This paper is concerned with the development of a computational methodology based on fractal geometry for determining 3D structure of protein with imagery projection operations. In this investigation, the density-map image is a 2D projection of the 3D electron density map according to its depth of the density distribution along the projection direction. We extract fractal features of the densit...

On power system operation status monitoring, operating performance analysis and assessment is to ensure the safe operation of its important components. This paper presents a new type of data mining based on the fault mode analysis and the fast diagnostic reasoning algorithm. Fault appearance to be collected and cleaned up in a fault information dimension table, the relationship rule dimension t...

Theorem 1.1 (Number of Samples for Class with Bounded VC-Dimension) Suppose (X,C) has VC-dimension at most d. Then, suppose S is a subset obtained by sampling from X independently m times. If m ≥ max{ log 2 δ , 8d log 8d }, then with probability at least 1− δ, S is an -net. Using VC-dimension, we can bound the number of effective boolean functions on the random subset S. However, after conditio...

Cold start is one of the main challenges in recommender systems. Solving sparsechallenge of cold start users is hard. More cold start users and items are new. Sine many general methods for recommender systems has over fittingon cold start users and items, so recommendation to new users and items is important and hard duty. In this work to overcome sparse problem, we present a new method for rec...

We give a short and simple argument that proves, in a uniform way, the Auslander-Buchsbaum formula, relating depth and projective dimension, and the Auslander-Bridger formula, relating depth and G-dimension. Moreover, the same type of argument quickly reproves the fact that, in the degrees above the codepth, the syzygy modules of a finite module over a commutative local ring have no free summan...