658 research outputs found

    Double Dirichlet series and quantum unique ergodicity of weight 1/2 Eisenstein series

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    The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for {\Gamma}_0(4) leads to the study of certain double Dirichlet series involving GL2 automorphic forms and Dirichlet characters. We study the analytic properties of this family of double Dirichlet series (analytic continuation, convexity estimate) and prove that a subconvex estimate implies the QUE result.Comment: 45 pages, 4 figures. Several minor corrections. To appear in Algebra and Number theor

    Brain-derived neurotrophic factor is more highly conserved in structure and function than nerve growth factor during vertebrate evolution

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    Mammalian nerve growth factor (NGF) and brain-derived neurotrophic factor (BDNF) are members of a protein family with perfectly conserved domains arranged around the cysteine residues thought to stabilize an invariant three-dimensional scaffold in addition to distinct sequence motifs that convey different neuronal functions. To study their structural and functional conservation during evolution, we have compared NGF and BDNF from a lower vertebrate, the teleost fi.sh Xiphophorus, with the mammalian homlogues. Genomic clones encoding fish NGF and BDNF were isolated by cross-hybridization using probes from the cloned mammalian factors. Fish NGF and BDNF were expressed by means of recombinant vaccinia viruses, purified, and their neuronal survival specificities for different classes of neurons were found to mirror those of the mammalian factors. The half-maximal survival concentration for chick sensory neurons was 60 pg/ml for both fish and mammalian purifi.ed recombinant BDNF. However, the activity ofrecombinant fish NGF on both chick sensory and sympathetic neurons was 6 ng,lml, 75-fold lower than that of mouse NGF. The different functional conservation of NGF and BDNF is also reflected in their structures. The DNA-deduced amino acid sequences of processed mature fish NGF and BDNF showed, compared to mouse, 63% and 90% identity, respectively, indicating that NGF bad reached an optimized structure later than BDNF. The retrograde extrapolation of these data indicates that NGF and BDNF evolved at strikingly different rates ftom a common ancestral gene about 600 million years ago. By RNA gel blot anaJysis NGF mRNA was detected during late embryonie development; BDNF was present in adult brain

    An Approach to Complement Model-Based Vehicle Development by Implementing Future Scenarios

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    Today, vehicle development is already in a process of substantial transformation. Mobility trends can be derived from global megatrends and have a significant influence on the requirements of the developed vehicles. The sociological, technological, economic, ecological, and political developments can be determined by using the scenario technique. The results are recorded in the form of differently shaped scenarios; however, they are mainly document-based. In order to ensure a holistic approach in the sense of model-based systems engineering and to be able to trace the interrelationships of the fast-changing trends and requirements, it is necessary to implement future scenarios in the system model. For this purpose, a method is proposed that enables the consideration of future scenarios in model-based vehicle development. The procedure of the method is presented, and the location of the future scenarios within the system architectures is named. The method is applied and the resulting system views are derived based on the application example of an autonomous people mover. With the help of the described method, it is possible to show the effects of a change of scenario (e.g., best-case and worst-case) and the connections with the highest level of requirements: stakeholder need

    Tensor networks for quantum machine learning

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    Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems that classical computers are unable to solve efficiently. Their nature at the interface between physics and machine learning makes tensor networks easily deployable on quantum computers. In this review article, we shed light on one of the major architectures considered to be predestined for variational quantum machine learning. In particular, we discuss how layouts like MPS, PEPS, TTNs and MERA can be mapped to a quantum computer, how they can be used for machine learning and data encoding and which implementation techniques improve their performance
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