Annotating geological faults on three dimensional seismic volumes is a laborious process. Typically, only a fraction of the actual faults are manually interpreted, leaving many others unlabeled. This is due to the way attention selectivity works to drive human perception. The human brain selectively focuses its attention to certain salient regions in a visual scene marked by prominent changes in color, contrast, and other low level signal cues. This bottom-up attention is further modulated by the individual’s goals, expectations, and constraints with respect to the task at hand, also called top-down attention. The fault annotations created by seismic interpreters reflect this cognitive process comprising of both bottom-up and top-down attentional mechanisms. 3D convolutional neural networks pretrained on synthetic seismic data for fault mapping can be finetuned on select seismic lines extracted and labeled on a real seismic volume of interest. Traditional finetuning approaches treat all pixels on labeled sections as the absolute ground-truth. This leads to the network incorrectly learning to predict regions of missing fault labels as negatives. We propose an attention-guided training framework that models and incorporates human visual attention to (1) condition the process of sampling training data and (2) modulate the loss value for each pixel. Through quantitative and qualitative evaluation of results on a real seismic volume from North Western Australia, we demonstrate that the proposed approach is able to predict both the annotated as well as the unlabeled faults significantly better compared to baseline approaches.

The main theme of this paper is the enumeration of the order-isomorphic occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence $f_r^v(k,n),$ the number of $n$-array $k$-ary words that contain a given pattern $v$ exactly $r$ times. In addition, we study the asymptotic behavior of the random variable $X_n,$ the number of pattern occurrences in a random $n$-array word. The two topics are closely related through the identity $P(X_n=r) = $ $\frac{1}{k^n}f_r^v(k,n).$ In particular, we show that for any $r\geq 0,$ the Stanley--Wilf sequence $\bigl(f_r^v(k,n)\bigr)^{1/n}$ converges to a limit independent of $r,$ and we determine the value of the limit. We then obtain several limit theorems for the distribution of $X_n,$ including a central limit theorem, large deviation estimates, and the exact growth rate of the entropy of $X_n.$ Furthermore, we introduce a concept of weak avoidance and link it to a certain family of nonproduct measures on words that penalize pattern occurrences but do not forbid them entirely. We analyze this family of probability measures in a small parameter regime, where the distributions can be understood as a perturbation of a uniform measure. Finally, we extend some of our results for words, including the one regarding the equivalence of the limits of the Stanley--Wilf sequences, to pattern occurrences in permutations.

In this paper we obtain bounds on the probability of convergence to the optimal solution for the compact genetic algorithm (cGA) and the population based incremental learning (PBIL). Moreover, we give a sufficient condition for convergence of these algorithms to the optimal solution and compute a range of possible values for algorithm parameters at which there is convergence to the optimal solution with a predefined confidence level.

The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.

In this paper, we study the dynamical properties of the population based incremental learning (PBIL) algorithm when it uses truncation, proportional, and Boltzmann selection schemas. The results show that if the population size tends to infinity, with any learning rate, the local optima of the function to be optimized are asymptotically stable fixed points of the PBIL

In this paper we introduce an estimation of distribution algorithm based on a team of learning automata. The proposed algorithm is a model based search optimization method that uses a team of learning automata as a probabilistic model of high quality solutions seen in the search process. Simulation results show that the proposed algorithm is a good candidate for solving optimization problems.

The CLA-EC is a model obtained by combining the concepts of cellular learning automata and evolutionary algorithms. The parallel structure of the CLA-EC makes it suitable for hardware-based applications including evolvable hardware. In this paper, based on the SIMD model, a parallel architecture is proposed and implemented on FPGA. Simulation results show that the proposed architecture can solve optimization problems thousands times faster than the sequential implementations.

Here we propose a convergence proof for the population based incremental learning (PBIL). In our approach, first, we model the PBIL by the Markov process and approximate its behavior using Ordinary Differential Equation (ODE). Then we prove that the corresponding ODE doesn’t have any stable stationary points in [0,1]n, n is the number of variables, except the local maxima of the function to be optimized. Finally we show that this ODE and consequently the PBIL converge to one of these stable attractors.

In this paper, a new fuzzy clustering algorithm that uses cellular learning automata based evolutionary computing (CLA-EC) is proposed. The CLA-EC is a model obtained by combining the concepts of cellular learning automata and evolutionary algorithms. The CLA-EC is used to search for cluster centers in such a way that minimizes the clustering criterion. The simulation results indicate that the proposed algorithm produces clusters with acceptable quality with respect to clustering criterion and provides a performance that is superior to that of the C-means algorithm.

The particle swarm is one of the most powerful methods for solving global optimization problems. This method is an adaptive algorithm based on social-psychological metaphor. A population of particle adapts by returning stochastically toward previously successful regions in the search space and is influenced by the successes of their topological neighbors. In this paper we propose a learning automata based discrete binary particle swarm algorithm. In the proposed algorithm the set of learning automata assigned to a particle may be viewed as the brain of the particle determining its position from its own and other particles past experience. Simulation results show that the proposed algorithm is a good candidate for solving optimization problems.