The simplest graph drawing method is that of putting the vertices of a graph on a line and drawing the edges as half-circles either above or below the line. Such drawings are called 2-page book drawings. The smallest number of crossings over all 2-page drawings of a graph G is called the 2-page crossing number of G. Cimikowski and Shope have solved the 2-page crossing number problem for an n-ve...

In this paper, an unsupervised parallel segmentation approach using a fuzzy Hopfield neural network (FHNN) is proposed. The main purpose is to embed fuzzy clustering into neural networks so that on-line learning and parallel implementation for medical image segmentation are feasible. The idea is to cast a clustering problem as a minimization problem where the criteria for the optimum segmentati...

Developing technologies have made significant progress towards linking the brain with brain-machine interfaces (BMIs) which have the potential to aid damaged brains to perform their original motor and cognitive functions. We consider the viability of such devices for mitigating the deleterious effects of memory loss that is induced by neurodegenerative diseases and/or traumatic brain injury (TB...

For an integer r ≥ 0, we say that state x∗ is r-stable if it is an attractor for all states with Hamming distance at most r from x∗. Thus, if a state x∗ is r-stably stored, the network is guaranteed to converge to x∗ when exposed to any corrupted version not more than r bit flips away. For positive integers k and r, is there a Hopfield network on n = ( 2k 2 ) nodes storing all k-cliques r-stabl...

There are three existing connection::;t models in which network states are assigned a computational energy. These models-Hopfield nets, Hopfield and Tank nets, and Boltzmann Machines-search for states with minimal energy. Every link in the network can be thought of as imposing a constraint on acceptable states, and each violation adds to the total energy. This is convenient for the designer bec...

It is known that an analog Hopfield neural network with time delay can generate the outputs which are similar to the human electroencephalogram. To gain deeper insights into the mechanisms of rhythm generation by the Hopfield neural networks and to study the effects of noise on their activities, we investigated the behaviors of the networks with symmetric and asymmetric interneuron connections....

Artificial Immune System (AIS) algorithm is a novel and vibrant computational paradigm, enthused by the biological immune system. Over the last few years, the artificial immune system has been sprouting to solve numerous computational and combinatorial optimization problems. In this paper, we introduce the restricted MAX-kSAT as a constraint optimization problem that can be solved by a robust c...

We test four fast mean-field-type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low-temperature regime, the simulated annealing technique is adopted. Although performances of these network reconstruction algorithms on the simulated network of spiking neurons are extensively studied recentl...

This paper presents a study on the performance of the Hopfield neural network algorithm for the graph path search problem. Specifically, performance of the Hopfield network is studied from the dynamic systems stability perspective. Simulations of the time behavior of the neural network is augmented with exhaustive stability analysis of the equilibrium points of the network dynamics. The goal is...

In this paper, a new Hopfield-model net called Compensated Fuzzy Hopfield Neural Network (CFHNN) is proposed for vector quantization in image compression. In CFHNN, the compensated fuzzy c-means algorithm, modified from penalized fuzzy cmeans, is embedded into Hopfield neural network so that the parallel implementation for codebook design is feasible. The vector quantization can be cast as an o...