System Information Sciences

Mathematical System Analysis II B02

  • Prof. Nobuaki Obata      
  • Assoc. Prof. Reika Fukuizumi    
KeywordsQuantum probability, Infinite dimensional stochastic analysis, Complex network, Stochastic differential equation, Partial differential equation

Foundations of Mathematical Analysis and Applications

(B02-1) Obata Laboratory

Quantum (Non-commutative) Probability

Our main concern is to develop the quantum white noise theory with applications to quantum and classical differential equations. Fundamentals and applications to spectral analysis of graphs, random matrices, and orthogonal polynomials.

Network Dynamics

A graph with some additional structure is generally called a network. We are interested in the structure of growing and random networks as well as the critical behavior of relevant dynamics by means of statistical physics and numerical analysis.

Applied Mathematics Forum (AMF)

promoting interdisciplinary studies together with international joint research projects. In particular, mathematical approach to network science is of our central interest, along with applications to quantum technology, life and social sciences.

(B02-2) Fukuizumi Laboratory

Stochastic Partial Differential Equations

We study, by Ito calculus, the existence, blow-up, asymptotic behavior of solutions of a nonlinear dispersive equation with a stochastic perturbation. In particular, model equations arising in quantum device, Optical fiber or in Bose-Einstein Condensation are objects of study as applications in Engineering or Physics.

Stability of Solitary Waves and Travelling Waves

We treat the stability and instability problem of solitary waves. Main tools are variational methods related to nonlinear elliptic equations, and spectral analysis of operators on an infinite dimensional Hilbert space.

Numerical Analysis

We are interested in numerical simulations using MATLAB which give effectively some intuitive ideas to solve the phenomena mentioned above rigorously.

  • Giant component of a configuration model

  • Finding critical point by the 1st and 2nd connected components