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  • 1
    Book
    Book
    Basel u.a. :Birkhäuser,
    Title: Erfahrung Mathematik
    Author: Davis, Philip J.
    Contributer: Hersh, Reuben
    Publisher: Basel u.a. :Birkhäuser,
    Year of publication: 1985
    Pages: 466 S.
    Type of Medium: Book
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  • 2
    Title: Descartes Traum: über die Mathematisierung von Zeit und Raum. Von denkenden Computern, Politik und Liebe : Descartes' dream : the world according to mathematics, dt.
    Author: Davis, Philip J.
    Contributer: Hersh, Reuben
    Publisher: W. Krüger,
    Year of publication: 1988
    Pages: 422 S.
    Type of Medium: Book
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  • 3
    Book
    Book
    Cambridge, MA u.a. :MIT Press,
    Title: Data-parallel programming on MIMD computers
    Author: Hatcher, Philip J.
    Contributer: Quinn, Michael J.
    Publisher: Cambridge, MA u.a. :MIT Press,
    Year of publication: 1991
    Pages: 231 S.
    Series Statement: Scientific and Engineering Computation Series
    Type of Medium: Book
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  • 4
    Book
    Book
    Mineola, N.Y. :Dover,
    Title: Interpolation and approximation
    Author: Davis, Philip J.
    Publisher: Mineola, N.Y. :Dover,
    Year of publication: 1975
    Pages: 393 S.
    Type of Medium: Book
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  • 5
    Publication Date: 2014-02-26
    Description: In an array of coupled oscillators {\em synchronous chaos} may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries and this leads to the idea of {\em symmetry breaking bifurcations of chaotic attractors}. Finally the results and ideas are illustrated for several systems of coupled oscillators.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 6
    Publication Date: 2022-07-19
    Description: SpiNNaker is a digital, neuromorphic architecture designed for simulating large-scale spiking neural networks at speeds close to biological real-time. Rather than using bespoke analog or digital hardware, the basic computational unit of a SpiNNaker system is a general-purpose ARM processor, allowing it to be programmed to simulate a wide variety of neuron and synapse models. This flexibility is particularly valuable in the study of biological plasticity phenomena. A recently proposed learning rule based on the Bayesian Confidence Propagation Neural Network (BCPNN) paradigm offers a generic framework for modeling the interaction of different plasticity mechanisms using spiking neurons. However, it can be computationally expensive to simulate large networks with BCPNN learning since it requires multiple state variables for each synapse, each of which needs to be updated every simulation time-step. We discuss the trade-offs in efficiency and accuracy involved in developing an event-based BCPNN implementation for SpiNNaker based on an analytical solution to the BCPNN equations, and detail the steps taken to fit this within the limited computational and memory resources of the SpiNNaker architecture. We demonstrate this learning rule by learning temporal sequences of neural activity within a recurrent attractor network which we simulate at scales of up to 2.0 × 10^4 neurons and 5.1 × 10^7 plastic synapses: the largest plastic neural network ever to be simulated on neuromorphic hardware. We also run a comparable simulation on a Cray XC-30 supercomputer system and find that, if it is to match the run-time of our SpiNNaker simulation, the super computer system uses approximately 45× more power. This suggests that cheaper, more power efficient neuromorphic systems are becoming useful discovery tools in the study of plasticity in large-scale brain models.
    Language: English
    Type: article , doc-type:article
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  • 7
    Publication Date: 2022-07-19
    Language: English
    Type: poster , doc-type:Other
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  • 8
    Publication Date: 2023-02-06
    Description: This article considers non-stationary incompressible linear fluid equations in a moving domain. We demonstrate the existence and uniqueness of an appropriate weak formulation of the problem by making use of the theory of time-dependent Bochner spaces. It is not possible to directly apply established evolving Hilbert space theory due to the incompressibility constraint. After we have established the well-posedness, we derive and analyse a time discretisation of the system.
    Language: English
    Type: article , doc-type:article
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  • 9
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    BJOG 102 (1995), S. 0 
    ISSN: 1471-0528
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Medicine
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 9871-9881 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Fluids of hard bent-core molecules have been studied using theory and computer simulation. The molecules are composed of two hard spherocylinders, with length-to-breadth ratio L/D, joined by their ends at an angle 180°−γ. For L/D=2 and γ=0,10,20°, the simulations show isotropic, nematic, smectic, and solid phases. For L/D=2 and γ=30°, only isotropic, nematic, and solid phases are in evidence, which suggests that there is a nematic-smectic-solid triple point at an angle in the range 20°〈γ〈30°. In all of the orientationally ordered fluid phases the order is purely uniaxial. For γ=10° and 20°, at the studied densities, the solid is also uniaxially ordered, whilst for γ=30° the solid layers are biaxially ordered. For L/D=2 and γ=60° and 90° we find no spontaneous orientational ordering. This is shown to be due to the interlocking of dimer pairs which precludes alignment. We find similar results for L/D=9.5 and γ=72°, where an isotropic-biaxial nematic transition is predicted by Onsager theory. Simulations in the biaxial nematic phase show it to be at least mechanically stable with respect to the isotropic phase, however. We have compared the quasi-exact simulation results in the isotropic phase with the predicted equations of state from three theories: the virial expansion containing the second and third virial coefficients; the Parsons–Lee equation of state; an application of Wertheim's theory of associating fluids in the limit of infinite attractive association energy. For all of the molecule elongations and geometries we have simulated, the Wertheim theory proved to be the most accurate. Interestingly, the isotropic equation of state is virtually independent of the dimer bond angle—a feature that is also reflected in the lack of variation with angle of the calculated second and third virial coefficients. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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