442 research outputs found
On the solutions of a functional equation arising from multiplication of quantum integers
No full textAbstractThis paper is the first of several papers in which we prove, for the case where the fields of coefficients are of characteristic zero, four open problems posed in the work of Melvyn Nathanson (2003) [1] concerning the solutions of a functional equation arising from multiplication of quantum integers [n]q=qn−1+qn−2+⋯+q+1. In this paper, we prove one of the problems. The next papers, namely [2–4] by Lan Nguyen, contain the solutions to the other 3 problems
On a nilpotent lie superalgebra which generalizes Qn
No full textIn [6] and [7] the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra Ln are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Qn, which only exists in even dimension as a consequence of the centralizer property. Certain central extensions of Qn which preserve both the nilindex and the cited property are also generalized to obtain nonfiliform Lie superalgebras.In [6] and [7] the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra Ln are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Qn, which only exists in even dimension as a consequence of the centralizer property. Certain central extensions of Qn which preserve both the nilindex and the cited property are also generalized to obtain nonfiliform Lie superalgebras
QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction
No full textInverse problems span across diverse fields. In medical contexts, computed
tomography (CT) plays a crucial role in reconstructing a patient's internal
structure, presenting challenges due to artifacts caused by inherently
ill-posed inverse problems. Previous research advanced image quality via
post-processing and deep unrolling algorithms but faces challenges, such as
extended convergence times with ultra-sparse data. Despite enhancements,
resulting images often show significant artifacts, limiting their effectiveness
for real-world diagnostic applications. We aim to explore deep second-order
unrolling algorithms for solving imaging inverse problems, emphasizing their
faster convergence and lower time complexity compared to common first-order
methods like gradient descent. In this paper, we introduce QN-Mixer, an
algorithm based on the quasi-Newton approach. We use learned parameters through
the BFGS algorithm and introduce Incept-Mixer, an efficient neural architecture
that serves as a non-local regularization term, capturing long-range
dependencies within images. To address the computational demands typically
associated with quasi-Newton algorithms that require full Hessian matrix
computations, we present a memory-efficient alternative. Our approach
intelligently downsamples gradient information, significantly reducing
computational requirements while maintaining performance. The approach is
validated through experiments on the sparse-view CT problem, involving various
datasets and scanning protocols, and is compared with post-processing and deep
unrolling state-of-the-art approaches. Our method outperforms existing
approaches and achieves state-of-the-art performance in terms of SSIM and PSNR,
all while reducing the number of unrolling iterations required.Comment: Accepted at CVPR 2024. Project page:
https://towzeur.github.io/QN-Mixer
Performing the Author
No full textchs wird in seinem Aufbau durch die drei Phasen des Selbstfindungsprozesses, genauer der Selbsterfindung der ‚Schriftstellerin Yū Miri‘ in ihren Werken und ihren medialen Selbstinszenierungen strukturiert. Es gelingt Iwata-Weickgenannt sehr überzeugend, das Sichtbarmachen der performativen Konstruiertheit von Identität im Werk und Leben Yūs herauszuarbeiten. Sie zeigt dabei auch, dass das Konzept der Performativität ein sehr geeigneter Bezugsrahmen für die Analyse von Identitätsbildungsprozessen ist.The Japanese-Korean author Yū Miri (born in 1968), still fairly unknown in Germany, belongs to those successful contemporary Japanese authors for whom it is typical to be known and celebrated not only for their texts but also for their excessive media presence. The multimedia staging by the author of her self as the ‘author Yū Miri’ sparks just as much interest in the Japanese public and literary scene as do her literary texts. In her book, published by the Munich-based house Iudicium Verlag, Iwata-Weickgenannt provides not only a comprehensive overview of Yū’s literary works published between the years of 1994 and 2005, but she also thematizes the medial representation of ‘Yū Miri’ in her analyses. In the first section of her book, Iwata-Weickgenannt provides a very good overview of the field out of which Yū’s identity problematic as a Japanese-Korean author arises. The second main section of the book is structured along the three phases of the self-discovery process, or rather the self-creation process, o
Asymptotics of degrees and ED degrees of Segre products
No full textFunding Information: We thank Jay Pantone for very useful conversations. We thank the referees for useful comments. The first two authors are members of INDAM-GNSAGA. The third author would like to thank The Department of Mathematics of Universit? di Firenze, where this project started in June 2018, for the warm hospitality and financial support. The first author is supported by the H2020-MSCA-ITN-2018 project POEMA. The second author is partially supported by the Academy of Finland Grant 323416. The third author is supported by Vici Grant 639.033.514 of Jan Draisma from the Netherlands Organisation for Scientific Research. Publisher Copyright: © 2021 The Author(s)Two fundamental invariants attached to a projective variety are its classical algebraic degree and its Euclidean Distance degree (ED degree). In this paper, we study the asymptotic behavior of these two degrees of some Segre products and their dual varieties. We analyze the asymptotics of degrees of (hypercubical) hyperdeterminants, the dual hypersurfaces to Segre varieties. We offer an alternative viewpoint on the stabilization of the ED degree of some Segre varieties. Although this phenomenon was incidentally known from Friedland-Ottaviani's formula expressing the number of singular vector tuples of a general tensor, our approach provides a geometric explanation. Finally, we establish the stabilization of the degree of the dual variety of a Segre product X×Qn, where X is a projective variety and Qn⊂Pn+1 is a smooth quadric hypersurface.Peer reviewe
Single-Shot Readout of Singlet-Triplet Qubit States in a Si/SiGe Double Quantum Dot (abstract)
No full textQN/Quantum NanoscienceApplied Science
Alkali-doped Metal-phthalocyanines: Electronic Properties and Structure
No full textQN/Quantum NanoscienceApplied Science
Single Dopant Implantation into a Nanoscale MOSFET Devices
No full textQN/Quantum NanoscienceApplied Science
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