Tensor renormalization group (TRG) approach is a variant of the real-space renormalization group to evaluate the path integral defined on the thermodynamic lattice, without resorting to any probabilistic interpretation for the given Boltzmann weight. Moreover, since the TRG can directly deal with the Grassmann variables, this approach can be formulated in the same manner for the systems with bosons, fermions, or both. These advantages of the TRG approach have been confirmed by the earlier studies of various lattice theories, which suggest that the TRG enables us to investigate the parameter regimes where it is difficult to access with the standard stochastic numerical methods, such as the Monte Carlo simulation. In this talk, explaining our recent applications of the TRG approach to several lattice models, we demonstrate the efficiency of the TRG as a tool to investigate lattice theories particularly in higher dimensions and future perspective.

In this lecture, basic concepts in quantum measurement theory are introduced, including measurement operators and POVM's. The related topics are also picked up.

Lecture 1: Nov. 10, 10:30 - 12:00
Lecture 2: Nov. 10, 13:30 - 15:00
Lecture 3: Nov. 10, 15:30 - 17:00
Lecture 4: Nov. 11, 10:30 - 12:00
Lecture 5: Nov. 11, 13:30 - 15:00
Lecture 6: Nov. 12, 10:30 - 12:00

Sociogenesis is a project that aims to study emergent social behaviors of multi-agent systems. In its simplest form, and agent simply seeks to survive by consuming food and maximizing some happiness score. In this presentation, I will discuss some motivations and inspirations of this project, as well as the challenges to get an agent to survive on its own. I will then showcase some methods to evaluate the quality of agents and their underlying architecture beyond simply looking at their lifespan. I will then conclude with some potential applications. No prior knowledge in reinforcement/deep learning is required to attend this presentation. This work is still mostly at an exploratory stage, so discussions and inputs from the audience are more than welcome!

The study of self-maps of algebraic varieties is a relatively new and active area in mathematics. Such a self-map can be considered as a discrete dynamical system, and we can study the asymptotic properties of such systems from various points of views, including number theoretic viewpoint. I will introduce several problems in arithmetic dynamics and some of my results in this area.

"MCME SYMPOSIUM 2022" will be held at the Musashino Center of Mathematical Engineering (MCME), Musashino University. This symposium is free of charge and open to everyone.
Colleagues of iTHEMS will also be speaking. Below is an excerpt from the program.

Wednesday, November 16, 13:30 - 14:40 Takemasa Miyoshi
Thursday, November 17, 10:00 - 11:10 Hidetoshi Taya
Thursday, November 17, 14:50 - 16:00 Hidetoshi Nishimori

Registration is open until November 14. Please register from the related links below.

Organized by Musashino Center of Mathematical Engineering (MCME), Musashino University
Co-organized by RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS)

Physiological states of bacterial cells exhibit a wide spectrum of timescale. Under nutrient-rich conditions, most of the cells in an isogenic bacterial population grow at certain rates, while a small subpopulation sometimes stays in a dormant state where the growth rates slow down by orders of magnitude. For revealing the origins of such heterogeneity of timescales, we studied the kinetic model of Escherichia coli central carbon metabolism. We found that the model robustly exhibits both the growing- and the dormant state. Performing the model reduction, we have revealed the necessary conditions for the distinct behaviour, namely, the depletion of energy due to the futile cycle and its non-uniform impact on the kinetics because of the coexistence of the energy currency-coupled and uncoupled reactions as well as branching of the network.

Abstract for the 1st hour: Enumerative Geometry has been a feature of mathematics from its beginnings, just think about the number of lines in the plane passing through 2 points. I will take you on a history of the subject and its relationship to other areas of mathematics and physics.

Abstract for the 2nd hour: Many problems in mathematics are solved by taking a limit and solving the limiting problem. Tropical geometry is a key technique that allows us to do this systematically. I will talk about the following problem. Take the complex projective plane S and an elliptic curve E in S. Count algebraic maps from the affine line into the complement S \ E. This counting problem is solved via tropical geometry as I will describe in this talk.

The continuous space Schrödinger equation is reformulated in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. A binary encoding of position produces a spin-1/2 Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code (BRGC), and a Hamming distance 2 Gray code (H2GC) reduces the model complexity down to the XZ and transverse Ising model respectively. Any real potential is mapped to a series of k-local Ising models through the fast Walsh transform. As a first step, the encoded Hamiltonian is simulated for quantum adiabatic evolution. As a second step, the time evolution is discretized, resulting in a quantum circuit with a gate cost that is better than the Quantum Fourier transform. Finally, a simple application on an ion-based quantum computer is provided as proof of concept.

People's incentives during an infectious disease outbreak influence their behaviour, and this behaviour can impact how the outbreak unfolds. Early on during an outbreak, people are at little personal risk of infection and hence may be unwilling to change their lifestyle to slow the spread of disease. As the number of cases grows, however, people may then voluntarily take extreme measures to limit their exposure. Political leaders also respond to the welfare and changing desires of their constituents, through public health policies that themselves shape the course of the epidemic and its ultimate health and economic repercussions. In this talk I will use ideas from the study of differential games to model how individuals’ and politicians’ incentives change during an outbreak, and the epidemiological and economic consequences that ensue when these incentives are acted upon. Motivated by the COVID-19 pandemic, I focus on physical distancing behaviour and the imposition of stay-at-home orders by politicians. I show that there is a fundamental difference in the political, economic, and health consequences of an infectious disease outbreak depending on the degree of asymptomatic transmission. If transmission occurs primarily by asymptomatic carriers, then politicians will be incentivized to impose stay-at-home orders earlier and for longer than individuals would like. Despite such orders being unpopular, however, they ultimately benefit all individuals. On the other hand, if the disease is transmitted primarily by symptomatic infections, then individuals are incentivized to stay at home earlier and for longer than politicians would like. In this case, politicians will be incentivized to impose back-to-work orders that, despite being unpopular, will again ultimately be to the benefit of all individuals.

This is joint work with David McAdams, Fuqua School of Business and Economics Department, Duke University.

Lattice gauge theory is a powerful computational approach in quantum field theory. It is also utilizable for investigating quantum phenomena in curved spacetimes, such as rotating frame, torsion, and gravitational backgrounds. In this talk, I would like to overview the formulation and results of lattice simulations in curved spacetimes.