulae for these statistical properties using a randomization theory of infinite-modal maps. Furthermore, a parameter estimation method for infinite-modal maps is proposed, utilizing the derived analytical formula, which enables practical application of the theoretical results. Finally, the study demonstrates the applicability of the approach in analyzing non-stationary data with time-dependent parameters. These findings provide a foundation for the prediction of extreme events based on their mechanism.

nlin.CD↗
arXiv2024

Understanding changes in traffic demand during the Tokyo 2020 Olympic and Paralympic Games

This paper evaluated the effects of the Tokyo 2020 Olympic and Paralympic Games on traffic demand on the Metropolitan expressway. We constructed panel data for both passenger and freight vehicles' demand using longitudinal disaggregated trip records from the Metropolitan expressway. Subsequently, we established a demand function and used a difference-in-differences method to individually estimate the impacts of toll surcharges and other Olympics-related factors by leveraging the fact that the toll surcharges were not applied to freight vehicles. The results indicate that toll surcharges resulted in a decrease of 25.0 % for weekdays and 36.8 % for weekends/holidays in passenger vehicle demand on the Metropolitan expressway. The estimated toll elasticities are 0.345 for weekdays and 0.615 for weekends/holidays, respectively. Notably, analysis of the Olympics-related factor demonstrated that travel demand management (TDM) strategies effectively curbed demand on weekends/holidays with a reduction of 2.9 % in traffic demand. However, on weekdays, induced demand surpassed the reduction of demand by other TDM strategies than tolling, resulting in a 4.6 % increase in traffic demand. Additionally, We developed a zone-based demand function and investigate the spatial heterogeneity in toll elasticity. Our findings revealed small heterogeneity for weekdays (0.283 to 0.509) and large heterogeneity for weekends/holidays (0.484 to 0.935).

physics.soc-ph↗
arXiv2023

Handwriting recognition and automatic scoring for descriptive answers in Japanese language tests

This paper presents an experiment of automatically scoring handwritten descriptive answers in the trial tests for the new Japanese university entrance examination, which were made for about 120,000 examinees in 2017 and 2018. There are about 400,000 answers with more than 20 million characters. Although all answers have been scored by human examiners, handwritten characters are not labeled. We present our attempt to adapt deep neural network-based handwriting recognizers trained on a labeled handwriting dataset into this unlabeled answer set. Our proposed method combines different training strategies, ensembles multiple recognizers, and uses a language model built from a large general corpus to avoid overfitting into specific data. In our experiment, the proposed method records character accuracy of over 97% using about 2,000 verified labeled answers that account for less than 0.5% of the dataset. Then, the recognized answers are fed into a pre-trained automatic scoring system based on the BERT model without correcting misrecognized characters and providing rubric annotations. The automatic scoring system achieves from 0.84 to 0.98 of Quadratic Weighted Kappa (QWK). As QWK is over 0.8, it represents an acceptable similarity of scoring between the automatic scoring system and the human examiners. These results are promising for further research on end-to-end automatic scoring of descriptive answers.

cs.LG↗
arXiv2022

The universal factorial Hall-Littlewood $P$- and $Q$-functions

In this paper, we introduce {\it factorial} analogues of the ordinary Hall--Littlewood $P$- and $Q$-polynomials, which we call the {\it factorial Hall--Littlewood $P$- and $Q$-polynomials}. Using the {\it universal} formal group law, we further generalize these polynomials to the {\it universal factorial Hall--Littlewood $P$- and $Q$-functions}. We show that these functions satisfy the {\it vanishing property} which the ordinary factorial Schur $S$-, $P$-, and $Q$-polynomials have. By the vanishing property, we derive the Pieri-type formula and a certain generalization of the classical hook formula. We then characterize our functions in terms of Gysin maps from flag bundles in the complex cobordism theory. Using this characterization and Gysin formulas for flag bundles, we can obtain generating functions for the universal factorial Hall--Littlewood $P$- and $Q$-functions. Using our generating functions, we can show that our factorial Hall--Littlewood $P$- and $Q$-polynomials have a certain {\it cancellation property}. Further applications such as Pfaffian formulas for $K$-theoretic factorial $Q$-polynomials are also given.

math.AT↗
arXiv2021

A Transformer-based Math Language Model for Handwritten Math Expression Recognition

Handwritten mathematical expressions (HMEs) contain ambiguities in their interpretations, even for humans sometimes. Several math symbols are very similar in the writing style, such as dot and comma or 0, O, and o, which is a challenge for HME recognition systems to handle without using contextual information. To address this problem, this paper presents a Transformer-based Math Language Model (TMLM). Based on the self-attention mechanism, the high-level representation of an input token in a sequence of tokens is computed by how it is related to the previous tokens. Thus, TMLM can capture long dependencies and correlations among symbols and relations in a mathematical expression (ME). We trained the proposed language model using a corpus of approximately 70,000 LaTeX sequences provided in CROHME 2016. TMLM achieved the perplexity of 4.42, which outperformed the previous math language models, i.e., the N-gram and recurrent neural network-based language models. In addition, we combine TMLM into a stochastic context-free grammar-based HME recognition system using a weighting parameter to re-rank the top-10 best candidates. The expression rates on the testing sets of CROHME 2016 and CROHME 2019 were improved by 2.97 and 0.83 percentage points, respectively.

cs.CL↗
arXiv2021

Recurrent neural network transducer for Japanese and Chinese offline handwritten text recognition

In this paper, we propose an RNN-Transducer model for recognizing Japanese and Chinese offline handwritten text line images. As far as we know, it is the first approach that adopts the RNN-Transducer model for offline handwritten text recognition. The proposed model consists of three main components: a visual feature encoder that extracts visual features from an input image by CNN and then encodes the visual features by BLSTM; a linguistic context encoder that extracts and encodes linguistic features from the input image by embedded layers and LSTM; and a joint decoder that combines and then decodes the visual features and the linguistic features into the final label sequence by fully connected and softmax layers. The proposed model takes advantage of both visual and linguistic information from the input image. In the experiments, we evaluated the performance of the proposed model on the two datasets: Kuzushiji and SCUT-EPT. Experimental results show that the proposed model achieves state-of-the-art performance on all datasets.

cs.CV↗
arXiv2021

Global Context for improving recognition of Online Handwritten Mathematical Expressions

This paper presents a temporal classification method for all three subtasks of symbol segmentation, symbol recognition and relation classification in online handwritten mathematical expressions (HMEs). The classification model is trained by multiple paths of symbols and spatial relations derived from the Symbol Relation Tree (SRT) representation of HMEs. The method benefits from global context of a deep bidirectional Long Short-term Memory network, which learns the temporal classification directly from online handwriting by the Connectionist Temporal Classification loss. To recognize an online HME, a symbol-level parse tree with Context-Free Grammar is constructed, where symbols and spatial relations are obtained from the temporal classification results. We show the effectiveness of the proposed method on the two latest CROHME datasets.

cs.CV↗
arXiv2021

GSSF: A Generative Sequence Similarity Function based on a Seq2Seq model for clustering online handwritten mathematical answers

Toward a computer-assisted marking for descriptive math questions,this paper presents clustering of online handwritten mathematical expressions (OnHMEs) to help human markers to mark them efficiently and reliably. We propose a generative sequence similarity function for computing a similarity score of two OnHMEs based on a sequence-to-sequence OnHME recognizer. Each OnHME is represented by a similarity-based representation (SbR) vector. The SbR matrix is inputted to the k-means algorithm for clustering OnHMEs. Experiments are conducted on an answer dataset (Dset_Mix) of 200 OnHMEs mixed of real patterns and synthesized patterns for each of 10 questions and a real online handwritten mathematical answer dataset of 122 student answers at most for each of 15 questions (NIER_CBT). The best clustering results achieved around 0.916 and 0.915 for purity, and around 0.556 and 0.702 for the marking cost on Dset_Mix and NIER_CBT, respectively. Our method currently outperforms the previous methods for clustering HMEs.

cs.CV↗
arXiv2021

Darondeau-Pragacz formulas in complex cobordism

In this paper, we generalize the push-forward (Gysin) formulas for flag bundles in the ordinary cohomology theory, which are due to Darondeau-Pragacz, to the complex cobordism theory. Then we introduce the {\it universal quadratic Schur functions}, which are a generalization of the (ordinary) quadratic Schur functions introduced by Darondeau-Pragacz, and establish some Gysin formulas for the universal quadratic Schur functions as an application of our Gysin formulas.

math.AT↗
arXiv2021

Learning symbol relation tree for online mathematical expression recognition

This paper proposes a method for recognizing online handwritten mathematical expressions (OnHME) by building a symbol relation tree (SRT) directly from a sequence of strokes. A bidirectional recurrent neural network learns from multiple derived paths of SRT to predict both symbols and spatial relations between symbols using global context. The recognition system has two parts: a temporal classifier and a tree connector. The temporal classifier produces an SRT by recognizing an OnHME pattern. The tree connector splits the SRT into several sub-SRTs. The final SRT is formed by looking up the best combination among those sub-SRTs. Besides, we adopt a tree sorting method to deal with various stroke orders. Recognition experiments indicate that the proposed OnHME recognition system is competitive to other methods. The recognition system achieves 44.12% and 41.76% expression recognition rates on the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) 2014 and 2016 testing sets.

cs.CV↗
arXiv2020

Text-independent writer identification using convolutional neural network

The text-independent approach to writer identification does not require the writer to write some predetermined text. Previous research on text-independent writer identification has been based on identifying writer-specific features designed by experts. However, in the last decade, deep learning methods have been successfully applied to learn features from data automatically. We propose here an end-to-end deep-learning method for text-independent writer identification that does not require prior identification of features. A Convolutional Neural Network (CNN) is trained initially to extract local features, which represent characteristics of individual handwriting in the whole character images and their sub-regions. Randomly sampled tuples of images from the training set are used to train the CNN and aggregate the extracted local features of images from the tuples to form global features. For every training epoch, the process of randomly sampling tuples is repeated, which is equivalent to a large number of training patterns being prepared for training the CNN for text-independent writer identification. We conducted experiments on the JEITA-HP database of offline handwritten Japanese character patterns. With 200 characters, our method achieved an accuracy of 99.97% to classify 100 writers. Even when using 50 characters for 100 writers or 100 characters for 400 writers, our method achieved accuracy levels of 92.80% or 93.82%, respectively. We conducted further experiments on the Firemaker and IAM databases of offline handwritten English text. Using only one page per writer to train, our method achieved over 91.81% accuracy to classify 900 writers. Overall, we achieved a better performance than the previously published best result based on handcrafted features and clustering algorithms, which demonstrates the effectiveness of our method for handwritten English text also.

cs.CV↗
arXiv2020

Online trajectory recovery from offline handwritten Japanese kanji characters

In general, it is straightforward to render an offline handwriting image from an online handwriting pattern. However, it is challenging to reconstruct an online handwriting pattern given an offline handwriting image, especially for multiple-stroke character as Japanese kanji. The multiple-stroke character requires not only point coordinates but also stroke orders whose difficulty is exponential growth by the number of strokes. Besides, several crossed and touch points might increase the difficulty of the recovered task. We propose a deep neural network-based method to solve the recovered task using a large online handwriting database. Our proposed model has two main components: Convolutional Neural Network-based encoder and Long Short-Term Memory Network-based decoder with an attention layer. The encoder focuses on feature extraction while the decoder refers to the extracted features and generates the time-sequences of coordinates. We also demonstrate the effect of the attention layer to guide the decoder during the reconstruction. We evaluate the performance of the proposed method by both visual verification and handwritten character recognition. Although the visual verification reveals some problems, the recognition experiments demonstrate the effect of trajectory recovery in improving the accuracy of offline handwritten character recognition when online recognition for the recovered trajectories are combined.

cs.CV↗
arXiv2019

End to End Recognition System for Recognizing Offline Unconstrained Vietnamese Handwriting

Inspired by recent successes in neural machine translation and image caption generation, we present an attention based encoder decoder model (AED) to recognize Vietnamese Handwritten Text. The model composes of two parts: a DenseNet for extracting invariant features, and a Long Short-Term Memory network (LSTM) with an attention model incorporated for generating output text (LSTM decoder), which are connected from the CNN part to the attention model. The input of the CNN part is a handwritten text image and the target of the LSTM decoder is the corresponding text of the input image. Our model is trained end-to-end to predict the text from a given input image since all the parts are differential components. In the experiment section, we evaluate our proposed AED model on the VNOnDB-Word and VNOnDB-Line datasets to verify its efficiency. The experiential results show that our model achieves 12.30% of word error rate without using any language model. This result is competitive with the handwriting recognition system provided by Google in the Vietnamese Online Handwritten Text Recognition competition.

cs.CV↗
arXiv2019

Pattern Generation Strategies for Improving Recognition of Handwritten Mathematical Expressions

Recognition of Handwritten Mathematical Expressions (HMEs) is a challenging problem because of the ambiguity and complexity of two-dimensional handwriting. Moreover, the lack of large training data is a serious issue, especially for academic recognition systems. In this paper, we propose pattern generation strategies that generate shape and structural variations to improve the performance of recognition systems based on a small training set. For data generation, we employ the public databases: CROHME 2014 and 2016 of online HMEs. The first strategy employs local and global distortions to generate shape variations. The second strategy decomposes an online HME into sub-online HMEs to get more structural variations. The hybrid strategy combines both these strategies to maximize shape and structural variations. The generated online HMEs are converted to images for offline HME recognition. We tested our strategies in an end-to-end recognition system constructed from a recent deep learning model: Convolutional Neural Network and attention-based encoder-decoder. The results of experiments on the CROHME 2014 and 2016 databases demonstrate the superiority and effectiveness of our strategies: our hybrid strategy achieved classification rates of 48.78% and 45.60%, respectively, on these databases. These results are competitive compared to others reported in recent literature. Our generated datasets are openly available for research community and constitute a useful resource for the HME recognition research in future.

cs.CV↗
arXiv2017

Universal Gysin formulas for the universal Hall-Littlewood functions

It is known that the usual Schur $S$- and $P$-polynomials can be described via the Gysin homomorphisms for flag bundles in the ordinary cohomology theory. Recently, P. Pragacz generalized these Gysin formulas to the Hall-Littlewood polynomials. In this paper, we introduce a {\it universal} analogue of the Hall-Littlewood polynomials, which we call the {\it universal Hall-Littlewood functions}, and give Gysin formulas for various flag bundles in the complex cobordism theory. Furthermore, we give two kinds of the {\it universal} analogue of the schur polynomials, and some Gysin formulas for these functions are established.

math.AT↗
arXiv2014

Generalized Lyapunov exponent as a unified characterization of dynamical instabilities

The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov exponent, as a unified characterization of non-exponential and exponential dynamical instabilities in one-dimensional maps. Chaos is classified into three different types, i.e., super-exponential, exponential, and sub-exponential dynamical instabilities. Using one-dimensional maps, we demonstrate super-exponential and sub-exponential chaos and quantify the dynamical instabilities by the Lyapunov pair. In sub-exponential chaos, we show super-weak chaos, which means that the growth of the difference of nearby orbits is slower than a stretched exponential growth. The scaling of the growth is analytically studied by a recently developed theory of a continuous accumulation process, which is related to infinite ergodic theory.

nlin.CD↗
arXiv2014

Generalized (co)homology of the loop spaces of classical groups and the universal factorial Schur $P$- and $Q$-functions

In this paper, we study the generalized (co)homology Hopf algebras of the loop spaces on the infinite classical groups, generalizing the work due to Kono-Kozima and Clarke. We shall give a description of these Hopf algebras in terms of symmetric functions. Based on topological considerations in the first half of this paper, we then introduce a universal analogue of the factorial Schur $P$- and $Q$-functions due to Ivanov and Ikeda-Naruse. We investigate various properties of these functions such as the cancellation property, which we call the $\mathbb{L}$-supersymmetric property, the factorization property, and the vanishing property. We prove that the universal analogue of the Schur $P$-functions form a formal basis for the ring of functions with the $\mathbb{L}$-supersymmetric property. By using the universal analogue of the Cauchy identity, we then define the dual universal Schur $P$- and $Q$-functions. We describe the duality of these functions in terms of Hopf algebras.

math.AT↗