Practical, Computation Efficient High-Order Neural Network for Rotation and Shift Invariant Pattern Recognition

In this paper, a modification for the high-order neural network (HONN) is presented. Third order networks are considered for achieving translation, rotation and scale invariant pattern recognition. They require however much storage and computation power for the task. The proposed modified HONN takes into account a priori knowledge of the binary patterns that have to be learned, achieving significant gain in computation time and memory requirements. This modification enables the efficient computation of HONNs for image fields of greater that 100 × 100 pixels without any loss of pattern information.

Sequencing Jobs with Uncertain Processing Times and Minimizing the Weighted Total Flow Time

We consider an uncertain version of the scheduling problem to sequence set of jobs J on a single machine with minimizing the weighted total flow time, provided that processing time of a job can take on any real value from the given closed interval. It is assumed that job processing time is unknown random variable before the actual occurrence of this time, where probability distribution of such a variable between the given lower and upper bounds is unknown before scheduling. We develop the dominance relations on a set of jobs J. The necessary and sufficient conditions for a job domination may be tested in polynomial time of the number n = |J| of jobs. If there is no a domination within some subset of set J, heuristic procedure to minimize the weighted total flow time is used for sequencing the jobs from such a subset. The computational experiments for randomly generated single-machine scheduling problems with n ≤ 700 show that the developed dominance relations are quite helpful in minimizing the weighted total flow time of n jobs with uncertain processing times.

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.

Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version

Mathematics Subject Classification: 26D10.

On Supra-Bayesian Weighted Combination of Available Data Determined by Kerridge Inaccuracy and Entropy

2010 Mathematics Subject Classification: 94A17.

Pseudodifferential Operators and Weighted Normed Symbol Spaces

2000 Mathematics Subject Classification: 35S05.