The Hopfield neural network is extensively applied to obtaining an optimal/feasible solution in many different applications such as the traveling salesman problem (TSP), a typical discrete combinatorial problem. Although providing rapid convergence to the solution, TSP frequently converges to a local minimum. Stochastic simulated annealing is a highly effective means of obtaining an optimal sol...

Consider the Hopfield network [3], a “neural network,” with symmetrical connections between binary neural “units.” Hopfield showed how such a network could learn: patterns were “imposed” on the network, and connections modified by local Hebbian learning. Remarkably, the network could “fill in” patterns from fragments, providing a form of “content-addressable memory.” Hopfield showed, too, that ...

One of the models for RNA secondary structure prediction is to view it as maximum independent set problem, which can be approximately solved by Hopfield network. However, when predicting native molecules, the model is not always accurate and the heuristic method of Hopfield network is not always stable. It is because that the class information is lost and the accuracy is not determined by the n...

The Sparse, Distributed Memory (SDM) model (Kanerva. 1984) is compared to Hopfield-type, neural-network models. A mathematical framework for cornporing the two models is developed, and the capacity of each model is investigated. The capacity of the SDM can be increased independent of the dimension of the stored vectors, whereas the Hopfield capacity is limited to a fraction of this dimension. T...

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Nat. Acad. Sci., USA, vol. 79, pp. 2254-2258, Apr. 1982. R. J. McEliece, et al., “The Capacity of the Hopfield Associative Memory,” IEEE Transactions on Information Theory, vol. T-33, pp. 461-482, 1987. B. L. Montgomery et al., “Evaluation of the use of Hopfield Neural Network Model as...

T his pap er defines a form al pr obabilist ic notion for the information capac ity of the Hopfield neur al network model of associat ive memory. A mathematical express ion is derived for the number of random binary pat terns that can be stored as stable states in a Hopfield model of memory with n neur ons with a given probab ility. The derivati on is based on a new approach using two powerfu l...

Satellite communication systems suffer from the systematic error of tropospheric delay. Accurate estimation this delay is essential for budget and planning. This study investigates in three Nigeria cities: Abuja, Lagos, Port Harcourt using two different models (Saastominen Hopfield). Three-year atmospheric data surface pressure, relative humidity temperature obtained at 5-min interval were acqu...

This paper evaluates the positioning performance of a single-frequency software GPS receiver using Ionospheric and Tropospheric corrections. While a dual-frequency user has the ability to eliminate the ionosphere error by taking a linear combination of observables, a single-frequency user must remove or calibrate this error by other means. To remove the ionosphere error we take advantage of the...

In our recent work [9] we looked at a class of random optimization problems that arise in the forms typically known as Hopfield models. We viewed two scenarios which we termed as the positive Hopfield form and the negative Hopfield form. For both of these scenarios we defined the binary optimization problems whose optimal values essentially emulate what would typically be known as the ground st...

An approach to storing and retrieving static images using multilayer Hopfield neural network is analyzed. Here, the Hopfield network is used as a memory, which stores images in predefined resolution. During the image retrieval, down sampled version of the stored image is provided as the query mage, The memory initially gives out a coarse image. The finer details of the image are synthesized lat...