4,877 research outputs found
The relation between the Toda hierarchy and the KdV hierarchy
Under three relations connecting the field variables of Toda flows and that
of KdV flows, we present three new sequences of combination of the equations in
the Toda hierarchy which have the KdV hierarchy as a continuous limit. The
relation between the Poisson structures of the KdV hierarchy and the Toda
hierarchy in continuous limit is also studied.Comment: 11 pages, Tex, no figures, to be published in Physics Letters
A three-by-three matrix spectral problem for AKNS hierarchy and its binary Nonlinearization
A three-by-three matrix spectral problem for AKNS soliton hierarchy is
proposed and the corresponding Bargmann symmetry constraint involved in Lax
pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax
systems possess classical Hamiltonian structures, in which the nonlinearized
spatial system is intimately related to stationary AKNS flows. These
nonlinearized Lax systems also lead to a sort of involutive solutions to each
AKNS soliton equation.Comment: 21pages, in Late
Study and Prospects: Adaptive Planning and Control of Supply Chain in One-of-a-kind Production
Based on the research project titled “Adaptive Planning and Control of Supply Chain in One-of-a-kind Production”, the research group performed a systematic review of supply chain integration, risk prediction and control and trace ability. Studies of a computer-aided and integrated production system for cost-effective OKP systemare included. Our efforts relevant to integration of supply chain in OKP, modeling &control of ripple effects in OKP supply chain and the trace ability of the OKP supply chain are introduced in this paper
Design Space Exploration of Neural Network Activation Function Circuits
The widespread application of artificial neural networks has prompted
researchers to experiment with FPGA and customized ASIC designs to speed up
their computation. These implementation efforts have generally focused on
weight multiplication and signal summation operations, and less on activation
functions used in these applications. Yet, efficient hardware implementations
of nonlinear activation functions like Exponential Linear Units (ELU), Scaled
Exponential Linear Units (SELU), and Hyperbolic Tangent (tanh), are central to
designing effective neural network accelerators, since these functions require
lots of resources. In this paper, we explore efficient hardware implementations
of activation functions using purely combinational circuits, with a focus on
two widely used nonlinear activation functions, i.e., SELU and tanh. Our
experiments demonstrate that neural networks are generally insensitive to the
precision of the activation function. The results also prove that the proposed
combinational circuit-based approach is very efficient in terms of speed and
area, with negligible accuracy loss on the MNIST, CIFAR-10 and IMAGENET
benchmarks. Synopsys Design Compiler synthesis results show that circuit
designs for tanh and SELU can save between 3.13-7.69 and 4.45-8:45 area
compared to the LUT/memory-based implementations, and can operate at 5.14GHz
and 4.52GHz using the 28nm SVT library, respectively. The implementation is
available at: https://github.com/ThomasMrY/ActivationFunctionDemo.Comment: 5 pages, 5 figures, 16 conferenc
Classical Poisson structures and r-matrices from constrained flows
We construct the classical Poisson structure and -matrix for some finite
dimensional integrable Hamiltonian systems obtained by constraining the flows
of soliton equations in a certain way. This approach allows one to produce new
kinds of classical, dynamical Yang-Baxter structures. To illustrate the method
we present the -matrices associated with the constrained flows of the
Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a
2-dimensional eigenvalue problem. Some of the obtained -matrices depend only
on the spectral parameters, but others depend also on the dynamical variables.
For consistency they have to obey a classical Yang-Baxter-type equation,
possibly with dynamical extra terms.Comment: 16 pages in LaTe
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