Applications of the Sufficiency Principle in Acceleration of Neural Networks Trainig

One of the problems in AI tasks solving by neurocomputing methods is a considerable training time. This problem especially appears when it is needed to reach high quality in forecast reliability or pattern recognition. Some formalised ways for increasing of networks’ training speed without loosing of precision are proposed here. The offered approaches are based on the Sufficiency Principle, which is formal representation of the aim of a concrete task and conditions (limitations) of their solving [1]. This is development of the concept that includes the formal aims’ description to the context of such AI tasks as classification, pattern recognition, estimation etc.

A Fractional Analog of the Duhamel Principle

Mathematics Subject Classification: 35CXX, 26A33, 35S10

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball

2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05

Application of Subordination Principle to Log-Harmonic alpha-spirallike Mappings

MSC 2010: 30C45, 30C55

Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary

Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.

Mathematical Modeling of the Weaving Structure Design

Красимир Йорджев, Христина Костадинова - В работата се разглежда една релация на еквивалентност в множеството от всички квадратни бинарни матрици. Обсъдена е комбинаторната задача за намиране мощността и елементите на фактормножеството относно тази релация. Разгледана е и възможността за получаване на някои специални елементи на това фактормножество. Предложен е алгоритъм за решаване на поставените задачи. Получените в статията резултати намират приложение при описанието топологията на различните тъкачни структури.

Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

2000 Mathematics Subject Classification: 62G07, 62L20.