425 research outputs found

    Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations

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    We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges.Comment: Talk given at the Workshop "Nonlinear Physics: Theory and Experiment. V", Gallipoli (Lecce, Italy), 12-21 June, 200

    ELAC2/RNaseZ-linked cardiac hypertrophy in Drosophila melanogaster

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    A severe form of infantile cardiomyopathy (CM) has been linked to mutations in ELAC2, a highly conserved human gene. It encodes Zinc phosphodiesterase ELAC protein 2 (ELAC2), which plays an essential role in the production of mature tRNAs. To establish a causal connection between ELAC2 variants and CM, here we used the Drosophila melanogaster model organism, which carries the ELAC2 homolog RNaseZ. Even though RNaseZ and ELAC2 have diverged in some of their biological functions, our study demonstrates the use of the fly model to study the mechanism of ELAC2-related pathology. We established transgenic lines harboring RNaseZ with CM-linked mutations in the background of endogenous RNaseZ knockout. Importantly, we found that the phenotype of these flies is consistent with the pathological features in human patients. Specifically, expression of CM-linked variants in flies caused heart hypertrophy and led to reduction in cardiac contractility associated with a rare form of CM. This study provides first experimental evidence for the pathogenicity of CM-causing mutations in the ELAC2 protein, and the foundation to improve our understanding and diagnosis of this rare infantile disease. This article has an associated First Person interview with the first author of the paper

    Dressing chain for the acoustic spectral problem

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    The iterations are studied of the Darboux transformation for the generalized Schroedinger operator. The applications to the Dym and Camassa-Holm equations are considered.Comment: 16 pages, 6 eps figure

    Experimental evaluation of digitally verifiable photonic computing for blockchain and cryptocurrency

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    As blockchain technology and cryptocurrency become increasingly mainstream, photonic computing has emerged as an efficient hardware platform that reduces ever-increasing energy costs required to verify transactions in decentralized cryptonetworks. To reduce sensitivity of these verifications to photonic hardware error, we propose and experimentally demonstrate a cryptographic scheme, LightHash, that implements robust, low-bit precision matrix multiplication in programmable silicon photonic networks. We demonstrate an error mitigation scheme to reduce error by averaging computation across circuits, and simulate energy-efficiency-error trade-offs for large circuit sizes. We conclude that our error-resistant and efficient hardware solution can potentially generate a new market for decentralized photonic blockchain

    Gauge-invariant description of some (2+1)-dimensional integrable nonlinear evolution equations

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    New manifestly gauge-invariant forms of two-dimensional generalized dispersive long-wave and Nizhnik-Veselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous two-dimensional generalization of dispersive long-wave system of equations, Nizhnik-Veselov-Novikov and modified Nizhnik-Veselov-Novikov equations and other known and new integrable nonlinear equations arise. Miura-type transformations between nonlinear equations in different gauges are considered.Comment: 13 pages, LaTeX, no figure

    Functional representations of integrable hierarchies

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    We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which `functional representations' of particular hierarchies (like KP, discrete KP, mKP, AKNS), i.e. formulations in terms of functional equations, are systematically and quite easily obtained. The formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative (typically matrix) algebra. The obtained functional representations can be understood as `noncommutative' analogs of `Fay identities' for the KP hierarchy.Comment: 21 pages, version 2: equations (3.28) and (4.11) adde
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