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YouTube: Less could be more - diagonalize matricesPublic

2024-07-12

Less could be more - diagonalize matrices

多田 司 (数理創造プログラム 副プログラムディレクター)

When we handle matrices, which are ubiquitous, especially in quantum physics and information theory, we try to diagonalize them. While diagonalized matrices exhibit familiar features with ordinary numbers, such as commutativity, they sometimes elude our intuition. In this talk, I introduce a new approach that has recently attracted much attention: one that handles matrices by not totally diagonalizing but leaving two upper and lower adjacent elements to the diagonal elements non-zero, which yields tridiagonal matrices.

2024-07-05

Superconductors and superfluids as macroscopic quantum condensates

関野 裕太 (数理創造プログラム 特別研究員 / 理化学研究所 開拓研究本部 (CPR) 濱崎非平衡量子統計力学理研白眉研究チーム 特別研究員)

Superconductors and superfluids are states of matter where dissipationless transport occurs due to macroscopic manifestations of quantum mechanical effects. These states of matter appear in various physical systems, such as Bose-Einstein condensates of ultracold atomic gases, liquid helium, superconductors in solids, and probably nuclear matter inside neutron stars, attracting interest across various fields of science. In this talk, I will explain the basics of quantum condensation, the mechanism behind macroscopic quantum effects in superconductivity and superfluidity.

2024-06-28

Y chromosome – An entity of an evolutionary dead-end?

野澤 昌文 (東京都立大学 准教授)

In many organisms with genetic sex determination, sex chromosomes (X and Y or Z and W, hereafter) have emerged from a pair of autosomes. Then, the X and Y (or Z and W) stop recombination in meiosis to maintain stable sex determination, which is inevitable in many cases. Consequently, many genes on the Y are nonfunctionalized or lost due to inefficacy of natural selection. Indeed, our humans only have ~70 genes on the Y while maintaining >800 genes on the X. However, the Y is still indispensable because the Y harbors the male-determination gene. Therefore, the Y has been regarded as an evolutionary dead-end, i.e., a sandwich between two evolutionary forces: degeneration and maintenance. I will introduce the situation of the Y in several organisms.

2024-06-21

A brief introduction to data-driven dynamical systems

黒澤 元 (数理創造プログラム 専任研究員)

Imagine that you are in a cave. The room is in a cave so that temperature and light-intensity are constant over time. Can you wake up tomorrow or day after tomorrow? In fact, most humans can wake up tomorrow and day after tomorrow almost regularly. How is it possible? To consider such a question, dynamical systems provide a mathematical framework to model interactions between quantities that evolve over time. Usually, the equations governing these systems are unknown or only partially known. Predicting and controlling such systems can be challenging. Recently, data-driven approaches have made significant strides in uncovering the equations of dynamical systems, predicting their behavior, and controlling them. In this presentation, I will review these approaches from the literature, which can be possibly applicable not only to daily rhythms but also to various other fields.

2024-06-14

What is density functional theory?

横田 猛 (数理創造プログラム 基礎科学特別研究員)

Matter in the world consists of numerous quantum particles, such as electrons and nucleons. Its properties are dictated by the Schrödinger equations for many-body systems. However, directly solving these equations poses a formidable computational challenge. Density Functional Theory (DFT), established by Hohenberg, Kohn, and Sham in the 1960s, represents one of the most successful methods for addressing many-body systems. It offers scalable approximations based on the variational principle concerning density. DFT is particularly notable for its perspective on the quantum world, wherein the ground-state density serves as an alternative to the wave function. In this talk, I will provide a brief introduction to DFT.

2024-06-07

An intriguing property of neural networks (up to date)

田中 章詞 (数理創造プログラム 上級研究員 / 理化学研究所 革新知能統合研究センター (AIP) 上級研究員)

Neural networks have played a central role in the recent development of machine learning technology, but their properties remain mysterious, and it would be interesting if these could be mathematically modeled. For example, in word embedding in a language model, it is known that "king vector" representing the word "king" appears in the learning process, and that the vector obtained by subtracting "queen vector" from "king vector" becomes a vector representing the change of words from female to male. In this talk, I would like to briefly explain that this kind of "concept arithmetic," is also possible among the weight parameters of trained neural networks, which is called "task arithmetic".

2024-05-31

An Introduction of Room Acoustics: Theory of Reverberation Time

儀保 伸吾 (数理創造プログラム 特別研究員)

It is important to predict and optimize the acoustics of a room before building the room. One of the most important indexes in the room acoustics is the reverberation time, which is defined as the time it takes for the sound energy to decay by a factor of 10^{-6}. If the reverberation time is too long, understanding speech in the room becomes difficult. Conversely, if the reverberation time is too short, we may not enjoy music in the room. In this talk, I will briefly explain the theory of the reverberation time.

2024-05-24

Unique Characterizations of Thermodynamic Entropy

横倉 祐貴 (数理創造プログラム 上級研究員)

Entropy has special properties related to heat, microscopic degrees of freedoms, and macroscopic irreversibility. I will explain that these are connected each other through dynamics, and add a new characterization: symmetry of entropy.

2024-05-17

Weather forecast and deep learning

大塚 成徳 (数理創造プログラム 研究員 / 理化学研究所 計算科学研究センター (R-CCS) データ同化研究チーム 研究員)

In this talk, I will introduce application of deep learning to weather forecasting. Recent years, tech companies, such as NVIDIA, Huawei, and Google, reported their deep learning-based global weather prediction models. These models were trained on so-called atmospheric reanalyses to emulate computationally demanding numerical weather prediction models. Although we still need physically-based models for various purposes, deep learning may change the future of weather predictions.

YouTube: Forming black holes from starsPublic

2024-05-10

Forming black holes from stars

ルーシー・マクニール (数理創造プログラム 特別研究員)

Black holes which are the remnants of stars are being detected at a rate of a few per month using various optical telescopes and gravitational wave interferometers. They provide fruitful opportunity to test and challenge stellar evolution theory, which depends sensitively on our understanding of general relativity, quantum mechanics, particle physics and nuclear physics. In this coffee talk, I will present the physical concepts and mathematical scalings behind the formation of a black hole, after a star’s iron core collapses. I will quantify the key length, time and energy scales involved, and the (possibly surprising) importance of neutrino transport.

2024-04-26

Exotica in Mathematics

佐野 岳人 (数理創造プログラム 基礎科学特別研究員)

Since the discovery of an exotic 7-dimensional sphere by J. Milnor in 1956, the study of exotic phenomena has become one of the central topics in topology. Here, an exotic sphere is a smooth manifold that is homeomorphic, but not diffeomorphic, to the standard sphere. In this talk, I will briefly explain the history of the discoveries of exotic phenomena and discuss some of the recent achievements related to knot theory.

2024-04-19

A gentle introduction to fluid turbulence

カミリア・デミデム (数理創造プログラム 研究員)

Turbulence is everywhere around us, manifesting itself in seemingly trivial aspects of daily life, such as the act of pouring milk into coffee, while also shaping critical processes in fusion reactors, atmospheric dynamics and astrophysical phenomena. In this talk, I will try to review some fundamental aspects of turbulence and explain why it is so challenging to model it.

YouTube: Singularity TheoremsPublic

2024-04-12

Singularity Theorems

長瀧 重博 (数理創造プログラム 副プログラムディレクター / 理化学研究所 開拓研究本部 (CPR) 長瀧天体ビッグバン研究室 主任研究員)

I am happy to introduce the Singularity Theorem, which was proved by Roger Penrose in 1965. He won the Nobel Prize in Physics in 2020 by the proof. I hope you will feel the outline of the proof and understand that the Singularity corresponds to a point outside of spacetime. If there is 1 minute left in my presentation, I would like to mention that Roger Penrose and Stephen Hawking proved the existence of (a) singularity(ies) in natural conditions at the beginning of our universe. Einstein's equation for general relativity is a kind of God's equation, but singularity theorems strongly suggest the limitation of general relativity. I want to thank Prof. Fujikawa, who requested that I give a presentation on the Singularity Theorems. His request motivated me to prepare for my presentation (originally, I was planning to give a short talk on stellar physics using a part of my notebook that I used in my lecture course at OIST).

2024-03-29

Quantum channel characterization

松浦 俊司 (数理創造プログラム 客員研究員 / Senior Researcher, Hardware Inovation Lab, 1QBit, Canada)

The greatest challenge in building a quantum computer is noise. Suppressing noise in quantum systems is extremely difficult, which has led to a long-standing skepticism about the feasibility of quantum computers. So, what exactly is noise in the context of quantum computers? How is it characterized, and how is it measured? In this talk, we will discuss the nature of noise and, as specific examples of methods for characterizing it, we will talk about randomized benchmarking and tomography.

2024-03-22

ORCID to auto-report your research contributions & manage your online visibility

カトゥリン・ボシゥメン (数理創造プログラム 副プログラムディレクター / Professor, Department of Physics, Toronto Metropolitan University, Canada)

We all have to report our papers (and grants) activities at least once per year to the institutions we work for. Different employers have different systems (e.g. RIKEN has RARS) and it is tiresome to fill these forms again and again. We also want to share or make this information visible to the wider scientific community, as part of looking for a new jobs or for new collaborators. Again a lot of different tools and databases exist (Scopus, Web of Science, Dimensions, Google Scholar, ResearchGate, Pubmed, etc.). In this talk I want to tell you about ORCID: what it is and what it can do for you. Especially, how it can help you solve the problems of reporting and widely disseminating your research accomplishments to the community across the different platforms, while managing it in just one place: your ORCID record. I'll demonstrate some of nice applications.

2024-03-15

What is a Mathematical Model to Replicate Filtration Phenomena?

古川 賢 (数理創造プログラム 特別研究員 / 理化学研究所 開拓研究本部 (CPR) 三好予測科学研究室 特別研究員)

I will discuss a mathematical model concerning filtration of water and air. I will demonstrate how filtration phenomena can be mathematically replicated using special (less known) boundary conditions. I will also explain why these boundary conditions are necessary and discuss future possibilities.

2024-03-08

Kin selection and social evolution

トーマス・ヒッチコック (数理創造プログラム 基礎科学特別研究員)

All of life is social, yet the evolution of social traits posed a problem to classical Darwinian thinking for over a century. I will introduce the concepts of kin selection, relatedness, and inclusive fitness and talk about how these resolved the puzzle of altruistic behaviours and revolutionised behavioural ecology in the process. I will then discuss how the scope of social evolution has expanded over the years to tackle a wider set of questions, including the origins of individuality itself.

2024-03-01

Molecular evolution and the neutral theory

ジェフリ・フォーセット (数理創造プログラム 上級研究員)

Understanding how biological diversity is created is one of the most fundamental goals in biology. While the work of Charles Darwin formed the basic framework of Evolution, especially by highlighting the role of natural selection, it was the work of Motoo Kimura, who proposed the Neutral Theory and highlighted the role of stochastic processes, that formed the theoretical framework of molecular (i.e., DNA/RNA/protein) evolution. Here, I will explain the basic ideas of the Neutral Theory and the processes involved in creating the diversity at the molecular level.

2024-02-16

Welcome to the new world, "Particle Zoo 2.0"

土井 琢身 (数理創造プログラム 専任研究員)

In 1960s, many new "fundamental" particles were found and called "Particle Zoo". Their systematic classification lead to the discovery of elementary particles, quarks. Since the beginning of 21c, however, a new kind of mysterious (exotic) particles are unexpectedly being discovered. In this talk, I will introduce this new world of "Particle Zoo 2.0" and its impact.

2024-02-09

The undervalued and misunderstood importance of taxonomy in century 21th

ホセ サイード・グティエレス オルテガ (数理創造プログラム 基礎科学特別研究員)

Taxonomy, the branch of biology that classifies the living beings and give them scientific names, is not a hypothesis-driven science but a descriptive discipline that suffers of a great undervaluation in century 21th. Taxonomic papers will never be published in high impact journals, they won’t get many citations (if any), and getting funding for pure taxonomic research is basically impossible. Furthermore, taxonomy is often criticized for its apparent arbitrariness on how researchers decide to give name to a species, and attaching a scientific name to a group of organisms often seems trivial in a moment when in biology the definition of “species" is heavily discussed. Certainly, this is not a good moment for a biologist to specialize in taxonomy. (Un)fortunately, my research line somehow directed me to become a “part-time taxonomist”, which compels me to try to understand and overcome the challenges of this discipline. I will tell a few of my experiences as a taxonomist and will tell you about, in my opinion, the hottest topic in the modern history of taxonomy: should taxonomy be reinvented by updating its conventional rules?