Elliptic Ding-Iohara-Miki Algebra and Related Topics (String theory, integrable systems and representation theory)

"String theory, integrable systems and representation theory". July 30～August 2, 2013. edited by Koji Hasegawa and Yasuhiko Yamada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.The elliptic Ding-Iohara-Miki algebra [Sa1] is an elliptic quantum group obtained from the free field realization of the elliptic Ruijsenaars operator. In this article, we review the free field realization of the elliptic Ruijsenaars operator, the elliptic Ding-Iohara-Miki algebra and related topics

On the sets of maximum points for generalized Takagi functions

Let φ be a continuous and periodic function on ℝ with period 1 and φ(0)=0. We consider the generalized Takagi function ƒφ defined by ƒφ(x)=Σ[n=0,∞]1/2ⁿφ(2ⁿx) and the set Mᵩ of maximum points of ƒᵩ in the interval [0,1]. When φ₀(x) is the function defined by the distance from x to the nearest integer, ƒᵩ₀ is just the Takagi function. Our aim is to seek a condition on φ in order that Mᵩ⊂Mᵩ₀

The Law of Military Operations and Self-Defense in the U.S.-Japan Alliance

While the United States and Japan share many values, their legal systems take distinct approaches to authorizing military operations. But the two approaches converge within the alliance structure—especially important with regard to implementing the international law of self-defense

Cognitive and neural underpinnings of goal maintenance in young children

Active maintenance of goal representations is an integral part of our mental regulatory processes. Previous developmental studies have highlighted goal neglect, which is the phenomenon caused by a failure to maintain goal representations, and demonstrated developmental changes of the ability to maintain goal representations among preschoolers. Yet, few studies have explored the cognitive mechanisms underlying preschoolers' development of goal maintenance. The first aim of this study was to test whether working memory capacity and inhibitory control contribute to goal maintenance using a paradigm for measuring goal neglect. Moreover, although recent studies have shown that preschoolers recruit lateral prefrontal regions in performing executive functions tasks, they could not specify the neural underpinnings of goal maintenance. Thus, the second aim was to examine whether lateral prefrontal regions played a key role in maintaining goal representations using functional near-infrared spectroscopy. Our results showed that developmental differences in inhibitory control predicted the degree of goal neglect. It was also demonstrated that activation in the right prefrontal region was associated with children's successful avoidance of goal neglect. These findings offer important insights into the cognitive and neural underpinnings of goal maintenance in preschoolers

Event-based Camera Tracker by ∇\nablat NeRF

When a camera travels across a 3D world, only a fraction of pixel value changes; an event-based camera observes the change as sparse events. How can we utilize sparse events for efficient recovery of the camera pose? We show that we can recover the camera pose by minimizing the error between sparse events and the temporal gradient of the scene represented as a neural radiance field (NeRF). To enable the computation of the temporal gradient of the scene, we augment NeRF's camera pose as a time function. When the input pose to the NeRF coincides with the actual pose, the output of the temporal gradient of NeRF equals the observed intensity changes on the event's points. Using this principle, we propose an event-based camera pose tracking framework called TeGRA which realizes the pose update by using the sparse event's observation. To the best of our knowledge, this is the first camera pose estimation algorithm using the scene's implicit representation and the sparse intensity change from events