Related papers: An interview with Tsuyoshi Ando
A large body of research demonstrates how teachers' questioning strategies can improve student learning outcomes. However, developing new scenarios is challenging because of the lack of training data for a specific scenario and the costs…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
This is a survey lecture note on the applications of Langlands functoriality which were obtained recently by some people at the Langalnds school. This lecture was delivered at the Department of Mathematics, Kyoto University, Japan on June…
The theory of one-sided coupled operator matrices, recently introduced by K.-J. Engel, is an abstract framework for concrete initial value problems and allows complete information on well-posedness, and stability of solutions. These notes…
This text reviews, hopefully in a pedagogical manner, a series of work on the automatic calculations of Feynman diagrams in the context of quantum nanoelectronics (Keldysh formalism) with an application to the Kondo effect in the…
Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this…
In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of complementability in the sense of Ando for operators, and study the…
In this dissertation I would like to guide the reader to the research on dialogue but more precisely the research I have conducted during my career since my PhD thesis. Starting from modular architectures with machine learning/deep learning…
The interplay between the Kondo effect and disorder is studied. This is done by applying a matrix coherent potential approximation (CPA) and treating the Kondo interaction on a mean-field level. The resulting equations are shown to agree…
This review article provides an overview of the physics of the two-channel Kondo impurity model as manifested in two-level systems in metals and certain actinide/lanthanide ions in metals. Basic models are presented, followed by a…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
The main goal of this paper is to discuss the recent advancements of operator means for accretive matrices in a more general setting. In particular, we present the general form governing the well established definition of geometric mean,…
This article reports the argumentation work of a group of trainee mathematics teachers in an experiment carried out in a virtual class (due to the emergence of COVID-19) during 2020. They worked with a task on fractions in an online…
The aim of this paper is to study some aspects of matrix theory through Pasting and Reversing. We start giving a summary of previous results concerning to Pasting and Reversing over vectors and matrices, after we rewrite such properties of…
The word 'researcher' is loaded and often confusing. It takes years to become one and to master all of its aspects. In this paper, we investigate whether or not this process of 'becoming' can be catalyzed through education. The focus will…
Not only did Turing help found one of the most exciting areas of modern science (computer science), but it may be that his contribution to our understanding of our physical reality is greater than we had hitherto supposed. Here I explore…
We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding…
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
Machine learning is currently involved in some of the most vigorous debates it has ever seen. Such debates often seem to go around in circles, reaching no conclusion or resolution. This is perhaps unsurprising given that researchers in…