The short-time behavior of the turbulent viscosity is inferred from the immediate response of the Reynolds stress deduced by Crow [1] for the problem of isotropic turbulence subjected to a mean strain at time t=0. The...
In this paper, a spectral method is formulated as a numerical solution for the stochastic Ginzburg-Landau equation driven by space-time white noise. The rates of pathwise convergence and convergence in expectation in ...
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A second moment turbulence closure model of the type used before for flows with density stratification, frame rotation and streamline curvature is augmented to describe MHD flows with small magnetic Reynolds number. I...
A measure preserving homeomorphism f determines a discrete dynamical system. Measurable sets in phase space are moved or transported by f. It is shown that the asymptotic rate of escape of phase space volume from neig...
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It is shown that the theory presented in the paper cited in the title can be extended almost effortlessly to encompass a class of gauge transformations that is considerably more general than that treated originally. 1...
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When evolution plays a role, population dynamic models alone are not sufficient for determining the outcome of multi-species *** an expansion of Maynard Smith's concept of an evolutionarily stable strategy, evolut...
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A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are *** initialization schemes as well as...
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A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are *** initialization schemes as well as general regimes for the network width and training data size are *** the overparametrized regime,it is shown that gradient descent dynamics can achieve zero training loss exponentially fast regardless of the quality of the *** addition,it is proved that throughout the training process the functions represented by the neural network model are uniformly close to those of a kernel *** general values of the network width and training data size,sharp estimates of the generalization error are established for target functions in the appropriate reproducing kernel Hilbert space.
The concept of association measure generalizing the Pearson correlation coefficient is introduced. The methods of generation of association measures by means of pseudo-difference associated to some t-conorm and by sim...
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We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine lea...
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We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine learning models and algorithms,such as the random feature model,the two-layer neural network model and the residual neural network model,can all be recovered(in a scaled form)as particular discretizations of different continuous *** also present examples of new models,such as the flow-based random feature model,and new algorithms,such as the smoothed particle method and spectral method,that arise naturally from this continuous *** discuss how the issues of generalization error and implicit regularization can be studied under this framework.
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