Mathematics that used to be considered pure often addresses real world problems in unexpected and surprising ways. The concept of information entropy helps us to distinguish between valuable and worthless information. A nontrivial group called eliptic curve helped us to settle the longstanding Fermat's Last Problem, and also gave us a cryptosystem being used to protect credit card transactions. Algebraic topology successfully explains the phase transition of 2-dimensional materials like graphene and created a new area called topological physics to which 2016 Nobel Prize was awarded. Topology, by observe the shape of big data, also gave us a new way of predicting/diagnosing diabetes and breat cancer.

The renormalized spectral zeta function of the quantum Rabi Hamiltonian is considered.

It is shown that the renormalized spectral zeta function converges to the Riemann zeta function as the coupling constant goes to infinity. Moreover the path measure associated with the ground state of the quantum Rabi Hamiltonian is constructed on a discontinuous path space, and several applications are shown.

In this talk, we discuss the use of parallel computing  for mathematical problems. In particular, we provide a GPU-friendly algorithm for obtaining all weak pseudo-manifolds whose facets are all in an input set of facets satisfying given conditions.

Finite-time singularities in differential equations, such as blow-up and extinction, are ones of significant events which breaks solvability and/or regularity of solutions. In the present talk, a unified description of such singularities by means of dynamics at infinity is provided.

Starting at basic descriptions, computer-assisted proofs via rigorous numerics for “saddle-type” blow-ups (i.e., blow-ups with sensitive dependence on initial values), a novel correspondence between asymptotic expansions and dynamics at infinity are developed.

NIMS operates a support process aimed at addressing industrial challenges through mathematics, and this talk provides a summary of a problem-solving process requested by a company. Unlike traditional industrial robots that are isolated from humans, collaborative robots operate in shared spaces with humans without physical barriers. To analyze the motion of these robots and perform safety evaluations, it is necessary to estimate the via points of the path plan using the observed robot motion data. This talk covers algorithms used for estimating via points and discusses the difficulties encountered during the process.

This talk summarizes and reviews some of my recent results on the inverse design and optimization of functional materials and nano-architectures for specific functionalities. In the first part, I will describe an AI-assisted platform that combines Density Functional Theory, Machine Learning, and evolutionary algorithms for optimizing ring-opening in nano-switches.

Starting from a minimal initial parent set, our program iteratively generates cascades of candidate pools, performing optimization and down-selection without requiring human supervision at any stage. We use Density Functional Theory in conjunction with transition state theory to elucidate the exact mechanism leading to ring opening. The program successfully identifies a large class of derivatives with enhanced ring-opening properties. Our platform is modular, and our current implementation could be further generalized to more complex systems by substituting the quantum chemical and fingerprinting modules.

In the second part of my talk, I will focus on the modeling and analysis of mechanical systems at the continuum scale. The main modeling question we address is how to tailor topological defects in crystalline membranes to achieve desired Gaussian curvature. This task requires the construction of a rigorous variational theory for modeling systems of interacting topological defects (disclinations and dislocations) on a lattice, as well as modeling the coupling of 3D deformations with lattice mismatches in plates. Future developments on the integration of these two approaches at the continuum and nano-scale will also be discussed.

We consider a system of nonlinear partial differential equations modeling the steady motion of an incompressible non-Newtonian fluid, which is chemically reacting. The governing system consists of a steady convection-diffusion equation for the concentration and the generalized steady Navier--Stokes equations, where the viscosity coefficient is a power-law type function of the shear-rate, and the coupling between the equations results from the concentration-dependence of the power-law index. This system of nonlinear partial differential equations arises in mathematical models of the synovial fluid found in the cavities of moving joints. We construct a finite element approximation of the model and perform the mathematical analysis of the numerical method. Key technical tools include discrete counterparts of the Bogovskii operator, De Giorgi’s regularity theorem in two dimensions, and the Acerbi-Fusco Lipschitz truncation of Sobolev functions, in function spaces with variable integrability exponents.

This presentation introduces an elementary theorem in graph theory. Specifically, we examine an operation that assigns orientations to the faces of a triangulated planar graph based on vertex labeling and discuss its properties. As a particular corollary, we derive Sperner’s lemma, a well-known discrete version of the fixed-point theorem.

Textual data is generally large-sized and complicated to interpret, therefore effective dimensional reduction and information extraction is needed to understand the data. Hence, traditional and well-known methods for dimension reduction is not enough to be applied to textual data due to its various characteristics. In this talk, we propose the FDR control method-based text visualization algorithm in form of network structure, which implies word-to-word relationship as an edge interconnecting words. Furthermore, to minimize the information loss, LDA(Latent Dirichlet Allocation) topic modeling by the optimal number of topic decided by coherence is applied.

We explore the concept of obtaining control gains through the Linear Quadratic Regulator (LQR) method in control systems. We begin to introduce the fundamental principles of LQR, mathematical formulation, and the assumptions underlying its application. We then discuss step-by-step process of designing an LQR-based controller, emphasizing criteria to minimize cost function subject to a given system and the derivation of the Riccati equation.

Underground utility detection plays a critical role in modern construction and maintenance, ensuring the safety and integrity of infrastructure projects. The data was collected using electrical resistivity method using numerical analysis module. This study introduces a novel feature engineering method that using Kriging interpolation to extract spatial features from data to accurately detect buried utilities, especially pipes. Then using deep learning techniques, particularly Convolutional Neural Networks (CNNs) to analyzed the spatial features more and achieved high predictive accuracy.

The speaker is a lawyer conducting research on applying mathematics to solve legal problems. Such attempts are uncommon in Japan, and probably in other countries as well. In this presentation, the speaker will introduce various approaches to modeling legal problems mathematically, using probability, mathematical logic, and graph theory. Although these approaches are still in their early stages, the speaker believes that these efforts will eventually provide more objective and quantitative criteria for legal reasoning to enhance its precision, consistency, and transparency.

This study aims to provide early intervention strategies and improvements in mental health outcomes by identifying key risk factors for healthy populations.

Mood disorders represent a significant public health concern, making early detection crucial for timely intervention. While previous research has focused on analyzing sleep-wake patterns in individuals already diagnosed with mood disorders, this study aims to evaluate the risk of mood disorders by analyzing sleep-wake pattern data collected from healthy individuals using wearable devices. The dataset, which is publicly available, provided detailed information on various aspects of sleep behavior and quality.

We extracted 20 sleep indices from the dataset, capturing different dimensions of sleep patterns. To assess the potential risk of mood disorders, we employed the XGBoost algorithm for regression analysis. This approach enables us to predict mood disorder risk with a high degree of accuracy, potentially allowing for the early identification of at-risk individuals before clinical symptoms emerge.

Furthermore, we plan to conduct a subsequent analysis to determine which specific sleep indices are the most critical in predicting mood disorders.

We investigate the existence and regularity of solutions to the Von Kármán equations, which are a widely used model for nonlinear deflection in thin plates, in the presence of kinematic incompatibility for the membrane strain. Our proof utilizes the direct method in the calculus of variations, following a similar approach to Ciarlet's classical proof for kinematically compatible plates. A direct application of our analysis is in the continuum modeling of graphene sheets in the presence of disclinations in the crystal lattice. Additionally, we present numerical solutions obtained via a Finite Element formulation of the equations.  As the Von Kármán equations are a set of non-linear, coupled, 4th order elliptic equations, we employ the discontinuous Galerkin finite element methods for boundary-value problems involving the biharmonic operator.