108,495 research outputs found
Hiroshi, Takaharo, and Kaneko Yasumura
No full textPhotograph of Hiroshi, Takaharu, and Kaneko Yasumura. Kaneko is holding a baby on her lap. A photo from: Kuni Yasumura Fuchita photo album (janm_akfu_01).The Fuchita Family Collection contains one photograph album with newspaper clippings compiled by Kuni Yasumura Fuchita. Subjects include the Manzanar incarceration camp, Buddhism, the Koyasan Buddhist Temple, Ikebanas, Japan, and Japanese Americans. Credit line: Japanese American National Museum (Gift of Lynn T. Akamine, 2005.163.25). The collection was digitized and made accessible online by CSUDH Gerth Archives and Special Collections
The Arakawa-Kaneko Zeta Function
No full textWe present a very natural generalization of the Arakawa-Kaneko zeta function introduced ten years ago by T. Arakawa and M. Kaneko. We give in particular a new expression of the special values of this function at integral points in terms of modified Bell polynomial. By rewriting Ohno’s sum formula, we are in a position to deduce a new class of relations between Euler sums and the values of zeta
A Method to Compute Averages over the Compact Stiefel Manifold
No full textThe aim of the present contribution is to extend the algorithm introduced in the paper S. Fiori and T. Tanaka, “An algorithm to compute averages on matrix Lie groups,” IEEE Transactions on Signal Processing, Vol. 57, No. 12, pp. 4734 - 4743, December 2009, to compute averages over the Stiefel manifold. The idea underlying the developed algorithms is that points on the Stiefel manifold are mapped onto a tangent space, where the average is taken, and then the average point on the tangent space is projected back to the Stiefel manifold. Based on this idea, a fixed-point algorithm is developed, and numerical examples are shown to support the analysis
Proof of Kaneko--Tsumura Conjecture on Triple T-Values
Full text linkMany -linear relations exist between multiple zeta values, the most interesting of which are various weighted sum formulas. In this paper, we generalized these to Euler sums and some other variants of multiple zeta values by considering the generating functions of the Euler sums. Through this approach we are able to re-prove a few known formulas, confirm a conjecture of Kaneko and Tsumura on triple -values, and discover many new identities.11 pages, streamline the draft so that only results relevant to the proof of the conjecture are presente
A Trigonometric Variant of Kaneko–Tsumura ψ-Values
No full textMany variations of the multiple zeta values have been found to play important roles in different branches of mathematics and theoretical physics in recent years, such as the cyclotomic/color version, which appears prominently in the computation of Feynman integrals. In this paper, we introduce a trigonometric variant of the Kaneko–Tsumura ψ-function (called the Kaneko–Tsumura ψ˜-function) and discover some nice properties similar to those for ordinary Kaneko–Tsumura ψ-values using the method of iterated integrals, which was first studied systematically by K.T. Chen in the 1960s. In particular, we establish some duality formulas involving the Kaneko–Tsumura ψ˜-function and alternating multiple T-values by adapting Yamamoto’s graphical representation method for computing special types of iterated integrals
Tangent-Bundle Maps on the Grassmann Manifold: Application to Empirical Arithmetic Averaging
No full textThe present paper elaborates on tangent-bundle maps on the Grassmann manifold, with application to subspace arithmetic averaging. In particular, the present contribution elaborates on the work about retraction/lifting maps devised for the Stiefel manifold in the recently published paper T. Kaneko, S. Fiori and T. Tanaka, “Empirical arithmetic averaging over the compact Stiefel manifold,” IEEE Trans. Signal Process., Vol. 61, No. 4, pp. 883-894, February 2013, and discusses the extension of such maps to the Grassmann manifold. Tangent-bundle maps are devised on the basis of the thin QR matrix decomposition, the polar matrix decomposition and the exponential map. Also, tangent-bundle pseudo-maps based on the matrix Cayley transform are devised. Theoretical and numerical comparisons about the devised tangent-bundle maps are performed in order to get an insight into their relative merits and demerits, with special emphasis to their computational burden. The averaging algorithm based on the thin-QR decomposition maps stands out as it exhibits the best trade off between numerical precision and computational burden. Such algorithm is further compared with two Grassmann averaging algorithms drawn from the scientific literature on an handwritten digits recognition data set. The thin-QR tangent-bundle maps-based algorithm exhibits again numerical features that make it preferable over such algorithms
Empirical Arithmetic Averaging over the Compact Stiefel Manifold
Full text linkThe aim of the present research work is to investigate algorithms to compute empirical averages of finite sets of sample-points over the Stiefel manifold by extending the notion of Pythagoras' arithmetic averaging over the real line to a curved manifold. The idea underlying the developed algorithms is that sample-points on the
Stiefel manifold get mapped onto a tangent space, where the average is taken, and then the average point on the tangent space is brought back to the Stiefel manifold, via appropriate maps. Numerical experimental results are shown and commented on in order to illustrate the numerical behaviour of the proposed procedure. The
obtained numerical results confirm that the developed algorithms converge steadily and in a few iterations and that they are able to cope with relatively large-size problems
Learning on the Compact Stiefel Manifold by a Cayley-Transform-Based Pseudo-Retraction Map
No full textThe present research takes its moves from previous contributions by the present authors on two topics, namely, neural learning on differentiable manifolds by manifold retractions and averaging over differentiable manifolds. Learning on differentiable manifolds is a general theory that allows a neural system that insists on curved smooth spaces to adapt its parameters without violating the constraints on the geometry of the parameter spaces. In particular, the present contribution focuses on learning on the compact Stiefel manifold by manifold retraction with application to averaging `tall-skinny' matrices and generalizes some contributions recently appeared in the scientific literature about such a topic
Totally dissipative systems
No full textIn a totally dissipative behavior, all non-trivial trajectories dissipate energy. A characterization of such behaviors is given in terms of properties of the one- and two-polynomial matrices associated with the supply rate and with their kernel- and image representation
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