This paper reports two-dimensional parameter-space plots for both, the hyperbolic tangent and the piecewise-linear neuron activation functions of a three-dimensional Hopfield neural network. The plots obtained using both neuron activation functions are compared, and we show that similar features are present on them. The occurrence of self-organized periodic structures embedded in chaotic region...

We consider the notion of shift tangent vector introduced in [6] for real valued BV functions and introduced in [8] for vector valued BV functions. Using a simple decomposition of u ∈ BV in terms of its derivative, we extend the results of [8] to more general shift tangent vectors. This extension allows us to study the shift differentiability of the flow generated by a hyperbolic system of cons...

We study two classes of sigmoids: the simple sigmoids, defined to be odd, asymptotically bounded, completely monotone functions in one variable, and the hyperbolic sigmoids, a proper subset of simple sigmoids and a natural generalization of the hyperbolic tangent. We obtain a complete characterization for the inverses of hyperbolic sigmoids using Euler's incomplete beta functions, and describe ...

PURPOSE To evaluate the error in T1 estimates using inversion-recovery-based T1 mapping due to imperfect inversion and to perform a systematic study of adiabatic inversion pulse designs in order to maximize inversion efficiency for values of transverse relaxation (T2) in the myocardium subject to a peak power constraint. METHODS The inversion factor for hyperbolic secant and tangent/hyperboli...

Any single-hidden-layer feedforward network based on Gaussian or asymptotically constant odd or even rational non-polynomial activation functions has the same property as such networks based on hyperbolic tangent: input-output function determines weights and biases up to a permutation of the hidden units and sign-flips.

This paper presents an approach for the personal authentication using rank-level fusion of multispectral palmprints, instead of using multiple biometric modalities and multiple matchers. The rank level fusion involving the non linear combination of hyperbolic tangent functions gives the best recognition rate for the Rank 1 obtained from two types of features, viz., sigmoid and fuzzy. The result...

Designing a neural network (NN) for processing complex signals is a challenging task due to the lack of bounded and differentiable nonlinear activation functions in the entire complex domain C. To avoid this difficulty, 'splitting', i.e., using uncoupled real sigmoidal functions for the real and imaginary components has been the traditional approach, and a number of fully complex activation fun...

The 13C NMR chemical shift of sp2 carbon atoms in acyclic alkenes was estimated with multilayer feedforward artificial neural networks (ANNs) and multilinear regression (MLR), using as structural descriptors a vector made of 12 components encoding the environment of the resonating carbon atom. The neural network quantitative model provides better results than the MLR model calibrated with the s...