The first meeting of the semester.

Let us gather, greet new members to the Department, and set a plan for the semester before us.

- Speaker: Ran Wang

*Control Systems Theory Group*

**Topic:**

**Deep Reinforcement Learning for Continuous-time Self-triggered Control**

In recent years, the trade-off between communication cost and control performance has become increasingly important. Among various control architectures, self-triggered controllers decide the next communication (state observation and action determination) timing online in a state-dependent manner. However, it should be emphasized that most of the existing methods do not explicitly evaluate the resulting long-run communication cost. In this seminar, I'd like to introduce how to formulate an optimal continuous-time self-triggered control problem that takes the communication cost into an explicit account and proposes a design method based on deep reinforcement learning.

- Speaker: Jianshen Zhu

*Discrete Mathematics Group*

**Topic:**

**An Integer Programming Formulation for Inferring Chemical Compounds with Prescribed Topological Structures**

An Improved Integer Programming Formulation for Inferring Chemical Compounds with. Prescribed Topological Structures Abstract: Various intelligent methods have recently been applied to the design of novel chemical graphs. As one of such approaches, a framework using both artificial neural networks (ANNs) and mixed integer linear. programming (MILP) has been proposed. Recently an MILP has been designed to deal with a graph with any cycle index and the computational results on a system with the MILP showed that chemical graphs with around up to 50 non-hydrogen atoms can be inferred. However, this MILP is computationally costly for some instances, e.g., it takes about 10 hours to solve some instances with 50 atoms. One of the main reasons for this is that the number of constraints and variables in the MILP is relatively large. In this research, we improve the MILP by reducing the number of constraints and variables. Our experimental results show that the improved MILP can be solved around 20 times faster than the previous MILP.

- Speaker: Shinji Kakinaka

*Physical Statistics Group*

**Topic:**

**Cryptocurrency market efficiency in short- and long-term horizons during COVID-19**

This study investigates market efficiency of the major cryptocurrencies during the COVID-19 pandemic while accounting for different investment horizons. By applying the asymmetric multifractal detrended fluctuation analysis, we show that the outbreak affected the efficiency property of price behaviors differently between short- and long-term horizons. After the outbreak, the markets exhibited stronger inefficiency in the short-term but weaker inefficiency in the long-term. We also analyze asymmetric market patterns between upward and downward trends and between small and large price fluctuations and confirm that the outbreak has greatly changed the level of asymmetry in cryptocurrency markets.

The first meeting of the semester.

Let us gather, greet new members to the Department, and set a plan for the semester before us.

**Update:**

This year it was decided to have six meetings
with two presenters at each meeting.
The seminars will be mainly held online by Zoom,
And a local screening will be arranged.

Presenters may choose to give their presentations locally,
and be broadcasted on Zoom.

- Speaker: Ran Wang

*Control Systems Theory Group*

**Topic:**

**Formation Control of Multiple Drones with Limited Local Measurements**

This talk will introduce formation control theory firstly and show you some application cases, e.g. how to make a drone show. Then a Real-time Operating System (RTOS) based mini-drone called Crazyflie will be introduced including its hardware and software. Also, the limitation of sensors will be considered and an Extended Kalman Filter is used to obtain an optimal states estimation. Finally, we will discuss some limitations in applying formation control theory into practical projects and my future work.

- Speaker: Shunji Kakinaka

*Physical Statistics Group*

**Topic:**

**Asymmetric volatility dynamics in cryptocurrency markets**

Asymmetric correlation between price and volatility is a prominent feature of financial market time series. In this short presentation, the stylized facts of the relationship between price and volatility in cryptocurrency markets are introduced. In addition, the presence of asymmetric volatility effect between uptrend (bull) and downtrend (bear) regimes are investigated using the nonlinear cross-correlation coefficient measures.

- Speaker: Hiroki Tanaka

*Physical Statistics Group*

**Topic:**

**Bayes’ theorem on marked point process and its application to seismicity-like time-series**

Probabilistic forecasting of large earthquakes is based on the statistics on the time intervals of past earthquakes at a large magnitude threshold, and the information on the small events are less utilized. In this presentation, as a method to use such information for the probabilistic evaluation, the Bayes’ theorem between the inter-event times of different magnitude thresholds is considered. By applying the method to the synthetic earthquake catalog, the effectiveness for the forecasting is discussed briefly.

- Speaker: Hiroki Tanabe

*System Optimization Group*

**Topic:**

**Accelerated proximal gradient methods for multiobjective optimization**

In recent years, many researchers have studied descent methods for multiobjective optimization problems. For example, Fliege and Svaiter proposed the steepest descent method for differentiable multiobjective optimization problems. Afterward, a proximal gradient method, which can solve non-differentiable problems, was also considered. However, their accelerated versions are not sufficiently studied. Recently, El Moudden and El Mouatasim proposed a natural extension of Nesterov’s accelerated method for multiobjective optimization problems. They proved the global convergence rate of the algorithm O(1/k^2) under the assumption that the sequence of the Lagrangian multipliers of the subproblems is eventually fixed. However, this assumption is restrictive because it means that the method is regarded as the Nesterov’s method for the weighting problem. In this paper, we propose new accelerated algorithms, in which we solve subproblems with terms that only appear in the multiobjective case. We also prove the proposed methods' global convergence rate O(1/k^2) under a more natural assumption, using merit functions as a way to measure the complexity.

- Speaker: Atsushi Hori

*System Optimization Group*

**Topic:**

**Distributionally Robust Expected Residual Minimization for Stochastic Variational Inequality Problems**

The stochastic variational inequality problem (SVIP) is an equilibrium model which includes random variables and has been widely used in economics, engineering, and others. The expected residual minimization (ERM) is known as one of models to get a reasonable solution to the SVIP, and its objective function is an expected value of a suitable merit function for the SVIP. However, the ERM is restricted to the case where the distribution has already been known. We extend the ERM so that robust solutions can be obtained for the SVIP under the uncertainty distribution (we call the extended one DRERM), where the worst case distribution is taken from the set of probability measures whose expected value and variance take the same sample mean and variance, respectively. Under suitable assumptions, we show that the DRERM can be reformulated as a deterministic convex nonlinear semidefinite programming to avoid numerical integration.

- Speaker: Veronika Nguyen

*Discrete Mathematics Group*

**Topic:**

**Using expander graphs to test whether samples are i.i.d.**

Expander graphs are sparse but well-connected graphs and it is indeed difficult to explicitly construct such graphs. However, a result of Friedman shows that a randomly selected d-regular graph with enough vertices is an expander graph with high probability. Using Friedman's result Steinerberger suggests a new test on whether samples are i.i.d. by assigning a graph to a sequence of numbers and then looking at the spectral values of the adjacency matrix of the graph.

- Speaker: Tomoyuki Mao

*Physical Statistics Group*

**Topic:**

**Estimation of Physiological State Focused on Chaotic Properties of Heart Rate Variability**

In physiology, autonomic nervous system activity is evaluated by analyzing heart rate variability (HRV) using methods of statistical analysis or frequency analysis. In this presentation, I will introduce the experimental result of analyzing the heart rate (RRI) data in physical load and mental load from the viewpoint of chaos, which has been attracting attention in recent years.

- Speaker: Jiahao Huang

*Control Systems Theory Group*

**Topic:**

**Secure State Estimation and Attack Detection in the Cyber-Physical Systems**

In the Cyber Physical Systems (CPSs), the malicious cyber attackers can intrude the wireless network and modify the transmitted data to degrade the system performance. Hence, it is extremely important to develop some methods of attack detection to isolate the attack impact on the CPSs. In view of this, I mainly focus on the remote estimation scenario and the distributed consensus filtering, and aim to address their secure state estimation problems caused by integrity attack.

- Speaker: Yuika Kajihara

*Dynamical Systems Group*

**Topic:**

**An introduction to the direct method in the calculus of variations**

Variational problems appear in various parts of mathematics and physics. First half of this talk is devoted to an introduction to a basic concept of calculus of variations and a useful method (called “the direct method”) for searching a solution of differential equations. In the rest of the talk, I will state a brief explanation of my research theme and difficulties for study of this field.

- Speaker: Atsushi Maeno

*Applied Mathematical Analysis Group*

**Topic:**

**Linearization of the generalized box-ball system**

The box-ball system (BBS for short) is a cellular automaton that exhibits solitonic behavior. Since Takahashi and Satsuma introduced it in 1990, it has been studied from a variety of aspects such as ultradiscretization of soliton equations, crystal base, combinatorics, and others. The time evolution of the BBS can be linearized with KKR (Kerov-Kirillov-Reshetikhin) bijection, which was originally introduced in the analysis of solvable lattice models. Kakei et al. simplified and gave a new interpretation to the procedure to compose KKR bijection with "01-arc lines". By generalizing this method, we can linearize the generalized BBS that KKR bijection cannot be applied to.

- Speaker: Hardik Tankaria

*System Optimization Group*

**Topic:**

**Stochastic Nystrom approximation with variance reduced gradient for Large Scale Training Problems in Machine Learning**

One of the important tasks of machine learning and data science is to train models with massive amounts of data. Training such model is formulated as a solution to empirical risk minimization problem. We consider the problem of minimizing the average of strongly convex functions for large-scale empirical risk minimization problems. In order to solve this optimization problem, the first-order stochastic algorithm such as stochastic gradient and its variants are useful in practice due to its low per iteration cost and easy implementation strategies. However, the first-order methods are highly sensitive to hyper-parameters choices and not effective with ill condition problems. These challenges call the most popular stochastic quasi-Newton methods. It provides the second-order information by approximating the Hessian. These approximations use the first-order derivatives. Therefore, the quasi-Newton methods are sometimes unable to provide the exact curvature information near the solution. We propose the Nystrom approximation to approximate the Hessian. The significant difference between the quasi-Newton approximation and the Nystrom approximation is that we use the sketch of the actual Hessian. Moreover, in order to eliminate the effect of inherent variance, we use the stochastic variance reduced gradient in the usual quasi-Newton framework. We also propose a variant with mini-batch for the Nystrom approximation to reduce the computational complexity. For the stability in the search direction, we propose to use the Levenberg-Marquardt technique on the Nystrom approximation. The experimental results on the several benchmark data sets depict the efficacy of the proposed method. Numerical experiments show that it is possible to give approximation with the actual Hessian information and provide the competitive results to the state-of-the-art first order and the stochastic quasi-Newton methods within the same computation time.

- Speaker: Ryuta Moriyasu

*Control Systems Theory Group*

**Topic:**

**Structured Hammerstein-Wiener Model Learning for Model Predictive Control**

This study aims to improve the reliability of optimal control using models constructed by machine learning methods. Optimal control problems based on such models are generally non-convex and difficult to solve online. In this study, we propose a model that combines the Hammerstein-Wiener model with input convex neural networks, which have recently been proposed in the field of machine learning. An important feature of the proposed model is that resulting optimal control problems are effectively solvable exploiting their convexity and partial linearity while retaining flexible modeling ability. The practical usefulness of the method is examined through its application to the modeling and control of an engine airpath system.

*Applied Mathematical Analysis Group*

*Discrete Mathematics Group*

*System Optimization Group*

*Control Systems Theory Group*

*Physical Statistics Group*

*Dynamical Systems Group*

*Applied Mathematical Modelling Group*

Last-modified: 2022-02-10 (木) 16:53:41 (289d)