External Stimuli on Neural Networks: Analytical and Numerical Approaches

Based on the behavior of living beings, which react mostly to external stimuli, we introduce a neural-network model that uses external patterns as a fundamental tool for the process of recognition. In this proposal, external stimuli appear as an additional field, and basins of attraction, representing memories, arise in accordance with this new field. This is in contrast to the more-common attractor neural networks, where memories are attractors inside well-defined basins of attraction. We show that this procedure considerably increases the storage capabilities of the neural network; this property is illustrated by the standard Hopfield model, which reveals that the recognition capacity of our model may be enlarged, typically, by a factor 102. The primary challenge here consists in calibrating the influence of the external stimulus, in order to attenuate the noise generated by memories that are not correlated with the external pattern. The system is analyzed primarily through numerical simulations. However, since there is the possibility of performing analytical calculations for the Hopfield model, the agreement between these two approaches can be tested—matching results are indicated in some cases. We also show that the present proposal exhibits a crucial attribute of living beings, which concerns their ability to react promptly to changes in the external environment. Additionally, we illustrate that this new approach may significantly enlarge the recognition capacity of neural networks in various situations; with correlated and non-correlated memories, as well as diluted, symmetric, or asymmetric interactions (synapses). This demonstrates that it can be implemented easily on a wide diversity of models.

Analogous Hawking Effect in Dielectric Media and Solitonic Solutions

We review some aspects of our longstanding research concerning the analogous Hawking effect in dispersive dielectric media. We introduce nonlinear contributions in the polarization field in the relativistically covariant version of the Hopfield model and then, in order to provide a simplified description aimed at avoiding some subtleties in the quantization of the original model, we discuss the so-called ϕψ-model. We show that the nonlinearity allows for introducing in a self-consistent way the otherwise phenomenological dependence of the susceptibility and of the resonance frequency ω0 on the spacetime variables, and this is a consequence of the linearization of the model around solitonic solutions representing propagating perturbations of the refractive index, to be then associated with the Hawking effect.

Quantum Hopfield Model

We find the free-energy in the thermodynamic limit of a one-dimensional XY model associated to a system of N qubits. The coupling among the σ i z is a long range two-body random interaction. The randomness in the couplings is the typical interaction of the Hopfield model with p patterns ( p < N ), where the patterns are p sequences of N independent identically distributed random variables (i.i.d.r.v.), assuming values ± 1 with probability 1 / 2 . We show also that in the case p ≤ α N , α ≠ 0 , the free-energy is asymptotically independent from the choice of the patterns, i.e., it is self-averaging.

Evaluation of Tropospheric & Clock Errors for Precision GPS Positioning & Navigation

Positional inaccuracies in GPS are caused by severalerrors such as Ionospheric, Tropospheric, Satellite Clock, Receiver Clock etc., Instantaneous correction of these error aids in precise navigation. In the present work Original Hopfield model is considered for the tropospheric correction. The instantaneous tropospheric correction results in more precise position using GPS. The decreasing order of components on basis of effect are Ionospheric delay, Tropospheric delay, Clock error, satellite bias error, Receiver error, multipath error, Ephymeris error, random errors etc. It is a time taken process to calculate the individual error separately.so in this paper we only concentrated on simulation and analysis the tropospheric delay, clock error, ephemeris error. We used Modified Hopfield model to analysis Tropospheric delay, receiver instrumental bias for analysis Clock error in between we eliminate Ephymeris error, after obtained results are compared with and without time correction in original Hopfield model

Storage Capacities of Twin-Multistate Quaternion Hopfield Neural Networks

A twin-multistate quaternion Hopfield neural network (TMQHNN) is a multistate Hopfield model and can store multilevel information, such as image data. Storage capacity is an important problem of Hopfield neural networks. Jankowski et al. approximated the crosstalk terms of complex-valued Hopfield neural networks (CHNNs) by the 2-dimensional normal distributions and evaluated their storage capacities. In this work, we evaluate the storage capacities of TMQHNNs based on their idea.