Mathematical Informatics Faculty List

● Cryptography
We study post-quantum cryptography based on the mathematical problems (such as coding theory, lattice theory, multivariate polynomials, graph theory, etc), which are computationally intractable even in the era of quantum computing.

● Information Security
We are engaged in the development of new efficient cryptographic algorithms and implementation secure against physical attacks, which can be used in our life, for example, copyright protection, electronic voting, cryptocurrency, and so on.

● Research on public-key cryptography, in particular, the construction and security proofs of post-quantum cryptosystems.
● Research on attack and solution algorithms for mathematical problems related to public key cryptosystems and their security.

・Theory and Applications of succinct data structures

I am working on machine learning and mathematical optimization, aiming to construct general and efficient methodologies fordecision-making under uncertainty.
In particular, I have recently been working on the following topics:
1. development and analysis of algorithms for online learning and bandit problems
2. development and analysis of algorithms for mathematical optimization problems involving uncertainty
3. application of mathematical optimization to revenue management and portfolio management

(2) Algorithmic game theory: Design and analysis of mechanisms in strategic behavior.

There are many differential equations that have important physical properties such as conservation or dissipation. A "good" numerical method for such a equation refers to a numerical method that retain the conservation/dissipation properties in a discrete sense. Such a method is called a structure-preserving numerical method. Compared with a versatile numerical method, the structure-preserving method not only provides a qualitatively correct result but also achieves numerical stability. Currently, I'm engaged mainly in the study of high-order (highly accurate) methods for conservative/dissipative systems.

1. Parallel numerical computation, parallel algorithms
2. Numerical linear algebra, parallel preconditioning
3. Computational dynamics, forms processing, visualization

Function approximation and numerical integration are bases of various computational methods for problems in mathematical analysis such as differential equations. I have been engaged mainly in design and analysis of accurate approximation formulas for analytic functions by means of complex analytic methods. In particular, I'm interested in analysis and application of formulas (such as the DE formulas and DE-Sinc formulas) derived by the double-exponential (DE) transformations proposed by Takahasi and Mori. Recently, I'm developing general frameworks for designing accurate approximation formulas.

Statistical Modeling
　Statistical models and data analysis in neuroscience and seismology.

2. Computational statistics: development of algorithms for data analysis
3. Applied statistics: modeling and analysis of data from various fields such as neuroscience

1.データ同化
数値シミュレーションと観測・実験データを、ベイズ統計学の枠組みで統融合するための基盤技術であり、シミュレーションモデルに含まれるパラメータおよび各時刻における状態を逐次推定しながら、将来予測が可能なシミュレーションモデルを創出することができる。主に気象学や海洋学で大きく発展を遂げ、例えば日々の天気予報はデータ同化そのものであり、予報円（確率密度関数）付きの台風の進路予測は、データ同化の結果が端的に表れた好例と言える。気象学とは異なる観点から、地震や津波に代表される固体地球科学に資するデータ同化技術の構築を目指している。

2.逐次ベイズフィルタおよび4次元変分法
データ同化では、数値シミュレーションから算出される予測モデルと観測データを比較するため、 カルマンフィルタ、アンサンブルカルマンフィルタ、粒子フィルタに代表される逐次ベイズフィルタや、 4次元変分法などの極めて多種多様な手法が提案されており、目的や計算負荷を勘案して選択する。 固体地球科学の諸問題に適した、独自の逐次ベイズフィルタおよび4次元変分法の開発を実施している。

1: Efficient algorithms of continuous optimization problems focusing on non-convex optimization problems
2: Decision-making method for uncertain optimization problems: development of algorithms for robust optimization problems
3: Application of optimization methods to problems appearing in various fields (machine learning, financial engineering, energy system, etc.)

1.Applications of optimization theory to control systems theory: We study what control systems problems can be solved using Riemannian optimization, proximal algorithm, submodular optimization, and so on.
2.Applications of control systems theory to optimization theory: We study what optimization problems can be efficiently solved using control systems theories such as hybrid systems, passivity, and so on.
3.Data-driven modeling for controlling systems: We study efficient modeling methods for controlling systems from time series data using optimization, machine learning, numerical analysis, and so on.

2. データマイニング基礎（異常検知、変化検知、潜在的ダイナミクス）
3. データマイニング応用（セキュリティ、マーケティング、ヘルスケア、交通）

具体的には機械学習，統計的学習理論，数理統計学，データ解析についてその理論から応用を研究している．これらの研究分野はデータ科学とも呼ばれており，限られた観測データからいかにして有用な情報を取り出し予測や推論に活かすかという方法論を研究する分野である．
１．機械学習の数理：カーネル法や深層学習など機械学習には様々な手法が存在するがそれらの汎化誤差（予測誤差）を理論的に解析することで高い汎化性能を実現させる機構を探求している．
２．高次元統計学：高次元データに埋もれた重要な情報を抜き出す方法論とその理論を研究している．
３．機械学習の高速計算手法：確率的最適化などを用いて大量データ上で効率的に学習を実行する計算方法を開発している．

For the statistical modeling side, my focus is on developing models that take into account various characteristics and empirical regularities found in the economy and utilizing information from multiple sources in the form of a heterogeneous information network. For the latter model building research, I mainly develop network mining (simple, temporal, heterogeneous information network) and text mining methods. By combining the two research topics, my goal is to model complex issues in society (e.g., propagation and mitigation of shocks, hidden industrial block structure, aggregate fluctuation, matching among firms, network formation, bubbles, crashes, financial statements, systemic risks, the velocity of money, news events and reliability of information) to not only contribute to academic research but better understand risks and accelerate evidence-based policymaking.

- Discrete Optimization: Design and Analysis of Efficient Algorithms on Matroids and Submodular Functions
- Discrete Mathematical Engineering: Engineering Applications of Discrete Optimization Methods (Systems Analysis and Chemoinformatics)

● Discrete Algorithms
Design and analysis of algorithms for discrete optimization problems. Topics of particular interest are: graph algorithms and combinatorial optimization.

My main research focus is on designing fair resource allocation mechanisms that satisfy desirable fairness and efficiency properties. Applications include rent division among roommates, property division among family members, course assignment to students, and so on. I am also interested in developing multi-winner voting rules, where each group of voters has a fair influence on the outcome.

- Synchronization
- Complex networks
- Biological rhythms, circadian rhythms, jet lag
- Locomotion
- Power grids, transportation networks
- Self-organization, pattern formation
- Chemical reactions
- Micro-Macro links in nonlinear non-equilibrium systems

I am studying fundamental aspects of complex and dynamical systems described by nonequilibrium statistical mechanics and nonlinear dynamics through mathematical modeling of specific systems in physics, engineering, and biology. The research subjects I have being working on include theory of thermodynamic efficiency of nonequilibrium heat engines, dynamical modeling of a low-temperature-differential Stirling engine and elucidation of its rotational mechanism, and construction of energetics of synchronization in coupled oscillators.

・Continuous optimization and applied mechanics: convex optimization, complementarity, duality and their applications to structural optimization, contact mechanics, plasticity, etc.
・Robust optimization and its applications: Optimization with uncertain data, robust optimization of structures, robustness evaluation of uncertain systems, etc.

1. Computational algebraic statistics: application of the holonomic gradient method to statistics.
2. Statistical modeling of rare events and time series data.
3. Statistical methods using optimal transport maps.

I am studying maximum-likelihood- and Bayes-type estimation for diffusion processes, jump diffusion processes and self-exciting point processes, and the theory of asymptotic efficiency of estimators by using Malliavin calculus. I am also working with high-frequency data in Japanese and US stock markets and forecasting stock volatility and covariation.

Neuronal system modeling

Quantitative biology, Bioinformatics

1. Computational Neuroscience
Mathematical modeling of neural networks. Modeling various neuronal phenomena such as learning and adaptation.
2. Data Analysis of Neural Systems
Establishing mathematical theories and novel analysis method of neuronal data.
3. Biological Information Processing
Mathematical modeling of pancreatic beta cell and diabetes.

Our research is in the field of Computational Neuroscience. Computer models are used to study how information is processed in the brain and how the brain circuits adapt to and learn from the environment. We employ analytical techniques from statistical physics and information theory to investigate key functional properties for neuronal circuits. We use these techniques to reduce diverse experimental findings into a few core concepts that robustly explain the phenomena of interest. We are particularly interested in activity-dependent forms of plasticity in the brain, which are known to have large impacts on learning, memory, and development. With the aid of mathematical models, we seek a theory that unites the cellular level plasticity rules and the circuit level adaptation in different brain areas and animal species. Efficacy of neurons to represent and retain information is estimated from the structure and behavior of resulting circuits.

To accomplish this, we continuously develop electrophysiological and optical techniques to measure and control neural activity in multiple brain regions during behavioral tasks that engage cognitive function. By analyzing the obtained data using dynamical systems and machine learning approaches as well as computational models of brain activity, we seek to unravel the computational principles underlying cognitive functions such as perception and inference.