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- [Math and Info]Year Started : 2020

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Large scale quantum computers are said to threaten public key cryptosystems that are currently in use. Researches and the standardization of post quantum cryptography which is resistant to cryprtoanalysis done by both classical and quantum computers are now in progress. However, there are still many issues about the security and efficiency of such cryptography. This project studies post quantum cryptography using elliptic curves from the perspective of number theory. Through solving security and efficiency problems, this project aims to realize safety and security in the future quantum information society.

Technologies for automatic analysis for academic literature is desired to utilize a vast amount of knowledge in the literature. As the first step for such an analysis, this research project aims to focus on the small structures, tokens, in formulae, and develop a new methodology to associate each token to corresponding mathematical concepts. Formulae and texts are complementary to each other, and thus those in documents cannot be understood independently. Moreover, formulae in texts have various ambiguities. Synthetic analysis on mathematical expressions and natural language will be necessary to overcome these large barriers.

Most virtual machines employ just-in-time (JIT) compilers to achieve high-performance. Trace- and method-based compilations are two major compilation strategies in JIT compilers. In general, the former excels in compiling programs with more in-depth method calls and more dynamic branches, while the latter works good for a wide range of programs.

Koopman operators have been getting popular in the fields of nonlinear dynamical system and machine learning in the context of dynamical system. In this study, we propose a new theoretical framework of Koopman operators for data analysis. We employ the theory of function space that has been extensively developed in pure mathematics, and clarify a relationship between dynamical systems and mathematical structures of function spaces where Koopman oeprators are acting. We introduce the theory of generalized spectrum for linear operators as well, and aim to establish its computation method for empirical study for data analysis.

In supervised learning, Bayes error is the best achievable prediction error for a given problem or task. The aim of this study is to propose a Bayes error estimation method. I am also interested in using Bayes error estimation in order to study overfitting and regularization methods.

We intend to study and develop mathematical models that can be applied to the recommendation of educational materials to learners to improve their abilities in a stable manner. Systems deploying this recommendation technology base can analyze the content of educational resources based on natural language understanding, estimate the risks of learning failures, and consider their effects on learning to ensure effective material recommendation. Unlike lectures, which typically require learners to have sufficient prior knowledge, the proposed technology base enables learners to train themselves by merely following the recommended educational materials without prerequisites. The ultimate objective is to dramatically improve the level of learner achievement through self-study and change the shape of education by facilitating systematic education without prerequisite knowledge.

For a sustainable society, transferring and preserving the skills of experts is an important issue. The purpose of the project is to formalize “tacit knowledge” through skill acquisition by human-imitative AI. I build an action recognition model by data-driven learning in first-person videos and an imitation agent that reproduces expert behavior by generative modeling, such as reinforcement and imitation learning. I take the approach to understand human behavior from both sides of these cognitive and generative aspects.

Autonomous robots in dynamic and/or unknown environments still have many problems. This research focuses on Subsumption Architecture (SA), a method to generate robot behaviors in real time based on synthesis of local feedback control laws. Though it experimentally works well, its theoretical analysis and design is hard. To tackle this problem, this research applies Riemannian geometry and tries to establish a way how to build SA whose stability and optimality are theoretically guaranteed. To evaluate results, a child-size humanoid robot will be developed and used to complete complex manipulation tasks autonomously.

I extend the existing graph rigidity theory of finite frameworks to periodic frameworks and create a theory of analyzing crystals. I also study the combinatorial characterization of generic global rigidity of frameworks and design a fast algorithm which does not involve coordinate calculation. Furthermore, I apply these method to the analysis of chromatic number or kissing number.

From a perspective of geometric group theory, this research addresses various notions of nonpositively curved groups, and aims to clarify relationships among them. We feature Artin groups and study their actions on nonpositively curved spaces. We focus on algorithmic properties of nonpositively curved groups and aim for applications to cryptography.

Widespread research is being conducted on microrobots that form swarms. One of the goals of these studies is to build a distributed computing system by installing a processor and wireless communication circuit. The challenge is how to mount circuit hardware on microrobots, which have restrictions on size and power consumption. In this research project, I will try to integrate a low-power processor and wireless communication/power supply circuits on a single small chip. The realization of shape-changeable information devices consisting of a group of microrobots that are smaller than ever before will be achieved.

Integer programming has been used to solve optimization problems in, e.g., production planning, human resource planning, logistics, finance, sports, and entertainment. On the other hand, current algorithms for the integer programming has limitation on the amount of data that can be handled and/or applicable problems. The aim of this project is to develop faster and more-general-purpose algorithms for integer programming using polymorphisms, a generalized concept of automorphisms of a solution set.

The goal of this research is to classify mapping class groups of surfaces by quasi-isometry. Particularly, we focus on the mapping class groups of nonorientable surfaces. In this research, we construct right-angled Artin subgroups of the mapping claass groups of nonorientable surfaces and determine whether the embeddings are quasi-isometric, and we make clear whether the mapping class groups of nonorientable surfaces are quasi-isometric to the mapping class groups of orientable surfaces. Furthermore, we try to apply mapping class groups and quasi-isometry maps to machine learning.

Statistical machine learning is a mathematical technology that aims to extract useful information hidden in data. Despite recent developments in machine learning, there are still challenges to design valid and robust algorithms for incomplete settings where we cannot collect fully informative data or we can only observe data partially. In this project, we aim to develop a new learning paradigm for such settings based on both mathematical optimization and statistics.

In this project, we aim at establishing a new research field, data-driven computer-algebraic geometry, which incorporates the data-driven framework of the modern applied information science (e.g., machine learning) into the computation and algorithms in computer algebra and algebraic geometry. In data-driven computer-algebraic geometry, all computations are not handled in a symbolic manner and instead realized by efficient numerical computation focusing on the evaluated values of symbolic objects (e.g., monomials and polynomials) at given data.

There are various machine learning problems in various domains. However, it is hard to perform theoretical analysis individually for various learning problems. This project aims to develop a framework that can reduce various learning problems to another learning problem. This framework enables unified analysis across various learning problems beyond the domains. The first step is to consider the reduction framework to multiple instance learning problems. The final goal is to construct a general reduction framework.

Online conferencing is becoming more and more popular, where users need to hold conversations with people in remote locations and sometimes with those around them. As a result, it is becoming increasingly important for users to concentrate on hearing only what they are interested in from online and offline speakers. This work will utilize the cocktail party effect and propose an audio processing system that supports selective listening between online and offline speakers.

To reducce the parameter size related to embeddings, this study aims to propose a method to construct embeddings whose parameter size is independent from the vocabulary size. In detail, the proposed method assigns random vectors to each word to construct a unique vector, and then applied some neural networks to the unique vector to increase its expressiveness. I investigate whether the proposed method can achieve the comparable performance to the conventional embeddings with fewer parameters through experiments on widely used natural language generation tasks: machine translation and summarization.

It is known that “Asymptotic Geometric Analysis” (AGA) is one of the methods on basic quantum information theory. The aim of that field is to study properties of convex bodies in high dimensional spaces. In particular, a recent important object of research is the class of log-concave probability measures which is wider than one of convex bodies. The purpose in this project is to reveal geometric properties of log-concave probability measures by applying optimal transport theory and information theory. This project is expected to apply to basic quantum information theory in the future.

Several information technologies use techniques of string data processing. Development of efficient methods for processing string data requires to understand string structures and their characteristics. There are many string structures that are based on lexicographic orders. This project aims to clarify the effects to lexicographical string structures by changing the lexicographic order. Moreover, we will develop a new approach for string data processing which is based on the properties.

Rigid origami structures can be easily enlargened when used and easily folded when unused, which is a great advantage for creating large scale structures. However, their manufacturing and assembling processes often become complicated, which hinders the technology to be widespread. In this project, we will create an algorithm that generates from the users’ input 3D shape a polygonal net, which can be easily assembled using rigid panels and strings. To achieve this goal, we will not only construct mathematical theories but also fabricate objects in practice and find the constraints on the final shape. The resulting system will allow novice users to create large scale and deployable structures, which opens up the possibilities of personal fabrication.

Clay is an excellent material that has plasticity and adhesiveness, and can be easily made into arbitrary three-dimensional shapes. However, it is difficult to capture the shape of the clay during modeling, resulting in lack of assistive tools for clay modeling. This research aims to develop a technology to capture the 3D shape of the clay without interfering with the modeling process by embedding multiple wireless sensors that can measure the shape of the clay. We also propose an interactive system for supporting the modeling process.

The robots working in our everyday lives have to robustly comprehend their surrounding environments even when they are in crowded spaces such as station platforms, busy streets, and airports. As a step to develop such a robot, the goal of this project is to establish a robot audition system that can precisely recognize crowded acoustic scenes in real time with few prior information. Specifically, this project aims to develop a robust robot audition system based on a deep Bayesian spatio-temporal model that can handle the real crowded scenes in a unified framework.

Modern machine learning methods are designed, often implicitly, with optimal average performance in mind; this is embodied in the ubiquity of the risk (expected loss) in the guarantees attached to algorithms in traditional statistical learning theory. While in many cases strong performance on average is desirable, there are countless other ways of evaluating (off-sample) performance, and committing to the expected value is, and should be recognized as, a substantial value judgement. In this work, we explore new notions of performance beyond the expected loss, seeking to obtain a new class of performance metrics which effectively balances flexibility and interpretability of the new metrics with the computational and theoretical tractability of algorithms designed to optimize the new criteria.

Second, I will propose new post-quantum cryptography “Shimura Variety Cryptography” by using Shimura varieties instead of algebraic surfaces and generalizing Algebraic Surface Cryptography to higher dimensions.

Finally, by studying in pure mathematics and applied mathematics, I will strengthen the connection between them and introduce the methods to each other.

The development of periodic/aperiodic separation control redefines a state as a periodic/aperiodic state composed of a periodic state and aperiodic state by introducing a periodicity/aperiodicity point of view to the single state. For control and analysis of the separated periodic and aperiodic states, the project conducts 【A】Construction of an optimal periodic/aperiodic separation filter, 【B】Construction of robust periodic/aperiodic separation control, and【C】Development of periodic/aperiodic interactive robot.

End-to-end media transfers based on deep learning techniques have little affinity with exploratory design processes, and thus, have not been widely used for creative purposes. This research aims to establish a framework to alternate them by exploring with explicit and intuitive parameters. It is expected to lead to the development of a creative support system and the introduction of new design processes.

The development of word embeddings has led to significant advances in the field of natural language processing. However, for sentences that are larger textual units than words, neither the meaning representation nor the comparison method has been established. Consequently, it is still difficult to even detect fatal errors of language processing systems. In this study, we first aim to attribute the geometric information of word vectors to linguistic information, and then construct a sentence-similarity metric that is sensitive to differences in the information contained in sentences using optimal transport as a foothold. By doing so, we aim to solve the issue in computing the inter-sentence similarity.

An application of activity recognition technology using wearable sensors is being investigated for monitoring workers in factories and distribution warehouses. To realize automatic monitoring in these places, it is necessary to recognize work processes, which consist of multiple atomic actions, with a small amount of training data. In this research, I call this kind of activity ”complex activities”, and aim to realize the Few Shot segmentation of complex activity by utilizing the image representation of time-series signals to learn the short term and long term dependencies of complex activity data in advance.

Conventionally, systematic quality assurance of cyber-physical systems (Safe CPS) utilizes rigorous mathematical models (Safe CPS 1.0) or search-based techniques (Safe CPS 2.0). These methods have issues in practicality and explainability, respectively. This research aims to achieve both practicality and explainability (Safe CPS 3.0) by combining the mathematical methods from Safe CPS 1.0 and search-based techniques from Safe CPS 2.0.